Elements and Relations: Aspects of a Scientific Metaphysics 3030994023, 9783030994020

Table of contents :
TABLE OF CONTENTS
TO THE READER
Who is this book for?
What is the central idea of this book?
How is this book organized?
Why does this book have a complicated structure?
Different possible sequences to read this book
On the parallel structures of Essay and Notes
Some personal information
Part I. ESSAY: Ontology of Problems
1.1 Synchronics (Being)
1.2 Diachronics (Becoming)
Chapter 1 Being and Becoming
1.1 Synchronics (Being)
1.1.1 Wholeness
1.1.2 Constraint
1.1.3 Distinction
1.1.4 Persistence
1.1.5 Identity
1.1.6 Agency
1.1.6.1 Texture
1.1.6.2 Other Systems
1.1.6.3 Embeddedness
1.1.7 Complexity
1.1.7.1 Networks
1.1.7.2 Hierarchies
1.1.8 Cognition
1.1.9 Summary
1.2 Diachronics (Becoming)
1.2.1 Origin
1.2.2 Development
1.2.3 Limitation
1.2.4 Complexification
1.2.4.1 Segregation
1.2.4.2 Systematization
1.2.5 Internal opposition
1.2.6 Texture
1.2.7 Other systems
1.2.8 Embeddedness
1.2.9 Impermanence
Part II. COMMENTARY: Recovery of Coherence
Chapter 2 An exact and scientific metaphysics
2.1 The illusion of the fundamental
2.2 The systems alternative
2.3 A new conception of metaphysics
2.4 The epistemological niche of systems theories
2.5 Theories and models; the idea of “system”
Chapter 3 Concepts and categories
3.1 Substance and form
3.1.1 A “stuff-free” metaphysics
3.1.2 Concrete, abstracted, and conceptual systems
3.2 Matter, energy, information; utility
3.2.1 Matter, energy, and information
3.2.2 Utility
3.3 Isomorphism and emergence
3.4 Aspects of complexity and holism
3.5 Structure, function, and history
3.5.1 Structure and function
3.5.2 Adding history
Chapter 4 Related fields
4.1 Not just mathematics
4.2 The relevance of physics
4.2.1 Thermodynamics and statistical mechanics
4.2.2 Quantum mechanics
4.2.3 Other theories in physics
4.3 The centrality of biology
4.4 Sciences of the artificial
4.5 Systems theory and systems analysis
Chapter 5 The challenge of integration
5.1 No singular systems theory
5.2 Hierarchy of system types
5.3 Categories of complexity
5.4 Ontology of problems
5.5 Metaphysician’s desk manual
Chapter 6 Science, religion, politics
6.1 A macro-historical model
6.1.1 A model of diachronic processes
6.1.2 The model applied to history
6.1.3 On the inescapability of grand narratives
6.2 The new science
6.2.1 A supplementing process
6.2.2 Understanding what we know
6.2.3 Fact and value
6.2.4 Horizons
6.2.5 Personal knowledge
6.3 Natural religion
6.3.1 Secular Theodicy
6.3.2 Metaphysics, a bridge to religion
6.3.3 Inner science
6.3.4 Revisiting the historical model
6.4 Fixing the world
6.4.1 Sustainability and globalization
6.4.2 Modernization as differentiation systems
6.4.2.1 The Parsonian model of social systems
6.4.2.2 Problems of differentiation
6.4.2.3 Subsystem differentiation
6.4.2.4 The world system
6.4.3 On the gap between the actual and the ideal; on the incoherence of the ideal
6.5 Summing Up: promise of the systems project
Part III. NOTES: Systems Theory
Chapter 7 Notes on Being and Becoming
7.1 Notes on Synchronics (Being)
7.1.1 Wholeness
1. System
2. Organizing principle
3. Relation
4. Incompleteness
5. Structure
6. Inconsistency
7. Networks
8. Incompleteness vs. inconsistency
7.1.2 Constraint
9. Relation as constraint
10. Dynamic relation
11. Echoing the primary tension
12. The potential and the actual
13. Order
14. Entropy
15. Scale
16. Order and disorder are intertwined
17. Chaos
18. Unity and multiplicity
19. Aggregates vs. systems
20. Reconciling constraint and variety
7.1.3 Distinction
21. Distinction
22. Environment
23. Disequilibrium and existence
24. Boundary
25. Fuzziness
26. Fractals
27. External relation
28. Extension
29. Nothing, many, one, all
30. One, two, three, ten thousand
31. Assertion vs. integration
32. Emergence
33. Engaging/disengaging
34. Active vs. passive
35. Function
7.1.4 Persistence
36. Stability
37. Catastrophe theory
38. The fold catastrophe
39. The Second Law
40. Rigidification vs. disintegration
41. Openness and Closedness
42. Dissipative systems
43. Openness necessary and hazardous
44. Law of Requisite Variety
45. Feedback control
7.1.5 Identity
46. Information (and matter-energy, utility)
47. Autopoiesis
48. Algorithmic information
49. Genotype and phenotype
50. Internal vs. external identity
51. Paradoxes of autonomy
52. Dangers of filtering out noise
53. Boundary subsystem
7.1.6 Agency
54. Utility
55. Environmental types
7.1.6.1 Texture
56. Decision theory
57. Chaos and long-term forecasting
58. Nature resists
59. Multiplication of effects
60. Externalities
61. Counterintuitive effects
62. Weakening by strengthening
63. No terminus
64. Discounting the future
65. Binding the future and sunk costs
66. Pareto-optimality
67. Multiple objectives
68. Aggregating preferences
69. Computational complexity
70. Optimization
71. Optimality, stability, and resilience
72. Purposeful action as a tetrad
7.1.6.2 Other Systems
73. Assertion, integration, exchange
74. Eating and being eaten
75. Game theory
76. Coalition instability
77. Discerning which game is being played
78. Prisoner’s Dilemma
79. Chicken
80. Symmetry or altruism may be harmful
81. Sharing elements
7.2.6.3 Embeddedness
82. Heteronomy
83. Recruitment and predation
84.Embeddedness as a solution to the PD
85. Turbulent fields
7.1.7 Complexity
86. Complexity
87. Individuality and complexity
88. Hierarchies and networks
7.1.7.1 Networks
89. Complexity, stability, and chaos
90. Small worlds
91. Scale-free networks
7.1.7.2 Hierarchies
92. Homogeneity, heterogeneity, and scale
93. Three levels
94. The highest is not the whole
95. Hierarchical egalitarianism
96. Distillation and alienation
97. Informational parasitism
7.1.8 Cognition
98. A naturalistic epistemology
99. The modeling subsystem
100. Tetrad of modeling
101. Pragmatic, semantic, syntactic
102. Multiple subselves
103. Self and non-self
104. Embeddedness of cognition
105. Cognition and time
106. Constructing reality
107. Representation
108. Cognition and autopoiesis
109. Relativity of models
110. Fallibility
111. Modeling constraint
112. Sensitivity and specificity
113. Wrong perception
114. Self-reference
7.1.9 Summary
115. Binary oppositions
116. Dyadic correlations
117. Dialectics
118. The extremes are attractors
119. The war of universality on uniqueness
7.2 Notes on Diachronics (Becoming)
7.2.1 Origin
120. System formation
121. Self-organization
122. Offspring
7.2.2 Development
123. Disequilibrium and change
124. Order through fluctuations
125. Development vs growth
126. Contradiction and its consequences
127. Self-development
7.2.3 Limitation
128. Dialectics and catastrophe theory
129. History: idiographic or nomothetic
130. Trajectories of development
131. Cusp catastrophe
132. Augustinian vs. Manichean devils
133. Environmental types, again
134. Failures in meeting new challenges
7.2.4 Complexification
135. Movement toward the extremes
136. Centralization
137. Mechanization (rigidification)
138. Form limits growth
139. Temporalization of complexity
140. Two universal processes
141. Optimal segregation vs. systematization
7.2.4.1 Segregation
142. Progressive segregation
143. Partial decomposability
7.2.4.2 Systematization
144. Systematization
145. Levels of structure and dynamics
146. Integration of stable substructures
147. Limits of complexification
148. Non-decomposability under stress
149. Connectedness for good and ill
150. Self-organized criticality
7.2.5. Internal opposition
151. Something intractable
152. Cusp of negation
153. Excess and overshoot
154. Chance and necessity
7.2.6 Texture
155. Environment is a limited source and sink
156. Wastes are inevitable
157. Closing the circle
158. Limits to growth
159. Temporal traps
160. Growth as a PD
161. Difficulty of reversing bad effects
162. Destroying the environment that sustains
7.2.7 Other systems
163. Natural selection
164. The organized exploits the unorganized
165. Two kinds of dialectic
166. Butterfly catastrophe
167. Butterfly of reconciliation
7.2.8 Embeddedness
168. Succession
169. Punctuated equilibria
170. Adaptation vs. adaptability
171. When to change
172. Generalized evolution
173. Evolution of modeling subsystem
7.2.9 Impermanence
174. Things fade
175. Thermodynamics vs. kinetics
176. From being to non-being
177. Failing all at once
178. Dissolution
179. Its effects may endure
180. Decay is inherent in composite things
APPENDICES
A. Auto-critique
A.1 Structure
A.1.1 Abstraction
A.1.2 Inexactness
A.1.3 Metaphor
A.1.4 Rhetoric
A.1.5 Scope
A.2 Function
A.2.1 Problematics
A.2.2 Diagnostics, Therapeutics
A.2.3 Euphorics, an antidote
B. Lists of figures, tables
B.1 All figures, tables
TO THE READER
COMMENTARY
NOTES
Synchronics
Diachronics
B.2 Dyadic figures, tables
B.3 Triadic figures, tables
B.4 Tetradic figures
B.5 Pentadic figures, table
B.6 Hexadic figure
REFERENCES
ACKNOWLEDGMENTS
INDEX

Citation preview

IFSR International Series in Systems Science and Systems Engineering

Editor One Editor MartinTwo  ZwickEds.

Elements and Relations Aspects of a Scientific Metaphysics

IFSR International Series in Systems Science and Systems Engineering Volume 35

Editor-in-chief George E. Mobus, Institute of Technology, University of Washington Tacoma, Tacoma, WA, USA

About this book series Editor-in-Chief: George E. Mobus [email protected] Springer Editorial Contact: Donna Chernyk [email protected] Purpose of the Series: The IFSR International Series on Systems Science and Systems Engineering book series is devoted to the demonstration of systems science and engineering as a body of integrated concepts, principles, methodologies, tools, and perspectives all directed toward a better understanding of the nature of systems (systemness) and how to use systems approaches in the other sciences and engineering practice. This series seeks to provide systems knowledge to a broad and diverse audience of those interested in a much deeper understanding of how the world works. Submission of Proposals The Editorial Board will solicit high quality monographs, edited collections, and textbooks that focus on research in areas of Systems Science and Engineering with the intent of making systems science, literacy, and thinking available to all involved in formulating the future of humanity. Topics of great interest include complex adaptive and evolvable systems. The research topics can be either theoretical or applied (e.g. action research) as long as they incorporate theories or principles specific to systems science. Book proposals should demonstrate the integration of subjects across disciplinary lines within the system sciences, such as showing relations between cybernetics and hierarchy theory and other fields (see list below). The ideal proposal will provide both quantitative and qualitative explanations that allow those with strong mathematical backgrounds to absorb the quantitative aspects, but also allow those with more qualitative interests to gain substantial insights into the work. Some examples of subject areas are: Systems Science and Engineering Areas of Interest:             

Complexity Theory Network Theory Hierarchy, Holarchy, and Panarchy Theories Dynamics Emergence and Evolution Modelling (System Dynamics, Agent-based, Dynamical Systems, etc.) Computational Intelligence and Learning Systems Systems Analysis and Synthesis Application Areas: Biological & Ecological Systems Human Social & Organization Systems Economics Management & Governance Methodologies (Applied Systems Science or Engineering)

Editorial Board: Editor-in-Chief: George E. Mobus, Ph.D. (Emeritus) University of Washington Tacoma 1900 Commerce St. Box 358426 Tacoma, Washington USA 1-253-692-5894 [email protected] Dr David Rousseau Centre for Systems Philosophy 30 Leigh Close, Addlestone Surrey KT15 1EL United Kingdom +44 (0) 7714 677 687 [email protected] [email protected] Jennifer M. Wilby, Ph.D. ISSS, Past-President and VP Administration +44(0)07711042438 [email protected] Javier Calvo-Amodio, Ph.D. Oregon State University 204 Rogers Hall Corvallis, Oregon 97331-6001 [email protected] Mary C. Edson, Ph.D. President International Federation for Systems Research Vienna, Austria U.S. Eastern +1 (561) 632-5436 [email protected] Prof. Dr. Gerhard Chroust J. Kepler University Linz c/o Donaustr. 101/6, A-2346 Maria Enzersdorf, Austria +43 664 28 29 978 [email protected] www.gerhard-chroust.at Gary Metcalf, Ph.D. Vice President International Federation for Systems Research 1408 ½ Central Ave. Ashland, KY 41102 - USA [email protected] Gary Robert Smith Airbus Defence and Space Quadrant House Celtic Springs Coedkernew Newport United Kingdom NP10 8FZ [email protected] Submission Instructions: Proposals for books to be published in the IFSR Book Series should be submitted to the Editor, George Mobus, either by e-mail to [email protected] or by regular mail to the Editorial Office: 401 Manchester Road, Vestal, New York 13850, USA.

Martin Zwick

Elements and Relations Aspects of a Scientific Metaphysics

Martin Zwick Systems Science Program Portland State University Portland, OR, USA 97207-0751 [email protected] https://works.bepress.com/martin_zwick/

ISSN 1574-0463 ISSN 2698-5497 (electronic) IFSR International Series in Systems Science and Systems Engineering ISBN 978-3-030-99402-0 ISBN 978-3-030-99403-7 (eBook) https://doi.org/10.1007/978-3-030-99403-7 Mathematics Subject Classification (2020): 00Axx, 00A06, 00A09, 00A30, 00A69, 00A71, 00A72 © Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

For my students and colleagues

vii

TABLE OF CONTENTS PART I. ESSAY: Ontology of Problems Chapter 1 Being and Becoming 1.1 Synchronics 1.2 Diachronics

1 7 7 24

PART II. COMMENTARY: Recovery of Coherence 39 Chapter 2 An exact and scientific metaphysics 2.1 The illusion of the fundamental 2.2 The systems alternative 2.3 A new conception of metaphysics 2.4 The epistemological niche of systems theories 2.5 Theories and models; the idea of “system”

43 43 48 54 63 71

Chapter 3 Concepts and categories 3.1 Substance and form 3.2 Matter, energy, information; utility 3.3 Isomorphism and emergence 3.4 Aspects of complexity and holism 3.5 Structure, function, and history

79 79 88 97 100 109

Chapter 4 Related fields 4.1 Not just mathematics 4.2 The relevance of physics 4.3 The centrality of biology 4.4 Sciences of the artificial 4.5 Systems theory and systems analysis

123 123 130 135 139 141

Chapter 5 The challenge of integration 5.1 No singular systems theory 5.2 Hierarchy of system types 5.3 Categories of complexity 5.4 Ontology of problems 5.5 Metaphysician’s desk manual

149 149 154 160 167 174

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Table of Contents

Chapter 6 Science, religion, politics 6.1 A macro-historical model 6.2 The new science 6.3 Natural religion 6.4 Fixing the world 6.5 Summing Up: promise of the systems project

193 193 207 226 247 278

PART III. NOTES: Systems Theory

285

Chapter 7 Notes on Being and Becoming 7.1 Notes on Synchronics 7.2 Notes on Diachronics

295 295 496

APPENDICES

591

REFERENCES

619

ACKNOWLEDGMENTS

669

INDEX

679

ix

TO THE READER I hope you will read this personal message from me. It will make everything that follows more comprehensible. Perhaps you’ve heard that physicists are working on a “theory of everything,” a TOE. You might suppose that if they’re successful, we will learn a lot about literally everything. This isn’t true. Success would be a great scientific achievement in physics, but it wouldn’t help us understand the human-scale world that we live in. There is, however, another scientific project aimed at what would truly be a theory of (nearly) everything. This project has the prosaic name of “systems theory,” 1 also known as the theory of “complex systems.” Systems ideas are – not surprisingly – complex, so a book about them like this one will not yield to a casual reading. But if you make an effort to engage with these ideas, I’m confident that you will expand your understanding of many things. “According to the effort is the reward” (Mishna Avot 4:23). Who is this book for? This book, the culmination of my professional career in systems theory, is written for multiple audiences. First of all, it is for people interested in the systems/complexity field and can be used in systems courses at the undergraduate or graduate level. The book is also for general readers in the natural or social sciences or mathematics, since systems theory is rooted in these areas. Within the humanities, systems ideas are especially relevant to philosophy, which is a bridge between science and religion. Systems ideas have political implications. Since systems theory draws upon all the sciences, this book is also for readers interested in how science bears on religion or politics. 1

“Systems theory” is not really a theory but rather an intellectual project encompassing multiple theories, such as information theory and game theory. Referring to this project as a single theory is just for convenience.

x

To the Reader

Systems theory is not only academic. It informs practice in systems engineering and other professional fields such as public policy, business, and social work. Although the content of this book is theoretical rather than practical, and abstract rather than concrete, non-academic readers with a more worldly bent will find many of its ideas valuable. This book includes some math, but interest in or aptitude for math is not required. The mathematical content is mainly in the part called Notes (Chapter 7). Although this part is large, a non-technical reader can regard it as an optional appendix. But some notes are not mathematical at all, so Notes can be skimmed for its non-mathematical content. What is the central idea of this book? The book is built around the central proposition that systems theory is an attempt to construct an “exact and scientific metaphysics,” an ESM. “Metaphysics” here means ideas that have wide applicability; an “exact” metaphysics is one that is or could be made mathematical. A “scientific” metaphysics is one that draws upon and contributes to the sciences. So an “exact and scientific metaphysics” means a system of general ideas that are relevant to science and that at least in principle can be expressed mathematically. The notion of an ESM is discussed at length in Chapter 2. To many people, the word “metaphysics” suggests something of (at best) limited usefulness. The opposite is the case. A systems metaphysics offers important, indeed urgently needed, insights. Systems theory offers new ideas that are relevant to science, religion, and politics. With respect to science, it supplements discipline-specific knowledge by offering an alternative to the dominant paradigm of materialist reductionism. With respect to religion, it offers a metaphysics transcending the science–religion divide which can help us to recover the cultural coherence lost in the transition to modernity. With respect to politics, it identifies underlying patterns in societal problems such as climate change, environmental

To the Reader

xi

degradation, public health, political conflict, economic instability, and cultural strife. Without understanding these deep patterns, such problems cannot be effectively addressed. How is this book organized? The book consists of three basic parts, named Essay (Chapter 1), Commentary (Chapters 2 through 6), and Notes (Chapter 7). Essay is a dense sketch of a scientific metaphysics, and Notes adds mathematical and scientific content, so Essay + Notes together is a candidate ESM. Commentary explores the character and value of this ESM. The relations of these three parts to one another can also be visualized with the double cone image of Figure 1. A system, viewed as a unitary whole, is shown in Figure 1(a) as the common apex of upper and lower cones. The upper cone is the system’s external function; the lower cone is its internal structure. Figure 1(b) depicts the organization of this book with this double cone image. The figure identifies Essay as an ESM, although since its mathematical aspects are only offered in Notes, Essay itself is really only a (very compressed) SM. Figure 1 Structure and function of the systems project

function

Commentary

system

Essay

structure

Notes

(a)

(b)

ESM value ESM ESM content

ESSAY: An Ontology of Problems is organized around problems (difficulties, imperfections, hazards) that afflict many kinds of systems, including the systems that we are and the larger systems that we are part of. Its message is that all (finite)

xii

To the Reader

systems (of some degree of complexity) are flawed. It explores the essence of these flaws, which must be understood if the flaws are to be fixed. Essay is short, abstract, and dense. COMMENTARY: Recovery of Coherence discusses the nature of systems thinking and describes the context of and the motivation for Essay. It develops in detail the notion of an ESM. It also explains why Essay is oriented toward the flawedness of systems. Commentary is written in a conventional expository style and is the most accessible part of the book. NOTES: Systems Theory elaborates on the systems ideas in Essay by repeating every sentence in Essay and adding technical explanations. This allows the reader to engage with the flow of ideas of Essay without being distracted by footnotes. Many (but not all) notes are mathematical, unlike Essay and Commentary which are strictly verbal. To summarize, the purposes of the three parts of this book are to: •

offer an (E)SM organized as an ontology of problems (Essay, i.e., Chapter 1);

•

explain what systems theory is and argue for its value (Commentary, i.e., Chapters 2-6);

•

present much of the content of systems theory (Notes, i.e., Chapter 7).

After Notes, Appendix A considers some problems with Essay. The argument that all systems are flawed applies also to organizations of ideas, so consistency requires that Essay itself will have the deficiencies that it discusses. It does and Appendix A acknowledges this fact. In the section titled Euphorics, it also provides an antidote to the problem-oriented view of Essay.

To the Reader

xiii

Why does this book have a complicated structure? Here is how this book came to be written. Essay began in my papers on the need in systems for both order and disorder and on a catastrophe-theoretic interpretation of dialectics. 2 These themes were joined together in a paper 3 about the sorry fact that bad results are often produced by political movements with initially good intentions and that even spiritual teachings are limited or distorted by the incompleteness and inconsistencies of their truths. This line of thought broadened into a look at the universality of difficulties faced by systems of widely different types. 4 Because Essay utilized many components of systems theory but was itself very terse, its allusions needed to be unpacked and its key ideas explained. There thus emerged a second organizing purpose: to present an overview of systems ideas. Essay was not only an ontology of problems but also a way of integrating ideas from multiple theories, such as information theory, game and decision theory, dynamical systems theory, and thermodynamics, by narrative means. This second organizing purpose was assisted by the theme of an ontology of problems because integrating systems theories would be difficult if the goal was a TOE without any specific focus. But the idea of constructing an ontology of problems did not actually arise as a way of integrating systems ideas. 5 It was my initial motivation. 6

2

“Requisite Variety and the Second Law” (1978b) and “Dialectics and Catastrophe” (1978a) 3 “Dialectical Thermodynamics” (1981) 4 “Incompleteness, Negation, Hazard: On the Precariousness of Systems” (1984), “Ontology of Problems” (1995), and “Understanding Imperfection” (2000). 5 The challenge of integrating systems ideas is discussed in 5.1 No singular systems theory, p. 149 6 See the discussion of this motivation in 5.4 Ontology of problems, p.167.

xiv

To the Reader

This second purpose of presenting an overview of systems ideas overshot its original impulse. Strictly speaking, such an overview should restrict itself to systems ideas that are well developed and accepted, but Essay includes a few ideas of my own or from other people that are preliminary, idiosyncratic, or speculative. 7 This might be justified by the fact that systems are defined, after all, not only by structure and function but also by history, and not only by history as established past but also by history as possible future. 8 In exploring some future possibilities for systems theory, I occasionally relaxed the ESM constraint of exactness. Although most of Essay consists of accepted systems ideas that have mathematically rigorous foundations, some of its ideas are not like that. Hopefully Notes will allow recognition of the status of each idea. The goal of an ontology of problems and the need for a coherent narrative dictated that the central essay be compact. The density and abstraction of Essay then required Notes to unpack it by offering mathematical interpretations. Essay and Notes together then generated the need to explain the context and motivation for this way of thinking. Thus Commentary came into being with a third organizing purpose for the book: to explain the systems project and argue for its value. Essay was systems theory/philosophy per se, Notes surveyed its internal structure, and Commentary its external function. But these three organizing principles were still insufficient. But also needed were real-world examples of the problems that Essay speaks about abstractly. So a fourth part was initially added called Examples, which like Notes was keyed line-by-line to Essay. But, as Essay itself declares, multiplicity of purpose is a recipe for trouble, especially when each individual goal is too ambitious to be realized. It soon became apparent that an adequate Examples was not achievable. Every example of an 7

An example is Note #147 Limits of complexification, p. 544; much of 7.1.8 Cognition is also idiosyncratic and speculative. 8 3.5 Structure, function, and history, p. 109; Figure 98 System formation; system as temporal center, p. 498

To the Reader

xv

abstract systems principle called for more detail and the acknowledgment of the relevance of other principles. Worse, asserting that a particular real-world problem exemplified a particular systems principle would evoke endless argument. And two sections keyed line-to-line to Essay were one too many. So Examples was finally dropped as a separate part of the book and shortened into one section in a chapter in Commentary. 9 I had to accept the impossibility of exemplifying all the assertions of Essay and thus accept the book’s flaw of being incomplete. As Essay’s complexity grew, incorporation of additional ideas while preserving the narrative flow also became increasingly difficult. Essay itself explains such problems. 10 More fundamentally, it also became clear that explanation and exemplification of the ESM idea were so inherently open-ended a task that it was not susceptible to any reasonable criterion of closure. That “books are never completed; they are only abandoned” 11 is especially true of this project. So you have in your hands a book that has been abandoned despite being incomplete (and no doubt also inconsistent) in many ways. Still, it is my belief and hope that there is enough in this book for it to be useful. And the flaws in it might also stimulate new ideas. Different possible sequences to read this book Because the structure of this book is complex, readers with different backgrounds and interests might prefer to read this book in different sequences. Here are some suggestions:

9

5.5 Metaphysician’s desk manual, p. 174. This section only samples the ideas of Essay; it does not exemplify them all. 10 Nucleation, expansion, limitation: this sequence of early stages is the norm. As development continues, the factors limiting it also intensify (1.2.3.4.1). As Boulding notes (1970), “growth produces form but form limits growth.” 11 The original quote by E. M. Forster is about art.

xvi

To the Reader

The simplest sequence: One normally reads a book simply from beginning to end in the order of the chapters. Essay (Chapter 1) is the most difficult part of the book, but if the reader is willing to jump into the pool and not mind the cold shock of unfamiliar ideas, Essay will provide a sense of the exact and scientific metaphysics that is being explored. Commentary (Chapters 2-6) will then make the case for this way of thinking, and Notes (Chapter 7) will finally explain what the abstract assertions of Essay refer to. The sequence that I recommend: Since the notion of an ESM is so central to this book, I actually recommend first reading Chapter 2, the first chapter in Commentary, which explains this ESM notion. After that, I suggest going back to reading Essay, finishing Commentary, and then going on to Notes. For readers mainly interested in math or science: If exactness or scientific content is a main concern, I suggest going directly to Notes, which defines terms and associates them with scientific ideas. Reading Commentary next will then explain the underlying coherence of this technical material, and Essay will show how this material can be weaved into an integrated narrative. For readers mainly interested in philosophy, religion, or politics: I suggest reading Commentary first, then Essay, and then those parts of Notes that are of interest. A highly skeptical reader might look at the Appendix first and then Essay, Commentary, and Notes. Starting a book with an Appendix is unconventional, but it might make reading Essay easier, as acknowledgment of the failings of Essay might allow better appreciation of its virtues. The argument against looking at the Appendix first, however, is that one ought to read a text before reading its deconstruction.

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On the parallel structures of Essay and Notes Part I. ESSAY: Ontology of Problems consists only of Chapter 1 Being and Becoming, which has two sections, 1.1 Synchronics (Being) and 1.2 Diachronics (Becoming.) Part III. NOTES: Systems Theory also consists of a single chapter, namely Chapter 7 Notes on Being and Becoming, and also has two sections: 7.1 Notes on Synchronics and 7.2 Notes on Diachronics. Chapter 7 repeats every sentence in Chapter 1 and adds explanations in a series of numbered notes. 1.1 Synchronics and 7.1 Notes on Synchronics each have nine subsections: 1 Wholeness, 2 Constraint, 3 Distinction, 4 Persistence, 5 Identity, 6 Agency, 7 Complexity, 8 Cognition, and 9 Summary. For example, Persistence is subsection 1.1.4 of 1.1 Synchronics and 7.1.4 of 7.1 Notes on Synchronics. 1.2 Diachronics and 7.2 Notes on Diachronics each have nine subsections: 1 Origin, 2 Development, 3 Limitation, 4 Complexification, 5 Internal Opposition, 6 Texture, 7 Other Systems, 8 Embeddedness, and 9 Impermanence. For example, Internal Opposition is subsection 1.2.5 in 1.2 Diachronics and 7.2.5 in 7.2 Notes on Diachronics. Some personal information I’ve been working in systems theory since 1976, when I took my current position as Professor of Systems Science at Portland State University. My previous position was in the Department of Biophysics at the University of Chicago, where I worked on macro-molecular crystallography. Before that, I obtained my PhD in biophysics at MIT. Prior to my years at MIT, I spent three years as an officer assigned to the Physics Branch of the Office of Naval Research. Earlier, as an undergraduate at Columbia University, I was a physics major and math minor. Senior year courses in electrical engineering also introduced me to systems theory and cybernetics to which I later returned.

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With respect to the political aspects of this book, I’ve had a interest in these subjects since the 1960s and ′70s. My religious interests intensified also in that period but date back earlier to the religious education that I received in elementary school and high school. I decided to pursue a professional life in science, but the systems view that I eventually arrived at – that all systems are flawed and that our obligation is to perfect them – is, I’ve come to realize, also a religious view. My research/scholarly publications can be downloaded from https://works.bepress.com/martin_zwick/. The pull-down menu on this page allows one to jump to “Systems Theory and Philosophy,” the category most relevant to this book, but publications under two other categories, namely “Discrete Multivariate Modeling” and “Artificial Life / Theoretical Biology” are also relevant. This is a brief autobiographical sketch; for more details see the ACKNOWLEDGMENTS section near the end of the book.

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Part I. ESSAY: Ontology of Problems ESSAY 12 makes abstract assertions about general problems that afflict many but not all systems. These ubiquitous problems are those of systems in the world, not in our models of such systems, although problems in our models are included among the problems of systems in the world. The perspective here is thus primarily ontological rather than epistemological. 13 Bear in mind that, because of its focus on problems, Essay does not offer a balanced or complete view. Thus, for example, it asserts that “Presence of other systems enables competition and conflict.” The presence of other systems clearly also enables cooperation and synergy, but this is not mentioned because Essay is intended as an ontology of problems. 14 The limited scope of Essay (its specific focus on problems) is discussed further in the Appendix. 15 Three types of system 16 are defined later in Commentary: concrete (typically systems studied in the natural sciences), abstracted (typically systems studied in the social sciences), and conceptual (typically systems for which material grounding is absent or not essential). 17 Essay mainly talks about the first 12

An early version of Essay is (Zwick 1984). The difference between the ontological and epistemological perspectives is discussed in 2.3 A new conception of metaphysics, p. 54; see also Note #98 A naturalistic epistemology, p. 461. Epistemological problems are treated as special cases of ontological problems and are covered in Cognition (1.1.8, p. 20, and 7.1.8, p. 461). 13

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5.4 Ontology of problems, p. 167 A.2.1 Problematics, p. 604. See also A.1.4 Rhetoric, p. 598, which cautions that Essay “succumbs to some extent to rhetoric.” For example, Essay asserts, “Every action by a system is resisted by its environment.” Action in harmony with the environment is possible, but Essay focuses on problems to give them salience. 16 A comment on use of the word “system”: a set of very similar systems that cohere in some way might also be called a system or suprasystem, but to avoid confusion, such a set is usually referred to as a “population.” 15

17

3.1.2 Concrete, abstracted, and conceptual systems, p. 85

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two, only occasionally about the third. Think of Essay as a repertoire of general ideas, where any individual idea may or may not apply to any particular system. Essay is the first part of this book because it illustrates the idea of an ESM. However, it does not explain the assertions that it makes. If you find that the absence of explanations makes these assertions obscure, consider going directly to Notes. Notes repeats Essay sentence by sentence or paragraph by paragraph and then offers explanations. Some words or expressions in Essay may present stumbling blocks to reading. Generally, for explanation of a word, see if there is an entry in Notes for that word. 18 For example, the way that the words “inconsistency” and “contradiction” are used in Essay is unconventional and thus easily misinterpreted. The idiosyncratic way these words are used in this book is explained in some detail in Notes, 19 and further commented on in the Appendix. 20 Essay also does not offer examples of all the problems it speaks of. Some examples are given in Commentary 21 and a few others in Notes. These examples of the ideas of Essay should not be regarded as definitive or mandated; other examples will likely occur to readers. Finally, a cautionary note. If, when you plunge into the dense and abstract ideas of Essay, you find them obscure or difficult, read the first chapter of Commentary, 22 and then 18 19

The List of Notes starts on p. 288.

See especially Note #6 Inconsistency, p. 311. Also relevant are Notes #123 Disequilibrium and change, p. 507, and #126 Contradiction and its consequences, p. 512. 20 See the discussion in Appendix A.1.5 Scope, p. 601, of issues raised by considering concrete, abstracted, and conceptual systems. 21 5.5 Metaphysician’s desk manual, p. 174, and Chapter 6 Science, religion, politics, p. 193. 22 Chapter 2 An exact and scientific metaphysics, p. 43

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afterward come back to Essay. That Commentary chapter presents the critique of reductionism that motivates Essay and the alternative systems view that Essay offers. Essay is divided into two parts: Synchronics and Diachronics. Synchronics means “at the same time,” so the first part views systems as already in existence and considers their characteristics at an extended present moment. Most basic ideas about systems are introduced in this part. Diachronics means “at different times,” so the second part of Essay views systems as they originate and change over time. Synchronics and diachronics are not simply the same as statics and dynamics. There is dynamics in synchronics, but it is short-term dynamics which typically is reversible and doesn’t involve qualitative change. The dynamics in diachronics is long term and typically irreversible and does involve qualitative change. 23 Synchronics and Diachronics are organized differently. Synchronics proceeds from very general ideas in the sections titled Wholeness, Constraint, Distinction, and Persistence, to less general ideas in the sections titled Identity, Agency, Complexity, and Cognition. The ideas in the first four sections apply to very many systems and thus are fundamental to systems theory. The ideas in the second four sections apply to only special types of systems, especially living systems. Among the first four sections, Persistence is less general than the sections that precede it because not all systems persist. Among the second four sections, Cognition is less general than the sections that precede it, since only complex organisms have cognition. 24 So, roughly, the sections in Synchronics move from more general to less general, from simple to complex. 25 Sections vary considerably in length; for example, Agency is particularly 23

The synchronics–diachronics distinction is discussed further in Commentary, 3.5 Structure, function, and history, p. 109. 24 Synchronics tells a “story”; see p.162. 25 This progression is discussed further in Commentary, 5.3 Categories of complexity, p. 160

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large. Ideally, the first four sections would not attribute to systems any properties that are not very general, but this constraint has only been imperfectly obeyed. For example, it has not been possible to avoid all connotations of agency in the first four sections of Synchronics. The most complex (least general) systems discussed in Essay are those, such as organisms, that exhibit some form of cognition. Systems more complex than these, for example social systems, are not directly addressed in Synchronics (this is an incompleteness) but they are addressed to some extent in Diachronics and are also discussed in Commentary. Diachronics is organized differently – as a progression through stages of a system “life cycle,” moving from system formation to development to maturation to ultimate dissolution. The sections of Diachronics thus don’t parallel those of Synchronics, except that they continue discussion of the Agency subtopics of Texture, Other Systems, and Embeddedness. In summary the sections of Essay are as follows: 1.1 Synchronics (Being) 1.1.1 Wholeness 1.1.2 Constraint 1.1.3 Distinction 1.1.4 Persistence 1.1.5 Identity 1.1.6 Agency 1.1.6.1 Texture 1.1.6.2 Other Systems 1.1.6.3 Embeddedness 1.1.7 Complexity 1.1.7.1 Networks 1.1.7.2 Hierarchies 1.1.8 Cognition 1.1.9 Summary

7 7 8 10 11 13 13 15 17 18 18 19 20 23

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1.2 Diachronics (Becoming) 1.2.1 Origin 1.2.2 Development 1.2.3 Limitation 1.2.4 Complexification 1.2.4.1 Segregation 1.2.4.2 Systematization 1.2.5 Internal opposition 1.2.6 Texture 1.2.7 Other systems 1.2.8 Embeddedness 1.2.9 Impermanence

24 25 25 27 29 30 31 33 34 35 36

Note that in Synchronics, the sections named Texture, Other Systems, and Embeddedness (which are about three different types of environment), are subsections included under Agency, but in Diachronics they are separate sections. 26 A remark about notation: Essay is not only repeated in Notes sentence by sentence but is also quoted in several places in Commentary. Quotes are identified by adding the paragraph number and the sentence number in the paragraph to the section number. For example, a quote of the second paragraph third sentence of 1.1.4 Persistence (Synchronics) is identified as 1.1.4.2.3. However, Agency and Complexity in Synchronics and Complexification in Diachronics also have sub-subsections. So a quote of the third sentence of the second paragraph of 1.1.6.1 Texture (Synchronics) is identified as 1.1.6.1.2.3, i.e., it has six numbers rather than five. A quote of the third paragraph fifth sentence of 1.2.4.2 Systematization (Diachronics) is identified as 1.2.4.2.3.5.

26

For more information, see Note #133 Environmental types, again, p. 525.

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Chapter 1 Being and Becoming 1.1 Synchronics (Being) 1.1.1 Wholeness The whole cannot be embraced. Every system has an organizing principle, and every organizing principle is limited. In any system, only some elements and relations are encompassed; others are left out. Unity is gained at the cost of partialness. In the impossibility of totality, every system is incomplete. The relations that structure a system are either organized by a unitary principle, or they remain separate, unharmonized at the level of the whole. Unity coexists with multiplicity. Multiplicity allows inconsistency. Every system is flawed. Every organizing principle is finite in scope. Within a restricted domain, a network of relations can achieve coherent order, but consistency and completeness cannot both be attained. 1.1.2 Constraint Wholeness is constraint upon variety. Variety, in the multiplicity of elements in the system, and constraint, in the relations that tie these elements together. Variety, in the multiplicity of states of the elements, and constraint, in the relations that restrict the variation of these states, simultaneously or sequentially in time. A system is a union of variety and constraint, but variety and constraint are opposites, and the tension between them echoes the primary tension between completeness and consistency. Constraint makes the actual less than the possible. Constraint is limitation. Possibilities are excluded in every actualization. This exclusion may not be permanent or unconditioned. What exists is more than the actual. What is potential also exists and can influence the actual. © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_1

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Constraint is order. Variety is disorder. Order is necessity, certainty, homogeneity, invariance; disorder is chance, uncertainty, heterogeneity, plasticity. Disorder may arise from order on smaller or larger scales; order may alternatively arise from disorder. Order and disorder are intertwined and linked by more than opposition or complementarity. Disorder may be order that is complex or compressed or sensitively dependent on present context or past state. Constraint is the basis of unity. When the organizing principle is not single or when constraint is not maximal, multiplicity coexists with unity. Indeed, unity presupposes multiplicity. All systems encompass both, and each afflicts and augments the other. In particular circumstances either may predominate but not fully or permanently. When constraint is minimal, multiplicity is extreme, and the system is a mere aggregate. Unity may be reconciled with multiplicity by constraint of medium strength or by partition or timing, but intermediate conditions are often unstable. Even were these opposites reconciled, the solution would have its own opposite. 1.1.3 Distinction Wholeness implies distinction from context. Every system has an environment with which it exists in disequilibrium. A boundary both separates the two and joins them together. Every system bears the imprint of a demarcation, sharp or blurred, simple or complex, enduring or ephemeral. No system is alone. Every system is enmeshed in a larger whole, a web of external relations that extends indefinitely outward. This web is not homogeneous or seamless but is a network that is structured. System is one and many, partitioned from the all and silhouetted against zero. One implies two: system and

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environment. Two brings three: system and environment in relation. From three, everything follows. The system is an element in its context and a relation for its elements. Internal constraint brings both contraction and expansion: as the source of unity for the system, contraction; as the source of emergent attributes which enable interaction with the environment, expansion. Every element of the system is a system on a smaller scale. Every whole is a part; every part is a whole. Constraint upon variety characterizes not only internal relations but also external relations. The system is not only distinct from its environment but is constrained by it. Either extreme – being constrained too much or too little – is diminution. A system too tightly coupled to its environment is a diminished whole; one too loosely coupled to its environment is a diminished part. No intermediate condition is permanently optimal. Constraint has not only strength but polarity: one pole active, the other passive. Because of difference in scale of the system and its environment, it is commonly the system that is passive, but polarity varies. Context does more than bind; it defines. The system is subject to dual determination: It is constituted not only by its internal order but also by its participation in an external order. As a nexus of being and behaving, every system has not one organizing principle but at least two: a principle of internal structure and a principle of external function. Structure does not uniquely specify function nor does function uniquely specify structure. Both define system attributes. Between structure and function there is tension. What is determined from within and what is determined from without are never in complete accord. Unity is opposed by multiplicity in both structure and function. Rarely is there only one external organizing principle. The system also interacts with its environment not merely as a single element. Parts of the system engage parts of the

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environment, so multiplicity in structure passes through into function. The environment is neither single nor constant. A system may exist in more than one environment. Environments change. Although a system may partially alter or transcend the limitations of its environment, no possibility exists of complete escape from external constraint. Context is unbounded. Although the system interacts only with a limited environment, these limits are provisional. What is relevant to the system is dynamic and open-ended. Insofar as the system is determined by external relations, this determination is never final. When external conditions change, the system is affected. 1.1.4 Persistence Constraint and distinction do not ensure persistence. The environment does not only bind and delimit the system; it is a source of disturbance. To endure, the order of the system must to some extent be insulated from external change. Even small disturbances may undermine this order or impact behavior. Thus every system must in some degree or manner be closed. The organizing principle provides for the closedness of the system and is protected by it; in another sense, the organizing principle is itself this closedness. But to the degree to which and the manner by which a system is closed, it is vulnerable to a dual risk. It tends to either disintegrate or rigidify. Disintegration resolves the tension between constraint and variety in favor of variety. Constraint does not spontaneously arise, but it may spontaneously vanish. Rigidification resolves the tension in favor of constraint. Disintegration is countered, but dynamic activity is reduced. Though disintegration and rigidification are opposites, they are often linked; systems may suffer both processes simultaneously.

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Complete isolation, however, is impossible. Every system is also open to its environment in some degree or manner. Openness brings vulnerability to external disturbance, yet in openness there is the possibility of preserving internal order. Openness may even be necessary. A flux across the boundary of the system may be required for its existence. Through openness, tendencies toward disintegration or rigidification may be blocked or balanced. External order absorbed and internal disorder expelled may counter disintegration; internal disorder retained or external disorder assimilated may counter rigidification. But the proper balance of order and disorder is contingent and subtle. In openness, there is only the possibility of self-maintenance, not its guarantee. Openness may cause disintegration to occur even more rapidly than if the system were closed. Extreme openness, like extreme closedness, undermines persistence. Thus, every system must be partially closed and partially open, or closed and open at different times, or closed in some aspects and open in others. This dual imperative echoes the tension between constraint and variety. The existence of the system depends upon constraint. Yet variety is needed to block the internal effects of environment disturbance. But variety is beneficial disorder and differs from harmful disorder only by its consequences for the system, which change with circumstance. Alternatively, the effects of the disturbance can be countered after they arise, but regulation may take hold only after a lag, making control difficult, even unstable. 1.1.5 Identity Persistence is a precondition for identity. The system may have an informational domain that governs self-construction through the specification of process. The invariant core of this domain is the organizing principle of the system, its structural identity. But identity is not simply invariance, since the organizing principle may provide for plasticity. Structural identity and the environment determine the system’s nature.

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If the system is embedded in an organized environment, a second identity is imposed from without. For the system, the internal has priority; for the environment, the system’s external identity has priority. Identity of structure and identity of function are never exactly the same. If the system is a member of a population of similar systems, its generic identity is supplemented by identity specific to itself. Neither identity that is universal nor identity that is unique has intrinsic priority. The identity of the population is dispersed among its constituents. Closedness and openness are temporal as well as spatial. Closedness is the residue of the past. Openness is contact with the present. Being determined by the internal past is inertia; by the external present, drift; by past or present at random, incoherence. What is necessary for the system is an active and balanced synthesis of the legacy of the past and the imperative of the present, a synthesis not easily achieved. Being active requires information and energy. Balance is precarious. Synthesis requires a principle neither internal nor external. Change must at times be resisted, at times embraced. Viability requires openness to the outside, yet internal patterns must have some priority over external influences. No general principle exists for joining past and present, interior and exterior, to secure autonomy. The prerequisites for change undermine it. Multiplicity is needed for change but harbors resistance to the new. Unity is needed for change, but the new cannot take hold of what is unitary. Closedness may be provided for by subsystems that distinguish between what should be taken in and what should be kept out, between what conforms to the identity of the system and what is foreign to it. These functions may be performed by the boundary, which regulates transactions across the systemenvironment interface. Or there may exist a subsystem that distinguishes self from non-self and counters deviations from identity. By such provisions for closedness, the system protects

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identity but acquires new vulnerabilities. Failure of these subsystems leaves the system defenseless; their hypertrophy engenders rigidity; their errors of identification destroy order. 1.1.6 Agency Identity is made secure through agency. The system must be active toward a relevant environment that presents both utility and hazard. The environment is not spatially uniform or temporally invariant. There is texture in its distribution of resources and noxiants. The environment may include a network of other systems. It may constitute a more encompassing order in which the system is embedded. Texture in the environment exposes the system to the vagaries of chance. Presence of other systems enables competition and conflict. Being embedded in a larger whole compromises autonomy. 1.1.6.1 Texture Variability of the environment calls for optimization by the system, but requirements for optimal action are never fully met. No algorithm exists for the specification and evaluation of all actions open to the system in the present or future. The environment is unbounded and its potential impacts on the system cannot all be assessed. Even within a restricted context, the possible states of the environment and their probabilities may not be known even in the present, and forecasting future states is at best reliable only in the near term. One action precludes another, and the joint result of system action and environmental state may be unpredictable. No plan survives contact with reality. Every action by a system is resisted by its environment. The nature of this resistance cannot fully be foreseen. No action generates only one effect. There are always externalities. Actions have unanticipated consequences, even counterintuitive effects. What should suppress perversely stimulates; what should stimulate unexpectedly suppresses. Effective action may require pursuit of apparently undesirable ends.

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There is no terminus to the effects of action. Outcomes multiply into the future, and a final outcome never arrives. Even if initial effects are small, later effects can be large. Even were outcomes predictable and future utilities known, the relative weights that ought to be given to near- and far-term outcomes remain uncertain. For unrestricted action, the present must be free to bind the future, yet when the future arrives, action is restricted. Moreover, optimization requires unity of purpose, but purpose is multiple and inconsistent. Purposes conflict. Imperatives of structural identity differ from those of functional identity. Multiple objectives are usually incommensurable, but even when they have a common utility scale, arbitrariness cannot be avoided. When utility is ordinal, no method exists to aggregate multiple preferences into a rational, decisive, and equitable choice. Even when the context for decision is clear, a single utility can be assigned to every outcome, and the dependence of outcome on action is known, optimality may still be impossible in principle or unattainable in practice. Discovery by enumeration is limited by resources. Discovery by search requires global knowledge, yet only local knowledge is readily available, and acquisition of global knowledge is in conflict with its utilization. Local optimization is usually suboptimal since the risky search for maximal gain foregoes assured, though inferior, benefits. The good is the enemy of the best; the best is the enemy of the good. What is optimal is not necessarily stable, and what is stable is not necessarily optimal. The dynamics of the system may take it far from optimality. Moreover, in a changing environment, optimality is an ever-receding mirage. But even if attained, optimality brings risk. It reduces diversity and redundancy, which diminishes resilience. Ground, goal, direction, instrument: the components of purposeful action are commonly flawed. The actual states of

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system and environment are unknown; the ideal is unrealistic; the guidance of action is inadequate; the implements of action are insufficient. Rational action is difficult to achieve. 1.1.6.2 Other Systems Every system is a center to a periphery of other centers. In being ordered and distinct from their environments, all systems are alike, but this similarity is always joined to difference. If sufficiently complex, systems differ even from others of the same type, although in the commonality of uniqueness there is similarity of another sort. Either similarity or difference provides a basis of interaction, for benefit or for harm. Interaction with other systems is via assertion, exchange, or integration. Every system is both a whole and a part. As a whole it asserts or exchanges; as a part it is integrated into larger wholes. Assertion is force, which engenders conflict. Exchange allows reciprocity, which promotes connectedness. Integration is communality, which approaches union. Assertion is contested by competition. The system may also be the object of predation. Systems are food for other systems, and participation in the flux of substance cannot be declined. Success itself invites danger. A system effective at acquiring resources is a target for takeover, parasitism, or theft. In situations of competition, no principle of rationality is fully satisfactory. Rationality may require behavior that is partially random. If there are more than two agents, coalitions are unstable. Just as an incorrect assumption of the absence of adversaries is a prescription for failure, so too is an incorrect assumption of fixed total gain. More commonly, total gain is variable, so cooperation is not precluded. But even where cooperation is to the advantage of all, defection may be compelling. Individual rationality may lead to collective irrationality, to the disadvantage of all, even to disaster. A principle of altruism or of symmetry does not always solve these

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dilemmas: The best outcome may occur when agents act in selfinterest or differently from one another. Via exchange, incompleteness is ameliorated. But exchange also reinforces incompleteness by fostering dependence. Neither extreme of dependence or self-sufficiency is ideal, nor can an optimal and enduring balance be found between the two. When survival depends on exchange, external identity prevails over internal identity. When exchange is extensive, the system loses autonomy and becomes embedded in a larger whole. When exchange is unequal, it becomes exploitation. Exchange cannot be completely controlled. Acquisitions via exchange retain traces of their origins. What passes from one system to another is not fully specified by either. Even when openness is regulated by the organizing principle of the system, it is impossible to allow entry into the system of the beneficial and reliably exclude the harmful. Function, like structure, is afflicted by the tension between unity and multiplicity. Interactions may be with few other systems or with many. Relations with few are thicker but are limited, so identity is incomplete. Relations with many lessen dependence but are incoherent, so identity is inconsistent. Neither narrowness nor breadth of interaction is fully or permanently satisfactory, and intermediate conditions are unstable. Exchange may solidify into integration. Integration with similar systems multiplies capacity but risks redundancy. Integration with different systems offers complementarity but risks dependence. Since every system is both similar to and different from every other system, integration brings both benefits and risks. The system may overlap other systems that organize different attributes of common elements. This compromises the integrity of boundary. Or, the environment may consist not of

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many other systems but only one. Because of incompleteness, every system at least potentially has a complement with which it must coexist. 1.1.6.3 Embeddedness The embedding of a system in a more encompassing order poses the deepest challenge. Systems have the capacity and the tendency to become integrated into larger wholes. Yet every system is also a whole unto itself. The competing needs of system and suprasystem may for a time be harmonized, but the interests of part and whole never completely coincide. There is renunciation or suppression in every integration of one system into another. In being a part, autonomy is relinquished. The system must present attributes required by function, and the locus of identity becomes external. Being embedded may offer security, but the price of security is heteronomy, and this security cannot be relied upon. Wholes sometimes sacrifice or consume their parts. A system may be embedded but yet not integrated into the larger whole. It suffers the harm of exclusion. Or it may be integrated into this whole to the advantage of other systems but to its own disadvantage. There may be more than one encompassing order into which the system might be integrated. Even if it can select its location, the opportunities and risks of available environments are never fully known, and movement from one to another is not always possible. The system may become integrated into more than one encompassing order; the resulting tensions may be mitigated by differentiation but at the cost of coherence. No escape is possible from being the object of competing attempts at recruitment by larger wholes. Alternatively, it may be the absence of a larger whole that endangers the system. Unrestrained competition with other entities may be detrimental, and higher-level constraints may be

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needed to assure cooperation. In turbulent environments, with the system at the mercy of large-scale forces, isolated action may be ineffective. Survival may require being embedded in a suprasystem order. Yet systems resist the loss of autonomy. Every system is bound to a particular scale of existence and is vulnerable to environmental disturbances on much larger or smaller scales. 1.1.7 Complexity Identity is articulated in complexity. Complexity is a source of uniqueness. Uniqueness in the organizing principle is individuality. If the system is embedded in a population of similar systems, what is universal within the population is in tension with what is unique in the system, but in populations of sufficiently complex systems uniqueness is itself universal. Complexity may be dispersed horizontally in a network or vertically in a hierarchy. Each archetype is an attractor. Neither is optimal, but a balance between the two is unstable, and organization by both is inconsistent. 1.1.7.1 Networks A network of interactions can be stable or unstable. Either condition can have adverse effects. Stability can lock the system into dysfunctional states; instability can lead to runaway dynamics that also produce such states. The presence of non-local interactions in addition to local ones makes connectedness global. This may deamplify some local disturbances, but it amplifies others, allowing them to propagate through the entire network. The absence of global connectedness is likewise both beneficial and harmful. Local disturbances are contained, but the system is fragmented. Networks are more flexible than hierarchies and less vulnerable to local disturbance, but laterally dispersed order makes coordination and unified action difficult. This can be

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partially remedied by the network becoming more hierarchical, but it then becomes vulnerable to failure of critical hubs. 1.1.7.2 Hierarchies In hierarchy, multiplicity is not only horizontal but also vertical. Each level is a system subject to disintegration or rigidification. Each has an environment of higher and lower levels. Each level thus has a dual identity: one based on structure with its imperative of autonomy, the other based on function with its imperative of interaction. If autonomy is excessive or interaction insufficient, the level will have nothing to contribute. Constraint and variety oppose one another at each level and between levels. Micro-homogeneity engenders macroheterogeneity; micro-heterogeneity macroengenders homogeneity. Either arrangement can generate harm. In both arrangements, unity and diversity coexist but neither principle is consistently maintained. Each level is a center of structure and function. Neither complete separation nor complete merging of levels is optimal. Separation causes conflict or fragmentation. Merging deprives higher levels of the independence needed for regulation and lower levels of the integrity of basic process. Every level has its function. Upper levels organize; lower levels ground; intervening levels mediate. No function has permanent priority. Every level is subject to pressures from other levels, pressures that do not subside and whose reconciliation is temporary. The extremes of a hierarchy are its fundamental levels, which determine it from above and below, but commonly one extreme has primacy. Even the dual prominence of both highest and lowest is harmful, if it undermines intermediate levels no less critical for the system. Whatever empowers either extreme,

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without enhancing the mediating levels, invites disorder. Beyond its proper function, the fundamental disrupts. At the highest levels, opportunity and hazard are maximal. The privileged status of these levels, their greater scope of action, their distillation of principle, and their concentration of power all tend to weaken lower levels, for which the benefits of coordination do not compensate. Higher levels can buffer lower-level dysfunction, but the devaluation of lower levels and the preemption of their function ultimately impair viability. The highest is not the whole. It represents the whole and gives it coherence, but it is still only a part. The whole depends on all levels performing their unique functions and on the fluidity of interactions between levels; only in this way is harmonious integration possible. The interests of higher levels and the system as a whole are never identical. Any privileged position within the system is used for gain, and increasingly so over time. Because of the inherent inequality between higher and lower levels, exploitation of the latter by the former is the rule. Where the system is embedded in a more encompassing order, higher levels become the locus of external control. In complex systems, hierarchy often consists of informational regulation of transformations of substance. Distillation of an informational domain is a refinement that facilitates adaptation, but it also introduces vulnerability – to failures of coordination, to dysfunction between levels, and to informational parasitism. 1.1.8 Cognition Agency is informed by cognition. The informational domain may include a subsystem that models the environment, other parts of the system, the system-environment interaction, and even itself. Incompleteness extends to this subsystem. There are limits to the scope and complexity of any model.

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Regulation by a modeling subsystem requires an instrument that can affect the environment or other parts of the system. Action by the instrument must serve some goal and be given proper direction. But instrument, goal, and direction are often flawed, and the practical, meaningful, and formal components of agency are rarely well integrated. Moreover, multiplicity in system-environment interactions induces a corresponding multiplicity in the modeled self, which poses a challenge of integration. The modeling subsystem internalizes the primal distinction between self and non-self. Although an embedding environment may provide an informational framework that amplifies cognition, the modeling subsystem then comes to harbor the tension between system and suprasystem. Through this subsystem the environment acquires a beachhead of control over the system. Cognition extends agency in time and space. The present moment widens into past and future. Through extension in time, potential is represented in a model that is actual. Through extension in space, the relevant environment expands into distant realms. But a system released from the here and now loses contact with it. The modeling subsystem ingests external and internal impressions. Although novel impressions carry maximum information, the metabolism of impressions by pre-existing structures inhibits the recognition of novelty, so this subsystem, an apparatus for assimilating information via openness, becomes itself a source of closedness. Or impressions may not be assimilated. Their complexity or number may be too great or the modeling subsystem too passive. Modeling is representation and construction. Representation compresses impressions; construction organizes them, since structures of understanding cannot be ingested whole but must be developed internally. Impressions are incomplete and may be unreliable. The internal construction of

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reality partially compensates, but since construction exercises some independence from fact, it produces a web of representation, inference, and invention that cannot be disentangled. Construction is distorted by pressures of utility. The modeling subsystem depicts a world and a self that are in part illusion. Just as variety and disorder are not intrinsically but only functionally distinguishable, there is no inherent difference between a model that is adequate to reality and one that is not. There is always more than one adequate model, and the degree to which any model is valid cannot be specified by the model itself. By representing the constraints through which the environment is organized, the system may be able to exploit these constraints to its advantage. But constraints may be inaccessible to observation or too complex to model, or may be unstable or evanescent, being altered by even small changes in the environment. Or, constraints may be absent, and their modeling a false inference. External order can never be completely and accurately discerned. Modeling may allow detection of hazards and opportunities. There is a tradeoff between responding to weak signals and avoiding false alarms. Unreliable perception and worst-case assessments of internal or external events can be self-defeating. There is no way to be certain when a protective response can be safely relinquished. The modeling subsystem mirrors the whole of which it is a part. Through this self-reference, incompleteness is both fixed and transcended. It is fixed in resistance to change by the model of self. It is transcended in the recognition of incompleteness that self-reference allows. In the modeling of self, inconsistency is hidden, so the illusion of unity prevents its accomplishment. When modeling is itself modeled, information is distilled to a higher level. This brings enhanced autonomy but also vulnerability to pathologies of self-reference.

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1.1.9 Summary A system is constituted in two ways: as an instantiation of order and as the result of a system-environment distinction. Structure is the internal order of parts that is the legacy of the past; function is the participation in the external order of the present. A permanent harmony between structure and function cannot be established. All systems encompass constraint and variety, unity and multiplicity, closedness and openness, invariance and plasticity, autonomy and dependence. Constraint, unity, closedness, invariance, autonomy, and structure are allied, as are variety, multiplicity, openness, plasticity, dependence, and function. No fixed priority obtains between these constellations of features. Multiplicity, openness, and plasticity protect the integrity of the system, but integrity requires unity, closedness, and invariance. Yet, unity is flawed by partialness, closedness brings dissolution or rigidification, and invariance is unattainable. These conflicting requirements arise from incompleteness. There are no enduring and context-free solutions to these dialectical dilemmas. In every polarity, each extreme exerts a powerful attraction, yet rarely is either extreme optimal or even viable. No principle of synthesis or balance can compare in simplicity and thus in potency with the imperative of an extreme; in some cases, of both extremes simultaneously. Synthesis of opposing attractors is particular and contingent, not universal and necessary; balance between them remains precarious. Multiplicity wars on unity. Closedness wars on openness. Universality wars on uniqueness. Environments change. Hazard is implicit in the fabric of existence. Indefinite persistence is impossible.

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1.2 Diachronics (Becoming) 1.2.1 Origin A system comes into being via distinction and constraint. Through distinction, the unity of the primal field is sundered. System and environment are separated and thereby also joined. Through constraint, the multiplicity of the primal field is organized. A limited order of elements and relations emerges. Distinction is disequilibrium engendered by the descent of differentiation. Constraint is order engendered by the ascent of integration. The newly arisen system is incomplete and often also inconsistent. What flaws its origin will condition its future. System formation occurs either spontaneously by selforganization or through the action of other systems. In the moment of origin, either internal structure or external function dominates, but the other organizing principle coexists, either at the outset or thereafter. Fragility of the newly arisen system is the rule. What spontaneously organizes can spontaneously disorganize. Where other systems engender or facilitate this arising, they shape the character of the new system. Either excessive proximity or excessive distance poses risk. Excessive proximity hinders the independent development of the new system. Excessive distance deprives it of necessary support. No prescription exists for optimality of distance. A system generated by other systems may face tension between fidelity to the matrix of its arising and assertion of its distinctive attributes. Total continuity is impossible. So is total change. If the organizing principle of the newly formed system privileges continuity, autonomy is not gained. If it favors change, identity is not grounded. Every mixture of continuity and change is unstable. If continuity and change are both embraced, the new negates the old and seeks to supersede it.

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1.2.2 Development The order of the system may be evanescent and the systemenvironment distinction a transient, but the newly arisen system often has a capacity for increased complexity. What flaws a system at its origin – its incompleteness or inconsistency – is potential for its development; the deeper the flaw, the greater the potential. Incompleteness reflects a disequilibrium, as does inconsistency, and disequilibrium is the basis not only of existence but of change. But the flaw may instead be a source of dysfunction, even a force toward dissolution. Incompleteness in engenders becoming. being Disequilibrium with the environment is a force that drives a flux of substance through the system. The flux not only organizes the system but through random fluctuations may increase its complexity. Openness allows more than self-maintenance. Order initially only potential may become actual. Assimilating external elements, the newly arisen system may augment its initial endowment. It may grow and develop. Yet what is assimilated may fail to be integrated; marked by its origin, it may remain an accretion, an implant, even an agent of the environment. Inconsistency in being engenders becoming. If contradiction does not cause stasis, it gives rise to dynamics, most simply cyclicity. Contradiction may for a while be hidden or partially resolved in complexification. It is rarely harnessed as the engine of development that it might be. The polarities that exist in the system constitute an internal disequilibrium, which, suitably mediated, generates change. Commonly, however, opposing poles either lack such mediation or merge with one another, thereby dissolving the disequilibrium and squandering its potential. Development is not guaranteed. All development is internal development, but its necessary preconditions may be absent. Support by the environment may be lacking. External affordances may come too late – or too soon. Internal factors

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may block development or cause uncontrolled growth. Nor is the absence of early challenge an unmixed advantage. Postponement of risk allows rigidification, which lays a foundation for future dysfunction. 1.2.3 Limitation Becoming does not escape the finitude of being. Eventually the momentum of expansion slows, and consequences of the restricted scope of the system’s organizing principle begin to manifest. Obstacles are encountered to continued development. Thus the dialectical trajectory: the development of the system proceeds from nucleation to expansion to the encountering of limitation. What is missing in the system may afflict it, if not initially then subsequently. Expansion may mitigate original incompleteness, but what is not subsumed initially may be difficult to assimilate later. Or, too much may be subsumed. If the capacities of the organizing principle are exceeded, disorder or contradiction is introduced into the system. Obstacles appear in many forms: in exhaustion within the environment of elements suitable for incorporation or transformation; in the difficulty of maintaining coherence while integrating new elements; in the fragility of the order achieved; in conflict generated by internal structures not subordinate to the organizing principle; in constraints or dangers posed by other systems or a higher-level order. Circumstances vary, but unimpeded development rarely occurs. Nucleation, expansion, limitation: this sequence of early stages is the norm. As development continues, the factors that limit it also intensify. If the system proceeds on this trajectory, a critical phase is eventually reached in which the intensification of hazard emerges as a lawful feature of development. The unique attributes of the system, its particular structure, function, and history, become more important than its generic attributes, and its future becomes uncertain. The system enters a region of

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bifurcation in which its actual state is accompanied by a potential state that corresponds to restructuring by a new organizing principle. This coexistence of actual and potential states defines the principal contradiction which now characterizes the system. Thesis leads to antithesis, and not by failure but by success. Limitation is internal or external. When limitation is internal, it is general or specific: It derives from general difficulties of systems maintenance and development or from the existence of a specific opposing organizing principle. When limitation is external, it is general or specific or both: It arises from the general texture of the environment, from specific other systems, or from embeddedness within a more encompassing order. Many problems elude solution. They may be unanticipated; or the system may fail to perceive them when they arise; or the system may perceive them but not respond adequately in time; or attempted solutions may fail. 1.2.4 Complexification Limitation may be internal and general. Closedness, needed to protect the nascent order against external disruption, deprives the system of vital resources. Openness, needed to augment the endowment of system formation, puts internal control of development at risk. An organizing principle based on unity promotes an extreme of order; one based on multiplicity, an extreme of variety. The system may be subject to and unable to arrest a movement toward either extreme or even both simultaneously. Development is hindered by both rigidity and plasticity. After a degree of development, tension invariably arises between what for identity must be fixed and what for adaptability must vary. But rigidity and plasticity are not strictly opposed. Rigidity is the foundation for plasticity. Where there is a differentiation between center and periphery or between domains of substance and information, rigidity and plasticity

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may predominate in different parts of the system. Higher levels may rigidify while lower levels remain plastic; or the reverse: lower levels may rigidify, while higher levels remain plastic. Similarly, closedness is the foundation for openness, and closedness and openness may predominate in different parts of the system. Growth engenders form but form constrains growth. Development entails the modification and non-proportional growth of parts. Eventually this requires a change of structure, often difficult to accomplish. Or, development may be organized by a principle that governs the temporal unfolding of structure. If the unfolding process is complex, errors in scheduling are likely. Optimizing the schedule is also difficult. Moreover, even if achieved, optimality increases vulnerability, since optimality requires the sacrifice of resilience. Because of multiplicity, temporalization of complexity yields inconsistency of purpose. No course is held steady. Fluctuations in salience of different parts of the system cause constant change of both direction and goal. A goal that constantly changes is unlikely to be realized. Direction that constantly shifts gives unreliable guidance. Every part, when dominant, acts for the whole and binds its future, but the dominance of each part is ephemeral, so the future is not truly bound. The ever-changing locus of dominance also interferes with integration into more encompassing orders. A larger system may require or even induce a degree or semblance of unity, but imposition of unity from without cannot indefinitely overcome a multiplicity within. Or, the situation may be reversed. The environment may require greater variety of function than is provided by the internal order. Even if achievable, temporal consistency may thwart development. What is beneficial in early stages of development is often not beneficial later. And if the development of a system is programmed, so too may be its demise.

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In complexification, wholes and parts undergo progressive segregation or progressive systematization or both. These two universal phenomena govern diachronic change in all systems. A movement of expansion, differentiation, or decomposition flows downward from unity to multiplicity. A movement of concentration, integration, or composition flows upward from multiplicity to unity. Both currents may be simultaneously present, but they oppose one another; rarely are they optimally balanced or blended. Differentiation undermines any organizing principle favoring unity; integration undermines any organizing principle favoring multiplicity. 1.2.4.1 Segregation Progressive segregation, if controlled, is differentiation. Higher ordinality relations weaken, and the system becomes partially decomposable. Parts of the system gain autonomy, but the whole suffers inefficiency or strife. To one part, other parts are competing agents, and what is optimal for a part is rarely optimal for the whole. Differentiation separates center and periphery. The center is the locus of unity; the periphery, of multiplicity. In centralization, the center tends to rigidify and the periphery to disintegrate. The asymmetrical relation between center and periphery may be complementary and reciprocal but may instead harbor unequal exchange, exploitation, and conflict. Differentiation may lead to fragmentation, resulting in new systems consisting of parts of the original whole. If the lowest levels are lost, the new system is bereft of foundation; if the highest levels are lost, it is bereft of horizon. If the new system consists only of higher levels, the benefits of being untethered are compromised by the hazards of being ungrounded. Progressive segregation, if uncontrolled, is not complexification but disintegration. The destruction of order occurs far more readily than its creation, and the danger of disintegration inheres in the relentless passage of time.

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1.2.4.2 Systematization Development may exhibit not the descent of segregation but the ascent of systematization, in which elements become increasingly constrained by higher ordinality relations. The system gains integrality, but the parts lose autonomy. Optimization becomes more difficult. Stability is stratified, and higher levels of organization are generally possible. The system can become more complex through the accretion and integration of pre-existing wholes, but rarely does this avoid inconsistency. Even when stratification proceeds smoothly, there are limits to the scope of proceeds any organizing principle. Systematization spontaneously only so far. Barriers to development are encountered well before the limits of self-organization are may allow although conditions reached, special complexification to continue. Support may be provided by external factors. The chance emergence by fluctuation of a more encompassing order may stabilize structures that would otherwise be transient. A second process might augment the first and give it momentum. Or, systematization may be joined to segregation, ascent to descent, enabling both. Possible facilitating conditions are varied, but there is no guarantee that complexity will increase or even persist. Ascent of systematization is sometimes too rapid, with new levels poorly integrated with those already present. Salience of new levels may undermine basic function. Through the emergence of higher levels, the system rises above lower-level constraint. But lower levels are supplemented, not eliminated. What is transcended may be routinized or ignored but it persists and under adverse conditions it claims its due. Only harmonious integration of levels, not transcendence of the lower by the higher, can endure. Systematization may increase connectedness without adding higher levels. Greater connectedness is a multiplier that can neutralize disturbance or amplify it and thus can either

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increase or decrease stability. Some systems in their development move toward critical points where disruptive events at all scales become both unpredictable and inevitable. 1.2.5 Internal opposition Limitation may be internal and specific. Incompleteness and inconsistency engender development but also obstacles to development. As a response to incompleteness or as an intensification of inconsistency, there may emerge within the system a competing order. Every system is flawed, and every flaw in a system is a potential nucleation site for an alternative organizing principle. The alternative may derive from what was originally missing in the system. What is ignored or suppressed will eventually have its moment. The alternative may reflect the increased importance of function as a basis of identity, one not congruent with identity determined from within. Or the reverse: an internal order may emerge that competes with a previously dominant external function. More generally, every system is pulled in opposite directions by fundamental polarities. If it is organized around one extreme, the other extreme is a potential challenger. Alternatively, difficulties of development may arise not from what was absent in the system in its formation but from what was present: not from original incompleteness but from original inconsistency. The system may contain two organizing principles: one dominant and the other subordinate. Confrontation of the organizing principle and its negation may grow into conflict, leading in some cases to ascendancy of the challenger. Usually, the system remains structured for a time in its earlier form, but continued shifts toward dominance of the alternative principle may finally make visible what has hitherto been latent. A crisis may ensue in which change accomplished in deep structure manifests also in surface structure. Finally, there may be transformation. The system may yield to its negation.

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But to the degree that the alternative principle is only a denial it offers no basis for a new order. What succeeds as negation never succeeds as affirmation. Negation, to supplant what is rejected, must be more than a corrective; it must offer a positive principle. But to be effective, negation yields to excess and distortion: excess in promotion of the new, distortion in rejection of the old. No order was ever overturned while being granted its due. In the heat of conflict, no delicate titration of opposing principles can be accomplished. Means can never be calibrated precisely to ends. Every correction overshoots. In transformation there is no remedy for the lawful presence in all systems of incompleteness or inconsistency. Imperfections may be mitigated; they may be replaced with different deficiencies, but imperfection is an ineradicable condition. At the very moment when dominance of the new principle is finally established, when negation attempts to recast itself as affirmation, a price is exacted for the excess and distortion that brought victory. At that moment, the deficiencies of the new organizing principle are crystallized, and in this crystallization, the corruption of the new order begins. It is not merely that any new order has imperfections. However flawed the old system was, it had attributes that were not deficient, that could be valuable to the new order, conceivably even to any order. What is essential and necessary or accidental and contingent are difficult to distinguish. In its excess of rejection, the new is inaugurated with incompleteness. And what is rejected in the struggle for dominance is not easily recoverable. The original principle may be vanquished and disappear. Or it may persist in the surface structure, while the deep structure has been transformed. The system may thus appear unchanged despite negation of its organizing principle. Every system has the capacity, through an unbroken line of development, to turn into its opposite without seeming to have done so.

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The struggle of principles may instead yield the triumph of the original order, but its victory is never complete. Those aspects of the system that gained coherence by the opposing principle remain and produce in the system a persistent strain. Recognition of the continued presence of this alternative is suppressed. But the success of this suppression cannot last forever; contradiction may be hidden for a while but not indefinitely. Or, the struggle may lead to a synthesis reflecting a third alternative. Conflict between the opposing principles then shifts to conflict with this synthesis. Just as opposing principles enable and stimulate one another, so too does a newly dominant center incite both extremes. Those parts of the system ordered by the alternative principle may detach themselves or be expelled and may form a new order. For the original system, inconsistency is resolved, but incompleteness remains. The problem is externalized but not thereby solved. Conflict with the new system ensues. The old and the new endanger one another. Partition leaves both marred. In the old system, the original principle is distorted; in the new system, aspects of the old are retained or the new order is incomplete. 1.2.6 Texture Limitation may be external and general. Only certain external substances are beneficial to assimilate; only certain internal substances are beneficial to retain. The environment, as a source for resources and a sink for wastes, is finite, not infinite. Resources may be depleted; disorder or noxiants may hinder the capacity of the environment to support the system. The production of order for maintenance and development, for exchange, or for modification of the environment may or may not occur, but the production of disorder, either retained internally or expelled into the environment, is unavoidable. Wastes are a necessary consequence of self-maintenance. The

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wastes of the system are harmful to it and other systems of its kind and often to other kinds of systems. Only some wastes can be taken in by other systems and removed from the environment, but such other systems are not always present. The neutralization of harmful waste cannot be guaranteed. The circle is not always or easily closed. In circumstances of limitation, the system must shift from expansion to steady state. This shift may be difficult to achieve or come too late to prevent overshoot and collapse. Expansion inheres in an organizing principle that dictates the repeated priority of short-term gain over long-term necessity. Uncontrolled growth of subsystems may enlarge the system beyond sustainable size. It may be difficult to reverse the degradation of the environment already produced by such growth. Even if the long term is considered, the future is an externality that is never fully encompassed. Moreover, a steady state, even if achieved, may not be sustainable. Systems often destroy the environments on which they depend. 1.2.7 Other systems Limitation may be external and specific. When environmental resources are limited, there is a struggle for existence. The system may face competition or predation. If it is large and complex, small and numerous antagonists may be difficult to counter. If it is small and simple, large and complex antagonists may overwhelm. No size or complexity is optimal for all situations of competition, predation, or conflict. Systems suffer unequal exchange with larger or more coherent systems. Unequal exchange drains resources, stunts development, and compromises autonomy. Even where there is mutual benefit, exchange also brings dependence and thus vulnerability. If dependence is extreme, determination becomes external rather than internal, and the system is partially absorbed into the more developed system on which it depends.

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Opposition between systems may be reconciled by a synthesis in which the system and its antagonist are integrated and harmonized. The dialectics of reconciliation are more demanding and subtle than the dialectics of victory or defeat. Additional factors must balance and bind contending forces. If such factors are present, conflict may be overcome, but the existence of these factors and the synthesis they enable may be transitory. 1.2.8 Embeddedness Limitation may be external and both general and specific. When a system is embedded in a more encompassing order, it is subject to constraints imposed by this order. If the order is itself only a transient in a process of development, the system’s functional niche will eventually disappear. Either sudden change or long-term gradual change in the embedding order can undermine the system. Sudden change following prolonged stasis poses a special risk since successful adaptation inhibits adaptability. When an environment remains constant, adaptations rigidify and resilience degrades. Longterm gradual change may escape detection. Change in the suprasystem requires change in the system’s adaptive strategy. The precise moment when an old strategy must be abandoned and a new one adopted is elusive. The system may remain bound to an obsolete specialization, once optimal or at least viable, now harmful if not fatal. Or, the system may adapt by relinquishing ties to its organizing principle. It is then not the original system that persists. Viability is gained at the cost of identity. The system may be a population which adapts to the suprasystem through evolution. Its lower-level constituent systems, untethered to fixed identities, undergo open-ended change; their multiplicity allows evolutionary innovations to be explored in parallel. Although the utility of innovations cannot

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be anticipated, selection allows beneficial innovations to be retained and harmful ones to be discarded. The population adapts in this way to the suprasystem. The rationality in adaptation via selection is extrinsic and at the level of the population. If, however, an evolutionary advance enables a system to estimate the utility of an innovation and adapt before the verdict of selection takes effect, the rationality inherent in this advance becomes intrinsic and at the level of the individual system. But estimates of utility cannot adequately consider all possible future actions and environmental states. In an additional advance, there may emerge within the system a subsystem that models the environment, the system-environment interaction, and the system itself. Such a modeling subsystem further internalizes rationality. Long-term adaptation is superseded by short-term learning which empowers agency. But the modeling subsystem has its own deficiencies. New solutions generate new problems. 1.2.9 Impermanence What flaws being is not remedied in becoming. Development, which negates incompleteness, is itself negated, as the limitations of the organizing principle reveal their consequences. The difficulties necessarily joined to any degree of successful development can be met only if these limitations are accepted. This may require deep change in the organizing principle, perhaps even its abandonment. Ultimately, all systems are composites and thus decomposable. Decomposability may be controlled and limited and may be specified by the organizing principle, but decomposition may be uncontrolled and extensive, resulting finally in dissolution of internal order and the systemenvironment boundary. Things fade, although the onset and rate of decay is not prescribed. Disintegration may be the sudden failure of a seemingly successful process of segregation or systematization that

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outstrips the capacity of the organizing principle to integrate. Decay may be protracted and for a long time indistinguishable from differentiation. Complexification may hide or neutralize the primal incompleteness or inconsistency, but it cannot produce an order that is forever sustainable. Confrontation with limitation may be postponed but not indefinitely. Order eventually succumbs to disorder. Disintegration is the final victory of multiplicity over unity. Multiplicity does not differ intrinsically from disorder, and no system can be organized exclusively on the principle of multiplicity. A loss of necessary rigidity may set the stage for disintegration by destabilizing a complex or fragile order. Existence implies constraint, both internal and external. Modification of constraint is sometimes possible but never its complete absence. Existence implies distinction between system and environment. Modification of the distinction is sometimes possible but never its complete eradication. No means exist to assure the indefinite persistence of constraint and distinction. Loss of constraint and abolition of distinction is dissolution. The system may follow the archetypal route of organisms. Having achieved some measure of development, it suffers its preordained fate. It ages, and with the inevitable and irreversible weakening of its capacity to maintain order and distinction, it passes away. It leaves behind its effects on its environment, which may be considerable and may persist. The system is not, by reason of impermanence, unsuccessful, for how can permanence be a criterion of success? Decay is inherent in all composite things.

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Part II. COMMENTARY: Recovery of Coherence The purpose of Commentary is to explain what systems theory 27 is and argue for its value. The Commentary chapters discuss systems theory and its environment in this sequence:

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Chapter 2 Exact and Scientific Metaphysics presents the organizing principle of systems theory, which is the notion of an ESM, a genuine “theory of everything.”

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Chapter 3 Concepts and Categories presents several key systems concepts to augment and clarify Chapter 1. An extensive exposition of systems ideas is, however, the task of Notes.

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Chapter 4 Related Fields discusses some fields that systems theory draws upon and/or contributes to, i.e., parts of its environment. The chapter asserts the centrality to systems theory of biology and not physics. It also introduces systems analysis, a project that complements the project of systems theory.

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Chapter 5 Challenge of Integration discusses the challenge of constructing an ESM. This chapter proposes two ways to integrate diverse systems ideas: a structural approach that sequences ideas from more general to less general, and a functional approach that uses systems ideas to construct an ontology of problems.

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Chapter 6 Science, Religion, Politics illustrates the significance of the systems project by applying some systems ideas to topics in science, religion, and politics. A systems theoretic model of world history is used to organize these applications.

To repeat Footnote #1, “systems theory,” in the singular, is shorthand for the systems intellectual project.

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The structure of Commentary can be visualized by the pentad of Figure 2(a) depicts a system consisting of three elements and its environment consisting of two elements. 28 The system’s elements are an essence (an “organizing principle”), the full manifestation of this essence, and the system’s constituents. The environment’s elements are what the system draws upon and contributes to. The chapters of Commentary have a similar structure, shown in Figure 2(b). Figure 2 Structure of Commentary (a) is a general depiction of a type of pentadic structure. (b) applies it to the (numbered) Commentary chapters.

what it contributes to manifestation essence

SYSTEM

ENVIRONMENT

constituents (a) 5 Challenge of integration 2 Exact and scientific metaphysics

what it draws upon 6 Science, religion, politics

SYSTEM THEORY

ITS ENVIRONMENT

3 Concepts and categories (b)

28

4 Related fields

This pentadic diagram derives from Bennett (1961, 1966); see also Note #74 Eating and being eaten, p. 428.

COMMENTARY

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The contents of the five chapters of Commentary are: Chapter 2 An exact and scientific metaphysics 2.1 The illusion of the fundamental 2.2 The systems alternative 2.3 A new conception of metaphysics 2.4 The epistemological niche of systems theories 2.5 Theories and models; the idea of “system”

43 43 48 54 63 71

Chapter 3 Concepts and categories 3.1 Substance and form 3.2 Matter, energy, information; utility 3.3 Isomorphism and emergence 3.4 Aspects of complexity and holism 3.5 Structure, function, and history

79 79 88 97 100 109

Chapter 4 Related fields 4.1 Not just mathematics 4.2 The relevance of physics 4.3 The centrality of biology 4.4 Sciences of the artificial 4.5 Systems theory and systems analysis

123 123 130 135 139 141

Chapter 5 The challenge of integration 5.1 No singular systems theory 5.2 Hierarchy of system types 5.3 Categories of complexity 5.4 Ontology of problems 5.5 Metaphysician’s desk manual

149 149 154 160 167 174

Chapter 6 Science, religion, politics 6.1 A macro-historical model 6.2 The new science 6.3 Natural religion 6.4 Fixing the world 6.5 Summing Up: promise of the systems project

193 193 207 226 247 278

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Chapter 2 An exact and scientific metaphysics 2.1 The illusion of the fundamental 2.2 The systems alternative 2.3 A new conception of metaphysics 2.4 The epistemological niche of systems theories 2.5 Theories and models; the idea of "system"

43 48 54 63 71

2.1 The illusion of the fundamental Are there, after all, things to be discovered about the entire universe, or about the place of humanity within that entirety, whose very generality allows them to transcend the fragmented insights of electromagnetic theory, cell biology, neurophysiology, and the rest? - Stephen Toulmin (1982) The reason why people are often baffled and maddened by metaphysics is that they do not see why these vast things are being said at all. They do not see…what previous widespread trouble with the conceptual drains caused the metaphysical plumber to be sent for in the first place...But it is also sometimes hard to see the error because it has not been cured – because we are still living with the bad smell, and are so used to it that it never occurs to us to want it removed. - Mary Midgley (1992) Philosophy is spineless without ontology. - Mario Bunge (2010) What does the world consist of? Can our understanding of the world have unity and coherence? To these questions, the prevailing scientific viewpoint offers the familiar hierarchy of reduction. Physics is the foundational science, which concerns the ground of “what is.” Chemistry reduces to physics, and biology to chemistry; the social sciences are grounded in psychology (and, for some, biology); and so on. Unity of

© Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_2

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scientific understanding of the world is achieved by formulating all descriptions of the world in physical terms. The traditional scientific paradigm seeks explanation by reducing phenomena at one level to those of lower levels, levels being defined usually by types of things, typically in the natural sciences by their materiality and the energetics of their interactions. The unity of science is affirmed in the assumption that in principle everything ultimately reduces to the stuff of physics and its interplay, whether this stuff is defined as quarks and leptons or strings or whatever. Reductionism is a methodological perspective, a position on what research is likely to be fruitful. More generally, it is an epistemological perspective, a view about what understanding is and how it can be justified. Most radically, it is an ontological 29 perspective, an assertion about what exists. The reductionist paradigm has been very successful, as is shown by our powerful manipulations of atoms and genes. But this paradigm is deficient on two counts: (1) the identification of what is fundamental in the physical universe is a goal that continues to recede, and difficulties limit the advance of the reductionist program, and (2) even if fundamental units of matter-energy were actually finally discovered, the reduction of all phenomena to interactions between these units would still be impossible. Although some physicists hold that in superstring theory we are approaching the rock bottom of a “final theory,” there is reason to doubt that this is true, that there exists a rock bottom of reality which can be reached and that we are actually near this point now. The claim is too reminiscent of similar confident assertions of the past, especially proclamations of the end of physics around the turn of the 20th century before the discovery of relativity and quantum mechanics. One might instead argue, invoking the “Copernican principle” (Gott 1993), that it is a 29

The author prefers a terminology that contrasts “epistemology” with “ontology,” rather than with “metaphysics,” which some writers use as synonymous with “ontology.”

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priori unlikely that we are nearing the end of physics at this particular moment in history. The fundamental may be a mirage, always receding as we approach it. Yet expectation of indefinite scientific progress may be equally misleading. The search for the fundamental may have “limits to growth.” We may be wrong about the precise location of these limits but perhaps not far wrong. As physicists investigate realms increasingly distant from the human scale, progress is hindered by both conceptual and experimental difficulties. The revolution of quantum theory has left a residue of hard-to-resolve interpretive problems, and experimental investigation in particle physics has become more technically and financially difficult. As specialization and fragmentation relentlessly increase in every scientific discipline, a coherent understanding of the vast body of scientific knowledge becomes impossible to attain. It is speculated below 30 that, in general, developmental processes often proceed smoothly only up to a point, beyond which complexity begins to block continued development. It may be that the research program built around the search for the fundamental, through its very success, has entered a realm of difficulties in which some new organizing principle needs to replace or augment the old. 31 Moreover, a “final theory” in physics, assuming it is achievable, would still not deliver on its promise. Even if the fundamental were finally reached, i.e., even if all four forces of nature were satisfactorily integrated, and the elementary particles reduced to a respectable number, and the constants of nature explained, and the initial conditions of the physical universe somehow ascertained, the unity of science that would thereby be accomplished would still be illusory. One will never be able to describe human behavior, or biological phenomena, or even much of physics and chemistry, in terms of the interactions of fundamental particles. Laplace’s image of a 30 31

Note #147 Limits of complexification, p. 544 This theme is taken up again in 6.2.1 A supplementing process, p. 207.

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hypothetical spirit, who from knowledge of the initial positions and momenta of the particles of any system might deduce all of its subsequent behavior, reflected the initial ambition and arrogance of the Newtonian worldview. Today, the dream of a final theory, a quantum version of Laplace’s fantasy, might similarly be admired for poetic boldness, but even if such a theory were in our hands, it would not truly be a “theory of everything” (TOE). Because of mathematical undecidability or computational intractability, even the physical world would not be fully encompassed. The theory’s claim of providing complete explanation and unity of scientific knowledge would still be a promissory note that could never be redeemed. Of course, this research program never promised to reduce all phenomena to the quantum level in one step. The attempt to reach rock bottom in physics and the building of bridges from physics to chemistry, from chemistry to biology, from biology to psychology, and so on are separate tasks. But even if all the necessary bridges were in place, all we would have is a sequence of bridges connecting separate disciplinary landmasses, i.e., local integration. Global unity would not be achieved. Moreover, the material world is not “everything.” A final theory, a “theory of everything” of the sort spoken of by physicists, would not cast a single additional photon of illumination upon the everything that human beings encounter in the world. As an explanation of the world, it would be hopelessly incomplete; as a source of meaning, a great evasion. All the important issues would be left out. As Steiner writes (1994), Current scientific claims to final truths, to “theories of everything,” are nearly monstrous in their simplistic arrogance. What do they tell us of the conflicting ideals and values of human possibilities, of the unquenched savageries in the individual and collective psyche, of the desolate scandal of death? It is in the company of Plato

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or Spinoza or Kant, not in that of Einstein, that I would be immeasurably grateful to [confront] 32 that scandal. This is not to denigrate the magnificence of a “final theory,” were such a theory achieved. Success in this project would be among the loftiest of human accomplishments. But a theory of everything cannot be reached by a research program aimed at the search for fundamentals. The problem with this approach is precisely that it is a fundamentalism, with all that fundamentalism usually entails, namely self-importance, narrowness, and disdain for whatever lies outside the domain that it privileges. What is needed to gain a coherent view of the world is a very different approach, one more capable of integrating the full variety of scientific knowledge. Murray Gell-Mann, whose work on quarks exemplifies par excellence the reductionist project, yet who also advocates the study of “complex adaptive systems,” quotes a line from a poem by a friend, “The world of the quark has everything to do with a jaguar circling in the night” (Gell-Mann 1994). This is a great truth, in the anthropic principle sense (Barrow and Tipler 1986) that if the fundamental physical constants were different, there would be no galaxies, no planets, no life, and thus no jaguars. But as Niels Bohr noted (the quotation is attributed also to Thomas Mann), “A great truth is a truth whose opposite is also a great truth.” The quark also has nothing at all to do with a jaguar circling in the night, in the sense that knowledge about quarks adds not one iota to our knowledge of jaguars. The level of the quark and the level of the jaguar, as Simon (1981) would say, are insulated from one another. That Gell-Mann has worked on both attests only to the breadth of his interests, not to the actual connectedness of these two domains. Reduction is a great idea and a powerful method, but a unity of science or a theory of everything cannot come from it. Also, reduction, even when successful, cannot restrain the 32

The bracketed word below is “affront” in the original, but this is probably a typographical error.

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fragmentation of scientific knowledge. This fragmentation and the accelerating increase of scientific knowledge are beyond the capacities not only of individuals but of whole societies to assimilate. Even worse than the fragmentation of scientific knowledge is the separation, lamented by C. P. Snow (1959), between science and other aspects of human culture. What is the intersection of science with literature or religion or the arts? As long as science is dominated by physics, especially the physics of fundamental particles and cosmology, there can be no significant substantive intersection. Although physics offers some valuable metaphors, they are often used in a way that borrows illicitly from the prestige of physics. These metaphors also have limited scope. The scientific metaphors we need must be connected not with the fundamental, which is inaccessible, but with the general, which is everywhere we look. 2.2 The systems alternative There is an alternative view about what the world consists of and how unity of scientific explanation might be gained. In the post-World War II period this view was called general systems theory and cybernetics; today it is associated with theories of chaos, complexity, and complex adaptive systems. This systems view stands in relation to standard materialist reductionism as the Pythagoreans were to the Greek atomists. Although ontologically and epistemologically, modern science gives priority to the fundamental, the systems view gives priority to the central. Systems thinking sees every system 33 as a “partial whole” (Murdoch 1992), a focal point of existence (ontologically) and of human knowledge (epistemologically). Each focal point is a center that expands internally in structure and externally in function (Figure 3); to this structure-function dyad, a third term, history, will later be added. 34 “Function” here 33

Note #1 System, p. 295 3.5 Structure, function, and history, p. 109. This double cone image also unites ontology and epistemology: ontology is structure, what is in-itself; epistemology is function, what is for-us; in Kantian terminology, noumenon 34

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does not mean purpose, just relation to context (environment). It reflects structure on a larger scale. A system is an order in itself (structure) and participates (function) in more encompassing orders. Instead of denying reality to any level that is not fundamental, the systems view accords full reality to all levels. Every system is as real as every other system. This “ontological parity” (Ross 1980) is a shift of perspective that challenges the hegemony of the fundamental. With this shift, unity of scientific knowledge is imaginable. Figure 3 System as center This double cone diagram should be viewed three dimensionally, with structure and function seen as cones opening downward and upward, joined at their common apex. function space

system structure

external context of the system system as focal center internal order of the system

To privilege the central, to say that the world consists of systems, does not deny the fundamental, but it does deny that the fundamental is identical with the real. Physicists often comment about the “mind of God,” but a God eternally aware only of quarks and leptons or superstrings would be bored; surely the contents of the mind of God includes galaxies, grains of sand, people, beetles, mathematical theorems, scriptures, and poems. These are not less real than elementary particles. A physicist’s TOE is not a theory of everything. In the systems view the central is given priority, but this is to augment the standard view, not replace it. The fundamental and phenomenon, except that the in-itself is accessible – structure is disclosed through function: atoms are smashed, surgeons open up bodies.

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must be given its due. Ontological parity applies to systems under the aspect of similarity, but under the aspect of difference 35 one level may indeed be more fundamental than another. But note: lower (smaller-scale) levels are more fundamental only under the aspect of structure; under the aspect of function, it is the higher (larger-scale) levels that are more fundamental, since the whole can be viewed as being more fundamental than its parts. In the most complete view, neither structure nor function is privileged. There are two fundamentals; one at the bottom, which might be called “the foundational,” the other at the top. They are similar (and perhaps even linked), but under the aspect of difference, top is top and bottom is bottom. A systems metaphysics thus insists on these two negations: •

The real is not (only) the fundamental.

•

The fundamental is not (only) the foundational.

Within the perspective of ontological parity – more expressively, “ontological egalitarianism” – the central is the general. This is what we are really interested in, not the fundamental of the bottom, and not even the twin fundamentals of bottom and top. To be sure: what everything has in common is not very informative, but what is general is informative. The systems view in its focus on emergence 36 accommodates differences between systems, while still being oriented toward 35

Similarity and difference are opposites but each also depends on the other, since things cannot be similar if they are not also different, and vice versa. If two things were not similar we could not speak them together; if they were not different we would not speak of two things. Understanding requires the recognition of both similarity and difference. For example, the meaning of a sentence inheres both in its saying the same thing as nearly equivalent sentences and in its saying something unique (Wittgenstein 1953). Similarity exemplifies the principle of symmetry, difference the principle of symmetry-breaking. Both are essential to human communication. “We celebrate both our commonalities and differences, because if we had nothing in common we could not communicate, and if we had everything in common, we would have nothing to say” (Sacks 2010). 36 3.3 Isomorphism and emergence, p. 97

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the general. Reduction flattens the world, seeing reality only at the foundational level, but ontological parity takes systems as they are, and the notion of emergence also allows qualitative distinctions to be made between levels of being. If the fundamental is privileged, nothing is what it seems to be; the general, however, lets everything be what it seems to be; it “saves the phenomena.” As Whitehead (1929) wrote, “Metaphysical categories are not dogmatic statements of the obvious; they are tentative formulations of the ultimate generalities.” Above Figure 3 is spatial, but if one rotates this vertical double cone by 90°, one obtains a horizontal double cone in which structure-system-function become past-present-future. 37 The present is the central; system formation and dissolution are its corresponding fundamentals. In time as in space, in the systems view the central is given priority over the fundamental. The idea of system is compatible with either the epistemological or ontological perspective and can integrate the dualism of materialism and idealism. It applies to the external reality of objects and the internal experience of subjects, to both things and ideas. The notion of “system” is as general as the philosophical notion of “being,” but it is more modest in its connotations. Though it does not have the resonance of the word “being,” it has the virtue that it can be made mathematically exact and linked to scientific theory. The systems view crystallized in modern form after World War II around mathematical theories such as information theory, game theory, feedback control theory, automata theory, and the like, and around the applications of these theories in the natural and social sciences and in engineering and other professions. The Society for General Systems Research was founded in 1954 by the economist Kenneth Boulding, the mathematical biologist Anatol Rapoport, the physiologist Ralph Gerard, and the 37

Note #105 Cognition and time, p. 476, and Figure 98 System formation; system as temporal center, p. 498

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biologist Ludwig von Bertalanffy, who proposed the idea of a general systems theory 38 (GST) in 1932. Von Bertalanffy wrote (1968): 1. There is a general tendency towards integration in the various sciences, natural and social; 2. Such integration seems to be centered in a general theory of systems; 3. Such theory may be an important means for aiming at exact theory in the nonphysical fields of science; 4. Developing unifying principles running “vertically” through the universe of the individual sciences, this theory brings us nearer the goal of the unity of science; 5. This can lead to a much needed integration of scientific education. The field of cybernetics (Heims 1980, 1991) was launched by Wiener in his book by that title published in 1948. Shannon and Weaver wrote their monograph on information theory in 1949. In 1943, von Neumann and Morgenstern wrote their classic book on the theory of games and economic behavior. Rapoport, one of the major figures of the general systems movement, was also an early and major contributor to game theory research. Over time, aspects of systems and cybernetics thought became absorbed into specific disciplines. Control theory, while stimulating interest in feedback mechanisms in the natural and social sciences, as Wiener had hoped, was assimilated into electrical engineering and applied mathematics. Automata theory became an important area in electrical engineering and computer science, although its impact on linguistics and related disciplines has also been significant. Some systems and cybernetic research became subsumed by Artificial Intelligence and the related field of Cognitive Science. 38

Von Bertalanffy called it general system theory – in the singular – but the plural became the convention.

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For example, early work on perceptrons (Rosenblatt 1958) was the precursor of contemporary connectionism. Beginning roughly in the 1980s, the systems program was revitalized by the emergence of the field of complex systems, launched by the discovery of chaos, and associated with new sciences and technologies “of the artificial” 39 such as Artificial Life and virtual reality. These developments were made possible by advances in computer power, simulation techniques, and theory. But the orientation and many research interests of this field are not new. In a statement prominent in the early cybernetics/systems literature, Warren Weaver observed (1948) that while understanding of “organized simplicity” and “disorganized complexity” was available, a science of “organized complexity” was undeveloped. Complexity, 40 selforganization, and emergence were major themes of the early systems and cybernetics literature. Contemporary complexity research can thus be viewed as a renaissance that renews classical (mid-20th century) general systems theory and cybernetics. The historical analogy is not perfect. Scholars of the Renaissance were conscious of their debt to classical learning, but many complexity researchers today do not appreciate or acknowledge the continuity of their enterprise with the earlier systems project. Why this is the case is a task for historians and sociologists of science to explain. Suffice it to say, complexity research is now widespread, and numerous centers, professional organizations, and journals in complexity, complex systems, complex adaptive systems, and nonlinear science have been established. The most famous of these centers 39

Sciences of the Artificial is the title of a classic by Herbert Simon (1981) that describes aspects of the systems field. 40 The word “complexity” has the virtue of sounding more specific than “system” but has the deficiency of implying that scientific disciplines have not dealt with complexity adequately and that systems and complexity theories will finally do so. The presumptuousness and incorrectness of such a claim should not obscure the fact that the “systems” and “complexity” labels are associated with a vision of science genuinely different from the conventional vision.

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are the Santa Fe Institute and the New England Complex Systems Institute, and the productivity and creativity of their researchers have been extraordinary. For an overview of the field, see Mitchell (2009). The systems project continues today. It counters the centrifugal forces of conventional research. It aims at synthesis, while standard research focuses on analysis. The pursuit of the fundamental has led to diminishing returns and to the fragmentation of knowledge. The systems project, by augmenting the ideas and methods of the specialized disciplines, can help science meet the challenge of its own complexity. This project also offers a new and more encompassing and meaningful scientific view of the world. 41 2.3 A new conception of metaphysics Consequently any books, such as most works on Metaphysics and Theology, that contain neither mathematical demonstrations nor empirical reasoning concerning matters of fact, can contain “nothing but sophistry and illusion,” and should be “committed to the flames.” - MacNabb (Urmson and Rée 1989), interpreting and quoting from Hume It’s what I call “metaphysical repression.” It’s in our culture and it’s much worse than sexual repression. - Jacob Needleman (2001) All serious and systematic thought metaphysics. - Henri Bergson (1932)

aspires

to

The success – even the existence – of the systems project has not been given its due, in part because systems ideas and methods do not come labeled as such and rapidly become assimilated into the main body of science. Although books 41

Some cultural implications of the systems view are discussed briefly in Chapter 6 Science, religion, politics, p. 193.

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periodically appear that proclaim a “new science” or a “new kind of science,” 42 each usually presents only one current of systems research and is thus received as a simple addition to the diversity of scientific approaches. What escapes notice is that these currents collectively offer a new systems-oriented scientific worldview. Bunge’s (1973) analysis of the early systems movement makes plain the ambitious worldview at which it aims. He characterizes systems and cybernetics theories as attempts to construct an “exact and scientific metaphysics” (Figure 4). Figure 4 An exact and scientific metaphysics (ESM)

Exact

Metaphysics

Scientific

“Metaphysics” here means a system of abstract concepts that are widely applicable. An “exact” metaphysics is one that is or could be mathematical. 43 A “scientific” metaphysics is one that connects strongly to the sciences. Bunge illustrates his notion of an exact and scientific metaphysics (ESM) with information theory, game theory, and automata theory, and the like; this notion applies also to contemporary complexity research. The idea of “scientific metaphysics” derives from C. S. Peirce, whose “scientific philosophy project views ontology as general science” (Bunge 2010). “Metaphysics,” as used here, means either ontology or epistemology, i.e., about what exists or about 42

For example, Gleick’s Chaos: A New Science (1987) and Wolfram’s A New Kind of Science (2002). 43 Bunge actually includes exactness within his definition of a metaphysics that is “scientific.”

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our knowledge of what exists. The difference between these stances appears in sharp relief in the story of an encounter between the analytic philosopher, A. J. Ayer, and the continental philosopher, George Bataille, recounted by Critchley (2001). …the thesis under discussion was very simple: did the sun exist before the existence of human beings? Ayer saw no reason to doubt that it did, whereas Bataille thought the whole proposition meaningless. For a philosopher committed to a scientific view of the world, like Ayer, it makes sense to say that physical objects like the sun existed prior to the evolution of human beings. Whereas for Bataille, more versed in phenomenology, physical objects must be perceived from the position of a human subject in order to be said to exist. The gap between Ayer and Bataille is extreme; the point here is just to illustrate these two stances. Using the second and third terms of Rosenzweig’s (1921) triad of God-World-Human, one might identify the ontological stance as “world-centered” and the epistemological stance as “human-centered.” Or one might describe them as objective versus subjective. The ontological stance accords with Aristotle’s use of the term “metaphysics” to refer to the science of existence in general, or the study of “being as such” (Urmson and Rée 1989); this stance is also what Thomas Nagel (1989) called “the view from nowhere” (really, from anywhere). This is contrasted with a stance explicitly centered in the human observer, an anthropocentrism exemplified by Descartes and Kant, 44 by phenomenologists, constructivists, and others. Some of these dyads, roughly correlated with one another, are given in Table 1. Actually, the distinction between these stances is not sharp, because all epistemology is ontology-laden, and all ontology is epistemology-laden.

44

Kant “Copernican” turn toward the subject was really Ptolemaic since it had everything revolve around human cognition.

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Table 1 Ontological vs. epistemological stances

Ontological scientific realist world-centered objective positivist

Epistemological phenomenological human-centered subjective constructivist

Some systems thinkers prefer the ontological stance; others, the epistemological stance. Systems thought is neutral about which stance should being taken and accommodates both. Because it privileges the central and advocates ontological egalitarianism, it might be characterized as “a view from anywhere,” i.e., from any system, but such a systems-centered view still aims at being objective. In general, this book favors the ontological stance 45 and treats epistemology within a naturalist framework, 46 although some discussion is explicitly epistemological. 47 Most scientists view science as the study of things-in-themselves, not merely things-as-they-are-for-us, and thus favor the ontological stance. Since the systems project is primarily a scientific undertaking, it is world-centered and thus needs to be complemented by the human-centered stance. A systems theoretic TOE will thus not really be about everything, but it will be about a lot more than a physics-only TOE. 45

Klir’s (1985) The Architecture of Systems Problem Solving, which takes the epistemological and methodological stance, is an alternative view to the ontological stance adopted here. Despite this difference of orientation, many ideas advanced in this book overlap with Klir’s constructivist views. The epistemological stance also characterizes second-order cybernetics of von Foerster (1981) and others. 46 This is offered in Cognition (1.1.8, p. 20, and 7.1.8, p. 461), which considers the “modeling subsystems” of some complex adaptive systems. This section does not tackle the “hard problem” of understanding the fact of subjective experience. 47 The next two sections, 2.4 The epistemological niche of systems theories and 2.5 Theories and models; the idea of “system”, are explicitly epistemological; so too is 6.3.3 Inner science, p. 240.

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The requirement that metaphysics be exact and scientific imposes the restriction that metaphysical ideas – ideally or eventually – should be expressed with mathematical precision, and also tested – ultimately if not directly – by empirical knowledge. Though abstract in content, an exact and scientific metaphysics makes no Kantian a priori claims and no claims of certainty; instead, it holds with Schopenhauer that metaphysics must be based in and testable by empirical knowledge. 48 The metaphysics spoken about here does not inquire about the existence of God or the soul. It is not defined as the study of reality as opposed to appearance or the capacities and limitations of human intellect, though these issues are partially dealt with. Metaphysics here means simply a description of the most general features of the world. The joining of metaphysics to science is an attempt to recover an older conception of the relation between mathematics, science, and philosophy, a conception aptly described by the title of Newton’s book, Mathematical Principles of Natural Philosophy. In the early 20th century, a substantive relationship between science and philosophy was rejected by positivists, who regarded metaphysics as empty, and sought criteria of demarcation by which valuable science might be distinguished from valueless metaphysics. For the positivists, “metaphysics” was a term of condemnation, and an “exact and scientific metaphysics” would have been dismissed as an oxymoron. But in the late 20th century, the notion of a sharp separation between science and metaphysics proved rigid and 48

Kant (Prolegomena to Any Future Metaphysic) argued that metaphysics “is thus knowledge a priori, or out of pure understanding and pure reason,” but Schopenhauer objected to this notion that metaphysics should be nonempirical and said, “We have no grounds for shutting ourselves off, in the case of the most important knowledge, [from] inner and outer experience, in order to work only with empty forms. I therefore say that the solution of the riddle of the world must proceed from the understanding of the world itself; that thus the task of metaphysics is not to pass beyond the experience in which the world exists, but to understand it thoroughly ...” (Schopenhauer 1818, translated by Murdoch 1992).

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unproductive, and even untenable due to developments in quantum theory, relativity, and other aspects of modern physics. It was undermined in a different way by the emergence in the mid-20th century of systems theories. A clean cut between science and metaphysics cannot be made, and even if it could, it would impoverish both. G. Spencer-Brown (1972) noted that “distinction is perfect continence.” But perfect continence is sterile. Metaphysics may be vacuous and “not even wrong,” 49 but it may instead be fruitful for science, and what seems obscurantist and vacuous in one historical period might be revealed later to be prescient and substantial. The systems project has this for its goal: where ordinary metaphysics was, there exact and scientific metaphysics shall be. 50 For example, Wiener’s feedback control provided a scientific explanation of (one type of) “purposefulness” (Rosenblueth et al. 1943). Other aspects of living systems, once ignored by the mechanistic paradigm and the subject of vitalist speculation, similarly gained exact and testable explanations via cybernetic mechanisms. When scientists fail to acknowledge the reality of phenomena for which theory is unavailable, explanation is left by default to non-scientists. The vitalist critique of Newtonian mechanism was correct, but vitalist ideas about life were empty mystifications. It took the neo-mechanism of systems theories and cybernetics, i.e., ideas of feedback and feedforward control, open systems and steady states far from equilibrium, informational macromolecules, and the like, to explain many biological phenomena. Other ideas, once dismissed as metaphysics in the pejorative sense, can become candidates for scientific status by being reinterpreted as precise assertions, so they become 49

Wolfgang Pauli used this dismissive phrase to characterize theories that could not even be tested (Peierls 1960). 50 This borrows the style of Freud’s comment on the desirability of replacing id by ego.

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capable of being tested. For example, aspects of the dialectics of Hegel (1837) and of Engels (1883) can be made exact via catastrophe theory (Zwick 1978a) and fuzzy set theory. 51 Angyal’s (1939) holism, which insisted that wholes involve more than merely pairwise relations, can be expressed precisely by reconstructability analysis (Zwick 2004). Being expressed mathematically does not mean that metaphysical ideas are true, but it opens up the possibility of empirical assessment. Metaphysics, as a repository of general ideas not formally expressed or empirically tested, provides the ESM project with a reserve of intellectual raw materials. 52 The positivist goal of eliminating vague or ungrounded speculation is accomplished not by eschewing metaphysics but by subjecting it to the dual discipline of explicitness and verifiability by joining it to mathematics and science. Metaphysical ideas must cohere – they can do so if they are exact; they must correspond to empirical reality – they can do so if they are scientific. Both coherence and correspondence must be satisfied. Coherence is structural (internal) truth; correspondence is functional (external) truth (Figure 5); to these, one must add the criterion of history 53: Ideas must be generative, useful, pragmatic; as Goethe said, “what is fruitful, that alone is true.” 54

51

Hegel would not have been pleased. Reflecting the Romantic reaction to Newtonian mechanics and the prominence it gave to mathematical law, Hegel thought that historical development was governed by a dialectic not amenable to scientific explanation. But there is nothing about history, even seen through the lens of idealism, that makes it unsuitable for mathematical treatment. Some aspects of Hegel’s dialectic can in fact be mathematically formalized (Zwick 1978a). See 3.5.2 Adding history, p. 116. 52 Heidegger’s (1966) answer, “Cybernetics,” to the question of what might replace the integrative function of philosophy expresses a view that has some similarity to the ESM idea discussed here, but analysis of this similarity and Heidegger’s understanding of cybernetics is beyond the scope of this book. 53 3.5 Structure, function, and history, p. 109. Issues of coherence and correspondence arise in the “context of justification” of scientific

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Figure 5 Coherence and correspondence S of ESM requires correspondence; E requires coherence. CORRESPONDENCE scientific function metaphysics structure exact COHERENCE

From this perspective, metaphysics mediates between science and mathematics. Kant struggled with the difficulty of joining empiricism and rationalism, fact and mathematics. How could a truly empirical, contingent, or “synthetic” natural science lend itself to a purely formal and mathematical, i.e., necessary, exposition? If Newton’s physical system simply presented straightforward empirical discoveries about the world of facts, was it not incongruent to set out these discoveries – as Newton did – in necessary (or “apodictic”) mathematical arguments? - Stephen Toulmin (1982)

knowledge, as distinguished from the “context of discovery” (Popper 1959), in which scientific knowledge is viewed in terms of its historical genesis (Adorno 1965) and development. A historical orientation also characterizes the pragmatic notion of truth which sees justification of scientific knowledge only in its final acceptance. An alternative pragmatic notion focuses on the practical consequences of assertions/beliefs about what is true. These pragmatic interpretations of truth (Capps 2019) are fused together in a “reliability” notion of truth (Hazony 2012). 54 The Goethe quote exaggerates. What is fruitful (history) but does not also have the virtues of coherence (structure) and correspondence (function) is an inadequate basis for a reliable ontology.

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More recently, the same question was posed by Wigner (1960) in his famous article, “On the unreasonable effectiveness of mathematics in the natural sciences.” The answer to the puzzling harmony of the science-mathematics dyad is in the sciencemathematics-metaphysics triad. Metaphysics provides a semantics that binds the pragmatics of science to the syntactics of mathematics, 55 a glue that holds together correspondence and coherence. Metaphysics reflects our need for meaningfulness. It makes mathematics more than empty but consistent formalism. It makes science more humanistic, bringing scientific thought to bear on perennial philosophical issues and inviting philosophical critique of facile misinterpretations of science. It allows mathematical and scientific truths to be expressed in ordinary language; however obscure philosophical discourse may be, it is still more accessible than mathematics. As Murdoch (1992) argues, “We must ... preserve and cherish a strong truth-bearing everyday language, not marred or corrupted by technical discourse or scientific codes...” Philosophy is also a bridge from science to the arts and humanities and to religion and also politics, although of course not a philosophy that sees itself as a referee of linguistic games or a disciple of literature. A future metaphysics must not only be exact and scientific; it must be connected to all of human experience. Such a metaphysics cannot derive from cosmology and elementary particle physics. A coherent scientific view of the world requires generality, precision, and relevance; hence the need for all three components: metaphysics, mathematics, and science. Metaphysics provides generality, mathematics offers precision, and science brings relevance, i.e., testability and practical import. Generality is a semantic virtue; precision is a syntactic virtue; testability and impact are pragmatic virtues. Mathematization can perhaps be deferred but not indefinitely.

55

Note #101 Pragmatic, semantic, syntactic, p. 468

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Presence of the scientific component is, however, essential. 56 For example, a philosophical generalization of Gödel’s proof that did not establish a scientific significance for undecidability would have a limited role in a systems ontology. Similarly, fuzzy and other non-standard logics (Zadeh 1965; Kosko 1993) are relevant to the systems notion of distinction 57 but haven’t yet seen widespread use in scientific theories, despite their extensive use in engineering. An exact metaphysics (EM) that was not also scientific (ESM) would be “scholasticism” in its worst sense. ESM is a three-legged stool; absence or insufficiency of any leg would be a serious deficiency. 2.4 The epistemological niche of systems theories Bunge's idea of an exact and scientific metaphysics accords with the views of von Bertalanffy, Wiener, Boulding, Rapoport, Ashby, and others on the possibility of a “general theory of systems.” Boulding (1968), for example, writes: General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Von Bertalanffy (1968), quoting Ashby, speaks of two lines of systems study:

56

The importance of science for metaphysics was stressed by Quine, whose early work (1948) triggered a renewal of interest in metaphysics within analytic philosophy, but this interest has conformed to the reductionism that prevails in physics and has not aimed at a transdisciplinary ESM. The mathematical component of contemporary metaphysics is often only firstorder logic, and a scientific component is frequently absent. The position advocated here is succinctly expressed by Ross (2004): “We believe … that metaphysics only matters if it matters to science, and finally we believe and argue ... that metaphysics matters to science.” 57 Note #25 Fuzziness, p. 352

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…an empirico-intuitive line which “remains rather close to reality and can easily be illustrated and even verified by examples taken from the individual fields of science but which is mathematically unsystematic and perhaps even naive, and a deductive line, strongly based in mathematics, highly rigorous, but weakly linked to the phenomena of direct concern to the sciences. Ashby’s first approach is inductive and is a search for isomorphisms (exact similarities of form) of models and theories in different disciplines. His second approach is deductive and originates in mathematics. To this latter approach one can add a deductive path originating in philosophy (specifically, metaphysics), which offers what Boulding calls “highly generalized constructions.” These ideas of Bunge, Boulding, and Ashby can be represented by Figure 6, 58 as follows: Figure 6 Between math/philosophy and scientific theories

Mathematics (E) abstraction

Philosophy (M)

Systems theories (ESM)

Theories in the various sciences (S)

deductive inductive

At the highest level of abstraction there is mathematics and philosophy. Less abstract are the theories of particular scientific disciplines; one might add theories in engineering and other professional fields. Intermediate between these levels is the niche claimed for systems theories. One ascends to them from theories of the scientific disciplines by induction, e.g., through the search for isomorphisms; one descends to them from mathematics and philosophy by deduction and specification (by concretizing mathematical or philosophical statements). 58

This is a variation on Figure 4 An exact and scientific metaphysics (ESM), p. 55.

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An example of a theory at the ESM level is information theory (Shannon and Weaver 1949), which is not only about communication (signal processing) and information (prediction, measurement) but also about order and organization. The mathematical foundations of this theory are well articulated, and its applications extend to virtually every scientific discipline. Chaos – nonlinear dynamics – as a “new science” (Gleick 1987) is another theory at the ESM level. Research on chaos occurs in diverse fields, such as fluid mechanics, neuroscience, population biology, weather, and finance; mathematical investigations of chaos use a variety of formalisms, such as differential equations, iterative maps, and discrete automata; philosophical issues raised by chaos touch on relationships between determinism and randomness and between determinism and predictability. Game theory, about competition and cooperation and rational action in general, is another systems theory with applications to the social and biological sciences. Thus systems theories 59 do not stand alone but are linked to specific theories in the sciences (Figure 7). A systems theory might relate to multiple scientific theories, and a specific scientific theory might be informed by more than one systems theory. Figure 7 Systems theories and specific scientific theories

Systems theories (ESM)

Specific theories in the various sciences Figure 7 does not explicitly depict the transdisciplinary 60 nature of the systems project. This is shown in Figure 8 which 59

Information theory, chaos theory, and game theory are discussed respectively in Notes #9 Relation as constraint, p. 324, #17 Chaos, p. 338, and #75 Game theory, p. 429. 60 The systems project is not merely interdisciplinary, a characteristic of hybrid disciplines such as biophysics; it is transdisciplinary, being aimed at higher-level abstraction. The “transdisciplinarity” program of Nicolescu

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adds four other “systems theories” to information theory, nonlinear dynamics, and game theory: graph theory 61 borrowed from mathematics; thermodynamics 62 from physics; control theory, 63 initially a theory of cybernetics, from electrical engineering; and evolutionary theory generalized from biology. 64 The diagram displays von Bertalanffy’s (1968) idea of “unifying principles running “vertically” through…individual sciences.” Fractal geometry, automata theory, and other theories could be added. Graph theory and generalized evolution 65 illustrate deductive and inductive routes to ESM: the former by descent from mathematics; the latter by ascent from biology. Figure 8 indicates that some theories, e.g., graph theory, information theory, and nonlinear dynamics, are nearly universal in scope, while other theories have restricted applicability. For example, thermodynamics applies rigorously only to the natural sciences; game/decision theory and generalized evolution apply only to the biological and social sciences. 66 This list of theories is illustrative, not exhaustive.

(1998, 2002) resembles the systems project, but appears to be an independent development. 61 Notes #5 Structure, p. 308, and #7 Networks, p. 317. Some researchers refer to graph theory when applied to scientific phenomena as network theory, reserving the graph theory label for the purely mathematical theory, but a distinction between the two is not made in this book. 62 4.2 The relevance of physics, p. 130 63 Note #45 Feedback control, p. 386 64 Notes #70 Optimization, p. 424, and #163 Natural selection, p. 568 65 Generalized evolution differs from the other six columns of Figure 8 which all name mature theories. Generalized evolution, by contrast, is a theory under construction. A recent contribution to this theory is (Hodgson and Knudsen 2010). However, the genetic algorithm (Note #70 Optimization, p. 424) is a component of this theory that is already well developed, and the idea of variation and selection is widely used informally in a variety of fields. 66 The scope of applicability of game theory has been extended to chemistry (Yeates et al. 2016).

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Figure 8 Transdisciplinarity of some systems theories Generalized Nonlinear Control Graph dynamics theory Game- evolution theory decision Information ThermoDISCIPLINES theory theory dynamics Sociology Psychology Biology Chemistry Physics

That some of the above discussed theories are “borrowed from” mathematics, physics, biology, and other disciplines highlights the fact that calling something a “systems theory” here only asserts its generality and thus its value to the systems project; it is not a statement of academic ownership or one about the intellectual community in which the theory was developed (although the systems community has been involved in the development of some of these theories). This suggests the alternative ESM representation of Figure 9 which shows systems theories as the intersection of mathematics, philosophy, and scientific theories. Figure 9 Intersection of math, philosophy, scientific theories

philosophy

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But it is more illuminating to treat systems theories as filling a distinct epistemological niche, as shown earlier in Figure 6, which can be approached inductively from below or deductively from above. This organizes Bunge’s (1973) six ways to construct a scientific metaphysics: (i) taking over from science or technology without further ado or nearly so. Example: automata theory. (This example might be more suitably assigned to iii); (ii) adapting or generalizing an existing scientific theory. Example: generalizing the algebra of chemical reactions to obtain a theory of analysis and synthesis; (iii) endowing a ready-made mathematical formalism with a metaphysical content. Example: converting ring theory into a general theory of juxtaposition and superposition; (iv) formalizing insights of plain metaphysics. Example: building a general theory of qualitative change; (v) overhauling theories in exact metaphysics. Example: revising Whitehead's theory of space and time to render it consistent with relativity physics; (vi) building fresh theories. Example: constructing an exact theory of integrative levels. These six ways are diagrammed in Figure 10(a). The downward (deductive) approach from mathematics is represented by (iii), and from philosophy by (iv) and, downplaying exactness, (v); the upward (inductive) approach from the sciences or professional disciplines by (i) and (ii). Creating a systems theory at its own epistemological level is represented by (vi).

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Figure 10 ESM as aim and source (a) Constructing and (b) applying systems theories

(iii)

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The arrows in Figure 10(a) oversimplify the route to an ESM. Formalizing plain metaphysics (iv) is shown as an arrow from M (philosophy) to ESM (systems theories) but the process passes through mathematics (E) for formalization and through scientific theories (S) for concretization. The arrows indicate the primary source of a systems theory, but E, S, and M are all ideally present in any such theory. The arrow directions in Figure 10(a) represent the centripetal aspiration toward an ESM; the reverse directions of Figure 10(b) represent the reciprocal impact of an ESM on mathematics, science, and philosophy. The reversed arrows in Figure 10(b) also show the centrifugal tendencies that make the systems research program difficult to sustain. 67 The ESM niche may be unstable, i.e., a repellor rather than an attractor. Systems research has a centripetal aspiration – to draw together material from these three sources for a broad synthesis. But centrifugal forces are 67

Alternatively, the outward arrows represent contributions that an ESM might make to E, M, and S. For example, basic systems ideas in Notes #1 System, p. 295, and #5 Structure, p. 308 (Zwick 2004) are relevant to the metaphysical literature on mereology (e.g., Harte 2002), which deals with wholes and parts and the ontological status of composites. This literature is mostly ordinary metaphysics but occasionally is exact (mathematical); its scientific component is usually undeveloped.

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also powerful. Much of what carries a (complex) systems label reflects a flight toward the natural attractors of pure mathematics, philosophy, or scientific theory. In the face of these centrifugal forces, it is difficult to stay at the ESM level. This is illustrated in the words of Libchaber, A physicist would ask me, “How does this atom come here and stick there”? And what is the sensitivity to the surface? And can you write the Hamiltonian of the system? And if I tell him, I don’t care, what interests me is this shape, the mathematics of the shape and the evolution, the bifurcation from this shape to that shape to this shape, he will tell me, that's not physics, you are doing mathematics .... Yes, of course, I am doing mathematics. But it is relevant to what is around us. That is nature, too. - Stephen Kellert (1993) The physicist tells Libchaber that he is doing mathematics (E), but if Libchaber were to talk to a mathematician, he would probably be told that he was doing physics (S). Just as the specific worldly concern of any particular scientific discipline – in this case, physics – might make the discipline inhospitable to systems research, so, too, might the uncompromising unworldliness of mathematics make it equally inappropriate as a disciplinary home for this type of research. But this situation may be changing. The recent Nobel Prize awarded to Parisi for his work on spin glasses (2006) which has wide applicability outside of physics was explicitly awarded not as a breakthrough in physics, but as a breakthrough in complex systems. Figure 8 above mentions some systems theories, but there are general phenomena 68 for which systems theories do not yet exist. For example, there is no general theory of development, although there are theories of biological morphogenesis, economic development, and ecosystem maturation. Nor is there 68

The term “phenomena” is not intended in its Kantian sense of how things appear to us (the epistemological stance), as opposed to how they are “in themselves” (the ontological stance). This term as used here includes both.

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a theory of system formation, or of integrative levels. A partial list of phenomena of interest to the systems project is given in Table 2 Some general phenomena (systems themes); only some are covered by existing theories. Table 2 Some general phenomena (systems themes) Order and distinction are paradigmatic systems themes. 69 • • • • • • • • • • • •

system formation order and disorder; dynamics distinction from and interaction with environment stability; self-organization; regulation and control metabolism; self-maintenance; reproduction growth, development, maturation, senescence complexification; hierarchy; networks differentiation/integration; (de)centralization information processing; learning rational action; adaptation competition and cooperation, predation generalized evolution

2.5 Theories and models; the idea of “system” General phenomena are the subject of theories; specific phenomena are the subject of models. Both are addressed in Bunge’s (1973) epistemological hierarchy shown in Table 3, which includes the three levels of the ESM diagram of Figure 6. The hierarchy in Table 3 is slightly modified from Bunge’s account. It begins at the bottom with a (1) “model object,” a set of variables that describe the phenomenon under investigation. Next, here added to Bunge’s scheme, are (2) laws or constraints (relations) that link the variables, i.e., specific hypotheses which might be tested empirically. A group of related hypotheses is a (3) model (for Bunge, a “specific theory”). A model describes a 69

Note #1 System, p. 295

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specific phenomenon which is the subject of an investigation (more specific than phenomena listed in Table 2 Some general phenomena (systems themes)); the relations of a model are interconnected statements about a model object. A model is (ideally) subsumed in a (4) formal theory – within a particular scientific discipline – which concerns a general phenomenon. Table 3 Epistemological hierarchy Bunge’s terms are in brackets; he does not include level (2). E = exact; M = metaphysics; S = theories in the sciences E M

(5) systems theory [generic semi-interpreted theory] (4) theory [general theory]

ESM S

(3) model [specific theory] (2) relation, law, hypothesis (1) observables [model object] To illustrate: the attributes (e.g., masses, positions, momenta) of the sun, its planets and satellites, and smaller entities in the solar system constitute a model object [level (1)]. Relations between observables, e.g., Kepler’s laws, are specific hypotheses [level (2)]. The set of relationships between the sun, planets, satellites, etc. constitutes a solar system model [level (3)], which is encompassed within Newtonian mechanics, a theory [level (4)] applicable to other model objects (e.g., molecular motion in gasses). Generalizing from this astronomical example, a model is a set of elements having attributes linked by relations. This is the definition of “system.” 70 Elements having attributes constitute a model object, i.e., level (1) of Table 3. Ascending to level (2) of law or hypothesis posits one relation, while ascending to level (3), model, adds a set of relations. A model is thus a system, 70

Note #1 System, p. 295

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viewed epistemologically. The word “system” is neutral, capable of being understood either ontologically or epistemologically: Systems are focal points of existence or of conceptions of an observer. In the ontological stance, systems (entities or processes) exist, and models encompass only certain aspects of them; for example, a Newtonian model of our solar system ignores electromagnetism. But in the epistemological stance, “system” and “model” are synonymous. 71 The idea of isomorphism, the search for which is the deductive route to an ESM, can now be explained more precisely. An isomorphism is an exact (mathematical) analogy. Two systems are isomorphic if there is a one-to-one mapping of elements (variables and parameters) of one system onto those of the other that preserves the relations. (Alternatively, the mapping might relate states of elements.) Perhaps the most famous isomorphism is the sameness of relations in certain electrical and mechanical systems, shown in Figure 11(a); in Bunge’s terminology, two model objects here map onto one another since the same laws apply to both. Similarity can be looser, namely a many-to-one mapping, which is called a homomorphism. In Figure 11(a), torque (τ) in the mechanical system is exactly analogous to voltage (V) in the electrical circuit; rotation of the shaft (θ) to electric charge (q); viscous inhibition of rotation (J) to electrical resistance (R), etc. In the mechanical system, K is a spring that intervenes between a torque on the left part of the shaft and the resulting rotation of the right part of the shaft. This illustrates an isomorphism between single relations (laws) at level (2); 72 at level (3), systems (models) would be isomorphic if they have the same multiple relations. 71

Cognition (1.1.8, p. 20; 7.1.8, p. 461) discusses epistemology viewed ontologically, and “system” is viewed as “model.” 72 The equations describing the systems are: mechanical system I d2θ/dt2 + J dθ/dt + Kθ = τ, and electrical system L d2q/dt2 + R dq/dt + q/C = V,

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Figure 11 Isomorphisms (a) Mechanical-electrical isomorphism. The figure is borrowed from Ashby (1956: Figure 6/8/1, p. 95). Reproduced with permission of the Estate of W. Ross Ashby, all rights reserved. (b) Spatially visible isomorphism between two graphs.

(a)

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One can illustrate isomorphisms more simply by letting elements be qualitative (nominal) variables and relations to be uninterpreted graph-theoretic links. As shown in Figure 11(b), a system with elements A, B, and C and relations AB and BC is isomorphic to – has the same structure as – another system with elements P, Q, and R and relations PQ and QR. In Bunge’s hierarchy, theory at level (4) deductively generates a model at level (3) by addressing a model object at level (1), as depicted in Figure 12. Though model objects and where θ = angular rotation, q = electric charge, dθ/dt = rotational velocity, dq/dt = current, I = moment of inertia, J = coefficient of angular viscosity, K = rotational spring constant, L = inductance, R = resistance, C = capacitance, τ = torque, V = voltage. If one maps θ onto q (and dθ/dt and d2θ/dt2 onto dq/dt and d2q/dt2), I, J, K onto L, R, 1/C, and τ onto V, the same second-order differential equation governs both systems.

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thus observations are often “theory-laden,” they are not necessarily laden with the theory that eventually explains them. Kepler’s observations were not laden with Newton’s theory. Figure 12 Model derived deductively

(4) theory [general theory] (3) model [specific theory] (1) observables [model object] A model might draw upon more than one theory; also, a single theory may support models of different specific phenomena. A model might alternatively be derived inductively by aggregating empirical laws when there does not yet exist an applicable theory; Kepler’s model was of this type. Such a model will be sui generis, and runs the risk of being completely ad hoc. Rarely will this purely inductive approach yield a theory, which requires some broader creative insight. 73 As shown in Table 3 Bunge has an additional level in his hierarchy, namely level (5) theories [generic semi-interpreted theories] that are still more general than level (4) theories. These are systems theories that are intermediate in abstraction between mathematics (E) and philosophy (M) at level (6), and the theories of particular scientific (S) disciplines at level (4). 74 Bunge’s conception of generic semi-interpreted theories corresponds closely to the ideas of Boulding, von Bertalanffy, and Ashby. Finally, note that systems theories also include models as components. Game theory includes the Prisoner’s Dilemma and Chicken models. Catastrophe theory includes several elementary 73

Note #147 Limits of complexification, p. 544, discusses the idea that a high level of integration that amounts to a new organizing principle is rarely achievable simply by bottom-up stepwise increases in complexity. 74 To pursue the Newtonian example further: Newton’s theory is further abstracted in generalized mechanics (Goldstein 1959) which might be considered to be a level (5) theory applicable even outside of physics.

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catastrophes, of which the fold, cusp, and butterfly models are used in this book. Systems theory models, not shown in Table 3, should not be confused with level (3) models which concretize discipline-specific theories (e.g., a Newtonian model of the solar system that concretizes Newtonian mechanics). Systems models also exist outside fully developed systems theories. Although the deductive route to an ESM (Figure 6), which emphasizes formalisms, generally produces systems theories with models as components, the inductive route, which emphasizes isomorphisms, can arrive at models not embedded in any theory. For example, some phenomena are said to exhibit “selforganized criticality.” 75 SOC models of these phenomena are similar, but there is no formal SOC theory that deductively generates them. Holling and Gunderson’s “adaptive cycle” model 76 is another example of an inductively derived model. By adding subject-specific knowledge – descending from level (5) to level (4) – a systems theory can contribute to a theory within a particular scientific discipline. But applying a systems theory directly to a particular phenomenon, without such augmentation, is ill-advised, because of the large gap between the abstract theory and the concrete phenomenon. For example, adding economic content to game theory might yield a theory of economic competition and cooperation, which, when applied to some specific economic phenomenon, e.g., auctions, might model this phenomenon. Often, a systems theory fosters theory development in more than one discipline. For example, game theory is used not only in economics but also in political science to understand conflict and in biology to understand altruism. Chaos is important not only for the physics of fluids but also in theories of ecological and evolutionary dynamics. The “metaphysical” character of systems theories inheres not only in their generality and abstraction but also in their remoteness from empirical test. A systems theory can be tested 75 76

Note #150 Self-organized criticality, p. 551 Note #130 Trajectories of development, p. 517

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only by descent to a lower level of the epistemological hierarchy. Experiment or observation can confirm or disconfirm a particular hypothesis or proposed law, i.e., level (2). But a model – level (3) – that includes a rejected hypothesis is not automatically falsified, and may be rescued, as Bunge notes, by ad hoc hypotheses. Only if a significant fraction of the hypotheses of a model are falsified will the model be rejected. Moreover, the rejection of specific models does not invalidate the level (4) theory that encompasses them; the theory simply may not apply to the phenomenon. Systems theories, such as game theory, information theory, nonlinear dynamics, etc., at level (5), are even further removed than ordinary scientific theories from empirical test. So, as Bunge argues, systems theories are only “vicariously testable,” that is, testable only with additional specifications. Systems theorists need not be defensive about this. Ashby (1956), for example, boldly proclaims that his Law of Requisite Variety, 77 based on a model that unites information theory and game theory, has nothing to fear from any possible empirical finding. The LRV cannot be falsified; it either applies or does not apply, although if it applies it might be applied either correctly or incorrectly. Similarly, game theory cannot be empirically disconfirmed. If a game-theoretic model of auctions is disconfirmed, the fault lies in the detailed information about auctions that were added to the game theory formalism and not in game theory itself, which can be assumed to be internally consistent. This assertion about vicarious testability – that a systems theory either applies or doesn’t apply and cannot be empirically falsified – may suggest that such theories are just mathematics. They are not; this issue is discussed later. 78 To the extent that systems research is oriented toward mathematics or philosophy but not yet toward specific scientific theories, this research may seem “fact-free” or involve “models 77 78

Note #44 Law of Requisite Variety, p. 384 4.1 Not just mathematics, p. 123

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in search of data” (Horgan 1995). Systems theories not applied to specific scientific problems are indeed fact-free; they are exact metaphysics that is not yet also scientific. For example, the work of Mitchell, Hraber, and Crutchfield (1993) on cellular automata evolved by genetic algorithms explores some general issues in complexity, computation, evolution, and emergence. This exploration is rigorous in its analytical and computational formalisms. It needs to be judged by the insights generated, the assessment of which is a long-term matter. Systems theories are not unique in being “fact-free.” So are Newtonian mechanics and thermodynamics. High-level (very abstract) theories within specific disciplines are also fact-free, and properly so. Systems theories must be judged primarily by their fruitfulness in generating or enriching scientific theories. 79 Popper (1959), well known for his commitment to falsifiability as necessary for scientific theory, also speaks of metaphysical ideas as pointing to research programs and being evaluated for their generativity. By the criterion of fruitfulness, systems theories such as information theory, game theory, automata theory, feedback control theory, and chaos theory have been extremely successful. They are widely used in the sciences. They make sudden appearances in the most unexpected places. For example, the Prisoner’s Dilemma model of game theory has been linked to brain imaging, virus behavior, and quantum logic. The diversity of such appearances is not anomalous because systems theories are background knowledge valuable for research in every field. Of course, they do not come labeled as systems or complexity theories, and most certainly not as “components of an exact and scientific metaphysics,” but such labels characterize what these theories actually are.

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This historical criterion of truth supplements the structural criterion of coherence and the functional criterion of correspondence; see earlier Footnote #53, p. 60

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Chapter 3 Concepts and categories 3.1 Substance and form 3.2 Matter, energy, information; utility 3.3 Isomorphism and emergence 3.4 Aspects of complexity and holism 3.5 Structure, function, and history

79 88 97 100 109

Beyond its focus on the central rather than the fundamental and its insistence on the duality and symmetry of the fundamental (the fundamental of structure being complemented by the fundamental of function), several additional properties distinguish a systems metaphysics from the metaphysics implicit in standard science: (a) Systems metaphysics is oriented toward form as opposed to substance (sections 3.1, 3.2), (b) its integrating ideas embrace both similarity and difference (3.3), and (c) its primary themes are about holism and/or complexity (3.4, 3.5). 80 3.1 Substance and form 3.1.1 A “stuff-free” metaphysics In terms of the dyad of form and substance (Figure 13), the systems project is an attempt to construct a theory of everything by focusing on similarities of form and ignoring differences of substance; in Bunge’s (1973) terms, it analyzes the “stuff-free” aspects of phenomena. (To be stuff-free does not mean to be immaterial; it means to be independent of any particular materiality.) The word “substance” is used here synonymously with “matter,” but in the triad of matter-energy-information introduced below, “substance” means matter-energy. Matter is “stuff”– atoms, water, rocks, organisms, etc. Form is how stuff 80

This chapter introduces some basic systems categories and concepts and thus overlaps with Notes, so some themes, e.g., emergence and complexity, appear in both places. Where this is the case, discussion of a theme in this chapter is general and philosophical, while discussion of the same theme in Notes is more specific and technical. © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_3

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is organized in static order or dynamic process. As contrasted with substance, form is a more general than simply spatial pattern. It means any type of organization. In terms of the dyad of matter and form, 81 reductionism gives primacy to matter. The systems alternative gives primacy to form. 82 Figure 13 Substance and form (a) Platonic view; (b) Aristotelian view

form (a)

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The primacy of matter (and energy) leads to the classic hierarchy of the sciences (physics, chemistry, biology, etc. 83) and to the conception of explanation as reduction to a more fundamental science or a more fundamental theory within a particular science. What is more fundamental is usually more 81

In the Platonic view, there is a world of forms independent of and higher than matter. In the Aristotelian view, form and matter are intertwined as complementary aspects of everything, so the circles are shown above as side-by-side (alternatively, they could be shown as overlapping or as a single circle divided in two), although for Aristotle as well, form was higher than matter (Adorno 1965). The Platonic view looks at matter and form under the aspect of difference, while the Aristotelian view looks at them under the aspect of similarity. The systems perspective encompasses both views. The Platonic view is particularly relevant to the later discussion in this chapter on conceptual systems and on the distillation of information from matter-energy. 82 In Aristotelian terms, the systems view focuses on formal cause rather than material cause. 83 This hierarchy is shown in Figure 8 Transdisciplinarity of some systems theories, p. 67.

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microscopic 84 than what is explained, i.e., it typically refers to the parts of some whole, especially the materiality of these parts. The world of appearance is explained by the materiality of an underlying world of greater reality; for example, genes are explained in terms of nucleic acids and their interactions. Rejecting the primacy of matter, the systems project offers an ontology based on the primacy of general – more precisely, ubiquitous – form. It thus focuses on phenomena 85 such as order and disorder, information processing, regulation and control, morphogenesis, and learning that are not less real than DNA, atoms, or quarks. How form can have primacy is perhaps not easily grasped. To the contemporary mind, form is not “substantial,” is not quite real. Geldard (2001) notes that this was not always so. We have to go back to Pythagoras and Plato to see principle as a substance. 86 In that Greek tradition, a law, a number, an idea, a form were all substantial. They existed outside the mind as entities, like a god, or, to use the Greek term, a daemon. A principle actually existed, like a bird or a cloud or wind... In giving primacy to form over substance, the systems view is not materialistic; or, to be more precise, less 84

It would be incorrect, however, to attribute the privileged status of physics to an exclusive concern with the very small. It is equally concerned with the very large, indeed ultimately the universe, which is equally fundamental. This dual focus justifiably earns physics its special status among the sciences. 85 Table 2 Some general phenomena (systems themes), p. 71 86 The use of “substance” to denote matter is post-Greek; for Plato and Aristotle, form was more substantial than matter. Note also that in the philosophical literature, “substance” is sometimes a broader idea encompassing both matter and form; for example, Spinoza’s “substance” had attributes of both extension and thought. In Chinese thought, there is a notion of li – principle – apart from and higher than chi – matter-energy (Needham 1956). With virtual reality, the Internet, and the idea of memes, forms have become substantial for the 21st-century mind.

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materialistic than the dominant scientific paradigm since this view addresses both form and matter. In the idea of system discussed above, elements and relations are matter and form, respectively, and are Janus-faced unities (Koestler 1969, 1978). Looking downward (inward) toward its parts, system is form; looking upward (outward) to what it is part of, system is matter. For example, a water molecule is form relative to its constituent hydrogen and oxygen atoms; it is matter as a molecule that interacts with other molecules. Form is as real as matter; more generally, relations are as real as elements and in the systems view are given priority (especially complex or holistic relations, as discussed later). Form includes distinction and order, which are basic systems themes. A form rather than a substance-based ontology is not less mathematical than the standard ontology of physics, but it emphasizes those mathematical notions best suited to explicate distinction and order in their many manifestations. To illustrate: information theory is about organization or communication in general, without regard to the substance of what is organized or the nature of the sender and receiver of a message. Game theory is about cooperation and competition in general, whether cooperating or competing units are organisms, persons, organizations, social systems, computer programs, or engineered artifacts; the materiality of the interacting units is irrelevant. Chaos theory is about order and disorder in deterministic dynamics in general and applies to aspects of chemical reactions, solid-state phenomena, weather, organizational behavior, financial markets, and neuronal activity. Fractal geometry is about form as such, utterly divorced from materiality; it characterizes mountains, clouds, coastlines, protein structures, the Internet, and certain mathematical objects. Feedback control theory describes technological artifacts, interpersonal communication, and physiological homeostasis. Generalized evolution applies not only to the origin and descent of the species but to the immune system, neuronal organization, non-equilibrium economic phenomena, and mathematical optimization. Theories of branching processes and distribution

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networks describe trees, roads, blood vessels, and bronchial systems. Ideas about center and periphery apply to international political and economic relations and to spatial order in market systems. Self-organized criticality characterizes earthquakes, forest fires, and ecological extinctions. Scale-free networks are found in natural and social systems and in human artifacts. The materiality of these phenomena is secondary; their form is what is primary. To expand upon the game theory illustration: suppose that a zero-sum game is used to model an interaction between two persons. The theory says that a rational solution to such games is a mixed maximin strategy. Nothing about physiology is necessarily relevant. 87 Or suppose that a linguistic or automatatheoretic model is used to describe plant morphogenesis; specific cellular or biochemical facts need not be invoked, although if they can be added to the model, it will be the richer for it. Automata theory, 88 which is about (deterministic) interactions of a system with its environment, ignores the materiality of both (Bunge 1973) and is the basis of the theory of computation; it is “stuff-free,” as is most of computer science, in which material and energetic aspects of computing are deemphasized and the formal – informational – aspects are stressed. Computation is not specific to a particular medium; it may involve wooden beads, metal gears, vacuum tubes, transistors, integrated circuits, etc. 89

87

The “separability” of explanation by form versus by substance may be bridged in interesting ways, as in a brain imaging study (Rilling et al. 2002) of the mental processes involved when people detect defection in Prisoner Dilemma games. 88 Note #27 External relation, p. 354. Materiality is equally peripheral to dynamics described by continuous differential equations, but discrete dynamics is privileged here because it is more general. 89 Quantum computing may require a modification of this story. In a medium that exhibits quantum phenomena, software possibilities are different from those in a medium which does not. But even quantum

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The materiality independence of dynamics is even more accentuated in the view held by some researchers that all dynamics is computation. 90 This usually refers to the discrete dynamics of automata (Wolfram 2002), but continuous dynamics can be regarded as analog computation, and for some, discrete and continuous dynamics are not deeply different. The very notion of materiality can be taken as a “stuff-free” metaphor. For example, the distinction between solids and fluids can be reinterpreted as the distinction between dynamic order and disorder, as these occur in automata-theoretic or differential equation models. Constant or cyclic behavior is “solid,” while random or chaotic behavior is “fluid.” To quote Langton (1990), We propose that the solid and fluid phases of matter, with which we are so familiar from everyday experience, are much more fundamental aspects of nature than we have supposed them to be. Rather than merely being possible states of matter, they constitute two fundamental universality classes of dynamical behavior. We know solids and fluids primarily as states of matter because up until quite recently, everything that exhibited dynamical behavior was made up of some kind of material. Now, however, with the availability of computers, we are able to experiment with dynamics abstracted from any particular material substrate. Thus, the stuff-free metaphysics that Bunge recognized as central to the post-World War II systems project is also a computing might be instantiated in different material media, so it too might be regarded as stuff-free. 90 One needs, however, to distinguish between dynamics and computation if a distinction between signified and signifier is taken to be an essential ingredient in computation. That is, computation is regarded as such in relation to us (function), but in itself (structure) the computing process is just dynamics. It is the computer simulation of dynamics, not the dynamics itself, that is computation.

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dominant theme of the contemporary renaissance of this project associated with chaos, complexity, Artificial Life, emergent computation, and the like. 3.1.2 Concrete, abstracted, and conceptual systems In terms of the earlier definition of “system,” elements and relations are typically (but not necessarily) substance and form. To say that a systems theory is stuff-free really means that it privileges relations over elements and nonmaterial attributes over material ones. It is useful to introduce here Miller’s (1978) nomenclature of concrete, abstracted, and conceptual systems (Figure 14). Call systems concrete when material attributes are involved, such as mass, charge, and momentum. Call systems abstracted when materiality is present but ignored, e.g., omitted in what Bunge called the model object. Finally, call systems conceptual when material attributes do not exist, as in formal mathematics. Abstracted systems are thus midway between concrete systems and conceptual systems. The vertical placement of concrete and conceptual systems echoes the placement of substance and form in Figure 13. An exact and scientific metaphysics addresses both concrete and abstracted systems; by also including conceptual systems, the systems project goes beyond the concerns of the natural and social sciences. Figure 14 Concrete, abstracted, and conceptual systems

conceptual abstracted concrete

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For example, ecological thermodynamics is concrete, but a game-theoretic model of the behaviors of organisms is abstracted. Although there is a correlation between the ontological stance and concrete systems and the epistemological stance and abstracted systems, each type of system can be viewed ontologically or epistemologically. Epistemologically, concrete and abstracted systems are models, but ontologically they actually exist in the world. Although the word “abstracted” has epistemological connotations, a social network is a nonmaterial system that is no less ontological than the organisms that are its material basis. Moving from the natural to the social sciences shifts the subject from concrete to abstracted systems. Conceptual systems might be viewed as inherently epistemological, but in a Platonic view, they have ontological status; the systems perspective can be agnostic on this point and does not have to weigh in on such issues as the “existence” or “non-existence” of numbers. The difference between concrete and non-concrete systems is illustrated by the difference between entropy in physics (statistical mechanics) and entropy in Shannon’s information theory. Entropy in physics has physical units, e.g., ergs per degree Kelvin, units carried by Boltzmann’s constant. Shannon entropy does not have physical units (“bits” are not physical). 91 Like Shannon entropy, Feigenbaum’s constant in nonlinear dynamics has no physical units. Concrete systems involve variables having physical units; abstracted and conceptual systems do not. A melody instantiated in a nervous system is abstracted but the melody itself is conceptual. For the Aristotelian position that form is always embodied in matter, the category of abstracted system suffices, and one does not need an additional category of conceptual system, which perhaps implies a Platonic world of forms. But one can take the Aristotelian position but still insist that material embodiments of a melody are not its deepest 91

Note #14 Entropy, p. 334

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reality. A conceptual system could be regarded as a limiting case of an abstract system, without separate ontological status; or, one could give conceptual systems a Platonic reality of their own. Platonism is not anomalous in a postmodern world comfortable with memes, virtual reality, and an Internet noosphere. Encompassing concrete, abstracted, and conceptual systems accommodates both materialism and idealism. The notion of conceptual systems also is neutral about whether mathematical truths are discovered or constructed. One can accommodate both the world-centered stance and the humancentered stance, or be neutral between them; so the philosophical reach of the systems orientation could extend even to continental philosophical traditions. Many controversial polarities in the history of philosophy need not be resolved for a systems metaphysics to be fruitful. In addressing not only concrete systems but also abstracted systems, and not only abstracted systems but also conceptual systems, the systems project goes beyond the natural and social sciences and extends also to the humanities and the arts. Substance-based reduction is possible only for concrete systems; for abstracted and conceptual systems it is irrelevant. Systems theories privilege form over substance and thus emphasize abstracted systems. The inclusion of conceptual systems shows the proximity of the systems project to mathematics. For conceptual systems, one must replace the form-substance dyad with the form-content dyad (a systems focus would be on form, rather than content). Concrete systems are encompassed in the systems project, but are generalized, and discipline-specific details are often ignored. For example, the concrete details of metabolism are essential to biochemistry, but an abstract notion of metabolism (matter-energy transformations that sustain an open system far from equilibrium) is of wider interest.

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3.2 Matter, energy, information; utility 3.2.1 Matter, energy, and information First all is matter, then all is energy, now all is information! - Anthony Blake (1998) For concrete systems, the substance-form dyad leads to the matter-energy-information triad, where, most simply, substance is matter-energy and form is information, 92 as in Figure 15(a). Figure 15 Triad of matter, energy, and information M = matter; E = energy; I = Information. The substance-form dyad applies only to (a) and (b). +, –, = mean active, passive, and mediating, respectively. (b) and (c) show different choices of a mediating factor, absent in (a).

(a) M

I +

–

I +

FORM

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SUBSTANCE

M –

E + (c)

I = M –

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Note #46 Information (and matter-energy, utility), p. 389

E =

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Information, like form, is stuff-free (Figure 15(a)); it does not involve the physical units of distance, mass, and time. Although information is normally instantiated by some pattern of matter (e.g., the structure of DNA) or energy (e.g., electromagnetic signals), the specific matter-energy that carries the information is not essential. The same information could be represented in many different ways, such as patterns of light, fluctuations of voltage, or waves in different media; the continuing change in the way music is stored illustrates this idea. Analog information is implicit in patterns of matterenergy, but information is explicit when embodied in digital form. To use an alchemical metaphor, information is “refined” or “distilled” from matter-energy. One might reverse the metaphor, regard matter-energy as “precipitated” or “condensed” from information, or, more generally, take information as more fundamental than matter-energy. A two-storied structure, of matter-energy processes below and informational processes above, the latter serving to regulate the former, is ubiquitous in systems. 93 In this structure, information might be considered to be active, while matterenergy is passive, i.e., acted upon, where “passive” means both resistant and receptive. 94 A functionalist schema based on this two-story structure is offered by James G. Miller (1978) in his living systems theory. Miller proposes a set of “critical subsystems” that process matter-energy, information, or both and are found in cells, organisms, organizations, etc. 95 For 93

Note #47 Autopoiesis, p. 393 Note #34 Active vs. passive, p. 368 95 Miller’s scheme of functional subsystems presents a forceful case for the ubiquity of this two-story architecture. The scheme overreaches, though, in its insistence on the necessary presence of all the subsystems he defines, and is arbitrary in its list of levels of analysis (cell, tissue, organ, organism, group, organization, society). It is also non-developmental and nonhistorical. It is a framework rather than a theory, and it is hard to imagine a mathematical formalization of it. Its most serious limitation is the absence of significant links between matter-energy and informational subsystems, without which the very reason for this two-story architecture remains 94

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example, within cells one can distinguish between metabolic processes, whose purpose is to extract free-energy and material building blocks from food, and informational processes (e.g., DNA replication, protein synthesis, protein catalysis), whose purpose is to preserve and apply the informational order, which specifies how metabolism is regulated. Molecules that carry coded representations or convey signals or regulate processes are functionally different from molecules that are incorporated as units in larger structures or are catabolized to extract energy. Figure 15(b) gives an alternative correlation of matterenergy-information with substance-form. It identifies substance with matter and form with information; energy then is the means by which information acts on matter. The matter-information dyad is static and tense; the mediation of energy between active information and passive matter yields a triad that is dynamic. The triad defines an upward hierarchy, matter-energyinformation, that can be supplemented with a fourth category of utility, discussed later. Figure 15(c) gives a third ordering, matter-information-energy, that is not associated with the substance-form dyad. Here energy is active, matter is passive, and information is the mediating link that allows energy to interact with matter. This ordering is the basis of the triad of hyponomic-autonomic-hypernomic discussed later. 96 Each of the three representations in Figure 15 depicts a hierarchical ordering of matter, energy, and information, but one can also view these categories under the aspect of similarity, rather than difference, and see them all at the same level. In this perspective, matter, energy, and information enter into every concrete phenomenon. Every entity or process has material, energetic, and informational aspects. For example, consider a DNA molecule whose nucleotide sequence constitutes genetic information; here information is carried on material markers. obscure. It is the emergence, i.e., distillation, of information from matterenergy that is so interesting; on this, Miller's scheme sheds little light. 96 This triad comes from Bennett (1956); see pp. 166, 280.

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This molecule may be considered “under the aspect of information” as coding for particular mRNA or protein molecules. It may also be considered “under the aspect of matter” as a macromolecular constituent of cells that needs to be synthesized. It may also be considered “under the aspect of energy” in the chemical energy required to make it and that might be recovered from it if it were used as an energy source. A DNA molecule – even more simply, a single ATP nucleotide – has all three aspects. ATP is in fact the main energy currency in cells, is used as a material building block in the making of DNA, and contains one of the four informationally meaningful DNA coding elements (A, T, G, and C). Which aspect – energy, matter, or information – is salient in any circumstance – also which aspect mediates – depends on the particular interactions in which the molecule participates in that circumstance. (This reflects the ontological stance; in the epistemological stance, one would say that what is salient depends on the observer.) The DNA molecule, comprehensively viewed, is simultaneously matter, energy, and information. Information is concrete in that it is carried on matterenergy markers and its transformations involve the interactions of these markers. But the triad of matter, energy, and information is also relevant to abstracted systems. For example, money has matter, energy, and information aspects. Concretely, the materiality of money is exemplified superficially by coins and bills, more deeply by precious metals or other scarce materials, and still more deeply in the thermodynamics that partially underlies economic value. 97 But in an abstracted view, money as matter is wealth; money as energy is power that makes things happen; and money as information is a number in a computer that can be wired electronically from one place to another. In economic theory, money is mostly treated abstractly; that is, it is not grounded in thermodynamic and ecological realities. Although systems thought is usually oriented more 97

6.4.1 Sustainability and globalization, p. 248; 6.4.2 Modernization as differentiation, p. 253

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toward abstracted than concrete systems, and tends to deemphasize substance in favor of form, it often leans the other way when correctives are needed to theories that are not sufficiently grounded in concrete reality; hence, for example, the advocacy by systems-oriented thinkers (Odum 1971; Georgescu-Roegen 1976; Rifkin 1980) of energy and entropy accounting in economic analysis. Information is of interest to the systems project because it is stuff-free and complements the categories of matter and energy. Unlike matter and energy, however, it applies not only to concrete systems but also to abstracted and conceptual systems. Shannon’s theory of information (Shannon and Weaver 1949) was originally about communication, but communication can be defined more broadly than signal processing. Information theory is also about what it means to be organized as opposed to disorganized and thus about the relations between wholes and parts. 98 It connects to statistical mechanics and to algorithmic information theory 99 which addresses process rather than state descriptions. It quantifies chaos. It bears on learning, adaptation, and evolution, central to Artificial Intelligence, Artificial Life, and the study of complex adaptive systems. It is important for control theory and the theory of computation. Information theory is a component of semiotics, the study of sign systems (generalized language), which plays a role in the social sciences, humanities, and arts that is analogous to the role information theory plays in the natural and social sciences. In its ubiquitous presence in many fields, information theory is a salient component of the exact and scientific metaphysics that the systems project is constructing. The three categories of matter, energy, and information are reflected in the historical development of science and technology – its early concern with the materiality of things, the 19th-century discovery of domain of energy governed by the 98 99

Notes #9 Relation as constraint, p. 324, and #13 Order, p. 332. Note #48 Algorithmic information, p. 395

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laws of thermodynamics, and the articulation of a distinct domain of information in the post-World War II era. In the world of practical affairs, there has been the parallel emergence of information-centered economic activity clearly distinguishable from processing or distribution of materials (e.g., mining, construction, and transportation) or the production and distribution of energy (e.g., oil extraction and refining, hydroelectric power generation, electric power networks). This informational domain includes, telecommunications, the media, the educational sector, the world of computation, the financial system, regulatory institutions, the Internet, etc. Within economic organizations, especially those engaged in manufacturing, one can see the same dichotomy: between production processes per se, which involve matter-energy transformations, and their management and coordination which occurs at the higher informational levels in the organization. 3.2.2 Utility Under the aspect of similarity, information supplements the categories of matter and energy, but under the aspect of difference, information is a higher-level emergent. One might ask if additional categories emerge beyond matter, energy, and information. The question, “Matter, energy, information ...what?!” was once raised by the systems theorist Stuart Kauffman at a systems meeting. 100 In another session, he also posed the question, “What is required of a system for us to say that it ‘acts on its own behalf’?” An answer to the first question, utility, partly answers the second question: A system acts “on its own behalf” if it can gain utility. Utility 101 is a fourth basic category, related to but going beyond the matter-energyinformation triad. Like information, it is “stuff-free” and relevant to both concrete and abstracted systems and is a category articulated in the post-WWII crystallization of the systems movement. Roughly at the same time that Shannon 100 101

International Conference on Complex Systems, 1998 Note #54 Utility, p. 403

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formulated information theory, von Neumann developed game and decision theory in which the notion of utility plays a central role. This notion had antecedents in the writings of Hume, John Stuart Mill, Adam Smith, and other philosophers, but in this book, the word refers to von Neumann’s technical conception, only loosely connected to the concept of utility in utilitarianism. The idea of utility as a fourth fundamental category is displayed in Figure 16. The diagram is derived from Bennett (1966) 102 and is explained later. 103 Figure 16(a) shows the matter-energy-information sequence of Figure 15(b) augmented by utility and should be visualized as a flat two-dimensional form; the zigzag bold line connects the lowest term, matter, to the highest term, utility. Figure 16(b) should be visualized as a tetrahedron; it shows utility as a point of value above a plane of fact defined by a matter-energy-information triad. Figure 16 Utility as a 4th fundamental category M = matter, E = energy, I = information, U = utility

(a)

U

I

(b) E

M

U

I

E M

Adding the category of utility alters the prior categories of matter, energy, and information. Just as form in the substanceform dyad is related to but is not the same as information in the matter-energy-information triad, information in this triad is really not the same as information in the matter-energy102

References to Bennett in this book refer to John G. Bennett except for one on p. 444 which refers to Charles Bennett (1988). 103 Figure 25 Tetrad of problem solving, p. 146. A list of tetradic structures used in this book is given on p. 617. An article that discusses various examples of this structure in the scientific literature is (Zwick 2018).

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information-utility tetrad. For concrete systems, information in the triad is illustrated by chemical or biological catalysis, where the catalyst provides information but not matter-energy to the reaction. But information in the tetrad needs to be defined in the context not only of matter and energy but also of utility. For example, understanding the genetic information of organisms involves not only its relation to matter-energy processes but also its relation to evolutionary fitness, a form of utility. Genetic information persists because it confers utility. One might speak of informationtriad and informationtetrad, where informationtriad is defined in relation to matter-energy and informationtetrad relates also to the notion of utility. Ideally, one should have different words for these two kinds of information, just like “husband” in the husband-wife dyad and “father” in the father-mother-child triad are two specializations of “man.” 104 All four terms in the matter-energy-information-utility tetrad are potentially related. Just as information is carried on matter and/or energy, utility is carried on either information, as in the fitness value of genetic information or in money as electronic funds, or on matterenergy, as in the value of precious metals or in thermodynamic aspects of utility. The category of utility differs from the categories of matter, energy, and information not only in its salience for biological and social systems, but in the fact that it has normative in addition to descriptive applications. 105 “Utility” seems to presume the existence of a rational actor, and explanations involving utility appear teleological and thus radically different from causal accounts. But this presupposes too narrow a view of rationality and too restrictive a view of causality. Von Neumann developed the notion of utility for application to human decision-making and economic behavior, 104

See the discussion of this type of progression in Note #30 One, two, three, ten thousand, p. 359. A related hierarchy of kinds of information is also given in Table 9 Levels of autonomy and information, p. 158 105 See 4.3 The centrality of biology, p. 135; 4.4 Sciences of the artificial, p. 139, 4.5 Systems theory and systems analysis, p. 141.

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but it is a broader notion. “Fitness” in evolutionary theory is a form of utility, as is evident from evolutionary game theory (Maynard-Smith 1978, 1982). 106 This does not mean that all individual organisms are rational actors as human beings and higher animals are to some degree. Rationality for cells and other simple organisms is vicarious, one achieved for populations of organisms by natural selection. The notion of “agency” is used in this book for this broader concept of rational action; used in this way, even simple living systems exhibit agency. But evolution also gives rise to systems in which utility gains an internal representation that guides action. The organism is then less at the mercy of evolutionary forces, because rationality is no longer vicarious. “Utility” is then more than an epistemological shorthand; it is an emergent property with causal effects. 107 If systems are able to learn, agency reflects the more familiar kind of rational action that is present in higher organisms. But to reiterate: utility and agency are relevant even to simpler forms of life. There is a fifth category that might be interpolated between information and utility. In feedback control systems, 108 which are components of living systems or are designed by such systems, a kind of information is used that has implicit utility. For example, the set-point of a thermostat, the specified ideal temperature, is not mere information like the signal that represents the actual temperature, but a norm, meaningful only in the context of utility. This accords with Deutsch’s (1966) discussion of feedback in social systems, where norms depend on values, i.e., on utility. Adding norm to matter-energyinformation-utility gives the pentad, matter-energy-information106

Both the general concept of utility and the specialized concept of fitness are close to tautology: utility is what decisions optimize; fitness is what evolution maximizes. Neither is easily amenable to a priori as opposed to a posteriori definition, though heroic attempts have been made to disguise the latter as the former. Also, both concepts are usually one-dimensional. 107 See Cognition (1.1.8, p. 20; 7.1.8, p. 461), which considers “modeling subsystems” (e.g., nervous systems) which some complex systems have. 108 Note #45 Feedback control, p. 386

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norm-utility. The information-norm-utility triad encompasses three post-WWII systems theories: information theory, control theory, and game/decision theory (Table 4). Table 4 Some categories and systems theories

Category (what?) utility norm information energy matter

Systems theory game/decision theory control theory information theory thermodynamics/statistical mechanics; generalized chemistry 109 thermodynamics/statistical mechanics; generalized chemistry

3.3 Isomorphism and emergence A focus on isomorphisms, in which systems are considered under the aspect of similarity, has a complement in a focus on emergence, in which systems are considered under the aspect of difference. 110 While interest in isomorphisms arises from a priority of form over substance and the recognition that some forms are ubiquitous, 111 interest in emergence arises from the fact that attributes of a system often differ from those of its elements. In Figure 17, isomorphisms are shown as typically (but not invariably) occurring in phenomena at the same level, 109

One of Bunge’s (2010) paths to a scientific metaphysics is “(b) …generalizing the algebra of chemical reactions…” which should be expanded to encompass Artificial Life research on generalized metabolism (Bagley and Farmer 1992; Fontana 1992). 110 See Note #32 Emergence, p. 363. Emergence is not the only basis for difference. Uniqueness also implies difference. There are also differences in system types; see 5.2 Hierarchy of system types, p. 154, and 5.3 Categories of complexity, p. 160. 111 In the abstract sense of “ontological parity” (Ross 1980), all systems are similar.

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while emergence – and reduction, its inseparable partner 112 – involves vertically separated levels. Figure 17 Isomorphism vs. emergence/reduction.

B DIFFERENCE reduction

SIMILARITY isomorphism

B′

emergence A

Not represented by this figure are cross-level isomorphisms, prominent in Miller’s (1978) Living System Theory, where A and B are isomorphic. Multi-scale isomorphisms are ubiquitous in the self-similarity of fractals. 113 There are also isomorphisms of emergence, i.e., similarities among different instances of emergence (Baas 1994). For example, self-organized criticality (Bak 1996) is emergence of a critical state in different open systems driven far from equilibrium. Another example of isomorphisms of emergence is convergent evolution. In the Artificial Life literature, there is a conjecture (Langton 1992, Kauffman and Johnsen 1992) that systems are optimal at and evolve toward the “edge of chaos 114;” if true, this would be an isomorphism of emergence. In one sense, emergence is the opposite of reduction, but in another sense these are two sides of the same coin and are inseparable. Reduction looks downward from level L to level L1; emergence looks upward from L-1 to L. Since reduction is explanation in terms of a lower level, what is explained emerges from this lower level. For example, statistical mechanics reduces the macroscopic properties of pressure and temperature to a 112

Discussed earlier in 2.1 The illusion of the fundamental, p. 43. Note #26 Fractals, p. 353 114 Note #17 Chaos, p. 338 113

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microscopic description of molecules in motion, but from the opposite perspective, pressure and temperature emerge from the microscopic level. It might seem therefore that a focus on emergence cannot imply a critique of reduction, but this does not do justice to the fact that the perspective of emergence highlights the creativity of nature, ignored or suppressed by reductionism. As Jonas (1966) notes, unlike reduction which explains the higher by the lower and thus discounts its ontological legitimacy, emergence explains the lower by the higher that is implicit in it and thus in a sense even privileges the higher because of its novel features. Reduction is indeed the opposite side of the coin of an emergence that is understood, but of greater interest are emergents that are difficult or impossible to explain because of computational complexity, mathematical intractability, or undecidability. Emergence is usually considered in the context of explanation, as epistemological rather than ontological (Crutchfield 1994). Pressure and temperature of a gas are explained by molecular motion, but even if accepted as being as real as molecular motion, the gas does not gain advantage from these emerged macro-properties. However, there are phenomena in which emerged properties are significant to the system or its environment. For example, flocking and schooling, both examples of self-organization where simple rules give rise to complex behavior, are significant for the birds and fish involved in this collective behavior. Such ontological emergence is different from epistemological emergence which is merely the inverse of reduction. A focus on emergence corrects fallacies that derive from overemphasizing similarity. Properties of some systems are sometimes treated as properties of all (or most) systems; that is, isomorphism is assumed rather than demonstrated. For example, “mind” may be conflated with pattern, interiority (Mattesich 1978), or information processing. Informational macromolecules such as DNA and RNA might be regarded as proto-mental, but what is really present in these molecules is

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just form or information. “Mind,” in the usual sense of the word, emerges only at higher levels of complexity. A related fallacy, that everything is alive, results from “life” being conflated with energy or dynamics. Here, too, a focus on difference corrects an overemphasis on similarity. Life and mind arise at different levels. Life emerges from non-living matter; mind emerges from non-sentient life. A perspective based on emergence puts the question sharply: What are the necessary and sufficient conditions for life or mind to occur? The animist or pan-psychic alternative, that everything is alive or has mind, exaggerates similarity and inhibits scientific inquiry. If everything is alive or has mind, further investigation is not very necessary. Science cannot advance if a phenomenon is assumed to be understood when it is not. Life is no longer a mystery but once was. Mind – in the sense of subjective experience as opposed to information processing – is still a mystery. Along with the everything-hasmind and everything-is-alive fallacies, there is the related fallacy that conflates mind with life. Bateson (1979) makes this error when he defines mind as hierarchical information processing that controls an internal energy source and involves feedback with the environment; Maturana and Varela (1980) also err in conflating cognition with self-construction. 115 3.4 Aspects of complexity and holism Aside from taking relations rather than elements as primary, systems theories are oriented toward (a) complexity and (b) holism (Smuts 1926). These terms are not the same, but they are sometimes used interchangeably, and Table 5 lists nine different meanings associated with one or the other or both. 116 Table entries 1-7 are discussed below; entry 8 (emergence) in the previous section; entry 9 (structure/function/history) in the next section. These entries are discussed from an 115

Note #47 Autopoiesis, p. 393 For a more technical discussion that augments this section, see Note #86 Complexity, p. 441. 116

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epistemological perspective but might also be understood ontologically. The entries are not independent of one another. For example, open systems may have high ordinality relations, nonlinearities, mutual causality, and “frozen accidents” (GellMann 1994) of history. Table 5 Some aspects of “complexity” and “holism”

Simplicity/reductionism:

Complexity/holism:

1. 2. 3.

low ordinality relations linear relations lineal causality

high ordinality relations nonlinear relations mutual (feedback) and branching causality

4. 5. 6.

local causality necessity or chance fine-grained view of some parts

global causality necessity and chance coarse-grained view of the whole

7. 8. 9.

one (or two) levels no emergent phenomena structure (or function or history) only

multiple levels emergent phenomena structure and function and history

1. High ordinality relations. “Complexity” or “holism” could mean the presence in a system of relations that involve many elements. 117 Consider, for example, a family consisting of a father, mother, child, and dog. Family interactions might be adequately described with low ordinality relations, i.e., by the behaviors of individual members (elements) and some pairwise relations, e.g., father-mother, mother-child, and child-dog. Or, they might exhibit high ordinality relations involving three or even all four elements. A holistic or complex system could be defined as one that is not decomposable without loss into 117

Note #3 Relation, p. 304, especially Figure 41 A triadic nondecomposable relation, p. 305, and Note #5 Structure, p. 308, especially the discussion of the Lattice of Structures.

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individual or groups of elements; this is one precise meaning that might be given to “The whole is greater than the sum of its parts.” (A system in which the whole is less than the sum of its parts is also holistic.) Of course, it is as much an error to posit that nondecomposable high ordinality relations exist when they do not as it is to ignore them when they do. 118 Whether they exist or not is an empirical question that cannot be settled a priori; 119 this is obviously also true for other types of complexity/holism. 2. Nonlinear relations. Another aspect of complexity is the presence of nonlinear relations. 120 (Nonlinearities are less associated with the idea of holism.) In linear systems, when causes and effects are quantitative, changes in effects are proportional to changes in causes. In complex systems, however, causes and effects can be related nonlinearly. Small causes can have large effects, hence the existence of leverage points; conversely, large causes can have small effects, hence the possibility of resilience in the face of major disturbance. Linearity also means that the effects of multiple causes are additive; in nonlinear systems, causes may be either more or less than additive; there may be interaction effects. It has long been the default assumption that quantitative relations in nature are linear. This assumption made a virtue out of necessity and exemplifies the phenomenon of denial. As long as satisfactory methods for dealing with nonlinearity did not exist, scientists ignored it. In the natural sciences, nonlinear systems were treated by local approximations that were linear; where these approximations were invalid, analysis was assumed 118

Even though maximal holism (Figure 41 A triadic non-decomposable relation, p. 305) is in one sense maximal complexity, it can be as much an oversimplification and an error to assert maximal holism as it would be to assert minimal holism, when neither of these conditions actually applies. 119 See the comment on ideological assertions of holism in Footnote #281, p. 219. 120 Notes #9 Relation as constraint, p. 324, #10 Dynamic relation, p. 327

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to be unimportant, as in the joke of the man searching for a lost object under the lamppost because the light was better, despite the fact that the object was lost elsewhere. Linear static relations have long been the norm in the social sciences. Thus until recently linearity was privileged and nonlinearity was denied or ignored. With the discovery of chaos, 121 however, and advances in computer power, all this has changed, and the study of nonlinear systems has rapidly expanded. It is now generally thought that most relations in nature are nonlinear. Of course, some relations are linear, and because linear relations are simpler, it is reasonable to try linear models first as possible explanations of phenomena. But understanding complex systems requires considering nonlinearities, interaction effects, non-additivity, and the distinction between local and global properties. 3. Mutual and branching causality. Another aspect of complexity/holism is the importance of mutual and branching as opposed to lineal 122 causality. “Lineal” means (i) unidirectional, where causation goes in one direction, as opposed to exhibiting feedback, and (ii) converging, where causation is multiple, as opposed to diverging. Lineal causation is shown in Figure 18(a), where A and B are the cause of C and C is the cause of D. In Figure 18(b), the presence of feedback makes it impossible to identify A, C, or D as either cause or effect; each element is both. In feedback loops, causality is not transitive but cyclical. Even if unidirectional, causality can be diverging (branching) as well as converging, as in Figure 18(c).

121

Note #17 Chaos, p. 338 Notes #5 Structure, p. 308, and #7 Networks, p. 317. The word “linear” is reserved for relations such as y = mx + b; “lineal” is used to mean being in a line.

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Figure 18 Lineal, mutual (feedback), branching causality (a) Lineal, (b) mutual, (c) branching causality.

A

A C B

D (a)

C C

B

D (b)

A

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Ignoring feedback often makes understanding a system impossible. 123 When a system consists of many interacting elements, mutual causality is the norm and lineal causality is rare. What is left of simple cause-and-effect is that external parameters, if unaffected by the system, are causal determinants. In the internal network of interactions, instead of causes there may be “leading parts” 124 (von Bertalanffy 1968), i.e., elements that are especially critical to the behavior of the network. Such elements, for example, could be hubs of scale-free networks. 125 One can think of causes versus leading parts in terms of the fundamental versus the central. Searching for causes is searching for a fundamental, which does not exist for systems exhibiting mutual causality. But the central may exist. Despite the fact that many phenomena in social systems exhibit feedback, lineal models remain the norm in social science. This is another example of the “lamppost effect.” Lineal causality is conceptually and mathematically more tractable. That a single cause can have multiple effects is obvious, but the obvious is often ignored. This fact is critical to holistic understanding. As Garrett Hardin writes (1963), “It is impossible to do only one thing.” So-called side effects of 123

The regulation of the complex network of biochemical reactions inside cells only began to be understood when cybernetic mechanisms such as end-product inhibition and gene repression became known (Monod 1972). 124 Note #7 Networks, p. 317 125 Note #91 Scale-free networks, p. 450

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actions are unavoidable and are different from main effects only in being unintended. Speaking of “side effects” suggests that such additional effects can be avoided, but this is rarely true. Multiple effects are the rule, and single effects the exception. Because one cannot do only one thing, and because knowledge is never completely adequate to reality, every action produces unintended or unanticipated consequences. A rich exploration of unintended consequences of the adoption of various technologies is offered by Tenner (1996). Some unintended consequences may even be counterintuitive, 126 a testimony to the limits of our intuition; among these, some effects may be the opposite of what is intended. 4. Global causality. Causality is often not local. Explanations of the form, “For want of a nail … an empire was lost” or “The power grid crashed because this particular circuit breaker failed,” ignore the global facts that the empire depended critically on one battle and this battle on one rider, and that the structure of the power grid allowed point disruptions to spread rapidly through the network. A small cause can only have a large effect if the cause operates within a highly organized cotext, one that includes high ordinality, nonlinear, and/or feedback relations. In reality, “the cause” includes the sensitivity and vulnerability of the entire system. This perspective is salient in self-organized criticality. 127 5. Necessity and chance. Traditionally, causation is associated with ontological determinism – the view of Spinoza and Einstein – with stochasticity (the absence of determinism) assumed to be epistemological, the result of imperfect knowledge. However, stochasticity is ubiquitous in the natural and social sciences, and many complex phenomena involve both chance and necessity (Monod 1972), not merely one or the other. Chaos exhibits both determinism and pseudo-randomness 126

Note #59 Multiplication of effects, p. 411, Note #61 Counterintuitive effects, p. 413 127 Notes #149 Connectedness for good and ill, p. 551, and #150 Selforganized criticality, p. 551

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(but not true stochasticity), and “edge of chaos” 128 phenomena also combine deterministic order and disorder. Stochasticity may be inherent in the open-endedness of structure and function or derive from spontaneous symmetry-breaking. There is no reason to regard stochasticity as acausal; probabilities can be as caused as certainties. Stochasticity is joined to determinism even in foundational theory (quantum mechanics) in physics. 6. A coarse-grained view of the whole. Another idea associated both with complexity and holism is the value of conceptualizing the whole (Gell-Mann 1994). Ideally, one would include in a model all elements and relations that pertain to the phenomenon, but this is rarely possible. However, a finegrained model that only samples the elements and relations may be qualitatively wrong. For example, some properties of graphs depend on the full set of nodes and links. Or, if a model is inclusive, it may be too complex to understand. This is known as the “monster-monster” effect: If reality is monstrously complex, a model faithful to reality will also be monstrous, and little is gained by modeling. Given that a description of parts of a system will likely be inadequate, a holistic perspective strives to grasp at least a coarse approximation of the whole. It is better for a view of the whole to be explicit and subject to refinement than remain implicit and unexamined. For example, consider a fine-grained dynamic model of an economy, or one of its sectors, with 100s or 1000s of variables and interactions. However big such a model might be, it will still be incomplete. If the missing variables and interactions are critical or if its behavior is not robust to parameter values, not only will the detailed dynamics of the model be unreliable, but its emergent qualitative behavior will be unreliable as well. Its very complexity may prevent it from yielding useful insights. In contrast, a simple model, with only a few aggregated variables, may be more illuminating. On the other hand, fine-grained models connect more easily to data, and this may more than 128

Note #17 Chaos, p. 338

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compensate for the model’s complexity. In general, comparing two models of different complexities is difficult. For example, it is not clear how to compare Forrester’s (1961) system dynamics model of business cycles with Zeeman’s (1977) simple cusp catastrophe model. 129 Choosing between coarseand fine-grained models requires trade-offs between accuracy and parsimony. It is easier to compare models having comparable complexity. 7. Multiple levels. Most simply, level is scale, defined in space-time. A coarse-grained view of the whole often requires a multi-scale 130 analysis, rather than analysis at one or two scales. A one-scale analysis is exemplified by the Voltera-Lottka preypredator model; one might add levels that specify the food of the prey and factors affecting its availability. Holistic views of ecosystems consider multiple scales of space-time (Allen and Starr 1982; Holling and Gunderson 2002). The multi-scale aspects of weather are reflected in the “butterfly effect,” wherein a small local change – a butterfly flapping its wings – may generate a large effect far away via the nonlinearity of chaotic dynamics. Where levels are insulated from one another (Simon 1962), each level is a whole unto itself, but where level coupling is strong, wholes are inherently multi-scale. Causality occurs at all levels. A systems perspective rejects the restriction of causation to the lowest level of analysis, which is the hallmark of physicalist reductionism. It is absurd to hold that, if a lion eats an antelope, the death of the antelope is ultimately really explained by reference to quarks. The reductionist might respond by insisting on a distinction between reality and its explanation, but this ignores the fact that effective epistemology should carve nature at its ontological joints. Some philosophical positions on mereology (the relation between parts and wholes) are more extreme than reductionism. The 129

Zeeman’s paper concerns cycles in financial markets, but could be adapted to other boom-bust economic cycles. 130 Note #15 Scale, p. 335

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mereological “nihilist” denies the very existence of composites, i.e., systems. The equally absurd opposite position of “universalism” affirms the existence of all imaginable composites. So much for pure or even exact metaphysics. But an exact and scientific metaphysics avoids these extremes and opts for “restricted composition” which asserts that only some composites can be meaningfully said to exist (Zwick 2014). Modeling high-level phenomena only in terms of low-level elements and relations does not eliminate the need to actually understand intermediate-level emergents. For example, hoping to understand the brain by modeling Hodgkin-Huxley dynamics – or simpler representations – of very many neurons, without adequate theories of memory, cognition, emotion, etc., is sheer folly. Modeling that ignores the qualitative properties of intermediate levels has dubious value. 131 A notion of level related to scale arises from the basic definition of system which is recursive. A system is a set of elements and relations between elements, and the system is an element in a higher-level order. 132 This type of hierarchy is mereological, i.e., defined by composition or decomposition, and a speculative approach to such hierarchies is offered in Diachronics. 133 Some other types of hierarchy discussed in this book are listed below. It is important not to confuse one type of hierarchy with another.

131

There are, for example, forest infestation models that model individual trees; but just because this can be done computationally does not mean that modeling at this micro-scale will yield correct and useful insights into forest infestations. 132 Note #1 System, p. 295, e.g., Figure 38 Hierarchy of Janus-faced systems, p. 299; Note #5 Structure, p. 308; Note #93 Three levels, p. 454, 1.1.7.2 Hierarchies, p. 451 133 Note #147 Limits of complexification, p. 544

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•

Hierarchy of scientific disciplines 134

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Hierarchy of system types 135

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Hierarchy of categories (for concrete systems) 136

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Hierarchy of categories in Synchronics 137

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Hierarchy of structure 138

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Hierarchies of pragmatics 139

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Hierarchies of catastrophes 140

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3.5 Structure, function, and history 3.5.1 Structure and function The subject of this section is the ninth entry of Table 5 namely structure/function/history. A holistic view of any phenomenon concerns not only structure, the prime focus of reductionist explanation, but also function and history. Recall, that “structure” in this book usually means the order internal to a system; “function” means the external order in which the system participates. 141 Both structure and function include dynamics, i.e., structure and function here do not mean statics and dynamics. Recall also that function here does not imply purpose. Earlier, a system was depicted as the vertex of a double

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Figure 8 Transdisciplinarity of some systems theories, p. 67 Table 8 Boulding’s hierarchy of system types, p. 156, and Table 9 Levels of autonomy and information, p. 158 136 Table 4 Some categories and systems theories, p. 97; Figure 70 Autopoiesis; additional information input, p. 394 137 5.3 Categories of complexity, p. 160 138 Figure 33 Parsons’ tetrad of social systems, p. 253; Figure 89 The modeling tetrad, p. 465 139 Table 14 Two syntactic-semantic-pragmatic hierarchies, p. 470 140 Figure 116 A hierarchy of cusp equilibria, p. 542 141 Note #35 Function, p. 370 135

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cone 142 whose projection is an X. The X expands downward (internally) into structure and upward (externally) into function; this expansion becomes less significant as the distance increases from the central vertex. To the extent that structure and function extend indefinitely, they are open-ended, although these extensions would ultimately be limited if there exists some smallest or largest possible system. For concrete systems, internal and external are spatial, but the structure-function distinction can apply also to (non-spatial) abstracted and conceptual systems. For concrete systems, standard explanation in science is oriented toward substance as opposed to form and privileges structure as opposed to function by explaining phenomena downward, i.e., internally. 143 As Kauffman (2008) notes, the reductionist view is stated plainly by the physicist Steven Weinberg: “All the explanatory arrows point downwards, from societies to people, to organs, to cells, to biochemistry, to chemistry, and ultimately to physics.” The awkward mixing here of entities and disciplines should not obscure the point that explanation is structural. Function is important but still viewed as having less ontological 144 or epistemological status. This is in accord with the following philosophical observation that views a 142

Figure 3 System as center, p. 49 In this book, the substance-form distinction is different from the structure-function distinction, but it is interesting to note that a substancefunction dyad appears in Western and (translations of) Chinese philosophical works. Substance-function might mean matter/energyinformation (assigned here to substance-form) or internal-external (assigned here to structure-function), or Spinozistic substance-mode (assigned here, approximately to element-system) or static-dynamic, unity-multiplicity, universal-unique. Relative to the terminology in this book, substancefunction is an odd recombination of substance-form and structure-function; similarly, Tillich’s (1951) dynamics-form is an odd recombination of dynamics-statics and substance-form. 144 In the doctrine of primary versus secondary qualities, primary qualities inhere in the system (are intrinsic), while (extrinsic) qualities that are contingent upon the environment (or observer) are secondary. 143

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system as a center of open-ended structure and function, but still privileges structure: What a [system] is, that is the content, is its own affair; but what it does concerns everything around it. There is no end to the repercussions of the smallest act – even the splitting of an atom. Every monad – being the form of a structure – bears within it the two-fold significance of its source. It is infinite in its external connectedness, and it is also infinite in its internal diversity. - John G. Bennett (1966) If structure is what a system is and function is only what it does, then, ontologically speaking, structure is privileged, and a system is really the lower cone of the X diagram of Figure 3 as opposed to both cones. In fact, systems thought encompasses both perspectives. Under the aspect of difference between structure and function, “is” is narrowly defined and distinguished from “does,” so system is structure, but under the aspect of similarity between structure and function, “is” is more broadly defined and includes “does,” so a system is both structure and function. The narrower conception can be called the closed systems view and the broader conception the open systems view. 145 The dominant conception in systems thought is the broader one – a system is structure and function (to which history will soon be added). The hegemony of the fundamental – really, the foundational – in the closed systems view is displaced by the priority of the central in the open systems view. Both views are necessary because structure and function must be considered under aspects of both similarity and difference. While a structural orientation explains phenomena downward, a functional orientation explains phenomena upward. Since the former is called reductionism, one might call the latter expansionism, were the term not awkward, or upward reductionism. In physical explanations, boundary conditions treat the environment as fixed and are considered arbitrary, and 145

Note #1 System, p. 295

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focus is placed on the laws governing the internal interactions. If one focused instead on explaining the hierarchy of ever-more encompassing boundary conditions, one would have an upwardoriented reductionism. Of course, by considering a larger whole, function becomes structure. From the perspective of one person, relations with family members are function, but from the perspective of the family, these relations are structure. What is structural or functional is the directionality of explanation, which depends on the scale at which the phenomenon is viewed, which in turn depends on the focal point, i.e., the vertex of the X (the system as center). This is to speak epistemologically; ontologically all focal centers are real and systems extensively overlap. In the open systems view, external relations 146 are constitutive. Along with internal relations, they define what the system is. One might argue that external relations are often contingent or insignificant, but this can be true also of internal relations. In general, internal and external relations differ in number and strength, which determine their salience. 147 For example, money – coins or bills – is constituted primarily externally and tied to information rather than matter-energy. In general, systems range from an extreme where structure is far more important than function to the extreme where function is far more important than structure. For complex systems, there may be a subset of the internal relations that is more important than the rest, an essence 148 which may specify what many of the external relations will be. For such systems, structure is more salient than function, external relations are less constitutive than 146

Note #27 External relation, p. 354 A hemoglobin molecule consisting of thousands of atoms binds and releases oxygen molecules, each having two atoms. The structural interactions (especially the covalent bonds) holding the molecule together are vastly more numerous and stronger than the functional interaction with oxygen. Here, structure is “large” and function “small,” but the oxygen molecules released are vital for the cells of the body, so function is not less important than structure. 148 Note #49 Genotype and phenotype, p. 395 147

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internal ones, and speaking about what a system is versus what it does is appropriate. But for systems in general, external relations may be as constitutive as internal ones. Note that epistemological and ontological orientations are both included in this discussion: “salience” is in the language of epistemology and “constitutiveness” is in the language of ontology. Systems thought compensates for the usual privileging of structure by giving special attention to function. This explains its affinity for the theories of ecology, which concern the external relations of organisms, not their internal structures. Note by the way that Darwin’s original theory (before being supplemented by ideas about germ- and somato-plasm and, later, by their molecular interpretations) did not explain structure, i.e., the basis for heredity and variation, but had much to say about function and history, i.e., natural selection. Darwin explained things upward. So much for Weinberg’s assertion that explanation in science is exclusively downward. In psychology, a functional orientation would focus on interpersonal relationships and de-emphasize internal (physiological or psychological) aspects. This explains why family therapy, which focuses on external relationships as opposed to internal psychodynamics, is often given a systems label even though psychodynamic theory is also systems theoretic but in a different way. 149 One of the impacts that the systems orientation has had on psychology has been to stimulate a greater interest in the environments in which individuals live, but it is still a mistake to define a systems approach as merely adding considerations of the environment. 149

Freud’s model of the psyche has systems theoretic aspects. Superego is the beachhead within the system of its environment: Through this [modeling] subsystem the environment can acquire a beachhead of control (1.1.8.3.3.) See also 7.1.8 Cognition, p. 461. The ego is the modeling subsystem at the sensitive level, centered in its direction component; the id is (generalized) energy manifesting in the modeling subsystem in its goal and instrument components.

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There is a natural affinity between systems thought and functional explanations in the social sciences. Although “function” may be interpreted as purpose, it can never be assumed that a part actually serves the interests of the whole or that the existence of the part is explained by such service. Such claims require evidence. In sociology, systems thinking was once identified with Parsonian functionalism (Parsons 1966, 1971), and due to an incorrect assumption that functionalism implies harmony some critics wrongly believed that a systems view intrinsically neglected conflict and dysfunction. 150 An orientation toward function rather than structure, and information rather than matter-energy, also characterizes Artificial Intelligence, a spin-off from early cybernetics, and Artificial Life. But just as there is affinity between systems thinking and functionalism, there is also an affinity with structuralism (Piaget 1970; Caws 1988), not surprising since structure and function are just internal and external order, respectively. Just as one can err by ignoring function, one can also err by overemphasizing function at the expense of structure. Purely functional black box input-output explanations 151 that totally ignore internal factors are wrongly taken as sufficient. In behaviorist psychology ignoring structure was a principle, improperly justified by the impossibility of observing internal mental states. The same unnecessary limitation was applied to language understood only behaviorally, as if this could be adequate for understanding meaning. Structure is sometimes implicitly assumed to be infinitely plastic and thus able to instantiate any function. Just as biological determinism is downward reductionism, the extreme privileging of structure, 150

Essay demonstrates that this conception of systems thinking is not true, but the charge has some basis in the emphasis early systems literature gave to regulation by negative feedback. Still, game theory is precisely about conflict and competition. The tendency to associate systems ideas with an assumed natural harmony persists (Capra 1996). 151 Note #27 External relation, p. 354

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the “blank slate” position – the belief in the non-existence of a human nature – is upward reductionism, an extreme privileging of function, which is equally incorrect (Pinker 2002). Both extremes – “all is nature” and “all is nurture” – are simplistic, but, unfortunately, simplistic extremes are the attractors of thought. 152 A systems approach would try to redress any imbalance and allow the relative importance of structure and function to be decided on scientific and not ideological grounds. It would also focus on the interaction of structure and function, where the challenging questions lie. For example, in human society, biological realities are embedded in socio-cultural realities, but the degree to which the latter can neutralize, shape, replace, or even reverse the former is an open question. Similarly, for individual human beings, the physiological is embedded in the psycho-social; the degree to which higher-level phenomena can neutralize, shape, replace, or even reverse lower-level ones cannot be established a priori but must be investigated empirically. The Turing Test in AI, a functional definition of intelligence, is inadequate because the understanding of intelligence needs also an internal dimension, although intelligence may not require a particular material instantiation. Contemporary cognitive science focuses primarily on function rather than structure, on “roles” rather than “realizers”; Fodor’s (1968) “mousetrap” is a paradigmatic example. This allows type (general) as distinct from token (specific) explanations of the mental. Physicalist reduction cannot encompass multiple realizability and thus misses the point, since scientific advance also requires understanding the structural bases of function. Classical economic ideas about value focus on exchange value, which is functional, de-emphasizing use value, which, relative to exchange, is structural, and also labor value, which adds the dimension of history. Thermodynamic considerations, which are 152

When the direction component of the modeling subsystem operates at the automatic level (Note #114 Self-reference, p. 487), thought gets stuck in irresolvable dyadic aporias (Summary 1.1.8 and 7.1.8, pp. 23, 491).

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structural and often the basis of use value, are also ignored. For example, a barrel of oil has an exchange value, but it also has energy/entropy aspects. In an economic equilibrium, there might be relations between exchange value, use value, and thermodynamic value, but actual markets are rarely at equilibrium, and thermodynamic realities are inadequately encompassed in market prices. In summary, explanation only through function is no less reductive and narrow than explanation only through structure. A theory that is exclusively internal or external explains less than a theory that encompasses both structure and function. As Ross (2004) argues in discussing Salmon’s bottom-up (structural) point of view and Kitcher’s top-down (functional) point of view, both must be embraced. This is the systems theory view 153 (Salmon in fact advocates it). 3.5.2 Adding history Nothing in biology makes sense except in the light of evolution. -Theodosius Dobzhansky (1973) The February revolution, like any other great event of the kind, was born of general causes fertilized, as it were, by accidents. It would be as superficial to say that it derived inevitably from general causes as to ascribe it solely to accidental ones. - Alexis de Tocqueville (1896) Even an inclusive consideration of both structure and function is insufficient. Structure and function change over time; call this “history” (the word here does not connote the discipline). It is a third kind of blindness to ignore history. 154 Holistic analysis requires considering structure and function and history. Structure and function together are “synchronics,” meaning “at the same time”; history is “diachronics,” meaning 153

Figure 3 System as center, p. 49; Note #93 Three levels, p. 454 Insistence on the importance, or the priority, of history for understanding human systems is referred to as “historicism.” Systems theory accepts the usual importance of history but not necessarily its priority.

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“at different times.” In a synchronic view, systems already exist, considered at an extended present moment. Diachronics includes development or irreversible or qualitative change in structure and/or function; this is depicted in Figure 19(a). Figure 19 Structure, function, and history S = structure; F = function; H = history (a) structure-function changing in time (the later time is shown as a prime); (b) cyclicity of structure, function, history

F space

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Gerard (1958) advocated use of the triad of being (structure), behaving (function), and becoming (history): Synchronics includes the first and second, diachronics the third. Structure (being) is the basis of function (behaving), which through irreversible processes generates history (becoming), leaving structure as residue; this cycle is shown in Figure 19(b). The flow shown in this figure assumes a minimal conception of synchronics; for greater generality, it needs to be supplemented with an arrow that feeds back from function to structure. Synchronics includes phenomena stationary in time, shortterm quantitative change, i.e., reversible dynamics. It excludes long-term change that is qualitative and irreversible, e.g., origin, development, transformation, dissolution, which are the subjects of diachronics. This is relative to some time-scale. A periodic phenomenon without long-term tendencies and considered over many periods is synchronics, but over a smaller time interval, less than a period, is diachronics.

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Without history, understanding structure and function may be difficult. This is illustrated by the critical role that evolutionary explanation has in biology, despite the availability of only limited evidence about the past. (Evolutionary theory is actually not purely historical, but really functional-historical. 155) In geology and cosmology, historical explanation is also central. 156 In psychoanalysis, history, i.e., the earliest experiences of childhood, is similarly critical. Ideally, one wants structural, functional, and historical views to be integrated, but to the extent that these views are very different, their integration may be difficult. Dupré (1993) notes that there are three different concepts of species in biology: the morphological (how organisms are similar or different in their features), the biological-ecological (whether organisms can mate with one another and the niches that they occupy), and the phylogenetic (their evolutionary lineages). These concepts are structural, functional, and historical, respectively, and do not fully coincide; all three are necessary. Similarly, structural and functional understandings of disease require supplementation by evolutionary perspectives (Nesse and Williams 1998). Another illustration of the importance of using structure and function and history to define a system is the controversy over the planetary status of Pluto. To resolve this controversy the International Astronomical Union (2006) set out three conditions for an astronomical object to be called a planet: (1) It 155

Evolutionary fitness (a type of utility) is functional-historical, although it is assigned to an organism or genotype as if it were an internal property. Darwinian theory’s silence about “internal factors in evolution” (Whyte 1965) made it anomalous among scientific theories. The theory needed to be augmented – which it finally was in neo-Darwinism – by structural knowledge from genetics and molecular biology. Without a structural component, evolutionary theory would in effect assume that organisms are indefinitely malleable, but internal structure, a residue of the evolutionary past, constrains the future and limits plasticity. 156 Some other examples, outside of the natural sciences, of a focus on historical explanation are Hegel’s dialectic, Marx’s historical materialism, Nietzsche’s genealogical method, and Foucault’s archaeological method.

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must be massive enough that its gravity makes it spherical – a structural consideration; (2) it must orbit the sun –a functional consideration; (3) it must have “cleared the neighborhood around its orbit” – a historical consideration about planetary formation. The salient qualitative changes of systems are formation, growth and development, maturation, and dissolution, so the dyad of synchronics and diachronics is connected to the categories of creation, destruction, and maintenance 157 (Figure 20). Synchronics is maintenance, and diachronics is creation and destruction, i.e., formation and dissolution. Figure 20 Creation, Destruction, Maintenance

creation

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If the structure-function-history triad of Figure 19(b) and the creation-maintenance-destruction triad of Figure 20 are superposed, the resulting hexad (Figure 21) has the following interpretation. The relation between structure and function is maintenance; the relation between function and history is destruction (e.g., selection in biological evolution); the relation between history and structure is creation, the genesis of new structures. 158 157

A Hindu triad of divinity: Brahma, Shiva, Vishnu; see also Footnote #188, p. 145, about aspects of destruction. 158 This mode of interpretation, where terms of one triad relate pairs of terms of the other triad, is borrowed from Rosenzweig (1921), who

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Figure 21 Hexad of synchronics and diachronics Mixed triads, e.g., {history, creation, structure} are dashed. .

history

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maintenance It may not be obvious that scientific understanding based on structure and function can be supplemented by considerations of history. History, especially the study of human history, has long been viewed as the domain of the idiographic, i.e., the contingent and unique, in contrast to science, the domain of the nomothetic, the lawful and universal. Even where historical issues are addressed in science, the goal has been to encompass explanation within the context of scientific law. Questions of history, especially about origins 159 (of the universe, galaxies, solar systems, life, the human species, etc.), are notoriously difficult. But in recent years, systems theories 160 such as nonlinear dynamics, non-equilibrium thermodynamics, and generalized evolution have opened up new possibilities for the scientific modeling of history. In these theories, time is different from the way it is viewed in physics, where the reversibility of fundamental processes (in Newtonian physics conceptualized a hexad of two interlocking religious-philosophical triads: God-World-Human and Creation-Revelation-Redemption. The relation between God and World is Creation; between God and Human is Revelation; between Human and World is Redemption. For a systems theoretic discussion of Rosenzweig’s hexad, see Zwick (2020). This hexad has no apparent relation to Bennett’s hexad discussed in 5.3 Categories of complexity, p. 160. 159 Note #120 System formation, p. 496 160 Figure 8 Transdisciplinarity of some systems theories, p. 67

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and also in quantum mechanics) seems to imply that the directionality of time is illusory. In these theories, time is directional as it is on the human scale; “frozen accidents” (GellMann 1994) exhibit both randomness and determinism. In both nonlinear dynamics and non-equilibrium thermodynamics, there is a fusion of the idiographic and the nomothetic, the contingent and the necessary. 161 Initial conditions, internal fluctuations, or external changes may be arbitrary or random, but subsequent unfolding is at least partially lawful. The arbitrary and random are accommodated within these theories. History, and fusion of the random and lawful, is also addressed by evolutionary models involving replication, variation, and selection that have been developed for diverse phenomena. Such models have been applied to the immune system (Cziko 1995) and to neural systems (Edelman 1987). They have been used metaphorically in the social sciences and have generated new scientific and mathematical methods such as wetware syntheses of molecules and evolutionary computation. 162 It was von Bertalanffy’s (1968) conviction that the tendency in the study of human history to dismiss scientific models is in part a reaction against the simplicity of common diachronic models, such as linear change (e.g., progress), cyclicity, life cycle models, and random drift. Systems models, such as those from nonlinear dynamics, non-equilibrium thermodynamics, and generalized evolution, are more complex than these. Von Bertalanffy hoped that systems theories might thus facilitate the modeling of history. Though events never repeat exactly, they repeat in some sense; otherwise they would be utterly incomprehensible. This is in fact the position of the nomothetic camp, whose adherents do not totally deny historical uniqueness. By contrast, there are many historians who take the 161

See Notes #129 History: idiographic or nomothetic, p. 516, and #150 Self-organized criticality, p. 551. 162 Note #70 Optimization, p. 423

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extreme idiographic position, exaggerating the requirements of scientific explanation and denying the feasibility of diachronic social science. They assume that lawfulness means determinism and predictability, ignoring the fact that probabilistic models are common in science and the fact, shown by chaos, that the absence of predictability does not imply the absence of law. The sciences can take up issues of history, and the discipline of human history can benefit from sophisticated theories already in use in the social sciences. Although historians have largely been unreceptive to macro-theories about large-scale societal change, for example, the theories of Spengler, Marx, and Toynbee, this has changed somewhat recently with the renewed interest in world history and “big history” (McNeil and McNeill 2003; Christian 2004), but the mathematical tools used by historians have not yet markedly changed. Chapter 5 below 163 offers a macro-model of human history as a framework for discussing some scientific, religious, and political implications of the systems program. It draws on ideas about dynamics (feedback, catastrophes), hierarchy, and computational complexity. Though this model does not yet qualify as a successful realization of von Bertalanffy’s hope, since it is mainly conceptual and not yet formal, it is still more complex than most historical models. In summary: to overemphasize structure as reductionists do (or function or history 164) is – using the words of William Blake 165 – to have “single vision.” To see structure and function (or function and history) is double vision. Only the triple vision of structure, function, and history sufficiently widens perception to allow adequate understanding of many phenomena. 163

6.1 A macro-historical model, p. 193 One should also not exaggerate the importance of purely functional or purely historical considerations; see the end of 3.5.1 Structure and function, p. 109, on the former error, and 6.2.2 Understanding what we know, p. 210, on the latter error. 165 Blake (1802) criticized Newton’s physics as a “single vision,” impoverished compared to his “four-fold vision.” 164

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Chapter 4 Related fields 4.1 Not just mathematics 4.2 The relevance of physics 4.3 The centrality of biology 4.4 Sciences of the artificial 4.5 Systems theory and systems analysis

123 130 135 139 141

4.1 Not just mathematics Systems theories focus on form rather than substance. So does mathematics. Systems theories are transdisciplinary. So is mathematics. Systems theories are arrived at deductively from formal systems or inductively via isomorphisms, which are mathematical similarities. So why are systems theories not simply mathematics? How is an “exact and scientific metaphysics” different from mathematics? There are at least five inter-related responses to this challenge; these are listed in Table 6, and the last of them sums up the others. Table 6 Systems theories are not simply mathematics 1. 2. 3. 4. 5.

They focus on form that is ubiquitous and important, not merely logically possible. They are organized around phenomena and not formalisms. They extensively use simulations and do not impose a demand for proofs. They are often, especially in the social sciences, not mathematical at all. Collectively, they differ from mathematics in scope and ambition.

First, isomorphisms are mathematical similarities, but the study of form in the world, divorced from material embodiment, is not what is conventionally defined as mathematics. Systems theories are concerned not with the set of forms that logically can exist, which is the domain of mathematics, but with the © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_4

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subset of forms that actually exist, and that not only exist but are ubiquitous, and are not only ubiquitous but also important for us. Recall that it was suggested above that systems theories could be viewed as the intersection 166 of mathematics, scientific theories, and philosophy. Only some aspects of mathematics are relevant to the systems project, namely those that bear significantly on our view of the world. Knot theory, for example, has applications to elementary particle theory in physics and to analysis of certain DNA structures, but from the systems perspective, these applications are few and unrelated. However, to the degree that knot theory is important to the theory of dynamic systems, it is of considerable interest to the systems project, because dynamic systems are ubiquitous and important. Second, the mathematical forms used in systems theories are organized by the phenomena 167 (self-organization, metabolism, replication, morphogenesis, learning, evolution, etc.) modeled with these forms, without regard to the location of these forms within the intellectual edifice of basic or applied mathematics. For example, generalized metabolism can be modeled with differential equations or automata or graphs or the λ-calculus. Being centered in phenomena rather than formalisms, systems theories differ from mathematics, even from applied mathematics, which is organized around formalisms and is indifferent to the phenomena to which these formalisms might be relevant. Third, mathematics is centered on proofs, but systems theories and models, when arrived at inductively, are not. Systems research often involves computer simulations, the robustness of whose conclusions may be uncertain. Results may be displayed graphically, with pictures offered instead of proofs. This, for example, characterizes much research on chaos. Systems theorists are not afraid to study problems which 166 167

Figure 9 Intersection of math, philosophy, scientific theories, p. 67 Table 2 Some general phenomena (systems themes), p. 71

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mathematicians are disinclined to consider because proofs are hard to discover. In fact, one might even say that systems researchers eagerly seek out such problems; the difficulty, even impossibility, of proofs might even be one definition of complexity. Systems research is often a kind of “experimental mathematics,” with the computer as experimental instrument. This is what Wolfram (2002) means by a “new kind of science.” Indeed, the chaos-complexity revitalization of the systems project was made possible by the increased use of computer simulation, rather than mathematical derivation, to explore theoretical ideas. Systems research often does not have the rigor to qualify as mathematics, but this research aims at a different goal for which exactness is not the sole virtue. Fourth, a significant part of the systems literature is not mathematical at all, or, one should say, not yet mathematical. Indeed, all grand theory in the social sciences is systems theoretic, and nearly all is non-mathematical; this is exemplified by the work of the sociologists Parsons (1966, 1971) and Luhmann (1982). What is not exact may be rich and subtle, perhaps precisely by being expressed in natural language, although natural language also has the possibility of exactness, as analytic philosophers have demonstrated. Premature insistence upon mathematical formulation would drastically limit a scientific metaphysics. In the development of systems theories, core insights have often been expressed verbally well before they were formalized. 168 168

Angyal’s (1939) description of the insufficiency of dyadic relations as a basis of systemic organization was an early recognition of the importance of hypergraphs, later exploited by reconstructability analysis (Zwick 2004). Maruyama (1963) noted the insufficiency of Shannon’s information theory to describe information stored in procedures (metaphorically, recipes) rather than blueprints – in process rather than state descriptions (Simon 1981) – before the development of algorithmic information theory by Kolmogorov(1965) and Chaitin (1975). Von Bertalanffy (1968) pointed out the need in biology for a thermodynamics of open systems well before Prigogine (1961) and other workers developed such a thermodynamics.

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Nevertheless, mathematical formulation remains the sine qua non of a mature systems theory. Although there will always be important insights into reality that can be captured only in words, we can also be certain that many phenomena that now elude mathematics will become amenable to formal treatment as mathematics expands. There are no important ideas that are intrinsically and permanently beyond the possibility of mathematical treatment. To be convinced of this, just note the range of phenomena now dealt with in systems theories. The amorphous quality of natural formations such as clouds, mountains, and coastlines yields to fractal description, the inherent imprecision in categorization to fuzzy set theory, the interdependence of qualitative and quantitative change to catastrophe theory, the inherent unpredictability of some deterministic phenomena to chaos theory, etc. It is often incorrectly assumed that mathematical description must involve continuous variables that change according to linear differential equations. Such descriptions are salient in physics, but they do not exhaust the repertoire of mathematics. Mathematics is not inherently quantitative; it is inherently exact, i.e., precise. 169 For example, topological notions are precise, but do not depend on a metric. Many phenomena, especially those studied in the social sciences, are qualitative but can be analyzed by the mathematics of nominal variables. Nominal variables are more general than ordinal, interval, and ratio variables, and thus nominal variable analysis – using set theory, graph theory, and information theory – has special status in systems research. To model changes in nominal variables, time must be treated as discrete rather than continuous, because qualitative variables cannot change continuously. This accords with Whitehead’s 169

Mathematics is precise, yet fuzzy set theory and related formalisms are part of mathematics, and important parts of systems theory. Sometimes, however, the “fuzzy” label generates confusion. It suggests a mathematics that is imprecise, but fuzzy mathematics is as precise as crisp mathematics. Imprecision is a property of linguistic terms, which fuzzy mathematics renders precise. See Note #25 Fuzziness, p. 352.

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“temporal atomicity” (Ford 1984). It also justifies the significance attached by Wolfram (2002) to automata-theoretic dynamics. Fifth, systems theories are less abstract than mathematics. 170 Their goal is collectively to constitute an “exact and scientific metaphysics.” Mathematics is only one aspect of this goal, and only some mathematics is relevant to it. Mathematics is constrained by the requirement of internal coherence but not also by any requirement of external correspondence; it is generative in a very different sense than metaphysics. Mathematics is not explicitly concerned with ontology and epistemology. Exactness is necessary but not sufficient for a scientific metaphysics. Systems theories are thus transdisciplinary in a way that is different from (but also similar to) the way mathematics is transdisciplinary. Some additional insights into this difference can be gained from the following historical fantasy. Imagine that the Pythagoreans had triumphed over the Democriteans (atomists) in determining the organization of scientific knowledge. Imagine that universities housed, instead of departments of physics, biology, economics, etc., departments of order and disorder, dynamics, competition and cooperation, information processing, and the like. There would be many who would bemoan the fragmentation of knowledge and would seek to rectify this situation in interdisciplinary departments like information dynamics, dynamical competition and cooperation, etc. These hybrid disciplines would still be inadequate to unify scientific knowledge, so in this alternative world there would arise a movement dedicated to a new project called “object theory,” that would integrate knowledge around the notion of different kinds of objects: physical objects, chemical objects, biological objects, and so on (Figure 22).

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Figure 6 Between math/philosophy and scientific theories, p. 64

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Figure 22 Object theory in a Pythagorean university (a) Pythagorean university in alternative world; (b) Democritean university in the present world

(a) Materiality Object theory Theories of self-organization, competition/cooperation, etc. (b) Mathematics Systems theory Theories in physics, chemistry, biology, etc. Many, however, would argue that object theory is simply the subject of the already existing and very large department of materiality, important in the university because of its service courses, which explain the similarities and differences between order and disorder in solar systems and psyches, between competition and cooperation in commodity markets and nations, etc., these explanations being based in the common ground – materiality – uniting all of the disciplines. Hopelessly challenging the unassailable position of the field of materiality, the queen of the sciences, the object theorists would argue that materiality was too general to unify the sciences and would insist that an epistemological niche existed for some field intermediate between the highly abstract areas of order and disorder, dynamics, competition and cooperation, etc., and the completely grounded field of materiality. But the organizational framework of university life would be too entrenched for object theory to gain any foothold as a recognized academic field, and teaching and research programs based in this doctrine would eventually disappear or be forced to serve alien agendas.

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At the risk of belaboring the obvious: this is the mirror image of the current organization of scientific knowledge, and its relation to mathematics and systems theories. In the imaginary academic world invoked above, the fields of organization, dynamics, information processing, etc., would share the common language of materiality, but this language would be too concrete to unify these fields. While the interdisciplinary notion of “object” might successfully integrate the phenomenon-based disciplines in this world, this question would arise: how exactly is object theory is different from the well-articulated discipline of materiality? This mirrors the situation in which the systems project finds itself today. In the existing academic world, physics, chemistry, etc. share the common language of mathematics, but this language is too abstract to unify these fields. While the interdisciplinary notion of “system” promotes such integration, systems research is continually challenged with the question of how it differs from mathematics. Obviously it is deeply connected with mathematics, but as explained above the differences between the systems project and the mathematical enterprise are both definite and multiple. Finally, it is interesting to note that there is a part of mathematics – category theory – whose relation to the rest of mathematics resembles the relation that systems theories have to theories in the sciences. Category theory focuses on isomorphisms between different formalisms within mathematics and might thus be considered a systems theory for (within) mathematics. Being more abstract than what it represents, it is regarded by some as fundamental for mathematics, competing for this role with set theory. So it might be pictured above the rest of mathematics, just as systems theories are displayed above scientific theories (to seek fundamentals in the Platonic world of forms one goes higher, not lower). Category theory might perhaps be taken as fundamental for systems theories, competing with graph theory and set theory.

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4.2 The relevance of physics It is argued above that the traditional view that physics is the foundational science to which all other sciences 171 are reducible privileges substance over form and is relevant only to concrete systems and not also to abstracted and conceptual systems. In contrast to this, the systems project has been presented as rejecting reductionism and the primacy of substance, focusing instead on holism and complexity and the primacy of form. This argument needs qualification. The relationship between physics and the systems project is more complex than this. 4.2.1 Thermodynamics and statistical mechanics Physics is not only concerned with reduction via substance. Although particle physics, which is about foundational levels of materiality, is motivated by the program of reduction and is thus of interest only to physics, the discipline of physics is about more than elementary particles. In thermodynamics, it offers a general theory that does not depend on the materiality of the phenomena to which it is applied. Weinberg (2002) regards thermodynamics 172 as one of a number of “free-floating theories ... applicable in a wide (though not unlimited) variety of very different contexts.” He illustrates his conception of such theories – here these are called systems theories – with chaos, thermodynamics, and symmetry-breaking. He writes, “Thermodynamics, the science of heat, is a less trendy example. Concepts of thermodynamics like temperature and entropy are applicable to black holes as well as to steam boilers.” Both of these applications are within physics, but applications in chemistry and biology, such as biochemical reactions and energy flows in ecosystems, can also be added. 171

Sometimes other sciences are called “special sciences,” a euphemism that avoids the blatant disrespect for them expressed by Rutherford, who said (Birks 1962) that “All science is either physics or stamp collecting.” 172 It is included in Figure 8 Transdisciplinarity of some systems theories, p. 67.

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While an elementary particle theory applies to chemical or biological systems only reductively and thus only in principle, thermodynamics applies directly. Thermodynamics is not normally seen as a theory of everything, but it applies to all concrete systems and is thus important to all the natural sciences. Thermodynamics is irrelevant to the social sciences insofar as they treat human systems as abstracted systems and use “energy” only as metaphor. However, in the contemporary world there is every reason for these sciences – especially economics – to consider the material aspects of human societies (Georgescu-Roegen 1976; Rifkin 1980) and model them as concrete systems. To grasp the idea (Adams 1975) that the flow of energy through a society organizes it and that technology accelerates this flow and allows it to support increasingly complex social structures, a social scientist needs to know some thermodynamics. How energy flows organize ecosystems, economies, and the biosphere as a whole is knowledge essential to the social sciences. The relevance of thermodynamics to the systems project extends to the more abstract concerns of this project. Thermodynamics explicitly addresses the twin themes of systems metaphysics, namely order vs. disorder and systemenvironment interactions. It concerns relations between order and energy, transformations of energy, and transfers of energy between system and environment. These are very general phenomena. Central to thermodynamics is the Second Law, whose significance for science was compared by Snow (1959) to the significance of Shakespeare for the humanities. Although conclusions from the thermodynamics of isolated systems have sometimes been improperly generalized to systems that are not isolated, 173 recent developments in non-equilibrium and open173

A fascination with the ineluctable increase of entropy proclaimed by the Second Law was part of a 19th-century pessimistic zeitgeist. However, the Second Law applies only to the matter-energy aspects of isolated systems, so application of this Law to social systems is metaphor; moreover, social

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system thermodynamics have provided necessary correctives (and new sources of confusion). The work of Prigogine (1980) and collaborators has shown that the entropic processes about which the Second Law speaks not only describe the increase of disorder in isolated systems but also the increase in order in certain open systems far from equilibrium. This thermodynamics of open systems far from equilibrium is of special significance to systems research. Statistical mechanics, closely related to thermodynamics, is similarly important for the systems project. 174 Entropy in statistical mechanics is deeply connected with entropy (which means uncertainty) in Shannon’s information theory. 175 Statistical mechanics has been applied to phenomena that do not involve energy transactions; any conserved quantity can play the role of “energy” in the formalism. For example, the simulated annealing 176 optimization algorithm uses this formalism and includes analogs of energy, temperature, specific heat, etc., despite the fact that the subject matter to which this algorithm is applied need not be physical (a concrete system). Statistical mechanics has also been applied to the social sciences in other ways. The study of phase transitions in statistical mechanics has led to the discovery of “universality,” in which systems with radically different micro-properties are similar near phase transitions in some (but not all) of their macro-properties. Universality has been reported in the dynamics of networks and in multi-agent simulations.

systems are not isolated and are far from equilibrium. Assertions about the thermodynamic status of the entire universe are extremely speculative. 174 It could be added to Figure 8 Transdisciplinarity of some systems theories, p. 67, or its inclusion might be considered already implied by thermodynamics. 175 Note #14 Entropy, p. 334 176 Note #70 Optimization, p. 423

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4.2.2 Quantum mechanics Just as the scope of thermodynamics and statistical mechanics is different in kind from the scope of elementary particle theories, so too is it different in kind from the scope of quantum theory. Although any concrete system phenomenon can in principle be described by quantum mechanics, for most phenomena, such description is impossible. Nicolescu (1998) puzzles over the fact that systems theorists tend to ignore quantum mechanics and regards this as a blindness. It isn’t. What is foundational for physics is only of marginal interest to the systems project. Generality via reduction is very different from generality via isomorphism. Quantum theory might, however, be relevant to the systems project in some non-reductionist ways. For example, in quantum mechanics, observing a system affects it; this is also true of social systems. The complementarity in quantum mechanics of certain pairs of properties might be said to reflect a ubiquitous property of systems. Also, quantum measurement implies that entities are not defined strictly internally (by structure), but are partially constituted by their interaction with their environments (by function). And the phenomenon of entanglement, which arises from the non-locality of quantum interactions, exemplifies the systems principle that holism implies the existence of non-decomposable relations. 177 These arguments are not compelling. Such invocations of quantum theory are metaphorical, and the metaphors are limited and inexact. There are no analogs in other scientific disciplines to Planck’s constant, wave functions, Schrödinger’s equation, or matrix mechanics. Issues of self-reference are extensively discussed in the literature of Second Order Cybernetics, the cybernetics of observing systems (von Foerster 1981), and quantum theory is irrelevant to these discussions. One does not need quantum mechanics to argue that complementarity is a ubiquitous property of systems, or that the external interactions 177

3.4 Aspects of complexity and holism, p. 100

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of a system partially constitute it. Cross-level isomorphisms do not have as their basis the existence of an underlying quantum reality. 4.2.3 Other theories in physics Similar arguments discount the relevance to the systems project of special relativity, which is inextricably tied to the velocity of light. The idea, associated with relativity, that alternative representations of the same system may radically differ, is already well established in the systems literature on other grounds (Ashby 1976). In general, any theory dependent on constants that have physical units, like Planck’s constant or the velocity of light, can be relevant to systems theory only if it has a generalization that omits these constants. A paradigmatic example is information theory, in which Shannon entropy, a measure of uncertainty, omits Boltzmann’s constant – and thus physical units – from the expression for entropy in statistical mechanics. The nonphysical character of Shannon entropy makes it possible for information theory to apply to abstracted and conceptual systems. Though it is conceivable that similar generalizations might be developed for other theories, there is no systems theory comparable to information theory that offers an abstract notion of energy that has no physical units and that is widely applicable to abstracted systems, although, as noted above, statistical mechanics might perhaps be viewed as such a theory. 178 A constant in a systems theory should be dimensionless, as is, for example, Feigenbaum’s constant in chaos theory. In this sense, (some) systems theories are just mathematics. There are other systems theories besides thermodynamics and statistical mechanics that derive from physics. Nonlinear dynamics (chaos theory) was largely developed because of its importance to fluid mechanics, but it is more mathematics than 178

Statistical mechanics does not, however, accomplish a generalization of energy that provides a rigorous version of old and potentially still valuable metaphors of “vital energy” and “psychic energy.”

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physics and is inherently stuff-free, more so than thermodynamics. As Kellert (1993) notes, “...chaos theory introduces no new postulates about the physical world at all.” The current interest in complex systems owes much to the discovery of chaos. The study of cellular automata, another complex systems research area, was also largely developed within physics. One might consider Lagrangian or Hamiltonianbased generalized mechanics (Goldstein 1959) to be a systems theory, and quantum computing and quantum information theory may yet become relevant to systems research. Finally, physics also prominently includes the very general principles of symmetry and symmetry-breaking. These principles, taken philosophically, underlie this book’s insistence on looking at things under both an aspect of similarity and an aspect of difference, on conceiving a fundamental at the top as well as the bottom, and on the salience of both terms in any dyadic symbolic structure. Series and perturbation expansions, widely used in mathematical physics, are also here 179 transformed and appropriated for philosophical use. 4.3 The centrality of biology Biology is the domain of the utterly complex. - Walter Elsasser (1966) An ontological appreciation of the organism would close the gap that separates the self-awareness of the soul from the knowledge of physics. - Hans Jonas (Wolin 2001) It is difficult to challenge the primacy of physics in our scientific worldview. Physics is about fundamentals, and the fundamental is compelling. But if there is to be a metaphysics that integrates scientific knowledge from many fields, an alternative orientation is required. If the organizing principle of the fundamental is to be rejected, something must take its place. What the systems project offers instead of the fundamental is the 179

5.3 Categories of complexity, p. 160

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central, which can be interpreted in terms of the idea of system 180 or in terms of the hierarchy of scientific disciplines. 181 Physics, being foundational, is at the base of this hierarchy. Biology is central, lying above chemistry and physics but below psychology and the social sciences. Biology, Elsasser notes, is the domain of the complex. We are more interested in the very complex than the very small or large or the very fast or slow. It is in biology that information 182 and utility emerge as essential categories, and function and history gain equal status with structure. A metaphysics not only centered in biology but also capable of encompassing social systems without indulging in physicalist reductionism, treating social systems as abstracted and not as concrete systems, is one that can offer a theory of everything that addresses the human scale. Privileging biology over physics is not a mere shift of priorities. Kauffman (2008) argues that biology is not reducible to physics. He does not mean that biological phenomena violate physical laws, and he does not deny the advances made by the reductionism of molecular biology; his argument is that in addition to downward (structural) explanation, biology also needs upward (functional) explanation and diachronic (historical) explanation, both of which are central to Darwinism. Moreover, biological phenomena could in principle be instantiated on multiple platforms. Kauffman writes:

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Figure 3 System as center, p. 49; Note #1 System, p. 295 Figure 8 Transdisciplinarity of some systems theories, p. 67 182 In biology, information is related to matter-energy in at least three ways, as shown in Figure 15 Triad of matter, energy, and information, p. 88. Figure 15(a), in which an informational domain exists above a matterenergy domain, is illustrated on the cellular level by genetic information and enzymatic catalysis and on the organismic level by nervous systems. Figure 15(b), in which information uses energy to act on matter, is exemplified on the cellular level by protein synthesis and on the organismic level by intentional behavior. Figure 15(c), in which information mediates the action of energy on matter, is illustrated by the biosphere’s receiving and transforming solar energy that reaches the earth. 181

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Darwin is completely agnostic about the physical basis of heritable variation…Since natural selection can ‘run’ on many physical realizations of life, it cannot be reduced to any necessary and sufficient set of statements about this or that set of atoms or molecules...While any one case of life and evolution is a specific realization, Darwin’s idea is not confined to that realization. Agency, which is central to life, cannot be explained only downward, and utility, a fundamental concept in biology and the social sciences, has no physical units, just as information has no physical units. It is not only function but also structure that is stuff-independent. In living systems, form is freed from dependence on a fixed base of substance (Jonas 1966, 1996): the self-construction and self-repair of biological systems are more organizational properties than material ones. 183 Form, not substance, is the essence of the organism; that is, living systems are not only concrete systems but must be understood also as abstracted systems. Because of this, generalized evolution is a systems theory,181 and Artificial Life is a systems field. Uniqueness in biology is not fully encompassed by the universality of physics since randomness, “frozen accidents” (Gell-Mann 1994), and emergence play critical roles. Although the reductionist paradigm has been powerful and fruitful, it is not adequate to biological phenomena. A scientific metaphysics centered in biology is very different from one built upon physics. A focus on biology is not anthropocentric, and properly so. To take the human being as the center of gravity for an exact and scientific metaphysics is too difficult; a compromise must be made between human significance and scientific tractability. A focus on the domain of life, intermediate between the domains of matter and mind, is such a compromise. The organism is the paradigmatic subject of investigation for systems research, though not its exclusive concern. This does 183

Note #47 Autopoiesis, p. 393

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not mean, however, a naive embrace of the organismic metaphor. Phenomena of life (metabolism, reproduction, morphogenesis, learning, etc.) are of particular interest, but the scope of systems research extends also downward to physical and chemical systems and upward to populations and ecosystems, to the human organism, and to social and cultural systems. Of particular interest are ideas that apply to multiple levels in significant ways, to abstracted as well as concrete system. This would thus exclude, for example, the physical notion of mass, which, though it applies to all concrete systems, is not illuminating for the study of human phenomena. To say that systems research focuses on theories of the organism that are applicable also to the human realm does not mean that it privileges biological explanations for social and cultural phenomena, as is done in sociobiology or in its current manifestation, evolutionary psychology. The systems project aims at something completely different from the “consilience” of Wilson (1998), which in plain language just means the reduction of the behavioral and social sciences to biology. Sometimes such reduction may be valid, but systems research emphasizes a different kind of biology-social science unity, namely one based on isomorphisms. For example, gametheoretic ideas (e.g., the Prisoner’s Dilemma model) are used both in biology and in the social sciences. These ideas are relevant to both not because people are organisms, but because competition and cooperation manifest similar patterns regardless of the entities involved. Game-theoretic ideas could apply as well to cooperating and competing robots or computer programs. No reduction is involved here at all. But a focus on isomorphisms between different kinds of systems is not the only way that systems research bears on the relationship between biology and the social sciences. Human society and culture are emergents from the biological domain, and the systems project has a strong interest in emergence. It is not accidental that the group that first articulated the idea of general systems theory included several biologists, i.e.,

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von Bertalanffy and Gerard, a mathematical psychologist, Rapoport, and a psychiatrist, Miller. Biological interests were of compelling importance to the early cyberneticians like Wiener, von Neumann, Ashby, and Bateson, and early cybernetic work joined with the new sciences of automata and computation to give rise to the field of Artificial Intelligence (AI). Contemporary systems research on complex adaptive systems focuses on the biological and social sciences and on technologies produced by social systems. The field of Artificial Life, an augmentation of the AI program, is obviously also centered in biology. Of all the scientific disciplines, it is biology that has pioneered the development of systems understanding. This is reflected in the many phenomena that have been the focus of systems research. 184 It is exemplified by the well-established field of systems ecology, in the rapid development of systems biology, and in the beginnings of a new systems medicine. By contrast, physicists and sociologists have felt no need to distinguish a systems physics or systems sociology, despite the fact that systems ideas and methods are widely used in these disciplines. 4.4 Sciences of the artificial Another scientific perspective that privileges form over substance and function over structure is Simon’s (1981) conception of the “sciences of the artificial.” These include Artificial Intelligence and Artificial Life as well as fields concerned with design, such as computer programming, engineering, architecture, and city planning. (Simon does not pursue this possibility, but literature and the arts in their design aspects might also be included.) There is some overlap between these sciences and the project of an exact and scientific metaphysics, but the enterprise Simon speaks of is basically normative: one wants to design better computer programs, 184

See, for example, the list of phenomena in Table 2 Some general phenomena (systems themes), p. 71.

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engineering artifacts, buildings, etc. By contrast, the goal of an ESM – to describe the general features of reality – is descriptive. But the descriptive/normative divide is not a sharp one, as discussion in the next section will show. Among the sciences of the artificial, Artificial Intelligence and Artificial Life (ALife) overlap strongly with the natural sciences, especially with biology. AI advances the assumption that wetware is not a precondition for intelligence. Although the intelligence of organisms naturally depends upon the material organization that sustains life, the details of this embodiment are regarded as historically contingent and not necessary. Intelligence is viewed as software, not hardware, which could in principle be skimmed off from its material substrate or instantiated in other media. This classic AI position sees intelligence as symbolic computation and matter-energy aspects of intelligence in natural systems as irrelevant. The newer connectionist (neural network) AI, which favors bottom-up rather than top-down modeling of cognitive function, is no less stuff-free in its orientation. The materiality of neurons is rarely considered relevant. 185 ALife is similar to AI in its focus on form as opposed to substance. It studies not only life as it actually exists on this planet but also life as might be synthesized in other media, as it might occur on other planets, and as it can be understood in abstractio. An ALife model of metabolism (Bagley and Farmer 1991) might thus speak of mathematical entities instead of organic molecules. Whether such models are considered to be about life depends on whether life is considered to be inextricably tied to carbon. If life inheres in the form rather than the substance of certain phenomena, then models not based in organic chemistry are legitimate approaches to theoretical biology. (It must be admitted, however, that there is no 185

In some recent models of neural networks, there is a tendency toward greater realism and detail, such as the representation of spatially distributed processes in individual neurons. This brings these models closer to nature.

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assurance that other types of materiality can in fact support the forms and processes necessary to life.) The orientation toward form as opposed to substance is illustrated in an observation made by Gleick (1988) about ALife simulations of flocking behavior in computer-generated “boids” (Reynolds 1997). Gleick noted that those studying flocking in birds and those studying schooling in fish rarely communicated with one another. Fish biologists and bird biologists rarely meet at scientific conferences, yet, flocking and schooling are similar, and both are modeled in the boid simulation. Both are phenomena of self-organization, the spontaneous emergence of higher-level order from the dynamic interactions of lower-level agents. While a biologist specializing in fish or bird behavior may not be interested in similarities of collective selforganization, this is precisely the kind of phenomenon that the systems theorist wants to study. The methodology of agentbased modeling is precisely designed for such studies. 4.5 Systems theory and systems analysis Since we cannot know all that there is to be known about anything, we ought to know a little about everything. - Blaise Pascal (1670) Beyond the project of constructing an exact and scientific metaphysics, the systems movement also includes a related enterprise that began during World War II in the use of mathematical modeling for military decision-making. This enterprise developed into Operations Research (OR), and then into systems analysis, systems engineering, management science, policy analysis, and technology management. These fields 186 are referred to here as systems analysis, and systems 186

There are a variety of other systems approaches to problem solving that might be subsumed under “systems analysis” as this label is used here, such as “soft systems methodology” and “critical systems theory” (Bausch 2001).

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theory – using the singular for simplicity – will refer to (i) general systems theory, cybernetics, and theories of complexity or complex adaptive systems, or equivalently to (ii) the multiple systems theories discussed above. This shorthand usage of systems analysis and systems theory is close to common understanding of these labels. Systems theory and systems analysis are different but overlapping projects (Figure 23). Figure 23 Systems theory and systems analysis (The sizes of the circles and of their overlap are arbitrary.)

SYSTEMS THEORY transdisciplinary theoretical synthesis; exact and scientific metaphysics

SYSTEMS ANALYSIS real-world problem solving

Systems analysis aims at problem solving in the real world of business and government. Its practical orientation differs from the academic orientation of systems theory. Systems theory aims at understanding, not intervention, and since generality is desired, theory is abstract and complexity often emerges from simple laws. By contrast, systems analysis is problem solving where problems are often assumed to be understood. Models deal not with the universal but with the unique; complexity arises from concrete detail. While systems theory is descriptive, systems analysis is normative, reflecting instrumental rationality (Mattesich 1978). Systems analysis has its own theory which concerns stages of problem solving, creativity, group process, expert opinion, implementation, decision support systems, benefit-cost analysis, etc. Despite the differences between the motivations and intellectual origins of systems theory and systems analysis, their

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literatures and professional associations have become intermingled. A striking illustration of this is the publication of Boulding’s classic article, “General Systems Theory – The Skeleton of Science” (1956), in the journal Management Science. If there was ever an essay unambiguously aimed at an exact and scientific metaphysics and not practical problem solving, it was this one, and yet at the outset, systems analysts were listening eagerly. Intermingling of systems theory and systems analysis occurred in part because it was assumed that they reflected the difference between theory and practice. This assumption is not correct: systems analysis is not the application of systems theory, despite assertions to the contrary for example by von Bertalanffy (1968), who claimed systems analysis as an application of his GST, and van Gigch, whose Applied General Systems Theory (1974) is really about systems analysis. The differences between systems theory and systems analysis are illustrated by the differences between a theoretical ecologist and an ecological resource manager, as discussed by May (1974). A theoretical ecologist is interested in models that are widely applicable and thus are simple and abstract. These models give insights into many ecosystems, but apply exactly to none. By contrast, the resource manager is interested at any time in one particular ecosystem. To be useful, a model of this ecosystem needs maximum concrete detail, but such a model will not be applicable to any other system. To the systems analyst (resource manager), a model is a means, a tool for decision-making. To the systems theorist, a model is an end, a summary of understanding that comes from applying a theory to some phenomenon. This is shown in Figure 24, which indicates that the goal of the systems theorist is to obtain a model of a phenomenon, while the goal of the systems analyst is to use a model to solve a problem. For the theorist, the model should be as simple as possible; for the analyst, it should be as realistic as necessary.

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Figure 24 Models in systems theory and systems analysis

(understanding) systems theory phenomenon

model

systems analysis (intervention) Despite these differences between systems theory and systems analysis, the distinction between the two is often missed. One frequently finds systems analysis included within systems theory. Bunge, after presenting the idea of an “exact and scientific metaphysics” as the concern of systems theory, goes on to mention the teaching of metaphysics in schools of engineering. Here he is referring to systems analysis, which can be called “metaphysical” only in a different sense. Because systems theory and systems analysis are often conflated or mistakenly viewed as having the relation of theory and practice, attacks really aimed at systems analysis (Hoos 1962, Lilienfeld 1978) have inappropriately also attacked systems theory. But differences should not be overemphasized; there are also similarities. To return to May’s distinction between resource management and theoretical ecology, a resource manager focuses at any time on a particular system, but because many systems need to be managed, systems analysis needs general problem-solving techniques. The search for universal method is not unlike the search for universal knowledge. Universality is opposed to uniqueness, concreteness, and detail. Systems theory avoids the concrete by constructing general models that apply to many systems but say little about any one. Systems analysis cannot avoid concreteness when modeling specific problems, but it downplays the importance of detail when it focuses on methodology. Insofar as methodology involves modeling and the modifications of models based on the

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results of interventions, and insofar as problems are characterized by abstract archetypes, general methodology and general theory are similar to one another. Systems theory and systems analysis also overlap in the common use of basic systems concepts and general ideas and methods of mathematical and computer modeling. Simulation tools, such as classic techniques of system dynamics and the newer agent-based methods, 187 have both academic and worldly uses. To the extent that systems theory is considered epistemology, or as researchers with engineering backgrounds might prefer, methodology, its contents are useful in systems analysis. Specific systems theories, such as game/decision theory and optimization, are also in the region of overlap. Used descriptively, they are part of systems theory; used normatively, they are part of systems analysis. Although Operations Research originated in practical wartime imperatives, its problem archetypes (e.g., allocation decisions, queueing problems) are also descriptive and ontological, as are the problem archetypes of Senge (1990) which derive from the methodology of system dynamics. Simon’s “sciences of the artificial” (1981), which include disciplines about design, are also in this overlap. In the creation-destruction-maintenance 188 triad, design is creation, problem solving is maintenance. Problem solving itself can be represented with a tetradic structure 189 deriving from Bennett’s (1966) model of purposeful activity, shown in Figure 25. A problem is a gap between an actual state (ground) and an ideal state (goal); a gap that can be 187

See Wakeland et al. (2004, 2005) for discussion and comparison of these two simulation methods. 188 Figure 20, p. 119. Destruction is spontaneous in the absence of maintenance, but many systems worthy of destruction manage to resist it, hence the importance of the tradition of critique within systems analysis. 189 This was introduced in Figure 16 Utility as a 4th fundamental category, p. 94, and used in the tetradic “action” of Talcott Parsons (6.4.2.1 The Parsonian model of social systems, p. 253). Other tetrads are listed at B.3 Triadic figures, tables, p. 617.

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reduced by practice (instrument) guided by theory (direction). Goal and ground define a vertical “axis of motivation”; direction and instrument define a horizontal “axis of operation.” A relation to the matter-energy-information-utility tetrad is easy to discern. In purposeful activity involving concrete systems, matter is ground, energy is instrument, information is direction, and utility is goal. Figure 25 Tetrad of problem solving Alternative formulations: (a) used in this book; (b) Bennett’s associations for the tetrad. 190

GOAL ideal

(a) DIRECTION theoretical

INSTRUMENT practical GROUND actual

(b) DIRECTION final cause

GOAL formal cause INSTRUMENT efficient cause GROUND material cause

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The diagram reverses Bennett’s convention of direction on the right and instrument on the left. Also, (b) shows Bennett’s associations of the tetrad with Aristotle’s causes: ground is associated with material cause, for which formal cause is the natural opposite. Alternative (a) associates ground with actual, for which ideal, in the sense of final cause, is the more natural opposite. See Note #72 Purposeful action as a tetrad, p. 426.

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Problem solving can be regarded as an objective phenomenon of interest to scientific metaphysics. If this view is taken, the normative is subsumed within the descriptive because the existence and consequences of values are facts. But priority can be reversed. Problem solving is proposed in the next chapter as an organizing principle for systems theory; if this organizing principle is adopted, the normative is prior to the descriptive, which it organizes and justifies.

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Chapter 5 The challenge of integration 5.1 No singular systems theory 5.2 Hierarchy of system types 5.3 Categories of complexity 5.4 Ontology of problems 5.5 Metaphysician’s desk manual

149 154 160 167 174

5.1 No singular systems theory In the previous chapter, systems theory was referred to in the singular rather than the plural to contrast the ESM project with the problem-solving project of systems analysis. 191 But this use of the singular is just shorthand for convenience. What is referred to is really an ensemble of systems theories, such as automata theory, information theory, game theory, and the like, as well as models and ideas that are relevant to the systems project. These theories, models, and ideas are far from being formally integrated. Whenever it appears that a comprehensive and unitary systems theory is being proposed, it covers only a restricted subject area – the books of Padulo and Arbib (1974) and Miller (1978) illustrate this. Only rare attempts have been made to integrate a sizeable body of material from the systems literature, because this literature is large and diverse, and integration presents a formidable intellectual challenge. 192 In the post-World War II period, some researchers did, however, speak of a singular “general systems theory” 193 (GST), 191

4.5 Systems theory and systems analysis, p. 141 It is interesting that attempts to give a coherent account of the systems movement have often been the work of early critics, such as Hoos (1962), Berlinski (1976), and Lilienfeld (1978), who by undertaking this daunting task – either to their chagrin or to their delight – quickly lost their outsider status. Insider books, for example, those of Casti (1995), Bar-Yam (1997, 2004), Mitchell (2009), and Mobus and Kalton (2015), have been much more successful. 193 Von Bertalanffy spoke of a “general system theory” but common usage changed “system” to “systems.” 192

© Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_5

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as if such a theory existed or could exist in the sense that information theory and game theory are individual theories. The error is repeated today in talk about a theory of complexity, as if such a theory exists now or might exist in the near future. Occasionally particular approaches to complexity have been advanced as constituting such a comprehensive theory, but even a cursory look at the diversity of the complexity literature reveals that such claims are unjustified. Just as the goal of GST was too ambitious, so too are current hopes for a complexity theory unrealistic. But collecting together systems/complexity theories and creating new ones is a reasonable project. What was meant by GST was really a research program, not an individual theory. And this research program includes not only theories, models, and ideas having explicit systems, cybernetics, or complexity identifiers, but also theories, models, and ideas of specific disciplines that do not carry such identifiers but are still general enough to be applicable to other fields 194 and to be considered contributions 195 to the exact and scientific metaphysics that is under construction. Many components for an ESM already exist, and new components are continually being added. However, since these systems theories of organization, dynamics, regulation and control, etc., have not been synthesized into a single coherent theory, they remain disjoint phenomenon-specific theories. The result is fragmentation, though of a different sort than the 194

To use an example given earlier, statistical mechanics as an extension of Newtonian mechanics is part of physics, but statistical mechanics as used outside of physics is here considered a “systems theory.” Game theory was conceived of as related to economics, but it also bears on evolutionary biology and all of the social sciences. 195 Some authors have been surprised to find their work labeled “systems theory” or “complex systems” research and have disavowed the label, for reasons best left to the sociologists of science to analyze. Such disavowals are not always credible. Herbert Simon (1962) disclaims belief in the possibility of constructing a general systems theory, but contributes to this very project. Simon’s book, The Sciences of the Artificial (1981) is now a classic of the systems literature.

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fragmentation of conventionally organized science. This unsatisfactory state of affairs was bemoaned in the fable of the Pythagorean university. 196 If the systems perspective is to offer a new and coherent way of looking at the world, some progress must be made toward integrating these theories. From a certain point of view, this situation is not troubling. Systems theories, models, and ideas might be considered to collectively define “systems science” (Klir 1991, 2002), and it is perfectly respectable for a science to contain components not well integrated with one another. Viewing systems theories as components of a science is also more appropriate than regarding them each as individual sciences. Although the chaos field was called a “new science” (Gleick 1987) and discrete automata simulation a “new kind of science” (Wolfram 2002), a more accurate assessment would identify the first of these as a systems theory (in Bunge’s terms, a generic semi-interpreted theory) and the second of these as a systems methodology and locate both of them, along with other systems and complexity theories and methodologies, within systems science. This is a reasonable way to view the systems field, especially if one wants to include the project of a “sciences of the artificial” and the related project of systems analysis. Yet a collection of components not well integrated with one another is not fully satisfactory. A science should have coherence, the more coherence the better. One might argue that automata theory, dynamic systems theory, decision theory, etc., are unified just by being mathematical. But a unity of ESM deriving only from the unity of mathematics would not be more compelling than a unity of science based on in-principle reduction of all the sciences to elementary particle physics. Integration of systems theories should be at the ESM level of abstraction, not above it. Moreover, ESM will necessarily include important non-mathematical components. One could 196

See the discussion of Figure 22 Object theory in a Pythagorean university, p. 128

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imagine a synthesis of a few formalized theories, like automata theory, information theory, and game theory. This would constitute what Ashby called the “deductive route” to systems theory. Ashby’s own Introduction to Cybernetics (1976), which integrates some ideas from specific theories at a simple mathematical level, illustrates such a synthetic effort. Klir’s Architecture of Systems Problem Solving (1985), which reflects a methodological perspective, is also a major achievement of synthesis. Bar-Yam’s (1997) text is a far-ranging and rigorous presentation of complex systems ideas in the sciences. More recently, Mitchell (2009), Mobus and Kalton (2015), and Sayama (2015) have offered major treatises that survey and integrate the systems field. Additional efforts of this sort are needed. Still, it must be acknowledged that since the systemscomplexity field is so diverse, a unitary formal theory is not a realistic goal. If constructing a theory of broad scope is too difficult, maybe the scope should be reduced. Both classical and contemporary systems research have also pursued a (slightly) more modest goal. Miller (1978), for example, tried to formulate a theory of living systems rather than a full GST. Some complexity researchers (Gell-Mann 1994; Holland 1995) speak of formulating a theory of complex adaptive systems (CAS), a goal that is less ambitious than a full theory of complexity. Studying complexity only in systems that are “adaptive,” e.g., that exhibit cognition and agency, narrows the field of study to living systems and their artifacts. Weather would not be encompassed within the domain of CAS; it is complex – nonlinear and multi-scale – but not adaptive. But even this narrower goal is too ambitious, if one wants a theory of CAS that is as rigorous as, say, information theory. And such a narrower goal omits important areas of complexity research. Work on chaos, or more generally, in nonlinear science, would not be encompassed; nor would research on networks that does not consider their adaptive role. The broader goals of systems research are essential to its original – metaphysical – goals.

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These considerations suggest that the development of an exact and scientific metaphysics needs to be done first conceptually, temporarily suspending the requirement of exactness. There is local exactness in many individual systems theories (information theory, game theory, etc.), but since there is no clear route to global exactness, integration must be done first informally. This approach has the virtues of accessibility, by being expressed in natural language, and breadth, because natural language is adequate to express the insights of most scientific theories. Striving for conceptual but not formal unity also allows inclusion of non-mathematical ideas. There are at least two different ways to approach conceptual integration. Viewing the systems field as itself a system, with its own internal structure and external function, 197 one might integrate systems theories around two different organizing principles: •

A structural organizing principle that focuses on these theories and the phenomena they address.

•

A functional organizing principle that focuses on the external (worldly) role systems theories play.

In sections that follow, both approaches are explored, with emphasis on concrete and abstracted rather than conceptual systems. The dual integration being explored is summarized in Table 7. Its structural organizing principle – ontology – is descriptive; its functional organizing principle– ethics – is normative (Figure 26).

197

A historical account of the development of the systems field is, however, not attempted, despite the fact that 3.5.2 Adding history, p. 116, argues that understanding must include a historical dimension. This is one of many incompletenesses of this book.

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Table 7 Organizing principles for integrating systems theory

Organizing principle

Structure

Function

Subject is discussed

internal unity of ESM

external use of ESM

in sections titled

5.2 Hierarchy of system types 5.3 Categories of complexity

5.4 Ontology of problems 5.5 Metaphysician’s desk manual

Figure 26 ESM organizing principles

ethics

ontology 5.2 Hierarchy of system types There are at least four possible approaches (Boulding 1956) to integrating systems theories using a structural organizing principle that focuses on their content: (1) One might seek a global theory applying to all – or nearly all – systems. (2) One might lower one’s expectations and search for a theory that applies to many systems, those most central to the systems research agenda. (3) One might construct a taxonomy of system types and develop local theories that explain their properties. (4) One might organize systems ideas in a conceptual network.

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The first two approaches focus on similarity between systems, i.e., on isomorphisms. The third, recommended by Boulding, focuses on differences between systems, on emergence. 198 The fourth 199 organizes knowledge, but does not provide a sense of the whole. A theory intended to apply to all systems – approach (1) – would develop the core ideas of “system”; 200 it would be mathematical (E) but have limited contact with scientific theories (S). It would represent the deductive route to an ESM. A theory restricted to one class of systems – approach (2) – for example, a theory of complex adaptive systems, would have a strong connection to science but modest philosophical aspirations. It would be more inductive than deductive. Approach (3) is the most ambitious of the four, because it could, at least in principle, encompass the first two. A local theory of the simplest (most general) type of system, focusing on isomorphisms, would be the global theory sought in approach (1); other local theories, focusing on emergent phenomena, would accomplish the aim of approach (2). Boulding offers a hierarchy of system types, shown in Table 8, suitable for this third approach. The hierarchy is reminiscent of the classical “great chain of being” (Lovejoy 1936). One almost expects angels and archangels to appear on this list, and, indeed, Boulding insists on a top level of “transcendental systems” to make the list open-ended. If anything in the systems literature qualifies as a “coarse-grained view of the whole” (Gell-Mann 1994), it is this list.

198

3.3 Isomorphism and emergence, p. 97 Troncale (1978); Principia Cybernetica (2002) 200 2.5 Theories and models; the idea of “system”; Note #1 System, p. 295 199

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Table 8 Boulding’s hierarchy of system types (ix) transcendental systems (viii) social organizations (e.g., systems of roles) (vii) humans (vi) animals (v) genetic-societal level (e.g., plants) (iv) self-maintaining open systems (e.g., cells) (iii) control mechanisms, cybernetic systems (e.g., thermostat) (ii) clockworks (dynamic systems) (i) frameworks (static systems) Boulding’s taxonomy is simple, perhaps even crude. One may differ with many aspects of it and be embarrassed by its boldness, 201 but it does provide an inspiration and point of departure. Beginning with static and dynamic systems seems reasonable, although the two might be merged into a single level. (But the label “clockworks” is not adequate for dynamics, since it does not include chaos.) Regarding ordinary dynamics as simpler than feedback control is appropriate, since equilibria of dynamic systems are distributed and implicit, while equilibria of control systems are local and explicit, i.e., specified informationally. 202 (But one might perhaps object to control systems as a distinct level, since these self-regulating systems only exist as parts of or as artifacts produced by more complex living systems.) Placing thermodynamically open and self-maintaining systems 203 above control systems is likewise plausible, but open systems are illustrated not only by cells, but by non-living systems such as flames or autocatalytic chemical networks 201

Boulding once observed that a general systems theorist must be willing to risk appearing ridiculous. He took the risk. 202 Note #88 Hierarchies and networks, p. 445 203 Note #42 Dissipative systems, p. 381

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(Eigen 1979). The label “self-maintaining” is ambiguous and could mean stable with respect to small perturbations (or “selforganizing”), which could be the property of any dynamic system, or it could mean autopoietic, 204 i.e., self-producing. But, pace Maturana and Varela (1980), self-producing is not synonymous with life, 205 so one should add a separate level for self-reproducing living systems, such as cells. Boulding’s hierarchy then shifts from abstractly defined categories to the old traditional typology of living things: plant, animal, human. In level (v), Boulding labels multicellular organisms as “genetic-societal,” societal in a multicellular, not populational, sense. Levels (vi) and (vii) – “animal” and “human”– are named but not characterized. One should not simply dismiss the plant-animal-human progression simply because it is so traditional or because the animal-human distinction is not fashionable, but one does need some scientific basis for such a progression. One might invoke “complexity,” but this word is neither precise nor illuminating, and the scorn it occasionally evokes is not completely undeserved. 206 Possibly the vertical dimension of Boulding’s hierarchy is more like autonomy, as opposed to heteronomy, in the Spinozistic and Kantian sense, i.e., the degree to which a system, rather than its environment, is sufficient cause of what happens to it, the degree to which it can be active with respect to its environment and not merely passive, or perhaps alternatively the degree to which it is both active and passive, where even passivity, understood here as sensitivity, augments autonomy. Spinoza 204

Note #47 Autopoiesis, p. 393. “Self-producing” means “selfconstituting/renewing/repairing.” 205 An adequate definition of life requires not only the structural aspect of autopoiesis but also certain functional (adaptive) and historical (evolutionary) properties. 206 Nicolescu (1998) offers the wry observation that in contemporary science, “nature is dead, but complexity remains.” A proper response is not to reanimate the world, i.e., to see “life” where the word does not apply, but to appreciate the scale and quality of the energies that make nature dynamic.

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(1677) linked the degree of activity and passivity to the complexity of both the internal order and external interactions of an entity. (Spinoza’s philosophy is especially systems theoretic in its recognition of the importance of both structure and function.) Boulding does not justify the hierarchy that he offers. Still, with all its deficiencies, something is captured – or hinted at – in his list. Spinoza would be pleased with it, and Lovejoy would find it familiar. Table 9 is an attempt to be slightly more explicit about autonomy. Various types of autonomy – inspired by Bennett’s (1956) hierarchy of categories (discussed in the next section) – are associated with the levels of a modified Boulding hierarchy. Self-organizing, assigned to dynamic systems, refers here to the action of dynamic attractors, though in the systems literature, this phrase often has a broader meaning. The self-adapting of plants refers to the capacities of differentiation associated with multi-cellularity. For animals, self-directing includes movement, which allows a choice of environment (although even bacteria have this capacity), and the autonomy enabled by learning. The capacities of autonomy are cumulative; every level has all the forms of autonomy of levels beneath it. Table 9 Levels of autonomy and information

Boulding level (modified) (vii) humans (vi) animals (v) plants (iv2) cells (iv1) autopoietic systems (iii) control mechanisms (ii) dynamic systems (i) static systems

Autonomy self-defining self-directing self-adapting self-reproducing self-producing self-regulating self-organizing self-stabilizing

Information neurological neurological meta-genetic genetic network control algorithmic form

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The levels in Boulding’s hierarchy might alternatively be described by the types of information that exemplify the different levels. Level (i) is information in its most general manifestation, namely form (pattern), measured in information theory by Shannon entropy 207 (Shannon and Weaver 1949) which applies to state descriptions of static and dynamic systems. Level (ii) is information in process descriptions, the subject of algorithmic information theory 208 of Kolmogorov (1965) and Chaitin (1975). At level (iii), information in control systems is concentrated and explicit, 209 while at level (iv1), selfproducing systems (e.g., flames, eddies, tornadoes) depend on distributed information implicit in the interaction network that constructs and maintains internal order. In these four levels, information is analog. In cells, genetic information (iv2) governs autopoiesis (metabolism) and directs reproduction and adaptation. Here for the first time, information is digital, and reproduction produces populations that have history, i.e., undergo evolution. Within cells, enzymes are analog informational catalysts at level (ii) specified by the digital genetic information at level (iv2); cells also include feedback control mechanisms at level (iii). In plants and animals, multi-cellularity is organized and governed by the meta-level control (v) of genetic information by chemical messengers. Higher organisms at levels (vi) and (vii) have nervous systems that process information of yet another kind. This is all inexact, but a reasonable “coarse-grained view of the whole.” 210 This hierarchy of information is inspired by Bennett’s philosophical hierarchy of energy (1956, 1964). It applies mainly to concrete systems but also to some abstracted systems. Table 9 does not go as high as Boulding’s original hierarchy; completing it is left as a task for the future. 207

Note #9 Relation as constraint, p. 324 Note #48 Algorithmic information, p. 395 209 In 3.2 Matter, energy, information, this was called a “norm”; see Note #45 Feedback control, p. 386. 210 Table 5 Some aspects of “complexity” and “holism” p. 101 208

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If form is given its most general meaning as complementary to substance, under the aspect of similarity (isomorphism), the types of information in Table 9 are all variations of form. Under the aspect of difference, however, these types vary in power, scope, and subtlety. This hierarchy also relates to the earlier distinction 211 between informationtriad, where information is considered only relative to matter and energy, 212 and informationtetrad, where information is considered in the context also of utility. Informationtriad is at levels (i) and (ii); informationtetrad is at levels (iv2) – (vi). Levels (iii) and (iv1) are intermediate or transitional. 5.3 Categories of complexity God made the integers; all else is the work of man. - Leopold Kronecker, in Bell (1986) Boulding proposed his hierarchy as a way of organizing knowledge that addresses both level-independent isomorphisms and level-specific emergents. However, the system types in his hierarchy do not have a consistent character, are weakly linked to phenomena 213 of interest to the systems project, and lack any conceptual basis. In its place, this book offers a set of abstract categories as a structural 214 framework for systems theory – more specifically, as an organizing principle for the Synchronics sections of Essay and Notes. The categories are for concrete and abstracted but not conceptual systems. The sections of Synchronics, namely Wholeness, Constraint, Distinction, Persistence, Identity, Complexity, Agency, and Cognition, consider system types that progressively increase – though not monotonically – in complexity. Some sections are oriented toward either structure 211

3.2.2 Utility, p. 93 See 3.2 Matter, energy, information, p. 88 and Note #46 Information (and matter-energy, utility), p. 389. 213 Table 2 Some general phenomena (systems themes), p. 71 214 Table 7 Organizing principles for integrating systems theory, p. 154 212

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or function. Constraint and Distinction discuss structure and function, respectively, for all systems and are paired. In Persistence and Identity, structure and function are not explicitly separated. Complexity and Agency discuss structure and function, respectively, for more complex systems and are also paired. In Cognition, structure and function are again not explicitly separated. The categories apply cumulatively. Constraint and Distinction apply to all systems, even simple ones, so ideas in these sections are maximally general. Persistence is less general and adds ideas specific to a smaller subset of systems. Identity, Complexity, and Agency add ideas mainly applicable to the still smaller subset of living systems. Finally, Cognition applies only to complex living systems. In terms of Boulding’s hierarchy this sequence of categories reaches up only to level (vii), human systems, although the discussion below about “operating systems” touches on ideas specific to Boulding’s level (viii), social organizations, and to systems that might be viewed as comparable in complexity. The categories Wholeness to Cognition are inspired by the Systematics 215 of Bennett (1956-1993) and Blake (1994, 1995, 1997). Bennett’s archetypes are: Wholeness or Universality (monad), Polarity or Complementarity (dyad), Relatedness or Dynamism (triad), Subsistence or Activity (tetrad), Potentiality or Significance (pentad), Repetition or Coalescence (hexad), and Structure or Transformation (heptad). The first three archetypes resemble Peirce’s (1958) Firstness, Secondness, and Thirdness. The sections of Synchronics roughly parallel Bennett’s scheme. Wholeness (the idea of a partial whole) resembles his monad, Distinction (the system-environment distinction) his dyad, Constraint his triad (since relation is constraint), Persistence his tetrad (since stability is subsistence), Identity his pentad (since generalized genotype-phenotype is potential becoming actual), Complexity and Agency his hexad (since complexity is a coalescence and agency implies repetition), Cognition his heptad (since cognition is informational transformation). 215

No relation to the term “systematics” as used in biology.

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Synchronics is a story about being, told through this progression of categories. The first three sections, Wholeness, Constraint, and Distinction, present the foundational ideas on which everything that follows depends. The beginning notion is “system” (Wholeness), whose critical property is finitude. A system is viewed under two aspects: internal and external, structure and function. Under the first, a system is ordered by its relations (Constraint); under the second, a system exists in and is distinguished from a context or environment (Distinction). That which is ordered and distinct may or may not endure (Persistence). It may possess an inner core (Identity) with a range of potential manifestations. Potential may be actualized in elaborations of function and structure (Agency and Complexity). A system may have a modeling subsystem, which may represent the environment, the system, the interaction between the two, and even the modeling subsystem itself (Cognition). The progression of categories in Synchronics stops here and does not encompass Boulding’s social organizations and transcendental systems (his levels viii and ix), which remain tasks for the future. All of the approaches to integrating systems theories discussed in 5.2 Hierarchy of system types are encompassed by this progression. The first three sections of Synchronics address the goal of a general theory that applies to many different systems; this was called approach (1) to the conceptual integration of systems theories. The sources for these categories largely reflect the deductive route to an ESM. Subsequent categories, more restricted in scope, are more associated with the inductive route to an ESM. Persistence discusses systems whose order is stable. Identity generalizes the biological idea of genotype into a notion of a system essence that is distinguished from appearance, the latter being the joint effect of essence and environment; 216 only some systems manifest such a 216

duCoudray (2011) uses a similar terminology of “essence” and “environment,” but his “essence” (roughly) corresponds to what is in this book called “structure”; in this book “essence” is an inner core of structure.

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(generalized) genotype-phenotype distinction. Further, only some systems exhibit agency, i.e., behavior that needs the idea of utility to be understood. Of these, only some include modeling subsystems. Thus Identity, Complexity, Agency, and Cognition roughly cover the subject of complex adaptive systems; this exemplifies approach (2) to the integration of systems theories which narrows the domain over which integration is sought. The overall organization of Synchronics, including the entire hierarchy of categories, thus illustrates approach (3) to conceptual integration, which subsumes both approach (1) and approach (2). Finally, Notes, to a limited degree, implements approach (4). The most basic categories, namely Wholeness, Constraint, and Distinction, apply to all systems and might be called fundamental. The word here has a different meaning from its conventional meaning in physics; there it refers to basic aspects of substance; here it refers to basic aspects of form. The distinction between the first three categories which have wide scope and the other categories which apply only to more complex systems parallels Heidegger’s (1962) distinction between the “ontological” and the “ontic.” “Ontological” refers to “being as such” while “ontic” refers to particular beings. What corresponds in systems theory to the philosophical notion of “being” is “system,” 217 and the three most basic systems categories can be regarded as defining the ontological. The monadic category of Wholeness proclaims that something exists. The dyadic category of Distinction partitions this unity into system and environment that differ from and constitute one another. The triadic category of Constraint has system and environment not merely distinct from but also in relation with one another. Relation is also a condition of possibility for 217

While “system” plays the role in systems theory that “Being” does in continental thought, “system” is less susceptible to being misused in the way Heidegger weaponized “Being” for metaphysical antisemitism. For Heidegger, “Being” had ontological enemies, namely the Jews (Fagenblat 2014), illustrating the fact that an ontology can be ethically pernicious.

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dynamics, a fundamental (ontological) aspect of being. 218 (In the Synchronics section of Constraint, relation is introduced as it applies to internal structure, rather than external function, but it applies to both. Similarly, Distinction also applies within internal structure.) What is fundamental for systems theory is what is most general, so there can be a systems theoretic fundamentalism. This would, for example, privilege the lowest levels of Boulding’s hierarchy or the first few categories of Synchronics. Such a systems fundamentalism would be reductionist via form, just as conventional scientific fundamentalism 219 is reductionist via substance. Both substance- and form-based reductionisms are, in the words of Blake (1802), “single visions.” Reductionism via form is illustrated by the view that everything is just dynamics. This appears in Wolfram’s (2002) principle of computational equivalence, where computation means discrete dynamics, 220 and where all instances of sufficiently complex dynamics are viewed as equivalent. This ignores the emergence of new properties (Kurzweil 2002). Dynamics is certainly relevant to everything, but everything is not adequately 218

For some postmodern thinkers (e.g., Donkel 1992) the dyad of Distinction (difference, to use their word) is sufficient to define the ontological, but Difference is static and the triad of Relation is needed to get dynamics, which must surely be an aspect of the ontological. Also, in the postmodern denial of “presence without difference” (Lucy 2004), there is a denial of the monad, but difference is often supplemented with “univocity,” which is the monad in disguise. There is a sense in which number begins with two (Figure 57 Tetrad of number; pentad of system, p. 359), but to this author the views of Lao Tzu and Peirce (Note #30 One, two, three, ten thousand, p. 359) which see the ontological in the monad, dyad, and triad seem more compelling. There is, however, an argument for including the tetrad in the ontological, i.e., Persistence, pp. 10, 373. 219 2.1 The illusion of the fundamental, p. 43 220 Dynamics might be regarded as computation when viewed epistemologically, but ontologically to say, for example, that the dynamics of planets around the sun manifests computation distorts the usual meaning of computation.

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explained by dynamics. Evolutionary and neurophysiological processes, for example, are dynamic, but to regard them as equivalent to many-body gravitational systems or “game of life” cellular automata just demonstrates the conceptual limitedness of the idea of dynamics. General ideas about dynamics shed as little light on evolution and cognition as quarks do. This highlights a point stressed by Boulding: any systems type can be approached with the ideas and methods of lower (more general) types, but this will miss the distinctive characteristics of that particular type. Kurzweil also makes this argument in his critique of Wolfram’s systems fundamentalism. One could model human behavior with automata theory (behaviorism), since some aspects of human behavior are indeed automaton-like, or with network models, since social systems are at least networks, but such models do not represent the higher-level capacities of human beings. Similarly, one could analyze socio-cultural systems using the ideas of simpler system types, 221 but this would not address level-specific properties of these systems. Since mathematical systems theories are less available the higher one ascends in the hierarchy of systems types, the criterion of exactness needs sometimes to be waived in the construction of an ESM. 222 A few additional observations are worth making here about socio-cultural (and more complex) systems, since Essay and Notes do not explicitly consider them. One might ask: what are the level-specific emergent properties of such systems? One possible answer is that they provide facilitating environments in which other systems can form, develop, and act. The role of language in human systems illustrates this idea. Language is a supporting environment for human “modeling subsystems.” 223 Another illustration is 221

For example, one might treat roles, actions, etc., as primitives that are not more deeply explained and model the dynamic interactions between social entities; this is typical of agent-based simulation. 222 It would be unreasonable to demand, for example, that Luhmann’s (1982) theory of societal systems be formulated mathematically. 223 See Note #104 Embeddedness of cognition, p. 475.

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provided by computer programs that are programming environments, e.g., Mathematica or SPSS, in which ordinary programs can run. At a higher level still than programming environments are operating systems that are governing environments for computers. One can generalize this notion of an “operating system.” Viewed as such, ecosystems are at a higher level than organisms or even populations of organisms and the biosphere as a whole is at a still higher level – an operating system for life. Regarding the biosphere or the entire planet as an organism (Gaia) or a system stabilized by negative feedback (but only for perturbations that are not too great) does not do justice to its level of being. The biosphere has a property even “higher” than agency. This idea needs further work, since many higher organisms are hosts for internal symbionts or parasites. Also, although systems that provide the conditions of possibility for other systems might be considered higher than systems whose existence they enable, in another sense a supported system is higher than what supports it. Systems that provide supporting environments for other systems are among those Bennett (1956) called “hypernomic,” as opposed to “autonomic” (living systems) or “hyponomic” (systems simpler than living systems). The hypernomic realm is the cosmological macro-hierarchy, e.g., planets, stars, and galaxies; the hyponomic realm is the micro-hierarchy of molecules, atoms, and the like. These three realms differ in the salience of energy, matter, and information. 224 In the hypernomic realm energy is salient; in the hyponomic realm matter is salient; in autonomic systems within the intermediate realm information is salient. According to Bennett, the autonomic mediates between the hypernomic and the hyponomic. The discussion so far has focused on Synchronics, but Diachronics also provides a conceptual integration of (other) systems ideas. Its integration is less deep, because Diachronics 224

Figure 15 Triad of matter, energy, and information, p. 88

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uses a life cycle model of system formation, growth, development, complexification, and eventual decline and disappearance, and the generality of life cycle models is inherently limited. Collectively, Synchronics and Diachronics – compressed in Essay and unpacked in Notes – represent an attempt to integrate systems theory structurally, by organizing its content. 5.4 Ontology of problems 225 Not to lament, not to curse, but to understand. - Baruch Spinoza (1677) Ethics precedes ontology. - Emmanuel Levinas (1989) Systems theory might alternatively be integrated functionally. It aims at constructing a metaphysics, but what is metaphysics for? A partial answer might be that a systems metaphysics would deepen the problem-solving project of systems analysis, in which problems are too often simply taken as given. A problem is a gap between an actual and an ideal 226 situation, where the gap has utility implications for some agent. One might question whether the scale and boundary of the problem are properly defined, or probe into the details of actual and ideal situations, but rarely in systems analysis is there a deep investigation of the reasons that actual and ideal do not correspond. If inquiry is made into causes, usually only proximal causes are considered, rather than ultimate ones. There is no time to study similar problems that afflict other systems. While general methodology is of interest to the systems analyst beyond solving the specific problem at hand, general ontology revealed by the problem is of no concern. Yet understanding the synchronic and diachronic essence of a problem can provide valuable insight, and insight is always needed to solve any problem. Offering insight is – part of – what metaphysics is for.

225 226

Early versions of the ideas in this section are in (Zwick 1995, 2000). Note #72 Purposeful action as a tetrad, p. 426

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To put it in another way: systems analysis suggests an ethical context for the ontology that systems theory constructs. Levinas argues that ontology is – or ought to be – preceded, i.e., motivated, by ethics; similarly for Murdoch (1992) metaphysics is a guide to morals. Spinoza’s Ethics (1677) builds on a foundation of metaphysics. At its best, systems analysis is about ethics. 227 “Ethics” here means, to use a Kabbalist phrase, tikkun olam, “fixing the world.” One cannot fix what one does not adequately understand. The systems theory aim of understanding might serve the systems analysis aim of fixing, by revealing the underlying essence and thus the lawful character of problems. Many problems, imperfections, difficulties are universal; to be more precise: ubiquitous, archetypal. Systems theory might provide an ontology of problems. What would an ontology of problems mean? Within a reductionist framework, a general and coherent view of problems is impossible. Problems divide up into unconnected domains: disease and death are assigned to biology and medicine; mental distress and dysfunction to psychology and psychiatry; economic and political injustice to the various social sciences. General statements about problems cannot be made, and similarities among problems in different domains are not noticed. Moreover, in physicalist reductionism problems are epiphenomena whose ontological reality is dissolved at fundamental levels. The in-principle unity of the sciences implicit in the reduction of scientific description from level to level fragments the notion of problem, and in descent to lower levels dismisses it. Admittedly, there is a pristine elegance to this view, and solace for those who internalize this Olympian vision, but the conception of the world it offers is impoverished. It does not save the phenomena in which we are interested. 227

Systems analysis at its worst was exemplified by Robert McNamara’s management of the Vietnam War. Systems theory is less worldly than systems analysis, so it less frequently presents ethical challenges, but see Pouvreau’s (2009) assessment of von Bertalanffy’s activities in Austria during World War II.

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If an ontology of problems is alien to the natural sciences, it is also not to be found in the behavioral and social sciences. These sciences would restrict such an ontology only to human problems, but vulnerability is the condition of all life. Although we alone define situations as problems, we are not alone in encountering difficulties. The notion of a problem is meaningful for any entity that has interests, i.e., for which the notion of utility is pertinent, namely for organisms. So, for a systems theory with biology as its center of gravity, 228 it is quite appropriate to take the idea of problem as an organizing principle. The ontology of problems being proposed here is thus biocentric, not anthropocentric. And since the biological realm links the microscopic and astronomical realms, a focus on problems has implications for a broader domain of science. An ontology of problems would give special attention to problems engendered by human action. This is still only a subset of the problems faced by human beings, and by living beings in general, and even where problems result from individual or collective human behavior or are magnified by human action, pointing to the human origins of such difficulties does not exhaust – or necessarily even clarify – their essence. It is natural to focus on human action or human nature. This has the endorsement of old and new religions, in doctrines as “original sin” or desire as the root of suffering, or in psychodynamic or economic reductionisms. It is a reflection of the human wish to be at the center of things, a wish that survives the Copernican, Darwinian, and Freudian revolutions. We want to be able to solve our problems, so we wish to believe that we are their sufficient cause. But if we take a larger view, we see that we are not actually the deepest cause for many of the problems that we and other forms of life experience. By abstracting the patterns that underlie a wide range of phenomena, this view sees the hazards of the human domain and, more broadly, the domain of life, as universal in character.

228

4.3 The centrality of biology, p. 135

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Hazard is lawful. We are indignant at this fact, and imagine that it was once not so. The constant theme which runs through all Utopian thought, Christian and pagan alike, is that once upon a time there was a perfect state, then some enormous disaster took place: in the Bible it is the sin of disobedience ... [or evil-doing or arrogance] ... So too in Greek mythology the perfect state was broken by some disaster, as in the story of Prometheus ... or of Pandora's box – the pristine unity is shivered, and the rest of human history is a continuous attempt to piece together the fragments in order to restore serenity, so that the perfect state may be realized once again. Human stupidity or wickedness or weakness may prevent this consummation; or the gods may not permit it; but our lives are conceived, particularly in the thought of Gnostics and in the visions of the mystics, as an agonized effort to piece together the broken fragments of the perfect whole with which the universe began, and to which it may yet return. This is a persistent idea which goes through European thought from its earliest beginnings; it underlies all the old Utopias and has deeply influenced western metaphysical, moral and political ideas. - Isaiah Berlin (1991) The myths that Berlin speaks about have lost their meaning for us, but the dominant scientific paradigm offers nothing in their place and denies the existence of the imperfection which these myths proclaim. There is no rent in the fabric of existence, as described by particle physics, a fabric that is alien to human reality and irrelevant to human concern. But a different conceptualization of the natural and social order, which looks to Pythagoras and Heraclitus rather than to the Greek atomists, a viewpoint that focuses on patterns rather than entities, would not be silent about the problems of human existence. In the late 20th century, such a viewpoint reemerged under the name of systems theory or, more recently, complex systems. It attempts

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to reorganize knowledge around such archetypal themes as order and disorder, part and whole, system and environment, structure and function, continuity and discontinuity, constancy and change, and other basic issues. It seeks mathematical formulation and links to the sciences, but also unabashedly takes up – or lends itself to – philosophical and even religious themes. A metaphysics based in systems and cybernetic ideas can contribute to an ontology of problems, i.e., to a coherent explanation of problems faced by living systems. While systems analysis has offered solutions to technical problems and has tried to develop a problem-solving methodology, it may well be that the most valuable contribution of the systems movement is its offering of a systems theoretic language for discussing problems in general terms. More critical than the methodology we use to deal with problems is the ontology we use to understand them. Rather than rushing to come up with solutions, which are usually simplistic, we need to grasp what problems really are and how they come about. Under the aspect of difference, every problem is unique, but under the aspect of similarity, (some) problems are ubiquitous. Systems theories clarify the universal character, the lawfulness as it were, of difficulties that afflict systems and compel our personal and societal concern. They unveil the abstract essence of these difficulties, their archetypal character, the general principles that manifest in them. Consider the following four systems ideas: deterministic chaos, informational parasitism, the Prisoner’s Dilemma, and the inherent limitations to optimization and decision-making. •

In the phenomenon of deterministic chaos, lawfulness does not guarantee order. For certain environmental conditions, systems exhibit the possibility of shifting from ordered to disordered behavior. Such shifts may be sudden and the resulting behavior unpredictable. This possibility is the rule for dynamic systems, not the exception, since most systems are nonlinear and most nonlinear systems can be chaotic. It

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is thus reasonable to expect that physical, biological, or social order may exhibit unpredictable fragility. •

Beyond some degree of complexity, systems often undergo a separation of coordination and control from production and maintenance, a separation between a domain of information and one of matter-energy. While this hierarchical differentiation may promote efficiency, the existence of an informational order distinct from what it oversees opens up the possibility of conflict, subversion, and parasitism. This is a source of vulnerability of organisms, computers, organizations, and economic systems to exploitation and dysfunction.

•

The Prisoner’s Dilemma (PD) is a game-theoretic model of situations where collective cooperation is advantageous but is difficult to achieve because individual cooperation is disadvantageous to every agent. In these situations, it is the structure of the interaction that is flawed and that condemns the agents to self-defeating action. This structure underlies many intractable dilemmas of collective action in social, economic, and political systems.

•

There is no optimal algorithm for simultaneous optimization of multiple objectives or for global as opposed to local optimization. There is no way to contain the combinatorial explosion that afflicts discrete optimization. There is no algorithm that always satisfactorily aggregates a set of ordered preferences. The possibility of optimal solutions to human problems that require rational decisions is limited, even theoretically.

In the systems literature there are also many other ideas that clarify the abstract essence of problems, notions about the relations of constraint and variety; about tensions between unity and multiplicity, openness and closedness, part and whole; about instabilities of cybernetic control; about the counterintuitive behavior of complex systems and the impossibility in any intervention of doing just one thing; about the ubiquity of

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hierarchical order and its inherent pathologies; about the gap in all models between image and reality, etc. From a systems perspective, the problems we face – and our incapacity to prevent them or solve them – have their source in difficulties such as these. Dysfunction, disintegration, hazard, and impermanence are natural, not anomalous; their appearance in human affairs can to a degree be ameliorated but not avoided. It is ironic that systems thought, because of its concern with self-organization, control, and adaptation, has been criticized as assuming stability and harmony. Not only is this accusation false, but insights into dysfunction, conflict, and change may be the most significant contributions that systems theories offer. Essay is a sketch for an ontology of problems. It is an abstract account of problems that afflict many systems and cannot be completely avoided. It demonstrates the coherence and breadth of systems ideas, which range from general (applicable to many kinds of systems) to specific (applicable only to restricted classes of systems). Essay is a verbal narrative, not a formal theory, and advantage is taken of the richness and elasticity of words as compared to mathematical notions. But the metaphysical ideas of Essay can be given exact meaning; this is shown in Notes. How these ideas can be applied to the natural and the social sciences has just been touched on in the above four ideas. It is considered further in the following section which offers a “desk manual,” as it were, for the ontology of problems sketched in Essay. 229 The reader may wonder if the imperfections that Essay speaks about are in the models we construct about the world or in the world as described (imperfectly) in these models, i.e., if the stance being taken here is epistemological or ontological. For example, the assertion is made in Synchronics that systems are incomplete (limited, partial). This could mean that our models are incomplete or that actual systems out there in the world are incomplete. The intention is to assert both, with 229

It is discussed also in Chapter 6 Science, religion, politics, p. 193.

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emphasis on the latter, although some statements apply only to the former. The orientation of Essay is more ontological than epistemological, though both are encompassed. Epistemological problems can be treated as ontological because the problems encountered or generated by modeling subsystems, which are components of certain complex adaptive systems, are objective phenomena. 230 This is the perspective of “naturalistic epistemology” (Quine 1969), especially its Darwinist form, “evolutionary epistemology” (Campbell 1974). This approach toward an ontology of problems joins other similar systems approaches. Much valuable work on a systems ontology of problems has been done by Troncale (2011, 2013, 2014), under the rubric of “systems pathology,” by workers in Systems Engineering (Davidz 2018; Davidz et al. 2018), by complex systems theorists (Bar-Yam 2003, 2004), and others. 5.5 Metaphysician’s desk manual Things fade and alternatives exclude. - Alfred North Whitehead, in Becker (1968) An ontology of problems might employ the terminology of medicine: a system is a patient and a problem is a disease. In these terms, Essay is a preliminary metaphysician’s desk manual that catalogs ontological afflictions of patients and epistemological deficiencies of physicians. 231 In religious terminology Essay might be regarded as a “secular theodicy,” 232 the view of systems theorist as theologian thus complementing the view of systems theorist as doctor. In fact, a metaphysician who specializes in the problems that afflict systems fuses the 230

Cognition (1.1.8, p. 20, and 7.1.8, p. 461) The medical metaphor is pursued in Appendix A.2 Function, p. 604, which notes that this manual catalogs diseases, but does not provide a guide for diagnosis or treatment. Elaborations of this metaphor that would discuss a metaphysician’s Hippocratic Oath, iatrogenic disease, and the imperative of “Metaphysician, heal thyself!” are beyond the scope of this book. 232 This notion is explained later in 6.3.1 Secular Theodicy, p. 226. 231

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tasks of doctor and theologian; for such a healer, an exact and scientific metaphysics would be a valuable intellectual resource. The previous section identified four systems ideas that contribute to an ontology of problems, and many more such ideas are offered in Essay. These ideas are abstract, and most of them are stated tersely. To make them more comprehensible they are illustrated with examples, so a list of selections from Essay is offered below, in which the individual idea in Essay 233 is shown in italics and numbered as explained below 234 and is then followed by one or multiple brief examples of the idea. Here is an idea-example pair from the list that follows: Even where cooperation is to the advantage of all, defection may be compelling. Individual rationality may lead to collective irrationality, to the disadvantage of all, even to disaster (1.1.6.2.4.6). Agents involved in arms races, exploitation of public goods, and collective action often find themselves in situations where acting rationally leads to deficient outcomes. Readers are encouraged to come up with their own examples of the ideas presented in Essay. Such idea-example pairs will inevitably be taken in ways that are not intended by the author, so here are some caveats to help avoid misinterpreting what is being claimed in these pairs. First, the example in each pair is offered only to answer the question, “To what specific problem might this abstract idea be relevant?” No claim is being made here that this systems idea 233

For ease of reading, some quotes omit introductory words in the Essay sentence, such as “But” or “Thus.” 234 Quotes from Chapter 1 Synchronics begin with “1.1.”; those from Diachronics begin with “1.2.”. These two numbers, in smaller font, are followed by subsection number, paragraph number, and sentence number for the first sentence of the quote. For example, 1.1.1.1.2 means Chapter 1.1 Synchronics, subsection 1 (Wholeness), paragraph 1, sentence 2. When four numbers are given, sub-subsections are referred to. For example, 1.1.6.2.4.6 is Chapter 1.1, sub-subsection 6.2 Other Systems, paragraph 4, sentence 6. This notation is also presented in To the Reader, p. ix.

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alone, even if it developed, can fully explain the example. The systems theory source of any idea will be too general to be adequate to any specific phenomenon. Not only must a system theory be augmented by a discipline-specific theory which generates a detailed model that addresses the specific phenomenon, 235 but multiple systems theories (and disciplinespecific theories/models) are also likely to be relevant. 236 A whole book could be written on each idea-example pair, so every example in the list that follows only illustrates what the idea from Essay could refer to. Moreover, the idea in each ideaexample pair is not only insufficient to explain the example; it is also insufficient to justify the example. Examples may contain assertions that are debatable or reflect biases of the author. However, the ideas themselves are relatively uncontaminated by the author’s views and could support positions with which the author disagrees. The ideas are what this book asserts, not the examples. Second, it’s not the individual idea that is the point. The point is the ensemble of these ideas. Individual ideas are trees; the ontology that Essay depicts is a forest, a whole greater than the sum of its parts. Note, though, that the list of idea-example pairs below includes only a small sample of the ideas in Essay, and that Essay presents only a small sample of the ideas available in the systems literature. The forest of systems ideas is too big to be comprehensively depicted. Third, while the claim is being made here that systems ideas offer insight into phenomena given as examples, insight is only the beginning of understanding. For an idea to adequately illuminate an example, extended discussion is needed. The list below of ideas-example pairs does not offer such discussion, but the next chapter 237 does. So Essay is unpacked in two ways: in the list of rather terse idea-example pairs immediately below 235

See the discussion of Table 3 Epistemological hierarchy, p. 72 Figure 7 Systems theories and specific scientific theories, p. 65 237 Chapter 6 Science, religion, politics, p. 193 236

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and in the more ample discussion of some systems ideas in the following chapter. With these caveats, consider the following idea-example pairs. Before examining this list, Essay in its entirety should ideally have been read. The order of these idea-example pairs follows the order of the ideas presented in Essay; the examples are simply tied to the ideas and do not themselves follow any logical scheme of progression. Ideas from Chapter 1, Synchronics (citations begin with 1.1) In any system, only some elements and relations are encompassed; others are left out (1.1.1.1.3). Every organism and every organization has only some capacities, not all capacities, performs only some functions in its environment, not all functions. Every ideology, every religion, and every philosophical system at best encompasses some relevant truths, not all relevant truths. Constraint makes the actual less than the possible. Constraint is limitation. Possibilities are excluded in every actualization (1.1.2.2.1). Consistency and completeness cannot both be attained (1.1.1.3.2). One cannot be both married and not married; as Whitehead noted (Becker 1968), “alternatives exclude.” One can attempt to have the pleasures but not the pains of both, but infidelity merely trades incompleteness for inconsistency. Every system has an environment…A boundary both separates the two and joins them together (1.1.3.1.2). In modern society boundaries between church and state and between economy and polity are contested. So too, at a personal level, are the boundaries between public and private, professional and personal.

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As a nexus of being and behaving, every system has not one organizing principle but at least two: a principle of internal structure and a principle of external function (1.1.3.6.3). In personalities, there is tension between inner-directedness and outer-directedness (Riesman et al. 1950). Businesses are pulled between being oriented toward their unique competences (their products) and being oriented toward external opportunities (the market). What is determined from within and what is determined from without are never in complete accord (1.1.3.6.7). The competing needs of being autonomous and being integrated into larger wholes afflict individual personalities (Unger 1984) and social entities. The system also interacts with its environment not merely as a single element. Parts of the system engage parts of the environment, so multiplicity in structure passes through into function (1.1.3.7.5). It is difficult for any organization, ethnic group, religion, or nation to present a united front to its environment. To the degree to which and in the manner by which a system is closed, it is vulnerable to a dual risk. It tends to either disintegrate or rigidify (1.1.4.2.3). Personalities, organizations, social movements, and ideologies tend over time to disintegrate or rigidify or both. Extreme openness, like extreme closedness, undermines persistence (1.1.4.3.10). A totally open or totally closed border undermines a nation, but it is difficult to find an ideal intermediate point. Every system must be partially closed and partially open, or closed and open at different times, or closed in some aspects and open in others (1.1.4.4.1). In a pandemic, closedness is needed to protect health and limit pathogen spread; openness is needed to maintain societal relations and protect the economy. No formula can specify an optimal balance between the two.

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Alternatively, the effects of the disturbance can be countered after they arise, but regulation may take hold only after a lag, making control difficult, even unstable (1.1.4.4.6). A vehicle cannot be safely controlled if its motion doesn’t promptly follow its steering apparatus. Failures in managing economic or public health crises often arise from time lags between responses to the crisis and the consequences of these responses. Closedness may be provided for by subsystems that distinguish between what should be taken in and what should be kept out, between what conforms to the identity of the system and what is foreign to it…Failure of these subsystems leaves the system defenseless; their hypertrophy engenders rigidity; their errors of identification destroy order (1.1.5.6.1). An immune system can ward off dangers to an organism from its environment, but can also be the site of disease of external origin, as in AIDS, or of internal origin, as in auto-immune diseases. The internal security subsystems of social systems often malfunction or are counterproductive. Even within a restricted context, the possible states of the environment and their probabilities may not be known even in the present, and forecasting future states is at best reliable only in the near term (1.1.6.1.1.4). Accurate forecasts of the weather, evolutionary/ecosystem change, business and financial markets, political events, or other phenomena are made difficult if not impossible by the presence of chaotic dynamics. Newtonian predictability is a property only of some systems, and not even fully of the solar system to which it was first applied. Actions have unanticipated consequences, even counterintuitive effects. What should suppress perversely stimulates; what should stimulate unexpectedly suppresses (1.1.6.1.2.6). Overuse of antibiotics promotes evolution of resistance; a bacterial strain has been found that is even dependent on the antibiotic used against it. New highways can increase congestion. Suppressing fires builds up flammable fuel. Adding nutrients to an ecosystem can cause it to collapse.

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For unrestricted action, the present must be free to bind the future, yet when this future arrives, action has become restricted (1.1.6.1.3.5). The loss of freedom that comes with parenthood is never fully anticipated. Multiple objectives are usually incommensurable, but even when they have a common utility scale, arbitrariness cannot be avoided (1.1.6.1.4.4). In decision-making by individuals, groups, organizations, and societies, optimizing multiple goals by first reducing them to a common denominator, e.g., dollars, is always highly arbitrary. When utility is ordinal, no method exists to aggregate multiple preferences into a rational, decisive, and equitable choice (1.1.6.1.4.5). Some democratic decision-making procedures are intrinsically imperfect. Specifically, preferential voting schemes, faced with three or more choices, suffer from irrationality, inequality, or indecisiveness (Blair and Pollak 1983). Local optimization is usually suboptimal since the risky search for maximal gain foregoes assured, though inferior, benefits. The best is the enemy of the good….The good is the enemy of the best (1.1.6.1.5.4). In politics, social and economic policy, organizational behavior, and personal choice, there is always tension between incremental improvement and radical change, realism and idealism, satisficing and optimizing. Even if attained, optimality brings risk. Iit reduces diversity and redundancy, which diminishes resilience (1.1.6.1.7.4). Minimizing inventories may enhance efficiency, but systems without reserves are fragile because they have no buffers to cushion external shocks. Optimality sought by being lean is often illusory because risk is merely ignored, transferred, or hidden. Nor is lean necessarily ecologically beneficial (Venkat and Wakeland 2006).

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A system effective at acquiring resources is a target for takeover, parasitism, or theft (1.1.6.2.3.4). “Successful systems accumulate parasites … This is a fundamental observation, rooted in the thermodynamic observation that it is easier to move (or steal) something than it is to make it. It accounts successfully for predation, crime, war, non-contributing authors on publications, taxation, lawyers, unproductive business practices and government programs, immune systems, a lot of ecology, and probably scientific literacy” (Culotta 1991). Even where cooperation is to the advantage of all, defection may be compelling. Individual rationality may lead to collective irrationality, to the disadvantage of all, even to disaster (1.1.6.2.4.6). Agents involved in arms races, exploitation of public goods, collective action, log-rolling in government, and traffic congestion often find themselves in situations where acting rationally leads to deficient outcomes. Exchange also reinforces incompleteness by fostering dependence. Neither extreme of dependence or self-sufficiency is ideal, nor can an optimal and enduring balance be found between the two (1.1.6.2.5.2). Conflict between self-sufficiency and participation in the global economy inheres in economic development. Economic exchange enhances efficiency but generates vulnerability to factors beyond a nation’s control. What passes from one system to another is not fully specified by either. Even when openness is regulated by the organizing principle of the system, it is impossible to allow entry into the system of the beneficial and reliably exclude the harmful (1.1.6.2.6.3). Cell membranes provide access to pathogens. Diseases can be spread via sexual relations. Computers are afflicted by Internet malware. Embassies are nests for spies. A nation accepting technology transfer from other nations is open also to external economic, political, or cultural influences.

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Being embedded may offer security, but the price of security is heteronomy, and this security also cannot be relied upon. Wholes sometimes sacrifice or consume their parts (1.1.6.3.2.4). An animal in a trap may sacrifice a limb to regain freedom. Organizations abolish departments and fire individuals. Nations sacrifice soldiers in wartime and give up territory in treaties. The system may become integrated into more than one encompassing order; the resulting tensions may be mitigated by differentiation but at the cost of coherence (1.1.6.3.4.3). Individuals partake in multiple communities – family, ethnicity, religion, locality, work – each of which attempts to appropriate all of a person’s time, energy, money, and commitment. A network of interactions can be stable or unstable. Either condition can have adverse effects. Stability can lock the system into dysfunctional states; instability can lead to runaway dynamics that also produce such states (1.1.7.1.1.1). Racial disparities in health and income exhibit both lock-in dynamics that prevent beneficial change and runaway dynamics that magnify inequitable differences. The presence of non-local interactions in addition to local ones makes connectedness global. This may deamplify some local disturbances, but it amplifies others, allowing them to propagate through the entire network (1.1.7.1.2.1). High connectivity of electric grids deamplifies some local disturbances, but amplifies others. High connectivity in the brain enhances information processing but brings vulnerability to seizures. Globalization spreads health science and technology, but increases the risk of pandemics. Constraint and variety oppose one another…unity and diversity coexist but neither principle is consistently maintained (1.1.7.2.2.1). In many universities in the United States, ethnic and racial diversity is valued, but ideological and political diversity is not.

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In complex systems, hierarchy often consists of informational regulation of transformations of substance. Distillation of an informational domain is a refinement that facilitates adaptation, but it also introduces vulnerability – to failures of coordination, to dysfunction between levels, and to informational parasitism (1.1.7.2.8.1). Biological and computer viruses are informational parasites. Management of companies and financial sectors of economies perform essential informational functions, but often siphon off more wealth than is justified by these functions. Through this [modeling] subsystem the environment may acquire a beachhead of control over the system (1.1.8.3.3). The educational system is the primary means of enculturating and indoctrinating the young with the beliefs and values of the dominant social order. Impressions are incomplete and may be unreliable. The internal construction of reality partially compensates, but construction must exercise some autonomy from fact, so modeling produces a seamless web of representation, inference, and invention that cannot be disentangled. A constructed reality is invariably warped by the pressures of utility… The modeling subsystem depicts a world and a self that are in part illusion (1.1.8.6.2). Nervous systems in organisms and media in societies define how these systems perceive their environments. For an organism, an organization, or a society, reality is what its modeling subsystem tells it is real, but the model is never fully reliable. There is a tradeoff between responding to weak signals and avoiding false alarms (1.1.8.9.2). Tradeoffs between false positives and false negatives complicate medical tests and make the promotion of public health difficult. Nuclear war could have been – and perhaps is still capable of being – triggered by a false positive.

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Ideas from Chapter 1, Diachronics (citations begin with 1.2) The newly arisen system is incomplete and often also inconsistent. What flaws its origin will condition its future (1.2.1.1.6). System formation of the United States was flawed in the original acceptance of slavery; the consequences of this incomplete liberty and inconsistent equality have yet to be adequately rectified. Where other systems engender or facilitate this arising, they shape the character of the new system. Either excessive proximity or excessive distance poses risk (1.2.1.3.3). In the mother-child relation, either excessive proximity or excessive distance endangers child development. A system generated by other systems may face tension between fidelity to the matrix of its arising and assertion of its distinctive attributes… Every mixture of continuity and change is unstable. If continuity and change are both embraced, the new negates the old and seeks to supersede it (1.2.1.4.1). Tensions between continuity and change afflict relations between children and parents. Similar tensions exist in emergence of organizations and nations from their antecedents. In the filial relations between Judaism, Christianity, and Islam, claims of supersession continue to produce intolerance, falsification of history, and violence. Contradiction may for a while be hidden or partially resolved in complexification (1.2.2.3.3). Complexification in law, intellectual theories, and ideological doctrines is a common result of attempts to resolve internal contradictions. All development is internal development (1.2.2.4.2). External nation-building efforts to create democratic institutions rarely succeed in societies where such institutions lack deep internal social and cultural support. Education is ineffective if students are not actively engaged.

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The system enters a region of bifurcation in which its actual state is accompanied, in the realm of potential, with a second state, which corresponds to restructuring by a new organizing principle (1.2.3.4.5) … Usually, the system remains structured for a time in its earlier form, but continued shifts in dominance towards the alternative principle finally make visible what has hitherto been latent (1.2.5.3.2). In political revolutions and the bursting of speculative bubbles the new makes its appearance suddenly despite being long under development. Many problems elude solution. They may be unanticipated; or the system may fail to perceive them when they arise; or the system may perceive them but not respond adequately in time; or attempted solutions may fail (1.2.3.5.4). Many avoidable deaths in a pandemic result from failure to prepare for its arrival, to monitor its scope accurately once it has arrived, to take action aggressively to limit its spread, and to anticipate opposition even to effective solutions. The asymmetrical relationship between center and periphery may be complementary and reciprocal, but it may instead harbor unequal exchange, exploitation, and conflict (1.2.4.1.2.4). International trade becomes differentiated, so a subset of countries – a center – have many trade relations with one another, while other countries – a periphery – trade only with one or a few partners, usually in the center (Hopkins and Wallerstein 1980, 1986; Gottman 1980). Political power differences are reinforced by such trade differences. Greater connectedness is a multiplier that can neutralize disturbance, or instead amplify it (1.2.4.2.4.2). Via globalization, local economic disruptions can impact distant countries. Disease is spread by global air travel. Falsehood, illusions, and other harmful memes are disseminated by social media. High connectivity in the electric grid can dampen fluctuations but can also expand the scope of power outages.

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Some systems in their development move towards critical points where disruptive events at all scales become both unpredictable and inevitable (1.2.4.2.4.3). Species extinctions, avalanches, forest fires, earthquakes, and epidemics all exhibit sudden disruptions at multiple scales. Development entails the modification and non-proportional growth of parts. Eventually this requires a change of structure (1.2.4.3.2). While economic growth requires only increase in output and favorable market conditions, development requires structural change. Economies that grow by manufacture and single product exports often forfeit opportunity for development. Optimizing the schedule is also difficult (1.2.4.3.6). Managing large projects requires sequencing many tasks with complex interdependencies. In the traveling salesman and equivalent problems, optimization of the schedule becomes computationally intractable as the problem size increases. Even if achieved, optimality increases vulnerability, since optimality requires the sacrifice of resilience (1.2.4.3.7). Justin-time supply chains may be efficient under conditions of stability but may fail when subject to large unexpected shocks, such as revolutions, earthquakes, and pandemics. Organizations optimized for efficiency by eliminating redundancy are fragile. A larger system may require or even induce a degree or semblance of unity, but imposition of unity from without cannot indefinitely overcome a multiplicity within (1.2.4.4.8). Under stress, societies that encompass multiple religions, ethnic groups, and/or political or economic subsystems may fragment in the absence of a compelling unifying factor. Differentiation undermines any organizing principle favoring unity; integration undermines any organizing principle favoring multiplicity (1.2.4.6.6). Market systems work efficiently if there are multiple producers and consumers. But concentration spontaneously reduces competition and must be actively prevented. Without regulation, markets are self-undermining.

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To the degree that the alternative principle is only a denial it offers no basis for a new order. What succeeds as negation never succeeds as affirmation (1.2.5.4.1). Marxism was a valuable critique of capitalism, but Communism provided no adequate positive basis for the social order. The movement crystallized by Marx and Engels led to Lenin, Stalin, Mao, and Pol Pot. Negation, to supplant what is rejected, must be more than a corrective; it must offer a positive principle. But to be effective, negation yields to excess and distortion: excess in promotion of the new, distortion in rejection of the old (1.2.5.4.3). Excess is common for revolutions and, indeed, for most radical political, social, or cultural movements. Every system has the capacity, through an unbroken line of development, to turn into its opposite without seeming to have done so (1.2.5.7.4). Religions, ideologies, and social movements exhibit inversions of principle, recognized by outsiders but justified or not even noticed by devotees. The dream of a society in which people were not judged by the color of their skin has morphed into the advocacy of policies based explicitly on race. The struggle of principles may yield the triumph of the original order, but its victory is never complete. Those aspects of the system that gained coherence by the opposing principle remain, and produce in the system a persistent strain (1.2.5.8.1). In the US Civil War, the Union triumphed, but racism was not thereby vanquished. The struggle may lead to a synthesis reflecting a third alternative. Conflict between the opposing principles then shifts to conflict with this synthesis. Just as opposing principles enable and stimulate one another, so too does a newly dominant center incite both extremes (1.2.5.9.1). Neoliberalism, a centrist position, stimulated populist reactions at both right and left extremes.

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Resources may be depleted; disorder or noxiants may hinder the capacity of the environment to support the system (1.2.6.1.4). Overexploited environments cease to provide the resources needed by organisms or social entities and cease to neutralize the wastes that these systems produce. Only some wastes can be taken in by other systems and removed from the environment, but such other systems are not always present. The neutralization of harmful waste cannot be guaranteed. The circle is not always or easily closed (1.2.6.2.4). Through long-term evolution, closing the circle (Commoner 1971), i.e., the transformation of waste into food, is widespread in the biosphere, but comparable closure of economic systems is very far from accomplished. There are no systems that can eat and thus neutralize radioactive wastes of nuclear power plants. In circumstances of limitation, the system must shift from expansion to steady state. This shift may be difficult to achieve or come too late to prevent overshoot and collapse (1.2.6.3.1). Failure to shift to a steady-state economy generates global ecological-environmental crises. Exponential growth in matterenergy utilization and waste production overshoots Earth’s carrying capacity. Uncontrolled growth of subsystems may enlarge the system beyond sustainable size. It may be difficult to reverse the degradation of the environment already produced by such growth (1.2.6.3.4). Topsoil is not readily restored after it is lost. Mining, fracking, and other forms of resource extraction produce difficult-to-reverse environmental damage. Even if the long term is considered, the future is an externality that is never fully encompassed (1.2.6.3.6). Markets have externalities that preclude the ideal results predicted by economic theory. Future generations are not adequately represented in economic decision-making, and high discount rates minimize consideration of their interests.

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Systems often destroy the environments on which they depend (1.2.6.3.8). Environmental collapse occurred in many societies in human history (Diamond 2005) even before industrialization. Systems suffer unequal exchange with larger or more coherent systems (1.2.7.2.1). In general, interaction between systems channels resources from the less organized to the more organized. Mature ecosystems exploit adjacent immature ones (Margalef 1963, 1968). Economic exploitation motivated and defined classical imperialism. Sudden change following prolonged stasis poses a special risk since successful adaptation inhibits adaptability. When an environment remains constant, adaptations rigidify and resilience degrades (1.2.8.2.2). Procedures of bureaucracies are organizational habits. Genotypes of organisms are evolutionary habits. Habits can increase efficiency but are difficult to alter when conditions change. The system may remain bound to an obsolete specialization, once optimal or at least viable, now harmful if not fatal (1.2.8.3.3). Species become extinct if their adaptations cease to be viable. Economic entities are undermined when the commodity or service they offer are not needed. Aspects of personality, once beneficial, become maladaptive in new social environments. The system may adapt by relinquishing ties to its organizing principle. It is then not the original system that persists. Viability is gained at the cost of identity (1.2.8.3.4). For individuals, social groups, and ideologies, adaptation may be necessary to survive, but adaptation often requires abandoning principles on which identity is based, so it is not the same person, religion, or political party that survives. Human groups cannot persist without delimiting boundaries. Religious, racial, ethnic, and national groups constantly struggle with the question of whether and how such boundaries are to be defined and enforced.

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The above list of idea-example pairs illustrates the notion of an ontology of problems based in an exact and scientific metaphysics; a more complete list would be the nucleus of a metaphysician’s desk manual. The examples make assertions that are interpretations of systems ideas, but to repeat an earlier caveat: the examples only offer possible illustrations of the ideas that inspire them. To be justified, the assertions would have to be supported by valid discipline-specific theories and models. In terms of the epistemological hierarchy presented earlier, 238 most of these assertions are proposed relations (laws, hypotheses) at level (2) that govern the elements specified at level (1). These relations must satisfy the truth criterion of correspondence, i.e., they need to be empirically verified. They must also satisfy the truth criterion of coherence: they must be capable of being consistently integrated with other scientific findings, i.e., they need to be part of a level (3) model that is an application of a discipline-specific level (4) theory which may or may not be an interpretation of a more abstract level (5) systems theory. Finally they must also satisfy the pragmatic criterion of truth: they must reflect insights that are actually useful for understanding and addressing problems. Most of the idea-example pairs offered above link a level (5) systems idea directly with a level (2) possible illustration of it, without the necessary intermediary levels. But assertions about worldly phenomena that are made directly from any metaphysics, however exact and scientific, are necessarily speculative. Level (5) theories and ideas do not obviate the need for levels (4) and (3), which must provide adequate basis for level (2) assertions. So except where an idea-example pair appears incontrovertible, all of these pairs should be taken only as illustrations of what the abstract statements of Essay could refer to. The examples are not deduced from any systems theory; nor are they specific claims actually being made here.

238

Table 3 Epistemological hierarchy, p. 72

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A more expansive discussion of a few systems ideas applied to contemporary issues is given in the next chapter. As is the case for the idea-example pairs in this section, the purpose of the next chapter is only secondarily to advocate for specific assertions. Its primary purpose is to further illustrate the idea of an ontology of problems as a functional organizing principle that integrates the diverse aspects of an exact and scientific metaphysics.

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Chapter 6 Science, religion, politics 6.1 A macro-historical model 6.2 The new science 6.3 Natural religion 6.4 Fixing the world 6.5 Summing Up

193 207 226 247 278

Section 6.1 describes a systems theoretic model of human history. The model provides a framework for discussing some applications of systems theory 239 to science, religion, and politics. Section 6.2 continues the discussion in Chapters 2-5 of the relation between the systems project and mainstream science. Sections 6.3 and 6.4 apply some systems ideas to religion and politics, respectively. 6.1 A macro-historical model An adequate explanation of any phenomenon requires the analysis not only of the structure and function of the phenomenon but also of its history. 240 So to discuss possible implications of systems theory for science, religion, and politics, it is helpful to have an account that organizes these subject areas via some historical framework. This section develops such an account using the resources of systems theory itself. As noted above, von Bertalanffy argued that systems theory could offer new models of history. 241 This section presents such a model, applying some ideas developed elsewhere in this book. 242 This model of history is discussed in this chapter in a compressed form but is elaborated in greater detail in (Zwick 2009).

239

To reiterate, “system theory,” in the singular, refers to a multiplicity of systems ideas, models, and theories. 240 3.5 Structure, function, and history, p. 109 241 3.5.2 Adding history, p. 116 242 Note #147 Limits of complexification, p. 544; also Note #120 System formation, p. 496 © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_6

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6.1.1 A model of diachronic processes First a general model of process is described; then this model is applied to human history. The main ideas of the general model are summarized as follows, and, except for vi, are depicted Figure 27 on the following page: i. ii. iii. iv. v. vi.

A process governed by a diachronic organizing principle (OP) develops in stages. The process usually encounters “barriers” (points of difficulty). After initial development, a minor barrier hinders further progress. After extensive development, a major barrier hinders the transition to a new OP. At points of difficulty, the process is especially vulnerable to external contingencies. Multiple processes can blend and either mitigate or exacerbate these difficulties. 243

The organizing principle OP1 results from a system formation 244 event. The minor barrier (shown in the figure as dotted) reflects the difficulty of reaching higher levels (later stages) by spontaneous complexification. The major barrier (shown in the figure as dashed) reflects the difficulty of achieving the integration needed to transition to a qualitatively new organizing principle, OP2. (Arbitrarily, only one level beyond OP2 is shown, but the process should be understood to continue further.) The process being modeled is not deterministic or closed. Contingency and openness are critical at points of difficulty but can also affect the process at any stage.

243

Note #167 Butterfly of reconciliation, p. 572, offers an idea about how one process might facilitate another. 244 Note #120 System formation, p. 496

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Figure 27 Process model OP = organizing principle. (a) levels of complexity shown spatially; (b) rotates (a) by 90° and offers a temporal view. Levels of complexity in (a) become stages (events) in (b). 245

OP2

major barrier minor barrier

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OP1 space (levels of complexity) (a)

time (b)

The figure does not depict the forces of disequilibrium that generate the process. 246 Disequilibrium occurs both at a microscale where it generates transitions from stage to stage, and at a macro-scale, where it generates the overall unfolding of the process and the limitations on this unfolding. Figure 27 also does not explicitly depict the differentiation and/or integration that characterize the process or the feedback or feedforward that may be present. Only the lineal aspect of the process is depicted; for the purpose of discussing how systems ideas bear on science, religion, and politics, this aspect suffices. OP2 is a completion and a reinitiation of OP1. The possibility of OP2 is contained in OP1. This is not merely a logical possibility; it is a potential inherent in the initiated 245

Figure 27(a) is the same as Figure 117 Limits of self-organization(a), p. 545. For (b), see also Figure 100 System formation: difference in similarity, p. 501, and Note #139 Temporalization of complexity, p. 532. 246 Forces of disequilibrium arise from inconsistencies or incompletenesses such as those described in Essay and Notes. Synchronics summarizes several kinds of disequilibria in Note #115 Binary oppositions, p. 492. Diachronics is about the unfolding of disequilibria, discussed in Notes #121 Self-organization, p. 502, and #123 Disequilibrium and change, p. 507.

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process; in Kauffman’s (2000) terminology, it is an “adjacent possible” implicit in what is actual, a reachable possibility. Such a possibility is like an ecological niche that might or might not be filled by some species, or an excited state of an atom that might or might not be filled by an electron. The ecological niche or the energy level exists as potential even if unfilled. 247 The possibility of completion of a process and the difficulty of achieving completion inhere in the inception of the process. 6.1.2 The model applied to history The Axial Age 248 was one of the most seminal periods of intellectual, psychological, philosophical, and religious change in recorded history; there would be nothing comparable until the Great Western Transformation, which created our own scientific and technological modernity. - Karen Armstrong (2007) Application of the above process model to human history is shown schematically in Figure 28. Depicted in the figure are three processes, PI, PII, and PIII, that blend with one another, but the blending is not shown. Stages of the process, shown in Figure 27(b), are here omitted; each process in Figure 28 is drawn simply as an arrow, with minor and major barriers dotted and dashed, respectively. The system formation events of A, B, and C, shown in the figure as short and bold vertical lines, are not ex nihilo: 249 These events have precursors drawn simply as horizontal lines leading up to the events, but the precursors of PII are really in PI and the precursors of PIII are in both PI and PII. 247

What exists is more than the actual. What is potential exists and can influence the actual (1.1.2.2.4). 248 The Axial Age, roughly 800-200 BCE, named by the philosopher Karl Jaspers, was a period which saw the emergence of enormously influential religious and philosophical figures, such as Aristotle and Plato, the Hebrew prophets, Buddha, the authors of the Upanishads, Confucius and Lao Tzu, and others. Their teachings became foundations for major civilizations. 249 Note #120 System formation, p. 496

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Figure 28 Macro-historical processes of complexification In PI, PII, and PIII, systems formation events (A, B, C) and completion-reinitiation events (Aʹ, Bʹ) are shown, but individual stages are not. Major barriers (1ʹ, 2ʹ) are dashed; minor barriers (1, 2, 3) are dotted. Time is more logarithmic than linear, especially for PI. The label for PIII, namely “science,” is just shorthand for the secularism, humanism, and scientific rationality of modernity. the present moment

PIII science B PII religion/culture A PI society 1

C 3 2 time

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Figure 28 is a coarse schema, like Boulding’s hierarchy of system types, a “crude look at a whole” (Gell-Mann 1994), here a historical whole. The figure summarizes human history in terms of three socio-cultural processes. PI is the primary societal process, which includes economic, political, and social development, as well as dependence of society on nature. PII refers to religion-centered culture, especially culture based in Axial religion and philosophy. PIII refers to the transition to modernity, quintessentially to the development of science that occurred initially in the West. Materialist views of history, such as that of Marx, focus on PI. Idealist views of history, such as that of Hegel, focus on PII. One purpose of this model is to join together materialist and idealist views. PIII mediates between PI and PII by linking the societal and cultural domains: Science is part of culture, and science-based technology is part of the material order of human society. Figure 28 shows PI, PII, and PIII separated from one another for visual clarity, but the model posits that these processes are blended, reflecting the presence of both differentiation and integration. For situations where

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multiple processes blend, tensions between the processes exacerbate the points of difficulty that afflict each individual process. In Figure 28, system formation events are indicated by letters, minor and major barriers by numbers. A, B, and C, the system formation events of PI, PII, and PIII, respectively, occurred in the past, as did points 1 and 2, the minor barriers of PI and PII. The figure associates the present historical moment with the major barrier of PI (point 1ʹ) and the minor barrier of PIII (point 3). Humanity today needs to accomplish a completion-reinitiation event, Aʹ, of the primary process, and overcome deeply connected difficulties in the tertiary process. People have always thought that they lived at a special time in history, so such thoughts should always be met with skepticism. The temporal version of the Copernican Principle (Gott 1993) – the principle that no point in time is privileged, just as the earth is not in a privileged location in space – is more plausible. Still, as viewed in this model, the present moment is a singular time in human history. If achieved, Aʹ would be a system formation event that put the relation between humanity and the biosphere on a new foundation, which would allow the continuation and further development of human civilization. Although PI is labeled “societal,” its beginnings (A) were biological; the reinitialization (Aʹ) of this process would also be biological but on a vastly larger – planetary – scale. The achievement of Aʹ, however, is not guaranteed. In this model, the bridging of barriers, especially major ones, is contingent, not inevitable. 250 To clarify the nature of this transition to Aʹ, one might ask what it is like, what other system formation transition 251 does it resemble? Insofar as Aʹ echoes A, one might say that Aʹ would 250

3.5.2 Adding history, p. 116; Notes #129 History: idiographic or nomothetic, p. 516, #147 Limits of complexification, p. 544 251 See Notes #120 System formation, p. 496, and #147 Limits of complexification, p. 544.

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be like the emergence of the human species. Perhaps only the conception of our entering the epoch of the Anthropocene gives the present era its true significance. However we characterize this moment in human history, it is clear that the challenge of Aʹ is multi-dimensional and complex. Its political dimension dates back at least to the two world wars of the 20th century; many thinkers saw these wars as the beginning of global politics. Its social and economic dimension, commonly referred to as globalization, is more recent. But it is the environmental dimension of this challenge that is the most critical: specifically the danger of climate change, and generally the imperative of sustainability. To get past the major barrier of PI, what is needed is not political unification in the sense of world government, but coordinated global action to protect the biosphere from humancaused collapse. System formation, A, the primary initiating event of PI, refers to the biological emergence of the human species and the formation of early human societies. While biological emergence happened only once, in Africa, human societies formed in all locations on the planet to which human populations became dispersed. By contrast, B refers to events that occurred only in a subset of these locations: in societies that encountered the dangers, disorders, and complexities (warfare, political oppression, alienation) of urban civilization (point 1). In these societies, the religious-philosophical innovations of the Axial period eased these difficulties and facilitated continued development (Jaspers 1953; Mumford 1956; Armstrong 2007). 252 The Axial period is defined very broadly here; for 252

The characterizations here of the difficulties encountered by these processes is inadequate; a fuller exposition needs to be given. But to illustrate: urban civilization increased tensions between the individual and the state. The Axial teachings lessened these tensions by linked innovations in human personality and culture. The new dignity given to the person simultaneously facilitated the integration of persons into urban society. In terms of the butterfly catastrophe model of Note #167, p. 572, tensions are modeled by a clash of conflicting factors; the lessening of tensions by the action of the harmonizing “butterfly factor.”

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example, Islam, which emerged well after the period defined by Jaspers, is included. While religion-based culture characterized most if not all human societies, Axial breakthroughs happened only in a few locations. These were system formation events (B) that transformed societies, launched civilizations, and radically altered human history. Even if a materialist account (Marxist, geographic, matter-energy-based, environmental, technological, etc.) might be adequate for PI, it would need to be supplemented by a culture-centered account, which here is PII. Human history is codetermined by base (PI) and superstructure (PII); any pure reductionism, either downward to the base or upward to the superstructure, is inadequate. The Axial religions, when they emerged, were major historical events. Although PII was rooted in PI, it emerged as an independent current, initially in opposition to PI. But with the unfolding of the Axial emergents, the two currents reunited. Socrates was condemned by Athens, but Stoicism became a mainstay of Rome; Christians were originally a persecuted minority, but Christianity became the religion of the empire. Islam opposed the pre-existing order but quickly established the Caliphate. Confucius was initially ignored and the tradition he launched even suppressed, but Confucianism became the official doctrine of China. Religion, society, and state became intimately related in Christian, Islamic, and Confucian societies. For a time, union of PI and PII fostered the creative development of the civilizations where this union occurred, but ultimately PII encountered difficulties, in part because religion-based culture was ultimately compromised by its fusion with the political order, by rigidification of this culture, and by other factors. The processes launched by the Axial teachings thus also encountered difficulties of development (the minor barrier at point 2), either internal (corruption, rigidification) or external (invasion) or both. 253 These difficulties manifested in Europe, 253

For some ways of thinking about these difficulties, see Notes #134 Failures in meeting new challenges, p. 525, #135 Movement toward the

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the Middle East, China, India, and elsewhere in different ways and at different times, but societies integrated around religionbased culture everywhere faced some form of limitation. In one location, however, these difficulties were overcome by a third system formation event, denoted as C in the figure, namely the Renaissance, Reformation, Enlightenment, and quintessentially, the Scientific Revolution. In Figure 28, PIII is labeled “science” for simplicity, but it is intended to include all forces promoting the priority of reason and experience over authority and revelation. This event (C) and the process it launched facilitated the continued societal development of the West and the transformation to modernity, strongly imprinted by humanism and secularism. Although technology is present in all societies, only in the West was technology deeply rooted in science, and only in the West did science crystallize as an autonomous aspect of culture that radically transformed society. This accounts for the spurt of development of Western societies and their world dominance in the last few hundred years. 254 Just as the stalling of societal complexification was relieved by liberating influences of religion-based culture (the differentiation of PII from PI, initiated at B), so too was the stalling of religion-based culture relieved – initially only in the West – by liberating influences of secular humanism and science (the differentiation of PIII from PII, initiated at C). Although science grew out of religion (Kepler was a mystic, Newton was devout if heterodox, natural religion was a mandate of the new science), secularism based in science eventually came into opposition to religious belief and to the fusion of religion and politics. In the undermining of religion by science extremes, p. 527, #137 Mechanization (rigidification), p. 530, #138 Form limits growth, p. 531, #150 Self-organized criticality, p. 551, #151 Something intractable, p. 554, #158 Limits to growth, p. 565, #174 Things fade, p. 584. 254 The model does not address the question of why this did not occur in other major civilizations, e.g., in China or the Islamic world; it is also silent on why Axial religions/philosophies developed only in some parts of the world.

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and the transition to a secular modernity, the coherence of Western culture was lost. 255 The model thus attributes the initial dominance of the West in the modern period to the fact that the transition to modernity (PIII) occurred first and most fully in the West. While literary theory may imagine an advance to a postmodernity, social, political, and economic realities in much of the world have not yet arrived at modernity. Whether due to internal socio-political or cultural factors or to the persistent effects of past imperialism and colonialism, democracy and economic development have not been achieved everywhere and are precarious where achieved. The Western origin of modernity complicates the challenges of globalization. A social compact between rich and poor nations, critical for addressing the challenge of climate change, has not been achieved, and international economic relations have not been brought under social control. The processes launched by the Scientific Revolution, and more generally by the transition to modernity, have reached their own realm of difficulties (point 3). Science and technology have become too complex and powerful to be understood and controlled. The horrors of the 20th century have undermined the confidence in reason that was the legacy of the Enlightenment; recognition of the racism and antisemitism of some of its major figures has undermined its moral claims. Secular modernity is under attack by resurgent, often reactionary, religion-based movements. Roughly simultaneously, societal development 255

The PI, PII, and PIII processes can be viewed as a macro-dialectical triad, using the philosophical-religious categories of Rosenzweig (2005) mentioned in Footnote #158, p. 119, namely World (PI)-God (PII)-Human (PIII). This is related to Hegel’s view that religions (PII) were an advance because they (particularly Western religions) “effected a radical break with nature, allowing Spirit to replace and oppose nature,” Hegel assigning both credit and blame for this to Judaism (Yovel 1998). Enlightenment philosophy (PIII) – particularly his own – was regarded by Hegel as a further advance of Spirit because it subsumed (incorporated and transcended) religion.

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(point 1ʹ of PI) and the exponential impacts of technology (point 3 of PIII) have led to grave dangers to the biosphere. The fate of civilization depends on achieving a transition to planetary order (Boulding 1965). In Figure 28, points 1ʹ and 3 together characterize “the present moment.” The current global climate danger is the direct result of technology-based industrialization, and to address climate change, the needs for scientific understanding, technological innovation, and political consensus are intertwined. It is because of the link between the difficulties in the societal process (point 1ʹ of PI) and the difficulties in the development of science and technology (point 3 of PIII) that the crisis in PI is not merely about societal integration but about planetary integration. For better and worse, science-based technology has achieved the domination of nature forecast by Francis Bacon. Not only did PIII undercut the sociocultural preeminence of PII, but science and technology reached for and gained God-like powers. Science itself also faces a crisis of complexity, and the limits of scientific understanding exacerbate the risks of the contemporary situation. Human impacts on the environment are inadequately comprehended, but even what is understood by scientists is not widely enough believed by the public. The continuing inability of some religious groups to accept scientific truth makes solution of global problems such as climate change and pandemics more difficult. To put this abstractly and schematically: the inadequate rectification of PII by PIII makes the crisis in PI more dangerous. The scientific community is itself too fragmented to weigh in effectively on these issues. It is also not immune to irrationalities not much less fantastic than superstitions of religion; for example, a technological “singularity” (“rapture of the nerds”) is regularly declared to be imminent. Technology-based economies have escaped societal control not only because of flaws in the sociopolitical order 256 but also because scientific assurances of safety are often unreliable. Social media disseminate misinformation. 256

6.4.2.2 Problems of differentiation, p. 257

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Access to weapons of mass destruction by state and non-state actors grows steadily. Technology expands the scale of terrorism, which cannot be deterred when based in fanaticism that glorifies death. Human societies, having diverged from a single origin, are now rapidly converging. But global societal integration (point 1ʹ), i.e., the completion and reinitialization of PI, is made difficult by developments in PII. The various religious traditions are far from the stage at which they might be integrated, so the socio-technical knitting together of the planet must occur in the face of tensions between religion-based civilizations (Huntington 1997). Figure 28 includes, as an event labeled Bʹ, a projected possibility of an integration of religious cultures, which might be reached after passage through some future point of difficulties (2ʹ). Bʹ would be to PII what Aʹ is to PI. But just as we are not assured of a successful societal transition (PI) in the 21st century to an order satisfactory for nature and humanity, so too is a corresponding integration in the realm of culture (PII) also not guaranteed. The model, not being deterministic, does not actually predict the reaching of Bʹ. Given the present historical challenge of PI, all that is necessary – and in fact possible – in PII is pluralism and tolerance, guided by the understanding gained in modernity (PIII). No speculations are offered here on a possible even more distant completion and reinitialization event for PIII (such a Cʹ event is not actually included in Figure 28). For a materialist account of PI, Marx’s historical theory may be the best framework we have. Marxism was valuable as a critique of capitalism and for its recognition of the existence of the world system that was crystalized by the transition to modernity. Its dream of a final transition to socialism was, however, a premature anticipation (Whyte 1948) of the more encompassing planetary transformation yet to be achieved. Marxism as a theory of societal development, i.e., of PI, was blind to the significance of religion, reflecting its shallow dismissal of the deepest achievements of human culture; it was

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also cynical about the liberal legacy of the Enlightenment. In viewing material production as the prime determinant of history, it was narrowly reductionist; yet, from a contemporary perspective, it was not reductionist enough. Its labor theory of value missed the significance of nature as the foundation of value, treating nature, as capitalist theory did, mainly as a factor of production. So it was not even an adequate theory of PI. Although needed as a critique of capitalism, it was a disaster as a conception of a new social order. In its secular messianism and its priesthood of the vanguard, it was ersatz religion; in its dialectical materialism, it was ersatz science. 257 6.1.3 On the inescapability of grand narratives We live at a time when models of the sort that has just been briefly sketched are looked upon with disfavor in the field of history, although there is a new interest in “big history” and a revival of interest in world history. What is offered above is a meta-narrative, and such meta-narratives are condemned by postmodernists as either “too epistemologically dangerous or too politically dangerous to warrant serious philosophical scrutiny.” 258 But there is actually no escape from macro-theories of history and meta or grand narratives. Rejecting them in effect asserts the null hypothesis that there is no pattern to human events, that events are mostly random (speaking ontologically) or unknowable (speaking epistemologically). The choice is not between having a meta-narrative or not having one; not having 257

Dialectical materialism fuses reductionist materialism and holistic dialectics. Its materialism is not different from that of the dominant scientific paradigm, but its dialectics and other versions of dialectics have continuing philosophical usefulness. Dialectical ideas are deployed in Essay. From an ESM perspective, dialectics is metaphysics that is not exact, although some dialectical ideas can be rationally reconstructed using catastrophe theory (Zwick 1978a), and not scientific, in not generating empirically testable scientific theories. Engel’s Dialectics of Nature (1883) might be viewed as proto-systems theoretic. 258 Pollock (2009) makes this observation to provide context for his analysis of Franz Rosenzweig’s systematic philosophy.

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one implies one. The intellectual and moral deficiencies of macro-theories or meta-narratives must be compared with the intellectual and moral deficiencies of this null alternative. The question really is: what is the best theory or narrative we can come up with; or – what is preferable – which multiple accounts are useful and partially true. That multiple accounts may resist integration does not actually imply that they are incommensurable. For example, the fact that extremely different (e.g., materialist and idealist) views can be taken of human history is no reason either to abandon inquiry or to reject both views; rather, it’s an indication of an intellectual challenge of synthesis that needs to be tackled. The objection that any theory or narrative accommodates only a fraction (even a small fraction) of what is known is just a reason to improve it or find better – or supplementary – accounts. To adapt an injunction from Pirke Avot: “It is not for us to comprehend the whole, but it would be foolish to abstain from trying.” 259 The blind men could have pooled their discoveries about the elephant. The above model also violates contemporary political norms by insisting on some centrisms. Although it acknowledges that all or nearly all societies had cultures that encompassed religion and technology, and thus PII and PIII in a sense everywhere blended with PI, it is a salient feature of the model that, while system formation event A happened everywhere, B happened in only some places, and C happened only in one. The salience given to B is Eurasian-centric, 260 and to C is Euro-centric, and perhaps both qualify as logo-centric, but views that are centric are not ipso facto incorrect, except politically, and centrism-phobia is a major cause of intellectual rigidity. Those who deny the importance of the Axial traditions in Eurasia or the transition to modernity in Europe should come up with an alternative account that is plausible and competitive. 259

In the original, the injunction is “It is not for us to complete the task, but we have no right to abstain from it.” 260 It is probably more accurate to refer to this as being Eurasia-North Africa-centric.

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6.2 The new science 6.2.1 A supplementing process The historical model sketched in the previous section provides a framework for discussing applications of systems theory to science, religion, and politics. The systems project is relevant to some of the difficulties encountered in PI, PII, and PIII. For example, potential impacts of this project include fostering a productive interaction between science and religion – harmonizing PII and PIII – and helping us to preserve our planetary home – the challenge in PI that is represented as point 1ʹ. Still, the primary task of the systems project is to assist in meeting the current challenge in the science process – represented as point 3 in PIII. The systems project supplements mainstream science. As depicted in Figure 29, this project is a secondary process, P′III, which augments the scientific component of PIII. Figure 29 Systems project assisting development of science This extends the historical model presented above. 261 (PIII is actually much more than science per se.)

the present moment P′III systems project PIII mainstream science

3

Saying that this project is only auxiliary to mainstream science accurately describes its role. Universities will never be reorganized along Pythagorean lines. 262 Transdisciplinary systems thought will never supplant the conventional 261

Figure 28 Macro-historical processes of complexification, p. 197 See the discussion of a hypothetical Pythagorean university in 4.1 Not just mathematics, p. 128. 262

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disciplinary organization of scientific knowledge. Systems ideas are too abstract for that. Yet identifying the systems project as a supplement also understates its potential significance. Only via such a supplement can science offer a genuine “theory of everything” and participate in a recovery of cultural coherence. In Figure 29 the present moment (point 3) is identified as the minor barrier for the scientific component of PIII. The difficulties subsumed in this barrier include the exponential growth of scientific knowledge which has resulted in fragmentation of knowledge both within and between scientific disciplines. Scientists even in the same discipline often cannot understand one another, not to speak of scientists in different disciplines. This slows the advance of science. Such slowing may not be altogether unfortunate, since the growth rate of science already outstrips society’s capacity to adjust to new technologies based on science. What is, however, unfortunate is that the fragmentation of scientific knowledge makes it difficult to assess the dangers in these technologies. The fact that scientific knowledge is largely incomprehensible to ordinary citizens allows the rapid and uncontrolled translation of scientific advances into technologies that are immediately deployed and whose potential consequences are global but unforeseeable. Moreover, at a more subtle yet profound level, this fragmentation leads to the absence of a coherent scientific worldview, especially a worldview with significant links to other aspects of human culture. The systems project cannot solve these problems, but it can help with their amelioration. It can augment mainstream science in three ways: (a) It can provide an alternative basis for a unity of science that connects with other aspects of culture; (b) it can offer the public a set of general scientific principles that make science accessible and meaningful and that avoids the oversimplifications of scientism; (c) it can provide transdisciplinary ideas and methods that are essential for understanding and addressing societal problems.

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Point (a) has been argued at length. 263 Unity of science can be achieved via an exact and scientific metaphysics. An ESM can provide a theory of everything that is more encompassing and more satisfying than what can be provided by mainstream science. From a physics-based TOE, one would get only a theory about things that physicists study. Such unification would add nothing to our understanding of life and human society. But around a general theory of systems or of complexity, one might organize knowledge that covers a broader domain and bears on issues closer to home. If we wish for a unity of science that has human consequence, that helps us understand ourselves and our natural and social environments, that has bridges from science to religion, literature, and the arts, that offers the possibility of experienced – not merely intellectualized – coherence, then that unity must be based upon universal ideas about relation and process. A systems ontology offers the possibility of linking the natural and social sciences, the humanities, and the arts. The systems project is already the major interdisciplinary movement in the sciences. Though integration by reduction can be achieved locally between vertically adjacent fields of science – this is what “consilience” (Wilson 1998) is about – a truly general view of the world requires a different approach, whose salient notions are isomorphism, emergence, and complexity. Graph theory, information theory, nonlinear dynamics, feedback ideas, game theory, and the like are the lingua franca of theory in the natural and social sciences. Familiarity with these theories is widespread. What is missing, however, is the recognition that collectively they offer a worldview complementary to that of mainstream science, as warp is complementary to weft.

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2.1 The illusion of the fundamental, p. 43, and 2.2 The systems alternative, p. 48

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6.2.2 Understanding what we know Beyond the possibilities that it holds for the integration of scientific knowledge, a systems perspective can offer a different understanding of what we already know. One does not need to descend to the quantum level to see the world that we inhabit in a different way, since the distinctive features of quantum mechanics are largely irrelevant to the middle-scale domain in which we live. Consider instead the implications of simply thinking about the world in terms of the categories of matter, energy, information, and utility, and with the framework of structure, function, and history. Truly assimilating these perspectives would transform our views. For example, if matter is viewed in light of its informational and functional aspects, our conception of materiality is altered. To give only one illustration: oxytocin is a hormone which functionally is central to maternal emotion and other bonding experiences. Its material structure reveals nothing about this significance. What is salient about oxytocin is its function, not its structure, and its function is informational. If one wants a notion of materiality that encompasses its functional and informational aspects, one could speak of oxytocin as exemplifying, as it were, a higher type of materiality. This kind of thinking is illustrated in anthropology by Levi-Strauss’ idea (1975) that the distinction between “the raw” and “the cooked” parallels the distinction between nature and culture. What is cooked undergoes a transformation, both a material one that converts a product of nature into something edible, and an informational and functional one by conferring the social status of “food” on the cooked material. Functional considerations are usually considered in philosophical analysis to be inessential because they are external, but why should the essential not include the interactions an entity has with its environment? In the systems view, what something is involves both structure and function (and also history). Though being a “food” depends on the presence of an organism of an

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appropriate species, why should this dependence make being a food ineligible for the status of an essential property? And why should even the potential of becoming a food not be viewed likewise, since what is the difference between potential versus actual food and potential energy versus actual (kinetic) energy? In both cases, the transition from potential to actual depends on external factors. At issue here is the distinction embedded in the reductionist paradigm, articulated by Galileo and Locke, between “primary” and “secondary” qualities. This distinction is valid in the closed systems view, but in the open systems view systems are constituted not only by structure but also function and are defined not only by matter-energy but also by information. In the open systems view, hormones are not merely molecules and cooking is not merely molecular reorganization. The systems view challenges other scientific orthodoxies. For example, just as it is possible to overemphasize structure and regard interactions an entity has with its environment as irrelevant to its being, or to overemphasize function and assume in effect that the internal nature of an entity is infinitely plastic, it is also possible to have a “single vision” (Blake 1802) by overemphasizing history and the idiographic (contingent) character of history at the expense of its nomothetic (lawful) character. An overemphasis on history is illustrated by the insistence of Gould (1997), Margulis (1998), and other evolutionary theorists that biological evolution shows no progress, i.e., nothing justifying a vertical (higher vs. lower) ordering of species (or other taxons). Margulis writes, All beings alive today are equally evolved. All have survived over three thousand million years of evolution from common bacterial ancestors. There are no “higher” beings, no “lower animals”... Even the “higher” primates are not higher. We Homo sapiens sapiens and our primate relations are not special, just recent; we are newcomers on the evolutionary stage. Human similarities to other life-forms are far more striking than the differences.

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This is only a partial truth. It privileges history over structure and function, the contingent over the lawful, and similarity over difference. The historical view of life as a tree (or bush) of branchings is a great achievement of evolutionary theory, and it is true that the genetics and biochemistry of all forms of life show overwhelming similarity. But if “higher” means more complex, autonomous, potent, diversely interacting, sustained by greater energy throughput, and manifesting more refined levels of information processing, can it be denied that single-celled eukaryotic organisms are “higher” than prokaryotic bacteria, that animals having nervous systems are “higher” than animals which do not, and that human beings are “higher” than other primates? Is the human species which creates and lives in the informational realm of culture, which theorizes about the origins of the universe, which manipulates massive amounts of energy, and which globally alters its environment, not “higher” than a bacterial species? Progress in evolution need not mean replacement or be monotonic and irreversible or imply a sequence of levels free of ambiguity. Rather, what it means is the incessant emergence of ever-more complex, autonomous, potent, and interacting entities, having new capacities to utilize matter, energy and information. Progress in this sense is undeniably an aspect of evolution. Although the specific character of these entities was contingent, since they first arise through random processes, their general character is lawful, since selection ratifies an order inherently necessary for the existence of organisms. As Wright (2000) argues, while the evolution of particular species exhibiting intelligence was not preordained, the emergence of intelligence per se probably was implicit in the evolutionary process (disregarding life-extinguishing global catastrophes). Of course complex forms when they arise do not supplant simpler forms but supplement them. Of course there is no onedimensional hierarchy of being that is sequentially traversed in evolutionary history. Still, the distinction between higher and lower forms is a necessary part of any coarse-grained (GellMann 1964) understanding of life.

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Overemphasizing history is often associated with the denial of essences, and with the nominalist as opposed to the realist philosophical position. If essence means something unitary and permanent, then multiplicity and historicity do indeed imply that there are no essences. But if essence only means deep as opposed to surface structure, then the facts of heterogeneity and diachronic change do not invalidate the idea of essence. A species genotype is an essence. Species evolve, yes; they are instantiated in actual populations, yes; but withinspecies and temporal genomic variation do not negate the fact of between-species difference. Boundaries of natural kinds do not need to be crisp. They can be fuzzy. Structure is the residue of history. When structure is differentiated into a relatively fixed and homogenous core and a relatively variable and heterogeneous periphery, and when this core supplies the algorithmic information for the structure, one can legitimately speak of the core as constituting the essence of the structure. 264 Arguments against essences are ideological, not scientific. The tendency in some expositions of science to misconstrue the significance of randomness also needs to be corrected. If, for example, a random collision of two gas molecules causes one of them to occupy a higher energy state, one could say that this state was randomly produced, but this would be imprecise. Only occupation of this state is due to randomness; the availability of an unfilled higher energy level pre-exists the random event. The real is not only the actual; it also includes the potential, what Kauffman (2000) called the “adjacent possible.” If a box containing two initially separated bar magnets is shaken, the magnets will accidentally meet and stick together. One could say that the resulting magnet pair arose randomly, but this would ignore the fact that the stucktogether magnets form a lower-energy and more stable structure. Randomness here merely affects a search over a space of pre264

Fuzziness, center-periphery (as related to genotype-phenotype), and algorithmic information are the subjects of Notes #25, p. 352, #49, p. 395, and #48, p. 395, respectively.

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existing possibilities, some of which are favored energetically or dynamically. Disorder (here, random shaking) actualizes order. In his concept of “order through fluctuations,” 265 Prigogine (1991) has promoted this idea in the domain of nonlinear dynamics and open systems far from equilibrium. Similarly, emphasizing the randomness that characterizes self-organized criticality 266 would miss the essential point of this phenomenon, which is the existence of the system in a critical state. Any presentation of theory of evolution as being only or mainly about random variation and specific selection plus heritability is incomplete because such an account would be a functional-historical account that ignores structure and in effect assumes limitless internal plasticity. A structural component is, however, articulated in the modern Darwinian synthesis (based on the ideas of Mendel and Weismann, updated by Watson and Crick and others). When this component is given its due, the significance of mutations and other variations is reduced. For example, convergent evolution shows that randomness by itself is not adequate to explain the emergence of specific structures. It is the interplay of chance and necessity (Monod 1972) that is creative in nature; for dynamic systems this is close to the idea of “the edge of chaos.” 267 The overemphasis of randomness in scientific explanations is often ideological: a random universe is a meaningless one, and some scientists delight in asserting meaninglessness because they see themselves engaged in a struggle with religion. There is also a complementary error. A totally determined world is also meaningless, with all due respect to Spinoza’s efforts to see meaning in such a world. In fact, we live in a world neither totally random nor totally determined, and it is this mixture that allows for meaning (Zwick 2015). 265

Note #124 Order through fluctuations, p. 509 Note #150 Self-organized criticality, p. 551 267 Note #17 Chaos, p. 338 266

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6.2.3 Fact and value A systems perspective also challenges the venerable distinction between fact and value. Under the aspect of difference, there is distinction, and thus perfect – and sterile – continence (Spencer-Brown 1972), but under the aspect of similarity, there are complex and meaningful interactions between fact and value, which are not at all sterile. Some of the components of systems metaphysics have both descriptive and normative uses. For example, game theory 268 is a descriptive theory about competition and cooperation and also a normative theory about how rational agents should act in such situations. Game theory provides a language in which some of the complexities inherent in questions of value can be clarified by being posed exactly. Another example is the Theory of Social Choice, 269 whose main result is Arrow’s finding of the impossibility of rationality, equality, and decisiveness in certain voting or multiple-attribute decision-making situations. Arrow’s result is embodied in a descriptive theory, but it is one that also has important normative implications. Being centered in biology rather than physics, a systems metaphysics situates itself squarely in that realm in which issues of value arise. To use a metaphor from nonlinear dynamics, the domains of fact and value are strange attractors whose basins of attraction 270 interpenetrate in complex ways. One can make a stronger claim than this. In the phenomenon of life, value is explicit. Just as life is emergent in a world of matter-energy, value is emergent in a world of fact. The existence and the causal power of values is a fact, and thus the preconditions and implications of this emergence are proper scientific issues. Utility, the central concept of game and decision theory, encompasses the idea of value. Fitness is a specific biological type of utility, and living systems would be utterly 268

Note #75 Game theory, p. 429 Note #68 Aggregating preferences, p. 420 270 Note #10 Dynamic relation, p. 329 269

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incomprehensible without the notion of fitness. Also, 271 information only fully manifests in the context of utility. One might give “value” a deontological meaning and “utility” a consequentialist one. Then value would be absolute (“categorical” in a Kantian sense) and inherent in an action or state of affairs, while utility would be contingent and derive only from the effects of that action or state of affairs. Utility would then have to terminate in value. The need to posit deontological value might be an adaptation to the pitfalls of a consequentialist conception of value, since the pursuit of utility can lead paradoxically to the reduction of utility. Like the hierarchy of types of information given previously, 272 one can posit a hierarchy of types of value, where utility is the bottom level, just as form is the bottom of the information hierarchy. Alternatively, one could use “utility” as a general concept including both deontological and consequentialist levels. Associated with utility is the notion of purpose, related to the idea of norm. 273 A norm makes sense only in the context of the utility it promotes. 274 To Rosenblueth, Wiener, and Bigelow (1943), purposefulness was explained by negative feedback, but such an explanation is inadequate even for a mechanistic conception of purposefulness, since other kinds of control mechanisms exist. 275 At best, negative feedback control is an account of one type of purposefulness. Purpose is also implicit in game and decision theory, which posits rational agents trying to secure or maximize utility, and to the related area of optimization, since what is optimized is at least implicitly some form of utility. One could construct a hierarchy of purposefulness, analogous to hierarchies of information and of utility. Feedback control or some other mechanistic type of 271

Figure 69 Information from matter-energy via utility, p. 393 Table 9 Levels of autonomy and information, p. 158 273 3.2.2 Utility, p. 96 274 Note #46 Information (and matter-energy, utility), p. 389 275 Notes #45 Feedback control, p. 386, and #44 Law of Requisite Variety, p. 384, for another type of control. 272

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regulation might be at the bottom of this hierarchy, its simplest form, but would be inadequate to describe purposefulness at the human level (Jonas 1966). In summary, purposefulness is now the subject of several systems theories, but once this topic was not within the realm of science. When vitalists denied that Newtonian mechanics was adequate to account for purpose, they were correct, but their own explanations of purpose were vacuous. 6.2.4 Horizons The systems orientation may not only help us think in new ways about familiar facts and counter the narrowness of received opinion, but it may also stimulate new scientific explorations. Given that the category of utility augments the categories of matter, energy, and information, 276 one wants to go further. Matter, energy, information, norm, utility,...what? Matter and energy carry information; information, especially when concentrated as a norm carries utility; what might utility carry? If matter-energy defines the material realm, and information spans the material and the living realms, and utility emerges only in the realm of the living, are there any further realms and, if so, what categories are basic to them? There is another realm one might consider. Just as life emerges from matter, mind emerges from life, so one might ask: what new scientific category central to some new scientific theory might help us understand mind, and most critically, subjective experience? 277 The possibility of new scientific categories yet to be discovered is not an idle reverie. Theories of matter, of the stuff of the universe, go back at least to the Greek atomists. Although 276

3.2.1 Matter, energy, and information, p. 88, 3.2.2 Utility, p. 93 An interesting speculation linking utility and mind is offered by Midgley (1994): consciousness might be an evolutionary emergent whose adaptive function was to manage internal collisions of value within agents. See related comments in Notes #102 Multiple subselves, p. 472, and #114 Selfreference, p. 487.

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ideas about energy may have been implicit in early philosophy (perhaps in Heraclitus) or prescientific thought, only in the development of thermodynamics in the 19th century was a scientific notion of energy available. Until the mid-20th century, there was no concept of information in the natural sciences and no formal concept of utility in the biological and social sciences. With the development of information theory and game/decision theory, there now exist exact and scientific notions of information and utility. It is hard to imagine not having these ideas at our disposal, but it is only about 75 years since they became available. Surely there will be other general ideas which future systems theories will formalize (make exact) and operationalize (make scientific). What will they be? Systems theory also connects science with the arts and humanities. This is possible because systems ideas apply not only to concrete systems but also to abstracted and conceptual systems, i.e., to systems abstracted from or not even grounded in material reality. Systems theories have the broad scope inherent to mathematics, but being less abstract than mathematics, they address themes ubiquitous in human experience, such as form, order and disorder, learning, cooperation, and conflict. 278 Connections of systems thought to the arts and humanities have been made in many ways. Ideas of entropy, information, and order have been applied to communication and form in the arts (Moles 1966; Arnheim 1971). Ideas from nonlinear dynamics have been used in literary studies (Hayles 1990). Computational approaches to art include evolutionary generation of visual and musical form (Sims 1994; Alfonseca et al. 2007); advances in Artificial Intelligence and Artificial Life have enhanced animation and special effects in the film industry. Connections to the arts and humanities go deeper than diverse borrowings and influences. The interest in science in a theory of systems or of complexity is paralleled by aspirations toward unity in the humanities. Structuralism, semiotics, critical 278

Table 2 Some general phenomena (systems themes), p. 71

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theory, and other movements in modernism and postmodernism reflect the wish for coherence in the arts, humanities, and social sciences. Often referred to simply as “theory,” these fields occupy an intermediate niche between the abstract domains of linguistics and philosophy and the more concrete domains of literature, political theory, psychoanalysis, and feminism. The similarity of this niche to the epistemological niche of ESM in the sciences 279 is plain. As in the systems project, there is rejection of disciplinary boundaries, and a privileged position given to the way the world is modeled – mathematics for systems theory and language for structuralism and semiotics. In both systems theory and structuralism/semiotics, there is pervasive abstraction. There is the same flirtation with denial of objective reality and affirmation of the arbitrariness of models, and with the abandonment of ontology in favor of epistemology (or methodology), 280 as if one could have one without the other. There is, however, at least one important difference between these two projects: critical and postmodern theories are highly political and ideological. Although one can find some ideological presuppositions and agendas in the systems literature (Hoos 1962, Lilienfeld 1978), this is true more for systems analysis than systems theory, 281 and the salience of ideology in systems analysis is also less pronounced than its salience in feminism, Marxism, and more generally in postmodern thought. 279

Figure 6 Between math/philosophy and scientific theories, p. 64 This orientation aligns well with the constructivism, represented in the systems camp in the work of Ashby (1956), who stresses the relativity of models, and Klir (1985), who sees systems theory as methodology. 281 Systems theory might even enable a critique of the use of ideas with a systems character to promote various ideologies. For example, the religious doctrine of “irreducible complexity” is an unfounded assertion of holism claimed as evidence for “intelligent design”; see Footnote #118, p. 102. The holistic linkage between forms of discrimination recognized in the political doctrine of “intersectionality” is narrowed by ideological agendas. Fictional and simplistic holisms underlie most if not all conspiracy theories, the classic example of which is antisemitism, omitted from the scope of intersectionality for political reasons. 280

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Not believing in “Truth” and espousing the relativity of narratives, postmodernism is shaped more by political and esthetic considerations than by empirical and rational ones. One can find in its literature denials and misinterpretations of scientific findings as well as attitudes that mirror the rejection of science by religious fundamentalism. Rejections of science arise from both the extremes of false uncertainty (postmodernism) and false certainty (religious fundamentalism), analogs of chaos and rigidity, respectively. Both reactions to modernity (PIII) focus on its deficiencies but fail to acknowledge its virtues. 282 There is also a bias among left-oriented postmodernists against invoking internal factors in explanations of social phenomena, a bias that assumes the unlimited plasticity and thus the intrinsic insignificance of structure. This shows up in the antiessentialist dogma that nothing is inherent, that everything is constructed from the outside – by society, by language, by discourses of power, and so on – that nothing, especially human beings, has any intrinsic nature. This denial is well intentioned, being motivated by the desire to combat racism, sexism, and other sources of human suffering, but while it is true that internal structure is not all-determining, it is simplistic to assert the opposite and say that external function is all-determining. Both structure and function have causal influence, and there are obviously interaction effects between the two. Although structuralism and semiotics have strong affinities with systems theory, the shift to poststructuralism and deconstruction has generated in postmodernism a fusion of ideology and skepticism that limits interaction with systems thought. Still, the systems project is not immune to the influence of these currents in the humanities and social sciences, and the reader may notice some postmodern ideas in this book. 283

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What succeeds as negation never succeeds as affirmation (1.2.5.4.2). Notes #8 Incompleteness vs. inconsistency, p. 320, #30 One, two, three, ten thousand, p. 359; #115 Binary oppositions, p. 492; #120 System

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6.2.5 Personal knowledge The ancient desire was…for kinds of explanation that are both much wider and more immediate. - Mary Midgley (1992) Very general metaphysical views ... are not just inert factual propositions which we might accept without altering our attitudes or policies. They speak to our imaginations in a way that changes our world-pictures. They affect our symbolism. They reshape the framework of our thought. They shift our mental postures. They affect that whole vital central area of human life which connects thought, feeling and action. Though they are not themselves value-judgments, they do much to determine our value-judgments. - Mary Midgley (1992) Systems theory offers a kind of scientific knowledge that can be personally acquired by individuals as “personal knowledge.” This phrase derives from Michael Polanyi (1964) who observed that the personal and subjective aspects of scientific knowledge are often ignored by philosophers and historians of science, who analyze science as a collective societal enterprise. This is appropriate, since while scientific knowledge is personalized to a degree by working scientists, scientific knowledge possessed by the general public is much less personal. Except where it touches on work or hobbies or the education of children, scientific knowledge is received as news from a distant world, as intellectual stimulation, or as a harbinger of economic or medical advances, but rarely as personally meaningful. Scientific knowledge is social, not personal. It is the basis of a broad range of economic activity and is accorded – though not by political ideologues – some cultural deference. It is too specialized, however, to be individually meaningful. It is also largely isolated from other formation, p. 496; #179 Its effects may endure, p. 588; see also the reflexive Appendix, p. 591.

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sources of human knowledge: from religion, literature, the arts, and politics. Although science is done by individuals, the knowledge it produces is not used by individuals, except for professionals who do research or develop technology. One reason for this is that knowledge is specialized, and thus comprehensible mainly by those who work in the specialized area. It is also specialized in a particular way. It is materially organized, and many domains of materiality are distant from ordinary human life. We have no direct access to the stars, to the molecules in our body, to the crustal plates of the earth, to the upper atmosphere. Knowledge about stars, molecules, crustal plates, and the upper atmosphere cannot be very personal. By contrast, systems knowledge is about form and process in general. Everything we have personal contact with exemplifies some systems theme. We have access, intellectually but also experientially, to order and disorder, variety and constraint, predictability and unpredictability, complexity, morphogenesis, adaptation and goal seeking, competition and cooperation, system formation, and many other phenomena addressed by systems theory. Systems knowledge is thus closer and more accessible to us in one way, but it is also more distant from us in another. Its abstraction makes it difficult to understand. But imagine if in our schooling, we were initiated into these ideas and trained in their use, not as an alternative to standard science, but as a supplement to it. Perhaps we might then be able to perceive, in our interactions with one another, with the natural world, and even within ourselves, the universality of constraint and variety, openness and closedness, feedback loops, differentiation and integration, hierarchical order, competition and cooperation, etc. Systems knowledge could then become personal knowledge. The concrete and specific facts of science are fascinating, but are often not directly usable by us, except occasionally when they bear on specific experiences that we have or decisions we have to make. The abstract and general principles of systems

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theory are no less interesting, at least to those with a taste for abstraction, but they also have widespread usefulness and relevance. We might pose this question to educators: which is it more important to learn: •

that what explains the world are its matter-energy fundamentals (quarks, strings, or whatever) – or – that what explains the world are the universal phenomena of order and distinction;

•

that atoms are made up of protons, neutrons, and electrons, which in turn are made of quarks and leptons – or – that all things are both wholes and parts and that wholeness and partness are always in tension;

•

that weather is produced by masses of air at different pressures and temperatures in interaction with one another – or – that even phenomena governed by simple laws with no source of external randomness may nonetheless be unpredictable;

•

that excess phosphates cause eutrophication in lakes – or – that all systems excrete disorder into their environment, which can only be neutralized by cyclic processes;

•

that genetic information is carried in nucleic acids by specific sequences of adenine, thymine (or uracil), guanine, and cytosine – or – that information is coded in patterns of matter-energy;

•

that viruses inject their DNA or RNA into cells and by doing so take over cellular metabolism – or – that the separation of material and informational processes always opens up the possibility of parasitism;

•

that it is difficult to prevent overfishing in the oceans – or – that in many situations, individual rationality produces collective irrationality;

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•

that volcanoes and earthquakes are the result of collisions of large tectonic plates moving on the surface of the earth – or – that many systems spontaneously move toward critical points where sudden changes occur at many scales;

•

that the evolutionary record shows biological extinctions in various specific geological periods – or – that long periods of stasis punctuated by sudden changes can be expected in dynamic systems even from internal causes;

•

that suppression of fires builds up a large flammable base which can fuel more severe fires, and the overuse of antibiotics leads to the evolution of resistant strains – or – that interventions in complex systems often produce counterintuitive effects, sometimes even exacerbating the very conditions intended to be prevented or alleviated;

•

that medicine X designed to counter disease Y has unfortunate “side effects” on organ Z – or – that one can never do just one thing and so-called side effects are never avoidable;

•

that bacteria inoculated into a nutritive medium grow exponentially – or – that growth in many systems (biological, social, technological) is initially exponential, producing rapid change that sometimes requires equally rapid human response;

•

And that such exponential growth in concrete systems cannot continue indefinitely – or – that growth governed by positive feedback is always eventually checked by negative feedback, at best yielding a stable steady state; at worst, producing collapse.

Many more paired alternatives could be listed. The study of scientific fact contributes to the growth of knowledge, but the study of scientific principle contributes to the development of understanding. There is potential power in knowledge, and

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potential wisdom in understanding. There is more than enough power in the world, but not enough wisdom. An exact and scientific metaphysics would be a resource for wisdom. Imagine that one systems idea – the Prisoner’s Dilemma – was taught effectively in all elementary and high schools. Imagine as a consequence that in a new generation this archetypal structure in which individual rationality leads to collective irrationality was easily recognized. Imagine that instead of the fruitless tension between “looking out for number one” and “doing what society says is right,” there was an appreciation of dilemmas of collective action; that instead of the habit of blame in conflict there was an understanding of how the structure of situations often binds the actors involved; that instead of the naive belief in a preordained accord between individual self-interest and the common good there was a more sophisticated realization that in some situations such accord exists but in other situations it does not. Would this not be a valuable contribution to the practical and moral education of our children? Imagine that a second systems idea – exponential growth – was also taught effectively in elementary and high schools. Is it not possible that this would provide the public understanding needed to respond adequately to short-term challenges of pandemics and the long-term challenge of climate change? 284 And would not understanding the impossibility of indefinite exponential growth promote acceptance of the need for an economy based on steady-state utilization of renewable resources rather than on irreversible depletion of one-time resource endowments? Thoroughly grasping just these two systems ideas – the Prisoner’s Dilemma and exponential growth – would contribute significantly to the capacity of our children to understand the world they live in. Multiply this contribution manyfold with 284

About harm that increases exponentially, see Note #134 Failures in meeting new challenges, p. 525.

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other systems principles. Deepen it with the understanding that these are the general archetypes that govern both the harmony and the disharmony of the world. Provide practice in the application of these ideas to both oneself and the world, to both the subjective and objective realms. Would not an exact and scientific metaphysics be a valuable component for genuine education in science? 285 6.3 Natural religion The notion of “natural religion” was historically opposed to that of “revealed religion,” and thus implicitly to “organized religion.” As used here, the phrase does not refer to its historical meaning, namely naturalistic arguments for the existence of God. What is meant here is “religion, naturalized,” specifically, religion from the perspective of science, more specifically, from the viewpoint of a non-materialist and non-reductionist component of science, namely systems theory. Beyond the significance of the systems project for science, this project is also significant for the productive interaction it can stimulate between science and religion. 6.3.1 Secular Theodicy 286 It is impossible for a man not to be part of Nature and not to undergo changes other than those which can be understood solely through his own nature and of which he is the adequate cause. - Baruch Spinoza, Ethics The ontology of problems of Essay is, in religiousphilosophical terms, a theodicy, although a secular one, if the oxymoron of a secular theodicy is permitted. Traditionally, theodicy is the attempt to reconcile the belief in divine justice 285

Recall von Bertalanffy’s manifesto (p. 52) which spoke of the “needed integration of scientific education.” 286 For an essay that overlaps with ideas expressed in this section but is more personal, see (Zwick 2008).

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and power with the reality of evil, the word “evil” being used not narrowly only for wrongful human action, commonly referred to as “moral evil,” but broadly to include also suffering, decay, imperfection, and death, referred to as “natural evil,” and still more broadly but abstractly to highlight the general principles, called “metaphysical evil,” that underlie moral and natural evil. One of the attractions of a scientific metaphysics is that it might offer an account of all three types of evil, expressed in general terms and linked to scientific understanding. Literally, a “secular theodicy” is a contradiction in terms, as reference to divinity has long since been abandoned in scientific discourse. Yet if we no longer feel a contradiction in the existence of evil in a divinely created order because we have relinquished belief in such an order, there still is a need for explanation and consolation, which are also functions of theodicy. Or, from a non-theistic perspective, one might seek to understand the origins of what Buddhism calls “dukkha,” the unsatisfactoriness of human experience. In terms of Rosenzweig’s (1921) God-World-Human triad, theodicy addresses human suffering in a God-centered way; Buddhism addresses it in a human-centered way; a systems theoretic ontology of problems approaches it in a world-centered way. 287 Systems ideas can help us understand the causes of human suffering, and it may be that the most valuable contribution that the systems project can make toward solving contemporary problems are not techniques of mathematical or computer modeling, but the abstract – indeed, metaphysical – clarification of the “lawfulness” of these problems. In a reductionist metaphysics, a secular theodicy would be impossible, since the problem of evil is divided into smaller unconnected problems, and at the level of fundamental physics it disappears. From the point of view of physics, evil is an illusion, not a well-posed problem. The systems view, while 287

For these different centered perspectives, see the discussion of Table 1 Ontological vs. epistemological stances, p. 57

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equally abstract, “saves the phenomena” and provides a general explanation of dysfunction, precariousness, and suffering. 288 A systems theodicy recognizes that constraint is the price of existence and is a property of the cosmos on all levels, yet also notes that constraint is opposed by variety, equally lawful and universal. In the language of Kabbalistic metaphysics, constraint is “severity,” intrinsic to existence. Scholem (1991) writes, ...But the act of tsimtsum itself, in which God limits Himself, requires the establishment of the power of Din, which is a force of limitation and restriction. Thus the root of evil ultimately lies in the very nature of Creation itself, in which the harmony of the Infinite cannot, by definition, persist; because of its nature as Creation – i.e., as other than Godhead – an element of imbalance, defectiveness, and darkness must enter into every restricted existence, however sublime it may be. It is precisely the rigorously theistic tendency of Lurianic Kabbalah that requires evil as a factor necessarily inherent in Creation per se, without which Creation would necessarily lose its separate existence and return to being absorbed in the Infinite. That the root of evil is inherent in Creation is already expressed in the Bible, well before the later development of Lurianic Kabbalah, in a simple emotionally charged image: there was a snake in the Garden of Eden. Also, the primordial condition before Creation was tohu va’vohu, absolute disorder, not totally vanquished by the order and distinction (i.e., system formation) that constitute Creation (Levenson 1987). To use the Kabbalistic ideas in the above quote in novel ways, consider the following: The contractive force of Din, systems theoretically, is constraint; in Kabbalah it is balanced by the expansive force of Hesed which, systems theoretically, is 288

See the related discussion in 5.4 Ontology of problems, p. 167

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variety. The result of Din is incompleteness, the constriction of a system within its environment. 289 This applies Lurianic ideas not to creation as a whole but to individual systems, which are the consequences of the cataclysm of creation. 290 Essay as a secular theodicy points not only to the tension between constraint and variety but also to the universality of many other tensions. 291 There is the possibility but not the inevitability of reconciling such conflicting imperatives, each of which in isolation causes precariousness and dysfunction. Although hazard and affliction are inherent in finitude, a systems theoretic secular theodicy does not preclude their being temporarily and locally overcome. If a systems theodicy provides a “defense of God” by explaining evil and suffering as inevitable aspects of the natural order, it also provides a defense of humanity against the charge, made by both western and eastern religious doctrines, that evil and suffering are fundamentally of human origin, due to action or ignorance. This accusation blames the victim. Although some victims are blameworthy, and even victims have responsibilities, the original sin of humanity is simply the sin of having originated. 292 This “sin” is common to all being, an imperfection that inherently afflicts all of creation: finitude, the unavoidable incompleteness and inconsistency of all things. In a more balanced view, however, finitude is also original virtue, or perhaps one should say original beneficence, a manifestation of the good that inheres in and blesses existence. 293

289

See Constraint 1.1.2 and 7.1.2, pp. 7, 324. See the Taoist-Kabbalist “poem” about the “One” and the many “ones” in Note #30 One, two, three, ten thousand, p. 359. 291 Summary 1.1.9 and 7.1.9, pp. 23, 491 292 Note #178 Dissolution, p. 587. An alternative systems theoretic “original sin” is the fact that utility first emerges in the self-interest of living systems. Yet this sin too is also original virtue since it is by this means that the good first becomes instantiated in the world (Zwick and Fletcher 2014). 293 A.2.3 Euphorics, an antidote, p. 608 290

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Imperfection is not simply the inadequate instantiation of form within substance. It is not only, as Plato said, that matter is recalcitrant and can embody form only approximately. Form is recalcitrant as well; both are afflicted with the consequences of finitude. It was once believed – perhaps inspired by geometry – that perfection and simplicity of form might point toward the domain of divine perfection, but there were always nagging doubts. The Pythagoreans suppressed their discovery of the irrationals. Kepler was forced to sacrifice the beauty of his Platonic solids model of the solar system, as well as the perfection of traditional spheres and circles, in favor of the much less mathematically elegant ellipse. 294 In our own time, a vision of a perfectly orderly world of form motivated Whitehead and Russell’s Principia Mathematica but was undermined by Gödel’s theorem, the implications of which are still being elaborated. It is commonplace now to note imperfections in the world of form and the capacities of reason. Game theory, the Arrow Impossibility Theorem, and the theory of computational complexity all declare the limits of order and rationality. Cybernetics reveals that signal and noise, representation and illusion, are fundamentally, i.e., intrinsically, indistinguishable. Chaos manifests the complexity implicit in simplicity and severs the connection between determinism and predictability. If the forms are in the heavens, there is strife there as well. This is not cause for alienation. We are at home in the universe not only because, as Hermetic philosophy asserted, the order within (below) is isomorphic to the order without (above) but also because the disorder within is isomorphic to the disorder without. As limited wholes, we are simulacrums of the larger whole, and in the isomorphisms of negative qualities, there is also a kind of order. Although our flaws echo the flaws in the cosmos, we can affect and are thus accountable for the quality of our own domain of existence. Many aspects of the 294

Kepler’s “ovals,” in their abandonment of divine symmetry, were to him a “cartful of dung” (Koestler 1959, quoting a letter from Kepler to Longomontanus).

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natural order that cause pain and suffering to life are partially remediable. Fundamentally we are not to blame, but we are still responsible. By accepting this responsibility, we become the mediating factor through which polarities may be integrated and transformed. 295 We are charged with the rectification of creation, and our actions have metaphysical significance. In the terminology of theodicy, what is under discussion here is metaphysical evil, an account of which is given in Essay. Leibniz held that metaphysical evil was the basis of both natural evil and moral evil (Neiman 2002), and the Lurianic and dialectical perspective of Essay supports this view. More precisely, metaphysical evil encompasses natural evil, which encompasses moral evil (Figure 30). Metaphysical evil is the most general conception, which includes natural evil as a concrete instantiation. Natural evil includes moral evil because humanity is part of the natural order. Both inclusions reflect the aspect of similarity (isomorphism), 296 but under the aspect of difference (emergence), moral evil is a special case, because humans have unique capacities and thus responsibilities. Human beings are part of the natural order and unique, a dual affirmation expressed by Jonas (1966). Figure 30 Metaphysical, natural, and moral evils

metaphysical evil natural evil moral evil

295

See discussion of the autonomic realm in 5.3 Categories of complexity, p. 160, and 6.5 Summing Up: promise of the systems project, p. 278. 296 3.3 Isomorphism and emergence, p. 97

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Referring moral evil back to natural evil and natural evil back to metaphysical evil reflects a kind of upward reductionism, 297 motivated like the more familiar downward reductionism by a dissatisfaction with multiplicity. But reducing moral and natural evils to metaphysical evil does not eliminate multiplicity, since real-world problems have multiple metaphysical essences; this inheres in the fact that phenomena usually must be addressed by multiple systems theories. 298 What then is gained by a systems conceptualization of a societal problem? Two answers might be offered to this question. First: essences are deeper (in the type of reductionism here being deployed, higher) than appearances, so it behooves us to grasp them. Second, one can have a unitary view of metaphysical evil in its most fundamental sense. The Lurianic account above is one such view. A simpler but related view is captured in the quote from Spinoza that opens this section: metaphysical evil has its ultimate source in incompleteness, in the finitude of every “mode” (system). The quote speaks of the fate of human beings, but Spinoza intends a more general proposition: every mode is finite – has a necessary environment – and is not the sufficient cause of its arising or of its future fate. This proposition accords with the Buddhist doctrine of codependent origination. Systems do not originate or sustain themselves. It is also the position of Essay: incompleteness, which follows from finitude and flaws wholeness, is the most general explanation for (metaphysical) evil. The hierarchy of categories in Essay 299 is an attempt to organize our conceptions of evils that, so to speak, are rooted in the heavens. Although Essay’s ontology of problems is Leibnizian in positing metaphysical evil, it is anti-Leibnizian in the implications drawn from this. Leibniz held that this is “the best of all possible worlds” – with emphasis on “possible” – for 297

“Up” metaphorically means more abstract. For upward reductionism, see 3.5.1 Structure and function, p. 109. 298 Figure 7 Systems theories and specific scientific theories, p. 65 299 5.3 Categories of complexity, p. 160

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which he was rightly mocked by Voltaire. The position advocated here is the opposite: perfection is not of this world, but perfecting is. The world is indefinitely perfectible, so it is never the best that is possible. Radical moral evil, to which the 20th century gave ample witness, cannot be neutralized by theodicy. Nor is perfecting guaranteed by history, as Hegel and Marx imagined. In a systems ontology, contingency plays both negative and positive roles. Hazard and thus also opportunity exist. The task of perfecting (in Kabbalistic terms, tikkun, i.e., “fixing,”) is in the hands of life; more specifically, human life. In game-theoretic language, this position asserts that conditions are hardly ever Pareto-optimal. 300 The task of perfecting is clarified by the Pareto diagram of Figure 31. The horizontal and vertical axes represent different needs, values, or utilities of one system, or a single need, value, or utility of two different systems. 301 The shaded area is the domain of the achievable, and the backward sloping line, called the Paretooptimal (PO) line, is the northeast border of this domain. Figure 31 Pareto-optimality U1 and U2 are competing utilities

U2 • U1 Along the PO line, increase in one utility (for simplicity, the discussion here refers to utilities) is accompanied by decrease in the other. The current state of the system is represented by the 300

Note #66 Pareto-optimality, p. 418 The diagram is applicable to all the dyadic tensions or aporias that afflict systems; see 1.1.9 Summary, p. 23, although some tensions are better represented one-dimensionally. Tensions can be triadic or of higher ordinality, but the present analysis is dyadic.

301

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interior point. Movement of the point in the northeast direction toward the PO line is a perfecting that increases both utilities for the single agent or, in the other interpretation, the utility values for both agents. 302 The interior point, not being on the PO line, is non-Pareto-optimal, which means that improvement of the system is possible by movement toward the PO line. 303 The position advocated here is that nearly all systems are in such non-Pareto-optimal states. 6.3.2 Metaphysics, a bridge to religion 304 You cannot shelter theology from science, or science from theology; nor can you shelter either one from metaphysics, or metaphysics from either one of them. There is no shortcut to the truth. - Alfred North Whitehead (1926) As his books show, Davies's claim [that “science offers a surer path to God than religion”] depends on treating virtually all religious questions as depending on cosmological propositions centering on the Big Bang. But actually, not many questions of general importance do depend on views about that bang, however big... Most religious questions arise within human life and begin by asking about its immediate meaning...Our metaphysical ideas are rooted in the life that we know. - Mary Midgley (1992) A systems metaphysics has relevance to religion beyond the secular theodicy that it offers. It is instructive to think about this in the context of the many connections to religion that have been claimed for modern science in general, and especially for physics. Religious significance has been seen in speculations 302

In games amenable to solution by negotiation, the PO line is also known as the “negotiation set.” This line in the figure is a linear trade-off between the utilities, but the boundary of the domain does not have to be linear. 303 This analysis is expanded in the discussion of Figure 103 Progress and Pareto-optimality, p. 511. 304 An article that augments this section is (Zwick 2007)

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about the origin of the universe and in the anthropic principle (Barrow and Tipler 1986), the exquisite match between the values of the fundamental physical constants and values necessary for a cosmos that supports life. Similarities have been noted between quantum theory and reports of mystics. Human consciousness has been asserted to be implicated in quantum measurement, and there is much talk about classical and quantum “levels of reality.” While such claims are intriguing, their scientific merit is uncertain; more importantly, their spiritual significance is insubstantial. These ideas appeal because they make us comfortable. They tell us that we live in a universe that is not alien but precisely tailored for our existence. They reassure us, despite our experience to the contrary, that reality is seamless and harmonious. They feed fantasies of self-importance. We ourselves reduce the cosmic wave function, so our own glorious consciousness creates the universe. They declare the limitlessness of our power by telling us that we tap into a primal subatomic energy. They flatter us by suggesting that we are the equals of the mystics because our quantum theory also speaks about the unity of existence. Interestingly, the inflation of our importance implicit in these ideas is the mirror image of the deflation of our importance that is the message of fundamentalist secularism. These ideas, which feed feelings of importance, are conducive to reverie, solipsism, and self-satisfaction, not to objectivity, presence, and effort. At best, they undermine narrow models of the world, nourish our sense of wonder, and provide a scientific echo, however metaphorical and remote, of important truths not encompassed by the dominant scientific worldview. But at worst they are moral distractions, spiritual soporifics, and invitations to intellectual dishonesty. They let us repress the humiliations of the Copernican, Darwinian, and Freudian discoveries. Through these ideas we hope to regain the significance we had in the medieval worldview that was undermined by science. But attempts to see spiritual

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implications in physics are a sign more of the wish for a reconciliation between science and religion than of accomplished movement toward this goal. Little progress has actually been made toward such a reconciliation. One reason for this is that the ideas of physics are weakly connected to human experience. Another reason is that attempts to reconcile science and religion have often tried to find scientific support for a belief in God. The history of attempted proofs of the existence of God is barren of convincing success, and it is unlikely that science can assist in such efforts. The anthropic principle is a possible exception: the sensitivity of cosmological order to values of the physical constants is suggestive of the classic argument by design, but this idea is neutralized by the multiverse hypothesis. For a productive exchange to occur between science and religion, methodological atheism (Habermas 2002) must be adopted, since God-talk is not appropriate for scientific discourse. What science might contribute, however, to such an exchange is a different metaphysics, one that is not distorted by materialist reductionism. Physics needs to be displaced by biology as the science most relevant to our worldview, and the philosophy of biology needs to correct the denial of progress and overemphasis on randomness that distorts our understanding of evolution. The philosophical implications of autopoiesis, the significance of the augmentation of the categories of matter and energy with those of information and utility, the linkage of fact and value in the domain of life, the differences of complexity and potency that indicate a qualitative hierarchy among living forms, the natural emergence of mind, the evolutionary ratchet of altruism 305 – these and other systems-oriented themes are more important to the science–religion dialog than any speculations on the origins of the universe or strained imaginings of a “God of the gaps” who intervenes in the interstices of natural processes. 305

Zwick and Fletcher (2014)

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We feel the absence of a worldview – Donne (1611) wrote, “Tis all in pieces, all coherence gone” – and we hope that what has been lost might be provided by science. This hope may be justified, but quantum mechanics, particle physics, and cosmology cannot provide the resources necessary for this task. What is needed is a metaphysics linked to science and mathematics that is oriented toward the central and not the fundamental and toward form rather than matter. Such a metaphysics could become the cornerstone of a new worldview that promotes a recovery of cultural coherence. A systems metaphysics makes conceivable a reconciliation of science and religion that is different from what has been sought after from physics. Such a metaphysics would accord ontological respect (but not priority) to phenomena on a human scale. It would be a modern version of the integrated view of science and religion that characterized Pythagorean thought and also permeated the origins of science as it emerged from its Western religious matrix. The systems view reasserts the Hermetic principle, “As above, so below.” 306 The laws governing all domains of existence are similar, not in the sense that everything is reducible to physics and is only the play of elementary particles, but in the sense that there are universal structures and processes, extensive isomorphisms, that exist between many different types of systems. Scientific knowledge was once partially organized in this way: it was not set apart from other forms of knowledge or divorced from wisdom. It might be so again. A systems metaphysics would join such isomorphisms to the understanding of emergence, and in this embrace of both similarity and difference, a reconciliation of science and religion becomes imaginable.

306

This principle asserts the ubiquity of isomorphisms. Isomorphisms, which are central to systems theory, are discussed in multiple sections: 2.4 The epistemological niche of systems theories, p. 63; 2.5 Theories and models; the idea of “system”, p. 71; 3.3 Isomorphism and emergence, p. 97; and 4.1 Not just mathematics, p. 123

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But the isomorphisms of contemporary science depict a cosmos quite different from the Pythagorean and Hermetic visions. Beyond the geometry of simplicity, of spheres and triangles, we now have a geometry of complexity, of mountains and trees, a fractal geometry of nature. Beyond statics with its simple musical analogies, we have complex dynamics, which can support isomorphisms worthy of Bach. The Pythagorean ideas were too simple and overemphasized harmony. The world is not strictly harmonious; nor is it only a vale of tears. The world is a blend of the harmonious and the unharmonious, at the edge between order and chaos. There is both perfection and imperfection. What links these opposites is hazard, 307 and it is not – pace Plato – that there is perfection at higher levels and imperfection at lower ones; there is both perfection and imperfection – and thus hazard – all the way up. Systems thinking has often touched upon religious themes. Churchman (1968, 1979) presents the religious perspective as an “enemy” of the “systems approach” and thus a part of it, because the systems approach must encompass every sensibility. Deutsch (1966), speaks eloquently of faith, love, and spirit using cybernetic ideas. For Deutsch, religious commitment requires a kind of closedness but responsiveness to the present requires openness; grace is a harmonious balance between the two. Beyond metanoia, individual spiritual work, there is tikkun olam, redeeming action in the world, to which many systems ideas are relevant. For example, Boulding’s work on conflict (1962) and Axelrod’s work on the evolution of cooperation (1984) show how game-theoretic ideas bear on ethical issues and bridge the fact-value divide. Kauffman (2008) discusses the inherent creativity of the universe, offering a systems theoretic version of the traditional principle of plenitude. Locker (2010, 2019) explores interfaces between systems theory and theology.

307

The emphasis on hazard is borrowed from Bennett (1976).

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There are many other links between systems and religious ideas. The view of system formation as the arising of order and distinction accords with the biblical account of creation (Levenson 1987). Boulding’s hierarchy (1956) of systems 308 is a scientific formulation of the “great chain of being” (Lovejoy, 1936). The triad of matter-energy-information echoes the three gunas of the Samkhya tradition of India. The refinement of information from matter-energy exemplifies alchemical distillation and etherialization. The noosphere of Teilhard (1959) is being instantiated by the Internet, and the difference between “angel” or “devil" and “meme” is not great. Numerous other religious ideas have systems theoretic cognates. 309 Beyond the actual links that exist between systems ideas and religious ideas, systems thought is more compatible with religious perspectives than the materialist reductionism of the standard scientific worldview. This is because the systems view privileges form and process over substance, wholes over parts, and emergence over reduction. It accords ontological status to function as well as structure and to potential as well as actual. It centers at the scale of living systems. It models levels of purposefulness and altruism. It sees planetary life in a cosmological context and as potentially self-regulating. The “edge of chaos” idea 310 has religious resonance in that it brings the order and the creativity of nature into relation and implies a cosmos in which hazard and opportunity are both real. So for both specific links and general compatibility, a systems theoretic exact and scientific metaphysics has religious implications. 308

5.2 Hierarchy of system types, p. 154 Several notes also touch lightly or indirectly on religious themes. Note #16 Order and disorder, p. 336, and Note #95 Hierarchical egalitarianism, p. 457, refer to Chuang Tzu, and Note #30 One, two, three, ten thousand, p. 359, to Lao Tzu. Note #18 Unity and multiplicity, p. 340, quotes from Augustine’s Confessions. Note #29 Nothing, many, one, all, p. 358, structures four concepts of number (Nothing, All, One, Many) that have been central to different notions of God. The Golden Rule is referred to in Note #80 Symmetry or altruism may be harmful, p. 436. 309

310

Note #17 Chaos, p. 338

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Systems ideas resemble conceptions that have guided some forms of religious practice. In the Pythagorean and Hermetic traditions, theory organized around isomorphisms and open to experiential verification gave spiritual practice a partially scientific character. For example, alchemy as a spiritualpsychological pursuit was a practice in which inner inquiry was guided by an intellectually elaborate and emotionally rich system of chemical metaphor (Jung 1944). Chinese philosophy emphasized “correlative tabulations” which posited extensive isomorphisms across the natural and social orders (Needham 1956), and Taoist meditation, t’ai chi, and acupuncture share with this philosophy a common set of theoretical ideas. The Arica school (Ichazo 1982, Horn 1983) which advertised itself as offering a “technology of consciousness” also taught a theory (“trialectics”) organized around isomorphisms. Certain aspects of religious traditions and spiritual disciplines thus can be seen to resemble scientific investigation, to constitute “inner sciences” centered in the empirical experimentation of individuals, undertaken in a community of investigators, and supported by relevant theory. Although such theory is primarily concerned with the psychological and spiritual, it has often had a wider scope, as the aphorism, “As above, so below” suggests. Insofar as spiritual practice is guided by theory said to apply to phenomena both internal and external to us, there is a link between modern science and aspects of religious and spiritual traditions that are science-like. Many issues involved in spiritual practice can be expressed in systems theoretic language: the need for both autonomy and interdependence, integrity and responsiveness, closedness and openness; the inescapability of external constraint yet the possibility of choosing the relevant environment that we live in; the dependence of open systems on external input and support; 311

For a more expansive discussion of ideas in this section, see Zwick (2010).

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the search for identity and authenticity, and the recognition of both uniqueness and universality in ourselves and others; the acknowledgment of and reconciliation with our multiplicity – and internal contradictions – and the striving to facilitate the emergence of internal unity; the promise and danger of “higher states” and the difficulty of harmoniously relating the higher and the lower in us; the slavery of being dominated by forces outside us and inside us and the difficulty of finding freedom in relation to these forces; the lawfulness of rigidification; the need to distinguish between what is subjectively constructed and what is objectively real; and more. Perhaps the single most important systems idea that illuminates spiritual practice is incompleteness. Morinis (2007) writes: The great Mussar 312 teacher Rabbi Moshe Chaim Luzzatto discusses this notion in his book Discerning Knowledge: “The one stone on which the entire building rests is the concept that God wants each person to complete himself body and soul…” He is telling us that we are created incomplete so we can complete the work of our own creation. Incompleteness, which is a lawful property of all that is, applies to every individual human being. We are not fully developed, but rather flawed and imperfect. With the self as with the world, perfection is impossible, but perfecting is always possible. And obligatory. One can conceive of a spiritual practice supported by a theory expressed in the language of systems laws. Something like this was imagined by Hesse in his Magister Ludi (The Glass Bead Game) published in 1943, a time when the systems movement was beginning to crystallize. Hesse was prescient in portraying the emergence of a systems (though he did not use

312

Mussar is a tradition of inner work (tikkun of self) within Judaism.

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this word) worldview and the religious potential inherent in it. A quote from the book’s Foreword makes this explicit: Members of the [Castalian] order must seek to coordinate all the arts and sciences into a whole which transcends the sum of the constituent parts; something akin to what Robert Bridges, I presume, had in mind, when in “The Testament of Beauty” he wrote of the “accord of Sense, Instinct, Reason, and Spirit.” For those who attain a proficiency in it the [the Glass Bead Game] is raised to the level of a mystic rite, in which the acutest mental awareness is coupled with a Yoga-like discipline of meditation. Music – in particular the “pure” music of Bach – and mathematics are the foundation stones upon which the whole complicated structure is erected. Coordination of many arts and sciences can only be accomplished at a high level of abstraction, and Hesse also expresses the insularity and the dangers of an exaggerated pursuit of the abstract. Excessive abstraction is common to religious tradition, which often reveres spirit – for example, pure consciousness – but disdains soul – the “mere” contents of consciousness. 313 Denigration of soul by spirit is endemic in the spiritual disciplines, a surefire prescription for intellectual error and moral failure. The relationship required between spirit and soul is “alchemical” union. There may be “sacred isomorphisms” capable of being expressed systems theoretically that can be experientially grasped and can guide spiritual inquiry. Religion speaks to our emotional nature through myth, but to address our intellect, it must use the language of reason. In the modern era, the 313

Hillman (1976) is eloquent about the duality of spirit and soul, and the differing concerns of spiritual practice and psychotherapy, which focus on what Bennett (1956, 1964) called consciousness and sensitivity, respectively (Figure 97 Levels of operation of the modeling subsystem, p. 488). See also Notes #94 The highest is not the whole, p. 456, and #95 Hierarchical egalitarianism, p. 457.

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dominant mode of reason is science, so sacred truths need to be cast also in scientific form. The idea of “two magisteriums” (Gould 1999), two kinds of understanding – religion and science – separate from one another, is the counsel of despair. More than this is both possible and necessary. Through systems ideas a link between science and religion could be made that offers more than intellectual fascination. It could provide a worldview centered at the human scale that connects science to religious truths discoverable only through practice. 6.3.4 Revisiting the historical model In our age, religious pluralism is the will of God. - Abraham Joshua Heschel (1996) The possibility of productive dialog between science and religion may seem unrealistic. Although the development of science initially seemed compatible with natural religion, it led to science–religion wars that continue to this day and make it appear that these two worldviews are incommensurable (Gould 1999). The tide is shifting, however, and a new encounter between science and religion is underway, now including Buddhism which in its Western manifestations is probably the religion that is most compatible with science. Buddhism was never involved in the science–religion wars; it is rooted more in experience than doctrine and its central practice of meditation lends itself to scientific study. 314 There are also efforts within Christianity to have a dialog with science. Competition among religions for the attentions of science would be a good thing. A productive relationship between religion and science will necessarily entail the continued secular critique of religion. This critique is well developed in the West, especially as applied to Christianity and Judaism, but even in the West this critique has not been sufficiently successful. As Wieseltier (2009) observed, “Spirituality is surrounded by superstition. It is a permanent siege.” This observation applies not only to 314

6.3.3 Inner science, p. 240

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spirituality defined narrowly but to religion in general. There has long been disbelief in evolution within religious communities. More recently, we have seen in such communities disbelief in climate science and belief that religious practice protects against infectious viruses. Rectification of religion is one of the functions of science, 315 and much work remains to be done. Science, more precisely secularism, is a sacred denial that could purify the sacred affirmation of religion (Kook 1978) by separating the wheat from the chaff in religious doctrine and practice. Religious critique of science might also deepen science. Whitehead thought that philosophy mediates between science and religion; hence the religious significance of an ESM mediating between science and philosophy. While the abandoning of creationism in favor of intelligent design by some opponents of evolution reflects a scientific maturing of Protestant fundamentalism, this shift is mostly tactical, and replacing the error of creationism with the vacuity of intelligent design is only a modest step. It should be acknowledged, though, that opposition to evolution is partly a reaction to ideological interpretations of evolutionary theory by scientists. 316 A systems perspective on evolutionary theory is less likely to evoke this reaction, although it will not convince Bible literalists. In the historical model presented above, the primary societal process (PI) at this moment of history is facing the hazardous major barrier to transformation to a new organizing principle. Simultaneously, the tertiary process of science, 315

In terms of Figure 28 Macro-historical processes of complexification, p. 197, the rectification of PII is one function of PIII. 316 See earlier comments on randomness and progress in evolution in 6.2.2 Understanding what we know, p. 210. Like intelligent design, vitalism was empty as a positive doctrine, but vitalism was correct in denying the adequacy of Newtonian mechanics to explain life. As an expression of dissent, theories that are false or “not even wrong” may keep alive a recognition of the need for further advances in science and for nonideological interpretations of its theories.

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secularism, and modernity (PIII) is facing its minor barrier, less momentous than the challenge faced by the primary process, but difficult nonetheless. These present-moment difficulties faced by PI and PIII are discussed in the next section as they relate to politics. What is asserted by the model about the present moment with respect to religion is that PII, having merged with PI in shaping the major world civilizations, is not yet facing its major barrier. It is too early for the world religions to confront their own moments of truth, although the model suggests that this might occur in the future – at point 2ʹ of PII, analogous to point 1ʹ of PI. In the present historical moment, PII manifests some positive developments: globalization has unleashed a modern echo of the original Axial teachings, namely the emergence from hiddenness and the new global accessibility of the esoteric cores of many religious traditions. Unfortunately, the unfolding of PII also encompasses conflict among religioncentered civilizations (Huntington 1997). Intercivilizational conflict has, for example, been generated by militant Islamism in reaction to internal failures of modernization and external impact of the West. Ultimately, this problem is internal: PIII, which might rectify PII, cannot be induced externally. 317 The Islamic world awaits its own Renaissance and Enlightenment. Embracing modernity ultimately requires accepting religious pluralism, the relinquishing of claims by every tradition to the exclusive possession of religious truth. None of the traditions is close to this, although Christianity was forced by its own confessional wars to see the value of religious tolerance. Sufism has also been remarkable in its respect for other religious traditions, and this is relevant to the challenges posed by political Islam. If Sufism could regain its former status, it would weaken the link between mosque and state and foster harmonious relations with other religions. The appeal of Sufism goes beyond its spirituality and openness. Its opposition to terrorism is principled, and its experiential, as opposed to dogmatic, orientation is compatible with cordial relations with 317

All development is internal development (1.2.2.4.2).

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science and modernity. But Sufism is unable to thrive under the threat of Islamist violence, and it has been attacked not only by fundamentalists who regard it as too ecumenical but also by modernists who see it as superstitious. More critically: modernity has not yet brought any tradition to fully face its errors and distortions. It is not merely that followers are imperfect. The sacred traditions themselves are imperfect systems of thought and practice. Reason and history make this plain. Acceptance of the value of pluralism and the fact of imperfection are bitter pills for any tradition to swallow, but is crucial to perfecting the traditions and easing interactions between religious civilizations. Belief in the perfection of any particular tradition, its central figures, even its sacred books, is ultimately idolatry. Universal imperfection is a central truth not only of modernity but of any spiritual tradition that faces itself honestly. A productive encounter between modern science and religion would contribute to the recovery of cultural coherence. It could also provide a neutral scientific background for dialog between different religious traditions. No aspect of science offers greater support for science–religion dialog than the systems worldview. Unlike the dominant scientific worldview based in physics, the systems view does not abandon the human scale. It seeks to embrace the whole, but admits the impossibility of doing so. It says more about “everything” than can be said by materialist reductionism. It can assist in the recovery of old forms of knowledge eclipsed by science, in the recognition of connections between religious and scientific understandings, and in the correction, refinement, and modernization of the great sacred approximations.

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6.4 Fixing the world To seek to understand something … without at the same time criticizing it is, in my view an impossible procedure; and I suspect that whenever a distinction is made between understanding and criticism there is some kind of authoritarian demand behind it. 318 - Theodor Adorno (2000) “To understand is to accept” is a familiar aphorism, but it is only a partial truth. Adorno provides its necessary complement: to understand is to criticize. And criticism should promote efforts to fix; as Marx wrote (1888), “The philosophers have only interpreted the world in various ways; the point is to change it.” But trying to change what is not adequately understood can make matters worse. The problem is that all understanding is incomplete. Systems theory cannot overcome this limitation, but it can offer additional insights into what we want to understand and what we need to criticize. Specifically, the systems project offers ideas and methods relevant to present day societal problems at both the national and international levels. In what follows, some systems ideas are applied to three themes, 319 two relatively concrete and the third more abstract:

318

•

sustainability and globalization international level) (section 6.4.1);

(at

the

•

modernization as differentiation (at the national level) (section 6.4.2);

•

the gap between actual and ideal and the incoherence of the ideal (section 6.4.3).

The subject of the quote is philosophy, but it is likely that Adorno would have approved a generalization of his assertion to include any subject . 319 5.5 Metaphysician’s desk manual, p. 174, offers a very different way of illustrating the application of systems ideas.

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6.4.1 Sustainability and globalization In the 1970s and 1980s, the systems community raised public awareness of the planetary crisis that we are now experiencing. Forrester, Meadows, and their colleagues (Forrester 1971; Meadows et al. 1972) in their “limits to growth” studies pointed out that exponential growth in population, the economy, and human impacts on the environment cannot continue indefinitely. Nothing grows exponentially forever. 320 Limits are always reached, and the system must either transition to a steady state or risk major collapse. These studies used system dynamics models 321 to explore the interactions of a small number of global (aggregated) variables. Later studies used more complex and disaggregated models, but even for a few variables, grasping the behavior of dynamic systems is beyond the capacity of mental models. Much was wrong with the models and analyses done in this period. They were “coarse-grained views of the whole” 322 that omitted critical variables and relations. They were sensitive to the values chosen for parameters and the forms of the relations assumed, yet the values and functional forms were not known or even knowable. (Still, sensitivity to values and functional forms is not always a sign of error; it may reflect true instability. 323) As a source of predictions, e.g., of population growth or resource depletion, the models were flawed, but they were not actually intended to make predictions. They were alarms, and it was hoped that they would be self-denying prophecies. Their aim was to stimulate discussion. Despite their flaws, the basic conclusion of these studies remains valid: that exponential growth in resource utilization cannot continue indefinitely, that industry must shift from open 320

Note #130 Trajectories of development, p. 517 Note #36 Stability, p. 373 322 Table 5 Some aspects of “complexity” and “holism” p. 101 323 Note #17 Chaos, p. 338 321

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processes to those that close the circle (Commoner 1971), 324 and that the impacts of human activity expose us to multiple global risks. Dangers to our planetary environment – in global warming, in damage to ocean and land ecosystems, in loss of biodiversity, and in the presence of toxic materials in the environment – are not only increasing but accelerating to the point where they may soon become, if they are not already, irreversible. Our current industrial system is not sustainable. In depleting our fossil fuels dowry, we are chicks living off the yolk of our egg before hatching, i.e., before a transition to global order. That is of course what the yolk is for, but the point is: we only get one yolk. 325 To use a different metaphor, our matterenergy 326 economy now is more like free-fall than flight (Hawken 1994). The stability of planetary conditions needed for human life is in doubt. We need to shift from exploitation to sustainability but do not have much time to make this shift, and we may not have the political will needed to accomplish it. Many valuable ideas and methods were introduced in these earlier systems studies, including computer methods for global modeling, energy and entropy accounting to augment conventional monetary accounting, life cycle costing, the idea of a steady-state economy, and the need to encompass interests of future generations and internalize externalities in space and time. The science and myth of Gaia coupled with views of our blue planet from space have enabled us to grasp the unity of our planetary home and our dependence on a biosphere whose stability is not assured. These systems ideas and methods have been further developed. Earth systems science, e.g., climate and ecological modeling, are active fields. Requirements of sustainability are becoming a central subject in the “sciences of 324

Note #60 Externalities, p. 412; Note #157 Closing the circle, p. 564 Note #155 Environment is a limited source and sink, p. 563 326 3.2.1 Matter, energy, and information, p. 88; Note #46 Information (and matter-energy, utility), p. 389. The informational realm of the economy is not immune to these considerations, since it is necessarily instantiated in the matter-energy realm. 325

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the artificial.” 327 Extensive work is being done on commons resource problems, although the frequent failure in discussions of these problems to note their game-theoretic essence (the Prisoner’s Dilemma, Chicken 328) suggests that they are not grasped deeply enough. The systems character of sustainable practices in many indigenous societies is being recognized. Many lines of systems inquiry contribute to understanding the major societal shift that we need to accomplish. The central concern of sustainability is the health of the planet, more specifically of the biosphere, in ordinary terms, the environment. The environment is strongly affected by the economic order, so it is mainly economic activity that needs to be environmentally sustainable, beyond being economically sustainable. The economic order must also assure that the quality of human life is sustainable. Realizing that these dimensions are linked has led to the idea of a triple goal for sustainability: environmental, economic, and social. Very relevant to this triple goal is the issue of globalization. Although this word is sometimes used narrowly to refer to the fact that the world economy is becoming integrated, globalization extends downward to the environmental dimension and upward to the social dimension. The global economy is becoming one, and so is the biosphere and human society. In terms of the historical model invoked in this chapter, globalization refers to the planetary transition now underway. 329 Assuming we can continue to avoid nuclear war, the central challenge of the current planetary transition is, most immediately, climate change, and in the medium term, sustainability.

327

4.4 Sciences of the artificial, p. 139 Notes #78 Prisoner’s Dilemma, p. 433, and #79 Chicken, p. 435 329 This transition is at point 1ʹ of PI in Figure 28 Macro-historical processes of complexification, p. 197. The scope of PI in this model includes the biospheric support system for humanity, although this was not explicitly discussed in the presentation of the model. 328

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The triple sustainability concept has both virtues and drawbacks. Its main virtue is that it reflects the truth that the environment is deeply interconnected with the social and economic dimensions of human life. Failure to consider these dimensions implies that it is both possible and desirable to protect the biosphere without changing anything in the economic and social orders. This isn’t possible; even were it possible, it would not be desirable. The main drawback, however, of the triple sustainability concept is that by defining sustainability to encompass economic and social issues, biospheric health is often conflated with economic viability and with human values such as social justice. This obscures the possibility that these three goals might actually conflict with one another, and that trade-offs between them might be necessary. There is also a terminological ambiguity: does “social sustainability” mean (a) social impacts (e.g., due to population growth) on environmental sustainability, or (b) values such as social justice that one wants realized and sustained, altogether apart from environmental considerations? What is normally intended by “social sustainability” is the latter meaning, so it would be better to speak directly of social justice; calling it “sustainability” might suggest that the main virtue of social justice is that it reduces conflict and promotes stability. And not only does social justice lose significance if it is called “social sustainability,” environmental sustainability also loses significance. The idea of sustainability is diluted if everything we value is included in it. So, while multiple values must be considered in a systems approach 330 to contemporary problems, these different values must be distinguished. The word “sustainability” should be primarily reserved for its environmental meaning. This said, the triad of goals encompassed by the triple sustainability concept is not even differentiated enough. The social dimension of sustainability includes politics and culture, 330

4.5 Systems theory and systems analysis, p. 141

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and it is useful to treat these explicitly as separate realms. Figure 32 below reformulates “social” as “socio-political” and adds “cultural” as an additional factor. The figure reflects the point of view advocated here that reserves the word “sustainability” for the environment and displays the environment as the ultimate concern, with economic, sociopolitical, and cultural realms as causal influences that affect it. This is not to deny the fact that these realms have their own values, apart from their effects on environmental sustainability, but the diagram focuses on environmental sustainability, narrowly defined. The arrows in the diagram represent the main interactions; other linkages, such as the effect of culture on the economy or the direct effect of the socio-political realm on the environment are not shown. Figure 32 Modification of the triple sustainability concept

cultural social-political economic environmental Dividing “social-political” in Figure 32 into separate factors yields Parsons’ (1966, 1971) model of social systems, shown below in Figure 33 (with “community” replacing “social”). This model connects to the macro-historical model previously introduced 331 in that the challenges of globalization and sustainability are not only a crisis in PI; they also relate to difficulties of PIII that arise from the differentiation brought by modernity. Parsons’ model depicts this differentiation, but does not explore impacts on the environment. 331

6.1.2 The model applied to history, p. 196

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6.4.2 Modernization as differentiation 6.4.2.1 The Parsonian model of social systems 332 In the macro-historical model presented earlier, the merging of PIII (for convenience labeled “science”) with religious (PII) and societal (PI) development marks the onset of modernity, which has led at this moment of history (point 1ʹ) to the necessity of shifting to a new societal order. Difficulties in accomplishing this shift stem in part from failures of differentiation since “modernization is differentiation.” Understanding our contemporary difficulties thus requires understanding differentiation. A framework for such an understanding is offered by the “action system” of Talcott Parsons (1966, 1971), which resembles the tetrad of problem solving. 333 It is a systems theory that is non-mathematical 334 but conceptually rich. Applied to social systems, it yields the structure shown in Figure 33. Figure 33 Parsons’ tetrad of social systems Left: the zigzag bold line shows the hierarchy of the elements. Right: information descends; matter-energy ascends.

culture

information

(d)

(c)

(b)

community (e)

(f)

polity (a)

economy nature 332

SYSTEM

matter-energy

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An article that develops ideas of this section more fully is (Zwick 2013). Figure 25, p. 146: Economy is ground, polity is instrument, community provides direction, culture defines goals. Parsons’ terms corresponding to ground, instrument, direction, and goal are adaptation (A), goal attainment (G), integration (I), and pattern maintenance (L). His “goal attainment” really refers to the instrument (efficient cause) by which goals are attained. 334 4.1 Not just mathematics, p. 123 333

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In this model, a social system has four elements: economy, polity, community 335 (systems of human relationship, such as families, neighborhoods, and associations; in a general sense, “civil society”), and culture (religion, science, media, literature, the arts). In terms of the tetrad of purposeful action, 336 economy is the ground of a social system, culture specifies goals, community provides direction, and polity is the instrument. In Boulding's (1978) terms, the exchange, threat, and integrative systems 337 roughly parallel the economy, the polity, and the community as influenced by culture. Outside the social system is its environment, which includes nature, coupled to the economy; this linkage is not shown in the figure and was not developed in Parsons’ theory. Also not shown are other social systems in the environment. Community + polity + economy + nature in Figure 33 are encompassed within “society” (PI) in the historical model. 338 Religion (PII) and science (PIII) in the historical model are part of culture in Parsons’ model, but technology in the historical model (PIII) is, in the Parsons model, within (e), the link between culture (specifically its science component) and the economy. The four elements are interconnected, and the dyadic relations are labeled (a) through (f) in Figure 33. The elements are also ordered hierarchically: from bottom to top the sequence is economy-polity-community-culture (the bold zigzag line). Informational regulation occurs downward (Parsons 1966, 1971): the polity regulates the economy, community is the basis of polity, and cultural values guide community. There is also an upward flow. Lower levels provide matter-energy support for the higher ones. In Marxist terms, the economy is the base and the other three elements are the superstructure. The Marxist 335

Parsons’ phrase “societal community” is shortened here to “community.” Although “community” often connotes intimacy and smaller scale, the word is used here with the looser and larger scale meaning of “society.” 336 Note #72 Purposeful action as a tetrad, p. 426 337 Note #73 Assertion, integration, exchange, p. 427 338 Figure 28 Macro-historical processes of complexification, p. 197

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claim of determination from below is incomplete; there is determination from both above and below. The upward flow of energy has its ultimate source in nature in the flux of matterenergy through social systems which organizes them (Adams 1975). 339 This dual flow reflects a universal principle. 340 The idea that modern social systems are differentiated means that the four elements are partially but not fully autonomous. These systems are “partially decomposable.” 341 Elements are regulated (constrained) by their linkages with other elements. Giving interpretations only to the dyadic linkages in Figure 33, “modernity” means, for example, that (a) The economy is partially autonomous and partially controlled by the polity. (b) Civil society is distinct from and determines and participates in the political order. (c) Cultural values guide but do not legally constrain private activity. (d) Religion is a significant part of culture but church is separated from state. (e) Interpersonal relations are not dominated by those of exchange. (f) Culture is independent commercial life.

of

yet

supported

by

This list is illustrative, not exhaustive or definitive. Since (a)-(b)-(c) is the primary upward path for matter-energy and downward path for information, these linkages are especially important. “Modernization is differentiation” means that differentiation increases with modernity, not that differentiation 339

Notes #42 Dissipative systems, p. 381, and #47 Autopoiesis, p. 393 Note #140 Two universal processes, p. 535 341 The terminology comes from Herbert Simon (1962); see Note #143 Partial decomposability, p. 540 340

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is total or extreme. In modern social systems, autonomy is balanced by interdependence, differentiation by integration. The economy and the polity need to be connected, since economies are not self-regulating. The polity and community need to be linked by principles of democracy and civic responsibility. Civil society needs to be guided by some coherent set of values which reflects the realities of social life. And so on. That problems of modernization imply problems of differentiation translates into the proposition that existing links might be too strong or too weak or of the wrong kind or direction. To relate this to the macro-historical model 342 presented earlier: where PIII has not occurred or has blended improperly with PI and PII, church, state, community, and economy are often not properly differentiated. For example, civil society (community) is not free of cultural, political, or economic domination; government is not constrained by consent and guidance of the governed. In the above tabulation, linkages are dyadic: economy and polity, economy and community, polity and culture, etc., but relations need not only be dyadic. There are triadic interactions between economy, polity, and community (e.g., in issues of health care) and between polity, community, and culture (e.g., in funding of the arts and humanities) that cannot be decomposed into pairwise relations. There could even be a tetradic relation of the elements that cannot be decomposed into triadic and dyadic relations. 343 Roughly speaking, archaic societies (in early stages of PI) were holistic in this way. Note also that in the simplest analysis relations are without direction; if one adds direction then bidirectional (dyadic) relations are more complex than unidirectional ones.

342

Figure 28 Macro-historical processes of complexification, p. 197 3.4 Aspects of complexity and holism, p. 100; further discussion in Note #5 Structure, p. 308, and Note #142 Progressive segregation, p. 539 343

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6.4.2.2 Problems of differentiation The simplest failures of differentiation are pathologies of too little or too much differentiation. Another failure occurs when one element, privileged as fundamental, dominates the others, an extreme version of what von Bertalanffy (1968) called a “leading part.” 344 This distortion of the system may be called a “fundamentalism.” One can thus define four fundamentalist distortions of the social system, listed below in Figure 34. Figure 34 Four fundamentalisms

(iv) THEOCRACY culture (religion)

(iii) NATIONALISM

(ii) TOTALITARIANISM

community

polity

economy (i) CAPITALISM These are “ideal types.” Mixtures of these types are of course possible and the elements and their relations may be salient to different degrees, but in each structure shown, one element is hegemonic and determines the whole. All four fundamentalisms deviate from the differentiation that is normative for modernity. Types (i) and (iv) bracket the other two, since in Parsons’ model, economy and culture are the bottom and the top, respectively. In a fundamentalism of capitalism (i), economic forces dominate the political order, the culture, and civil society. In the Marxist view, this is how social systems both are and 344

See discussion of this idea around pp. 104 and 317.

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should be determined. In a fundamentalism of type (iv), religion dominates the other elements. Contemporary United States illustrates (i), and contemporary Iran illustrates (iv). Fundamentalism of the polity is exemplified intellectually in Hegel’s idolatry of the state and historically in 20th-century totalitarianism. Fundamentalism of community is exemplified by populism, nationalism, and anarchism; 345 notions of Volk in Nazism and class structure in Communism can also be viewed as mythicized community. (Communism as political reality and Marxism as ideology are fundamentalisms of polity and culture, respectively.) Contemporary populism, allied with nationalism, is a reaction to neoliberalism, a fundamentalism of the economy. Fundamentalism of religion is allied with religious fundamentalism as usually understood. In terms of the macrohistorical model presented earlier, 346 hegemony of religion in the social system results from merging religion (PII) and polity (PI). Such merging, for example, was salient in Islam’s early expansion and reappears today in political Islam which has eclipsed streams within Islam that favor separation of mosque and state. 347 But where PIII has taken hold it has separated PI and PII, undermined the dominance of religion and promoted democracy. Even where PIII is not fully established, attempts to resist or reverse modernity cannot succeed in the long term. Aside from dreams of past empire and reaction to humiliations of Western imperialism, modernity has often been resisted out of a longing for the integrality of a premodern predifferentiated condition. But closed and totalistic social systems are no longer possible. The norm of separation of church and state is not a 345

Anarchism is a polar opposite to totalitarianism. A metaphor for this dyad is the top and bottom of the Lattice of Structures (Note #5 Structure, p. 308). Anarchism is a utopian doctrine that is blind to the natural forces that promote concentration; see Notes #137 Mechanization (rigidification), p. 530, and #144 Systematization, p. 541. 346 Figure 28 Macro-historical processes of complexification, p. 197 347 These modernity-compatible streams may yet regain influence. In the delay phenomenon of the cusp catastrophe (Note #131, p. 520), change in deep structure generally precedes manifestation in surface structure.

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Western idiosyncrasy but a universal norm of modernity, necessary for the rest of the world as it was for the West. Analogous to separation of church and state is a needed separation of science (and technology) and state. 348 Absent but sorely needed are institutions dedicated to the impartial and independent scientific analysis of critical problems (e.g., climate change, ecosystem degradation, species extinctions). Controversies over funding the arts and humanities are another problem area, whose essence is the proper relation between community, polity, and culture. Viewing this as a problem of differentiation provides neutral ground that might ease the tensions of the culture wars, if religious fundamentalists could accept differentiation of culture, community, and polity as normative for modern life. Fundamentalism of capitalism is central to the current crisis of PI, both internationally and intra-nationally. In a social system characterized by this type of fundamentalism, corporate power dominates politics. Culture is subservient to the market and adopts its forms. Societal needs are frequently overruled by commercial imperatives; the public domain is encroached upon and its legitimacy even denied. But what illustrates dramatically the failure of proper differentiation and the pathologies of fundamentalist capitalism is that nature itself, which is what is truly fundamental and which provides the support for all social systems, is controlled and appropriated by the economy; for example, life forms are patented, and privatization is promoted over other aspects of the natural world. In short, the economy rules, and its negative externalities are inflicted upon culture, community, polity, and, most dangerously, nature. In most Western countries, the social system is based on two organizing principles: capitalism and democracy. Capitalism is the organizing principle of the economy; democracy is the organizing principle of the polity and the 348

Relation (d) in Figure 33 Parsons’ tetrad of social systems, p. 253

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community-polity relation. It is common on the political right and in some views of liberalism to conflate the two, but political freedom and economic freedom are different as well as similar. The tension between democracy and capitalism is a disharmony of differentiation. 349 In an ideal system, the two would have a definite ordering: the economy would be partially autonomous, but part of the function of the polity would be to regulate it; the link that connects the two 350 should be directed from polity to economy, the former having hierarchical priority. Regulation should provide a legal framework to govern commerce and impose constraints on the economy in the interests of community. In fundamentalist capitalism, however, the direction of influence is reversed: from economy to polity. 351 Although government regulation may be accepted in principle, it is undermined in fact, and the fantasy lingers of the possibility and desirability of a fully autonomous market, an extreme as irrational as its polar opposite, the command economy of communism. To quote Butler (1872) again: “Extremes are alone logical, but they are always absurd.” The fantasy of the autonomous market is kept alive by the inadequacies of mainstream economic theory, such as its neglect of nature and the thermodynamic dimension of value, its unrealistic assumptions of equilibrium, rational decision-making, and perfect information, and its ineffective handling of the problem of externalities. Ideally, regulation of the economy by the polity would be the norm, and debates would concern only the degree and kind of optimal regulation. In the union of democracy and capitalism, Parsons’ model implies that democracy should be dominant, so the polity should be insulated from economic power, as it should also be from organized religion. Wealth and economic interests should not 349

The relations that structure a system are either organized by a unitary principle, or they remain separate, unharmonized at the level of the whole...Multiplicity allows inconsistency (1.1.1.2.1). 350 Figure 33 Parsons’ tetrad of social systems, p. 253 351 Figure 34 Four fundamentalisms (i), p. 257

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be allowed to corrupt the polity, as they now do to a greater or lesser degree in regulation of private campaign contributions will be necessary to safeguard the proper community-polity linkage. Also, from the perspective of Parsons’ model, the granting by the Supreme Court to corporations of the legal status of “person” is an example of wrong differentiation since the status of “person” is appropriate to individuals in the community sector, not organizations in the economy sector. The rights of persons, especially the right to free speech, apply to the community-polity relation, i.e., to the functioning of democracy, not to the economy-polity relation. Because regulation of the economy by the polity is often compromised, private gain from public service needs to be more effectively disallowed. In the terminology of Jane Jacobs (1994), the “guardian” ethic of the polity should be separated from the “commercial” ethic of the economy. For example, those who perform the polity function of regulating the economy should be disbarred from later serving the organizations which they previously regulated; failure to prohibit this guarantees corruption. Movement in the other direction, however, is desirable, to provide regulatory agencies with expertise, as long as this movement is not reversible. Numerous other implications might be drawn from the Parsonian model of societal differentiation. Regulation of the economy by the polity needs to be transparent to overview by the community. Additional indirect and partial regulation of the economy by the community would also conform to the model’s implications. Just as the polity derives its legitimacy from the consent of the governed, the economy derives its legitimacy by serving the needs of society. The polity is the community’s instrument, but if the instrument is not effective, the community sector needs back-up powers of intervention in the economy. For example, voter initiatives should be able to revoke corporate charters on grounds of harm to the public.

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Proper differentiation implies the importance of a robust public, i.e., community, sector not preempted by the economy. Functions not predominantly economic should not be primarily situated in the economy. For example, the link between medical insurance and employment is a “frozen accident” 352 of history that needs to be undone. Markets, and the economy in general, cannot be relied on to prepare for unpredictable disasters, since little profit can be gained by such preparation, so such preparation must be a mandate of the public sector. Control of the economy by the polity and indirectly by the community becomes increasingly important as the scope of economic activity gets large. (This is not an aspect of Parsons’ model but an important systems principle.) Both extremes of government-controlled economies and totally unfettered markets are dysfunctional. Social control needs to be proportional to the scale of economic activity, and especially to the scale of its negative externalities. Economic entities that are “too big to fail” are too big to be private, but it is not merely risk of failure that justifies social control. Mega-corporations, whose impacts are comparable to or exceed those of nations, need to be subject to social control or at least be transparent to public scrutiny. The importance of scale in determining the degree and kind of appropriate social control is not simply a matter of the need to limit monopoly power to preserve competition. Scaledependence of the proper relation between the polity and the economy should be central to economic theory. Many social problems reflect distortions or failures of differentiation. This perspective is more neutral than one formulated in terms of left versus right, but it does not preclude the argument of the left for more equitable distribution of wealth or the argument of the right for the intrinsic value and practical benefit of economic freedom. The failure of Marxism as a positive vision as opposed to a critique of capitalism along with the failure of democracy to prevent the negative aspects of 352

See discussion of history in the structure-function-history triad, p. 101

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capitalism suggest that new theory is needed in the social sciences. A theory of differentiation of social systems would be especially valuable. There is material for such a theory in the Parsonian corpus and in the systems theoretic work of Luhmann (1982). Two systems themes that need to be central to such an undertaking have been mentioned: scale and externalities. Other potentially useful ideas are discussed in Essay and Notes. Although a substantial amount of relevant material exists in the social science, historical, and philosophical literatures, there does not appear to be a widely known and accepted theory of societal differentiation. At least contemporary problems are not normally framed in terms of such a theory. From the perspective of the systems project, what is needed is even broader, namely a general theory of differentiation that applies to a variety of types of systems, not only social systems; 353 still more broadly, a general theory of maturation that would encompass not only social differentiation but economic development and even diachronic change in ecosystems. 6.4.2.3 Subsystem differentiation From the recursiveness of the idea of system, each of the elements of Parsons’ tetrad of social systems is a subsystem, with its own internal issues of differentiation. For example, there is internal differentiation within the economy in its matterenergy versus its informational aspects. 354 (Such differentiation characterizes the Parsons’ model as a whole in that its “higher” elements – culture and community – are more informational than “lower” ones – economy and polity.) The matter-energy aspect of the economy includes production and distribution of goods, while its informational aspect coordinates economic activity and allocates resources and is exemplified most clearly 353

See Note #142 Progressive segregation, p. 539, on differences between controlled and uncontrolled systems. 354 Parsons posited a recursiveness that was fractal: each of his four elements (A, G, I, L; see Footnote #333, p. 253) could be decomposed into A, G, I, L elements at the next lower level.

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in the financial sector. This differentiation within the economy is a prominent consequence of modern advances in science and technology. Although the economy, the primary matter-energy subsystem of the social system, may be dominant in the overall social system, finance may be dominant within the economy by being disproportionally large relative to the manufacturing sector. 355 In general the raison d’être of any informational order is optimization of a matter-energy domain beneath it, but such differentiation always brings also the possibility of “informational parasitism.” 356 Arguably, such parasitism occurs in this case: it is doubtful that the wealth appropriated by the financial sector can be justified functionally. One task in regulating the economy by the polity, e.g., by enforcing requirements of transparency, is limiting distortions of this kind. Note that the economy is the “bottom” of the social system, while finance is the “top” of the economy subsystem. One can thus have a fundamentalism of the bottom in society and a fundamentalism of the top in its economy. The internal structure of the polity of the United States provides an example of an attempt to solve the problem of differentiation via the separation of powers between executive, legislative, and judicial. A systems theorist might ask: what principle does this separation of powers illustrate? One answer might correlate these powers with the requirements that collective decision-making be rational, egalitarian, and decisive, requirements that Arrow showed cannot always simultaneously be met. 357 These desirable attributes for the polity correlate with the judicial, legislative, and executive sectors. Figure 35 shows that they also correlate with the polity’s links to culture, community, and economy, respectively, and with Fukuyama’s (2011) attributes of a modern political system: rule of law, accountability, and effective political structure. 355

Comparing (b) and (c) in Figure 87 Informational parasitism, p. 460, gives a symbolic representation of this distortion. 356 Note #97 Informational parasitism, p. 458 357 Note #68 Aggregating preferences, p. 420

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Figure 35 Separation of powers and the Arrow theorem Powers of the polity: the virtue column lists the Arrow criteria; the attribute column lists Fukuyama’s criteria.

culture community

b

a judicial legislative polity c executive

economy Power

Connected to

by

Virtue

Attribute

judicial legislative executive

culture community economy

a b c

rational egalitarian decisive

rule of law accountability effective structure

The judicial sector instantiates the rule of law, whose requisite virtue, endorsed by culture, is rationality. The legislative sector is the primary means of accountability to the community, which ideally is egalitarian. The executive sector requires an effective structure whose distinctive virtue is decisiveness; its field of action, internally, is the economy. Legitimacy of the polity is conferred by the community; it is based primarily on accountability, i.e., democracy, but might also be partially gained due to the rule of law or because of a successful economy (Fukuyama). 358 One might imagine the existence of principles that would promote a more perfect union of economy, polity, community, and culture and a better reconciliation of the triad of virtues. The Arrow result suggests that such principles might not be 358

In the language of Note #3 Relation, p. 304, legitimacy through accountability is a dyadic community-polity relation; legitimacy through the rule of law or a successful economy is a triadic relation: communityculture-polity or community-economy-polity, respectively.

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available, that an optimal general method for reconciling conflicts between these virtues might not exist. Note that the Arrow impossibility result is triadic, and thus more complex than the familiar dyadic oppositions (centralization vs. decentralization, command vs. market, etc.) that dominate our thinking. Differentiation, in Parsons’ framework, is a tetradic problem, and even more complex. No doubt there are problems of still higher ordinality (pentadic, hexadic, etc.) but mental models dealing with such complexity are beyond us. We count ourselves enlightened if we can see beyond a single factor to two, beyond two to three, and – what takes monumental effort – beyond three to four. A second type of differentiation 359 within the polity is different in kind from the separation of executive, legislative, and judicial. It is spatial differentiation into hierarchical political levels; in the United States: nation, region, state, county, city, neighborhood. 360 Distribution of powers between these levels is non-optimal and contested. For the multiplicity of units at each level, it is difficult to balance the competing virtues of homogeneity and heterogeneity. 361 And democracy itself is scale-dependent. On large scales, participation can only be via representation. One salient phenomenon of differentiation within the community is class division, which results from “informational parasitism” within the economy and improper control of the polity by the economy rather than the community. There is no functional justification for the extreme wealth inequality that results from runaway (positive feedback) processes not under 359

See Sutherland’s idea of segmentation mentioned in Note #142 Progressive segregation, p. 539. Segmentation is element-based differentiation; the tetradic structures being discussed are attribute-based differentiation. 360 The inherent tensions in hierarchical structures are discussed in Hierarchies 1.1.7.2 and 7.1.7.2, pp. 19, 451 361 Note# 92 Homogeneity, heterogeneity, and scale, p. 452

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negative feedback control. 362 Social differentiation also occurs by race, ethnicity, and religion. Some differentiation is often spatial, as in the segregation of subcommunities, which can lock in or accentuate class differences. Spatial differentiation on a larger scale, e.g., regionalization, can be a source of both beneficial diversity and conflict. There is internal differentiation also within culture. One might consider culture to be a tetrad of science, religion, the humanities, and the arts, as shown in Figure 36(a). 363 Figure 36 Tetrad of culture

religion arts

humanities religion humanities

(a)

science

religion

arts humanities (c)

(b) science

arts science

Before modernity, these components were relatively integrated; in modernity, with emergence of distinct and separate domains of culture, attempts to regain unity often entail attempts to establish hegemony of religion in the cultural sphere, shown schematically in Figure 36(b). Some argue that modernity inherently involves the attempt to establish hegemony of science, shown schematically in Figure 36(c). Science and religion are part of culture in the Parsons model but are separated in the macro-historical model developed 362

See the discussion of Figure 59 Negative and positive feedback, p. 374. In the figure philosophy is included within the humanities which obscures the fact that philosophy mediates between religion and science. An ESM has implications for religion through its philosophical dimension

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above. One major problem of cultural differentiation in modernity is the troubled relation between science and religion and the resulting absence of a coherent worldview. By contrast, the relationship between the humanities and the arts is amicable. It is argued in 6.3 Natural religion that complete separation of science and religion is unsatisfactory, both intellectually and spiritually, and that systems ideas might facilitate more harmonious relations between the two. Generally, there is great tension between the religious and scientific cultures, roughly correlated with the political right and left. There is also a wide gulf between the culture of science and that of the arts and humanities (Snow 1959). Differentiation within science has led to fragmentation of knowledge, to which the systems project is a response. Differentiation within religion is of course extensive, within and between different religious traditions, with strong pulls toward both unity and diversity. 6.4.2.4 The world system The discussion of Parsons’ framework has so far focused at the intra-national level. Applying this framework to the international level reveals a different situation. The most significant challenge facing the world system, short of the danger of nuclear war, is climate change and the associated problems of environmental degradation and species extinction; these have been discussed above in connection with a model of universal history. In the Parsons model, 364 these issues concern its environment element. But the world system itself is also challenged. Links between economy, polity, community, and culture are primitive, and these elements themselves are less developed and suffer from internal tension. Inadequacies of development, integration, and differentiation coexist. The world economy is perhaps robust, but the world polity is rudimentary, the world community is fragmented, and a world culture deserving of the name is absent. Because the other 364

Figure 33 Parsons’ tetrad of social systems, p. 253

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elements are weakly developed, the world system, insofar as it is an organized system, is a fundamentalism of capitalism virtually by default. This accentuates the critical challenge in the world economy of economic development, i.e., overcoming poverty in less-developed regions of the world. According to one view, the inequalities in the world are the result of past and present domination by the West: colonialism, imperialism, and other forms of exploitation. The truth in this functional view is incomplete. Underdevelopment is also due to inadequate or absent modernization and to lack of cultural and social capital. The truth in this structural view is also incomplete. Both external and internal explanations are implicitly encompassed in the macro-historical model presented in this chapter. PIII occurred only in the West, so other societies were late in securing its advantages, and societies that did not assimilate its advances were dominated by those that did. Internal and external causal impacts are not mutually independent. Their interaction generates a positive feedback (difference-amplifying) effect, which differentiates the world system between rich and poor, north and south, center and periphery (Wallerstein 1974). 365 The functional view stresses external economic, political, and military international factors; the structural view stresses internal community and cultural intra-national factors. It would be desirable to have a theory that did justice to both perspectives. Systems theory might provide a neutral orientation for such a theory. For example, a Parsonian model with its downward and upward flows might accommodate both. A related duality characterizes strategies of development. Functionally, the imperative for a developing nation is to integrate into the global economy, but this obscures the important difference between growth and development. 366 Structurally, what is imperative is to differentiate into a modern society, to develop a mature economy under social – ideally 365

See the INDEX, p. 679, for locations of the multiple discussions in this book of feedback and center-periphery ideas. 366 Note #125 Development vs growth, p. 510

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democratic – control, but this change is resisted by special interests and forces opposing modernization. With respect to social control at the global level, NGOs like the International Monetary Fund and the World Trade Organization are beginnings of a world polity that could in principle regulate the international economy. As Platt observed (1970), the difficulties of establishing order at level i+1, when nations define level i, can be partially bypassed by a network of level i-1 entities. However, these NGOs usually serve the interests of rich nations and corporations. Additional institutions of this sort with greater power and transparency are needed, but, as occurs within societies, the direction of influence is more economy→polity than the reverse. The power of global corporations is unchecked. This is illustrated by corporate attempts to limit even long-established community access to water, seeds, and other aspects of nature. In an international fundamentalism of capitalism nature is absorbed into the economy. As the world community is fragmented and weak, the primary path of control, community to polity to economy, is absent, hence the protest movement against globalization. Looking further at the possibility of a global polity, one notes that problems of differentiation are visible at every level of political structure. There is a basic tension between aspirations for a world order and the realities of national power and sovereignty. The primary instantiation of world order, the United Nations, is dysfunctional. At the regional level, some progress in political integration has been made in Europe, but this integration is fragile, and a common understanding of an ideal degree of political, economic, and cultural unity is lacking. In Africa and Asia, the regional integration needed to deal with the challenges these continents face is absent. At the national level, there are nations whose right to exist as states is blocked or denied and there are nation-states that are artificial and unstable. Overall, international political structure is still at an immature stage of development. Difficult as the economic and political problems of the world system are, they exist against the

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background of an environmental and ecological crisis whose imperatives are not sufficiently accepted and acted upon. The biosphere, the essential supporting environment 367 of the world system and all its subsystems, is in danger. The community and culture elements of the global system are undergoing integration in international movements of populations and in the globalization of information and beginnings of the noosphere in the Internet. These developments produce major challenges of their own. Reversing existing patterns of micro-homogeneity and macro-heterogeneity through the mixing of ethnic and religious groups often unleashes violent reactions. Viewed abstractly, there is no general solution to the tensions of unity vs. diversity or openness vs. closedness. 368 It is difficult to preserve national and ethnic identities and avoid communal and cultural strife on the one hand and promote the celebration of diversity and prevent xenophobia, ethnic chauvinism, and racism on the other. Neither extreme separation nor extreme mixing is tenable or desirable. With globalization, extreme separation is already impossible, but extreme mixing ultimately destroys the very diversity that is enriching. 369 No general principle exists with which to define a reasonable balance. Another major challenge in the realm of community is the establishment of equal rights for women. On this issue which is central to modernization, the intimate connection between culture and community is plain. While equality of men and women is approximately established in the West, elsewhere major disparities of status are a potential force that has not yet generated its full flux of change. As for the Internet, its capacity to promote discord and falsehood seems far in excess of its capacity to promote harmony and truth.

367

See the discussion of “operating systems” in 5.3 Categories of complexity, p. 160. 368 These are themes very prominent in Essay. See, for example, Synchronics discussion in 1.1.9 Summary, p. 23. 369 Note #92 Homogeneity, heterogeneity, and scale, p. 452

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This discussion of the world system is a sketch of some of the issues involved in the difficult historical transition referred to above as the major barrier (point 1ʹ) of the PI process. 370 6.4.3 On the gap between the actual and the ideal; on the incoherence of the ideal Fixing the world means closing the gap between “is” and “ought”; in the terminology of the tetrad 371 often used in this book, between the actual and the ideal. To close this gap, one must understand its source. In a systems view, the imperfections of social systems exemplify general problems for which there are no general solutions, certainly no solutions that attribute social problems to some unitary failing that can be corrected once and for all. To illustrate this point using Parsons’ model of social systems, 372 such a unitary failing might be regarded as either material or spiritual. The Marxist view that the fundamental source of social problems is inconsistency between forces and relations of production is reductionist downward toward the economy, ground in the Parsonian tetrad; the ideology of capitalism is reductionist in the same direction. The religious view that the fundamental source of social problems is absence of salvation or spiritual attainment is reductionist upward toward culture, goal in the Parsonian tetrad. Both ground- and goaloriented views harbor the dual belief, despite ample historical evidence to the contrary, that radical transformation at a level regarded as fundamental is achievable, and that transformation at this level will automatically spread upward or downward. The testimony of history is that this dual belief, on which the prestige of “the fundamental” rests, is illusory. What fundamental change is possible is limited, and the degree to which such change trickles up or down is equally limited. 370

Figure 28 Macro-historical processes of complexification, p. 197 Figure 25 Tetrad of problem solving, p. 146 372 Figure 33 Parsons’ tetrad of social systems, p. 253 371

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Some fundamental imperfection might exist in the intermediary levels that Parsons calls the polity or the community, but Essay makes it clear that there is a wide range of sources that might account for these imperfections. Although simplified models are needed to have any understanding of the world at all, the incompleteness of these models guarantees that social action guided by them will invariably generate unintended consequences. 373 A systems ontology of problems can provide a corrective to narrow understanding of the gap between “is” and “ought.” But narrow understanding of this gap is not the only hindrance to closing it. A second hindrance is the incoherence of the “ought,” the inconsistency that inheres in the multiplicity of cultural values. Whyte (1948) observed that “The penalty for any principle which fails to express the whole is the necessity to coexist with its opposite.” Bohr observed that “It is the hallmark of any deep truth that its negation is also a deep truth” (Delbrück 1986). These two assertions apply not only to principles and ideas but also to values. Taken together, they imply incessant conflict among both ideas and values. No single idea or value expresses the whole, so coexistence with its opposite, with its compelling claim, is unavoidable. 374 Isaiah Berlin (1991) writes eloquently about the fact that human ideals necessarily clash. He notes the moral concerns of mid-nineteenth century writers and thinkers, observing that despite the ideological differences betwen supporters of liberal Western democracy, proselytizers for the Christian gospels, and advocates of social and political revolution, what these thinkers all held in common was the underlying belief that consistent solutions to human problems existed, could be discovered, and with sufficient commitment implemented. Implicit in this belief was the assumption that answers to moral and social questions 373

Notes #59 Multiplication of effects, p. 411, and #61 Counterintuitive effects, p. 413 374 Every flaw in a system is a potential nucleation site for an alternative organizing principle (1.2.5.1.4).

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“must necessarily be compatible with one another and form a single whole, for one truth cannot be incompatible with another - that we knew a priori...” But this assumption – that ethics could be placed on a basis similar to mathematics – Berlin came to believe was incorrect. There is no perfect world in which all good things can be harmonized in principle. The following paragraphs from Berlin deserve to be grasped and taken to heart. What is clear is that values can clash – that is why civilizations are incompatible. They can be incompatible between cultures, or groups in the same culture, or between you and me... Values may easily clash within the breast of a single individual; and it does not follow that, if they do, some must be true and others false. Justice, rigorous justice is for some people an absolute value, but it is not compatible with what may be no less ultimate values for them – mercy, compassion – as arises in concrete cases. Both liberty and equality are among the primary goals pursued by human beings through many centuries; but total liberty for the wolves is death to the lambs, total liberty of the powerful, the gifted, is not compatible with the rights to a decent existence of the weak and the less gifted... ...We are all aware of the agonizing alternatives in the recent past. Should a man resist a monstrous tyranny at all costs, at the expense of the lives of his parents or his children? Should children be tortured to extract information about dangerous traitors or criminals? These collisions of values are of the essence of what they are and what we are. If we are told that these contradictions will be solved in some perfect world in which all good things can be harmonized in principle, then we must answer ... that the world in which what we see as incompatible values are not in conflict is a world altogether beyond our ken...

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The notion of the perfect whole, the ultimate solution, in which all good things coexist, seems to me to be not merely unattainable – that is a truism – but conceptually incoherent...Some among the Great Goods cannot live together. That is a conceptual truth. We are doomed to choose, and every choice may entail an irreparable loss. It is thus not only that our ideals are overwhelmed by the intractability of social realities; there are problems in the ideals themselves simply by virtue of their multiplicity. They do not cohere; impossibilities, contradictions, and instabilities abound. Every system of values includes such inherent flaws which may not be initially evident but which will inevitably give rise to adverse consequences. Insofar as social organizations are shaped by systems of ideals, they are similarly afflicted. The organizing principles of political parties, for example, are invariably inconsistent, since seekers after political power find that consistency weakens a party by endangering the alliances that are the basis of power. Thus, for example, a laissez-faire position in economic matters may be joined to a big government position in social matters. Or, the reverse. A denial that the marketplace of goods is intrinsically self-correcting may be coupled to an affirmation that the marketplace of ideas is intrinsically self-correcting; in fact, neither marketplace is reliably self-correcting. Pollution of the environment may be recognized, but the possibility of the pollution of culture is fervently denied; or, vice versa, adverse effects on the environment may be dismissed as self-mitigating, but the concern with adverse effects on culture may become obsessional. Positions on diverse political issues may be assumed to be either more linked or more decoupled than is intellectually or ethically warranted. In some contexts only binary alternatives are acceptable, but in other contexts a continuum of alternatives is insisted upon. Berlin speaks of classical contradictions between liberty and equality and between justice and mercy. Contradictions are

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most commonly but not necessarily dyadic. 375 Sometimes a dyadic contradiction can be resolved by mediation of a third factor, 376 but triads can also harbor problems. For example, the Arrow impossibility result 377 is triadic. Some voting systems cannot be simultaneously rational, egalitarian, and decisive. Marcus (1998) discusses other triadic incompatibles. 378 Nor do difficulties stop at the triad. Tetradic systems can also be problematic. For example, the Parsonian tetrad can be afflicted by tensions and contradictions, 379 which is one way to conceptualize problems of societal differentiation. Dyads are inherently conflictual, but harmony is also not preordained for triads, tetrads, and higher ordinality systems. The degree to which harmony can be achieved in any system is partial and contingent. As reason reveals its limits, we have come far from Enlightenment optimism. But it does not follow from reason being limited that it is wise to dismiss its value entirely. In the contemporary world, the tensions that exist between liberty and security are obvious but public discussion on this subject still leaves much to be desired. Those who are responsible for national security do not adequately justify the specific encroachments on civil liberties that they advocate or implement. Those who wish to protect civil liberties, on the other hand, do not appreciate the magnitude of the dangers that must be averted and do not realize or admit that not being responsible for security means not fully understanding its requirements. Differences in social roles lead to differences in the salience of competing values. The bottom-line is this: there is no general solution to the tension between liberty and 375

See the list of dyadic tensions in Summary 1.1.9 and 7.1.9, pp. 23, 491. Note #166 Butterfly catastrophe, p. 570 377 Note #68 Aggregating preferences, p. 420 378 An interesting candidate for possible incompatibility is the triad of Good-True-Beautiful (see Figure 90 Pragmatic, semantic, syntactic; regulatory triad, p. 468). Its Good-True projection is a salient source of societal tension; more subtle tensions might also afflict the Good-Beautiful and Beautiful-True dyads. 379 6.4.2.2 Problems of differentiation, p. 257 376

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security. To quote Butler (1872) again, “Extremes are alone logical, but they are always absurd.” Both God and the Devil are in the details of the trade-offs that must be made. The work of reconciling the values of liberty and security is always provisional and imperfect and never finished. Problems – here meaning difficult problems – are general, in the terminology of this book, “metaphysical”; solutions to these problems are necessarily particular: both context-dependent and timedependent. Systems ideas can guide our thoughts about problems that arise because multiple values conflict. Consider what game/decision theory says about such situations. When one wants to promote two or more values for one agent (the agent could be an aggregate, even a whole society) or one value for two or more agents, the utilities that correspond to these values can sometimes be put on a single scale by suitable weights, or one utility can be optimized subject to the others as constraints, or utilities can be prioritized, as in lexicographic ordering, so less important values are considered only when alternatives are equal with respect to more important values. 380 Game/decision theory also offers various decision rules 381 such as maximum expected value (average utility) or maximin (worst case utility) that can be used in comparing different policies or societal outcomes. These game/decision-theoretic ideas appear, for example, in Rawls’ (1971) treatise on justice. In considering the competing values of liberty and equality, Rawls proposes the lexicographic approach, taking liberty as more important than equality. 382 He applies this to situations where one agent has multiple values. For situations where multiple agents compete in trying to realize one value, Rawls proposes the maximin principle, not the maximum expected value principle, for 380

Note #67 Multiple objectives, p. 419 Note #56 Decision theory, p. 406; Note #75 Game theory, p. 429 382 One might question the tenability of simply prioritizing liberty over equality, since large improvements in equality surely outweigh minimal harm to liberty, so liberty and equality can’t be strictly incommensurable. 381

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comparing societies or social policies. He urges that societies/policies be judged by the lowest and not the average utility, a criterion that would push societies/policies with large inequality but higher average utility to redistribute some utility. This example is offered not to advocate for Rawls’ positions, but to show that systems ideas are relevant to such issues as multiple values and distributive equity. 6.5 Summing Up: promise of the systems project One might ask whether systems theory, which can clarify the underlying nature of problems, can offer solutions to these problems. 383 The answer is: by itself, no. Systems theory alone is too abstract to provide solutions to concrete real-world problems. 384 Understanding problems and (partially) solving them requires phenomenon-specific models from the relevant specialized disciplines, expertise of experienced practitioners and professionals, and involvement of stakeholders who have legitimate interests and valuable knowledge. Without these, applying general ideas to practical problems will usually produce undesirable consequences. However, as a conceptual and methodological supplement to such expertise and participation, systems theory can contribute new insights into a wide variety of different problems and their possible solutions. Some problems are ever-present in human affairs; other problems are unique to particular times. Although there is always a tendency to regard the present as a singular moment in human history, the challenges of today may in fact be singular. The historical model presented above 385 points to global challenges that have never before been encountered in human history: dangers of climate change, massive extinctions, and 383

This question is discussed in Appendix A.2.1 Problematics, p. 604 Systems theory describes phenomena abstractly, so it cannot provide a view of the whole that encompasses specifics. Figure 86 The highest is not the whole, p. 456, expresses this limitation in a hierarchical diagram. 385 6.1 A macro-historical model, pp. 193ff; 6.2.1 A supplementing process, p. 207; 6.3.4 Revisiting the historical model, p. 243 384

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ecological disaster – all against a background of the continued possibility of nuclear war. At the same time, we also face problems, such as economic exploitation, political oppression, social hatred, and inter- and intra-national violence, which societal systems have often encountered in the past and continue to encounter in the present. Deeply rooted problems are rarely susceptible to global or lasting solutions, but they can partially yield to solutions that are local and temporary. A systems theoretic understanding of the underlying character of problems can help us conceive of solutions. By focusing on their “lawfulness,” a systems ontology of problems 386 usually does not assign blame, seeing problems as emerging from complex situations rather than from the moral or cognitive failures of specific human actors. 387 Serious problems that are amenable to simple solutions are rare. Although there are situations where assigning individual blame is called for, in most critical problems faced by social systems fault is more systemic than individual. That fault is systemic does not mean it is unitary. Problems are usually multi-factorial, and multiple archetypes are needed to understand them. A systems ontology of problems provides a rich array of candidate archetypes 388 which can help us avoid the illusion that we fully understand the problems that we face. Superficial understanding leads to hasty action which typically worsens rather than improves conditions. 389 That problems are “lawful” does not preclude at least partial success in trying to solve them. A systems ontology unveils the underlying character of problems, not their incorrigibility. Perfection is not of this world, but perfecting is always possible. A systems metaphysics is thus both pessimistic and optimistic. It is pessimistic in declaring that problems are 386

5.4 Ontology of problems, p. 167 E.g., game theory absolves participants in a Prisoner’s Dilemma of blame; see Note #78 Prisoner’s Dilemma, p. 433. 388 Illustrated by Essay and by 5.5 Metaphysician’s desk manual, p. 174. 389 Note #61 Counterintuitive effects, p. 413 387

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deeply ingrained in reality – this is what “metaphysical evil” 390 means – and that solutions are at best only local and temporary. It is optimistic, however, in asserting that problematic situations are nearly always susceptible of improvement. 391 Progress, though slow and subject to reversal, can be made. What is subject to hazard is also an occasion of opportunity. Martin Luther King said, “The arc of the moral universe is long, but it bends towards justice.” A systems metaphysics cannot prove King’s conviction, but does not deny it. While there is no guarantee of a redemptive future, there is abundant evidence for the creativity of the universe, the distillation of progressively more refined informational processes, and the arising of systems that are increasingly unique, autonomous, and cooperative (Wright 2000); in short, for a domain of value that has emerged from the domain of fact. For Bennett (1956), this domain is the realm of the autonomic, i.e., life, which has cosmic significance. The autonomic, in which information and utility are salient, is the bridge connecting the hypernomic, the macroscopic realm (galaxies, stars, planets) in which energy is salient, with the hyponomic, the microcosmic realm (molecules, atoms, particles) in which matter is salient. 392 Roughly speaking, within the hypernomic and hyponomic realms, creation and destruction dominate; within the autonomic, realm, however, maintenance 393 gains in importance, and in maintenance there is the possibility of tikkun. 394 Life mediates between the order and disorder above and the order and disorder below and is both the agent and beneficiary of this mediation. 390

6.3.1 Secular Theodicy, p. 226 This asserts that problems usually reflect a state of non-Pareto-optimality in which win-win improvements are possible. Such improvements are discussed in Note #125 Development vs growth, p. 510. 392 Figure 15 Triad of matter, energy, and information, p. 88; see also discussion of the hypernomic realm at the end of 5.3 Categories of complexity, p. 160 393 Figure 20 Creation, Destruction, Maintenance, p. 119 394 5.4 Ontology of problems, p. 167 391

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Systems metaphysics thus appropriately centers in biology, 395 not physics, and broadly on living systems, not narrowly on humankind. But while systems theory is biocentric, systems analysis, 396 to assist in the work of perfecting, is necessarily anthropocentric. Human beings are the only agents who can undertake the task of perfecting, so accepting this Although “it is not responsibility is our obligation. 397 incumbent upon us to finish the task, neither are we free to abstain from it.” 398 Mending the world – ameliorating natural evil, which is a manifestation of metaphysical evil – is the charge of humanity, a task that begins with reducing moral evil, the part of natural evil for which we are directly responsible. 399 To put it positively: this mending enlarges the domains of moral good and thus natural good and thereby extends the scope of metaphysical good. Given the lawfulness of metaphysical imperfection, the work of perfecting in fact goes against the metaphysical grain; for concrete systems this is exemplified in the fact that entropy increase is easier and more natural than entropy decrease. 400 Perfecting is not spontaneous or automatic but requires skillful, dedicated, and intelligent action. 401 Nevertheless, just as entropy decrease can be driven by entropy increase, 402 so too is going against the grain provided for in the metaphysical scheme of 395

4.3 The centrality of biology, p. 135 4.5 Systems theory and systems analysis, p. 141 397 It is commonly accepted in the philosophy of ethics that “ought means can.” Here, the reverse is declared, namely that “can means ought.” This assertion is not justified by any principle of logic, but is implied if one endorses the position of Levinas that “ethics precedes ontology.” An imperative is implicit in a systems ontology of problems. 398 Rabbi Tarfon, Pirke Avot 2:21 399 6.3.1 Secular Theodicy, p. 226 400 See Note #140 Two universal processes, p. 535, especially Figure 114 Coupling of entropy increase and decrease, p. 538. 401 This echoes the need for joint action of all components of the regulatory triad; see Note #100 Tetrad of modeling, p. 465. 402 Incompleteness in being engenders becoming (1.2.2.2.1). 396

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things. The realm of the autonomic is, after all, a natural emergent, and perfecting is a natural impulse of human agency. For us, the absence of redemption is a palpable presence. Hope for a better future fuels perpetual arising of emancipatory movements. Anticipation of such a future creates a “not yet” 403 in the realm of potential that can influence the actual. 404 Evidence for the possibility of further perfecting in gains already achieved is visible and energizing. What stands in the way of perfecting is the absence of common cultural ground among the world civilizations, the loss of coherence in modernity within Western civilization, the lack of a framework that encompasses the different truths grasped by the political left and right, the narrowness of scientific reductionism, and the increasing fragmentation of knowledge. Underlying all of these deficiencies is a flawed metaphysics, 405 an inadequate understanding of the most general features of reality. What is needed is a new metaphysics, one that is exact and scientific, 406 that would integrate different worldviews and connect multiple disciplines in the sciences and humanities. Such an ESM could also preserve and modernize what is of enduring value in the entire history of philosophical thought on fundamental questions. It would be a true theory of everything (in the world-centered perspective), not one applicable only to concrete (material) systems, and not a promissory note incapable of ever being redeemed. A systems theoretic ESM is already partially at hand. It provides tools for thought, methods of analysis and synthesis, ideas for insight, and an approach to education 407 that is critically needed in the 21st century.

403

Note #105 Cognition and time, p. 476 …What is potential exists and can influence the actual (1.1.2.2.4). See Note #12 The potential and the actual, p. 331. 405 2.1 The illusion of the fundamental, p. 43 406 2.3 A new conception of metaphysics, p. 54 407 See the discussion of the knowledge most worth having in 6.2.5 Personal knowledge, p. 221. 404

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By linking the sciences and humanities, systems thought points to a possible recovery of cultural coherence. It is often declared that grand meta-narratives are things of the past that deserved being abandoned because they were both intellectually dubious and morally dangerous. This is a valid criticism of religions, political ideologies, and philosophical systems that claim completeness, consistency, and certainty and seek to advance these claims through dogmatism and force. But the exact and scientific metaphysics that the systems project aims at is different from this. It makes no claims of completeness, consistency, or certainty. Quite the opposite. It insists that there are patterns that can be discovered in the world that are ubiquitous and important. But recognizing the hostility the universal bears toward the particular when it refuses to submit to eradication of difference, the systems project does not prioritize universality over uniqueness. Nor does it prioritize difference over identity. It attempts to grasp the whole, but accepts the impossibility of doing so. It admits – even points to – its own incompleteness and inconsistencies, 408 while still trying where possible to rectify these faults. Being agnostic about “the all,” it constructs no totalistic system. Instead, it unites the general and the perspectival by privileging the central over the fundamental. And it accepts the complementarity of the human-centered perspective with its own world-centered perspective. Grand narratives are not a thing of the past. 409 By now we should be skeptical about assertions that this or that is a thing of the past, having discovered in the 21st century that religion is not a thing of the past, the alleged triumph in modernity of secularism notwithstanding. Meta-narratives are not only unavoidable; they are essential. We need the best ones we can construct, and we need more than one, in competition with one another. To paraphrase Brecht (1920), “The man with one meta408 409

See Appendix A. Auto-critique, p. 591. 6.1.3 On the inescapability of grand narratives, p. 205

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narrative is lost.” 410 This book offers a meta-narrative in the conception of an exact and scientific metaphysics 411 that the systems project is engaged in constructing. No claim is made here for the sufficiency of systems thought for scientific understanding or societal problem solving. As argued above, 412 systems/complexity science is a corrective supplement to mainstream science. It also offers only a supplement to philosophical, religious, and political thought. But the claim is made here of the necessity of systems thought for understanding our place in the universe and for solving both perennial and unprecedented societal problems. The supplement of systems ideas and methods is one we cannot do without.

410

The actual quote is “A man with one theory is lost. He must have several, four, many!” 411 This chapter also offers a historical meta-narrative – see 6.1 A macrohistorical model, p. 193 – but the idea of an ESM does not depend upon this meta-narrative. 412 6.2.1 A supplementing process, p. 207

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Part III. NOTES: Systems Theory Chapter 7 (which follows) repeats Chapter 1 of Essay sentence by sentence, and explains its assertions. The repeats of Chapter 1 are shown in italics. The explanations that follow are not italicized and are numbered sequentially. Explanations often refer to formal theories, e.g., graph theory or game theory, which collectively constitute systems theory. However, the coherence claimed for Essay is conceptual, not mathematical, so technical explanations in Notes are not necessary and intended interpretations of the statements of Essay, just demonstrations that its statements can be given precise interpretations. Occasionally, Notes also offers examples of the problems that Essay’s assertions speak about. Chapter 1 (Essay) and thus also Chapter 7 (Notes) are organized in two parts: Synchronics (Being) and Notes on Synchronics; and Diachronics (Becoming) and Notes on Diachronics. Synchronics includes structure and function at an extended present moment; it excludes system formation, development, and long-term change. The system is regarded as already existing. Synchronics is the study of what Klir (1985) calls “behavior” or “structure” systems. See also the discussion of synchronics and diachronics in Commentary. a Diachronics is the third term in the structure-functionhistory triad; it includes system formation, development, and long-term change; creation and destruction, as opposed to maintenance. b It concerns Klir’s (1985) “meta” systems, which are not support- (here, time-) invariant. The purpose of Notes is not only to unpack Essay; it is also to present the contents of systems theory. Essay provides a filing system that allows systems ideas to be organized. For a

3.5 Structure, function, and history, p. 109 3.5.2 Adding history, p. 116; see especially the discussion of Figure 20 Creation, Destruction, Maintenance, p. 119

b

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NOTES

example, its Synchronics sections progress roughly from more general ideas to less general ideas. So Notes discusses graph theory, which is fundamental for systems theory, in Constraint, the second section of Synchronics but discusses game theory, which is not fundamental for systems theory, in Agency, the sixth section of Synchronics. Many pages of Notes are needed to explain the first few sections of Synchronics because basic systems ideas must be introduced early on to provide a foundation for subsequent discussion. Later sections are shorter and sparser. Also, Notes for Diachronics is shorter than Notes for Synchronics, because most fundamental systems ideas have already been introduced in Synchronics. Notes uses multiple formal frameworks to discuss systems ideas, rather than providing a single coherent framework that might encompass them all. In the unavoidable choice between completeness and consistency, i.e., breadth of coverage and formal coherence, completeness has been given priority. Integration of multiple frameworks into a unitary structure is hypothetically possible, although Essay implies that such an undertaking would be difficult, and Commentary, Chapter 4. The Challenge of Integration discusses this difficulty in more detail. Explanations in Notes are mainly of two types: (a) miniessays that introduce major systems theories, e.g., Note #17 Chaos, and (b) explanations of concepts, e.g., Note #3 Organizing principle. It has been impossible to completely avoid reference to specific theories in advance of explicit notes about the theories. In such cases, however, there are usually footnotes that point ahead to where these theories are discussed. Notes is primarily a presentation of theories and ideas from the systems literature, but some material presented in this section – both ideas of the author and ideas of others – should not be regarded as already well established in the systems field. Such a fusion of common knowledge and idiosyncratic views is unavoidable in synthetic works of this kind. Hopefully, the

NOTES

287

degree of canonicity of the ideas in this section will be apparent from their presentation. Occasionally, explicit statements will indicate that certain ideas are speculative. Since Notes focuses on the mathematical ideas and models that underlie the statements of Essay, Notes will appear to be epistemological rather than ontological in character. The reader should be reminded, however, that Essay discusses problems viewed ontologically; epistemology is addressed “within” ontology by the section in Essay and Notes titled Cognition.

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List of Notes Synchronics Wholeness 1 System 2 Organizing principle 3 Relation 4 Incompleteness 5 Structure 6 Inconsistency 7 Networks 8 Incompleteness vs. inconsistency

295 303 304 306 308 311 317 320

Constraint 9 Relation as constraint 10 Dynamic relation 11 Echoing the primary tension 12 The potential and the actual 13 Order 14 Entropy 15 Scale 16 Order and disorder are intertwined 17 Chaos 18 Unity and multiplicity 19 Aggregates vs. systems 20 Reconciling constraint and variety

324 327 331 331 332 334 335 336 338 340 341 341

Distinction 21 Distinction 22 Environment 23 Disequilibrium and existence 24 Boundary 25 Fuzziness 26 Fractals 27 External relation 28 Extension 29 Nothing, many, one, all 30 One, two, three, ten thousand 31 Assertion vs. integration

344 347 349 350 352 353 354 357 358 359 363

NOTES

289

32 Emergence 33 Engaging/disengaging 34 Active vs. passive 35 Function

363 368 368 370

Persistence 36 Stability 37 Catastrophe theory 38 The fold catastrophe 39 The Second Law 40 Rigidification vs. disintegration 41 Openness and Closedness 42 Dissipative systems 43 Openness necessary and hazardous 44 Law of Requisite Variety 45 Feedback control

373 375 376 378 378 380 381 383 384 386

Identity 46 Information (and matter-energy, utility) 47 Autopoiesis 48 Algorithmic information 49 Genotype and phenotype 50 Internal vs. external identity 51 Paradoxes of autonomy 52 Dangers of filtering out noise 53 Boundary subsystem

389 393 395 395 398 399 400 401

Agency 54 Utility 55 Environmental types 56 Decision theory 57 Chaos and long-term forecasting 58 Nature resists 59 Multiplication of effects 60 Externalities 61 Counterintuitive effects 62 Weakening by strengthening 63 No terminus 64 Discounting the future 65 Binding the future and sunk costs

403 404 406 410 411 411 412 413 416 417 417 417

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66 Pareto-optimality 67 Multiple objectives 68 Aggregating preferences 69 Computational complexity 70 Optimization 71 Optimality, stability, and resilience 72 Purposeful action as a tetrad 73 Assertion, integration, exchange 74 Eating and being eaten 75 Game theory 76 Coalition instability 78 Prisoner’s Dilemma 79 Chicken 80 Symmetry or altruism may be harmful 81 Sharing elements 82 Heteronomy 83 Recruitment and predation 84 Embeddedness as a solution to the PD 85 Turbulent fields

418 419 420 422 423 424 426 427 428 429 431 433 435 436 437 438 439 440 440

Complexity 86 Complexity 87 Individuality and complexity 88 Hierarchies and networks 89 Complexity, stability, and chaos 90 Small worlds 91 Scale-free networks 92 Homogeneity, heterogeneity, and scale 93 Three levels 94 The highest is not the whole 95 Hierarchical egalitarianism 96 Distillation and alienation 97 Informational parasitism

441 445 445 449 450 450 452 454 456 457 458 458

Cognition 98 A naturalistic epistemology 99 The modeling subsystem 100 Tetrad of modeling 101 Pragmatic, semantic, syntactic 102 Multiple subselves

461 463 465 468 472

NOTES

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103 Self and non-self 104 Embeddedness of cognition 105 Cognition and time 106 Constructing reality 107 Representation 108 Cognition and autopoiesis 109 Relativity of models 110 Fallibility 111 Modeling constraint 112 Sensitivity and specificity 113 Wrong perception 114 Self-reference

473 475 476 477 479 480 481 481 482 484 486 487

Summary 115 Binary oppositions 116 Dyadic correlations 117 Dialectics 118 The extremes are attractors 119 The war of universality on uniqueness

492 492 493 494 495

Diachronics Origin 120 System formation 121 Self-organization 122 Offspring

496 502 505

Development 123 Disequilibrium and change 124 Order through fluctuations 125 Development vs growth 126 Contradiction and its consequences 127 Self-development

507 509 510 512 513

Limitation 128 Dialectics and catastrophe theory 129 History: idiographic or nomothetic 130 Trajectories of development 131 Cusp catastrophe 132 Augustinian vs. Manichean devils

514 516 517 520 522

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NOTES

133 Environmental types, again 134 Failures in meeting new challenges

525 525

Complexification 135 Movement toward the extremes 136 Centralization 137 Mechanization 138 Form limits growth 139 Temporalization of complexity 140 Two universal processes 141 Optimal segregation vs. systematization 142 Progressive segregation 143 Partial decomposability 144 Systematization 145 Levels of structure and dynamics 146 Integration of stable substructures 147 Limits of complexification 148 Non-decomposability under stress 149 Connectedness for good and ill 150 Self-organized criticality

527 529 530 531 532 535 538 539 540 541 542 543 544 550 551 551

Internal Opposition 151 Something intractable 152 Cusp of negation 153 Excess and overshoot 154 Chance and necessity

554 556 559 560

Texture 155 Environment is a limited source and sink 156 Wastes are inevitable 157 Closing the circle 158 Limits to growth 159 Temporal traps 160 Growth as a PD 161 Difficulty of reversing bad effects 162 Destroying the environment that sustains

563 563 564 565 566 566 567 567

Other systems 163 Natural selection 164 The organized exploits the unorganized

568 569

NOTES

293

165 Two kinds of dialectics 166 Butterfly catastrophe 167 Butterfly of reconciliation

569 570 572

Embeddedness 168 Succession 169 Punctuated equilibria 170 Adaptation vs. adaptability 171 When to change 172 Generalized evolution 173 Evolution of modeling subsystem

575 576 577 579 579 581

Impermanence 174 Things fade 175 Thermodynamics vs. kinetics 176 From being to non-being 177 Failing all at once 178 Dissolution 179 Its effects may endure 180 Decay is inherent in composite things

584 585 585 586 587 588 589

295

Chapter 7 Notes on Being and Becoming 7.1 Notes on Synchronics (Being) 7.1.1 Wholeness Notes:

page

1 System 2 Organizing principle 3 Relation 4 Incompleteness 5 Structure 6 Inconsistency 7 Networks 8 Incompleteness vs. inconsistency

295 303 304 306 308 311 317 320

Repetition of Essay is shown in italics; superscripts number the Notes that follow. For this Wholeness section, there are two clusters of notes: (a) System, Organizing principle, Relation, Structure, Network; and (b) Incompleteness, Inconsistency, Incompleteness vs. inconsistency. Cluster (a) discusses basic systems ideas; cluster (b) discusses ideas oriented toward the ontology of problems that Essay offers. The whole cannot be embraced. Every system1 has an organizing principle,2 and every organizing principle is limited.

1. System A system is a whole, a unity within multiplicity: unity in the whole and multiplicity in its parts. Every whole is limited in what it encompasses. Technically, the simplest definition of a system is a set of elements and relations between elements. Parts are organized, not merely aggregated. A whole is constituted from its parts via the internal order of the system. The parts come from a larger ensemble, so the limitedness of the © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7_7

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whole also reflects a system-environment distinction. A system thus manifests two constitutive properties: order and distinction. Beyond the internal order – call this “structure” – the system participates in some external order – call this “function.” (“Function” here does not connote purpose or usefulness.) Earlier, a system was depicted as a double cone opening upward and downward. a Regarding every system as a center resembles the use of a body-centered coordinate system in physics, where location is defined relative to the center of gravity of the body under consideration, as opposed to a space-centered coordinate system that is independent of any particular entity. A view of the system as center to its environment as periphery is obtained by projecting the upper cone (function) down its axis. Function is participation in structure of a larger whole, viewed from the perspective of the system, so order is both internal and external. A whole is distinguished not only from its external environment but from its internal parts, and parts are distinguished one from another, so distinction is both external and internal. Though order and distinction are both internal and external, order is discussed in Constraint in terms of internal structure, and distinction is discussed in Distinction in terms of external function. So, while order and distinction are discussed separately, they are actually linked. b Structure includes at least two kinds of parts: elements and relations. In concrete systems, c elements are components of substance or process that are organized by form. In conceptual systems, elements are variables, linked by mathematical relationships. The most general type of variable is a nominal (qualitative, categorical) one; its values are arbitrary labels that are discrete and unordered. Nominal variables are emphasized in this book, since their generality makes them relevant not only a

Figure 3 System as center, p. 49 Aspects of this linkage are discussed in Notes #23 Disequilibrium and existence, p. 349 and #47 Autopoiesis, p. 393. c 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 b

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to the natural sciences but also to the social sciences. This view of systems as consisting of elements and relations is dyadic but not dualistic, since as will be explained shortly, elements and relations are complementary aspects of a single reality. Elements are here indicated by letters, and relations are here indicated by letter combinations that state which elements are linked. A minimal system thus has two elements, say A and B, and relation, AB; the system is the set of elements and relations, {A,B, AB}. This set is a triad of two elements and one relation, but as explained later, every relation can be viewed as an element, so the triad might be considered to contain only elements. This definition of system includes both order (the AB relation) and distinction (between A and B), but it does not yet consider the environment. Writing relations in this way privileges relations over elements, since AB implies A and B, but A and B do not imply AB except potentially. For now, the directionality of a relation is ignored, so AB is equivalent to BA. A and B are either (1) two different state variables of the system, or (2) one state variable at two different points of space or time. Space and time are support variables (Klir 1985). The next few notes assume (1) and thus treat the system as static; when dynamic relations are covered later, (2) will be introduced. a Consider a system consisting of three elements and two relations, S = {A,B,C, AB,BC}, represented in one of the ways shown in Figure 37. This system is “neutral,” i.e., static and acausal, but it could be “directed” (Klir 1985) if relations are “directional,” which accommodates not only dynamics (A, B, and C might be the same element at different times) and causality but also any methodological distinction between inputs and outputs (independent and dependent variables) even when causality is not implied.

a

Note #10 Dynamic relation, p. 327

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Figure 37 Alternative representations of a neutral system Solid = element; dashed = relation. Here, dashed lines are used for relations to suggest that form is “finer” than substance. (a), (b), and (c) are discussed below. In subsequent figures, however, boxes (relations) are shown as solid and not dashed.

A

AB

B

BC

A

C

AB

B

BC

C

(b)

(a) (c)

AB

A

S ≡ ABCAB:BC ABCAB:BC BC

B

C

All three representations ignore the environment and reflect an internal or closed systems view. a Figure 37(a) is the most familiar representation. Elements are circles (or points) linked by lines (sometimes arrows). This representation has the visual effect of privileging elements, since circles are more salient than lines. In Figure 37(b), relations are prominent as boxes, and elements are lines; this privileges relations over elements and is common in systems modeling (Klir 1985; Krippendorff 1986). As noted, relation AB implies the existence of elements A and B, which might be considered to be “monadic relations” embedded in dyadic relation AB. Since elements are included in this way in relations, the system {A,B,C, AB,BC} could be written more simply as the structure AB:BC. The colon in AB:BC means “independent of.” AB and BC are mutually independent, except for the common element B. For a system {A,B,C,D, AB,CD}, i.e., AB:CD, the two relations are independent. (The sequence of relations and of elements within relations are here irrelevant, e.g., AB:BC = BC:AB = CB:BA.)

a

3.5.1 Structure and function, p. 109

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Figure 37(c) separates elements and relations vertically and adds one solid line and one dashed line that span AB and BC and represent the system as a whole. The dashed line, ABCAB:BC, indicates that the two dyadic relations AB and BC define an equivalent triadic ABC relation. The solid line, S = ABCAB:BC, indicates that this single relation is equivalent to system S as a higher-level element. Generally, (i) multiple relations, if consistent, define an equivalent single relation and (ii) any relation is equivalently a single element. A system is a “Janusfaced holon” (Koestler 1969, 1978): Looking down (in), it is a unitary relation, ABC; looking up (out), it is a unitary element, S. (Relations AB and BC might also be regarded as elements. a) This is explained further below when relation is seen as a constraint. b In concrete systems, form (relation) looking down is substance (element) looking up. Figure 38 gives an open systems view that adds the environment and shows elements as systems. In it, compositeness can be seen to be recursive upward and downward. A whole on another scale is a part; a part on another scale is a whole. As a part, a system is a higher-level element that has relations with other such elements; as a whole, an element is itself a system. c Figure 38 Hierarchy of Janus-faced systems A double (solid+dashed) line is a Janus-faced element/relation.

S

E

SE

ABC A

a

B

C

Figure 85 Two conceptions of three levels of analysis, p. 454 Note #9 Relation as constraint, p. 324 c When Essay speaks about wholes that contains very similar systems as elements, it refers to it as a “population.” b

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NOTES

The internal order of system S is relation ABC; the external order in which S participates is relation SE. This open systems view thus represents both structure and function which are openended downward and upward, respectively. By contrast, Figure 37 is a closed systems view that represents only structure. If openness continues indefinitely, there is no system that includes everything (Ross 1980) and no element that is non-composite; but recursion in one or both directions might stop, allowing these extremes. Figure 38 also shows the system as a unity within multiplicity: Unity is relation ABC, equivalent to unitary element S, and multiplicity is the set of elements, A, B, and C. Figure 39(a), simplified from Figure 38, is a minimal system in the open systems view. Distinction exists internally between A and B and externally between S and E. Internal order (structure) is AB, and external order (function) is SE. Figure 39(a′) shows the relation between this representation and the double cone image of system. a If levels are elements at different scales, the double cone has three levels of analysis: (1) the system as vertex of the double cone, (2) its elements (subsystems) in the lower cone, and (3) its context (suprasystem) in the upper cone. Function is structure of a more encompassing whole, but from the vantage point of the system (the vertex), structure and function are internal-external opposites. If there is “vertical decomposability” (Simon 1981), where everything inside the elements (A and B) is subsumed by them and everything outside the system is subsumed in its context (E), then the three levels in Figure 39(a) are sufficient for analysis. b A similar idea of the sufficiency of three levels is given by Lendaris (1986). In Figure 39(b), the environment is not unitary but has structure (CD), like the system. The BC relation does not link S and E as unitary wholes, but links their elements.

a b

Figure 3 System as center, p. 49 Note #93 Three levels, p. 454

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Figure 39 A minimal system S with environment E (a) System with unitary environment. (a′) Corresponding double cone image. (b) System with non-unitary environment; the system structure is AB; its function is BC.

function

SE E

S

system S

AB B

A

structure

(a)

(a′)

S = AB A

BC B

(b)

E = CD C

D

These graph theory ideas are elaborated in later notes. a Graph theory does not specify what a relation is; this is later done using set and information theory. b These later notes are all about order. 7.1.3 Distinction takes up the second fundamental idea of system and develops the open systems view. c Many definitions of “system” have been tabulated by Klir (1969). The “limited whole” formulation comes from Murdoch (1992). So far, the parts of systems have been elements and relations. In a more elaborate – triadic rather than dyadic – perspective, a system is a set of elements, attributes, and relations (Hall and Fagen 1956). As before, elements are linked by relations, but linkage is now mediated by attributes (Figure 40). Typically, attributes are universals and elements are particulars. Concrete a

Notes #5 Structure, p. 308 and #7 Networks, p. 317 Note #9 Relation as constraint, p. 324, and Note 10 Dynamic relation, p. 327 c Note #27 External relation, p. 354 b

302

NOTES

systems have attributes that refer to substance, e.g., charge is an attribute of an electron (element) or electromagnetic interaction (relation). In abstracted systems, attributes need not be material. Mathematically, attributes are variables. In concrete systems, the support variables of space, time, or a population identifier might index the elements. Extension a – in space, time, or population – is not obligatory for the simplest notions of system, but there must be some multiplicity of elements. Extension in space-time is, however, a necessary property of concrete systems. Figure 40 Adding attributes to elements and relations The unitary relation equivalent to the system as unitary element is omitted. Note that the attributes of the system (F, G) can be different from those of its elements (A, B, C).

G

F relations attributes A elements

AB′

BC′ B

e

B′

attributes system = element

C′ e′

Attributes belong to elements (solid), or to relations (dashed), or to both, as shown in the figure. Attributes are correspondingly either intrinsic or extrinsic to elements. For example, a mating instinct is intrinsic to an animal; a legal status in human society is extrinsic to a person. Attributes are intrinsic when they are upwardly emergent properties (solid) of the elements as systems. Attributes are extrinsic when they are downwardly emergent properties (dashed) of the relations or the system as a whole. b Elements bind attributes together, but differently from the way relations link attributes. Relations do so explicitly; elements do so implicitly by bundling and indexing attributes. a b

Note #28 Extension, p. 357 Note #32 Emergence, p. 363, Note #18 Unity and multiplicity, p. 340

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For mathematical simplicity one often omits attributes and considers relations to organize elements, taken as variables, but the triadic definition of system, in terms of elements, attributes, and relations, is richer. It allows for similarity and difference between elements: Two elements are similar either if they have the same attributes, or if they have the same values (states) of these attributes. (In Figure 40, elements, e and e′, are both similar and different: They both have attribute B but differ in their second attribute.) In social systems where elements are persons, relations organize roles (attributes), not whole persons. This triadic framework of object (entity, process), property, and relation is common to many fields. It applies to particles of physics (that have mass, charge, etc.) organized by forces (forces are relations, carried by particles, showing equivalence between relations and elements), as well as to database ideas in computer science.

2. Organizing principle The idea of an organizing principle (OP) has different interpretations in the different sections of Synchronics. In this section, 7.1.1 Wholeness, it refers to the relations that organize the system, where relation is some undefined linkage. In 7.1.2 Constraint, linkage is interpreted as constraint, so the OP is the overall constraint manifested in the system. In 7.1.3 Distinction, the OP is the defining difference or boundary between system and environment. In 7.1.4 Persistence, it refers to the system’s stable states, the attractors of its dynamics, or the constraints on essential variables that are needed for viability. In 7.1.5 Identity, the OP is the system’s essence as opposed to its appearance, in biological terms, its genotype as opposed to its phenotype, where appearance is the joint result of essence and environment. In 7.1.6 Agency, the OP is defined by some integrated utility function. In 7.1.7 Complexity, it is the basic structural architecture of the system. In 7.1.8 Cognition, it is a modeling subsystem or the central processes of this subsystem.

304

NOTES

In going from initial sections of Synchronics to later sections, the meaning of organizing principle moves from the general to the specific. Essay’s metaphysical aspirations are reflected in general interpretations, while exactness is achieved by specific interpretations. In these notes, sometimes a general idea is given a name commonly associated with a rigorous but narrow interpretation of it – for example, genotype. a The idea will still be intended in a generalized sense, as will be illustrated shortly by Notes #4, 6, 7 on incompleteness and inconsistency. This approach, applied above to information, b gives a hierarchy of meanings to a general concept. In any system, only some elements and relations3 are encompassed; others are left out. Unity is gained at the cost of partialness. In the impossibility of totality, every system is incomplete.4

3. Relation A relation is a linkage between elements. This linkage is not necessarily dyadic (Angyal 1939). When there are more than two elements, higher ordinality relations (triadic, tetradic, etc.) are possible; graphs including such relations are hypergraphs. In the example in Note #1, AB and BC are integrated into an equivalent triadic relation, ABCAB:BC, but this ABC is not irreducibly triadic; it is decomposable without loss back to these two dyadic relations. In general, however, a triadic relation may exist that is not decomposable without loss to dyadic relations. For example, there are ABC relations not equivalent to AB, BC, and AC. Although any set of consistent relations is equivalent to some higher ordinality relation, the converse is untrue. Every relation is not equivalent to a set of lower ordinality relations. a b

Note #49 Genotype and phenotype, p. 395 5.2 Hierarchy of system types, p. 154

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A relation having three or more elements has interaction effects. C may depend on A and on B, but its triadic dependence on both A and B cannot always be partitioned into A-effects and Beffects. This is one possible meaning of the word “holism” a: Systems are holistic if they include irreducible higher ordinality relations. “The whole is greater [or less] than the sum of its parts” then means that there are wholes that cannot be decomposed without loss into parts; e.g., ABC is holistic if it cannot be decomposed without loss into AB, BC, and AC. This is symbolically represented in Figure 41. The rings are elements A, B, and C. There is no AB or AC or BC relation connecting a pair of elements, but there is an ABC relation, which is thus maximally holistic. In general, however, saying that a system cannot be decomposed into parts without loss does not imply total irreducibility, only that an aspect of the system is irreducible. Later, when relation is defined as constraint, it will be possible to quantify the strength of relations of different ordinality. Concepts like holism can thus be defined rigorously. Figure 41 A triadic non-decomposable relation Removing one Borromean ring allows the other two to separate.

Figure 42 depicts triadic relations; relations have been given directionality just to offer an example of a directed system. The convention in Figure 42(a) is uncommon, since graph theory links are normally dyadic. The alternative convention of Figure a

3.4 Aspects of complexity and holism, p. 100

306

NOTES

42(b) uses boxes for relations and lines for elements, reflecting the salience in systems theory of form over substance. a Figure 42 Representations of (directed) triadic relations (For neutral triadic relations, just drop the arrowheads.)

A

(a)

(b) B C

A

ABC

C

B

4. Incompleteness “Incompleteness” here is a general concept like organizing principle. It is not intended to have the meaning it has in formal mathematical systems, namely the existence of well-formed but undecidable propositions. Note #1 describes a system as a “limited whole” (Murdoch 1992); “incompleteness” means this limitedness (partialness, finitude), but “incompleteness” is used instead because some meanings associated with it are in fact intended, and because this word is commonly paired with the word “inconsistency.” The incompleteness-inconsistency dyad, interpreted generally, has broad significance. Incompleteness is inherent in the closed systems view. Any system organizes only a portion of reality. For concrete systems, defined in space and time, limitedness is obvious. For abstracted or conceptual systems, what is figure and ground may be observer-dependent, but distinction between figure and ground is always necessary. Every system is incomplete just in having an environment, separate from it but relevant to it. No (finite) system is causa sui, a sufficient cause of itself (Spinoza); this is conveyed by “incompleteness” better than by “limitedness.” a

3.1 Substance and form, p. 79

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In the open systems view, relations to the environment (function) are aspects of the system. However, beyond external elements directly linked to the system – its “relevant environment” – that define function, there are further external elements connected to this relevant environment but once-removed from the system as center a; and elements still more distant. Similarly, sub-elements internal to the system’s elements and their sub-sub-elements are increasingly distant from the system as center. This is the meaning of the widening cones in the double cone system representation: more is encompassed but less tied to the center. This “spatial discounting” b is a kind of incompleteness. Aside from the fact that not all elements are included in any particular system, not all attributes of the elements are involved in the system’s relations. Possible attributes are numerous, and not all attributes are encompassed by the organizing relations. Nor does the system include all possible relations. Figure 43 illustrates an idea from the Gestalt literature (Angyal 1939) of a possible gap between actual and potential relations. Systems have unfilled niches, e.g., D, and elements have attributes that are not organized, e.g., B. A system whose structure is beneath the top level of a Lattice of Structures c does not have all possible organizing relations. Figure 43 Incompleteness involving attributes and relations Attributes B (of e) and D (of CD) manifest incompleteness.

AB′

CD B

A e a

B′

C

D

e′

Figure 3 System as center, p. 49 Spatial discounting is analogous to temporal discounting; see Note #64 Discounting the future, p. 417. c Note #5 Structure, p. 308 b

308

NOTES

The relations that structure5 a system are either organized by a unitary principle, or they remain separate, unharmonized at the level of the whole.

5. Structure A structure is a set of (non-redundant) relations. Possible structures define a Lattice of (specific) Structures (Figure 44). AB:BC means relations AB and BC are independent, given B. Figure 44 Lattice of (specific) structures for neutral systems

level-1

AB

level-2

A:B

ABC AB:AC:BC

level-3

AB:AC

AB:BC

BC:AC

level-4

AB:C

AC:B

BC:A

level-5 2 elements

A:B:C 3 elements

The right of Figure 44 shows the ways three elements can be organized. The level-1 structure is the triadic relation, the system as a unitary whole. Level-2 structures include all three dyadic relations, level-3 structures include two dyadic relations, and level-4 structures have one. Level-5 consists of unrelated elements; a “heap” as opposed to a “whole,” a distinction first made by Aristotle (Harte 2002). The lattice shows the range from full integration (unity) at the top to full differentiation (multiplicity) at the bottom. Going down is decomposition; going up is composition. a

a

Note #140 Two universal processes, p. 535

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These lattices might be considered to describe the internal structure of a system. In the closed system view, the system is defined by its internal structure; in the open system view, the system includes also the external order in which it participates. The three structures at levels 2 and 3 differ only in a permutation of elements, i.e., multiple specific structures have the same general structure. Figure 45 illustrates the (a) specific structure AB:BC, and (b) its general structure where identifying labels are removed. The figure exemplifies the idea (Feibleman and Friend 1945) that wholes have parts which share subparts: Parts (relations) AB and BC share the subpart (element) B. Figure 45(c) illustrates the one structure, AB:AC:BC, that is cyclic, i.e., has a loop. Figure 45 Specific and general structures; loops (a) specific structure AB:BC; (b) general structure for AB:BC, AC:CB, and BA:AC (the order of relations is arbitrary; for undirected relations the order of variables is also arbitrary); (c) specific directed (and cyclic) structure AB:BC:CA.

A

AB

B

BC

C (b)

(a) A (c)

AB

B

BC

C

CA AB:BC in the Figure 45(c) could represent a lineal causal chain a (A causes B which causes C); CA adds feedback. As the number of elements increases, loops are more prevalent. Figure 46 is the lattice of general structures for a 4-element neutral system.

a

Figure 18 Lineal, mutual (feedback), branching causality, p. 104

310

NOTES

Figure 46 Lattice of (general) structures for 4 elements The top is the holistic tetradic relation. Going down, the second structure has four triadic relations; the fourth has two triadic relations and one dyadic relation. The bottom is a heap.

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Each structure is a way that four elements (lines that can branch) can be connected without labeling the elements or specifying directions for the relations (boxes). All this is graph theory, the most general of systems theories. a Structures are graphs, more generally hypergraphs which allow linkages between more than two elements. Unity coexists with multiplicity. Multiplicity allows inconsistency.6

6. Inconsistency The word “inconsistency” b is used in Essay and Notes as a general concept with different interpretations depending on the system or attribute being discussed. This is like the concepts of “organizing principle” and “incompleteness” which also have multiple possible meanings. The word “contradiction” is used synonymously with “inconsistency.” Inconsistencies are forbidden by classical logic, so if a scientific metaphysics is to be exact these words must respect this prohibition. Three ways of doing so involve interpreting inconsistency in terms of (i) differences in support variables c or (ii) existence of opposing forces, tendencies, etc., in the system, or by (iii) adopting some non-classical logic. d (i) The word “inconsistency” might apply when a difference in a support variable, e.g., space, time, or an index over a population, is ignored; or, to express this differently, when the system

a

Figure 8 Transdisciplinarity of some systems theories, p. 67 The pairing in Essay of “inconsistency” with “incompleteness” suggests an association with Gödel’s proof. The relation between this proof and how these words are used in this book is explained in Note #8 Incompleteness vs. inconsistency, p. 320 c The notion of support variable is explained in Note #1 System, p. 295 d Even if one adopts a non-classical logic one might still reasonably object to this terminology; see the discussion in A.1.5 Scope, p. 599 b

312

NOTES

description aggregates a over such a variable. For example, consider a system with multiple relations. If these relations are consistent, there is an equivalent single relation that organizes all the elements. b But multiple relations might not be consistent. In structure ABC:BCD, BC1 in ABC might not be the same as BC2 in BCD if these two BC relations arise at different points in space or time or from different samples of a population. (In this case, no single ABCD relation can exist that encompasses both ABC and BCD.) BC1 and BC2 can thus be inconsistent if they are actually separated but the separation is ignored; they are not technically inconsistent. Bateson (1979) analyzes inconsistency that arises when time is ignored, i.e., that unfolds in time, e.g., in oscillation. He illustrates with a ringing bell: a closed electrical circuit “implies” – has the later consequence of – being open, and vice versa. (When the buzzer is pressed, a circuit is closed, activating an electromagnet, which attracts a hammer, which hits a bell. Movement of the hammer breaks the circuit and turns off the electromagnet, a spring pulls the hammer to its original position, and the cycle repeats.) Such a contradiction is a dialectical interpretation of dynamics. Because it involves different values of time, it is not technically an inconsistency. This temporal example illustrates the important point that coexisting incompatible states that result from aggregating over a support variable will be said to manifest inconsistency only when these different states reflect or produce change in the system c or at least the possibility of change. A difference in states that has no consequences for the system is not referred to in this book as an inconsistency.

a

In continental philosophy, the fundamental notion of “difference” is sometimes joined to the notion of “univocity.” This joining of the dyad to the monad is a philosophical analog of the aggregation described above. b Note #1 System, p. 295 c Note #123 Disequilibrium and change, p. 507, gives examples of differences that produce change in concrete systems.

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Inconsistency could also be seen in difference between what is actual and what is potential if this difference has consequences for the system. Actual and potential can coexist because they are separated, although not in space or time. To borrow an idea from Bennett (1956), the separation is in “eternity,” defined as a “storehouse of possibilities” only some of which become actual. An inconsistency between actual and potential might characterize alternative modes of organization of a system a which can clash if what is potential is modeled but remains only potential in the actual organization of the system. b In concrete systems, meta-stability – and more generally, disequilibrium – might be regarded as examples of inconsistency of actual and potential. Again, this inconsistency is not a technical violation of two-value logic. The difference between actual and potential might, for example, be the difference between actual and ideal. In the elementsattributes-relations definition of system, when attributes belong to both elements and relations, there can be a mismatch between the actual attributes of elements and ideal attributes presumed by relations (Angyal 1939). This is displayed in Figure 47. One can speak of this mismatch as an inconsistency if it affects or could affect the system. Figure 47 Inconsistency involving attributes and relations In AB′, the actual and ideal attributes agree for A but disagree for B′. Characterizing an attribute with a direction is here just an arbitrary way to indicate such inconsistency.

AB′ B

A e a

B′

C′ e′

Internal Opposition 1.2.5 and 7.2.5, pp. 31, 554 This is possible if the system or its parts have modeling subsystems; see Note #99 The modeling subsystem, p. 463

b

314

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(ii) One could say that inconsistency is present in any opposition of needs, tendencies, forces, principles, values, etc., in the system. a The next section introduces the dyad of variety and constraint, and other ubiquitous polarities are introduced later, such as closedness and openness, and autonomy and interdependence. What is inconsistent is not opposition per se but rather the coexistence of and tension between opposites. The “interpenetration (unity and struggle) of opposites” is a central feature of Hegelian and Marxist dialectics, b and of Taoist yin-yang and quantum complementarities. Ontologically, the coexistence of opposites is a universal attribute of being; epistemologically, a universal mode of thought. (iii) Even logical contradiction might be an acceptable form of inconsistency, if one abandons or augments 2-valued logic. Varela (1979), utilizing the work of Spencer-Brown (1972), explores a three-valued logic in which Q = not-Q is assigned a truth value of ½ (midway between 0 for false and 1 for true), an included (not excluded) middle, and proposes that some phenomena of dynamics, self-organization, and self-reference might be discussed with this formalism. Zadeh’s (1965) fuzzy set theory c is an example of a non-standard logic. Assigning non-0 truth values to both Q and not-Q resembles the possibility, in classical Indian philosophy (Catuskoti) also used in Buddhist philosophical logic (Wing-tsit 1969) and a similar Greek idea (Tetralemma) of asserting both Q and not-Q (Figure 48a). This might also be considered as dialectical logic if not-Q is considered implicit in Q or if a dialectical synthesis unites

a

Summary 1.1.9 and 7.1.9, pp. 23, 491; Note #115 Binary oppositions, p. 492 b Zwick (1978a) formalizes some aspects of Hegelian dialectics with catastrophe theory. See Notes #126 Contradiction and its consequences, p. 512, #131 Cusp catastrophe, p. 520, and #152 Cusp of negation, p. 555 c Note #25 Fuzziness, p. 352. Related formal systems are explored by Klir and Wierman (1999).

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thesis and antithesis. a One gains even greater freedom from the tension of opposites by asserting neither Q nor not-Q. The Buddha holds up a rose, exemplifying Wittgenstein’s (1921) admonition, “Whereof one cannot speak, thereof one should be silent.” The fourth possibility is an open horizon. It avoids both horns of the dilemma and achieves escape velocity. Figure 48 Four level logic (a) Level 4: Neither Q nor not-Q Level 3: Both Q and not-Q Level 2: Not-Q Level 1: Q

(b) Level 4: Neither Q nor P Level 3: Both Q and P Level 2: P Level 1: Q

In Figure 48(a), standard classical logic allows only levels 1 and 2. Level 2 is above level 1 in the sense that negation presumes a prior affirmation, at least implicitly. This is as far as one can go. The Law of the Excluded Middle forbids levels 3 and 4, which are logically equivalent. Levels 3 and 4 require non-standard, for example, fuzzy logic. Level 3 suggests that Q and not-Q are not mutually exclusive; level 4 suggests that Q and not-Q do not exhaust all possibilities. These suggestions can be made more consistent with standard logic if, as in Figure 48(b), b not-Q is replaced by P, whose relation with Q is contrariety (e.g., white vs black). P is not not-Q, whose relation with Q is contradiction (e.g., not-black vs black). In (b), Level 3 is still disallowed by c standard logic, but Level 4 is allowed.

a

This is one version of the dialectical triad of thesis, antithesis, and synthesis, wherein a synthesis combines both poles and becomes a new thesis. This triad, attributed to Hegel, was actually first formulated by Fichte. Yovel (1998) writes, “Hegel’s dialectics are far more flexible than Fichte’s and do not [always] conform to … rigid trinities.” b The tetrad of Q, not-Q, P, and not-P define the “semiotic square” of Greimas (Chandler 2002). c Level 3(b) is disallowed if Q and P contraries have crisp values, but if they are fuzzy, both-Q-and-P is quite possible.

316

NOTES

One might express the hierarchy of Figure 48(b) in terms of the system-environment distinction. Level 1: there is a system (Q). Level 2: it has an environment (P). Level 3: system and environment interact (Both Q and P, which is now allowed by virtue of the spatial aggregation that is implicit but ignored). The environment is the relevant environment, but it too has an environment, and the system also has an internal environment, a so Level 4 (neither Q nor P) asserts that system and (relevant) environment do not exhaust what is. This is suggested by the double cone system-environment figure, b open-ended both above and below. Just as different meanings of “organizing principle” apply to different categories of Synchronics, “inconsistency” can mean disharmonies between structure and function (1.1.2 Constraint, 1.1.3 Distinction), closedness and openness (1.1.4 Persistence), aspects of essence (1.1.5 Identity), multiple objectives (1.1.6 Agency), hierarchical levels (1.1.7 Complexity), or multiple subselves in the modeling subsystem (1.1.8 Cognition). Inconsistencies need not be dyadic; dyadic ones are just more ubiquitous. Inconsistency in a dyad may be resolved by a triad; tensions of the triad may be resolved by a tetrad, and so on; complexity grows. c Alternatively, the dyad might collapse and revert to the monad. Every system is flawed. Every organizing principle is finite in scope. Within a restricted 7 domain, a network of relations can achieve coherent order, but consistency and 8 completeness cannot both be attained.

a

Note #22 Environment, p. 347 Figure 3 System as center, p. 49 c Note #30 One, two, three, ten thousand, p. 359; 5.3 Categories of complexity, p. 160 b

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7. Networks a A “network” is usually a graph, although the word should allow hypergraphs, where relations can link three or more elements. In this note, only dyadic relations are considered. If elements (in graph terminology, nodes) A, B, C, etc., are numbered as 1, 2, 3,…n, the network is defined by a matrix, M, where M(i,j) = 1 means there is an i→j link, and M(i,j) = 0 means there is no link. For a neutral system, M(i,j) = M(j,i), but this is not true for a directed system, where M is asymmetric, and the graph is called a digraph (“di” for directed). M contains information about (a) individual nodes, of (b) pairs of nodes or subsets of nodes (subsystems), and the (c) graph (system) as a whole (Knoke and Kuklinski 1982): (a) Individual nodes. In-degree of a node is the number of other nodes with directed links to it; out-degree is the number of other nodes to which it has directed links. An important node attribute is centrality. One interpretation of von Bertalanffy’s (1968) notion of a “leading part” of a network is a node of high centrality. Centrality can be defined in different ways: as the fraction of other nodes directly linked to it; or the extent to which a node lies on the geodesics between pairs of other nodes; or the shortness of the average geodesic path length between it and other nodes; or the number of other nodes of high centrality that link to it. Attributes such as degree or centrality are not intrinsic to nodes but derive from all the system relations, i.e., from M. In fact, in the basic idea of a graph, nodes have no intrinsic attributes at all; all their attributes are extrinsic. b If a node is a system, it has only function and no structure.

a

To reiterate a point made earlier, graphs and networks are treated as synonyms in this book. b Notes #1 System, p. 302, and #35 Function, p. 370. To further illustrate the distinction between intrinsic and extrinsic attributes, consider the games of chess and go. Pieces in a chess game, like a knight or bishop, have intrinsic attributes and also extrinsic attributes based on location, but pieces in the game of go have only extrinsic attributes.

318

NOTES

(b) Pairs or subsets of nodes: One node may or may not be reachable from another; if reachable, a minimum path distance can be defined. Nodes are structurally equivalent if linked to the same other nodes; non-equivalence can be quantified. A clique is a fully connected set of nodes. (c) Graph as a whole: Matrix M also defines attributes of the entire system. Density is the fraction of possible links that are actual. Centrality of the graph is derived from the centrality of all its nodes. (A star is the most central graph.) Cohesion is the degree of reciprocity in binary relations. Such attributes are emergent attributes of the system as a whole. a In this book, “node” and “element,” used synonymously, mean (i) entity, (ii) variable, (iii) state of an entity, or (iv) state of a variable. “Link” and “relation” are also often used synonymously and can mean a relation between variables or entities or a process connecting states of variables or entities. With nodes as variables, digraphs can represent causation (Davis 1985). b Causation can be expressed by direct links between elements or states of elements, as illustrated below. c The links specified by M are direct connections, and they define a diagram of immediate effects (Ashby 1956). There may also be indirect paths between nodes and thus a more connected diagram of ultimate effects, defined by a reachability matrix, derived from M, that indicates whether any node is ultimately reachable via a path from another node, and a path distance matrix that specifies the number of links for the shortest path. Figure 49 shows the simplest (a) graph (neutral) and (b) digraph (directed), i.e., two nodes and one link. If nodes are quantitative variables, links can be (c) positive or negative, giving a signed digraph, or can have (d) a positive or negative magnitude.

a

Figure 40 Adding attributes to elements and relations, p. 302 Figure 18 Lineal, mutual (feedback), branching causality, p. 104 c Figure 53 An iterative graph b

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A sign or magnitude specifies (i) how y varies with x, namely ∆y / ∆x, or (ii) how the rate of change of y varies with x, namely ∆(dy/dt) / ∆x, or (iii) some flow from x to y (an output of x and an input of y), a or (iv) some time interval between x and y. b where x and y in (iii) are entities and in (iv) are states or events. This does not exhaust the uses of graph theory; it just illustrates how general it is and thus basic for systems theory. c Figure 49 Varieties of dyadic links in graphs (a) graph (b) digraph (c) digraph with signs (d) with magnitudes.

x

x

(a) + (c)

y

x

y

x

(b) + 0.5

y

y

(d)

Matrix M has so far been used to specify the relations in a system, where nodes are elements; this reflects a closed system view of internal order. Alternatively, a graph could be interpreted as the external order in which the system is one particular node. This just reflects a change of scale. A third possibility is that a subset of nodes and/or links defines the system and the remaining nodes/links its environment. Such an open systems view d includes both structure and function. a

Note #157 Closing the circle, p. 564 Note #139 Temporalization of complexity, p. 532 c Figure 8 Transdisciplinarity of some systems theories, p. 67 d E.g., Figure 39 A minimal system S with environment E, p. 301 b

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NOTES

8. Incompleteness vs. inconsistency Gödel showed that formal mathematical systems that are sufficiently powerful are incomplete or inconsistent (Gödel 1962; Nagel and Newman 1960). “Incompleteness” here means that there are grammatically correct statements that cannot be proven within the system to be either true or false, and thus are undecidable; “inconsistency” here means that there are statements that can be proven to be true and proven to be false. As explained above, a “incompleteness” and “inconsistency” are not used in this book with these technical meanings. What is asserted in Essay is that there is a general opposition between completeness and consistency when these terms are broadly conceived. This applies not only to conceptual systems but also to concrete and abstracted systems. Gödel’s proof is being invoked only informally, not rigorously. It is the inspiration for the notions of generalized incompleteness and inconsistency here being advocated; its terminology is used because of its expressiveness and familiarity. (However Gödel’s proof is not actually paradigmatic for these generalized notions because the proof requires self-reference and infinities, and generalizations of incompleteness and inconconsistency may not have such requirements.) Gödel’s finding has rich potential implications despite the fact that it does not apply to all formal systems. (For example, the propositional calculus is both complete and consistent, but although its limited scope is a kind of incompleteness, it is not the kind at issue in Gödel’s proof.) While Gödelian undecidability is a result in mathematics, it could be relevant to the sciences. b For example, the Halting Problem in automata theory is related to Gödel’s result and imposes limits on algorithms instantiated in physical machines; a formulation of Gödel’s proof within automata theory has been given by a

Notes #4 Incompleteness, p. 306, and #6 Inconsistency, p. 311 This author has speculated that it might even bear on the quantum measurement problem (Zwick 1978).

b

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Mesarovic (1968). Undecidability has been shown by Smale to be relevant to nonlinear dynamic systems (Baas 1994). Langton (1992) has suggested that virtually all interesting questions about the behavior of dynamic systems may be undecidable. Undecidability results exist in game theory. Given their technical meanings, incompleteness and inconsistency are not legitimate alternatives in formal systems. Incompleteness must be chosen, since inconsistency is unacceptable, because if a statement and its negation can both be proven, all statements can be proven. a However, if other meanings are given to these two terms, such as those suggested below, inconsistency is not excluded a priori, and the complementarity of the two conditions is more symmetrical. And systems might be flawed by being both incomplete and inconsistent. Set- and information-theoretic definitions of relation b assume that elements are nominal variables. If elements are quantitative and continuous variables, relations might be equations involving these variables. In this case, incompleteness and inconsistency are manifested by the distinction between underdetermined and overdetermined equations. The number of equations is less than the number of unknowns in the first and greater than the number of unknowns in the second. An underdetermined system of equations is incomplete in that variables can have an infinity of possible values. Overdetermined equations are inconsistent in that there are no values for the variables that will satisfy all the equations. In this context, completeness and consistency can both be attained – when the number of equations exactly equals the number of unknowns and equations are not ill-conditioned. But being underdetermined or overdetermined is more common.

a

For example, in the situation discussed above where relations ABC and BCD are independent, inconsistencies between the BC of ABC and the BC of BCD can be removed by eliminating one of these two relations, but this results in incompleteness. b Note #9 Relation as constraint, p. 324

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NOTES

The tension between actual and potential a has been viewed as an inconsistency when an actual state differs from a potential state, where the system in principle could be in either; it could alternatively be viewed as reflecting incompleteness in the sense that potential is unrealized, as in an unfilled ecological niche. When inconsistency is the impossibility of optimizing multiple objectives, b one can trade inconsistency for incompleteness by omitting all but one objective, by giving others lower priority, or by converting all but one into constraints. For zero-sum games with more than two players (coalition theory), either no satisfactory solution exists or too many solutions exist. c Alternatively, incompleteness or inconsistency might be analogized to concrete systems being under- or over-saturated (Feibleman and Friend 1945). This is chemical imagery. Atoms with nearly empty orbital shells are oversaturated; atoms with nearly filled shells are undersaturated; chemical solutions also may be oversaturated or undersaturated. As in the example involving equations and unknowns, both incompleteness and inconsistency are avoided when electron shells are complete, but other atom types are more common. Feibleman and Friend suggest a related tension between “complexity” and “integrality”: inconsistency is the price of complexity (multiplicity); incompleteness is the price of integrality (unity). As indicated in this Note and implied in Essay, the dyad of incompleteness-inconsistency is asymmetric. This exemplifies the deconstructionist idea – and the idea of symmetry-breaking – that in every binary pair, one member is privileged or favored (Derrida 1972). In Jakobson’s terminology (Andersen 1989), this member is “unmarked,” while the less favored term is “marked.” (It is ironic that in the marked-unmarked pair, the prefix “un” marks the “unmarked” term!) The notion of a marked state is also used by Spencer-Brown (1972). a

Note #6 Inconsistency, p. 311 Note #67 Multiple objectives, p. 419 c Note #75 Game theory, p. 429 b

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In the incompleteness-inconsistency dyad, incompleteness is favored, since incompleteness is a flaw that is tolerable, but inconsistency is unacceptable. Correspondingly, in the completeness-consistency dyad, it is consistency that is favored. Strictly speaking, consistency is attainable within a limited domain, but completeness, in the sense of encompassing everything, even only everything relevant, is not attainable. In the many dyads discussed in this book, one pole of the dyad is typically marked while the other is unmarked. However, the marked pole is not hopelessly locked into an inferior status; in another context or formulation, a it is unmarked. In the dyad of elements and relations, elements are unmarked (favored) in that the system of elements and relations defines a new element at a higher level and in that relations presuppose elements but not the reverse. But relations subsume the elements they organize, b and from this perspective, relation is unmarked. The open systems view is unmarked in its inclusion of the environment, but the closed system view is unmarked in that it recursively generates the open systems view. In the Lattice of Structures, c the unitary structure at the top has the virtue of the maximal integration of parts, but the fully decomposed structure at the bottom has the virtue of the maximal independence of parts. In a holistic view, the whole is unmarked; in a reductionist view, the parts are unmarked. The mark can thus be found on either pole of any dyad. The poles are equal ontologically, but context breaks the symmetry. Coexistence of both poles is inconsistency, but removing the inconsistency by omitting either pole produces incompleteness. This is what a dyad means, and the dyadic character of reality – or our descriptions of it – is a universal insight, as illustrated by the yin/yang of Chinese philosophy, the structuralism of LeviStrauss, the Secondness of Peirce, the dialectics of Hegel, etc. a

Notes #13 Order, p. 332, and #16 Order and disorder are intertwined, p. 336 b Note #18 Unity and multiplicity, p. 340 c Note #5 Structure, p. 308

324

NOTES

7.1.2 Constraint Notes:

page

9 Relation as constraint 10 Dynamic relation 11 Echoing the primary tension 12 The potential and the actual 13 Order 14 Entropy 15 Scale 16 Order and disorder are intertwined 17 Chaos 18 Unity and multiplicity 19 Aggregates vs. systems 20 Reconciling constraint and variety

324 327 331 331 332 334 335 336 338 340 341 341

Wholeness is constraint upon variety. Variety, in the multiplicity of elements in the system, and constraint, in the relations that tie these elements together. Variety, in the multiplicity 9 of states of the elements, and constraint, in the relations that restrict the variation of these states, simultaneously or sequentially in 10 time.

9. Relation as constraint In the earlier graph-theoretic definition of “system” as a set of elements and relations between elements, “relation” was undefined. Here, “relation” is defined as constraint, where constraint between A and B means that elements do not vary independently. Note, however, that relation viewed structurally as constraint must be supplemented by relation viewed functionally as the source of emergent attributes. a In this note, the relation is assumed to be static and internal; later, this a

Note #32 Emergence, p. 363

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approach is extended to dynamic and external relations. a Constraint here is either set-theoretic or information-theoretic: Set-theoretic definition: A constraint exists if the number of actual states is fewer than the number of possible states (Wiener 1914). For example, let elements A and B each have two states, {a1, a2} and {b1, b2}. If A and B are independent (written as A:B), there are four possible joint states, so A:B = {(a1,b1), (a1,b2), (a2,b1), (a2,b2)}. Relation AB is non-trivial if the actual states, at different times or locations or different population members, are fewer than the possible states; for example, if AB = {(a1,b2), (a2,b1)}. b Information-theoretic definition: A (non-trivial) relation AB exists if joint probabilities differ from what they would be if A and B were mutually independent, i.e., if p(aj,bk) ≠ p(aj) p(bk). Both set- and information-theoretic definitions of relation as constraint use the core idea of uncertainty, understood either as objective variability (the ontological stance) or as limitations in knowledge (the epistemological stance). Uncertainty reflects to absence of constraining relations; to use terminology introduced below, c disorder, which is a type of incompleteness. A nonzero-strength constraint exists if u(AB), the uncertainty of the relation, is less than u(A:B) = u(A) + u(B), the sum of uncertainties of the elements if they were independent of one another. The difference, o(AB) = u(A:B) – u(AB), is the strength of the constraint in AB (Figure 50). This is expressed equivalently as the loss of constraint T(A:B) in the A:B heap, also known as mutual information between A and B.

a

Notes #10 Dynamic relation, p. 327, and #27 External relation, p. 354 Note that a graph can be viewed as a constraint if the actual dyadic links between all the nodes is less than the full set of possible dyadic links. c Note #13 Order, p. 332 b

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Figure 50 Uncertainties of relations and elements Areas of circles, u(A) and u(B), are uncertainties of A and B taken independently. The union of circles is u(AB), the joint uncertainty. The strength of constraint, o(AB), is the overlap of the circles, the reduction of uncertainty going from A:B to AB.

u(AB) u(A)

o(AB)

u(B)

In the set-theoretic approach, uncertainty is Hartley entropy (Hartley 1928); in the information-theoretic approach, it is Shannon entropy (Shannon and Weaver 1949). Set- and information-theoretic frameworks are parallel – the same Lattice of Structures a is used in both. These ideas extend to relations of three or more elements and to structures. This fusion of graph theory and (set or) information theory is called reconstructability analysis (Klir 1985, Krippendorff 1986). Both set- and information-theoretic definitions of relation apply to nominal variables, which are emphasized in this book because they are the most general kind of variable. For quantitative variables, the simplest constraint is a linear relation, where independence means that effects are additive. For example, x and y have independent effects on z in the linear equation z = a0 + a1 x + a2 y; an example of adding a nonlinear interaction effect is z = a0 + a1 x + a2 y + a12 x y.

a

Note #5 Structure, p. 308

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10. Dynamic relation The idea of a relation as a constraint is here extended from statics to dynamics: from state descriptions to process descriptions. (Elements are still assumed to be internal – the closed systems view – external influences on dynamics are introduced later.) In terms of Boulding’s (1956) hierarchy of system types, a this shifts from frameworks to clockworks. From one perspective, dynamic relations are at the same level as static relations, having time rather than space as a support variable, but from another perspective, dynamics adds complexity to statics. For nominal variables with discrete states, dynamics involves only discrete changes of state. In such relations, time must be discrete rather than continuous. This accords with Whitehead’s (Ford 1984) temporal atomism and Wolfram’s (2002) preference for nominal dynamics. Dynamic systems where both states and times are discrete are called “automata.” A dynamic relation is a directed relation where the direction is specified by the arrow of time. Directed relations are deterministic or stochastic. Determinism manifests necessity; stochasticity manifests also chance. If directed relation XY is deterministic, u(Y|X), the conditional uncertainty of Y knowing X, is 0. If XY is stochastic, u(Y|X) > 0; thus knowing X doesn’t fully specify Y. If knowing X tells us nothing about Y, u(Y) = u(Y|X), and the elements are a heap, X:Y. Here, Y is either a different element or X at a different time or point in space. One can distinguish between system-like and heap-like dynamics. Suppose there are two elements, X and Y, whose states at a later time are X' and Y'. The system elements are either dynamically coupled or uncoupled (heap-like), as shown in Figure 51.

a

5.2 Hierarchy of system types, p. 154

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NOTES

Figure 51 Coupled and uncoupled dynamic systems Arrow from X to itself means X' depends on X; arrow from Y to X means X' depends on Y. (a) coupled (b) uncoupled. (a) (b)

X

X

Y

Y

If one adds elements, the resulting structure might be ordered spatially and be a cellular automaton; for example, if elements are arrayed on a line, coupled only to immediate neighbors, this gives the elementary cellular automaton shown in Figure 52. Or the elements might not be spatially ordered and define a random network. a Randomly connected automata are the subject of automata theory, basic to the theory of computation. Figure 52 Elementary cellular automaton

…

X

Y

Z

…

In Figure 51 and Figure 52, graphs display the connectivity of variables; graphs can alternatively display the (sequential) connectivity of states. This is shown in Figure 53. The global state, s, of the system could, for example, be the state at any time of (X, Y, Z) in Figure 52. A sequence of global states, e.g., s1 s2 s3 s4 s3 s4…., is a trajectory. It consists of a transient, a sequence of states that does not repeat, here s1 s2, followed by a limit cycle, a sequence of states that repeats, here s3 s4. If one state repeats, it is an equilibrium b (fixed) point; e.g., s10.

a

Note #7 Networks, p. 328 Terminology: in the context of dynamics, “equilibrium” just means nonchanging; in the context of thermodynamics “equilibrium” has the different

b

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Figure 53 An iterative graph In this deterministic system, the graph has two basins of attraction, one with limit cycle s3s4s3…, the other with the equilibrium point s10. The attractors are shaded. s6 s1

s2

s3

s4

s11

s8

s5

s10 s7

s9

s12

Limit cycles and equilibrium points are the endpoints of all transients; they are called attractors because, in a final cause sense, they attract the dynamics. Each attractor together with the states that drain into it is called a basin of attraction, and in nonlinear dynamic systems, there are generally multiple basins. The graph displaying all possible trajectories is called an iterative (or kinematic) graph; it characterizes the dynamics. A trajectory in the iterative graph represents a flow of time. For a system moving, say, from s1 to s2, states not actualized still exist as potential. This is obvious for states on this trajectory that are not yet reached, e.g., s3,s4,s3,…, but other transients and attractors that are not on this particular trajectory, e.g., s8, s10 also inhere in the dynamic relation. The entire iterative graph, including all trajectories from all possible initial states, is real in an atemporal yet time-like sense; one might even call it “eternity.” a The actual in time samples the possible in eternity. The dynamic system in Figure 53 is a deterministic system that is discrete in both state and time, but one can also use such graphs for stochastic systems by adding branching paths with

meaning of macroscopic stasis. For example, a gas in a container might be at thermodynamic equilibrium, but its component molecules (at a microscopic level) would still be in motion and not at dynamic equilibrium. a Note #6 Inconsistency, p. 313

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NOTES

magnitudes a that specify probabilities of state transitions. All of the above discussions assume discrete time and discrete (more precisely, nominal) states. Dynamic relations could be discrete in time but continuous in state, as in an iterative map of the form s' = f(s). Finally, a differential equation of the form ds/dt = g(s) is continuous in both time and state. The simplest differential equations are linear; e.g., dx/dt = k1 x + k2 y + k3 dy/dt = k4 x + k5 y + k6 These have only one basin whose attractor is an equilibrium point. Nonlinear equations with interaction effects, e.g., the classic “prey-predator” (Lotka-Volterra) model, dx/dt = k1 x – k2 x y dy/dt = – k3 x + k4 x y have multiple basins, much like those of automata, as in Figure 53 above. Their attractors have not only fixed points and limit cycles, as in automata, but also quasi-periodic and chaotic b attractors. Iterative graphs can also exhibit chaos. A type of dynamic system of special interest is a gradient system. In gradient dynamics, the state variable, x, changes to minimize/maximize an energy-like V: dx/dt = k dV/dx. (dV/dx is the gradient of V.) Change in x maximizes V for positive k and minimizes V for negative k. If one gives these mathematical terms thermodynamic interpretations, dV/dx represents a “force” and dx/dt represents a “flux.” c Gradient systems have only fixed point attractors. Catastrophe theory models, used often in this book, assume gradient dynamics. a

Figure 49 Varieties of dyadic links in graphs, p. 319 Note #17 Chaos, p. 338. Chaos in continuous systems requires at least three dimensions (three differential equations). c Notes #42 Dissipative systems, p. 381 and #123 Disequilibrium and change, p. 507 b

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A system is a union of variety and constraint, but variety and constraint are opposites, and the tension between them echoes the primary tension between completeness and 11 consistency. Constraint makes the actual less than the possible. Constraint is limitation. Possibilities are excluded in every actualization. This exclusion may not be permanent or unconditioned. What exists is more than the actual. What is potential also 12 exists and can influence the actual.

11. Echoing the primary tension In relations, incompleteness could be interpreted simply as insufficient constraint, or conversely as too much constraint so the set of actual states is much smaller than the set of possible states. Inconsistency is most easily interpreted as constraint that differs over space, time, or in a population. In structures, incompleteness can be interpreted as absence of constraint typical of simple structures, a and inconsistency might be the presence of conflicting constraints in structures formed by the composition of independent relations. b

12. The potential and the actual Constraints can change due to changes in the environment, c causing occurrence of new system states. Even if the environment does not change, attractors are potential states that influence – indeed, attract – the actual state. This is not a mysterious property of the attractor. A dynamic relation that changes the state of the system at successive times is an efficient cause, but by generating a sequence of states that approach the attractor, it in effect generates a final cause. The attractor is a

a

Figure 46 Lattice of (general) structures for 4 elements, p. 310 Note #6 Inconsistency,p. 311; see example (i). c Note #27 External relation, p. 354 b

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global emergent of all the local efficient causes. Final cause terminology merely reflects a different perspective. In physics, the potential often has consequences for the actual: for example, in the creation/annihilation of virtual particles, etc. In complex adaptive systems which have modeling subsystems (1.1.8 Cognition), the representation of the potential becomes actual in the subsystem’s models, which augments the system’s adaptive capacities. The resulting interplay between potential and actual might be modeled by catastrophe theory. For example, in the cusp catastrophe, a there can exist a potential state that is favored over (in the language of physics, having lower energy; in the language of economics, having higher utility) the current state of the system, but this preferred state is inaccessible because of an (energy or utility) barrier separating it from the current state. This alternative potential state exists and might influence the dynamics. The potential is a subset of the possible; the possible means all states that do not violate the laws of nature or logic. Potential states are those reachable from actual states through the unfolding of relations or their modification by environment changes or by fluctuations. Kauffman’s (2000) “adjacent possible” is roughly what is meant here by potential. 13

Constraint is order. Variety is disorder. Order is necessity, certainty, homogeneity, invariance; disorder is chance, uncertainty, 14 heterogeneity, plasticity.

13. Order The order produced by a constraint has two aspects: (1) its strength, i.e., the quantitative aspect of order; (2) its structure, i.e., the topological aspect of order

a

Notes #131 Cusp catastrophe, p. 520, and #152 Cusp of negation, p. 555

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(1) Quantitatively, information theory defines order as the reduction of uncertainty (Shannon entropy) . The strength of a constraint is the difference between the uncertainty of the system if its elements were independent and its uncertainty when elements are constrained by the relations. Independence is the reference condition. a For a system of a single relation, AB, b order, o(AB) = u(A:B) – u(AB) = (u(A) + u(B)) – u(AB). Maximum order means minimum uncertainty in the relation; minimum order means maximal uncertainty. o(AB), called mutual information, is more general than correlation, which measures linear relations between quantitative variables, because it applies to nominal variables. o(AB) is an attribute of relation AB. Relations having attributes were not mentioned in the definition of a system, but relations and elements are Janusfaced, so both can have attributes. (2) Topologically, order is structure, the presence of relations of varying ordinality. A relation or structure has maximum order if it is not decomposable without loss of constraint. The top of the Lattice of Structures c is thus maximally ordered, while its bottom is maximally disordered. Also, a coupled dynamic system is more ordered than a decoupled system. d Disorder, the absence of order in either of these two aspects is an incompleteness, in the generalized sense of this term used in this book. Inconsistency e is a different type of disorder.

a

In communication, this reference condition can be interpreted temporally. Order, i.e., information in the communication, is the difference in uncertainty, i = u(initial) – u(final), where initial and final mean before and after communication. If there is no final uncertainty, the information received is the amount of initial uncertainty. (This explains why Shannon’s mathematical expression is used both for information and for uncertainty, which may be confusing since information and uncertainty are opposites.) b Figure 50 Uncertainties of relations and elements, p. 326 c Figure 46 Lattice of (general) structures for 4 elements, p. 310 d Figure 51 Coupled and uncoupled dynamic systems, p. 328 e Note #6 Inconsistency, p. 311

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This dual aspect of order applies to both static and dynamic systems. Order is strong constraint and/or high ordinality relations; disorder is weak constraint and/or low ordinality relations. These two aspects of order do not necessarily go together; for example, a non-decomposable high ordinality relation might have weak constraint. For directed systems, necessity is order; chance is disorder. Deterministic systems, where the uncertainty of the next state given the present state is zero, are more ordered than stochastic systems, where this conditional uncertainty is greater than zero. One can also differentiate between different types of attractors in terms of order and disorder. Limit cycle behavior, where dynamics quickly reaches an attractor, is ordered; chaotic behavior, a which does not reach an attractor quickly, is disordered. Langton (1992) has analogized limit cycle attractors to solids (ordered) and chaotic attractors to fluids (disordered). Or, order vs. disorder might refer to attractor vs. transient. In the order and disorder dyad, order is unmarked (favored), b yet between variety and constraint, variety is unmarked, although order and disorder correlate with constraint and variety, respectively. The difference between variety and disorder is contextual, not inherent.

14. Entropy Entropy is a measure of disorder that is very closely related to uncertainty. Uncertainty c (Shannon entropy) is a mathematical notion that applies to any type of system: concrete, abstracted, or conceptual. d It has no physical units. Physical entropy, by contrast, applies only to concrete systems in space-time whose matter-energy aspects are analyzed by thermodynamics or statistical mechanics. For example, entropy, S, in statistical a

Note #17 Chaos, p. 338 Note #8 Incompleteness vs. inconsistency, p. 320 c Note #9 Relation as constraint, p. 324 d 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 b

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mechanics is given by S = k u, uncertainty times Boltzmann’s constant, k, where k gives the dimensionless uncertainty the physical units of energy per degree of temperature. Uncertainty is a generalization of physical entropy to any type of system. The relationship between statistical-mechanical entropy and information-theoretic uncertainty is the subject of an extensive literature about measurement, information, and the Maxwell Demon problem. This relationship is a perilous trap for the unwary. Because Shannon called uncertainty “entropy,” many people have been led to wrongly assume that thermodynamics applies to systems described by Shannon entropy. Schrödinger (1945) spoke of order in physical systems as negative entropy (negentropy). Really, order = S(reference) – S(actual), but since the reference could be 0°K, where entropy is zero, this yields order, o = – S(actual), i.e., order is negentropy. The reference could alternatively be the state of the system if it were at equilibrium with its environment. Generalizing beyond concrete systems, o = u(reference) – u(actual). In the previous Note, o(AB) = u(A:B) – u(AB); there the reference is A:B (independence) and the actual is AB (constraint). Disorder may arise from order on smaller or larger scales; order may alternatively arise 15 from disorder.

15. Scale Though many systems are vertically nearly decomposable (Simon 1981), i.e., are often largely insulated from events on adjacent smaller and larger scales, events on other scales can significantly impact some systems. Order on one scale may result from or even require disorder on a different scale, and vice versa. For example, heterogeneity (disorder) at a microlevel when aggregated yields homogeneity (order) at a macrolevel; conversely, micro-homogeneity when aggregated can

336

NOTES

yield macro-heterogeneity. a In Markov processes, a microsystem that is stochastic (disorder) may underlie a macro-system that is deterministic (order). Becoming subject to new attractors (order) in dynamic systems may result from random perturbations (disorder). b Variation by genetic mutation (disorder) gives rise via natural selection to adapted genotypes (order), but the mutation itself may be caused by a deterministic process. In general, order and disorder depend on scale in complex ways. The existence of multiple scales is further discussed elsewhere. c Order and disorder are intertwined and linked by more than opposition or complementarity. Disorder may be order that is complex or 16 compressed or sensitively dependent on 17 present context or past state.

16. Order and disorder are intertwined Two dangers never cease threatening the world: order and disorder. - Paul Valery (1919) Order and disorder depend on context or scale or point of view. A uniform probability distribution is usually considered to be maximum disorder, but its uniformity is a kind of order. Beer (1961) thus sees order in what thermodynamics calls disorder. A broad Gaussian (bell-shaped) distribution has high uncertainty, but its Fourier-transformed distribution in frequency space is sharp and has low uncertainty. The spread of the distributions in the direct and frequency spaces vary inversely with one another, so order in one space corresponds to disorder in the other. a

Note #92 Homogeneity, heterogeneity, and scale, p. 452 Notes #42 Dissipative systems, p. 381, #124 Order through fluctuations, p. 509 c Hierarchies 1.1.7.2 and 7.1.7.2, pp. 19, 451; 3.4 Aspects of complexity and holism, p. 100; Note #26 Fractals, p. 353; Note #130 Trajectories of development, p. 517 b

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A fully connected graph has maximal constraint in the sense of maximal linkage but minimal constraint in that the set of actual links equals the set of possible links; a fully disconnected graph has minimal or maximal constraint from the same two points of view. Every set-theoretic constraint that allows more than one state but less than all states embodies both disorder and order. Every structure less coherent than the unitary relation (the top of the Lattice of Structures a) but more integrated than the fully decomposed relation (the bottom of the Lattice) does likewise. Order and disorder are complementary. Except at the extremes, you can’t have one without the other. In discrete dynamic systems, transients are short for limit cycle behavior (order). For chaotic behavior (disorder), they are long if defined by micro-states; but short if defined by statistical macro-states (Langton 1992). So disorder can be different from or similar to order depending on scale. Order-disorder correlates with constraint-variety, though order is unmarked (favored) in the first dyad and variety is unmarked in the second. In unity-diversity, unity used to be unmarked, but more recently diversity has been favored. b In unity-multiplicity, unity retains its claim, because multiplicity suggests redundancy. The popularity of chaos led Kauffman (1991) to call order “anti-chaos,” revealing that order is no longer the default. The complementarity of order and disorder is a very old idea. To quote Merton (1969), expressing the thought of Chuang Tzu: Consequently: he who wants Order without disorder, Does not understand the principles Of heaven and earth. He does not know how Things hang together. a b

Note #5 Structure, p. 308 But see Note #92 Homogeneity, heterogeneity, and scale, p. 452.

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Can a man cling only to heaven And know nothing of earth? They are correlative: to know one Is to know the other. To refuse one Is to refuse both. Or, to quote A.R. Orage, summarizing Nietzsche (Hesse 1970) Life ... is the spectacle of the eternal play and conflict of two mutually opposing principles: Dionysus ever escaping the forms that Apollo is ever creating for him. And it is just this unceasing conflict that is the essence of life itself; life is conflict. ..The drama of life is thus a perpetual movement towards a climax that never comes. From another point of view, order and disorder are not even opposites. Bohm suggested (1980) that disorder is extremely complex order. This could be interpreted as chaos or as algorithmic information, which when maximally compressed is random. a

17. Chaos Chaos is deterministic nonlinear dynamics that depends sensitively on the initial state. Ontologically, small causes that change the state can eventually have big effects. Epistemologically, the future is unpredictable in the long term because of finite precision in specifying the initial state. Chaos severs the connection between determinism and predictability just as Gödelian undecidability b severs the connection between truth and provability. In chaos, an orderly dynamical law can produce disorderly, i.e., random-looking, behavior. The dynamic law can be simple, so simple laws can give rise to complex – here chaotic – dynamics. The apparent randomness of the chaotic behavior is not caused a b

Notes #86 Complexity, p. 441, and #48 Algorithmic information, p. 395 Note #8 Incompleteness vs. inconsistency, p. 320

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by fluctuations in the external environment or in the parameters of an internal environment. a Its source is in the dynamic relation that governs changes of state. Transitions between nonchaotic and chaotic behavior do, however, depend sensitively upon changes in the environment (either outer or inner). Linear dynamic systems have only fixed point attractors and one basin of attraction. Nonlinear dynamic systems also have limit cycle (for continuous systems, also quasi-periodic) behavior and have multiple basins of attraction. b For continuous systems, chaos adds the possibility of strange attractors that generate bounded but non-periodic dynamics, having complex, often fractal, c basins. Since most dynamic relations are nonlinear, and most nonlinear relations are chaotic (for some parameter values), the possibility of chaos is the rule, not the exception. Although chaos usually pertains to systems continuous in time and state, where three dimensions are needed for chaos, it can occur also in discrete-time continuous-state systems (iterative maps), where one dimension suffices, as in the discrete logistic equation, x(t+1) = a x(t) ( 1 – x(t) ), which is chaotic for appropriate values of parameter, a (May 1976). Something resembling chaos even occurs in discrete-time discrete-state systems (automata). Such systems can have many basins each containing few states, so transients are short and attractors are reached rapidly. Or, a few basins may contain many states (Walker and Ashby 1966), so transients are long (and get longer as the number of variables and their varieties increase); such systems could be called chaotic. Wolfram (1986) classifies discrete dynamic systems as limit cycle, chaotic, or “complex,” an intermediate condition known as the edge of chaos (Langton 1992). “Complexity” can refer to chaos, edge of chaos, or have other meanings. d a

Note #22 Environment, p. 347 Note #10 Dynamic relation, p. 327 c Note #26 Fractals, p. 353 d Note #86 Complexity, p. 441 b

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In chaotic systems, disorder and order are implicated in one another, just as in the Chinese symbol a small circle of yin is embedded in yang and vice versa. Since determinism is ultrasensitive to environmental parameters, order is insecure. In chaos, disorder is unmarked, a although it is tamed by being subsumed in order (Hayles 1990). Chaos in nonlinear dynamic systems is common, so disorder contaminates and vivifies order. Constraint is the basis of unity. When the organizing principle is not single or when constraint is not maximal, multiplicity coexists with unity. Indeed, unity presupposes 18 multiplicity. All systems encompass both, and each afflicts and augments the other. In particular circumstances, either may predominate but not fully or permanently. When constraint is minimal, multiplicity is 19 extreme, and the system is a mere aggregate.

18. Unity and multiplicity The system is a unitary element b having multiple states. This element is equivalent to the unitary relation that subsumes the multiple relations of the system. These relations unify the multiplicity of elements in the system. In the unity-multiplicity dyad, unity is usually unmarked (favored), as in the quote, To be is no other than to be one. In as far, therefore, as anything attains unity, in so far it “is.” For unity worketh congruity and harmony, whereby things composite are, in so far as they are: for things uncompounded are in themselves, because they are one; but things compounded, imitate unity by the harmony of their parts, and, so far as then attain to unity, they are. Wherefore order and rule secure being, disorder tends to not-being. - Augustine, Confessions a b

Note #8 Incompleteness vs. inconsistency, p. 320 Note #1 System, p. 299

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But the Zeitgeist has shifted to favor multiplicity. Now unity is suppressed. But neither maximal unity nor maximal multiplicity is fully satisfactory. Preference for unity privileges consistency; preference for multiplicity privileges completeness. For relations, the extreme of unity precludes variety; the extreme of multiplicity precludes constraint. For structures, the extreme of unity (the top structure, the unitary relation) makes change difficult; the extreme of multiplicity (the bottom structure, the heap) forgoes synergy.

19. Aggregates vs. systems Aggregation is total decomposition, a “heap,” i.e., the independence model, A:B:C:.... Multiplicity as an organizing principle harbors contradiction if the level-meta-level distinction is ignored. Multiplicity can embrace all possibilities except its own negation. To achieve full diversity a system organized around multiplicity would have to encompass also the alternative principle of unity. But this is the very negation of multiplicity. Multiplicity as the organizing principle of a system must deny multiplicity at the meta-level. Unity may be reconciled with multiplicity by constraint of medium strength, or by partition 20 or timing, but intermediate conditions are often unstable. Even were these opposites reconciled, the solution would have its own opposite.

20. Reconciling constraint and variety Constraint (unity) can be reconciled with variety (multiplicity) in trade-offs between novelty (information) and comprehensibility (meaning) in several ways (Zwick 1986). If each symbol in a message is unpredictable (completely uncertain) from previously received symbols, the string of symbols is random, and every new symbol brings fresh information. Information is reduction of uncertainty, so if initial uncertainty is high, its total reduction by the arrival of the signal

342

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is very informative. Yet, though minimal constraint allows maximum information, constraint (redundancy in the symbol sequence) is essential not only for error correction, but for order, and thus meaning, so maximal information carries minimal meaning (Shannon and Weaver 1949). This complementarity is explored in detail as it pertains to the arts by Moles (1966). Three modes of reconciliation of constraint and variety (order and disorder) are: (1) by compromise, i.e., an intermediate position, a golden mean, between maximal and minimal constraint, a plateau of viability between the extremes, as shown in Figure 54, which may instead by a narrow ridge, as suggested by the idea of the “edge of chaos”; a Figure 54 Plateau of viability

viable region

extreme order

extreme disorder

(2) by partition, in which order and disorder apply simultaneously to different parts or aspects of a system, on the same b or on different c levels; (3) by sequence, in which the two opposites dominate in some temporal succession, perhaps alternating in a cycle. d

a

Note #17 Chaos, p. 338 Note #44 Law of Requisite Variety, p. 384 c Note #92 Homogeneity, heterogeneity, and scale, p. 452 d See, for example, Bateson’s analysis of a ringing bell in Note #6 Inconsistency, p. 311. b

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Compromise, i.e., mode (1), may be either unstable or stable, illustrated for example by the cusp and butterfly catastrophes, a respectively. Partition, i.e., mode (2), implies that the system is extended in space, time, or population; this allows extremes to be separated and thus reconciled. Solutions that are hybrids of opposing extremes – or of organizing principles unrelated to one another – can be viewed as either compromises or partitions; the butterfly catastrophe can model the instability of such hybrids.

a

Notes #131 Cusp catastrophe, p. 520, #166 Butterfly catastrophe, p. 570

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7.1.3 Distinction Notes:

page

21 Distinction 22 Environment 23 Disequilibrium and existence 24 Boundary 25 Fuzziness 26 Fractals 27 External relation 28 Extension 29 Nothing, many, one, all 30 One, two, three, ten thousand 31 Assertion vs. integration 32 Emergence 33 Engaging/disengaging 34 Active vs. passive 35 Function

344 347 349 350 352 353 354 357 358 359 363 363 368 368 370 21

Wholeness implies distinction from context. 22 Every system has an environment with which 23 24 A boundary it exists in disequilibrium. both separates the two and joins them together. Every system bears the imprint of a 25 demarcation, sharp or blurred, simple or 26 complex, enduring or ephemeral.

21. Distinction A system is a “limited whole” (Murdoch 1992). Being a whole implies order and being limited implies the system-environment distinction. Order (its incompleteness) implies distinction. What is not included in the system’s internal order is its external environment. One reason for discussing order first (in 7.1.2 Constraint) and distinction second (in this section) is that system as order is a

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monad of identity, while system as distinct from environment is a dyad of difference. In the closed systems view, the constitutive role of the environment and of the S-E difference is ignored, but in the open systems view, a system is a nexus of structure and function, and function is constitutive to a greater or lesser degree. The two views complement one another. The open systems view is needed for those concrete and abstracted systems where the environment contributes significantly to what the system is. The closed systems view may be preferable for conceptual systems, since it allows one to speak of things that do not interact with any environment. The discussion here is about the distinction between system and environment and not about distinction in general, which is actually prior to order. Order as constraint on variety, discussed in the previous section, already presupposes distinction, since elements subject to constraint must be distinguished one from another, their different states must be distinguished, and actual states must be distinguished from merely possible states. So Notes could have taken up distinction before order (one could speak of the S-E distinction without reference to internal order). But Essay and Notes take up order first and distinction second, because distinction is naturally introduced in terms of the S-E distinction, which in living systems depends upon the internal order. a But this is a matter only of expository convenience, not an assertion of logical priority. Distinction is the starting point in The Laws of Form of George Spencer-Brown (1972). Brown speaks of the distinction as “immaculate” and “impenetrable.” “Distinction is perfect continence.” Distinction, for Spencer-Brown, is fundamental. The theme of this book is that a universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can a

Note #47 Autopoiesis, p. 393

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begin to reconstruct with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance...Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. A circumference of a circle in a plane is the most familiar way of representing the system-environment distinction, as shown in Figure 55(a). This might be compared with the double cone diagram introduced earlier and repeated in Figure 55(b). These depictions highlight different things. In (a), naturally (but not necessarily) interpreted as a spatial representation, a the boundary is emphasized and the finiteness of the system is salient while the environment is unbounded. In (b), the depiction is more abstract; the system is conceptualized not as a region of space but as that which binds b together the internal order (structure) and participation (function) in the external order of the environment, where both structure and function are openended (suggesting recursiveness) and not clearly delimited. Figure 55 Two depictions of system and environment In (b), function is participation in the order of the environment.

function (a)

system

environment

(b)

system structure

a

Note #28 Extension, p. 357 When “system” is interpreted in this way as an interface, the domain of structure might be viewed as an “internal environment,” a concept discussed in Note #22 Environment, p. 347. b

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Spencer-Brown clearly intends this mathematics to be relevant to systems viewed either objectively or subjectively, ontologically or epistemologically. His formalism is a novel approach to several areas of mathematics. It has stimulated systems theoretical/philosophical explorations and has been applied to logic and circuit design, to expert systems, and other areas. A system could conceivably be distinguished from its environment by its greater internal disorder rather than order; in this case only distinction defines the system, although this is still distinction based on order. Distinction, however, could be based on anything. Although distinction is logically prior to order, Essay still begins with order, for reasons given above, although a presentation of systems theory could alternatively begin with distinction. “Distinction” in systems theory is close in meaning and significance to “difference” in contemporary continental philosophy. “Difference” might be the preferable term, since it has a more objective connotation, one more in keeping with the ontological – as opposed to the epistemological – stance favored in this book. But “distinction” is more prominent than “difference” in the systems literature. Distinction reduces symmetry. An undifferentiated field (a monad) has high symmetry which is reduced to lower symmetry when the dyadic S-E distinction is made. Symmetry is not only reduced; it is also broken: S and E have different status, as commented on in the next note.

22. Environment In the dyad of system and environment, system is unmarked (privileged) and environment is marked. In Synchronics, the system is a given. The environment is defined in terms of it and is of interest only in its interaction with the system; a a

But see Note #55 Environmental types, p. 404

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epistemologically, it thus has subordinate status. Also, for systems that exhibit agency, system and environment are typically active and passive, respectively, which align with being unmarked and marked. However, the environment is larger and more powerful than the system. Also, from a Diachronics perspective, the environment is prior to the system, and persists after its dissolution, a so ontologically it is really the environment that is unmarked. Environment, like system, can be defined in terms of elements, attributes, and relations, b but its specification is usually less articulated. Mathematically, the system-environment distinction is often interpreted as partitioning elements into (a) system state variables and (b) environmental inputs or parameters, assumed to be constant or only slowly changing. Alternatively, some parameters might be viewed as internal. For example, in a system of objects linked by springs, the spring constants are parameters (spatially) inside the system. In such cases, and in general when system and environment exist in a dimensional domain, c one can invoke the idea of an “internal environment” (Simon 1981) that parameterizes the internal relations. In the closed systems view a system either has no environment – as in the thermodynamic notion of an isolated system (an idealization since no concrete system is fully isolated) – or the environment is not constitutive. In the simplest case of the open systems view, the interaction of system and environment is unidirectional (Churchman 1968): The environment affects the system but is not affected by it. d However, for most open systems, interaction is bidirectional. The boundary between system and environment may be viewed as either objective or subjective, but in either case, the world is not a seamless web. It is nearly decomposable (Simon 1962). a

Note #178 Dissolution, p. 587 Note #1 System, p. 295 c Note #28 Extension, p. 357 d Notes #27 External relation, p. 354, and #34 Active vs. passive, p. 368 b

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Everything does not interact with everything else, or at least not strongly. If the world were truly a seamless web, nothing would be comprehensible. In this section the environment is mostly taken to be the complement of system, i.e., everything else. For other categories of Synchronics, however, “environment” (like “organizing principle” or “incompleteness”) takes on multiple meanings. Under the aspect of Constraint, the environment has relations with the system, so it is only that part of everything else that is relevant to the system. Of course, this relevant environment itself has an environment, so relevance is openended. Under the aspect of Persistence, the environment is a source of disturbances. Under the aspect of Identity, it is a source of raw material. Under the aspect of Agency, it is a field of action and a world of other systems. And so on.

23. Disequilibrium and existence This statement in Essay – that the system is in disequilibrium with its environment – is specific to concrete systems, a for which distinction – the existence of an ordered system – requires thermodynamic disequilibrium (which is different from dynamic disequilibrium b). The fact that for concrete systems existence implies disequilibrium is one reason why thermodynamics is fundamental to systems theory. c Another reason is that order and disorder, for concrete systems, are also thermodynamic ideas. d Disequilibrium underlies diachronics e as well as synchronics.

a

3.1.2 Concrete, abstracted, and conceptual systems, p. 85 Note #10 Dynamic relation, p. 327 c See the discussion on thermodynamics in 2.4 The epistemological niche of systems theories, p. 66 d Note #14 Entropy, p. 334 e Note #123 Disequilibrium and change, p. 507 b

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24. Boundary As noted above, the boundary distinguishing system from environment can be viewed as either objective or subjective. The realist position takes the distinction as objective. The choice of boundary is rarely totally free for the physicist investigating thermodynamic phenomena, for the biologist researching intercellular interactions, for the sociologist examining organizations, or for the political scientist studying nations. Not all choices of boundary make sense. Moreover, biological and social systems not only have boundaries but also “critical subsystems” a (Miller 1978) that define and maintain these boundaries and govern transactions across them. In such systems, the boundary is part of the system, often generated by However, for other systems (not the internal processes. b default in this book), the boundary belongs more or even completely to the environment; e.g., for an ocean as a system, the land it washes up on defines its boundary. The nominalist position regards boundaries as arbitrary, imposed for the subjective purposes of the investigator. Boundaries are in the eye of the beholder; in the words of Blake (1874), “Madmen see outlines and therefore they draw them” (but Blake was being complimentary and not dismissive, so he may be asserting the objective character of what madmen see.) Boundaries are often seen as non-instantiated, as mere difference (the view of G. Spencer-Brown). The nominalist position stresses the legitimacy of defining system and environment in any consistent way that one wishes. Since system and environment are never completely immune to each other’s influence, the location of the split between them is always at least somewhat arbitrary. Systems theorists who are mathematicians tend to be nominalists about boundaries, since they study conceptual systems, for which boundaries are inapplicable, unnecessary, or a b

Note #53 Boundary subsystem, p. 401 Note #47 Autopoiesis, p. 393

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arbitrary. Natural scientists tend to be realists, since they study concrete systems, whose boundaries are often critical and salient. Social scientists, who study abstracted systems, may favor either orientation; Knoke and Kuklinski (1982) discuss both nominalist and realist orientations toward boundaries in social science applications of graph theory. Engineers resemble mathematicians since in design there is often latitude in choosing boundaries, but good versus bad design often hinges on a wise choice of boundary, so boundaries for an engineer are at least partially objective. In systems analysis, a poorly chosen boundaries lead to ineffective problem solving. Early systems movements encompassed both orientations. General systems theory was an inductive approach to “exact and scientific metaphysics,” starting from the sciences and going up in abstraction, while cybernetics was a deductive approach to ESM, starting in mathematics and going down in concreteness b; roughly speaking, GST was realist and cybernetics nominalist. (Von Bertalanffy and Boulding exemplify the first; Ashby and Bateson the second.) Essay reflects the author’s preference for the realist position. Although definition of system and environment in any model depends on the purpose of the undertaking, systems are in this book usually being considered ontological, not epistemological, with boundaries of concrete and abstracted systems having some objective character. Boundaries are often dictated by the scale of analysis. Analyses having different motivation but conducted on the same scale often end up recognizing the same boundaries, i.e., positing the same units engaged in different types of interaction. Like “organizing principle,” “environment,” and other concepts, “boundary” takes on different meanings under different categories of Synchronics. Viewed from the perspective of Distinction, a bare distinction is insubstantial, since to reify the a b

4.5 Systems theory and systems analysis, p. 141 2.3 A new conception of metaphysics, p. 54

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boundary would introduce a third term. Viewed from the perspective of Constraint between system and environment, the boundary is a relation, equivalently an element. In Persistence, the boundary is the locus of openness and closedness. In Identity, it is constructed by autopoiesis. And so on. In the thermodynamics of matter-energy exchange across boundaries and in the related concepts of isolated, closed, and open systems, boundaries are idealized notions that are arbitrarily sharp. In formalizations where system means state variables and environment means parameters, again the boundaries are sharp. Other mathematical treatments allow distinctions that are less sharp. For example, the systemenvironment boundary might be defined graph-theoretically and sharply as a subgraph. Or, if the boundary depends on the density of links, the system would be defined as a local concentration of links; this boundary might then not be sharp.

25. Fuzziness Another alternative to sharp boundaries is offered by the theory of fuzzy sets, a systems theory which is important in the analysis of natural language, which bridges the realms of the continuous and the discrete, adds new meanings to the notion of uncertainty, and is the basis for numerous technological applications (Zadeh 1965; Klir and Wierman 1999). Fuzziness can qualify the notion of attribute of an element, introduced earlier. a Consider the attribute “height” and one of its possible values, “tall.” Let T be the set of tall persons, let t be a person whose height is h, and let µ(h) be the membership function for “tall.” If T is a crisp set, t is either in the set or not, so µ(h), t’s degree of membership in T, can only be 0 or 1. For fuzzy sets, µ(h) can take on any value between 0 and 1. For example, values could be: µ(7′) = 1 and µ(4′) = 0, but µ(5.8′) = 0.6. Nonintegral µ(h) values are possibilities, not probabilities (possibilities do not add to 1); they can also be interpreted in terms of multi-valued logic. Note that while the boundary of T a

Note #1 System, p. 301

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is fuzzy, its membership function has precise values. This illustrates the need for both disorder – fuzziness – and order – sharpness – even in the description of fuzziness. Not only can values of attributes be fuzzy, but attributes themselves (e.g., the length of a nose) can be fuzzy (if there is variability in how length is defined); even the elements that have attributes might be fuzzy (e.g., the element “cheek” might have a fuzzy boundary with the element “nose”). Relations can also be fuzzy. Membership of (ai,bj) in relation AB might not be restricted to values of 0 or 1; this generalizes the notion of relation beyond its definition using standard (crisp) set theory. Since fuzziness can apply to elements, attributes, or relations, the concept is basic, although fuzziness is not an obligatory aspect of the idea of system. Fuzziness is relevant also to the basic system-environment distinction. If this distinction partitions elements and/or relations into different sets, then if the sets are fuzzy, the distinction is fuzzy as well. An element or relation may be partially inside the system and partially outside of it. As with the notion of boundary, such fuzziness can be regarded as either real or nominal.

26. Fractals Fractals (Mandelbrot 1982) are patterns with detail at multiple scales. When the detail is the same or nearly so, there is selfsimilarity, but technically speaking, fractals do not require identity of detail. The definition of “system” is itself fractal, being recursive upward and downward: Elements are systems in their own right and the system is itself an element at a higher level. At this abstract level, there is self-similarity, but the attributes of elements and the nature of their relations differ from level to level. Systems exhibit both similarity and difference. Thinking in terms of fractal properties privileges similarities across scales and focuses on isomorphisms; it needs

354

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to be balanced by considering differences across scales and focusing on emergence. a Boundaries in nature are often fractal. In ordinary geometry, boundaries are unproblematic. If one measures the circumference of a circle with rulers of varying size and approximates the circumference as the sum of chord lengths, the sum converges on the expected 2πr as the ruler becomes smaller. By contrast, if one measures the coastline of a country – or the boundary of some basin of attraction in state space or region in parameter space (e.g., the Mandelbrot set) – with smaller and smaller rulers, the measured length may increase in an unbounded way. Plotting length L against ruler size S may yield a power law, L = a Sn + b. Moreover, a fractal boundary of a two-dimensional object will not simply be a one-dimensional line, but will fill space to a greater or lesser degree; the boundary will then have a noninteger dimension, greater than 1 but less than 2. Fractal boundaries are often the result of emergent processes. b No system is alone. Every system is enmeshed in a larger whole, a web of external 27 28 that extends indefinitely relations outwards. This web is not homogeneous or seamless but is a network that is structured.

27. External relation Just as the system is constrained internally, c it is constrained externally. External relation SE links system S to environment E, as shown in Figure 56(a) and (a′). Order established by this relation is purely external. Internal order is not involved since the system here is a unitary element, S, with no specified internal elements. a

3.3 Isomorphism and emergence, p. 97 Note #32 Emergence, p. 363; Note #47 Autopoiesis, p. 393 c Notes #9 Relation as constraint, p. 324, and #10 Dynamic relation, p. 327 b

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Figure 56 External relation

SE

E

S

E

S (a)

(a′)

I

O (b)

If environment E is an input I to the system, and if the system state is replaced with external output O, relation IO describes the system as a “black box” (Figure 56(b)) that leaves the internal state of the system unspecified. The system is then an input-output relation between external observables (this typifies models in behaviorist psychology). It is pure function, with no structure. One could have a mixed internal-external relation, e.g., IAB, that links internal variables A, B, and external variable, I, which replaces E, treating environment as input. IAB could be conceived of as ABi, an internal AB relation parameterized by an external input. I might alternatively parametrize a dynamic relation SS', (S' is S at a later time) changing it to ISS', making dynamics depend on environmental input. Without environmental input, the iterative graph a of a deterministic dynamic system is fixed. Barring a direct perturbation of state, a system stays in one basin of attraction and eventually arrives at the basin’s attractor. With external input, however, the iterative graph may be different for each different environment input. States not now reachable may become reachable. Time (the trajectory of the system) is actual, eternity (the whole iterative graph) is potential; what links the two is the openness of the system, which subjects it to the additional influences of its relevant environment. Further influences come from the environment of the relevant environment. The horizon of influences is open. a

Figure 53 An iterative graph, p. 329

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For continuous-time continuous-state systems, the ISS' relation becomes the differential equation, dx/dt = f(x,p), where continuous (internal) x and (external) p replace S and I, respectively. If there is a reciprocal influence of the system on the environment, there is also dp/dt = g(p,x), which treats the environmental input as a system in its own right. Note that I in ISS' and p in dx/dt = f(x,p) could alternatively refer to an internal environment. a As used in this book, internal and external relations describe order inside and outside the system, respectively. These are to be distinguished from intrinsic and extrinsic relations, where an intrinsic relation is one that is inherent in the elements taken as systems, while an extrinsic relation is added to these elements by virtue of the system they are part of. b (In the philosophical literature, “internal” and “external” sometimes mean what here is called intrinsic and extrinsic.) In the intrinsic-extrinsic dyad, the first term is usually unmarked (favored). Only intrinsic relations are constitutive, i.e., if relation AB is intrinsic, then A is at least partially constituted by B, so the identity of A is not self-contained. Sometimes this is said to deny that A = A, i.e., that A is “self-identical”; hence the poststructuralist idea that difference (in this book, distinction) is constitutive. In the closed systems view, external relations are, by definition, always extrinsic, but in the open systems view, where a system is a center of structure and function, external relations might also be constitutive and thus viewed as intrinsic. c As systems become complex, this is less likely to be the case. For systems sufficiently complex to have an essence, d even internal relations not specified by this essence are thus extrinsic to the organizing principle.

a

Notes #6 Inconsistency, p. 311, #17 Chaos, p. 338, and #22 Environment, p. 347 b Note #1 System, p. 295 c Note #34 Function, p. 370 d Note #49 Genotype and phenotype, p. 395

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28. Extension The simplest meaning of extension is location in space and/or time. Concrete systems, by definition, have extension, but abstracted or conceptual systems, if represented as graphs, can also have a kind of extension in the path distances between elements. a For example, one can speak of center and periphery in a graph. So a more elaborate definition of system includes a “dimensional domain” (Angyal 1939) that indexes the system variables and environmental parameters with support variables. b Systems having extension means that elements have extension, since systems are higher-level elements. Elements bind together attributes, and the support variables assign locations to these elements. This binding together of attributes is different from the way attributes are linked by relations. Extension means having a location in a dimensional domain and being extended in this domain. This means being more than an indivisible point. If recursion downward is not endless, a fundamental and final element at the bottom would be point-like but have a location. If recursion upward is not endless, then a fundamental and final top system would not have a location but would be extended. Representations of systems often come in two closely related forms: one omitting explicit extension and the other incorporating it. For example, in networks of randomly connected automata, space is omitted, and the underlying structure is only a graph, but in cellular automata c space is explicitly included. In differential equations that model chemical reactions, space can be omitted (and the entire system taken as one chamber), but in reaction-diffusion systems, space is included. Introducing extension always adds complexity and in general produces qualitative change in system behavior.

a

Note #7 Networks, p. 318 Note #1 System, p. 295 c Note #10 Dynamic relation, p. 327 b

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System is one and many, partitioned from the 29 all and silhouetted against zero. One implies two: system and environment. Two brings three: system and environment in relation. 30 From three, everything follows.

29. Nothing, many, one, all George Spencer-Brown wrote, “...nothing is formally identical with everything, since by definition there are no distinctions within either.” (Johnson 1994). As John Cage wrote (Capra and Steindl-Rast 1992): “Each something is a celebration of the nothing that supports it.” Nothing is not actually nothing; it is an inexhaustible matrix of possible arisings, and the possible is as real as the actual, though in a different way. The void as plenum has a long history in philosophical and religious thought and receives modern endorsement by quantum physics. System is less than All and more than Nothing; it is one and many (lower case to indicate that these are not the One and Many that are on a par with All and Nothing, since there are many systems). System is one as a unitary element-relation and as the vertex of the structure-function double cone; it is many in the multiple elements and relations involved in structure and function. Being one is the highest manifestation of system, the top of the Lattice of Structures a; being many is the lowest manifestation, the bottom of this Lattice. Being both one and many produces inconsistency when the differences of the many are aggregated into one. Being less than All is incompleteness, and the system as actual is in a sense also less than Nothing, which harbors all possibilities. The tetradic structure of Nothing, All, One, and Many is symbolized in Figure 57(a). The relation between this tetrad and the system-environment dyad is shown in Figure 57(b); in it, the system has some intermediate location in the Lattice of Structure (is partially decomposable).

a

Note #5 Structure, p. 308

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Figure 57 Tetrad of number; pentad of system

all one

All One

Many

environment

system

Nothing (a)

many (b)

nothing

In Figure 57(a), Many, might begin with one (not One, another face of the All) if taken to mean Integer, or it might begin with two, which is minimal difference. Figure 57(a) is a hierarchy, whose upward (zigzag) sequence is Nothing, Many, One, and All. From another perspective, One and Many are at the same level, and Nothing and All ascend and descend, respectively, to both.

30. One, two, three, ten thousand In the language of gestalt, system and environment are figure and ground, both separated and joined. Figure and ground are not equal. The first is unmarked a while the second is marked. For Peirce (1958), they exhibit Secondness, which encompasses two terms, the First and the Second. The First descends from the prior Firstness, in which “a thing may be considered strictly in terms of itself, without regard to any other.” The Second supplements and opposes the First. The First has seniority; it represents Firstness within Secondness and is the precondition for appearance of the Second. For example, Newtonian action and reaction are First and Second, respectively. Action is unmarked because it starts it all and reaction is the consequence of action. Likewise in similarity-difference, similarity is First a

Note #8 Incompleteness vs. inconsistency, p. 320

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and difference is Second. Being unmarked is being privileged, but privilege is contested. The Second has its own virtue. It is the new, so it determines the character of Secondness; on these grounds, it is the favored term. The progression from Firstness to Secondness to Thirdness, and a perspective on the progression of number-symbolic categories, is abstractly represented in Figure 58(a). In the present context, the monad A1 is Firstness; A2 and B2 are First and Second. A2 derives from but modifies A1. Every category introduces a novel term, while the inherited terms readjust, i.e., are modified from their meanings in prior categories. An example from an earlier discussion: a if A2 and B2 are husband and wife, then A3, B3, and C3 might be father, mother, and child. Figure 58 Progression through the categories Two views on this progression: (a) asymmetric; (b) symmetric. In (a), what is inherited is modified and something new is also added. In (b), E is a notion midway between B and C; D and F are extreme or more specific modifications of B and C.

monad dyad triad etc.

(a) A1 A2 A3

(b) A B2 B3

B C3

D

C E

F

Firstness is flawed. It manifests incompleteness by not encompassing enough; or inconsistency by encompassing too much. Secondness eases the strain of deficiency or excess through dichotomy, but dichotomy is tension. First and Second tend to collapse together or fly apart. Secondness also needs correction, so it unfolds to Thirdness. Thus, Firstness is propelled into Secondness and Secondness into Thirdness. Thirdness brings relation which mediates the tension, but it introduces the challenge of dynamism. Still, there is quasia

3.2.2 Utility, p. 95

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completion in these categories. Peirce only goes up to Thirdness, but Bennett (1966), whose first three “systems” roughly resemble Peirce’s three categories, goes up to nine (and comments on the symbolism of twelve). Bennett does not discuss how these archetypes develop from one to another, but this is explored by Blake (1999), whose view of their progression has the structure of Figure 58(b). In the Secondness of system-environment (figure-ground), system is First and environment is Second. The First is unmarked and already-there; the Second supplements it with the new. The permanence of the distinction is not secure, since distinction is not indelible. The system owes its existence to the environment, so it is really the latter that is unmarked and already-there. Being, i.e., system, is difference from environment that is only provisional. a But while it lasts, this difference is reconciled through relation (Thirdness), at least temporarily stabilized (this would be Fourthness), and, in favorable conditions, infolded and articulated (Fifthness). Not only is the system-environment distinction never finally accomplished, as in Derrida’s (1980) notion of différance, it is said to manifest “contamination,” (Derrida 1982) in that system and environment are codependent. But since “Distinction is perfect continence” (G. Spencer-Brown), where genuine interpenetration occurs (to use the Hegelian term), and thus where contamination applies in a strong sense, must be at the level of the triad, where relation – more than mere distinction – exists between system and environment. Contamination is evidenced by the fact that the uncertainty of the system knowing the environment is less than the uncertainty of the system by itself, and vice versa. System and environment “invade” one another, just as the small circles of yang and yin “invade” the yin and yang parts of the double-teardrop Taoist diagram. In Buddhist terminology, this is “codetermination.” Contamination is still more pronounced when endurance of order and a

Note #178 Dissolution, p. 587, discusses its ultimate fate.

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distinction are at issue (7.1.4 Persistence). Persistence of the system, in both internal and external aspects, requires openness to flux from the environment. Here is another formulation of the story that is being told. As long as the All is One without any other, nothing happens. The action begins when the One contracts, a generating many ones (many systems, some of which may be unique), and sets the ball rolling. Each one (the monad of identity), being less than All, implies two (the dyad of difference). Two is under tension and unstable and runs to three (the triad of relation) to avoid returning to one, and thence to zero. From three everything follows. As Lao Tzu wrote in the Tao Te Ching, “The Tao begot one. One begot two. Two begot three. And three begot the ten thousand things.” This is still not the whole story. There is not only descent into multiplicity but also return to unity. b One-two-three is “ontological”; the ten thousand things are “ontic.” c Begetting is logical, not temporal; from another perspective, one, two, and three occur all at once. What “one” means is “system,” a simulacrum of the One, a Leibnizian “monad,” not “windowless” but in interaction with other ones. This is under the aspect of similarity; under the aspect of difference, complex ones are perhaps more in the image of the One than simple ones; yet the One represents all ones. The system is an element in its context and a 31 relation for its elements. Internal constraint brings both contraction and expansion: as the source of unity for the system, contraction; as 32 the source of emergent attributes that enable interaction with the environment, expansion. Every element of the system is a system on a smaller scale. Every whole is a part; every part is a whole. a

See the mention of tsimtsum on p. 228 Note #140 Two universal processes, p. 535 c 5.3 Categories of complexity, p. 160 b

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31. Assertion vs. integration As an element, the system faces outward and is “self-assertive”; as a relation it faces inward and is “integrative.” These terms come from Koestler’s (1978) idea that a Janus-faced holon, a his term for “system,” has both tendencies in relation with its environment. As a whole having coherence, the system asserts itself through agency. As a part that is incomplete, it is usually integrated into more encompassing systems. By considering only internal needs and not regarding integration also as a need, this account privileges the internal over the external and takes a closed systems view. Self-assertion and integration aim at the promotion and subordination, respectively, of the systemenvironment distinction. Essay supplements the specific term, “environment” with the general term, “context.” “Environment” has a connotation of concreteness, while “context” could refer to either concrete or conceptual systems. b The two words are used here synonymously.

32. Emergence The system faces outward with emergent attributes. Emergence is the arising of phenomena at one level generated by, but qualitatively different from, phenomena at another level. It is usually considered bottom-up (structure-generated), but can also be top-down (function-generated). Bottom-up emergence relates higher-level wholes to lower-level parts. It is paired with reduction c: Emergence looks upward from lower to higher; reduction looks downward from higher to lower. If the connections between the levels are understood, emergence and reduction reflect different orientations toward the same understanding. If they are not understood, emergence a

Figure 38 Hierarchy of Janus-faced systems, p. 299 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 c 3.3 Isomorphism and emergence, p. 97 b

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is paired with in-principle reduction. Top-down emergence explains parts in terms of wholes; this non-reductionist mode of explanation is widely used in the sciences. A salient principle of bottom-up emergence is “The whole is not equal to the sum of its parts.” It is both less than this sum and more than this sum. It is less than the sum of its parts in that the set of states that occur in the system is smaller than the set of possible states a allowed by the parts. In both set- and information-theoretic relations, the uncertainty of the whole is less than the sum of the uncertainties of the parts. Being less than the sum of parts means that the whole has order, being equal to the sum of parts would mean disorder (independence of the parts). The whole is more than the sum of its parts, not merely in the sense that a system is more than elements having attributes but involves also relations, and not merely in the sense that dyadic relations do not suffice to describe a system. A deeper meaning of being “more than the sum of parts” is the fact that the constraints make the system into an element at a higher level with emergent intrinsic attributes b that are different and perhaps unpredictable from attributes of the constituent elements. (Similarly, attributes of elements emerge from lower-level relations within the elements.) These emergent attributes are the basis of the external relations (function) of the system with its environment, though system need not act as a single unit. c This kind of emergence is bottom-up (structural), but emergence can also be top-down (functional). Functional emergence is illustrated by the fact that relations confer extrinsic attributes on the elements they link. d (An example from physics is the bootstrap idea, in which elementary particles derive their attributes from the set of particles that do or might exist. An a

Note #9 Relation as constraint, p. 324 Figure 40 Adding attributes to elements and relations, p. 302 c Figure 39 A minimal system S with environment E, p. 301 d Note #7 Networks, p. 317 b

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example from game theory is a player having a pivotal role in coalition formation, this role being dependent on the constellation of all the other agents.) To the degree that the environment determines system attributes, these attributes are not innate system properties. In sum, system attributes can be structural (internally generated) or functional (externally generated) or both. The problem of emergence is to explain how new attributes arise, either synchronically or diachronically, from internal or external relations. This involves issues such as (a) the relation of process to state descriptions; (b) the limitations of formal systems; (c) the relation of macro- to micro-phenomena; and (d) the open-ended character of the environment. These issues are implicated in the different meanings given to the idea of an emergent attribute, which might be defined as: (1) a collective property of a system quantitatively different from the sum of this property of the parts. For example, for whole ABC and parts AB, AC, and BC, the strength of constraint in the whole is usually greater than the sum of the strengths of constraint in the parts. In game theory, the payoff to a coalition is greater than the sum of payoffs obtainable by members acting separately (Hamburger 1979) (if the coalition payoff equaled this sum, there would be no need for a coalition.) Another example is superadditivity of nutritional value in complementary foods. (2) a collective qualitative property different from the properties of parts but that can be specified by fully describing the system and environment. An equilibrium point of a set of differential equations which depends on the parameters of these equation would be emergent, since it is implicit in these equations. By contrast, the set-point of a control system is an explicit and localized input (a single parameter) and is not an emergent. In some situations the mere number of elements or relations changes the character of the system, i.e., quantity transitions to quality. In decision theory, transitivity in three or more pairwise

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preferences is a property of the whole set that is not even defined for one or two pairs. The possibility of coalitions in 3(or more-) person games is absent in 2-person games. In nonlinear dynamics, two differential equations cannot exhibit chaos, but three can (and typically do). So far, the notion of emergent is not in the slightest mysterious or inaccessible; it is a property of the whole that is fully ascertainable from its detailed specification. A notion of emergent that is slightly less straightforward than this is: (3) a collective property similar to that defined in (1) or (2), i.e., definable in terms of the parts of the system, where the definition required prior recognition and description of the property at a higher level of organization or abstraction. Examples are thermodynamic properties of pressure and temperature of a gas, which are reducible to a Newtonian microdescription by statistical mechanics. By virtue of the possibility of this reduction, there is nothing undefined about such an emergent property, but nonetheless there is novelty associated with it, since one could not predict the relevance of the macroproperty from the micro-description alone. Next are meanings of emergence where the property of the whole is not readily definable in terms of the parts. (4) a collective property determined in principle by the parts of the system and its environment, where a formal solution is unavailable but whose evaluation can be done in practice via computer simulation. This has been called “weak emergence” by Bedau (1997). (5) a collective property determined in principle by the parts of the system and its environment but whose evaluation in practice is impossible because of computational complexity. a For example, if one had an exact description of the forces involved

a

Note #69 Computational complexity, p. 422

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in protein folding, the folded structure might still be unpredictable because of the intractability of simulating folding. (6) a property whose determination is precluded simply because it is not definable (at least at present), e.g., certain properties of fluids which we do not know how to express in terms of the properties of the constituent molecules. Many – perhaps most – interesting properties of dynamic systems are not capable of being represented in closed form in terms of the parameters of their equations. Macro-level phenomena in agent-based models usually cannot be expressed in terms of the micro-level behavior of the agents. (7) a property whose determination poses difficulties still more severe than analytic unsolvability plus computational complexity, namely a property whose presence or absence is subject to Gödelian undecidability or to its equivalent in automata theory, the Halting Problem. Such a property might still be definable outside the formal system but not derivable within it. Certain properties of nonlinear dynamic systems which can be specified only in some infinite limit, e.g., the fractal boundaries in state space of some domain of attraction or in parameter space of a domain having particular dynamic properties (Baas 1994, referring to work of Smale) may be undecidable. (8) a property arising in an incompletely specified system or one whose environment is incompletely specified. Such definitions of system and environment cannot be a priori prohibited, since the allowability of systems with vague, openended, or unspecified environments is precisely one of the raisons d'être of the system-environment distinction. These types of emergence are not ordered and partially overlap. The general phenomenon of emergence includes, as a specific phenomenon, the occurrence of counterintuitive effects a in complex systems. The above discussion mostly takes an a

Note #61 Counterintuitive effects, p. 413

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epistemological perspective but some of its ideas might be reformulated using an ontological perspective. a There is a big difference between a property that is only emergent in the eyes of some beholder, making no difference to the system itself, and a property whose emergence has causal consequences for the system. Constraint upon variety characterizes not only internal relations but also external relations. The system is not only distinct from its environment but is constrained by it. Either extreme – being constrained too much or too little – is diminution. A system too tightly coupled to its environment is a diminished whole; one too loosely coupled to its environment is a diminished part. No intermediate condition is permanently 33 optimal. Constraint has not only strength but polarity: one pole active, the other 34 passive. Because of difference in scale of the system and its environment, it is commonly the system that is passive, but polarity varies.

33. Engaging/disengaging What is required is not to be engaged or disengaged, but to have a clutch and manual rather than automatic transmission. The metaphor of a clutch allowing engagement or disengagement is used in 7.1.8 Cognition to describe the relation between two hierarchical levels. b

34. Active vs. passive Polarity refers either to the system-environment relation or to internal relations. The idea of “active” versus “passive” roles is not commonly invoked in systems theory, but is implicit in the a b

2.3 A new conception of metaphysics, p. 55 Note #99 The modeling subsystem, p. 463

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notions of directed versus neutral systems a and directional links in graphs. b Mathematically, it is implicit in the distinction between a function and its arguments. For an open system that has input from its environment but no output to it, one might regard the environment as active and the system as passive. However, for a system whose function is sufficiently complex that it may be said to be an agent, c or for an open system whose primary interaction with its environment is output rather than input (e.g., a star), this polarity can be reversed. See active, passive, and also mediating terms in the matter-energyinformation triad. d Strictly speaking, different names should be used for the terms of the dyad (active, passive) and corresponding the terms of the triad; see the discussion of naming corresponding terms of relations of different ordinality. e Context does more than bind; it defines. The system is subject to dual determination: it is constituted not only by its internal order but also by its participation in an external order. As a nexus of being and behaving, every system does not have just one organizing principle but at least two: a principle of internal structure and a principle of external 35 function. Structure does not uniquely specify function nor does function uniquely specify structure. Both define system attributes. Between structure and function there is tension. What is determined from within and what is determined from without are never in complete accord.

a

Note #1 System, p. 295 Note #7 Networks, p. 317 c Agency 1.1.6 and 7.1.6, pp. 13, 402 d 3.2.1 Matter, energy, and information, p. 88 e 3.2.2 Utility, p. 95. This issue is also discussed in Note #30 One, two, three, ten thousand, p. 359. b

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Unity is opposed by multiplicity in both structure and function. Rarely is there only one external organizing principle. The system also interacts with its environment not merely as a single element. Parts of the system engage parts of the environment, so multiplicity in structure passes through into function.

35. Function a The conventional view about what a thing “is” focuses on its structure, i.e., its internal elements and relations; this is the closed systems view. b An alternative conception of what something “is” is based on its function. In this conception, a system is defined by its context, by its external relations with its environment. c This is a different perspective from a purely structural orientation, in which function is contingent and not constitutive. The difference between a structural and a functional definition of “system” is reflected in alternative concepts of the idea of the attributes of an element. d From a structural perspective, attributes are properties of the element that emerge from a subelemental level. From a functional perspective, attributes are carried by relations that bind elements together and do not inhere in the elements per se. Analogously, from a structural perspective, the attributes of the system, taken as a higher-level element, are emergents e of internal structure, but from a functional perspective, they might instead be carried by the external relations in which system participates and which confer these attributes upon the system. Attributes that emerge upward from structure are intrinsic to the system as a higher-level a

3.5.1 Structure and function, p. 109 Note #1 System, p. 295 c Note #27 External relation, p. 354 d Note #7 Networks, p. 317 e Note #32 Emergence, p. 363 b

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element, but system attributes may also be extrinsic, and carried by the external relations in which the system participates. They depend on the environmental niche that the system occupies. For example, “being a spouse” is an extrinsic, not intrinsic, attribute of a person. This extrinsic attribute explicitly inheres in the marriage relation. Extrinsic attributes may also arise implicitly as downward emergents from a set of relations. For example, in graph theory, the centrality of any node is extrinsic and implicit; it depends on the entire graph and is not an intrinsic property of the node. Not only can wholes have properties emergent (upward) from its parts, but parts can have properties emergent (downward) from the larger whole in which they participate. To repeat points made earlier, to avoid possible confusion: “function” and “structure” as used in this book do not mean dynamic and static, nor does “function” mean designed or intended use. “Use” implies purposefulness. In the terminology employed here, “function” just means external relations and does not imply purposefulness. The moon’s effect on the earth’s tides is part of its function, but the moon has no purposes. A system may partake in several external organizing principles, so, as indicated in the next paragraph of Essay, just as inconsistency a from multiple internal relations afflicts structure, inconsistency from multiple external relations afflicts function. b The environment is neither single nor constant. A system may exist in more than one environment. Environments change. Although a system may partially alter or transcend the limitations of its environment, no possibility exists of complete escape from external constraint.

a b

Note #6 Inconsistency, p. 311 Note #81 Sharing elements, p. 437

NOTES

372

Context is unbounded. Although the system interacts only with a limited environment, these limits are provisional. What is relevant to the system is dynamic and open-ended. Insofar as the system is determined by external relations, this determination is never final. When external conditions change, the system is affected.

373

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7.1.4 Persistence Notes:

page

36 Stability 37 Catastrophe theory 38 The fold catastrophe 39 The Second Law 40 Rigidification vs. disintegration 41 Openness and Closedness 42 Dissipative systems 43 Openness necessary and hazardous 44 Law of Requisite Variety 45 Feedback control

373 375 376 378 378 380 381 383 384 386

Constraint and distinction do not ensure 36 persistence. The environment does not only bind and delimit the system; it is a source of disturbance. To endure, the order of the system must to some extent be insulated from 37 external change. Even small disturbances 38 or impact may undermine this order behavior.

36. Stability Persistence is dynamic stability despite disturbance. There are two types of disturbance: (1) a disturbance of state, where the new system state is either in the same basin a or in a different basin (having a different attractor) and (2) a disturbance of parameter, typically environmental input, where the new environmental state changes the basins and their attractors. a

Figure 53 An iterative graph, p. 329, in Note #10 Dynamic relation

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Ordinary stability or instability concerns disturbances of state; structural stability or instability concerns disturbances of parameter. For discrete-time discrete-state relation ISS', a S is the state and I is the parameter; for discrete-time continuousstate map x' = f(x,p) and for continuous-time continuous-state differential equation dx/dt = g(x,p), x and p are state and parameter. A prime on S or x indicates a later state (after the disturbance). This note is about ordinary stability; structural stability is discussed in the next note on catastrophe theory. In cyclic systems, stability depends on the type of feedback. b Negative feedback is deviation reducing; positive feedback is deviation amplifying. This applies if the graph of Figure 59(a,b) is interpreted to mean dx/dt = ( )y and dy/dt = ( )x, where parentheses are filled by positive or negative terms; in this case, a loop is stabilizing or destabilizing if the product of signs around the loop is negative or positive, respectively. If, however, the graph means y' = ( )x and x' = ( )y, the system is stable if the product of absolute values of magnitudes around the loop is ≤ 1. Figure 59 Negative and positive feedback (a) Stabilizing negative feedback; (b) destabilizing positive feedback (both signs might instead be positive); (a') and (b') are simpler examples; if the sign is first (+) and then changes to (–), one gets a logistic (S-shaped) growth curve. c

–

+ y

x – (a) a

x

x

y – (b)

–

(a')

x +

(b')

Note #27 External relation, p. 354 3.4 Aspects of complexity and holism, p. 100, and Note #7 Networks, p. 317 c Note #130 Trajectories of development, p. 517 b

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Loop structures can be more complicated and have both stabilizing and destabilizing loops, as illustrated in Figure 60, which shows four elements that have one destabilizing loop, xy-w-x, and one stabilizing loop, x-y-v-x. In the methodology of system dynamics, stabilizing loops are called “balancing” and destabilizing loops are called “reinforcing.” When arrows are causal links, the diagrams are “causal loop diagrams” (CLD). Figure 60 Stabilizing and destabilizing loops

x

+

y

+ ––

+

+ v

w

Many systems have stabilizing feedback only over some limited range of parameter values, which produces a “homeostatic plateau” (Figure 61). Figure 61 Homeostatic plateau

x

negative feedback

positive feedback

positive feedback parameter

37. Catastrophe theory Catastrophe theory (Thom 1975) is about how gradual continuous parameter (environment) changes can produce sudden discontinuous change in the system’s attractor. The

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theory applies only to gradient systems a having only a few parameters. For such systems, types of structural instability due to small changes in parameters near a topological singularity are catalogued by Thom’s elementary catastrophes. Although gradient dynamical systems are atypical of nonlinear dynamic systems, so catastrophe theory has limited scope, the theory offers conceptually rich models that can be applied rigorously or qualitatively. For up to four parameters, there are seven elementary catastrophes, of which three – fold, cusp, and butterfly – are used in this book. In catastrophe models, small causes can have big effects. This also happens in chaos, b where small changes in initial conditions or environmental parameters can have big effects, but chaos is different from catastrophe theory dynamics. Chaos in continuous systems requires at least three state variables, does not apply to gradient systems, and is not merely local, etc. Small causes can have big effects also in phase transitions and self-organized criticality c; such phenomena exhibit tipping points. These are all different ways of modeling phenomena in which change happens “gradually, then suddenly” d; perhaps the simplest examples of this are exponential processes. e

38. The fold catastrophe The most basic elementary catastrophe, the fold, is shown in Figure 62. Fold dynamics are governed by dx/dt = x2 – p. When parameter, p, moves to the right and passes the singularity, the system changes from having no equilibrium state to having both an attractor and a repellor. In this change, the fold represents the shift from instability to stability, from nonbeing to being, being here implying at least limited persistence a

Note #10 Dynamic relation, p. 330 Note #17 Chaos, p. 338 c Figure 102 Phase transition as system formation, p. 503; Note #150 Selforganized criticality, p. 551 d Buerkli (2020) e Figure 110 Failure of response to exponential danger, p. 526 b

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(if the system is on the attractor, not the repellor). a When parameter, p, moves to the left and passes the singularity, the attractor disappears, and the system no longer persists. Figure 62 The fold catastrophe Parameter (p) and state-variable (x) axes are dotted; the singularity is at (x,p) = (0,0). Equilibrium is on the parabola. Its solid bold upper half is an attractor (stable equilibrium) and its dashed lower half is a repellor (unstable equilibrium). Large arrows show transient changes of x.

x attractor no attractor

p repellor

Thus every system must in some degree or manner be closed. The organizing principle provides for the closedness of the system and is protected by it; in another sense, the organizing principle is itself this closedness. But to the degree to which and the manner by which a system is closed, it is vulnerable to a dual risk. It tends to either disintegrate or rigidify. Disintegration resolves the tension between constraint and variety in favor of variety. Constraint does not spontaneously 39 arise, but it may spontaneously vanish. Rigidification resolves the tension in favor of constraint. Disintegration is countered but dynamic activity is reduced. Though a

Note #120 System formation, p. 496

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disintegration and rigidification are opposites, they are often linked; and systems 40 may suffer both processes simultaneously.

39. The Second Law Things fade and alternatives exclude. - Alfred North Whitehead, according to Becker (1968). For thermodynamically isolated systems, that is, for systems with no matter or energy transport across their boundaries, the Second Law of Thermodynamics requires that entropy a either remain the same or increase. This law applies only to concrete systems, defined in space-time and viewed in physical terms b; thermodynamics does not apply to conceptual or abstracted systems, except metaphorically. The Second Law is taken up again later in the note on impermanence which includes a poem by Emily Dickinson which might be regarded as being about this Law. c The impermanence mandated by the Second Law is one of the two primary causes of suffering, according to the above quote from Whitehead.

40. Rigidification vs. disintegration Rigidification is excessive or inappropriate constraint, but rigidity bears the same relation to constraint as, in Ashby’s view, information does to noise. Just as there is no intrinsic difference between noise and information, so too there is no intrinsic difference between rigidity and order. What is rigidity in one context is order in another. Spontaneous rigidification can be given a mathematical meaning. A loss of variety (uncertainty) occurs spontaneously in deterministic systems (Ashby 1976), where every initial state can lead to only one subsequent state. Since several initial states can lead to the same subsequent state, the variety of possible a

Note #14 Entropy, p. 334 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 c Note #174 Things fade, p. 584 b

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states either stays constant or decreases over time. This is the opposite of the increase of entropy dictated for isolated concrete systems by the Second Law. Thus, the Second Law in which disintegration is prescribed and deterministic dynamics for which rigidification is prescribed are descriptions of a spontaneous tendency toward disorder and order, respectively. Either tendency may be lawful, i.e., dictated by nature in appropriate circumstances, but the two are very different. The first applies to isolated concrete systems viewed physically (or dynamic systems governed by similar laws), while the second is a mathematical property of deterministic dynamics. Deterministic chaos, however, generates increased variety. a The tendency of concrete systems to go to stable states (attractors) where energy (or free energy) is minimized is like variety-reduction in deterministic systems, so minimizing energy vs. maximizing entropy correlate with rigidification vs. disintegration. Bateson (1958) comments, But we actually know something about Nature's preferences: She prefers the probable to the improbable, and if she were guided only by this single preference, called the Second Law of Thermodynamics, the universe would be simple – if rather dull. But she has clearly another preference: she prefers the stable to the unstable. This preference, also, by itself would lead to a dull universe. It is the combination of – the conflict between – the two preferences which leads to the highly complex and strangely unexpectable universe in which we live.... At this point it is necessary to examine rather closely what I have called “probability” and what I have called “stability.” I invited you just now to consider two a

Note #17 Chaos, p. 338

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imaginary worlds. One in which only probability would obtain, and the other which would be governed only by stability. The first would rapidly end in total entropy, the Warmetodt, while the other would rapidly end up with all atoms combined into the most stable possible molecular forms. A general reconciliation of the opposites of rigidification and disintegration is not provided for in nature’s laws, although mediating factors may occur. a Complete isolation, however, is impossible. Every system is also open to its environment in some degree or manner. Openness brings vulnerability to external disturbance, yet in openness there is the possibility of preserving 41 internal order.

41. Openness and Closedness Thermodynamically closed and open – as opposed to thermodynamically isolated systems – may have steady states in which order (negentropy) is maintained or even increased. Note that the technical (thermodynamic) definitions of the terms “closed” and “open” differ from their informal use. Technically, an “isolated” system is one which has neither matter nor energy exchange with its environment; a “closed” system has energy but not matter exchange; an “open” system has matter and possibly also energy exchange. Informal use of these terms often treats “isolated” and “closed” as synonyms and makes no distinction between energy and matter exchange. The degree of openness or closedness may depend on parameters such as permeability of the boundary, b which defines the rate at which matter-energy gradients are reduced and a

Note #117 Dialectics, p. 493; Note #135 Movement toward the extremes, p. 527 b Note #24 Boundary, p. 350

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equilibrium is approached by the flows that such gradients cause. a For example, if a system differs from its environment in temperature or material composition, then the rate at which this disequilibrium is reduced via such flows might be a measure of the openness or closedness of the system. For systems whose exchanges with the environment are governed by their genotypes, closedness/openness might refer to the genetically controlled permeability of the system to its environment. In systems with informational inputs, it might refer to assimilation or blockage of external information. Openness and closedness, like other concepts discussed in Notes, such as “organizing principle” or “inconsistency,” have a precise meaning within a well-developed theory – here, thermodynamics – but they can also be given broader meanings. But great caution should be exercised in applying these ideas to abstracted systems such as social organizations, since the Second Law does not apply to systems that are not concrete. Openness may even be necessary. A flux across the boundary of the system may be 42 required for its existence.

42. Dissipative systems For thermodynamic systems far from equilibrium, internal order can be maintained through a flux of matter-energy from the environment (Figure 63). Such concrete systems exist by virtue of the disequilibrium produced by system-environment distinction b that drives matter-energy through the system. For a closed system, an energy flux through the system organizes it; for an open system, a matter or matter-energy flux organizes it. If the flux stops, the system disintegrates. When dissipative systems maintain or increase their internal order, they increase the total entropy in the system plus environment. a b

Note #123 Disequilibrium and change, p. 507 Note #23 Disequilibrium and existence, p. 349

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Figure 63 Flux is the basis for order Negentropic matter-energy input is used by the system to maintain or increase order; the system outputs unused negentropy. Some of the negentropy input is lost internally due to the entropy increase of irreversible processes. The gain in internal order is exceeded by the loss of order (the net increase of entropy) in the environment.

negentropy assimilated negentropy input

entropy increase

negentropy excreted

Through openness, tendencies towards disintegration or rigidification may be blocked or balanced. External order absorbed and internal disorder expelled may counter disintegration; internal disorder retained or external disorder assimilated may counter rigidification. But the proper balance of order and disorder is contingent and subtle. In openness, there is only the possibility of 43 self-maintenance, not its guarantee. Openness may cause disintegration to occur even more rapidly than if the system were closed. Extreme openness, like extreme closedness, undermines persistence.

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43. Openness necessary and hazardous Openness is necessary but not sufficient for self-maintenance, i.e., it makes self-maintenance possible but does not guarantee it. Closed or open systems far from equilibrium do not always reach a stable steady state in the way that isolated systems always approach equilibrium. To illustrate, the biosphere maintains and increases its order by capturing some of the incident solar energy, but the moon, also open to solar radiation, lacks the means to capture this energy to create and maintain order. Openness allows more than self-maintenance; by being open, systems can increase their order. a Even openness to disorder can be useful. Disorder can prevent the system from settling into non-optimal structure or function. (This is the basis for global optimization b via simulated annealing, in which the tendency toward rigidification is countered by useful but gradually diminishing disorder.) But openness is also hazardous. Miller (1978) discusses pathologies that arise not only from lacks but also from excesses or inappropriate inputs of matterenergy or information. Thus, every system must be partially closed and partially open, or closed and open at different times, or closed in some aspects and open in others. This dual imperative echoes the tension between constraint and variety. The existence of the system depends upon constraint. Yet variety is needed to block the 44 internal effects of environment disturbance. But variety is beneficial disorder, and differs from harmful disorder only by its consequences for the system, which change with circumstance. a b

Development 1.2.2 and 7.2.2, pp. 25, 507 Note #70 Optimization, p. 423

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NOTES

44. Law of Requisite Variety The Law of Requisite Variety, based in information theory a and decision theory, b illustrates one way that a system can persist in its environment. The environment is here viewed not as context (as in Distinction), nor as provider of sustenance (as it is earlier in this section), but as a source of disturbance. The LRV states a necessary condition for success in a type of feedforward control (Ashby, 1968), i.e., cause-controlled (open-loop) as opposed to error-controlled (closed-loop) regulation. The system has regulated and regulating parts: an essential variable E (not to be confused with environment E) and a regulator R (not to be confused with relation R) (Figure 64). E and R are center and periphery, respectively. c Entropy (disorder) in R is needed to assure negentropy (order) in E, but in the regulator “disorder” is beneficial variety. d The LRV illustrates the need for both unity (constraint) and multiplicity (variety). The regulated part of the system needs unity; the regulating part needs multiplicity. Figure 64 Cause-controlled (feedforward) regulation (a) Essential variable E is affected by disturbance D which is countered by regulator R which gets information (dashed arrow) on D but not on E (solid arrow: matter-energy); (b) E is system center; D is external influence; R (periphery) mediates.

R

(a) system

a

E

D environment

E

R

D

(b)

Information theory is discussed in Notes #9 Relation as constraint, p. 324, and #13 Order, p. 332. b Note #56 Decision theory, p. 406 c Note #28 Extension, p. 357 d Note #13 Order, p. 334

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Viability is possible if E stays within some viable subset of states, V. For example, body temperature of a mammal must have limited variability if the organism is to survive. The figure shows R receiving information about D, and responding with a matter-energy (causal) effect on E that counters the effect of the disturbance on E. Regulation can be diagrammed with the tetrad of problem solving. a The goal (the ideal state of the system) is E being in the viable subset V. The ground (the actual state of the environment) is disturbance D. Direction is the internalization by the regulator of E(D,R), the “laws of nature” that dictate what essential variable state will result from any combination of disturbance and regulator states. From E(D,R) and V, a mapping rule R(D) is derived that tells the regulator as instrument what state to take for any disturbance, so the joint effect of D and R will put E in V. The LRV specifies the minimum number of states that the regulator must have. The law can be paraphrased as only variety can destroy variety: Only variety (uncertainty, entropy) in the regulator can counter the effects of variety in environmental disturbances. The regulator needs a sufficiently large repertoire of responses. Given some assumptions, the law states a necessary but not sufficient condition for successful regulation. Essay goes on to note that there is no inherent difference between entropy that is useful (as in the regulator in the LRV) and entropy that is useless or even harmful. As Ashby (1956) observes, variety is not intrinsically different from noise. Noise is only useless or harmful variety, but whether variety is harmful or helpful depends on its context. For example, mutations are sources of new genomic variety in a population of organisms and may be either harmful or beneficial to that population (or its individuals), depending on the environment.

a

Figure 25 Tetrad of problem solving, p. 146

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NOTES

Alternatively, the effects of the disturbance can be countered after they arise, but regulation may take hold only after a lag, making control difficult, even 45 unstable.

45. Feedback control Feedback control is error-controlled regulation (closed-loop control) as opposed to the cause-controlled regulation (openloop control) that is the subject of the Law of Requisite Variety (the previous note). Error-controlled regulation (feedback control) is shown in Figure 65. As in Figure 64, solid lines are causal (matter-energy) influences; the dotted line is informational flow. The regulator, R, receives information about the state of the essential variable, not about the disturbance, and acts to counter the effect of D on E, after this effect has already taken place. Figure 65 Error-controlled (negative feedback) regulation

R

E

system

D environment

Error-controlled regulation is control by negative feedback, a which reduces deviations between ideal and actual values of the controlled (essential) variable(s). For example, a thermostat takes ideal and actual temperatures as inputs and directs an air conditioner/furnace to reduce the ideal-actual disparity by changing the actual temperature. This is diagrammed in Figure 66. In terms of the problem-solving tetrad, b actual and ideal temperatures are ground and goal, the thermostat provides direction, and the air conditioner/furnace is the instrument. a b

Note #36 Stability, p. 373 Figure 25 Tetrad of problem solving, p. 146

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Figure 66 Thermostat feedback control system The thermostat takes a difference between ideal (dotted, norm) and actual temperatures (dashed, information), and sends a signal to the furnace or air conditioner, which has an effect (solid, matter-energy) on the actual temperature.

Tideal

Tactual

furnace, a/c

thermostat

Control via negative feedback can stabilize the system against disturbances, but under some conditions it can itself cause instability, if the amplification and time delay (lag) of the feedback are not properly set. (Amplification is the instrument’s magnitude of action; time delay is how long this action takes to affect the controlled variable.) With proper amplification and delay, control can achieve monotonic convergence, as in Figure 67(a), but more commonly there is overshoot and oscillation, which eventually converges on the ideal, as in Figure 67(b). Stability and reaching the ideal are, however, not guaranteed. Although negative feedback by definition initially reduces the deviation between actual and ideal, over time deviation might increase rather than decrease, as in Figure 67(c). Note that errorcontrolled regulation necessarily always lags the effect of the disturbance. Like cause-controlled regulation, it also incurs a cost (Hardin 1963). Figure 67 Modes of negative feedback

(a)

(b)

(c)

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Figure 67 applies to an error-controlled system provided with an explicit ideal, e.g., Tideal in Figure 66, shown in the figure as a dotted line, but the behaviors shown in Figure 67 (as well as undamped oscillation intermediate between (b) and (c)) can also occur in an uncontrolled system, a where there is no explicit ideal set-point. Norbert Wiener, one of the founders of cybernetics and a pioneer in the theory of feedback control systems, argued that the phenomenon of feedback control was found not only in technological artifacts and in physiological systems but also in social systems, and hoped that improved insights into the laws of feedback control would yield greater understanding of failures of control in such systems. Deutsch (1966), for example, made use of these ideas in The Nerves of Government. Wiener thought that feedback control also gave a scientific explanation to the phenomenon of purposefulness. It should be plain from discussion above that cause-control regulation is another type of purposefulness; Ashby (1952, 1956) also analyzed the still simpler control mechanism of trial and error which he called “ultrastability” or “hunt and stick regulation.” All these mechanisms clearly describe only the simplest forms of purposefulness; they do not adequately model the purposefulness that occurs in higher organisms (Jonas 1966), in the terminology of this book – in systems that have modeling subsystems. Such systems are the subject of 7.1.8 Cognition.

a

See the discussion of controlled and uncontrolled systems in Note #88 Hierarchies and networks, p. 446.

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7.1.5 Identity Notes:

page

46 Information (and matter-energy, utility) 47 Autopoiesis 48 Algorithmic information 49 Genotype and phenotype 50 Internal vs. external identity 51 Paradoxes of autonomy 52 Dangers of filtering out noise 53 Boundary subsystem

389 393 395 395 398 399 400 401

Persistence is a precondition for identity. The system 47 may have an informational domain that governs self48 49 construction through the specification of process. The invariant core of this domain is the organizing principle of the system, its structural identity. But identity is not simply invariance, since the organizing principle may provide for plasticity. Structural identity 49 and the environment determine the system’s nature.

46. Information (and matter-energy, utility) The category of information supplements the categories of matter and energy a as basic for the analysis of concrete systems. b Information is carried on markers of energy or matter but is not itself material. From another perspective one might say that an entity or process has material, energetic, and informational aspects. For example, a stretch of DNA under the aspect of information is genetic memory that specifies a particular protein. Under the aspect of matter, it is a macromolecule synthesized from nucleotide building blocks. Under the aspect of energy, it embodies chemical energy, which could be used as an energy source. Another example: ATP, the a b

See also 3.2.1 Matter, energy, and information, p. 88 3.1.2 Concrete, abstracted, and conceptual systems, p. 85

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main energy currency in cells, is also used as a matter building block in the making of DNA, and contains one of the four informational DNA coding elements (A,T,G,C); which aspect is salient depends on the interactions the molecule has in some particular context, i.e., on its function. This is from an ontological perspective; from an epistemological perspective, the salient aspect depends on the observer. Within economic systems, one can likewise distinguish between activities focused on the processing or distribution of materials (e.g., mining, construction, transportation) or on energy production (e.g., oil extraction and refining, hydroelectric power generation, networks of electric power distribution), and those which are informational in function (e.g., telecommunications, the media, the financial system). Within individual economic organizations, e.g., those engaged in manufacturing, the same dichotomy exists between the production processes per se, which involve matter-energy transformations, and their management and coordination which occur at the informational levels in the organization. Information is related to distinction a in that, for Bateson (1979), information is “news of difference”; more precisely, “news of difference that makes a difference.” Defining information in this way privileges similarity, treating it as the default expectation, and only deviation from similarity as “news.” Since similarity (more precisely, sameness) in time is constancy, constancy would likewise be privileged over change. But change could be the default assumption (as it may be in some cultures), in which case constancy would constitute news. Symmetry would thus be restored to the dyads of similaritydifference and constancy-change. But if difference or change is the default assumption, how much or what kind of difference or change is assumed requires specification, while if similarity or constancy is the default assumption, no additional specification is needed. Similarity and constancy are thus more natural as the a

Note #21 Distinction, p. 344

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unmarked terms, which accounts for them usually defining the null hypothesis in statistics. Bateson’s additional requirement that difference “make a difference,” introduces pragmatic considerations which supplement the purely syntactic aspect of difference. Shannon’s theory only concerned syntactic information, defined by the bit pattern of an uninterpreted message (or measurement or pattern). Semantic information, based on syntactic information, is the meaning of the message. Pragmatic information, based on syntactic and semantic information, is the practical import of the message. This hierarchy, proposed by Weaver (Shannon and Weaver 1949) can be displayed on the structure-function double cone diagram by correlating syntactic and pragmatic information with structure (inner aspect of the message) and function (outer aspect of the message), respectively, tied together by semantic information, as shown in Figure 68. One could also reverse this hierarchy and consider pragmatic information as its foundation and syntactic information as its highest level. a Figure 68 Syntactic, semantic, pragmatic information Numbers are levels; “1” is the foundation of this hierarchy.

3 Pragmatic function 2 Semantic

1 Syntactic structure Syntactic and semantic information correlate with what the semiotician Saussure (Chandler 2002) called “signifier” and a

Note #101 Pragmatic, semantic, syntactic, p. 468

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“signified.” A “sign” maps a signifier onto a signified; For equivalently, the signifier codes for the signified. a Saussure, in human language this mapping is arbitrary. Human language is complex, but the genetic language, which resembles it in some respects, is simpler and well understood, so one can ask what explains the signifier-signified mappings in this molecular language. The genetic language maps nucleotide triplets onto amino acids; for example, the triplet UUU (U = uracil) is a signifier whose signified is the amino acid, phenylalanine. Pattee’s work (Pattee and Rączaszek-Leonardi 2012) on how symbol systems interact with physical laws has emphasized the fact that physical processes are involved in generating this mapping diachronically (evolutionarily) and instantiating it synchronically. Concretely, it is the protein synthetic translational machinery, whose key elements are the tRNA adaptors and their activating enzymes that do the synchronic work. So not only are the nucleotide triplets and their coded-for amino acids instantiated in matter-energy but there is also a mediating dynamic mechanism necessary for this mapping to function. The nucleotide triplet sequence is syntactic information; the amino acid sequence and the resulting folded protein is semantic information; the catalytic function of the folded protein is pragmatic information. The entire protein synthetic machinery must also be viewed from a diachronic perspective b, i.e., the history of the origin of life and of evolution, which requires the categories of matter, energy, and information to be

a

Peirce (Chandler 2002), in his semiotics, proposed a triadic icon-indexsymbol distinction among signs. An icon bears a physical resemblance to its referent, an index often implies a causal connection to it, and a symbol is arbitrarily associated with it. Icon, index, and symbol might be considered matter, energy, and information subcategories of the sign, viewed as information. Or, one might map icon-index-symbol onto semanticpragmatic-syntactic information. b 3.5 Structure, function, and history, p. 109

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supplemented with the fourth category of utility a (fitness). Matter-energy, via the emergence of utility in the phenomenon of life, comes to instantiate information; specifically, the symbol system of the genetic language. This is depicted in Figure 69(a). The matter-energy-information-utility sequence conforms to a previously noted hierarchical order, b where the (+), (-), (= ) labels indicate active, passive, and mediating roles. c Figure 69(b) shows that the connection between the syntactic signifier and semantic signified depends on pragmatic information that confers evolutionary fitness. Figure 69 Information from matter-energy via utility

utility (+) (b)

(a)

pragmatic

information (=) matter-energy (−)

semantic syntactic

47. Autopoiesis Closedness and openness are central to “autopoiesis” (Maturana and Varela 1980), which means “self-making,” as opposed to “allopoiesis,” which means being made by something other than self. Simple autopoietic systems are organizationally and informationally closed but materially open, as shown in Figure 70(a). (The study of such systems was Ashby’s (1976) definition of cybernetics.) Closedness and openness apply to different aspects of the system; in living systems, to the genetic order and matter-energy metabolism, respectively. Self-making refers both to internal order and distinction from environment: via autopoiesis the internal order maintains itself and also the boundary that sets the system apart from the environment. a

3.2.2 Utility, p. 93; see also Note #54 Utility, p. 403, in the section on Agency b Figure 16 Utility as a 4th fundamental category, p. 94 c Figure 15 Triad of matter, energy, and information, p. 88

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Order (organization) here is prior to distinction from the environment since creation of the boundary is a consequence of the internal order. Figure 70 Autopoiesis; additional information input In autopoiesis the system has two “stories” (in a building sense): a matter/energy story and an information story (this is a conceptual, not a spatial, distinction). The information story (which determines internal organization) is closed; the matterenergy story is open. The solid hemicircular arrow going up represents the material instantiation of information; the dashed hemicircular arrow going down represents informational control of metabolism. Not shown is the material instantiation – under informational control – of the boundary. information

information matterenergy

matter-energy

(a)

(b)

Closure to information refers only to information that determines structure. The informational organizing principle shown in Figure 70(a) is purely internal (this type of closure fails in viral parasitism); systems can be open, however, to environmental information relevant to behavior. a Figure 70(b) shows this openness to information in the upper story, depicts both stories as hierarchically organized, and indicates that the input of matter-energy and information provides only the lowest level of each hierarchy, the higher levels of which must be internally constructed.

a

Cognition (1.1.8, p. 20, and 7.1.8, p. 461)

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48. Algorithmic information Information can specify not only states but also processes. In Shannon’s theory, information, a concept closely related to order, is a reduction of uncertainty of a state description. It is complemented by the theory of algorithmic information of Kolmogorov (1965) and Chaitin (1975) which defines the algorithmic information content of a state indirectly – in terms of the smallest process (algorithm) needed to generate this state. An algorithm generalizes the idea of a dynamic relation. a The algorithmic information of some state is the size (e.g., in bits) of the smallest program (on a reference computer) that will produce this state. (How long it takes this minimal program to do this, called the logical depth b of the state, is not of concern here.) Similarly, any process description has some minimal encoding whose length is its algorithmic information. The significance of the difference between Shannon information and algorithmic information is that a quite complicated pattern might be produced by some simple recursive rule (e.g., a cellular automaton mapping) acting on a simple initial state, so that the program which stored the rule, the initial state, and a specification of how long to run, might be simpler (require many fewer bits) than the Shannon information of the pattern itself. Although a process description is also a state description (e.g., a recipe is also a text; in the LISP computer language, strings are both operators and operands) and might embody constraint, the minimal program is by definition random, since if it were not random, it could be recoded to take advantage of its redundancy and make it smaller. Only a random program is incompressible.

49. Genotype and phenotype Structural identity is to structure as essence is to appearance. To use a biological metaphor, some systems have “genotypes,” i.e., a b

Note #10 Dynamic relation, p. 327 Note #86 Complexity, p. 441

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points of concentration of an invariant order that define – both provide and limit – adaptive possibilities. (In contrast, populations of organisms adapt by continual change of gene pools and are thus untethered and free to evolve.) “Genotype” is distinguished from “phenotype,” the latter being the order in the system that is not fixed and is the joint consequence of both genotype and environment. The system-environment dyad thus expands into the genotype-phenotype-environment triad, shown in Figure 71. Figure 71 Phenotype determined by genotype, environment

P

G system

EP

E

environment (a)

G

GEP

E

G

P

E

P (b)

(c)

The simplest way that genotype and environment can determine phenotype is shown in Figure 71(a) as two separate directed dyadic relations. This conception ignores interaction effects between genotype and environment and incorrectly suggests that determination of phenotype can always be partitioned into separable dyadic interactions (hence the incorrect assumption that human traits can be partitioned into independent nature and nurture components.) What is present in general is a triadic interaction effect, which cannot be partitioned, shown in Figure 71(b) where the relation is displayed as a box. The distinction between genotype and phenotype can be described with the spatial metaphor of center and periphery, as shown in Figure 71(c). Note the similar depiction a of a regulator protecting essential variables against disturbances. “Genotype” and “phenotype” are here generalized beyond their biological meanings. Genotype is an organizing principle under the category of identity. It is the algorithmic information in the a

Figure 64 Cause-controlled (feedforward) regulation (b), p. 384

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information story of autopoiesis. In the terminology of linguistics, genotype is deep structure and phenotype is surface structure. This distinction echoes the philosophical difference between primary and secondary qualities, between essence and appearance. Genotype is essence. Internal identity has priority over external identity for systems that have an internal essence (not all do). This is one reason why the closed systems view is needed to supplement the open systems view which grants internal identity and external identity equal status. In the open systems view, what a system is is constituted by both inside and outside, structure and function, and structural identity is not necessarily privileged. But from a closed system view structural identity is privileged and is the organizing principle of the system. In this latter view, function is what a system does, not what it is. a For complex systems, this latter view is more appropriate. Even though the open systems view is more encompassing, the closed systems view is a necessary complement to it. Social and cultural systems differ in the degree to which they have a part that functions as a genotype. Some possess a core identity that reflects or defines their degree of closure. For example, religions have canonical texts and official dogmas; political systems have constitutions. The parallelism is limited since socio-cultural systems do not reproduce, but see Boulding's (1980) view of these as multi-sexual. Mathematically, the genotype-phenotype distinction can be generalized as the difference between algorithmic information and the computation it generates, or as the difference between a dynamic law and the actual dynamics (trajectories in state space) that it produces, where the parameters of the dynamic law define the system’s environment.

a

See the Bennett quote on p. 111.

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If the system is embedded in an organized environment, a second identity is imposed from without. For the system, the internal has priority; for the environment, the system’s external identity has priority. Identity of structure and identity of function are never exactly the 50 same.

50. Internal vs. external identity Two ways that identity of structure and of function might differ are shown in Figure 72, a which depicts three systems organized by an external relation. In s1, structure and function agree in attribute A1, so identity of structure and identity of function are the same. However, s2 shows an attribute upwardly emergent from internal structure that differs in value (arrow direction) from the value called for by the relation. Or, the attribute that is externally organized may not be the attribute that is salient for the system; this is the case for s3. The relation organizes A, on which structure and function agree, but B (arbitrarily chosen) is salient and defines the structural identity for s3. Figure 72 Inconsistent internal and external identity Salience of an attribute is shown by a bold and larger font.

A1

B1 s1

A2

B2 s2

A3

B3 s3

The tension that arises from embedding a system as an element of a larger system echoes the tension between element and relation. An element joins attributes from below. A relation joins attributes from above.

a

Figure 72 is an adaptation from earlier Figure 47 Inconsistency involving attributes and relations, p. 313

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If the system is a member of a population of similar systems, its generic identity is supplemented by identity specific to itself. Neither identity that is universal nor identity that is unique has intrinsic priority. The identity of the population is dispersed among its constituents. Closedness and openness are temporal as well as spatial. Closedness is the residue of the past. Openness is contact with the present. Being determined by the internal past is inertia; by the external present, drift; by past or present at random, incoherence. What is necessary for the system is an active and balanced synthesis of the legacy of the past and the imperative of 51 the present, a synthesis not easily achieved. Being active requires information and energy. Balance is precarious. Synthesis requires a principle neither internal nor external.

51. Paradoxes of autonomy This closely paraphrases the analysis of Deutsch (1966) of political systems: Is there perhaps a paradox in the nature of autonomy, in the self-steering and the self-rule of each individual personality, as well as of each autonomous human organization? Autonomy is impossible without openness to communication from the outside world; but at the same time autonomy is impossible unless the incoming flow of external information is overridden to a significant extent by internal memories and preferences. What can go wrong in this precarious pursuit of an ever-changing balance, and how great is the probability of the eventual failure and selfdestruction of every autonomous organization? Deutsch analyzes various modes of failure of autonomy. Change must at times be resisted,52 at times embraced. Viability requires openness to the

400

NOTES

outside, yet internal patterns must have some priority over external influences. No general principle exists for joining past and present, interior and exterior, to secure autonomy. The prerequisites for change undermine it. Multiplicity is needed for change but harbors resistance to the new. Unity is needed for change, but the new cannot take hold of what is unitary.

52. Dangers of filtering out noise Milsum (1968) conceptualizes this dilemma with a signalprocessing analogy: The tendency ... to resist change is not in itself necessarily unhealthy since this procedure represents a reasonable way in which to filter out the high frequency “noise” for which no change in the rules is really required. On the other hand, ... [a] non-trivial problem in this respect is that of judging how to match the desirable time constant of the filter to the time constant of “DC” or permanent change in the process, so that substantial changes in the ‘signal’ can be adjusted for as rapidly as desirable, while high-frequency noise is filtered out… [In] order to predict this effectively, an observer of godly powers is required. Closedness may be provided for by subsystems that distinguish between what should be taken in and what should be kept out, between what conforms to the identity of the system and what is foreign to it. These functions may be performed by the boundary, which regulates transactions across the system-environment 53 interface. Or there may exist a subsystem that distinguishes self from non-self and counters deviations from identity. By such provisions for closedness, the system protects identity but acquires new vulnerabilities.

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Failure of these subsystems leaves the system defenseless; their hypertrophy engenders rigidity; their errors of identification destroy order.

53. Boundary subsystem The boundary a of a system is often not a subjective distinction or a mere interface but an active and critical subsystem that creates or maintains the system-environment difference. In cells, the boundary subsystem – the cell membrane – regulates, as specified by the genetic order, what molecules enter or leave the cell. Organisms may have boundary subsystems, such as skin, that perform many essential input/output functions. Social and cultural systems often have boundary subsystems critical for self-definition. Political systems have borders, often well defended. Autopoietic systems b generate and maintain their boundaries; such systems are typically open, self-organizing, and dissipative. c James G. Miller (1978) discusses boundary subsystems in a synchronic analysis of functional subsystems commonly found in “living systems” at different levels of organization. He classifies subsystems into three groups: those that process matter-energy, those that process information, and those critical subsystems, such as the boundary and a subsystem concerned with self-replication, that process both. Miller's living systems theory includes an additional subsystem, which performs the functions of internal security. Organisms have immune systems that battle invading microorganisms; social systems have components that counter internal threats.

a

Note #24 Boundary, p. 350 Note #47 Autopoiesis, p. 393 c Note #42 Dissipative systems, p. 381 b

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7.1.6 Agency Notes: 54 Utility 55 Environmental types 56 Decision theory 57 Chaos and long-term forecasting 58 Nature resists 59 Multiplication of effects 60 Externalities 61 Counterintuitive effects 62 Weakening by strengthening 63 No terminus 64 Discounting the future 65 Binding the future and sunk costs 66 Pareto-optimality 67 Multiple objectives 68 Aggregating preferences 69 Computational complexity 70 Optimization 71 Optimality, stability, and resilience 72 Purposeful action as a tetrad 73 Assertion, integration, exchange 74 Eating and being eaten 75 Game theory 76 Coalition instability 77 Discerning which game is being played 78 Prisoner’s Dilemma 79 Chicken 80 Symmetry or altruism may be harmful 81 Sharing elements 82 Heteronomy 83 Recruitment and predation 84 Embeddedness as a solution to the PD 85 Turbulent fields

page 403 404 406 410 411 411 412 413 416 417 417 417 418 419 420 422 423 424 426 427 428 429 431 432 433 435 436 437 438 439 440 440

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Identity is made secure through agency. The system must be active towards an environment 54 that presents both utility and hazard. The environment is not spatially uniform or temporally invariant. There is texture in its distribution of resources and noxiants. The environment may include a network of other systems. It may constitute a more encompassing order in which the system is 55 Texture in the environment embedded. exposes the system to the vagaries of chance. Presence of other systems enables competition and conflict. Being embedded in a larger whole compromises autonomy.

54. Utility Utility a is a fourth basic scientific category, after matter, energy, and information. Every action of a concrete system has matter, energy, and information aspects, and the addition of utility to this triad transforms action into agency. Utility quantifies how much a state of affairs promotes the “interests” of a system. It is specific to living systems (and systems that embed living systems), since non-living systems do not have interests, and is central to decision and game theory (von Neumann and Morgenstern 1944). Utility, like information, has no physical units. Utility is cardinal (quantitative) or ordinal (relative preference); if cardinal, it is usually interval, which means that if all utilities are linearly transformed (U′ = a U + b), agents will not act differently (note: U is utility, not uncertainty). Utility is often assumed to be one-dimensional. Where it is multi-dimensional, reduction to one dimension requires inter-agent or inter-attribute comparisons to put utility components on a single scale.

a

See also 3.2.2 Utility, p. 93

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55. Environmental types Emery and Trist (1965) suggest a taxonomy of four environmental types that pose different adaptive challenges for the system; these are listed and illustrated below. Essay simplifies this scheme with a three-fold framework (Figure 73). •

Type I: the environment E has goods and noxiants randomly distributed; in such an environment an agent S can respond only randomly, using trial and error: Figure 73(a).

•

Type II: the environment E has goods and/or noxiants that are clustered; in response an agent must optimize or satisfice (explained below): Figure 73(a).

•

Type III: the environment has clustered goods and/or noxiants plus other agents S'; an agent cannot simply optimize its response relative to a passive environment, but must take into account the possible behaviors of other agents: Figure 73(b).

•

Type IV: the environment is still more complex and can exhibit major instability and turbulence; adaptation requires the stabilization of the environment, a task beyond the means of any individual agent: Figure 73(c).

In (a) the environment merely has “texture” (the word is borrowed from the Emery and Trist paper), i.e., is an unstructured and passive field in which the system is located. In game theory, the system (agent) faces a “game against nature,” also known as a decision under risk or uncertainty; for Elster (1979), such environments require “parametric” rationality, i.e., optimization. In a human context, the system-environment relationship is what Buber (1937) called an “I-It” relationship.

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Figure 73 Environmental types E represents environmental resources/noxiants. Emery and Trist environmental Types I and II are shown by (a); Type III, where the environment of S includes E and another agent S', by (b); and Type IV, in which S and two other agents are organized into a higher-level agent, by (c). a Seeing system as center, (a) is mono-centric, (b) is multi-centric, and (c) is supra-centric.

S

S

E (a)

S

E (b)

S′

S

S′

S′′

E

(c)

In (b) other agents are present. This is the subject of the theory of two- and many-player games, either zero- or non-zero-sum; for Elster, such environments require “strategic” rationality. In (b), instead of a triadic SES′ relation, three dyadic relations are depicted to highlight the difference between this environmental type and (c). In a human context, the S-E relation would be what Buber called an “I-it” relationship; the S-S′ relation might or might not be an “I-Thou” relationship. In (c) the environment is structured and constitutes a higherlevel suprasystem, S, consisting of three systems sharing a background context, E; this is represented as a tetradic relation. Emery and Trist emphasize the turbulence of S, but here structure is its salient property. This type of environment is partially addressed in game theory by coalition theory, b where analysis faces difficulties of a different sort than exist in simpler but still problematic two- or n-equivalent-person non-zero-sum games. Coalition theory analyzes the strengths of possible coalitions and the likely distribution of utility among members a

See (a) Texture 1.6.1 and 7.6.1, pp. 13, 406; (b) Other Systems 1.6.2 and 7.6.2, pp. 15, 427; (c) Embeddedness 1.6.3 and 7.6.3, pp. 17, 437 b Note #76 Coalition instability, p. 431

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of winning coalitions. If the game is non-zero-sum, coalition analysis is even more difficult. In a human context, to extend Buber’s terminology, this type of environment calls for an “IWe” relationship. In terms of Koestler’s (1978) idea of self-assertion versus integration, a (a), the realm of 7.1.6.1 Texture, calls for assertion, which is unproblematic. (c), the realm of 6.3 Embeddedness, requires integration, in tension with assertion. (b), the realm of 6.2 Other Systems, can evoke either tendency, or perhaps a third, exchange, which also occurs in the other realms but is salient in interactions with peers. 7.1.6.1 Texture Variability of the environment calls for optimization by the system, but requirements 56 for optimal action are never fully met. No algorithm exists for the specification and evaluation of all actions open to the system in the present or future. The environment is unbounded and its potential impacts on the system cannot all be assessed.

56. Decision theory Decision theory concerns rational action under risk, uncertainty, or conflict. In the standard decision-theoretic model for a decision under either risk or uncertainty, also referred to as a “game against nature,” the system (agent) has available to it a set of actions, A, and implements one of them. The environment (“nature”) is in one of a set of states, N, the probabilities of which are either known – this is called “risk” – or unknown – this is called “uncertainty.” If objective probabilities are unknown, subjective probabilities may be used, or unbiased (equal) probabilities may be assumed. In decision theory, the outcome, O, of an action given a state of nature is assumed to be a

Note #31 Assertion vs. integration, p. 363

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known: O(A,N). (Here, “O” does not mean system output.) Different outcomes have different utilities to the system: U(O). Putting U(O) and O(A,N) together gives U(A,N), utility as a function of actions by the system and the states of the environment. (Mathematically, this is a mapping A ⊗ N → O → U.) If probabilities of states of nature are known, this gives Table 10 for two actions and two states of nature. Table 10 Decision under risk If the agent does a1 and nature is in state n1, with probability p(n1), the agent gets U11, etc.

a1 a2

n1 U11 U21 p1

n2 U12 U22 p2

Utilities are either cardinal, i.e., quantitative and usually interval, or ordinal, i.e., ordered preferences. If they are cardinal and the probabilities of the states of nature are known, the expected utility of any action, ai, is the expected utility of that action averaged over the states of nature, U(ai) = ∑ Uij pj. The action with maximum expected utility is considered the rational choice. When probabilities are unavailable, one assumes maximum uncertainty and considers all probabilities to be equal, or one uses a decision rule, e.g., maximin or maximax, that does not require probabilities. The pure maximin rule chooses “the best of the worst,” the action whose worst outcome, over all possible states of nature, is better than the worst outcome of any other action, over all possible states of nature. In the above table, this rule selects a1 if the worst of U11 and U12 is better than the worst of U21 and U22 and selects a2 if the opposite is true. This rule might be called pessimistic or security-based or precautionary. (Sometimes the highest security level can be obtained only by using a mixed maximin where multiple actions are chosen with specific probabilities.) Sometimes even when probabilities of states of nature are available, one might still use

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maximin instead of maximum expected utility, if probabilities are of dubious relevance because decision events are infrequent and bad outcomes are very adverse. The maximax decision rule optimistically selects the action whose best possible outcome is better than the best outcomes for the other actions. Weighted mixtures of maximin and maximax rules or maximin and maximum expected value are possible. There are also decision rules that minimize the regret of a decision-maker in not choosing some other action. Instead of using maximum expected utility, maximin, maximax, or minimax regret, the system might “satisfice” (Simon 1981), i.e., adopt the first action encountered that assures a result above some acceptable utility. Satisficing might be considered optimizing when the cost of search is taken into account. In decisions either under risk or uncertainty, the system and nature act simultaneously, so the system acts without knowing the state of nature. One could alternatively assume that system and nature act sequentially. The simplest such game occurs when nature acts first and the system acts second and has perfect information about nature’s state. In such “decision under certainty,” for any state of nature, the system will choose the action that maximizes utility. The Law of Requisite Variety a models such situations. E(D,R) there is O(A,N) here, i.e., the essential variable state E is outcome O, the regulator state R is action A, and the disturbance D is state of nature N. Simple (instinctual) evolutionary adaptation to different environments is a decision problem of this sort; using the LRV, Fletcher et al. (1998) show that adapting populations map environmental diversity (different N states) to genomic diversity (different A responses). Essay discusses limitations to this decision-theoretic model; these are summarized in the following list (Lovell 1995). (“Unknown” includes partially or incorrectly known.) a

Note #44 Law of Requisite Variety, p. 384

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•

The full set of possible actions, A, may be unknown.

•

The full set of possible states of nature, N, may be unknown.

•

The probabilities of the states of nature may be unknown.

•

The consequences of actions given the states of nature, O(A,N), may be unknown.

•

The utilities of all outcomes, U(O), may be unknown.

The above describes only the simplest case, where for a given action and known state of nature, there is one outcome, which is known or predictable. In general, however, there may be a sequence of actions, which when coupled with the sequence of states of nature, N(t1), N(t2), N(t3), etc., gives a sequence of outcomes, O(t1), O(t2), O(t3), etc., and a sequence of utilities, U(t1), U(t2), U(t3), etc. These utilities must be integrated into a single value, requiring a properly chosen discount factor. a Such diachronic multiplicity is not the only source of complexity. Utility is usually not one-dimensional. A single outcome typically has multiple attributes, which have their own utilities, U1(t), U2(t), U3(t), etc. Only if attribute utilities are commensurable can they be aggregated with suitable weights into a single net utility value. Moreover, even if an outcome has one attribute, if assessed by multiple agents the assessments must also be integrated, which is analogous to integrating utilities of multiple attributes. These factors add additional complications to the decision-theoretic model:

a

•

Predicting future states of nature may be difficult or impossible.

•

Predicting future outcomes of actions and states of nature may be difficult or impossible.

Note #63 No terminus, p. 417

410

NOTES

•

The proper discount factor for integrating future payoffs is unknown.

•

The proper weights to integrate utilities of different attributes are unknown.

•

The proper weights to integrate multiple decisionmakers are unknown. Even within a restricted context, the possible states of the environment and their probabilities may not be known even in the present, and forecasting future states is at best 57 reliable only in the near term. One action precludes another, and the joint result of system action and environmental state may be unpredictable.

57. Chaos and long-term forecasting If the sequence of outcomes, O(t1), O(t2), O(t3), etc., goes beyond the near term, forecasting is precluded by chaos, a in which there is extreme sensitivity to initial conditions. Chaos is the rule and not the exception for nonlinear dynamics and most dynamics are nonlinear. Unpredictability is exemplified by the “butterfly effect” (not to be confused with the butterfly catastrophe), in which the flapping of the wings of a distant butterfly may produce significant perturbations on local weather conditions. Note that prediction is impossible even if one has knowledge of the exact form of the dynamic equations, because of unavoidable uncertainty about initial conditions. Moreover, one rarely knows the dynamic equations, since deducing them from observations is difficult, again because of chaos. Uncertainties about future states of nature, initial conditions, the form of relevant dynamic equations, and the like are all “known unknowns.” Bigger contributors to the impossibility of forecasting are the “unknown unknowns.” a

Note #17 Chaos, p. 338

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No plan survives contact with reality. Every action of a system is resisted by its 58 environment. The nature of this resistance cannot fully be foreseen.

58. Nature resists The sentence above is a paraphrase of “No plan survives contact with the enemy” (von Molke, ca 1892). Resistance comes from other agents in the environment or from embeddedness in a larger system. a Such resistance may be active b, but even when the environment is undifferentiated and passive, effects of action are usually unpredictable. Means can also never be precisely calibrated to ends. “Resistance,” with its connotation of active rather than passive opposition, is used here instead of “intractability” because its vividness suggests the fact that the environment is larger and more powerful than the system. 59

No action generates only one effect. There 60 Actions have are always externalities. unanticipated consequences, even 61 What should counterintuitive effects. suppress perversely stimulates; what should stimulate unexpectedly suppresses.

59. Multiplication of effects As Garrett Hardin (1963) observes, “It is impossible to do only one thing.” All actions have “side-effects.” Herbert Spencer (1890) makes a similar observation in his “Law of Multiplication of Effects. c” However, while one cannot do only one thing if action is simple, multiplicity of effects can be reduced by complexity of means. For example, thousands of atoms precisely arranged in space allow an enzyme to catalyze a specific reaction. a

Note #55 Environmental types, p. 404 Note #34 Active vs. passive, p. 368 c 3.4 Aspects of complexity and holism, p. 100 b

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NOTES

60. Externalities Given that effects are multiple, some will likely affect other systems. Externalities are utility consequences to other systems that result from an agent’s action. Positive externalities are beneficial and negative externalities are harmful (Figure 74). Speaking normatively, every system is responsible for the negative externalities caused by its actions. Figure 74 Externalities X and Y represent agents and their actions. Here, signs indicate conferred positive or negative utilities; this is a different use of a signed digraph than uses discussed earlier. a X’s action benefits itself via outcome (effect) O1 but harms Y, a negative externality, via outcome O2; Y’s action, aside from benefiting itself, also benefits X, a positive externality.

O1 +

X

O2 –

Y

+

+

The word “externalities” is also used to refer to utility considerations that do not enter into decision-making of an agent. The negative externality to Y due to X’s action could be prevented by making the external internal by enlarging the boundary b of X’s decision-making model (Figure 75). Even though O2 does not directly impact the system, it may adversely affect it indirectly or over the long term. This highlights the importance of closing the circle c (Commoner 1971) in decisionmaking and problem-solving.

a

Note #7 Networks, p. 317 Note #24 Boundary, p. 350 c Note #157 Closing the circle, p. 564 b

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Figure 75 Internalizing the external in decisions The ovals encompass what is included in a decision-making model. In (a), action X, based on state of nature N, is expected to cause O1; since O1 has positive utility, this action is favored (+). O2 is not considered. The more complete model of (b) adds the fact that X also causes O2 which harms Y (not shown). This negative externality can be avoided if O2 inhibits X. (Signs in these digraphs are positive or negative feedbacks.)

+

+ N (a)

X

O2

X

N

O1 (b)

–

O1 O2

61. Counterintuitive effects The decision-making model may not only ignore externalities; it may inaccurately depict the expected effects of action on the system itself. Actions cause unintended consequences; among these consequences are counterintuitive effects, outcomes that are even diametrically opposite to what was planned or expected. To quote Edmund Burke (1790), “Very plausible schemes, with very pleasing commencements, have often shameful and lamentable conclusions.” Such effects are more surprising and troubling than merely unforeseen consequences that occur in addition to intended results. Several explanations for counterintuitive effects can be imagined, as follows: (1) indirect effects in causal paths; (2) negative feedback overshoot; nonlinear dynamic effects; (3) emergent collective (macroscopic) effects.

414

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Environments which contain other systems are treated in the next section. In such contexts, the problem of counterintuitive effects is more severe. (1) A general framework for analyzing the production of counterintuitive effects is causal (path) analysis (Davis 1985) which makes use of signed and directed graphs. a For example, a factor, X, may have a positive direct effect on desired outcome O1. However, X may have a negative effect on O1 via an indirect path involving other variables, as shown in Figure 76, and this indirect path may be stronger than the direct path. One can never do only one thing, b and the multiplicity of effects can produce counterintuitive results. This is analogous to the fact, as behaviorists have noted, that intervention in systems sometimes reinforces through other pathways (e.g., by positive feedback) behavior intended to be countered (by negative feedback). The XYO pathway might be viewed as an unpredictable but not surprising “resistance” to X. c Figure 76 Indirect effects can cause counterintuitive results + O1 X

+

Y

–

Failure to include in the decision-making model all relevant indirect effects and the full relevant environment of the system is a common incompleteness. Full knowledge of all the relevant factors is never available; and if it were, the decision-making model would be too inclusive to be practical. Because of such specification error (model incompleteness), the possibility of counterintuitive effects is inescapable for systems beyond some minimal complexity.

a

Note #7 Networks, p. 317 Note #59 Multiplication of effects, p. 411 c Note #58 Nature resists, p. 411 b

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(2) Counterintuitive effects can occur when negative feedback generates overshoot. a What can be counterintuitive is the increasing deviation of a variable from desired values despite the negative feedback. Even when restoring forces move a system in a desired direction, these forces must have the appropriate magnitude and time delay to avoid overshoot. (In social systems, overshoot is the rule, not the exception, because of mass psychology and organizational inertia.) For complex nonlinear systems, intuitions about the likely effects of interventions are difficult to gain, and the danger of incomplete analysis more severe. Forrester's (1971) discussion of counterintuitive effects is an early exploration of this problem and the system dynamics methodology. A famous dynamic system example of a counterintuitive effect is the “paradox of enrichment” (Rosenzweig 1971), in which enriching an ecosystem causes it to collapse. (3) Effects may be counterintuitive because of the scale of analysis. Analysis may be focused on individual (“microscopic”) decisions and actions, while the emergent b collective (“macroscopic”) effect of multiple such actions may differ from the result expected at the individual level. This relates to the discussion above about direct versus indirect and single versus multiple paths and to problems of boundary definition. c Focusing on one or a small number of paths is a microscopic view, as compared to analyzing the entire system, in its full complexity, which may exhibit surprising macroscopic effects. In hierarchical systems, interventions at one level may create a problem at another level. d There are many situations, whose paradoxical character is revealed by game theory, e where individual rationality leads to collective irrationality. f a

Note #45 Feedback control, p. 386 Note #32 Emergence, p. 363 c Note #24 Boundary, p. 350 d Hierarchies 1.1.7.2 and 7.1.7.2, pp. 19, 451 e Note #75 Game theory, p. 429 f Note #78 Prisoner’s Dilemma, p. 433 b

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Effective action may require the pursuit of 62 apparently undesirable ends.

62. Weakening by strengthening Advice on agency from the Tao Te Ching (a loose paraphrase of some translations): To shrink it, let it expand To weaken it, strengthen it To eliminate it, allow it to flourish To take, first give. If actions can have results opposite to what is intended, interventions that perturb the system in apparently undesirable directions might – also counterintuitively – be beneficial. One might call such interventions “homeopathic.” In homeopathic medicine, cures are sought in remedies that produce symptoms similar to those exhibited by the patient, while remedies in “allopathic” medicine often oppose symptoms. However, counterintuitive intervention is also used in mainstream medicine in the widespread practice of immunization, and this practice does not constitute evidence for homeopathy, since the effectiveness of immunization does not imply that treatment by similars will in general be advantageous. Moreover, the assertion of homeopathy that extreme dilutions make remedies more powerful is incompatible with scientific knowledge. However, immunization may be generalizable, and “homeopathic” interventions may succeed in a variety of other situations, and mild interventions may succeed more often than drastic ones. Some psychotherapeutic interventions utilize paradoxical interventions that may appear designed to worsen the presenting symptoms at least slightly (Watzlawick et al. 1974). There may well be many occasions, as the Taoists argue, where one can achieve a desired effect by pushing the system in a direction opposite to the desired effect.

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63

There is no terminus to the effects of action. Outcomes multiply into the future, and a final outcome never arrives. Even if initial effects are small, later effects can be large. Even were outcomes predictable and future utilities known, the relative weights that ought to be given to near- and far-term outcomes remain 64 For unrestricted action, the uncertain. 65 present must be free to bind the future, yet when the future arrives, action is restricted.

63. No terminus “We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere” (Emerson 1899)

64. Discounting the future Utilities at future times, U(t1), U(t2), …, may first be adjusted by a “discount factor” and then aggregated to obtain an equivalent present value Unet. The discount factor is an interest rate that goes backward in time. Starting from an expected utility value in the future, it indicates what current utility value would produce this future value when this interest rate is applied. The value of the discount factor is always somewhat arbitrary. If it is high, it favors actions biased by short-term considerations; if it is low it gives too much weight to future considerations that are really uncertain. The problem of choosing an appropriate discount factor to convert future to present utility is like the problem of deciding on the optimal liquidity for the resources of a system (Deutsch 1966).

65. Binding the future and sunk costs “Binding the future” means making decisions in the present that constrain actions in the future. The phrase refers to Ulysses ordering his men to disregard orders he may give them that may be (irrationally) influenced by hearing the song of the Sirens

418

NOTES

(Elster 1979). From one perspective, binding the future is irrational, since it does not allow decisions to be reassessed when new information becomes available. From another perspective, however, it is rational to compensate in advance for expected weakness of will. Also, the constant reassessment of past decisions may not be rational, since the unwillingness to commit to a long-term course of action may have adverse consequences. For example, the unwillingness or incapacity to make binding decisions indicates that an agent is untrustworthy, and other agents will act accordingly. Also, choice has costs, and having to constantly remake choices is as burdensome as the absence of choice is confining. Unwillingness to ignore “sunk costs” may also prohibit changing course. By standard notions of rationality, sunk costs should be irrelevant to decisions (Robertshaw 1978).” Yet just as it may be rational to bind the future, it may be rational to be bound by the past; else what does commitment mean? Moreover, optimization requires unity of purpose, but purpose is multiple and 66 inconsistent. Purposes conflict. Imperatives of structural identity differ from those of functional identity. Multiple objectives are usually incommensurable, but even when they have a common utility scale, arbitrariness 67 cannot be avoided. When utility is ordinal, no method exists to aggregate multiple preferences into a rational, decisive, and 68 equitable choice.

66. Pareto-optimality The existence of multiple purposes means that utility is not a unitary scalar but a multi-component vector. In Figure 31 below, U1 and U2 are utility values associated with purpose1 and purpose2. If having high utilities for both purposes are incompatible, one has to trade off one utility for another. This is

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the case along the line with negative slope in the figure, which bounds the (shaded) region of possible states. At every point on this line, the system is “Pareto-optimal,” meaning that no gain is possible in one utility without loss in the other. If the system state is at an interior point, however, U1 and U2 can both increase without any trade-off. Nearly all situations in which a system finds itself are not Pareto-optimal since the boundary is an infinitesimal portion of the feasible region. a Figure 31 Pareto-optimality (figure from Commentary) Points on the line with negative slope are Pareto-optimal; interior points (e.g., the dot) are not.

U2 • U1

67. Multiple objectives The existence of multiple objectives that are at least partially incompatible is a kind of inconsistency that is ubiquitous in the realm of agency. When decisions involve multiple attributes, neither ordinal nor cardinal (interval) utilities are fully satisfactory. Interval utilities are problematic in two ways (ordinal utilities are discussed in the next note). First, they are inherently difficult to define since they require consistent preferences among indefinitely many probabilistic lotteries (Hamburger 1979). Second, one cannot simultaneously optimize the utilities of multiple attributes unless they are merged onto a common scale; but conversion factors (which translate, e.g., lives into dollars) raise difficult moral issues and are always at least partially arbitrary. Multi-voter situations are similar to a

Another way of putting this is to say that most games are non-zero-sum, since for utilities of agents to sum up to the same constant for all agent actions is a priori improbable; see Note #75 Game theory, p. 429.

420

NOTES

multi-attribute decisions in that merging utilities of different voters requires interpersonal comparison of utilities. In alternative approaches to the multi-attribute problem, one utility may be optimized subject to the others as constraints; or, solutions may be restricted to the Pareto-optimal (PO) subset. But for nonlinear systems, treating all attributes except one as constraints does not remedy the absence of methods that assure global rather than local optimality. Restricting solutions to the PO subset still requires picking one PO solution.

68. Aggregating preferences Arrow (1950) showed that, for aggregating preferences (ordinal rankings) of more than two alternatives by multiple deciders, no general method exists which is simultaneously •

rational;

•

decisive;

•

egalitarian.

(Blair and Pollack 1983). A rational method for aggregating ordinal preferences would exhibit, for example, preference transitivity, independence of irrelevant alternatives, and the absence of path dependence. A decisive method is not plagued by deadlock or indifference. An egalitarian method does not allow individuals or small groups to have greater influence on decisions. The theorem applies only when more than two alternatives are being assessed, since when only two choices are involved, majority vote is a satisfactory aggregation procedure. Although a shift from ordinal to cardinal utilities removes this triadic incompatibility, it raises the problems of interval utilities discussed in the previous note. The Arrow result can also be related to the tetrad of problem solving a, as follows.

a

Figure 25 Tetrad of problem solving, p. 146

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Figure 77 Arrow impossibility triad and tetrad The bold triangle incompatibility.

indicates

the

triadic

trade-off

or

EGALITARIAN goal-ideal DECISIVE instrument-practical

RATIONAL direction-theoretical Individual Preferences ground-actual

Arrow’s theorem reveals difficulties inherent in the utilitarian goal of “the greatest good for the greatest number.” Specifically, it points to a fundamental problem in democratic decision-making, the sole reputable means by which social systems integrate individual preferences into a just and rational social order. The manipulability of voting schemes (Barry and Hardin 1982) is one manifestation of this problem. While the subject of Arrow’s analysis is collective social choice, typically in voting where choices are ranked, the aggregation of ordinal preferences – by a single decision-maker – among actions based on multiple criteria is essentially the same problem, with the criteria (attributes) serving as the voters. In fact, the multi-attribute decision problem is not only isomorphic to the voting problem but provides the basis for it. If all voters can be assigned positions on a single attribute scale which is polar, e.g., a liberal-to-conservative spectrum (assuming this spectrum is non-circular), and if voter preferences derive from positions on this spectrum, then the possibility of intransitive preferences is precluded, and the Arrow theorem is inapplicable (Hamburger, Henry 1979). Experience with the liberalconservative polarity makes us suspect, however, that some such polarities are circular (horseshoe shaped) and thus preclude the

422

NOTES

possibility of consistent ordering. There is often proximity between extreme political left and the extreme political right. The Arrow Impossibility Theorem joins the Prisoner’s Dilemma a as another illustration of the Fallacy of Composition. Despite the fact that fractal b structure is ubiquitous, wholes do not necessarily inherit the properties of their parts. Wholes may have attributes that are precisely the opposite of those of their parts. The Arrow theorem and the PD show that parts can be rational but the wholes constituted by these parts may be irrational. Even when the context for decision is clear, a single utility can be assigned to every outcome, and the dependence of outcome on action is known, optimality may still be impossible in principle or unattainable in practice. Discovery by enumeration is limited 69 by resources.

69. Computational complexity There are problems that are intractable in practice when their size is sufficiently large, despite being solvable in principle. For example, in the traveling salesman problem, where a salesman wants to minimize the total distance traveled while visiting a sequence of cities, problem size is the number of cities to be visited. For 20 cities, there are of order 1062 possible sequences, more than the number of atoms in the sun. Many problems exhibit such a combinatorial explosion or curse of dimensionality, so that the task of discovering the best solution rapidly expands beyond any conceivable computational capability. This problem of computational complexity is distinct from and more pervasive than formal undecidability. c Although some problems have solutions whose computational a

Note #78 Prisoner’s Dilemma, p. 433 Note #26 Fractals, p. 353 c Note #8 Incompleteness vs. inconsistency, p. 320 b

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requirements increase linearly or polynomially with problem size, many problems require for their solution computational resources (time and memory) that increase more rapidly, e.g., exponentially or hyper-exponentially, with problem size. There is a large number of problems that have no known linear or polynomial solution; these problems are divided into complexity classes ranked according to their resource demands. Discovery by search requires global knowledge, yet only local knowledge is readily available, and acquisition of global knowledge is in conflict with its utilization. 70 Local optimization is usually suboptimal since the risky search for maximal gain foregoes assured, though inferior, benefits. The good is the enemy of the best; the best is the enemy of the good. a What is optimal is not necessarily stable, and what is stable is not necessarily optimal. The dynamics of the system may take it far from optimality. Moreover, in a changing environment, optimality is an ever-receding mirage. But even if attained, optimality brings risk. It reduces diversity and redundancy, 71 which diminishes resilience.

70. Optimization Optimization is choosing an action that gives maximum utility. The simplest approach is local optimization, which means finding better states near the current state. For continuous dynamic systems, such optimization often uses the gradient equation dx/dt = k dU/dx b to search for action, x that optimizes utility U. (An agent’s action was previously written as parameter “a”.) Some local optimization methods also use the second a b

Voltaire (1764) Note #10 Dynamic relation, p. 327

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NOTES

derivatives of U. Since attractors of gradient systems are equilibrium points, for nonlinear systems having multiple basins of attraction, the optimum reached depends on the initial state. Global optimization means finding an optimal state from all possible system states. There is no method that guarantees finding this state. Gradient optimization finds only the nearest local optimum. Given an arbitrary nonlinear function, there is no reliable way to find the global maximum (or minimum) of the function, aside from the brute force evaluation of the function for all values of its variables, which is generally impossible. There are optimization procedures, e.g., simulated annealing (Kirkpatrick et al. 1983) and the genetic algorithm (Goldberg 1989, Mitchell 1996), which are non-local. Simulated annealing (SA) generalizes statistical mechanics, and the genetic algorithm (GA) generalizes biological evolution. These procedures can improve on gradient optimization but do not in general achieve true global optimization. In the search for global optima, there is a trade-off between exploration and exploitation: between acquisition of global knowledge and its use. This is a trade-off between multiplicity and unity. Acquisition of global knowledge searches the space of possible actions, but use of such knowledge requires that search be narrowed to a portion of this space that is promising. Both GA and SA try to balance these conflicting imperatives. Essay goes on to note that even if the dynamics of the system are optimizing, the environment does not stay fixed, but changes by the impact of the system, so the dynamics of system plus environment may not optimize the system.

71. Optimality, stability, and resilience Resilience means the capacity of a system to stay viable under a range of conditions. In terms of dynamic systems, it is the capacity of a system to stay in the same basin of attraction. In

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the fold catastrophe a of Figure 78(a), the length of the bold vertical line from the attractor to the repellor is the size of the basin below the attractor. This line indicates how much state, x, can be displaced downward from the attractor and still return to it. Above the attractor, the basin extends indefinitely, so after any displacement upward, x will return to the attractor. At and to the left of the singularity (dot), the attractor disappears. In Figure 78(b), for the system on the attractor (dot), the length of the bold horizontal line indicates how much environmental parameter p can decrease before the attractor disappears (p=0). These lengths might define ordinary and structural stability, or stability and resilience, or two types of resilience. Figure 78 Stability and resilience p = parameter, x = state variable; large arrows are motion to the attractor. Solid bold lines are the degree of stability/resilience with respect to perturbation of (a) state (b) parameter.

x

x attractor

attractor

p

p

repellor (a)

repellor (b)

See Holling (1976) on the trade-off between optimality and resilience, Milsum (1968) on the trade-off between optimality and robustness, a notion similar to resilience. Optimality often diminishes diversity and thus fails to achieve Requisite Variety. b

a b

Note #38 The fold catastrophe, p. 376 Note #44 Law of Requisite Variety, p. 384

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NOTES

Ground, goal, direction, instrument: the components of purposeful action are commonly flawed. The actual states of system and environment are unknown; the ideal is unrealistic; the guidance of action is inadequate; the implements of action are 72 insufficient. Rational action is difficult to achieve.

72. Purposeful action as a tetrad Figure 79 adds directionality and temporality to Bennett’s (1966) tetrad. a Purposeful action starts from ground (actual), which is compared to goal (ideal); it moves to direction (theory) to understand how to reduce the actual-ideal gap, and then to instrument where practice, guided by theory, changes the actual; then the cycle repeats. Deficiencies can occur at any point. Figure 79 Tetrad of purposeful action Solid arrows are temporal flow: actual→ideal→theory→ action; dotted arrow returns to the starting point.

GOAL ideal DIRECTION theoretical

INSTRUMENT practical GROUND actual

a

Figure 25 Tetrad of problem solving, p. 146. For a list of all tetrads used in this book, see Appendix B.4 Tetradic figures, p. 617.

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7.1.6.2 Other Systems Every system is a center to a periphery of other centers. In being ordered and distinct from their environments, all systems are alike, but this similarity is always joined to difference. If sufficiently complex, they differ from other systems even of the same type, although in the commonality of uniqueness a there is similarity of another sort. Either similarity or difference provides a basis of interaction, for benefit or for harm. Interaction with other systems is via assertion, 73 exchange, or integration. Every system is both a whole and a part. As a whole it asserts or exchanges; as a part it is integrated into larger wholes. Assertion is force, which engenders conflict. Exchange allows reciprocity, which promotes connectedness. Integration is communality, which approaches union.

73. Assertion, integration, exchange The dyad of assertion and integration is discussed above. b Exchange, added here, mediates between active self-assertion and passive integration. c It can be symmetric with respect to its participants, while assertion and integration are inherently asymmetric. Since exchange is typically voluntary, the situation in which it occurs is non-Pareto-optimal, since all agents gain via exchange. The triad of assertion, exchange, and integration resembles Boulding's (1978) threat system (government), exchange system (economy), and integrative system (culture), which are three components of Parsons’ tetradic model of social a

Note #87 Individuality and complexity, p. 445 Note #55 Environmental types, p. 404 c Note #34 Active vs. passive, p. 368 b

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NOTES

systems. a Community, his fourth component, is organized mainly by integrative relations, partly by exchange and threat. Assertion is contested by competition. The system may also be the object of predation. Systems are food for other systems, and participation in the flux of substance cannot 74 be declined. Success itself invites danger. A system effective at acquiring resources is a target for takeover, parasitism, or theft. b

74. Eating and being eaten Figure 80 adapts Bennett’s (1961) idea that a pentadic structure can represent the idea of a system that “eats” and is “eaten.” This idea applies when the system coexists with other agents. c “Eating” is a principal mode of being in environments where other systems are absent, and “being eaten” is a principal mode of being when the system is embedded within a larger order. d Figure 80 Eating and being eaten (b) shows trophic levels of (a).

what eats the system phenotype genotype

SYSTEM

ENVIRONMENT

metabolism (a) a

what the system eats

(b)

6.4.2.1 The Parsonian model of social systems, p. 253 This sentence is a quote from Culotta (1991). c Such environments are discussed in Essay, 1.1.6.2 Other Systems. d These are discussed in Texture 1.1.6.1 and 7.1.6.1, pp. 13, 406, and Embeddedness 1.1.6.3 and 7.1.6.3, pp. 17, 437, respectively; see also Note #55 Environmental types. b

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“Eating” here has more general meaning than its literal meaning for organisms; for example, galaxies engulf smaller galaxies. Generalized “predation” is also intended here; it includes not only carnivores preying on herbivores but exponentially growing virus infections, indeed any interaction in which a system gains at the expense of another. The pentadic figure presumes some form of metabolism and genotype-phenotype distinction. The pentad centers in the genotype, the essence of the system, and the diagram might be recursively duplicated at the higher and lower trophic levels. The genotype specifies the metabolism that makes food usable by the system and how the metabolism constructs the phenotype. The pentadic structure is drawn as a 5-pointed star for simplicity; many dyadic links, and all higher ordinality links are not shown. 75

In situations of competition, no principle of rationality is fully satisfactory. Rationality may require behavior that is partially random. If there are more than two agents, coalitions 76 are unstable.

75. Game theory The interaction of a system with the environment or other systems is the subject of the theory of games of von Neumann and Morgenstern (1944). A game is a relation between actions of players and resulting utility outcomes. Decision theory a focuses on games between system and environment, where only the system is an agent that obtains utility; in game theory this is called a “game against nature.” If Nature is replaced with a second agent that obtains utility, there are utility functions, Ux and Uy, for both agents. (In decision theory, this situation is a “decision under conflict.”) Table 11(a) shows the normal form of a constant-sum game with agents x and y each with two possible actions. In each cell of the matrix, the first utility goes a

Note #56 Decision theory, p. 406, Table 10 Decision under risk, p. 407

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NOTES

to x, the second to y; so for agents doing (x1, y2), x gets 0 and y gets 3. (This is the upper-left point in Figure 81(a).) Table 11(b) shows the non-constant-sum game of the Prisoner’s Dilemma in which agents have actions, C and D. Since constants can be subtracted from all utilities without changing anything, constantsum games are called zero-sum. Table 11 Two-player games (a) Example of zero (constant)-sum 2x2 game; (b) example of non-zero-sum 2x2 game.

x1 x2

y1 y2 2,1 0,3 3,0 1,2 (a)

C D

C D 2,2 0,3 3,0 1,1 (b)

The utility outcomes for the games in Table 11 are shown in Figure 81. For the zero-sum game of (a), all four points are Pareto-optimal. For the non-zero-sum game (b), the three northeast points (0,3), (2,2), and (3,0) are PO; the interior point (1,1) is non-PO. a Figure 81 Utility outcomes for two-player games (x,y) utility outcomes for games in Table 11.

Uy

Uy

• •

a

• •

• (a)

•

• Ux

(b)

• Ux

Compare Figure 81 to Figure 31 Pareto-optimality, which is repeated in Note #66 Pareto-optimality, p. 418.

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Games can be two-player or multi-player and be zero (constant) sum or not; there are thus four types, of which only two-player zero-sum games are satisfactorily “solved” by game theory. In these games, there is a general solution: pure or mixed maximin. But for multi-player zero-sum games, analysis is complicated, so one simplifies it by considering possible alliances a among players and distribution of gains that result from these alliances. For non-zero-sum games, analysis is more problematic, since dilemmas of rationality arise, wherein strategies rational in zerosum games (maximin, even a dominant strategy) have aberrant outcomes. b In non-zero-sum games, there may also be inconsistency between choosing a rational strategy, and assuming that others will act rationally and acting optimally in response. c Thus, beyond two-player zero-sum games, game theory suffers both from incompleteness and inconsistency.

76. Coalition instability In zero-sum games with more than two players, a coalition is a set of players who act collectively and share the utility gained from doing so. This utility is superadditive, i.e., is greater than the sum of the utilities that individual players could gain by individual action; this is what motivates coalition formation. A core is a set of coalitions not dominated by other coalitions, i.e., where members of the original coalition are not tempted to shift their alliances. Such a core would be a satisfactory solution to the game-theoretic problem. Unfortunately, for many n-person zero-sum games, no core exists, i.e., no coalition is stable against disruption by competing coalitions. Just as an incorrect assumption of the absence of adversaries is a prescription for failure, so too is an incorrect assumption of fixed total 77 gain. More commonly, total gain is variable, so cooperation is not precluded. But even a

Note #76 Coalition instability, p. 431 Note #78 Prisoner’s Dilemma, p. 433 c Note #79 Chicken, p. 435 b

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where cooperation is to the advantage of all, defection may be compelling. Individual rationality may lead to collective 77 irrationality, to the disadvantage of all, even 79 to disaster. A principle of altruism or of symmetry does not always solve these dilemmas: The best outcome may occur when agents act in self-interest or differently from 80 one another.

77. Discerning which game is being played These errors need to be avoided: (1) Treating a situation as a one-player game against nature when it is actually a conflictual situation, i.e., a two or many-player game; (2) Treating a situation as zero-sum when it is actually non-zero-sum. Rapoport (1969) writes about the dangers of this error, e.g., in military thinking. The opposite is also possible – assuming a game is nonzero-sum and amenable to a win-win outcome when it is actually zero-sum – but this error is less common; (3) Assuming, in zero-sum games and more critically in non-zero-sum games, that there are only two players when there are actually more than two. Since zero-sum games are purely competitive, while non-zerosum games have both competitive and cooperative aspects, this suggests that an adversarial aspect of relationships is ineradicable, while a mutually beneficial component is optional. (In non-zero-sum games, some payoff is apportioned among the players; variation in this total is the cooperative aspect; its apportionment is the competitive aspect.) However, there do also exist “beneficence” games that only have a cooperative aspect, and in multi-level selection group structure can promote cooperation even if competition is individually rational.

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78. Prisoner’s Dilemma Much of non-zero-sum game theory deals with counterintuitive or anomalous effects, where individual rationality is insufficient or misleading as a guide to effective action. This note illustrates these effects in the well-known Prisoner’s Dilemma (PD), shown in Table 12(a); subsequent notes discuss Chicken and other games. In the table, utilities – with units of “utils” – are ordinal or cardinal. The row player is A; the column player is B. Table 12 Prisoner’s Dilemma (a) The first number in entries of the table is the utility payoff to A; the second is the payoff to B. So if (A,B) do (C, D), A gets 0 and B gets 3 (shaded box); (b) a digraph showing the changes in utility to the players if each shifts from C to D. For example, A gains 1 but causes B a loss of 2.

C D

C 2,2 3,0 (a)

D 0,3 1,1

+1

-2 B

A

+1

-2 (b)

In the PD, self-assertion (defection D) is individually rational – it is a dominant strategy, in that it is better for a player to defect no matter what the other player does. If B does C, it is better for A to do D (3 > 2); if B does D, it is better for A to do D (1 > 0). The table is symmetric, so the same is true for B. There is no strategy more rationally compelling than one that is dominant, yet this strategy is collectively irrational since when adopted by all, it yields adverse effects to all (Rapoport and Chammah 1965). When both players choose D, they obtain a deficient – non-Pareto-optimal – outcome (1,1). The players could in principle do better. The (C,C) outcome is (2,2). Yet for a single iteration of this game, this preferred outcome is not reachable. (D,D) is the natural result of individual rationality; it is stable in that neither player will unilaterally switch to C. Table 12(b) shows that by shifting from C to D, a player gains less for itself

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(+1 utils) than the loss it inflicts (-2 utils) on the other. Table 12(b) is additive for simplicity, so the effects of player actions are mutually independent, but PDs in general are not additive. Such negative externalities a are the essence of the PD. Negative externalities are related to suboptimization, which means both: (i) optimization by individual subsystems (players) and (ii) suboptimal results of such actions on the whole. By optimizing its own utility, a subsystem causes suboptimal utility for the system in which it is embedded if other subsystems use similar strategies. Optimality for the parts is not inherited by the whole; to assume otherwise is a Fallacy of Composition. In the PD, cooperation can be secured by external guarantee (the state solves the Hobbesian dilemma of the war of all against all) or by its internal equivalent (the introjection of socio-cultural norms and values, such as the Golden Rule or the Kantian categorical imperative). In general, the PD is an argument for a societal command mechanism, but in some circumstances, cooperation can spontaneously emerge without high-level intervention (Axelrod 1984). Such emergence requires that the game is repeated, that it has a small number of players, and that the players recognize and expect to encounter one another again in the future. These possibilities are not considered in the basic PD game and require augmentation of its formalism. PD situations are not always undesirable. The name of this game derives from the situation where a District Attorney tries to get two criminals to testify against each other; it is a dominant strategy for each prisoner to do so, but this gives a deficient outcome for both. The Adam Smith “invisible hand” of the market sounds like the opposite of the PD, but it in fact is based on the PD since it requires that each producer group is trapped in this game, which forces group members to lower prices, which benefits society.

a

Note #60 Externalities, p. 412

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The PD is generalizable to any number of (equivalent) players, yielding the n-player-PD (NPD). The “tragedy of the commons” is an NPD, a fact that is often not recognized. The PD, played repeatedly, can morph into the game of Chicken.

79. Chicken In Chicken (Table 13), the absence of a dominant strategy dictates a maximin strategy. a The joint maximin, however, is unstable, and joint defection gives the worst outcome for both. Table 13 The game of Chicken (a) Consider payoffs here as ordinal. (b) Cardinal payoffs can make the outcome a disaster. (c) For ε positive, this game is Chicken; for ε negative, it is a PD.

C D

C 2,2 3,1

D 1,3 0,0 (a)

C D

C 2,2 3,1

D 1,3 -∞,-∞ (b)

C D

C 2,2 3,1

D 1,3 1-ε,1-ε (c)

In (a) the worst result for doing D is 0 and for doing C is 1, so the maximin choice is C. The game is symmetric, so the maximin solution is (C,C) with players getting (2,2). This solution, however, is not stable. If one player assumes that the other will do maximin, it will defect to D and get 3. If the other player acts similarly and also chooses D, the result is (0,0), the worst outcome for both. This is not much worse than the 1 a cooperator gets when the other player defects, but in the more severe game of (b), (D,D) is a disaster. In the hypothetical situation from which the game gets its name, two teenage boys drive their cars at one another. The one who swerves (C) is Chicken; the other who continues to drive straight (D) is macho and gets the best outcome (3). However, if both players defect, both of them get killed (-∞,-∞). In (c) if ε = 0, the table is intermediate between Chicken and PD and structurally unstable. a

Note #56 Decision theory, p. 406

NOTES

436

80. Symmetry or altruism may be harmful The Golden Rule and Kant’s Categorical Imperative (and Hillel’s negative formulation, “Do not do unto others what you would not have done unto you”) are solutions to the PD that call for players in the same situation to act in the same way. Yet, symmetric “coordination games” may yield optimal outcomes if players adopt different actions. In the hero game (Hamburger 1979), if each player puts the other first, it is harmful to both, so joint altruism is self-defeating, but if one player pursues selfinterest while the other does not (symmetry is broken), both players benefit. Via exchange, incompleteness is ameliorated. But exchange also reinforces incompleteness by fostering dependence. Neither extreme of dependence or self-sufficiency is ideal, nor can an optimal and enduring balance be found between the two. When survival depends on exchange, external identity prevails over internal identity. When exchange is extensive, the system loses autonomy and becomes embedded in a larger whole. When exchange is unequal, it becomes exploitation. Exchange cannot be completely controlled. Acquisitions via exchange retain traces of their origins. What passes from one system to another is not fully specified by either. Even when openness is regulated by the organizing principle of the system, it is impossible to allow entry into the system of the beneficial and reliably exclude the harmful. Function, like structure, is afflicted by the tension between unity and multiplicity. Interactions may be with few other systems or with many. Relations with few are thicker but are limited, so identity is incomplete.

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Relations with many lessen dependence but are incoherent, so identity is inconsistent. Neither narrowness nor breadth of interaction is fully or permanently satisfactory, and intermediate conditions are unstable. Exchange may solidify into integration. Integration with similar systems multiplies capacity but risks redundancy. Integration with different systems offers complementarity but risks dependence. Since every system is both similar to and different from every other system, integration brings both benefits and risks. The system may overlap other systems that organize different attributes of common elements. This compromises the integrity of boundary. Or, the environment may consist not of many other systems but only one. Because of incompleteness, every system at least potentially has a complement with which it must coexist.

81. Sharing elements An element may be part of multiple systems, which organize different attributes of the element. Where elements are people and attributes are roles, individuals participate in multiple social systems, whose organizing principles are rarely harmonious. The individual is then a locus of intersystem tension. a 7.2.6.3 Embeddedness The embedding of a system in a more encompassing order poses the deepest challenge. Systems have the capacity and the tendency to become integrated into larger a

Note #83 Recruitment and predation, p. 439

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wholes. Yet every system is also a whole unto itself. The competing needs of system and suprasystem may for a time be harmonized, but the interests of part and whole never completely coincide. There is renunciation or suppression in every integration of one system into another. In being a part, autonomy is relinquished. The system must present attributes required by function, and the locus of identity becomes external. Being embedded may offer security, 82 but the price of security is heteronomy, and this security cannot be relied upon. Wholes sometimes sacrifice or consume their parts.

82. Heteronomy In terms of generalized genotype (center) and phenotype (periphery) and environment, a autonomy is being inner-directed and active, b as in Figure 82(a), where phenotype is primarily dictated by genotype (written as PG). Heteronomy is being outer-directed and passive, as in Figure 82(b), where phenotype is primarily dictated by the environment (written as PE). The phenotype is a ‘beachhead’ c of the environment in the system. Figure 82 Autonomy vs. heteronomy

G (a)

a

PG

E

G

PE

E

(b)

Note #49 Genotype and phenotype, p. 395 Note #34 Active vs. passive, p. 368 c A similar notion is applied to the modeling subsystem in Note #104 Embeddedness of cognition, p. 475. b

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A system may be embedded but yet not integrated into the larger whole. It suffers the harm of exclusion. Or it may be integrated into this whole to the advantage of other systems but to its own disadvantage. There may be more than one encompassing order into which the system might be integrated. Even if it can select its location, the opportunities and risks of available environments are never fully known, and movement from one to another is not always possible. The system may become integrated into more than one encompassing order; the resulting tensions may be mitigated by differentiation but at the cost of coherence. No escape is possible from being the object of competing attempts at recruitment by larger 83 wholes.

83. Recruitment and predation Systems can be recruited to serve purposes not their own because they are dependent, and they are dependent because they are incomplete. Recruitment that replaces internal identity with external identity readily morphs into predation. Alternatively, it may be the absence of a larger whole that endangers the system. Unrestrained competition with other entities may be detrimental and higher level constraints may be needed to assure 84 cooperation. In turbulent environments, with the system at the mercy of large-scale forces, 85 isolated action may be ineffective. Survival may require being embedded in a suprasystem order. Yet systems resist the loss of autonomy.

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Every system is bound to a particular scale of existence and is vulnerable to environmental disturbances on much larger or smaller scales.

84. Embeddedness as a solution to the PD The Prisoner’s Dilemma can be solved by a higher-level order, e.g., government, which penalizes defection so that it becomes no longer dominant, i.e., by changing the payoff matrix so it is no longer a PD. Or, the system might introject a higher-level principle, transcending its partialness and its imperative of defection, even in the absence of a visible suprasystem. In Boulding’s terms, these two solutions to the PD rely on the “threat system” and the “integrative system” respectively. a Religious or philosophical ideals such as the Golden Rule or Kant’s categorical imperative attempt to solve the PD in general by inducing individuals to identify with a moral order or a universal rationality that has priority over the (often selfdefeating) claims of self-interest. Although ethics is not merely collective rationality, one important function of ethical codes is the solution of ubiquitous game-theoretic dilemmas of collective action.

85. Turbulent fields The reference is to Emery and Trist’s Type IV environment. b

a b

Note #73 Assertion, integration, exchange, p. 427 Note #55 Environmental types, p. 404

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7.1.7 Complexity Notes:

page

86 Complexity 87 Individuality and complexity 88 Hierarchies and networks 89 Complexity, stability, and chaos 90 Small worlds 91 Scale-free networks 92 Homogeneity, heterogeneity, and scale 93 Three levels 94 The highest is not the whole 95 Hierarchical egalitarianism 96 Distillation and alienation 97 Informational parasitism

441 445 445 449 450 450 452 454 456 457 458 458 86

Identity is articulated in complexity. Complexity is a source of uniqueness. Uniqueness in the organizing principle is 87 individuality. If the system is embedded in a population of similar systems, what is universal within the population is in tension with what is unique in the system, but in populations of sufficiently complex systems uniqueness is itself universal.

86. Complexity This note a supplements earlier discussion b of complexity and holism by focusing on four meanings of complexity. This term can be taken as ontological or epistemological, as a property of things or of descriptions of things. a

Re complexity, see also Note #20 Reconciling constraint and variety, p. 341, Note #32 Emergence, p. 363, Note #44 Law of Requisite Variety, p. 384; and Note #69 Computational complexity, p. 422. b 3.4 Aspects of complexity and holism, p. 100

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Complexity1 is a general idea that groups together several related but not identical technical notions. It focuses on how many elements, attributes, and/or relations the system has. Also, relations have varying complexity. Higher ordinality relations are more complex than lower ordinality relations. For systems with continuous variables, complexity1 might be defined by the dimensionality of state space. The more state variables a system has, the more complex it is. For example, ten differential equations are more complex than two differential equations. And the dimension of a system may be non-integer. a Counting state variables may, however, be misleading; sometimes a system apparently of high dimension has behavior that can be described by a low dimension model. A high dimension chaotic system might have a low dimension strange attractor; similarly, a gradient system with many state variables might have its singularity neighborhood described by catastrophes with only one or two state variables. For qualitative variables linked by information-theoretic relations, b the number of probabilities that must be specified in a model is a measure of complexity. This depends on system structure c and how many values variables take on (degrees of freedom). Complexity2 is a more specific idea that identifies complexity with uncertainty, disorder, entropy, randomness, and the like. The more states a system can have, the greater the uncertainty is about its state; equivalently, the more information needed to describe a system, the more complex it is. The more ordered the system is, the less complex it is. For discrete dynamic systems, how long one needs to observe the system to predict its future behavior (its “disclosure length”) is a complexity2 type measure. Complexity of a dynamic relation given by its algorithmic information d is also a measure of randomness. a

Note #26 Fractals, p. 353 Note #9 Relation as constraint, p. 324 c Note #5 Structure, p. 308 d Note #48 Algorithmic information, p. 395 b

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The idea of complexity3 arises from the realization that randomness (uncertainty, multiplicity, entropy, etc.) is simple in its own way, especially when viewed at a higher (aggregated) level. The notion that extremes of order and disorder are in some sense similar and not opposites is introduced above. a In this view, solids and gasses, representing “organized simplicity” and “disorganized complexity,” respectively (Weaver 1948), are in a sense both simple. What Weaver calls “organized complexity,” i.e., complexity3, is in between the two – the liquid state – and is what really deserves to be called complexity. Interpreted in the context of nonlinear dynamics, this is like the idea of the “edge of chaos” (Wolfram 1986, Langton 1990, Crutchfield 1990)). b In cellular automata, a phase transition occurs between a domain of “solids” (fixed points or limit cycle attractors, what Wolfram calls Class I or II automata) and a domain of “gasses” (chaotic attractors, what Wolfram calls Class III automata). At the boundary between order and disorder, there is a small but distinctive set of (Wolfram’s Class IV) automata in which interesting phenomena emerge, such as the possibility of universal computation. These automata have high complexity3. Similarly, in the analysis of structure, while degrees of freedom decrease monotonically from the maximally composed structure, ABC, to the maximally decomposed structure, A:B:C, there is a sense in which both ABC and A:B:C are equally simple and are the duals of one another. The most topologically complex models occur closer to the midrange of the lattice. While only one structure has either the minimum or maximum value of df, there are many more structures at intermediate levels of the lattice.

a

Notes #16 Order and disorder, p. 336, and #20 Reconciling constraint and variety, p. 341 b Note #17 Chaos, p. 338

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In a simple graph-theoretic definition of system, where every element is either connected or not connected to every other element, a totally connected system is complex in the number of links that exist but simple in the topology of the links. A totally disconnected system, in which all elements are isolated, is simple as well. By contrast, a graph consisting of many but not all possible links is more complex. Charles Bennett (1988) has proposed an interpretation of complexity – call it complexity4 – that resembles complexity2 in being related to randomness and complexity3 in treating extremes of (non-)randomness as similar. He introduces the notion of the “logical depth” of an object, which is the length of time, or number of recursive iterations, required for a minimal program to compute the object. a Recall first that a minimal program is itself random. A simple object would be computable quickly by its minimal program; a random object, whose minimal program must necessarily contain a complete specification of the object, would also be quickly computable. Only an object intermediate between extremes of order and disorder would have a minimal program that required many steps for its generation. Complexity is basically a structural idea, but it has functional implications. Complexity3 may be associated with adaptability and evolvability. In the solid phase, a system is frozen and unable to change or adapt; in the gaseous phase, change is random and uncontrollable; only in some phase that is intermediate between the two are stability and adaptability, and continuity and change, both accessible. Kauffman (1991) has proposed that complexity3 might confer on genetic regulatory systems and ecological systems such versatile properties, although for such systems to be stable, their location in the spectrum of solid to gas must be on the ordered side of the edge of chaos.

a

Note #48 Algorithmic information, p. 395

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87. Individuality and complexity Uniqueness is an emergent of combinatorial complexity. As the number of elements and/or relations increases, the possible combinations soon pass beyond the point where the existence of all of them is impossible. To illustrate, since there are 20 types of amino acid, a protein 200 amino acids long could have 20200 possible sequences. All of these sequences could not be instantiated even if the entire universe were dedicated to this task. Human language is rich and powerful because the set of possible (not even very long) sentences could not have been uttered even if all sentient beings in the universe were speaking this language since sentience first arose. The uniqueness arising from complexity may be either central or peripheral to a system. Two automobiles of the same model and year, originally nearly identical, become more distinct over time, but such uniqueness may be inconsequential. However, uniqueness in the organizing principle (identity) of the system has special significance and warrants being called individuality. Individuality, even at the biochemical level, is salient for human beings. In the universality-uniqueness dyad, universality is commonly privileged, but an instantiation of what is universal may be redundant, while what is unique is irreplaceable. Uniqueness is as important as universality, and ethical imperatives derive from both. Complexity may be dispersed horizontally in a 88 network or vertically in a hierarchy. Each archetype is an attractor. Neither is optimal, but a balance between the two is unstable, and organization by both is inconsistent.

88. Hierarchies and networks Strictly speaking, a hierarchy is a special case of a network where cyclicity is disallowed, but for present purposes the network and the hierarchy will be considered two archetypal forms of structural complexity: the network (sometimes called a

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NOTES

“heterarchy”) exhibiting “horizontal” complexity and the hierarchy (sometimes called a “holarchy”) exhibiting “vertical” complexity. In networks, lateral organization of many elements is achieved by multiplicity of relations; in hierarchies, relations define higher elements that are the basis for a multi-level order. In networks, complexity is decentralized and diffuse; in hierarchies, it is centralized and concentrated. Ecosystems and market economic systems illustrate the first; organisms, organizations, and command economies illustrate the second. The network is a system archetype having the predominant character of multiplicity; the hierarchy is a system archetype having the predominant character of unity. In the classical systems literature, the organism (hierarchy) archetype is usually invoked, at least implicitly; examples of authors who mostly use this model are Beer (1972) and Miller (1978). The population or ecosystem (network) archetype represents a different model; Boulding (1978) is an advocate of this viewpoint. Simon (1991) offers an analysis of the differences between organizations and markets, emphasizing the advantages of the former. In contemporary complex systems literature, however, the network has become the unmarked term. The archetype implicit in most of Essay is the organism, not the population or ecosystem; the ontology it presents is thus mainly though not exclusively individual-centric. Certain ideas are appropriate only to one of these two types of organization. Evolution, for example, is a property of populations and sets of populations (ecosystems), and not individual organisms. One can speak of programmed development and a separate decision-making function only of (some) organisms. A related distinction by Kuhn (1974) is between “controlled” and “uncontrolled” systems. Organisms and command economic systems are controlled; ecosystems and market systems are uncontrolled. Kuhn notes the different meaning of feedback control a in these two types of system. In a

Note #45 Feedback control, p. 386

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controlled systems, information is localized and explicit (as in the temperature setting on a thermostat), but in uncontrolled systems, information is diffused throughout the system and only implicit. In an ecosystem, there is no location where equilibrium levels of different populations are specified; these levels are emergents of parameters distributed through the entire system. When it is said that regulation through negative feedback governs a market system, the meaning is quite different from the regulation achieved in a command system, where the set-points are localized, explicit, and manipulable. (However, neither the explicit negative feedback of a controlled command economy nor the implicit negative feedback of an uncontrolled market system can guarantee optimality and stability.) In terms of Boulding’s hierarchy, a uncontrolled systems are at level (ii) and controlled systems at level (iii). A personal anecdote offers another example. In the early days of computer time-sharing at MIT in the 1960s, it was noticed that when the number of computer users reached about 30, the system became sluggish, which evoked the hacker witticism, “Well, why not just locate the place in core where ‘30’ is stored and change it to ‘60’?” This joke is about the error of mistaking an uncontrolled system for a controlled system. It may be argued that organism-like systems are really populations or ecosystems made up of lower-level units, the distinction really being whether one is focused upon global properties, i.e., the attributes of the system as an entirety, or upon local properties, the composition of the system via the interaction of parts. This argument obscures the real phenomenon of centralization of information and regulation. In some systems, information and control is not uniformly dispersed among constituent parts and is not merely implicit but is explicit and concentrated at least to some degree. This is true in the genome of cells and in the nervous systems of organisms, which makes the cell and the organism a different kind of system than an insect colony, in which control is truly dispersed a

Table 8 Boulding’s hierarchy of system types, p. 156

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and information is only implicit in the network of interactions. A command economy is qualitatively different from a market economy, as an organization is different from an industry or a market economy. It is true that within systems that are organism-like, subsystems of control may internally be networks, but if such subsystems are dominant in the larger whole, this still constitutes a localization of function. One can define a spectrum from extreme hierarchical verticality to extreme network horizontality. Either extreme is a coherent organizing principle, but intermediate points are complex in a way analogous to the “edge of chaos.” a Even within hierarchical organization, control can be distributed among levels in a multiplicity of ways. Organization theory speaks of the formal and informal structures in human organizations, the former typically organismic and displayed in the organization chart, the latter being the actual network of interactions and associations, which rarely corresponds to the formal structure. Some organizations depart from an organismic architecture even in their formal structure; for example, functions may be contracted to independent entities as opposed to being done internally. In societal systems, b the community is like a network; the polity is like a hierarchy. This discussion has been restricted to synchronics. For some systems, there is a diachronic tendency to centralization, which von Bertalanffy called “progressive centralization,” c reflecting a fundamental instability in network-like structures.

a

Note #17 Chaos, p. 338 6.4.2.1 The Parsonian model of social systems, p. 253 c Note #136 Centralization, p. 529 b

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7.1.7.1 Networks A network of interactions can be stable or 89 unstable. Either condition can have adverse effects. Stability can lock the system into dysfunctional states; instability can lead to runaway dynamics that also produce such states. The presence of non-local interactions in addition to local ones makes connectedness 90 global. This may deamplify some local disturbances, but it amplifies others, allowing them to propagate through the entire network. The absence of global connectedness is likewise both beneficial and harmful. Local disturbances are contained, but the system is fragmented. Networks are more flexible than hierarchies and less vulnerable to local disturbance, but laterally dispersed order makes coordination and unified action difficult. This can be partially remedied by the network becoming more hierarchical, but it then becomes 91 vulnerable to failure of critical hubs.

89. Complexity, stability, and chaos Complexity may be associated with reduced stability. A reduction of stability with a higher number of elements or interconnections (an example of complexity1 a) is found in model systems by Levins (1973) and May (1974). In random Boolean networks known as NK systems, i.e., dynamic networks consisting of N elements, where each element has only two states and is on average connected to K other elements, increasing K beyond 2 typically moves the system into a chaotic a

Note #86 Complexity, p. 441

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regime (Kauffman 1993). Other things being equal, the more interconnected a dynamic network is, the more likely it is to be chaotic. In Holling and Gunderson’s adaptive cycle model, a high interconnectivity is associated with both the mature state (K phase) of ecological systems and its collapse (Ω phase).

90. Small worlds Random networks b or locally connected networks supplemented with some random links exhibit the “small worlds” phenomenon (Watts 1999), in which the average distance (number of links on a geodesic) between any two nodes is small. This is also known as the “six degrees of separation” phenomenon, in which people in networks are separated by at most about six links.

91. Scale-free networks Another type of network that exhibits short path lengths between most pairs of nodes is the scale-free network (Barabási and Albert 1999), in which N(L), the number of nodes having L links, varies with an inverse power of L, i.e., N(L) = a L-b (where b is positive). This results in few nodes with many links and many nodes with few links. On a log-log plot, this power law shown in Figure 83(a) becomes a straight line, log(N) = log(a) - b log(L), shown in Figure 83(b). Figure 83 Scale-free networks

(b)

(a)

log N(L)

N(L)

L

a b

Note #130 Trajectories of development, p. 517 Note #7 Networks, p. 317

log L

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There is no typical number of links for a node, i.e., no central tendency on either side of which N(L) gets increasingly smaller. (For a normal distribution, such a tendency is the mean; Poisson distributions, which characterize random networks, also have such central tendencies.) Many networks (ecological, genetic regulatory, the Internet, etc.) exhibit power laws often explained by the preference of new nodes to attach to those existing nodes that have many links. Scale-free networks are not vulnerable to inactivation of randomly selected nodes, since most nodes have only a few links, but loss of highly connected hubs can adversely impact the system. 7.1.7.2 Hierarchies In hierarchy, multiplicity is not only horizontal but also vertical. Each level is a system subject to disintegration or rigidification. Each has an environment of higher and lower levels. Each level thus has a dual identity: one based on structure with its imperative of autonomy, the other based on function with its imperative of interaction. If autonomy is excessive or interaction insufficient, the level will have nothing to contribute. Constraint and variety oppose one another at each level and between levels. Microhomogeneity engenders macro-heterogeneity; micro-heterogeneity engenders macro92 Either arrangement can homogeneity. generate harm. In both arrangements, unity and diversity coexist but neither principle is consistently maintained.

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92. Homogeneity, heterogeneity, and scale Consider a two-chambered system isolated from its environment. If one chamber is hot and the other cold with no heat flow between them, or if one chamber contains only molecules A and the other only molecules B with no matter flow between them, the system has low entropy, i.e., is ordered, because each chamber is homogeneous at a microscopic level. a If exchange occurs between the chambers, the system will change to a state in which both chambers are lukewarm or have both A and B molecules. This state has high entropy (disorder) since each chamber is microscopically heterogeneous. Macroscopically, the situation is the opposite. Initially there is macroscopic heterogeneity (disorder); finally, when both chambers are indistinguishable, there is macroscopic homogeneity (order). Symbolically, AA:BB changes to AB:AB. The initial state has micro-similarity and macro-difference; the final state has micro-difference and macro-similarity. The two (idealized) situations are illustrated in Figure 84. Figure 84 Macro- and micro-heterogeneity (a) Macro-heterogeneity and micro-homogeneity, written as AA:BB (order); (b) macro-homogeneity and micro-heterogeneity, written as AB:AB (disorder).

(a)

A A A A A A A A A A

a

B B B B B B B B B B

(b)

A B A A B B B A A B

B

AB

A A AB B B A

System (a) above is in a state of thermodynamic disequilibrium; see Note #123 Disequilibrium and change, p. 507.

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The point here is not only that homogeneity or heterogeneity depends upon the scale of discourse, but that microhomogeneity is the basis of macro-heterogeneity, and vice versa. In social systems, the quest for heterogeneity (diversity) – or homogeneity (unity) – paradoxically depends on the preservation, and perhaps even the cultivation, of precisely the opposite property at the subsystem level. Systemic emergents from AA:BB and AB:AB are quite different. Diversity, assessed as information-theoretic uncertainty, a is decomposable. Total diversity is the sum of diversity within subsystems plus diversity between subsystems. Without any input of new diversity, whatever increases diversity within subsystems reduces diversity between subsystems. This assumes only one dimension of unity vs diversity, but systems often have multiple dimensions. Heterogeneity may prevail on some and homogeneity on others. When heterogeneity or homogeneity is normative, it is never normative across all dimensions. Each level is a center of structure and function. Neither complete separation nor complete merging of levels is optimal. Separation causes conflict or fragmentation. Merging deprives higher levels of the independence needed for regulation and lower levels of the integrity of basic process. Every level has its function. Upper levels organize; lower levels ground; intervening 93 levels mediate. No function has permanent priority. Every level is subject to pressures from other levels, pressures that do not subside and whose reconciliation is temporary.

a

Information-theoretic uncertainty is defined in Note #9 Relation as constraint, p. 324.

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93. Three levels Beyond some level of complexity, the dyadic tension in which a system is both an organized whole and an element in a more encompassing order, expands into a triadic tension of element, subsystem, and system. Complex stratified systems have at least three tiers. The subsystems are relations binding the elements together. A three-tiered scheme of the organization systems a encompasses structure and function (open systems view); here it is just structural (closed systems view); the two conceptions are different, as shown in Figure 85. Figure 85 Two conceptions of three levels of analysis (a) Three structure levels: {A, B, C}, {AB, BC}, and {S, E}. (b) Three structure-function levels: {A, B, C}, {S, E}, and SE. Relations and elements in E are not shown.

SE

E

S ≡ ABC AB (a)

A

BC B

C

(b)

The three-level scheme of Figure 85(a) displays the idea of Feibleman and Friend (1945) that “organization is the sharing of subparts between parts.” A chemical example is the sharing in molecules of electrons by atoms. In set- or information-theoretic definitions of structure, subparts are variables and parts are relations; for S in Figure 85(a), parts AB and BC share subparts B. In social systems, there is the overall system, the individual, and the intermediate level of groups. (Individuals can be a

Note #1 System, p. 295

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members of multiple groups.) The interests of the whole differ from interests of individuals, and both are often opposed to the interests of groups. Linstone (1984) extensively developed the systems analytic implications of this viewpoint in his “multiple perspectives” model. a The extremes of a hierarchy are its fundamental levels, b which determine it from above and below, but commonly one extreme has primacy. Even the dual prominence of both highest and lowest is harmful, if it undermines intermediate levels no less critical for the system. Whatever empowers either extreme, without enhancing the mediating levels, invites disorder. Beyond its proper function, the fundamental disrupts. At the highest levels, opportunity and hazard are maximal. The privileged status of these levels, their greater scope of action, their distillation of principle and concentration of power all tend to weaken lower levels, for which the benefits of coordination do not compensate. Higher levels can buffer lower level dysfunction, but the devaluation of lower levels and the preemption of their function ultimately impair viability. The highest is not 94 the whole. It represents the whole and gives it coherence, but it is still only a part. The whole depends on all levels performing their unique functions and on the fluidity of interactions between levels; only in this way is 95 harmonious integration possible. a

The clash of group interests – and obviously also the alliances of groups – is the very definition of politics (Bentley 1908). Privileging groups implies the priority of the middle level in Figure 85(a). b 2.1 The illusion of the fundamental, p. 43, 2.2 The systems alternative, p. 48

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94. The highest is not the whole This is trivially true insofar as the whole includes the highest, but the statement refers to two different ideal types for the organizing principle of a hierarchical system. Figure 86 shows that an OP that encompasses either much breadth or much depth is possible, but an OP that does both is impossible. a Figure 86 The highest is not the whole The ovals represent different organizing principles. In this representation, a level does not subsume the levels beneath it but only adds new functionality. OPa illustrates horizontal integration at the highest level. OPb illustrates vertical integration which does not privilege any level. OPc represents the presence of both horizontal and vertical integration, rarely achievable.

OPa

OPb

OPc

For very simple systems, the OP is the system itself, but in complex systems, the OP is the core of the system, which is itself a subsystem. b All systems are incomplete. OPa is incomplete in that it omits the other levels. OPb achieves some integration of all levels but is incomplete in only encompassing small portion of each one.

a b

The whole cannot be embraced (1.1.1.1.1). Note #2 Organizing principle, p. 303

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95. Hierarchical egalitarianism Simon (1962) asserts that most systems are “nearly decomposable,” not only horizontally but also vertically. Every level is a system. Hierarchical egalitarianism follows: The harmonious co-operation of all beings arose Not from the orders of a superior authority external to themselves, But from the fact that they were all parts in a hierarchy of wholes Forming a cosmic pattern, and what they obeyed Were the internal dictates of their own natures. - Chuang Tzu (3rd Century BCE), quote from Loewy and Siekevitz (1969) Essay continues on to the end of this Hierarchies sub-subsection to make this point and to oppose the hegemony of the fundamental. It opposes not only the fundamentalism of the top and the fundamentalism of the bottom but even a dual fundamentalism of both top and bottom. What trickles down or up is always insufficient; one needs a reconciling middle. Earlier discussion a introduced the deconstructionist notion that in every polarity one pole is unmarked, i.e., privileged. In the polarity of highest vs. lowest, it is highest which is usually unmarked, but the fundamental, which is often privileged, commonly refers to the lowest. However, the fundamental sometimes refers to the highest level, either because a top-down orientation is favored over a bottom-up orientation or because what is taken as top and bottom is reversed. In this book, highest and lowest are both viewed as fundamental and by the principle of symmetry are given equal weight. Having two fundamentals deprives each of any exalted status, and adding mediating levels further reduces their importance. b a

Note #8 Incompleteness vs. inconsistency, p. 320 See the discussion of fundamentalisms in social systems in 6.4.2 Modernization as differentiation, p. 252

b

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The interests of higher levels and the system as a whole are never identical. Any privileged position within the system is used for gain, and increasingly so over time. Because of the inherent inequality between higher and lower levels, exploitation of the latter by the former is the rule. Where the system is embedded in a more encompassing order, the higher levels become the locus of external control. In complex systems, hierarchy often consists of informational regulation of transformations of substance. Distillation of an informational 96 domain is a refinement that facilitates adaptation, but it also introduces vulnerability – to failures of coordination, to dysfunction between levels, and to informational 97 parasitism.

96. Distillation and alienation “Information is an alienated experience” (Jaron Lanier 2000). The capacity of an informational order to take on a life of its own is a two-edged sword. To the degree that a symbol becomes autonomous both from material embodiment and referent, information becomes independently manipulable and thus more useful, but in the reification of information there is a weakening of groundedness, which makes possible not only representation but illusion, and not only reflective connection but alienation. The emergence of information as a facet of existence distinct from matter and energy is a distillation of and a detachment from substance and activity. Distillation is refinement, etherealization, concentration; it brings both benefit and harm.

97. Informational parasitism In the domain of life, a virus is an “informational parasite,” an informational entity that parasitizes a host system by stealing its matter-energy. It contains genetic material (DNA or RNA) with

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a delivery system that allows it to penetrate a target cell. The virus neutralizes the cell’s normal informational processes and exploiting its matter-energy processes to make copies of itself. Computer viruses represent a similar phenomenon in a purely informational domain. These and similar informational entities subvert the regulatory processes (operating systems) on computers and networks to multiply in and often damage such systems. Although the action of such viruses occurs strictly in the domain of software, where matter-energy transactions are irrelevant, one might regard the availability of CPU cycles as playing the role of energy and of core or disk memory as playing the role of matter. This is not a completely satisfactory analogy since the energy used for self-replication is not derived directly from the environment with which the virus interacts but from the computer meta-environment. Nonetheless, the parallels between computer viruses and biological viruses are substantial, reflecting the vulnerability of any informational order to subversion or parasitism. This is demonstrated by the simulations of Ray (1992), whose Tierra system is a contained computer medium for the investigation of evolutionary and ecological phenomena. After the medium is seeded by a replicating entity (resources for replication are CPU cycles and core memory), parasites spontaneously emerge that exploit these entities; so do “hyper-parasites” that exploit parasites. Ray speaks of “informational parasitism” in the context of his model; here the phrase is more general. Viruses are takeovers by an alien informational order, but informational parasitism can also occur within a system when informational subsystems are autonomous and self-serving and exploit their role in the overall system. The raison d'être of an informational order is its function of regulation, control, and optimization, but this function may become secondary to the interests of the informational subsystem itself. As Margalef (1963, 1968) has observed, “the organized exploits the

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unorganized”; a the informational order is more organized than the foundational strata of matter-energy processing, so the possibility of internal exploitation is ever-present. See also the discussion of a different type of informational parasitism in the section on Cognition. b Figure 87(a) shows the idea of foreign information inactivating (shown as crossed out) internal information and taking over a system. Figure 87(b) shows typical (generally normative) relative sizes of informational and mater-energy domains. Figure 87(c) shows (and exaggerates) the inversion of this normal balance due to exploitation of the matter-energy subsystem by the informational subsystem. Figure 87 Informational parasitism

information information matter-energy (a)

a

information

matter-energy (b)

information

matter-energy (c)

Note #164 The organized exploits the unorganized, p. 569 Note #104 Embeddedness of cognition, p. 475: embedding supra-systems are an external source of informational parasites.

b

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7.1.8 Cognition Notes: 98 A naturalistic epistemology 99 The modeling subsystem 100 Tetrad of modeling 101 Pragmatic, semantic, syntactic 102 Multiple subselves 103 Self and non-self 104 Embeddedness of cognition 105 Cognition and time 106 Constructing reality 107 Representation 108 Cognition and autopoiesis 109 Relativity of models 110 Fallibility 111 Modeling constraint 112 Sensitivity and specificity 113 Wrong perception 114 Self-reference

page 461 463 465 468 472 473 475 476 477 479 480 481 481 482 484 486 487

98. A naturalistic epistemology This book primarily adopts an ontological as opposed to epistemological stance. a By discussing knowledge that systems have about their environments and themselves, epistemology is naturalized and included within ontology. b Ontological incompleteness or inconsistency becomes epistemological. Beyond organisms (mainly animals, but in some sense also plants) that have “modeling subsystems,” other kinds of complex adaptive systems (CAS) also gain and utilize knowledge about their environments and themselves: social a

2.3 A new conception of metaphysics, p. 54 This differs from “second-order cybernetics” which fuses epistemology with ontology by including the observer in any model of a phenomenon (von Foerster 1974, 1981).

b

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systems, e.g., organizations and societies, and technological artifacts, e.g., robots and some software. (Populations of organisms and ecosystems might be said to exhibit cognition, but this section focuses on controlled systems a in which cognition is accomplished by a “modeling subsystem” and is not merely implicit.) In this section of Essay and Notes, hopefully it will be clear from context whether (i) cognition in general is being spoken about, or (ii) cognition in a narrower sense, applicable only to higher animals, is being spoken about, or (iii) the discussion is even more narrowly conceived so ideas presented are applicable only to humans. “Cognition” is used here broadly to mean “mind” in general, including information processing and experience. It includes affect, socially conditioned mental processes, etc. For Essay, the existence of the subjective is an objective fact, so the objective perspective is given primacy. The fact of subjective experience, however, is still a scientific mystery, so this aspect of mind is only touched on. b Only some concrete and abstracted c systems have modeling subsystems. Agency is informed by cognition. The informational domain may include a subsystem that models the environment, other parts of the system, the system-environment 99 interaction, and even itself. Incompleteness extends to this subsystem. There are limits to d the scope and complexity of any model.

a

Note #88 Hierarchies and networks, p. 445 Note #114 Self-reference, p. 487, reflecting a world-centered perspective, depicts subjective experience as the highest manifestation of the complex category of cognition and as a phenomenon yet to be understood, but in the human-centered perspective subjective experience is taken as axiomatic and thus unproblematic, the necessary starting point of any inquiry. c 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 d Note #86 Complexity, p. 441 b

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99. The modeling subsystem The modeling subsystem (MS) models the system, its relevant environment, and the system-environment distinction, as shown in Figure 88(a). In providing the system with a model of itself, it establishes an informational self-reference analogous to the matter-energy self-reference of autopoiesis a and thus a higherlevel locus of system identity. In generating models, it engages in system formation, b where “system” now takes on its epistemological meaning of “model.” c Figure 88 The modeling subsystem (a) The contents (dashed) of this example of a modeling subsystem (MS) are S, a model of the system, E, a model of the environment, and an S-E relation (block arrows). (b) An alternative diagram in which MS depicts the system as a structure-function nexus. function

(a)

E

S MS

S E (b)

S MS

S E

structure

Viewed as part of the system, the modeling subsystem is a regulator. Although “Every Good Regulator of a System Must Be a Model of the System” (Conant and Ashby 1970), not all regulators are complex enough to be considered modeling subsystems. For example, in the information hierarchy presented earlier, d cause- and error-controlled regulators e are listed at level a

Note #47 Autopoiesis, p. 393 Note #120 System formation, p. 496 c 2.5 Theories and models; the idea of “system” p. 71 d Table 9 Levels of autonomy and information, p. 158 e Notes #44 Law of Requisite Variety, p. 384, #45 Feedback control, p. 386 b

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(iii) and the genotype a at level (iv2), while a modeling subsystem, being more complex than either of these, is listed at level (vi). Figure 88(b) shows the contents of MS as a double cone with the system as focal center. It is a center (i) as a union of structure and function; also (ii) for concrete systems having spatial extension, the system is the reference point for everything else, i.e., it is the origin of the expanding upper cone. In the language of physics, this is a “body-centered” view, where all objects in space are located in a coordinate system centered in the system – as opposed to a “space-centered” view, where the system’s location is not privileged and the origin of the coordinate system is an arbitrary reference point. The spacecentered view, a “view from nowhere” (Nagel 1989), reflects the fact that the world exists independently of any particular system. Since the modeling subsystem has the function of regulating internal complexity and external agency, it is inherently body-centered; but this “subjective” orientation of the modeling subsystem can in principle be supplemented, even largely replaced, with a space-centered and more objective stance. The innate perspectival orientation can be transcended. Regulation by a modeling subsystem requires an instrument that can affect the environment or other parts of the system. Action by the instrument must serve some goal and be given 100 But instrument, goal, and proper direction. direction are often flawed, and the practical, 101 components of meaningful, and formal agency are rarely well-integrated. Moreover, multiplicity in system-environment interactions induces a corresponding 102 which multiplicity in the modeled self, poses a challenge of integration. a

Note #49 Genotype and phenotype, p. 395

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100. Tetrad of modeling Essay here applies the tetradic structure used to discuss problem-solving, regulation, and purposeful action a to the modeling subsystem. Figure 89 divides modeling into a triadic regulator (modeling subsystem) and a fourth part (the rest of the system) that is regulated. Figure 89 The modeling tetrad (a) The triadic modeling subsystem (MS) is shown in bold; what it regulates is the fourth (bottom) term. (b) Three interpretations of this tetrad, each in a different font. (c) Arrows indicate diachronic evolution of this system: ground→instrument→goal→direction. b

MS

S

E GOAL

(a)

(c)

emotion

utility critic

INSTRUMENT

DIRECTION

instinct/sensory-motor

intellect

energy controller

information model

GROUND

(b)

a

body

matter controlled

Figure 25 Tetrad of problem solving, p. 146; Figure 79 Tetrad of purposeful action, p. 426 b Table 14 Two syntactic-semantic-pragmatic hierarchies, p. 470; Figure 128 Tetradic evolution, p. 581

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The regulatory triad is goal, direction, and instrument, or, equivalently, ideal, theoretical, and practical. Direction (theoretical), informed by goal (ideal), guides instrument (practical), which acts on ground (actual), i.e., the (rest of the) system or the environment. Regulation is most effective when all three components exist, not merely one or two, and when they are fully developed and properly integrated. Excessive dominance of or specialization in any one component, analogous to the “four fundamentalisms” of dysfunctional societal differentiation, a will interfere with the proper functioning of the modeling subsystem. Figure 89(a) indicates that the regulator triad collectively interacts with S; there is no intention to imply that interactions are only pairwise. But the relation between MS and E is not shown (MS gets information from E and affects E through S). In Figure 89(b), each term of the tetrad is given three different interpretations, shown in different fonts: one biological, one abstract, and one from engineering design; for the instrument component, for example, instinct / sensory-motor, energy, and controller, respectively. In these interpretations, the natural sequence of regulator components is shown in Figure 89(c), namely ground→instrument→goal→direction. (This sequence differs from Parsons’ order b of ground → instrument → direction → goal. These two hierarchies capture different aspects of the tetrad.) The three interpretations are: 1. Biological: Body (GROUND) – Instinct / sensory-motor (INSTRUMENT) – Emotion (GOAL) – Intellect (DIRECTION): The most complex modeling subsystems are found in the higher primates, especially in human beings. Instrument, goal, and direction correspond to instinctive (internally oriented) and sensory-motor (externally oriented), emotional, and intellectual regulator components, respectively; informally: do, feel, and think. These components roughly a b

Figure 34 Four fundamentalisms, p. 257 Figure 33 Parsons’ tetrad of social systems, p. 253

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correlate with the reptilian, paleo-mammalian, and neomammalian parts of the “triune brain” (MacLean 1990). The regulator triad controls the regulated component, the body (GROUND). Instrument has the most direct connection with the body; its dyadic character stems from its dual role in inner (instinct) and outer (sensory-motor) regulation. (One could add history a to this structure-function dyad by narrowing the meaning of instinctive and explicitly adding reproduction as a third component of instrument, one inherently diachronic and both inner and outer.) Finally, in this interpretation of the tetrad, since the components are themselves complex, they might be fractally decomposable into self-similar tetrads or triads. For example, instrument might internally consist of (ground,) instrument, goal, and direction subcomponents; indeed Parsons proposed such fractal order for his tetrad. 2. Abstract: Matter (GROUND) – energy (INSTRUMENT) – utility (GOAL) – information (DIRECTION): The instrument (instinct/sensory-motor) component especially involves use of (generalized) energy, the goal (emotion) component is concerned with utility, and the direction (intellect) component is informational. Although all components involve energy, utility, and information, these are the salient aspects of these components. 3. Engineering: Controlled (GROUND) – controller (INSTRUMENT) – critic (GOAL) – model (DIRECTION): An artificial neural network architecture known as approximate dynamic programming (Lendaris and Neidhoefer 2004) resembles this tetradic structure. A controller (instrument) directly acts on the controlled system (ground). A critic (goal) component estimates the utility of actions now and in the future. A model (direction) component depicts how actions of the controller, guided by utility considerations of the critic, affect the controlled system.

a

3.5.2 Adding history, p. 116

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Following are some other correlations. a First, instrument, goal, and direction correspond to Aristotle’s efficient, final, and formal causes. b Second, the engineering components relate to difficulties of ordinal decision-making: c A controller must be decisive; a critic must be fair with respect to utilities being optimized; a model must be rational. Third, in terms of bodyvs. space-centeredness, d system-centeredness is the default in instrument, goal, and direction, but a non-system-centered view could characterize direction, which would then expand goal by broadening how utility is defined, and thus affect instrument.

101. Pragmatic, semantic, syntactic Direction, goal, and instrument correlate to some extent with syntactic, semantic, and pragmatic information, e as shown in Figure 90. Instrument (Instinct/sensory-motor) correlates with pragmatic information, goal (Emotion) with semantic information, and direction (Intellect) with syntactic information. Figure 90 Pragmatic, semantic, syntactic; regulatory triad GOAL

(ideal) emotion semantic The Beautiful DIRECTION

(theoretical) intellect syntactic The True a

INSTRUMENT

(practical) instinct / sensory-motor pragmatic The Good GROUND (actual)

Triads, even in the same domain, need not be correlated. For example, Lacan’s (Johnston 2018) “real” and “symbolic” correlate roughly with instrument and direction, but his “imaginary” does not correlate with goal. b Figure 25 Tetrad of problem solving, p. 146 c Note #68 Aggregating preferences, p. 420 d Notes #1 System, p. 295, and #99 The modeling subsystem, p. 463 e Note #46 Information (and matter-energy, utility), p. 389

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The simplest information that an organism gains about its environment is pragmatic: Information may directly trigger an action. This is illustrated by responses of a regulator a guided by an R(D) that maps environmental disturbances, D, onto regulator actions, R. Pragmatic information can alternatively be defined as information that brings utility. For example, assume that advance – and accurate – information about the future state of nature is available for purchase by an agent. Having such information changes a decision under risk to a decision under certainty. b The difference between expected utilities with and without information is the utility value of the information. A more complex type of information is semantic. A regulator consisting of instrument plus goal is no longer completely at the mercy of environmental selection, since the utility of the instrument’s response can be assessed by the goal component, which allows corrective action to be taken before the environment renders judgment on the system’s viability. In more advanced regulation, instrument and goal are supplemented by a direction component: Action is guided by a model, which contains knowledge of how regulation affects the system and/or the environment. An example of such a model in the Law of Requisite Variety is the E(R,D) function that specifies the joint effect of regulator action and environmental disturbance on the essential variable; this is a special case of O(A,N) in the decision-theoretic model. c Models are especially useful if they can be operated on purely syntactically (formally). The above discussion asserts an ascending sequence of pragmatic→semantic→syntactic information, briefly indicated above d and further discussed in Diachronics. e Weaver’s original conception has the order of Table 14(a), with Shannon’s a

Note #44 Law of Requisite Variety, p. 384 Note #56 Decision theory, p. 408. c Note #56 Decision theory, p. 406 d Figure 89(c) The modeling tetrad, p. 465 e Note #173 Evolution of modeling subsystem, p. 581 b

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information theory applying only to the syntactic level. Weaver’s order, in terms of the double cone diagram, correlates syntactic and pragmatic information with structure and function, a but categorizing information in terms of levels of abstraction b gives the order of Table 14(b). Table 14 Two syntactic-semantic-pragmatic hierarchies Two opposite orderings, appropriate to different contexts. In each ordering, level 1 is foundational. (a) Weaver 3. Pragmatic 2. Semantic 1. Syntactic

(b) here 3. Syntactic 2. Semantic 1. Pragmatic

In the scheme of Table 14(b), pragmatic information acts directly on the regulated part of the system. Semantic information might be considered to be second-order pragmatic information; syntactic information, information treated formally, is still more indirectly tied to action. This is the evolutionary sequence of emergence c of these three informational supports for agency. First, there was pragmatic information – “In the beginning was the deed” (Goethe) – then semantic information, and finally syntactic information. This phylogenetic order of Table 14(b) is the opposite of Weaver’s “logical” order of Table 14(a). Phylogeny is roughly recapitulated in ontogeny in that cognitive development of children more resembles (b) than (a). As schematized by Piaget (Phillips 1975), the ability to physically manipulate objects precedes the capacity to mentally manipulate representations of them. d

a

Figure 5 Coherence and correspondence, p. 61 See Figure 6 Between math/philosophy and scientific theories, p. 64; Figure 9 Intersection of math, philosophy, scientific theories, p. 67 c Note #173 Evolution of modeling subsystem, p. 581, in Diachronics d Pragmatic-semantic-syntactic of Table 14(b) correlates approximately with Lacan’s (Johnston 2018) sequence of real-imaginary-symbolic. b

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Pragmatic information is adequate or not adequate, but syntactic information, augmented with its semantics, is true or false apart from pragmatic considerations. Pragmatic information is natural (biological). Syntactic information is Platonic (about abstract form). Semantic information bridges the two. In its simplest manifestations, the modeling subsystem uses pragmatic information, and models are not representations, but simple heuristic rules (sensory-motor mappings) for action. But in its more complex manifestations, the modeling subsystem also uses semantic and syntactic information, which may include representations. a In reaching the syntactic level from a primal pragmatic base, the modeling subsystem enters the realm of abstracted systems. b As Peirce writes (Bloom 1975), “…the highest grade of reality is only reachable by signs.” Although grounded at the pragmatic level, a naturalistic epistemology is not confined to this level but points to access to a higher world of forms. Modeling, through its evolutionary emergence, comes to instantiate a naturalistic Platonism. Semantic information is the meaning of syntactic information. Meaning is the recognition of constraint (Zwick 1986), the isomorphism c – more generally, the correspondence – of the structure of syntactic information with a structure d already represented in the modeling subsystem. e As expressed by Gray (1974), “meaning is the digestion of newness into sameness.” The famous philosophical triad of The Good, The Beautiful, and The True can be mapped onto the regulatory triad, as shown above in Figure 90. The Good is the aim of the instinct/sensorymotor (instrument) component of the modeling subsystem, which focuses on the pragmatic. The Beautiful is the aim of its emotion (goal) component, which focuses on the semantic. The a

Note #107 Representation, p. 479 3.1.2 Concrete, abstracted, and conceptual systems, p. 85 c Figure 11 Isomorphisms, p. 74, 3.3 Isomorphism and emergence, p. 97 d Note #108 Cognition and autopoiesis, p. 480 e Figure 5 Coherence and correspondence, p. 61 b

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True is the aim of the intellectual (direction) component, which focuses on the syntactic. In a different sense, The Good, The Beautiful, and The True are three aspects of utility, which is correlated with the goal component, but the tetrad depicts the modeling subsystem as differentiated, and each component of this structure also has its own specialized virtue or type of utility. This scheme can be extended (Moore 2021) by correlating the bottom component with The Real, which grounds The Good, The Beautiful, and The True.

102. Multiple subselves The modeling subsystem’s distinction between system and environment does not imply that either is a simple unity. Figure 91 (ahead) shows, to the contrary, that system S is constituted by multiple subselves, S1, S2, etc., with different functions in different sub-environments, E1, E2, etc. This idea is akin to Minsky’s (1986) “society of mind.” The subselves are subagents providing requisite variety, a but their goals b are not integrated and change over time in salience. Agency, thus multiple and variable, is inconsistent, c while the unitary ground of the subselves, namely the body, provides an illusion of unity and constancy. Subselves are linked in networks with structural localization supporting functional differentiation. They relate to one another through both cooperation and competition, and form coalitions. d In any particular context and moment, there may be a dominant subself that claims the authority of the whole and binds its future. e

a

Note #44 Law of Requisite Variety, p. 384 Note #67 Multiple objectives, p. 419 c Note #6 Inconsistency, p. 311; Note #139 Temporalization of complexity, p. 532 d Note #76 Coalition instability, p. 431 e Note #65 Binding the future and sunk costs, p. 417 b

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Figure 91 Multiple subselves Each subself is a regulator, Sj, adapted to sub-environment, Ej.

S1 S

S3

E1 S2

E2 E3

E MS

SE

The modeling subsystem internalizes the primal distinction between self and non103 self. Although an embedding environment may provide an informational framework that amplifies cognition, the modeling subsystem then comes to harbor the tension between system and suprasystem. Through this subsystem the environment acquires a 104 beachhead of control over the system.

103. Self and non-self Although Essay is committed to a naturalistic realism, it echoes the idealist notion of Fichte (1794) that self1 – the modeling subsystem – posits self2 and non-self2, i.e., the basic distinction of system and environment. The two “self” terms are different; one should use different words, as Peirce did in Firstness and the First in Secondness. a Self1 as monad is the progenitor of self2 in the dyad just as Firstness is the progenitor of the First in Secondness. b In the dyad, as deconstruction insists, self2 implies not-self2, and vice versa, so self2 is not “self-identical” since it depends on its complement. But self1 in the monad is primal (and “self-identical”). For Fichte, non-self2 checks or limits the “I,” just as Peirce’s Second checks the First. a

See the discussion of terminology in 3.2.2 Utility, p. 95, and Note #30 One, two, three, ten thousand, p. 359 b Figure 58 Progression through the categories(a), p. 360

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Diachronics does not discuss the development of the modeling subsystem, so a comment here on this is appropriate. Psychoanalytic object relations theory asserts that a fundamental process in human cognitive development is the transition from an infant’s initially undifferentiated experience (self1) to the distinction it soon makes between self and other objects, especially its mother, i.e., to its positing of a self2 is based on its interactions with others (S′) in its environment E (Figure 92). In some higher organisms, codependence of self and other is reflected in a “theory of self,” in which cognitive capacities are attributed to similar systems, and mirror neurons, in which actions of other systems are modeled with the same neural circuits that model self. Figure 92 Codependence of modeling of self and other The modeling subsystem MS imputes a modeling subsystem MS′ in the other system, S′.

S′

S

E

MS′

MS

S E

In Figure 92, environment, E, is a type (b) a environment which, in addition to being textured, contains another system, S′, to which MS attributes a modeling subsystem (“theory of mind”), whose actions are modeled as if done by self, S. While in a type (a) environment, textured but without other systems, a bodycentered (subjective) perspective is natural, in a type (b) environment (multi-centric) containing similar systems points a space-centered (objective) perspective becomes useful. In a type (c) environment, both perspectives are needed.

a

Figure 73 Environmental types, p. 405

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104. Embeddedness of cognition If the system is embedded in a structured context a that organizes many systems, the larger whole may have a modeling subsystem that is a common resource for its constituents. For example, human beings are embedded in social systems that provide language and culture, technologically augmented in contemporary society by the Internet and social media. This is represented in Figure 93(a), where systems, S, S´, and S´´, and their modeling subsystems are embedded in MS of suprasystem, S. The modeling subsystem of the embedding system also colonizes the modeling subsystems of its constituents, which is not always to their advantage. In Figure 93(b) the memes b of the suprasystem are utilized by or infect the individual systems, i.e., are either resources or informational parasites. c Figure 93 Embeddedness of cognition (a) MS of systems S, S′, and S′′ are embedded in MS, modeling subsystem of suprasystem S. (b) mj = memes in MS. MS

MS′

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m1 m1 m1 m2 m2 m3 m1

m1 m2

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A type (c) = Emery and Trist type IV environment; see Note #55. The idea of “memes” here is intended to be very broad, to include not only concepts or expressions that spread extensively throughout the sociocultural supra-system, but the entire structure of language itself. c Note #97 Informational parasitism, p. 458. The idea of such parasitism is vividly expressed in The Mind Parasites (Wilson 1968), a science fiction horror novel. A related but different description of the pathological effects of social media would characterize these effects as the amplification and intensification of what in Buddhism is called “monkey mind.” b

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Cognition extends agency in time and space. The present moment widens into past and 105 future. Through extension in time, potential is represented in a model that is actual. Through extension in space, the relevant environment expands into distant realms. But a system released from the here and now loses contact with it.

105. Cognition and time The model of the present is augmented with a record of the past and a projection of the future. Figure 94(a) shows a horizontal temporal double cone diagram, a 90° rotation of the vertical spatial double cone diagram of structure and function. a Vertical and horizontal double cones are joined together b in Figure 94(b); in its vertical double cone, structure-function has been renamed as inner-outer. The space-time diagram of Figure 94(b) is used in Diachronics to depict system formation c; there the diagram is ontological; here it is epistemological. Figure 94 Temporal triad; space-time tetrad (a) Temporal double cone; (b) tetrad of joined spatial (dashed) and temporal double cones. outer

past

Present moment future (a) time

future

past (b) space

inner time

a

Figure 88 The modeling subsystem, p. 463 This tetrad is adapted from the tetradic “cross of reality” of RosenstockHuessy (1993) (Chrysalis 2016, Crystaudo 2019): {inner (subjective), outer (objective), past (trajective), future (projective)}. c Figure 101 System formation, a time-space tetrad, p. 501 b

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Instrument, goal, and direction, the components of the regulatory triad, have different temporal orientations. Instrument (sensory/motor) is oriented toward the present, direction (intellect) is oriented toward past or future, and goal (emotion) links past/future and present. The modeling subsystem ingests external and internal impressions. Although novel impressions carry maximum information, the metabolism of impressions by preexisting structures inhibits the recognition of novelty, so this subsystem, an apparatus for assimilating information via openness, becomes itself a source of closedness. Or impressions may not be assimilated. Their complexity or number may be too great or the modeling subsystem too passive. Modeling is representation and 106 107 construction. Representation compresses impressions; construction organizes them, since structures of understanding cannot be ingested whole but must be developed 108 Impressions are incomplete and internally. may be unreliable. The internal construction of reality partially compensates, but since construction exercises some independence from fact, it produces a web of representation, inference, and invention that cannot be disentangled. Construction is distorted by pressures of utility. The modeling subsystem depicts a world and a self that are in part illusion.

106. Constructing reality The modeling subsystem constructs an internal view of reality. For the modeling subsystems of organisms, the imperatives of survival suggest the relative fidelity of these constructions to

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“things in themselves” since natural selection winnows out nervous systems that offer poor guides to action. Similar assurances are not available, however, for the modeling subsystems of social systems, because adaptation often has not had sufficient time to get established. Human beings now live in social and cultural environments very different from those that shaped human nature and thus are not biologically well adapted to contemporary social realities. Modeling subsystems of social systems are invariably afflicted with fantasies and falsehoods. Given the constructive activity of the modeling subsystem, representation and invention are not inherently different, hence the possibility of creating virtual realities through the systematic deception of natural information processing (Rheingold 1991). VR simulation transforms the computer into a medium for vicarious experience. All this is implicit in the distillation of information from matter-energy. But vicarious experience and invented realities are not solely the products of technology or culture. They are endemic even for nervous systems without external augmentation. Although natural selection has guaranteed that the human modeling subsystem is roughly reliable, illusion is ubiquitous and not solely due to faulty perception or incorrect inference. Some illusions, e.g., denial of death, may have been evolutionarily advantageous. Pragmatic truth, which governs selection, does not assure correspondence truth. Cognition shapes, infers, invents, replaces, and recalls. This is the discovery of 20th century psychology in many of its disparate forms, but it is also an ancient doctrine. In the Buddhist and Platonic views, mind is corrupted by illusion, and thoughts and images have connections to reality that are not completely reliable. According to this doctrine, the human organism often lives in virtual reality and an artificial world, having become accustomed to a deception so complete that it goes unnoticed. This is probably an exaggeration. The extreme constructivist, Freudian, or Buddhist position, that illusion is

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inherent in human mentation, seems oblivious to the evolutionary arguments for the rough fidelity of mental models to external reality. But one need not accept an extreme position to acknowledge that modeling is imperfect. To model a complex reality, modeling must have the capacity for active construction. With this comes the inevitability of illusion. This is a matter of degree. Modeling subsystems can represent the possibility and dangers of illusion. But the very notion of illusion implies an objective reality, and the possibility of altering the proportions of illusion and truth. There are some who hold that there are multiple objective realities, that ideas about reality – and their acceptance or rejection – are matters merely of personal, social, or cultural choice or convention, subject perhaps to a requirement of internal coherence but not a requirement of correspondence to an objective external truth. There are even others who imagine that “reality” is really a simulation in some vastly larger world. Such positions are intellectual posturing; no one believes them who flies in an airplane or goes under a surgeon’s knife.

107. Representation Representation does not have to be explicit in the direction component or in modeling in general. For example, in both cause- and error-controlled regulation the direction component does not explicitly represent what is actual, a but representation might still be said to be implicit, since “every good regulator of a system must be a model of that system” (Conant and Ashby 1970). The character of representation depends also on the pragmatic, semantic, and syntactic b nature of the information modeled. In representation, input from instrument is used to build a model. See the note below on modeling constraint. c

a

Notes # 44 Law of Requisite Variety, p. 384, and #45 Feedback control, p. 386 b Note #101 Pragmatic, semantic, syntactic, p. 468 c Note #111, p. 482

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108. Cognition and autopoiesis Information from the environment and other parts of the system drive construction of MS structures. Figure 95(a) shows this process as partially autopoietic. a Structures of understanding, “schemata” in CAS terminology, cannot be ingested whole but must be constructed. (As in diachronics, all development is internal development. b) Figure 95(b) shows the constructed hierarchy as a 3-level neural network; with many more levels it would illustrate a “deep learning” neural network (Goodfellow et al. 2016). Existing levels of structure mediate both intake and construction. Intake mediation is part of “active inference” (Friston et al. 2011): Intake (instrument) is guided by model construction (direction). Construction includes assimilation and accommodation (Piaget 1967). In assimilation, information gained in practice (instrument) merely adjusts structures (direction) and in accommodation structures change. Figure 95 Cognition and autopoiesis (a) The dashed curved arrow shows a level mediating its own construction; the dashed straight lines show a level mediating information intake from the outside, E, or inside, S. n10 n8 n5

E

M

S

n1

(a) cognitive autopoiesis a b

Note #47 Autopoiesis, p. 393 Note #127 Self-development, p. 513

n6 n2

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n4

S (b) levels of (a) shown as a neural network

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Figure 95(b) depicts the upward flow of Figure 95(a). The first level, nodes (neurons) n1 to n4, is the instrument which receives inputs from the ground, i.e., the environment E and the rest of system S. The second and third levels are direction, which compresses (abstracts) information. These two figures emphasize upward arrows, but views of cognition as predictive a stress the importance of downward flows which are predictions, corrected by upward flows. Adjusting and radically revising predictions correspond to assimilation and accommodation, respectively. Just as variety and disorder are not intrinsically but only functionally distinguishable, there is no inherent difference between a model that is adequate to reality and one that is not. There is always more than 109 and the degree to one adequate model, which any model is valid cannot be specified 110 by the model itself.

109. Relativity of models Apart from the possibility of illusion or error, the same reality can be correctly represented by models that are qualitatively different. Ashby (1956) gives an example of two models that are isomorphic – express the same information – yet elements are dynamically uncoupled in one and uncoupled in the other, b and thus these two models are qualitatively very different.

110. Fallibility The modeling subsystem, like all systems, is flawed. This subsystem partly remedies the system’s incompleteness but is itself incomplete, and nearly always also inconsistent. In human beings, as Spinoza writes (Norris 1991), “The mind has no adequate knowledge of itself, nor of its body, nor of external a b

Note #111 Modeling constraint, p. 482 Figure 51 Coupled and uncoupled dynamic systems, p. 328

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bodies, but only a confused knowledge.” Rationality is bounded, to use the term popularized by Simon (1947), although its limits are not fixed or permanent. Flaws of the modeling subsystems include failures of coherence, correspondence, or pragmatics, and tensions between these different criteria of truth. a 111

By representing the constraints through which the environment is organized, the system may be able to exploit these constraints to its advantage. But constraints may be inaccessible to observation or too complex to model, or may be unstable or evanescent, being altered by even small changes in the environment. Or, constraints may be absent, and their modeling a false inference. External order can never be completely and accurately discerned. Modeling may allow detection of hazards and opportunities. There is a tradeoff between responding to weak signals and avoiding false 112 alarms. Unreliable perception and worstcase assessments of internal or external events 113 There is no way to be can be self-defeating. certain when a protective response can be safely relinquished.

111. Modeling constraint The direction component of the modeling subsystem constructs representations of constraints in the environment or the system. Representation is compression. Order (constraint) is captured and disorder is discarded. Order is the basis of meaning (Zwick 1986). b The model is simpler than the perceived data. This simplification is not a flaw of incompleteness but rather a a

See discussion of these three criteria of truth in 2.3 A new conception of metaphysics, p. 54, and Footnote #53, p. 60. b Note #20 Reconciling constraint and variety, p. 341

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valuable feature of models. Simplification is a flaw only if order not modeled is important to the system. Choice of model requires a trade-off between accuracy and simplicity. Accuracy can be quantified by mutual information (Shannon and Weaver 1949) between what is modeled (data gathered by the instrument component) and its representation (in the direction component) or by prediction error. Simplicity is important because modeling consumes resources and overly complex models generalize poorly to new data. Thus representation requires optimizing a a combination of accuracy and simplicity, such as the Bayesian Information Criterion (Schwartz 1978). Such combinations are related to free energy notions in physics (Friston et al. 2006). The topological (as opposed to quantitative) aspect of order b being modeled is its structure, one of a set of possible structures. c To the extent that the model accurately captures the structure of this external constraint, the two are isomorphic, d or, if the model aggregates variable states, homomorphic or if the similarity is looser, an analogy or metaphor. Making of analogies and metaphors is a basic activity of the modeling subsystem (Mitchell 1993). Modeling may employ only variables present in the data or may also postulate hidden (latent) variables. e Matter-energy aspects are relevant to resource requirements for modeling. Utility f aspects are also important. Modeling external a

Note #70 Optimization, p. 423 Note #13 Order, p. 332 c Figure 46 Lattice of (general) structures for 4 elements, p. 310. Searching the lattice up or down is synthesis or analysis, respectively; see Figure 113 Segregation and systematization, p. 536, of Note #140 Two universal processes. d See the discussion around Figure 11 Isomorphisms, p. 74. e Figure 95 Cognition and autopoiesis, p. 480 f Note #46 Information (and matter-energy, utility), p. 389, Figure 16 Utility as a 4th fundamental category, p. 94 b

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(or internal) states must be advantageous to the system; this is what pragmatic information means. a Bateson (1979) defines information as “news of difference that makes a difference.” News of difference is syntactic information; the difference it makes is (semantic and) pragmatic information. For example, systems can adapt to Type II environments b if information about the environment (i) can be captured and (ii) has utility; so ideal environments are characterized by high values of utils/bit (Fletcher et al. 1998). One might represent constraints and actions of other agents with a decision theory model, which estimates probabilities of states of nature, models how outcomes depend on actions and states of nature, predicts future states of nature, and updates knowledge with new information. This is referred to as Bayesian inference, Bayesian decision theory, or Bayesian cognitive science.

112. Sensitivity and specificity The trade-off between sensitivity to weak signals and vulnerability to false alarms is central to signal detection (Swets et al. 2000). If signal strength is a good indicator that the environment (or system) is in a dangerous (D) state, an agent may set a threshold for the signal above which the state is assumed and below which it is not. If the threshold is low, most occurrences will be detected; this is called high “sensitivity.” But there will also be false alarms (false positives); this is called low “specificity.” If the threshold is high, there will be fewer false alarms, but there will be missed detections (false negatives), i.e., specificity will be high but sensitivity low. This is summarized in Table 15, where a positive means a detection of D. Sensitivity measures how well the presence of D is detected; specificity measures how well the absence of D is detected. There is usually no way always to avoid both false alarms and missed detections. a b

Note #101 Pragmatic, semantic, syntactic, p. 468 Note #55 Environmental types, p. 404

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Table 15 Sensitivity and specificity D = an adverse condition (e.g., a disease) TN = true negatives; TP = true positives; FP = false positives; FN = false negatives sensitivity = TP / (TP+FN) = true positives/actual positives specificity = TN / (FP+TN) = true negatives/actual negatives.

True

not-D D

Predicted/Detected not-D D TN FP true negatives FN TP true positives

Trade-offs between sensitivity and specificity resulting from different thresholds define the ROC (receiver operating characteristic) curve of Figure 96. A detection threshold set very low gives (specificity, sensitivity) = (0,1), the upper-left endpoint of the curve; a threshold set very high gives (specificity, sensitivity) = (1,0), the lower-right endpoint of the curve. If utility values are given for TN, TP, FP, and FN, there exists a threshold that gives the highest expected utility. In general, a good threshold has high values to both sensitivity and specificity, i.e., some northeast point on the ROC curve. However, because a missed detection is typically more serious than a false alarm, sensitivity is often more valuable than specificity. Figure 96 Sensitivity vs. specificity (ROC) Points on the curve indicate the (specificity, sensitivity) for different threshold values. 1

Sensitivity

0

Specificity

1

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If the test randomly predicts D or not-D, the ROC will be the slope = -1 dashed line in the figure. If the test can discriminate perfectly between D and not-D, the ROC becomes the uppermost and rightmost lines; the optimum threshold is the upper right dot which gives (specificity, sensitivity) = (1,1). For an imperfect test, the area under ROC (from ½ to 1) measures how good the test is. Statistically, the trade-off between false positives and false negatives is the trade-off between Type I and II errors, assuming that the null hypothesis is not-D, and rejecting the null is predicting D. A type I error (false positive), the probability of incorrectly rejecting the null, varies inversely with the probability of incorrectly not rejecting this hypothesis (false negative, Type II error).

113. Wrong perception Even when response is not governed by the worst-case possibility, error in perception or action may cause harm. In simulations of the iterated PD, a Tit-for-Tat (responding in kind to another agent’s action) is vulnerable to noise. If an agent intends to cooperate, but defects due to noise in the instrument of action, or if the action is misperceived by the other agent, the result can be a reverberating loop of retaliations. A strategy of Tit-for-Two-Tats protects against such errors but is exploitable, a deficiency not shared by Tit-for-Tat. One wonders if there is a theorem declaring the non-existence of a perfect strategy for the iterated PD, a theorem like the Arrow impossibility result. b The modeling subsystem mirrors the whole of which it is a part. Through this self114 reference, incompleteness is both fixed and transcended. It is fixed in resistance to change by the model of self. It is transcended in the recognition of incompleteness that selfa b

Note #78 Prisoner’s Dilemma, p. 433 Note #68 Aggregating preferences, p. 420

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reference allows. In the modeling of self, inconsistency is hidden, so the illusion of unity prevents its accomplishment. When modeling is itself modeled, information is distilled to a higher level. This brings enhanced autonomy but also vulnerability to pathologies of selfreference.

114. Self-reference S has a model of itself. One part of S, namely MS, models the rest of S. But self-reference internal to MS is less simple and has at least two possible meanings. First, the contents of modeling can be recursive. Thoughts and feelings can be about thoughts or feelings, although from another point of view, firstand second-order thoughts or feelings are at the same level since they merely reflect changes in the state of MS viewed as a dynamic system. (If level and meta-level are separate, pathologies of self-reference can be avoided, but if meta-level is mapped onto level, such pathologies are probably not avoidable.) The MS could also model the process of modeling, illustrated by Bateson’s (1979) “deutero-learning.” A system can learn about learning. Another notion of self-reference is motivated by the informational hierarchy presented earlier. a In higher organisms, modeling is accompanied by subjective experience. Here a distinction is made between experience and the contents of experience. Rosenthal (1986) distinguishes between “transitive consciousness” or consciousness of some content, e.g., sensations, feelings, or thoughts, and “intransitive consciousness” or experience per se. Bennett (1956, 1964) correspondingly speaks of “sensitive energy,” b the lowest level at which subjective experience emerges, tied to its content, and a higher level of “consciousness,” in which awareness achieves a a

Table 9 Levels of autonomy and information, p. 158 ”Sensitive” in “sensitive energy” is not the same as “sensitivity” discussed in Note #112 Sensitivity and specificity, p. 484

b

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degree of autonomy often associated with a sense of self. He also posits a level below sensitivity, a where processes are automatic, and unavailable to subjective experience (Figure 97). Figure 97 Levels of operation of the modeling subsystem (after Bennett) Arrows signify the directions of attention.

• Conscious

MS S

• Sensitive

MS

S′

S′

S • Automatic

MS

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S The automatic secures the self by internal processes that maintain essential variables b in viable ranges; it establishes the neural informational domain, laying the foundation for the possibility at higher levels of subjective experience. The sensitive is a screen of salience for registering the effectiveness of these processes, and self is implicit. At the conscious level, self, however partial and transitory, becomes explicit in the contents of experience, in the capacity to direct attention, and in access to memory, which underlies the possibility of an autobiographical self. Self at the conscious level is “I”; at the sensitive level, “me”; and at the automatic level, “it.” a

Bennett also posits levels above consciousness, but there he departs what is plausible to contemporary science. b Notes #44 Law of Requisite Variety, p. 384, and #45 Feedback control, p. 386

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The conscious level is the vital integrating center that mediates between inner and outer and between past and future. a When this level is weakly developed or when the modeling subsystem is on auto-pilot, b balance between the poles of space (outer, inner) and between the poles of time (past, future) is lost, and the modeling subsystem predominantly functions at sensitive or automatic levels. Though levels may be coupled or decoupled c in different degrees, the modeling subsystem has greater functionality when higher and lower-level processes are separately developed and properly linked. As in any hierarchical system, there are tensions between levels, d and fluctuations in their relative salience. One might relate automatic, sensitive, and conscious, to the regulatory triad, e i.e., to instrument (instinct/sensory-motor), goal (emotion), and direction (intellect), or, more informally, to doing, feeling, and thinking. The regulatory components might manifest differently at automatic, sensitive, or conscious levels. Or perhaps the degree to which all three regulatory components are actively mobilized and integrated determines whether the modeling subsystem performs at the automatic, sensitive, or conscious levels. Simple modeling subsystems operate at the automatic level (these might involve, for example elementary hunt-and-stick, cause-controlled, and error-controlled regulatory mechanisms f); more complex subsystems operate at automatic and sensitive levels; still more complex subsystems operate at automatic, sensitive, and conscious levels. Modeling systems capable of all three levels vary in the level that is salient on average as well as from moment to moment and the intensity with which levels a

Figure 94 Temporal triad; space-time tetrad, p. 476 Note #137 Mechanization (rigidification), p. 530 c Note #33 Engaging/disengaging, p. 368 d 7.1.7.2 Hierarchies, p. 451, and associated notes. e Note #100 Tetrad of modeling, p. 465 f Notes #44 Law of Requisite Variety, p. 384, and #45 Feedback control, p. 386 b

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manifest. The automatic is relatively constant, but sensitivity and (even more so) consciousness fluctuate. In general, higher levels ameliorate the incompleteness and inconsistency of lower levels. The sensitive level allows the system to act when automatic responses are inadequate. The conscious level brings inconsistencies between subselves or within components of the regulatory triad into view. With consciousness, the system may partially transcend the subjective orientation of sensitivity, and the system-centeredness of the modeling subsystem (Zwick 2015, 2016). To summarize this Cognition section, it is useful to consider three dimensions of the modeling subsystem: (i) components of the regulatory triad, i.e., instrument, goal, and direction, (ii) agent subsystems, i.e., subselves, a and (iii) levels of operation, i.e., automatic, sensitive, and conscious, associated with levels of information or generalized energy. However, it needs to be stressed that this scheme makes no contribution at all to resolving the “hard problem of consciousness”; it just reformulates the problem as the question of how the sensitive level synchronically emerges (and how diachronically, i.e., evolutionarily, it emerged) from the automatic level.

a

Note #102 Multiple subselves, p. 472

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Binary oppositions Dyadic correlations Dialectics The extremes are attractors The war of universality on uniqueness

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A system is constituted in two ways: as an instantiation of order and as the result of a system-environment distinction. Structure is the internal order of parts that is the legacy of the past; function is the participation in the external order of the present. A permanent harmony between structure and function cannot be assured. All systems encompass constraint and variety, unity and multiplicity, closedness and openness, invariance and plasticity, autonomy 115 Constraint, unity, and dependence. closedness, invariance, autonomy, and structure are allied, as are variety, multiplicity, openness, plasticity, dependence, 116 No fixed priority obtains and function. between these constellations of features. Multiplicity, openness, and plasticity protect the integrity of the system, but integrity requires unity, closedness, and invariance. Yet, unity is flawed by partialness, closedness brings dissolution or rigidification, and invariance is unattainable.

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115. Binary oppositions Derrida has made us aware that in binary oppositions one pole is often dominant and privileged a – unmarked – while the other is subordinate and suppressed – marked, but that these attributes are rarely stable or universal. These ideas have been applied in previous notes to various dyadic polarities, many of which are repeated here in this summary section of Synchronics. When relations of dominance and subordination between poles of a dyad appear to be fixed, this may indicate that some fundamental insights have been ignored. Oppositions – more generally, tensions – do not have to be dyadic; they can be triadic, tetradic, or even of higher ordinality. For example, the Arrow Impossibility Theorem illustrates a triadic opposition. b Parsons’ structure of action harbors tetradic tensions. c But binary oppositions are the most ubiquitous.

116. Dyadic correlations The terms are not necessarily linked as listed, but these are default associations. Invariance is protected by closedness, which implies autonomy, and structural definition. Plasticity is allied with openness because openness allows an adaptive response to environmental disturbances which requires plasticity and multiplicity, as opposed to a response that blocks disturbances from reaching the system. Openness implies the existence of relations with external entities, on the basis of which a system is defined functionally, relations that are often the basis of dependence.

a

Note #8 Incompleteness vs. inconsistency, p. 322 Note #68 Aggregating preferences, p. 420 c 6.4.2.1 The Parsonian model of social systems, p. 253; also see (Marcus 1998). b

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These conflicting requirements arise from incompleteness. There are no enduring and 117 context-free solutions to these dialectical dilemmas. In every polarity, each extreme exerts a powerful attraction, yet rarely is 118 No either extreme optimal or even viable. principle of synthesis or balance can compare in simplicity and thus in potency with the imperative of an extreme; in some cases, of both extremes simultaneously. Synthesis of opposing attractors is particular and contingent, not universal and necessary; balance between them remains precarious.

117. Dialectics The conflicting requirements summarized in Essay are manifestations of generalized inconsistency a that exemplify the dialectical idea of “the unity and struggle of opposites.” b Some different consequences that can follow from such conflicts are discussed below. c The assertion in Wholeness that every system is inherently flawed is also a dialectical idea. The temporal unfolding of such flaws is interpreted in Diachronics using the formalism of catastrophe theory, d which makes aspects of the metaphysics of dialectics exact. e Very generally, Essay makes extensive use of the dialectical idea that the strength of a system is simultaneously its weakness and vice versa. Alternatively, the flaws that drive diachronics can be interpreted as instances

a

Note #6 Inconsistency, p. 311; Note #8 Incompleteness vs. inconsistency, p. 320 b The opposites are reconciled in a “synthesis,” which can be given at least two different interpretations; see Note #165 Two kinds of dialectic, p. 569 c Note # 126 Contradiction and its consequences, p. 512 d Note # 128 Dialectics and catastrophe theory, p. 514; Note #152 Cusp of negation, p. 555; Note #154 Chance and necessity, p. 560; Zwick (1978a) e 2.3 A new conception of metaphysics, p. 60

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of thermodynamic disequilibrium. a The historical model that is presented in Commentary also has a dialectical aspect. b

118. The extremes are attractors Not only can the extremes of order and disorder be viewed as attractors of the dynamics, but the extremes of all fundamental polarities might be so regarded. This is the essential property of the dyad, which characterizes all polarities. As Bennett (1993) writes, There is a starkness in the dyad that must be accepted, since its irreconcilable opposites cannot be otherwise. Any compromise between the dyad’s [two] natures presupposes a relationship between them, but there can be no dyadic relationship because relationship is a property of the triad. The absence of a general, satisfactory, and enduring reconciliation between the poles of a dyad is expressed by saying that both are attractors, c and the only attractors, so even a point of balance between them would be unstable, i.e., a repellor. To quote Butler (1872) again, “Extremes are alone logical, but they are always absurd.” The impulse to reject both extremes is best expressed in the strong words of Shakespeare (1599), “A plague on both your houses.” That neither extreme is viable is expressed in the mythological twin dangers of Scylla and Charybdis. Speaking of the poles of a dyad as attractors implies that these poles are quantitative and extrema that define a continuum. The poles may instead be inherently qualitative (nominal) and thus discrete alternatives, in which case such a continuum would not exist. a

Inconsistency in being engenders becoming (1.2.2.3.1); Note #123 Disequilibrium and change, p. 507 b 6.1.2 The model applied to history, p. 196; Footnote #255, p. 202 c Note #135 Movement toward the extremes, p. 527

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When both poles of these dyads are instantiated, these fundamental polarities reflect disequilibria that cause diachronic change. a It must be repeated, however, that not all tensions are dyadic; some might be triadic b or of even higher ordinality. This Summary section in Synchronics focuses on dyadic tensions because these are the most ubiquitous. Perhaps the most challenging dyad is the question of whether the difficulties posed by any particular situation are essentially dyadic or not. Multiplicity wars on unity. Closedness wars on openness. Universality wars on uniqueness. Environments change. Hazard is implicit in the fabric of existence. Indefinite persistence is impossible.

119. The war of universality on uniqueness “The moment that the particular…insists on self-determination, everything changes. We then find that the universal hates the particular, is appalled and disgusted by it. And this hate and disgust only grow more inflamed as the resistance of the particular proves itself resilient and enduring.” c

a

Inconsistency of being engenders becoming (1.2.2.3.1). Note #152 Cusp of negation, p. 555 b For example, see Note #68 Aggregating preferences, p. 420. c Hazony (2018)

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7.2 Notes on Diachronics (Becoming) 7.2.1 Origin Notes:

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496 502 505 120

A system comes into being via distinction and constraint. Through distinction, the unity of the primal field is sundered. System and environment are separated and thereby also joined. Through constraint, the multiplicity of the primal field is organized. A limited order of elements and relations emerges. Distinction is disequilibrium engendered by the descent of differentiation. Constraint is order engendered by the ascent of integration. The newly arisen system is incomplete and often also inconsistent. What flaws its origin will condition its future.

120. System formation Systems come into being at some point in time, but origins are difficult to understand because they often involve unique or rare events. The origins of the universe, our solar system, life on earth, the human species, and language all present hard challenges for formulating theory and obtaining evidence. Consider the definition of system a that focused on two basic ideas: (1) system as order as opposed to disorder and (2) system as distinction between an entity and its environment. In these terms, the problem of origins is the following: When order and distinction are initially absent, how do they arise? a

Note #1 System, p. 295

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The idea of system as order a is expressed in the definition of system as a set of elements with attributes and a set of relations organizing the elements through their attributes. So organized, a system becomes a new element, often with emergent attributes,” which can be linked to other elements in a higher order system, and so on. This idea of system presumes the pre-existence of elements and attributes, so the problem of system formation here is explaining (1a) the origin of the constraining relations and (1b) the generation by these relations of a new unitary whole. The idea of a system distinct from its environment, where distinction is understood to be at least partially objective, points to the question of the origin of the boundary that both separates the system from and joins it to its environment. (If the systemenvironment distinction is regarded not as objective but as the arbitrary choice of an observer, the choice of boundary is a normative rather than descriptive problem. Churchman (1968) has stressed the importance of boundary definition for systems analysis.) Just as the idea of system as order presupposes the existence of elements that become constrained, the idea of system as distinction presupposes the existence of domain on which a new distinction can manifest. The simplest order is a monad that results from the “ascending” integration of a prior dyad; the simplest distinction is a dyad that results from the “descending” differentiation of a prior monad. b So, defined either in terms of order or distinction, system formation is not ex nihilo, although a different analysis might be required for special cases, such as the universe as a whole or fundamental particles. Also, if “ex nihilo” is interpreted to mean without form (the tohu va’vohu of Genesis), but with substance preexisting, then system formation may indeed be ex nihilo.

a

Notes #9 Relation as constraint, p. 324 and #13 Order, p. 332 On the metaphor of integration of order and differentiation of distinction as ascent and descent, respectively, see Note #140 Two universal processes, p. 535.

b

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NOTES

System formation can be represented by turning the vertical double cone representation a of system on its side to yield the open systems view of Figure 98(a), in which verticality of space becomes horizontality of time. The nucleating event of system formation is the vertex of the double cone. As precursors of this event converge from the past, order is infolded into the system. As potential consequences of this event diverge into the future, order is outfolded (unfolded) as implication. The alternative to the open systems view is shown in Figure 98(b), which might be considered a closed systems view where the “system” is only what follows after its formation. In this view, system formation is ex nihilo since precursors to the system are not considered “part” of it. b The horizontal double cone represents more than the primal event of system formation. Just as the vertical double cone shows a system open-ended in space, so too can a system be considered open-ended in time; this is shown in Figure 98(c). Figure 98 System formation; system as temporal center System formation in (a) open systems view, (b) closed systems view. (c) In the open systems view, at any present moment the system extends into actual past and potential future; this reproduces a figure c introduced in discussing the modeling subsystem; there the figure is epistemological, here it is ontological. In both (a) and (c), regions of the double cone close to the vertex are synchronics, regions far away are diachronics.

past

a

system formationfuture

system future formation

present past moment future

time

time

time

(a)

(b)

(c)

Figure 3 System as center, p. 49 The dual conception here of system formation corresponds to the dual conception of system dissolution shown in Figure 130 Two views of system dissolution, p. 589. c Figure 94 Temporal triad; space-time tetrad (a), p. 476 b

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Defined narrowly, a system is just its present moment. a But the present moment can be viewed as extended rather than pointlike in time, fuzzy, b as opposed to crisp. Defined broadly, a system is more than its present moment. Qualitative and irreversible change occurred in the past which led to its origin and will occur in its future which is yet to come. In the open systems view, the system is also its past and its future, attenuated with their distance from the present moment. c Figure 98(c) can be interpreted epistemologically or ontologically. Epistemologically, the present cannot be fully known completely apart from the past and the future since what is present is always enriched (“contaminated”) by what is absent. Ontologically, one might say that a system is not merely what it is at a present moment but is also its past and future. (In metaphysics, as in law, much depends on what “is” is.) A system is a focal center in time. This perspective is essential (Smuts 1926) to understanding a living system that has implicit in itself both past and future, i.e., history that supplements structure and function. This perspective is also advocated by Derrida (Lucy 2004), who insists that “presence” (the system in the present moment, viewed as point-like) is supplemented by “absence,” the ghost-like past and future. One might use the fold catastrophe d to depict system formation as the onset of dynamic stability. Figure 99 captures the abruptness of the discontinuous transition from non-being to being (Thom 1975); this resembles the ex nihilo character of the closed systems view of system formation in Figure 98(b). In Figure 99(b), non-being (really non-stable being) is at the left of the singularity, before the singularity is reached in time (also below the repellor, where the dynamics also goes to negative infinity). Being is to the right of the singularity, after the a

Poststructuralism speaks of this as reflecting an impoverished “metaphysics of presence.” b Note #25 Fuzziness, p. 352 c Note #64 Discounting the future, p. 417 d Note #38 The fold catastrophe, p. 376

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singularity is reached in time, on the upper branch of the parabola, which is an attractor. The lower branch, which is a repellor, shows how far the vertical state variable (not shown in Figure 99) can be perturbed and still recover; later discussion a extends this idea to the cusp catastrophe. Figure 99 Systems formation and the fold The singularity of the fold is the system formation event. The system itself is the upper part of the parabola, which is an attractor. (The lower part is a repellor.) being

system formation

non-being

(a)

time

(b)

time

The fold catastrophe is about the appearance/disappearance of an attractor, so what is ex nihilo here is stability, not existence. This views persistence as ontologically fundamental. b One problem with the fold as a metaphor is that catastrophe theory applies only to gradient systems, but most dynamic systems are not gradient-based, so these ideas are not general. A simpler visualization of system formation is given in Figure 100, which represents it as an event (shown as a short vertical line) that punctuates a process (the horizontal line). The event does not eliminate the continuity (the non-ex nihilo character) of the process, i.e., the similarity between what is before and after the event. The precursors pass the baton, as it were, to the system to run the next leg in this relay race. Rather, the event marks the difference between the system and its precursors. From the perspective of the similarity, this difference is a negation of the precursors and simultaneously an affirmation of a

Note #132 Augustinian vs. Manichean devils, p. 522 5.3 Categories of complexity, p. 163, and Note #38 The fold catastrophe, p. 376

b

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the new system. The representation in Figure 100 is used in Commentary to depict processes and events in human history. a Figure 100 System formation: difference in similarity

precursors to system

similarity

system formation event

system

difference So far the discussion has focused on the temporal aspects of system formation. Aspects that are spatial (literally spatial for concrete systems, metaphorically spatial for abstracted and conceptual systems) are depicted by the vertical double cone diagram of structure and function. b A more complete depiction of system formation joins together temporal and spatial aspects, horizontal and vertical double cones, as shown in Figure 101. (In the horizontal double cone here, “precursors” and “unfolding” are substituted for “past” and “future.”) The event of system formation is symbolized by the central point, which represents the tetrad as a unity. This time-space diagram is used in Cognition to depict the activity of the modeling subsystem c; there the diagram is epistemological; here it is ontological. Figure 101 System formation, a time-space tetrad

function

space

precursors time

a

unfolding structure

6.1 A macro-historical model, p. 193 Figure 3 System as center, p. 49 c Figure 94 Temporal triad; space-time tetrad, p. 476 b

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System formation occurs either spontaneously 121 by self-organization or through the action 122 In the moment of origin, of other systems. either internal structure or external function dominates, but the other organizing principle always coexists, either at the outset or thereafter.

121. Self-organization Self-organization is system formation by internal ordering. The organizing principle is structural as opposed to functional, but self-organization is not independent of the environment. It can occur in several ways, including (1) a phase transition, (2) an autopoietic phenomenon, (3) an aspect of dissipative systems, (4) a solution to a game-theoretic dilemma. (1) Self-organization may be a disorder-to-order transformation, a phase transition in which, at some critical point of environmental conditions, interactions at a microscopic level generate macroscopic order from a prior disorder, as shown in Figure 102. Examples are transitions between gaseous, liquid, and solid phases of matter, or between disordered and ordered forms of biological macromolecules such as nucleic acids and proteins. Such transitions illustrate both aspects of system definition: the arising of order from previous disorder, as in the folding of macromolecules, and the demarcation of new boundaries, as in the separation of different phases of matter. The attributes of the new whole, the folded macromolecule or a new phase of matter, are not necessarily predictable from the micro interactions but emerge a as a result of the transition.

a

Note #32 Emergence, p. 363

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Figure 102 Phase transition as system formation event

order

disorder (2) Spontaneous self-organization can be discussed also in the language of autopoiesis a (Varela, Maturana, and Uribe 1974; Maturana and Varela 1980), which refers to the spontaneous creation and maintenance of a spatial boundary marking off the inside and outside of a system, this boundary being an emergent consequence of a set of metabolic reactions. An autopoietic system is closed to information, i.e., to external specification of the reactions occurring in the system, but open to matter and energy, the raw materials for generating the system via these reactions. “Autopoiesis” means making (of oneself) by oneself, as opposed to “allopoiesis,” making by others. Models of autopoiesis are often cast in the formalism of spatial automata. b Autopoiesis has been advanced as a conception of the essential properties of life, and especially relevant to the problem of origins, namely the origin of self-maintaining metabolism and the creation of boundary. Many such models derive from the work of Eigen (1979) on autocatalytic networks, i.e., networks of reactions which regenerate themselves. In these models, the agents and products of metabolism are depicted in various ways, ranging from abstract symbolic structures in some symbolprocessing language or graph-theoretic formalism, to representations of protein or nucleic acid macromolecules, treated by systems of differential equations. (3) Spontaneous self-organization, both in the sense of a transition to a new mode of order and in the sense of boundary a b

Note #47 Autopoiesis, p. 393 Note #10 Dynamic relation, p. 328

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creation and maintenance, is also the subject of Prigogine’s ideas about order through fluctuation a in dissipative systems, i.e., in systems driven far from equilibrium via a flux through the system of matter and/or energy. Although fluctuations in isolated and closed systems near equilibrium destroy order, fluctuations in closed and open systems far from equilibrium can (but need not necessarily) create or transform order. Prigogine’s theory seeks to ground nonlinear dynamic models of systems far from equilibrium in a new thermodynamic theory, just as standard chemical kinetics is grounded in the classical thermodynamics of isolated or closed systems at or near equilibrium. The creation of non-equilibrium thermodynamics has so far met with only partial success, as no principle has been found that is as powerful as the Second Law for isolated systems. Also, the link between this new thermodynamics and specific dynamic models of non-equilibrium systems is sometimes problematic. (4) One can also use game theory to model the nucleation of a system or its hierarchical development. System formation may be a solution of a game-theoretic dilemma. For example, solving 2- or many-agent Prisoner’s Dilemmas b (Hamburger 1979) may require a higher level of control; this is the Hobbesian account of the function of governmental institutions – to prevent the war of all against all. Or higher levels of control may be needed just for coordination, e.g., to eliminate waiting lines (Hamburger 1979) even in the absence of any conflict between individual and collective rationality. Of particular interest are games (e.g., “hero” or “battle of the sexes”) whose solution requires symmetry-breaking, that is, whose solution requires that agents do not choose the same action despite the fact that the game matrix has complete symmetry between the players. c The phenomenon of coalition formation analyzed in the theory of n-person games is system a

Note #124 Order through fluctuations, p. 509 Note #78 Prisoner’s Dilemma, p. 433 c Note # 80 Symmetry or altruism may be harmful, p. 436 b

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formation driven by superadditivity, i.e., by the whole (the coalition payoff) being greater than the sum of its parts (payoffs that would accrue to coalition members if they acted separately).

122. Offspring The biological model is an obvious example of system formation arising externally. Essay goes on to speak of the “fragility of the newly arisen system.” When the new system is generated by parental systems, fragility is typical, reflecting an inherent incompleteness in the result of system formation, but such fragility is more general. In disorder-order transformations, if environmental parameters do not move away from the critical point where transformation occurs, the new order will be only provisionally established and thus easily undone. On the other hand, being delicately poised near the critical point of such transformations may have adaptive advantages despite the risks of instability, and it is possible that some of the macromolecular structures in cells are so poised. Living systems, both individuals and populations, and the internal components of individuals, may exist “at the edge of chaos” a (Langton 1992; Kauffman 1992). Fragility of the newly arisen system is the rule. What spontaneously organizes can spontaneously disorganize. Where other systems engender or facilitate this arising, they shape the character of the new system. Either excessive proximity or excessive distance poses risk. Excessive proximity hinders independent development of the new system. Excessive distance deprives it of necessary support. No prescription exists for optimality of distance. A system generated by other systems may face tension between fidelity to the matrix of its a

Note #17 Chaos, p. 338

NOTES

506

arising and assertion of its distinctive attributes. Total continuity is impossible. So is total change. If the organizing principle of the newly formed system privileges continuity, autonomy is not gained. If it favors change, identity is not grounded. Every mixture of continuity and change is unstable. If continuity and change are both embraced, the new negates the old and seeks to supersede it.

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7.2.2 Development Notes: 123 124 125 126 127

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Disequilibrium and change Order through fluctuations Development vs growth Contradiction and its consequences Self-development

507 509 510 512 513

The order of the system may be evanescent and the system-environment distinction a transient, but the newly arisen system often has a capacity for increased complexity. What flaws a system at its origin – its incompleteness or inconsistency -- is potential for its development; the deeper the flaw, the greater the potential. Incompleteness reflects a disequilibrium, as does inconsistency, and disequilibrium is the basis not only of 123 But the flaw may existence but of change. instead be a source of dysfunction, even a force towards dissolution.

123. Disequilibrium and change As noted earlier, a for concrete systems distinction means disequilibrium, so the very existence of the system depends on disequilibrium. Here Essay points out that diachronic (macroscopic and irreversible) change also depends on the system being in disequilibrium, either internally or with its environment. (Recall that thermodynamic equilibrium differs from dynamic equilibrium. b) As Essay goes on to discuss, disequilibrium manifests in forces and fluxes. A force, in non-equilibrium thermodynamics a b

Note #23 Disequilibrium and existence, p. 349 Note #10 Dynamic relation, p. 328.

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(Prigogine 1980; Nicolis and Prigogine 1989), is a departure from equilibrium, e.g., a spatial difference (in continuous systems, a gradient) in temperature or in concentration of some material entity. Thermodynamically, this disequilibrium can be thought of as a diachronic organizing principle. A flux is a flow of energy or matter that this force produces if conditions allow, if the system is sufficiently open and not closed a to such flow. If the force is a difference or gradient of temperature, the flux is a flow of heat; if the force is a difference or gradient of concentration, the flux is a material flow; if the force is a difference or gradient of voltage, the flux is a flow of current. The flow is movement toward thermodynamic equilibrium, which involves entropy increase. b Disequilibrium thus inherently counters itself, but new disequilibria continually arise through system formation events. A force and flux can be modeled with a gradient system c where changes in a variable are driven by the maximization or minimization of a potential, i.e., dx/dt = k dV/dx. In a thermodynamic context, dV/dx, the gradient, typically spatial, is the force; dx/dt, the change this force produces, is the flux. Near thermodynamic equilibrium, fluxes are proportional to forces. Assume that T1, the temperature at x1, is different from T2, the temperature at x2. If location is ignored, the system exists at both T1 and T2. This difference could be called a “contradiction” if spatial extension is ignored, but if extension is considered, there is of course no contradiction. One might say that contradiction plus extension (separation of T1 and T2) means disequilibrium, which produces force. A voltage that is both positive and negative at the same point in space would be a contradiction that nullifies itself, but separation in space of

a

Note #41 Openness and Closedness, p. 380 Note #14 Entropy, p. 334 c Note #70 Optimization, p. 423 b

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positive and negative voltage generates a force, which gives rise to motion or change, in this case an electric current. Thermodynamics applies only to concrete systems, although some of its ideas might be generalized also to abstracted systems. In social systems, a spatial gradient of opportunity is a force that produces a flux of human migration. In psychology, cognitive dissonance (Festinger 1957) might be viewed as a disequilibrium that drives change. Catastrophe theory a can model change resulting from contradiction between an actual state and a preferred potential state, and such a model could be given a thermodynamic interpretation. Incompleteness in being engenders becoming. Disequilibrium with the environment is a force that drives a flux of substance through the system. The flux not only organizes the system but through random fluctuations may increase 124 Openness allows more than its complexity. self-maintenance. Order initially only potential may become actual. Assimilating external elements, the newly arisen system may augment its initial endowment. It may 125 grow and develop. Yet what is assimilated may fail to be integrated; marked by its origin, it may remain an accretion, an implant, even an agent of the environment.

124. Order through fluctuations The flow of matter-energy through a dissipative system b can organize the system. Spontaneous internal fluctuations, amplified by nonlinearities, can move the system from one basin of attraction c to a new basin corresponding to a different a

Notes #12 The potential and the actual, p. 331, and #131 Cusp catastrophe, p. 520 b Note #42 Dissipative systems, p. 381 c Note #10 Dynamic relation, p. 327

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NOTES

structure, which could be more ordered than the original one. Prigogine (1961) calls this “order through fluctuations.” In isolated systems, however, randomness only increases entropy.

125. Development vs growth Growth and development are different (Brinkman 1995). Growth is increase of size within a constant structure; development is change in structure. This is like the distinction between the quantitative and topological aspects of order. a Growth is quantitative change; development is topological change. In terms of the Lattice of Structures, b growth is change with structure remaining constant; development is movement from one structure in the lattice to another. Growth does not imply development, but development is usually accompanied by growth. For example, the transition from fertilized egg to embryo to infant to adult is development, in addition to growth. A computer program whose overall structure remains constant but in which subprograms get larger is undergoing growth, but a program whose structure is radically altered is undergoing development. In economic systems, development might be represented by significant change in an input-output model toward greater connectivity (Leontief 1951, 1963); for example, in the density of the economic network. c In ecosystems, development occurs in the process of ecological succession (Odum 1969; Ulanowicz 1997). A general theory of development, if one could be constructed, that applied to economic, ecological, and perhaps other systems would be a major contribution to the systems project. d

a

Note #13 Order, p. 332 Note #5 Structure, p. 308; Note #140 Two universal processes, p. 535 c Note #7 Networks, p. 317 d Such a theory would need to differentiate between controlled and uncontrolled systems (Note #88 Hierarchies and networks, p. 446). b

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Development might be conceptualized with the idea of Paretooptimality. a If U1 and U2 are two aspects of utility for a developing system or the utilities of two subsystems, development may allow both utilities to increase without any trade-off between them, as in “a rising tide lifts all boats”; this is shown in Figure 103. The system starts in a Pareto-non-optimal condition in (a) and moves toward the northeast Pareto-optimal (PO) line in (b), after which the system changes so the current state is no longer PO, as in (c). The system could then continue to improve by moving toward the new (bold) PO line. This is like dialectical progress in which thesis meets antithesis yielding a synthesis that is a new thesis, after which the process repeats. Figure 103 Progress and Pareto-optimality

U2

U2

U2 •

•

• (a)

U1

(b)

U1

(c)

Inconsistency in being engenders becoming. If contradiction does not cause stasis, it gives rise to dynamics, most simply cyclicity. Contradiction may for a while be hidden or partially resolved in complexification. It is rarely harnessed as the engine of development that it might be. The polarities that exist in the system constitute an internal disequilibrium, which, suitably mediated, generates change. Commonly, however, opposing poles either lack such mediation or merge with one another, thereby dissolving the disequilibrium and squandering its 126 potential.

a

Note #66 Pareto-optimality, p. 418

U1

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NOTES

126. Contradiction and its consequences Synchronics ends with a list of archetypal binary oppositions, many of which are correlated. a These “contradictions” can have various possible consequences. A contradiction can be fixed in the structure of the system – and often suppressed – and produce stasis and rigidity. Or, it can unfold in (synchronic) periodic dynamics, as in Bateson’s analysis (1979) of an electric circuit of a buzzer that is in opposite states at different times. b This is a dialectical conception. Or, contradiction can be neutralized in a non-productive short circuit, which restores equilibrium. If, however, there exists within the system a mediating factor that can harness the force of contradiction, the contradiction can be a source of dynamism. Incompleteness and/or inconsistency can provide the system with potential for diachronic development. Imperfection is an engine for change. The very notion of ‘perfection” undermines itself. It implies unity, because multiple states cannot all be perfect; thus perfection must mean stasis (Feibleman and Friend 1945), but stasis rules out life, which disqualifies it from praise. This is no cause for concern. Perfection is unattainable, so the world goes on. When contradiction remains at the level of the dyad, polarity is not reconciled and it generates separation, tension, and/or paralysis. When polarity is mediated – at the level of the triad – the result is either a static balance or a dynamic relation. Dynamics is not yet diachronic change which presumes stability as a point of departure. Stability is at the level of the tetrad. Given stability, there is the possibility of development, the unfolding of potential. This is the pentad, which implies a diachronic organizing principle. These notions of dyad, triad, tetrad, and pentad derive from Bennett (1966).

a

Summary 1.1.9 and 7.1.9, pp. 23, 491; Notes #115 Binary oppositions, p. 492, and #116 Dyadic correlations, p. 492 b Note #6 Inconsistency, p. 311

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Development is not guaranteed. All 127 development is internal development, but its necessary preconditions may be absent. Support by the environment may be lacking. External affordances may come too late – or too soon. Internal factors may block development or cause uncontrolled growth. Nor is the absence of early challenge an unmixed advantage. Postponement of risk allows rigidification, which lays a foundation for future dysfunction.

127. Self-development “The only kind of development possible is self-development” (Ackoff 2004). External function can constrain or support change, but development a cannot be done for a system. A weaker version of this general claim would assert that in processes of complexification, only significant structural transformations require internal self-development, b while less systemic increases in complexity might possibly be engendered by external factors.

a

Analogously, Note #108 Cognition and autopoiesis, p. 480, argues that cognitive structures cannot be ingested whole but must be internally developed. b See the discussion of passage through minor and major “barriers” in Note #147 Limits of complexification, p. 544.

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7.2.3 Limitation Notes: 128 129 130 131 132 133 134

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Dialectics and catastrophe theory History: idiographic or nomothetic Trajectories of development Cusp catastrophe Augustinian vs. Manichean devils Environmental types, again Failures in meeting new challenges

514 516 517 520 522 525 525

Becoming does not escape the finitude of being. Eventually the momentum of expansion slows, and consequences of the restricted scope of the system’s organizing principle begin to manifest. Obstacles are encountered to continued development. Thus the dialectical trajectory: the development of the system proceeds from nucleation to expansion to the 128 encountering of limitation.

128. Dialectics and catastrophe theory Essay uses a catastrophe-theoretic (Thom 1975; Zeeman 1977) interpretation (Zwick 1978a) of the dialectical idea that every system contains within itself the seeds of its own transformation (or destruction), the possibility of which manifests as the system develops. Progression from nucleation to expansion to limitation is displayed on the cusp catastrophe in Figure 104 which is explained in detail below a; further development of this idea is offered in later notes. b

a

Notes #131 Cusp catastrophe, p. 520, #152 Cusp of negation, p. 555 Notes #165 Two kinds of dialectic, p. 569, #166 Butterfly catastrophe, p. 570

b

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Figure 104 Nucleation, expansion, limitation BS = bifurcation set

nucleation BS

expansion limitation

What is missing in the system may afflict it, if not initially then subsequently. Expansion may mitigate original incompleteness, but what is not subsumed initially may be difficult to assimilate later. Or, too much may be subsumed. If the capacities of the organizing principle are exceeded, disorder or contradiction is introduced into the system. Obstacles appear in many forms: in exhaustion within the environment of elements suitable for incorporation or transformation; in the difficulty of maintaining coherence while integrating new elements; in the fragility of the order achieved; in conflict generated by internal structures not subordinate to the organizing principle; in constraints or dangers posed by other systems or a higher level order. Circumstances vary, but unimpeded development rarely occurs. Nucleation, expansion, limitation: this sequence of early stages is the norm. As development continues, the factors that limit it also intensify. If the system proceeds on this trajectory, a critical phase is eventually

516

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reached in which the intensification of hazard emerges as a lawful feature of development. The unique attributes of the system, its particular structure, function, and history, become more important than its generic 129 and its future becomes attributes, 130 uncertain.

129. History: idiographic or nomothetic In the catastrophe-theoretic model of development offered below, a the existence of an alternative organizing principle is lawful (nomothetic), but whether there is actually a transition to this new principle is historically contingent (idiographic). The model combines nomothetic and idiographic views, often regarded as mutually exclusive. b Among most historians, the idiographic view is the default hypothesis. The plausibility of a nomothetic view, to replace or to supplement the idiographic view, depends in part on the number of qualitatively distinct states that are possible for the social system. If this number is large, a nomothetic view is unlikely to be productive. But if the number of states is small or if they are mixtures of a small set of archetypes (“eigen-states” in the language of physics, “ideal types” in the language of sociology), then a nomothetic view is conceivable. Understanding the history of social systems requires combining the idiographic and nomothetic viewpoints. This is illustrated in the dynamic systems model of the cusp catastrophe presented below, where the qualitatively different states are basins of attraction. c The model is nomothetic in its catastrophe archetype but idiographic in the motion of the control point. Alternatively, motion of the control point might be lawful, but it might also be subject to stochastic perturbation. a

Note #131 Cusp catastrophe, p. 520 3.5.2 Adding history, p. 116; Note #154 Chance and necessity, p. 560 c Note #10 Dynamic relation, p. 327 b

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130. Trajectories of development Four possible trajectories of development are shown in Figure 105. All begin with nucleation (formation of an organizing principle), expansion (positive feedback), and limitation (negative feedback), described by the continuous logistic growth equation dx/dt = r x (K − x). The r x K term on the right hand side of the equation is positive feedback; the – r x2 term is negative feedback. a Figure 105 Four patterns of growth and development (a) single logistic growth (b) growth, decline, and disappearance (c) double logistic growth (d) growth, decline, and replacement

limitation expansion (a)

(c)

nucleation OP1

OP1

(b) OP2

(d)

OPA

OPB

Recall the distinction between growth and development. b The logistic equation is often used to describe the increase of population size, a measure of growth. Of the four patterns in the figure, only (c) intrinsically involves the formation of a new organizing principle that builds upon the previous OP and thus implies development. In (d), the new OP simply replaces the a b

Positive and negative feedback are discussed in Note #36 Stability, p. 374 Note #125 Development vs growth, p. 510

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old one. The other patterns could arise either from just growth or from development accompanied by growth. (a) The logistic (S-shaped) growth curve shows the simplest pattern of nucleation, expansion, and limitation. A process is completed in that potential for growth is exhausted and the process is sustained at some steady state. In the expansion phase, the logistic equation is dominated by r which governs the positive feedback; in the phase of limitation, the equation is dominated by the K parameter that sets a carrying capacity limit on x. The figure labels the entire process as governed by a single organizing principle, but the shift from exponential growth (rphase) to steady state (K phase) often requires a major shift of process or organization, i.e., a new OP. (b) Logistic growth is followed by decline and disappearance; this is like (a), except that the process is not sustained. Examples are aging and death of organisms and overshoot and collapse of ecosystems or societies. (c) The logistic growth launched by OP1 is followed by a second process that builds on the first and perhaps encompasses it. There is not only completion in reaching a steady state as shown in (a) but also completion in the consolidation of a new OP2 that reinitializes the potential for growth/development and generates a repeat of the logistic pattern. (d) Logistic growth leads to decline and disappearance but sometimes also to the emergence of a separate OP with its own logistic pattern. This second process either just accompanies the decline of the first process or actually causes it. Biological progeny and competitive exclusion between two species are examples, respectively. Unlike (c) where OP2 builds on OP1, OPB is an independent offshoot of or an alternative to OPA. A fifth possible trajectory would be a simple variation on (d), where OPB = OPA , i.e., the trajectory would be a cycle that repeats. The above archetypes relate to Holling and Gunderson’s (2002) adaptive cycle, shown in Figure 106, part of their

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“panarchy” model. The cycle begins with the r (exploitation) and K (conservation) phases of simple logistic growth, followed by a Ω (release) phase and then an α (reorganization) phase. The r and K phases are shown previously in Figure 105(a) and the alpha phase in the second growth curve in Figure 105(d). Figure 106 Holling's adaptive cycle model Vertical axis: potential; horizontal axis: connectedness; third axis, (not shown): resilience. From Panarchy edited by Lance H. Gunderson and C. S. Holling. Copyright © 2002 Island Press. Reproduced by permission of Island Press, Washington, DC.

One might relate these phases to the creation-maintenancedestruction triad of diachronics a: K is maintenance, Ω is destruction, and r and α promote and manifest the consequences of creation. The panarchy model posits a hierarchy of adaptive cycles at different scales in space and time, and there can be important interactions between events on adjacent scales. b The

a b

Figure 20 Creation, Destruction, Maintenance, p. 119 Note #15 Scale, p. 335

520

NOTES

adaptive cycle can be modeled with the cusp catastrophe (Zwick and Hughes 2017), described below. The system enters a region of bifurcation in which its actual state is accompanied by a potential state that corresponds to restructuring by a new organizing 131 principle. This coexistence of actual and potential states defines the principal contradiction which now characterizes the system. Thesis leads to antithesis, and not by failure but by success.

131. Cusp catastrophe Catastrophe theory is introduced earlier in Synchronics. a The fold b is the simplest catastrophe type and has one state variable and one control (environment) parameter. The cusp (Figure 107) is the second simplest catastrophe type and has one state variable and two control parameters. For certain parameter values (inside the bifurcation set), two distinct system states are possible: one actual and the other potential. The second state can represent restructuring of the system by a change of its organizing principle. Alternatively, this second state might represent the dissolution of the system, but the persistencedissolution dyad is better represented with the fold. c

a

Note #37 Catastrophe theory, p. 375 Note #38 The fold catastrophe, p. 376 c Note #132 Augustinian vs. Manichean devils, p. 522 b

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Figure 107 The cusp catastrophe (a) ES = equilibrium surface, σ = singularity, U and L = upper and lower surfaces; CS = control surface, BS = bifurcation set. When the control point is at 1, the equilibrium state is either 2 (on L) or 4 (on U); 3 is inaccessible. If the control point is to the left of BS, the equilibrium point is on U; if to the right of BS, the equilibrium point is on L. (b) A possible control point path.

ES U

σ 4 3

L

2

x (a)

CS 1

BS

(b)

nucleation expansion BS

limitation

Catastrophe theory assumes gradient dynamics a of the form, dx/dt = k dV/dx. The cusp equation is dx/dt = x3 – p1 – p2 x, where p1 and p2 are control parameters. (p1 corresponds to p in the fold catastrophe.) The system state, x, at equilibrium (dx/dt = 0) lies on an equilibrium surface (ES), shown in the figure; when not at equilibrium, the state moves vertically toward this surface. The surface has a singularity, forward of which it splits into upper (U) and lower (L) attractor surfaces; between these is an inaccessible repellor surface. The V that governs the dynamics depends on the system state and two parameters. The parameters define a control point that moves on the control a

Gradient dynamics is explained in Note #70 Optimization, p. 423

522

NOTES

surface (CS). One possible path of motion is shown in (b), a but the modeler, not catastrophe theory itself, dictates this path. The equilibrium state of the system is the point on an equilibrium surface above the control point. When the control point is in the bifurcation set (BS, e.g., point 1), there are two possible stable equilibrium points above it (points 2 and 4), one the actual system state and the other an alternative potential state. (Point 3 is unstable and not a candidate system state.) When the control point is outside the bifurcation set, there is one equilibrium state on either the upper or lower attractor surfaces. Control parameters here are called “conflicting factors” because they pull the system to opposing L and U surfaces. Catastrophe theory is especially useful for diachronic modeling because the theory does not specify the trajectory of the control point, which can be maximally idiographic. b Once the trajectory is given, the theory specifies what the equilibrium state will be. Limitation is internal or external. When limitation is internal, it is general or specific: it derives from general difficulties of systems maintenance and development or from the existence of a specific opposing organizing 132 principle.

132. Augustinian vs. Manichean devils The distinction between general and specific difficulties of maintenance and development echoes Whitehead's observation that “things fade and alternatives exclude.” Fading is a general difficulty; an opposing alternative is a specific difficulty. This is similar to Wiener’s (1967) distinction between Augustinian and Manichean views of evil. Wiener asks if disorganization is an Augustinian devil, evil being in Augustine’s (and Plato’s and Aristotle’s) view, privation, limitation, imperfection, or a a

Further analysis of the results of motion shown in (b) is given in Note #152 Cusp of negation, p. 555. b Note #129 History: idiographic or nomothetic, p. 516

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Manichean one, the work of an active agent of independent ontological status. He concludes that disorganization – decreed by the Second Law of Thermodynamics for isolated concrete systems – is an Augustinian enemy, a general difficulty not involving an opposing agent. Augustinian devils are also the subject in game theory a of “games against nature.” Manichean devils also exist, as Wiener also recognizes. Games against adversaries is the main subject of game theory. While two-player zero-sum game theory is complete and mostly satisfactory, behavior against more than one devil is harder to prescribe or predict since the theory of many-agent-zero-sum games is not satisfactory. b Games with agents who are not total devils are even more problematic, since non-zero-sum games c with two or more agents exhibit paradoxes of rationality. The distinction between general and specific opposition can also be modeled with the fold and cusp catastrophes. The fold models being vs. non-being, d i.e., struggle with the general opposition of Augustinian devils. The cusp e models the tension between alternative modes of being (Thom 1975) – in Figure 108, between being1 and being2 – i.e., struggle with the specific opposition of Manichean devils. Figure 108 Being1 vs. being2

being2 being1

a

Note #75 Game theory, p. 429 Note #76 Coalition instability, p. 431 c Notes #78 Prisoner’s Dilemma, p. 433, and #79 Chicken, p. 435 d Figure 99 Systems formation and the fold, p. 500 e Note #131 Cusp catastrophe, p. 520 b

524

NOTES

In the fold dyad of being and non-being, being is unmarked. Difference is salient, and the dyad is asymmetric. By contrast, the cusp is about the shift from one attractor to another. Similarity is salient; neither pole is marked, and the dyad is symmetric. Linguistically, the terms of a dyad are just words, so there is no linguistic difference between a dyad of non-being and being and a dyad of being1 and being2. But ontologically there is a deep difference between these dyads. The dyad of the fold is not really a dyad at all, but a transition between the “zero-ad” to the monad. a Only the cusp reflects an ontological, not merely a linguistic, dyad. Some of the above discussion is summed up in Table 16. Table 16 Devils, catastrophes, and games

Devils Augustinian Manichean

Catastrophes

Games

fold catastrophe

games against nature

cusp catastrophe

2-player zerosum games

Whitehead “things fade” “alternatives exclude”

When limitation is external, it is general or specific or both: it arises from the general texture of the environment, from specific other systems, or from embeddedness within a more 133 Many problems elude encompassing order. solution. They may be unanticipated; or the system may fail to perceive them when they arise; or the system may perceive them but not respond adequately in time; or attempted 134 solutions may fail.

a

Note #29 Nothing, many, one, all, p. 358

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133. Environmental types, again The three sources of external limitation – texture, other systems, embeddedness – that are discussed in 7.1.6 Agency are based on the environmental types of Emery and Trist. External limitation in each environmental type can also be classified as reflecting either (a) general difficulties or (b) specific opposition. Simple or textured environments create general difficulties; the presence of other systems poses specific opposition; the existence of an embedding environment might be viewed as either or both general or specific opposition. Internal and external limitation, both general and specific, is the subject of the next five sections, as summarized in Table 17. Table 17 Limitation: internal/external, general/specific The table classifies the five types of limitation discussed in Diachronics sections 4-8.

Internal External

General Specific 4. Complexification 5. Internal opposition 6. (Environmental) Texture 7. Other systems 8. Embeddedness

134. Failures in meeting new challenges Diamond (2005) offers a taxonomy of societal failures to meet challenges. His four modes of failure apply to all five types of limitation (Table 17) and map onto the tetrad (Figure 109). Figure 109 Tetrad of adaptive failures GOAL ideal

DIRECTION theoretical (1) failure to anticipate (3) failure to respond

INSTRUMENT practical (4) failure to be effective

GROUND actual (2) failure to perceive

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(1) Failure to anticipate reflects imperfection in theoretical understanding. (2) Failure to perceive means not seeing the actual, either due to absence of empirical knowledge, ignorance of what to look for (really a failure of theory) or failure to test. (3) Failure to respond adequately in time reflects an imperfect understanding of the severity of the danger and the urgency and scope of the necessary response to it. This is a common failure when the magnitude of the danger increases exponentially, depicted in Figure 110. (4) Failure to be effective reflects imperfection in the instrument of action or in the guidance given by theory. (1,3) Failure in the direction component may come from an intrinsic inadequacy of theory or from conflicting goals. Figure 110 Failure of response to exponential danger

response too late danger

no urgency weak response time While synchronic adaptive failure typically begins with failure to perceive the gap between actual and ideal in the present, diachronic adaptive failure begins with failure to anticipate the future. Most such failures are not “black swans,” i.e., intrinsically unpredictable, but follow from deficiencies in knowledge. After failing to anticipate, perceiving what is actual is often already too late, but not perceiving what is actual adds failure on top of failure. Failures can also occur if danger increases suddenly or wildly oscillates due to lags in response. a a

Figure 67 Modes of negative feedback, p. 387

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7.2.4 Complexification Notes: 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

page

Movement toward the extremes Centralization Mechanization Form limits growth Temporalization of complexity Two universal processes Optimal segregation vs. systematization Progressive segregation Partial decomposability Systematization Levels of structure and dynamics Integration of stable substructures Limits of complexification Non-decomposability under stress Connectedness for good and ill Self-organized criticality

527 529 530 531 532 535 538 539 540 541 542 543 544 550 551 551

Limitation may be internal and general. Closedness, needed to protect the nascent order against external disruption, deprives the system of vital resources. Openness, needed to augment the endowment of system formation, puts internal control of development at risk. An organizing principle based on unity promotes an extreme of order; one based on multiplicity, an extreme of variety. The system may be subject to and unable to arrest a movement towards either extreme or even 135 both simultaneously.

135. Movement toward the extremes It is conjectured here that systems tend toward extremes of order or disorder, i.e., that these poles are attractors, and that

528

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intermediate attractors that stabilize compromise positions are rare. This claim has several possible meanings. a If order means strong constraint, the conjecture asserts that strengths of relations tend toward maximum or minimum values. If order means high ordinality relations, the conjecture asserts that systems tend toward minimum or maximum decomposability. b If order means short transients, the conjecture asserts the existence of a meta-dynamics that leads to limit cycles or chaos. The last version of this conjecture is the opposite of the proposal that meta-dynamics moves systems to the edge of chaos (Langton 1992; Kauffman 1992), where both order and variety are accessible. Even if such meta-dynamics occurs it is unlikely to be universal phenomenon. One can, however, imagine it operating in evolutionary selection, where a balance of order and disorder is beneficial for proliferation and persistence. If order and disorder are viewed as dynamic attractors that vie for dominance, the two competing attractors can be represented by the cusp catastrophe. c A meta-dynamic promoting an intermediate solution can transform the cusp into the butterfly catastrophe, d in which the opposing attractors of the cusp are supplemented by a third attractor that offers a stable compromise. But though the butterfly adds this possibility, it does not guarantee escape from the harsh reality of cusp-like binary opposition. Alternatively, order vs. disorder might be viewed as the presence vs. absence of an attractor, which occurs in the fold catastrophe ein which a stable compromise also does not exist. Other polarities are also relevant to this conjecture. f

a

Note #13 Order, p. 332 Note #140 Two universal processes, p. 535 c Note #131 Cusp catastrophe, p. 520 d Note #166 Butterfly catastrophe, p. 570 e Note #38 The fold catastrophe, p. 376 f Summary 1.1.9 and 7.1.9, pp. 23, 491; Note #40 Rigidification vs. disintegration, p. 378; Note #20 Reconciling constraint and variety, p. 341; Note #118 The extremes are attractors, p. 494 b

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Development is hindered by both rigidity and plasticity. After a degree of development, tension invariably arises between what for identity must be fixed and what for adaptability must vary. But rigidity and plasticity are not strictly opposed. Rigidity is the foundation for plasticity. Where there is a differentiation between center and 136 periphery or between domains of substance and information, rigidity and plasticity may predominate in different parts of the system. Higher levels may rigidify while lower levels remain plastic; or the reverse: lower levels may rigidify, while higher levels remain 137 Similarly, closedness is the plastic. foundation for openness, and closedness and openness may predominate in different parts of the system.

136. Centralization Von Bertalanffy (1968) refers to the tendency of systems to centralize as “progressive centralization.” It is the tendency of network (horizontal) complexity to evolve into hierarchical (vertical) complexity, often accompanied by the emergence of “leading parts”; in contemporary network terminology, “hubs,” a or the tendency of growing networks to become scale-free. One mechanism for this is the preferential attachment of new nodes to existing nodes having high centrality; more simply, centralization is the tendency of centrality to increase. b A (hypothetical) example of centralization is the metabolismfirst conjecture about the origin of life, which posits autocatalytic networks of molecular reactions that evolved into the cellular life existing today. If this is what happened, then concentration of information into nucleic acid molecules from a b

Note #91 Scale-free networks, p. 450 Note #7 Networks, p. 317

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NOTES

being initially dispersed through the network would illustrate progressive centralization. Concentration of genetic information might allow for greater robustness and evolutionary adaptability. However, in replication-first conjectures about the origin of life, where RNA ribozymes catalyzed their own replication, centralization was present at the outset.

137. Mechanization (rigidification) Progressive centralization is related to progressive mechanization (von Bertalanffy 1968), the tendency of systems to rigidify. Mechanization is “chunking,” subroutinization, the formation of stable subassemblies. Functionally, such stable subunits provide reliable instruments for action; structurally, they allow further hierarchical complexification. a But mechanization is not only necessary, it is also hazardous. b Koestler (1969a) says that rigidification occurs in the center. If “center” refers to the lower (foundational) levels of substance, as opposed to the upper levels of information, rigidification of the center is illustrated in biology by conservation of metabolic processes common to all life. Generally, when there is a separation between basic processes and their control, the basic processes (the lower levels) become rigid while their control (the upper levels) stays plastic. This is largely true also in the informational realms of software and genomic regulation. However, in socio-cultural systems, the opposite may be true. In Parsons’ hierarchy, c the upper level of culture seems to be more fixed than the bottom level of the economy. Growth engenders form but form constrains 138 Development entails the growth. modification and non-proportional growth of parts. Eventually this requires a change of structure, often difficult to accomplish. a

Note #144 Systematization, p. 541 Note #170 Adaptation vs. adaptability, p. 577 c 6.4.2.1 The Parsonian model of social systems, p. 253 b

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138. Form limits growth This is nearly a quote from Boulding (1970), who writes that “growth produces form, but form limits growth.” Feibleman and Friend (1945) say similarly: “Rigidity is a condition of maintenance; flexibility is a condition of growth.” Boulding notes that centralization by enhancement of the means of communication and control and decentralization by segmentation or differentiation are opposite ways of coping with the increase of scale that results from growth. Centralization and decentralization are opposite changes of form, but either change might be produced by growth. To the extent that form is stabilized, growth is restrained. If growth continues nonetheless, the existing form becomes increasingly incompatible with the results of growth, and pressure builds up for restructuring. a Or, development may be organized by a principle that governs the temporal unfolding 139 If the unfolding process is of structure. complex, errors in scheduling are likely. Optimizing the schedule is also difficult. Moreover, even if achieved, optimality increases vulnerability, since optimality requires the sacrifice of resilience. Because of multiplicity, temporalization of complexity yields inconsistency of purpose. No course is held steady. Fluctuations in salience of different parts of the system cause constant change of both direction and goal. A goal that constantly changes is unlikely to be realized. Direction that constantly changes provides unreliable guidance. Every part, a

This is the subject of Internal Opposition 1.2.5 and 7.2.5, pp. 31, 554, which uses the cusp catastrophe to depict restructuring.

532

NOTES

when dominant, acts for the whole and binds its future, but the dominance of each part is ephemeral, so the future is not truly bound.

139. Temporalization of complexity The phrase comes from Luhmann (1978) who discusses complexity in social systems. Some undertakings cannot be done all at once and must be distributed over time, so complexity characterizes a process, not a state. a Diachronic complexity might be represented by a directed graph b with magnitudes, e.g., a Program Evaluation Review Technique (PERT) chart, that shows the subprocesses that constitute a process, which subprocesses must be completed before others can be initiated, and how much time the subprocesses require (Figure 111). This digraph represents a causal order. Figure 111 Critical paths among multiple processes This PERT chart is, an example of a critical path method. The critical path, CF, is explained below.

A3 s1

s2 B7 C5

D6 s3 s4

E2

s5 F8

In the figure, the process is the complete structure. Its states (milestones) are nodes, numbered s1 to s5. Subprocesses, labeled A through F, have magnitudes, representing the minimum time needed to accomplish the indicated state transition. Getting from the initial state, s1, to the terminal state, s5, requires at least 13 time units; this is the critical path, CF. The other paths have shorter length: ADE has 11 and BE has 9, so B could be delayed a b

See Simon's explication (1962) of state vs. process descriptions of systems Note #7 Networks, p. 317

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by as much as 2 units without any effect on the overall time. PERT and related methods, e.g., Petri nets, are widely used in project management, an important area of systems analysis and systems engineering. a Another type of temporalized complexity occurs when, instead of having to traverse all paths, the system seeks an optimum single path from an initial state to a desired final state, where some utility measure defines optimality. This is the subject of dynamic programming (Bellman 1954), illustrated by Figure 112. Here directed links between nodes are processes, and multiple paths are alternative possibilities. The task is to select the best path from initial state s0 to s5. Figure 112 Optimum path determination The path magnitudes from s1 to s5 are repeated from Figure 111.

(a) 3

3

s2 6 7

s1

s3 5

s0 4

s6 4 7

s4

9 1

s8

2 8

s7

(b)

2

3 s5

s1

9

s0

s5 4

s6

7

Assume that magnitudes in (a) are costs (time might be its surrogate) that are to be minimized. The shortest path from s0 to s5 is found by working backward. The optimal path from s1 to s5 is the dotted bold path of length 9, and the optimal path from s6 to s5, also dotted and bold, has length 7; these are summarized in (b). The optimal path from s0 to s5 must include one of these two subpaths – dynamic programming relies on hierarchical a

4.5 Systems theory and systems analysis, p. 141

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NOTES

decomposition – so this optimal path is the lower path s0-s6-s7s8-s5 (length 11) shown in (b) as bold solid, then dotted. Programmed development in biological systems is another example of temporalized complexity. This temporal process is coded for by the genotype, an example of algorithmic information. a Structurally, the genotype might be viewed as a state description, b but functionally it is a localized and compressed process description that guides morphogenesis. To use the terminology of Waddington (1977), the genetic order provides not only for synchronic homeostasis but also for diachronic “homeorhesis.” Homeostasis is stability of “essential variables” (Ashby 1976) c; homeorhesis is stability of development, of diachronic change. In the following paragraph of Essay, inconsistency refers to “endogenous change of preferences” (Elster 1979), d where at a one time, alternative (or outcome) A is preferred over B, but at another time, B is preferred over A. Such inconsistent time preference is the result of conflicts between multiple goaldetermining elements or changes in the discount factor. e The ever-changing locus of dominance also interferes with integration into more encompassing orders. A larger system may require or even induce a degree or semblance of unity, but imposition of unity from without cannot indefinitely overcome a multiplicity within. Or, the situation may be reversed. The environment may require greater variety of function than is provided by the internal order.

a

Note #48 Algorithmic information, p. 395 Note #49 Genotype and phenotype, p. 395 c Note #44 Law of Requisite Variety, p. 384 d See also Note #159 Temporal traps, p. 566. e Note #64 Discounting the future, p. 417 b

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Even if achievable, temporal consistency may thwart development. What is beneficial in early stages of development is often not beneficial later. And if the development of a system is programmed, so too may be its demise. In complexification, wholes and parts undergo progressive segregation or progressive systematization or both. These two universal phenomena govern diachronic change in all systems. A movement of expansion, differentiation, or decomposition flows downward from unity to multiplicity. A movement of concentration, integration, or composition flows upwards from multiplicity 140 Both currents may be to unity. simultaneously present, but they oppose one another; rarely are they optimally balanced or 141 Differentiation undermines any blended. organizing principle favoring unity; integration undermines any organizing principle favoring multiplicity.

140. Two universal processes Opposing processes of progressive segregation and progressive systematization (von Bertalanffy 1968) are shown in the lattice of Figure 113. a The lattice displays the possible structures for a four-element system; a system with any number of elements has a comparable lattice. Change of structure downward is segregation; change of structure upward is systematization.

a

This repeats Figure 46 Lattice of (general) structures for 4 elements, p. 310

NOTES

536

Figure 113 Segregation and systematization Differentiation, decomposition, and segregation have similar meanings, as do integration, composition, and systematization. Expansion and concentration are more general ideas.

progressive segregation differentiationdisintegration decomposition unity→multiplicity expansion

progressive systematization integration composition multiplicity→ unity concentration

In Klir’s framework (1985), change of structure defines a “metasystem.” Diachronic processes are represented by paths through the lattice. In segregation, going down one level in the lattice omits one relation (shown as a box) with its associated constraint. Recall that a relation includes all lower ordinality projections. Thus the top tetradic relation ABCD includes triadic relations ABC, ABD, ACD, and BCD. The purely tetradic aspect of ABCD might be weak, but as long as its strength is not zero, its loss in decomposition reduces constraint and degree of

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holism. What is left at the second level is ABC:ABD:ACD:BCD. Going down one more level loses one of these four triadic relations and so on. Going from top to bottom moves from maximal to minimal constraint and from high to low ordinality relations. In systematization, going up a level adds a relation; this gain of composition increases constraint and degree of holism. For example, going up from the bottom structure A:B:C:D adds a dyadic relation, say AB, yielding AB:C:D. Going up another level adds another relation, yielding, say, AB:BC:D or AB:CD. Going from bottom to top moves from minimal to maximal constraint and from low to high ordinality relations. Segregation generates distinction, while systematization generates order, so these two diachronic processes exemplify the two core systems principles. From the perspectives of segregation and systematization, the top and bottom structures are alternative organizing principles which unfold as one goes down or up the lattice; in either direction, there is first an expansion, then a contraction of the lattice. (This suggests an alternative double cone diagram in which the cones are joined in their wide bases rather than in their point apexes. a) These two processes apply to many concrete, abstracted, and conceptual systems. For isolated concrete systems, segregation is the Second Law increase of entropy from disequilibrium toward equilibrium. Progressive systematization is also a universal tendency; for concrete systems it can occur if systems are open. Entropy within the system can decrease, as long as the entropy of the system plus environment increases or at least stays the same, as depicted in Figure 114. The downward process can even drive the upward process, if the processes are suitably linked. Still, there is a sense in which the downward process of entropy increase is unmarked (favored) relative to the upward process of entropy decrease, since the former drives the a

Such a representation is used in Figure 117 Limits of self-organization, p. 545

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NOTES

latter. However, most systems are open, and whether the expansion of the universe means that it is closed or open is obscure. Also, the Second Law does not apply to abstracted or conceptual systems or to concrete systems that are not isolated; for these systems, segregation is not necessarily more natural than systematization. Figure 114 Coupling of entropy increase and decrease (a) Downward arrow shows entropy increase in isolated systems; (b) upward arrow indicates that entropy may decrease in open systems far from equilibrium

(a) order (negentropy)

(b)

system environment

141. Optimal segregation vs. systematization Structures at the top of the Lattice of Structures a are well integrated, which facilitates synergy. Structures at the bottom of the lattice allow subsystems to be separately improved, which makes them less vulnerable to failure of other subsystems. The top and bottom of the lattice might be attractors of dynamics that pull the system to one extreme or the other. b But if there is an optimal location distant from both extremes, there may be a meta-dynamic tendency to move toward such an ideal balance. In such cases, top and bottom are “fundamentals” that need to be rejected in favor of a “central” located somewhere between the extremes of the lattice.

a

Figure 113 Segregation and systematization, p. 536 Notes #117 Dialectics, p. 493, #118 The extremes are attractors, p. 494, #135 Movement toward the extremes, p. 527

b

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7.2.4.1 Segregation 142

Progressive segregation, if controlled, is differentiation. Higher ordinality relations weaken, and the system becomes partially 143 Parts of the system gain decomposable. autonomy, but the whole suffers inefficiency or strife. To one part, other parts are competing agents, and what is optimal for a part is rarely optimal for the whole.

142. Progressive segregation Progressive segregation (von Bertalanffy 1979) includes both differentiation and disintegration. Purely structurally, these do not differ, but differentiation can be advantageous for the system, while disintegration is not. Differentiation implies difference, so in general it is dissimilars, e.g., A and B, that become differentiated but similars, e.g., A and A′, can also be differentiated (the support variable of space or time might provide the necessary difference). Differentiation is usually accompanied by some integration; for dissimilars, via gestalt; for similars, via iteration. a Sutherland (1978) discusses iterative differentiation that produces segmentation into nearly identical units. Differentiation occurs differently in controlled and uncontrolled systems. b In biological organisms (ontogeny), it is controlled (programmed) unfolding of a genotypic essence c; in social systems it is unprogrammed and not predetermined. Biological organisms and social systems exhibit both iterative and gestalt differentiation. Social systems integrate components both different in kind and similar in kind but distributed spatially. d a

Note #92 Homogeneity, heterogeneity, and scale, p. 452 Note #88 Hierarchies and networks, p. 445 c Note #49 Genotype and phenotype, p. 395 d 6.4.2 Modernization as differentiation, p. 253 b

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NOTES

The dynamics of differentiation can be modeled on the cusp catastrophe (Figure 115). Initially close subsystems will diverge if they pass the singularity on opposite sides. This also models polarization caused by positive feedback. Figure 115 Differentiation on the cusp

143. Partial decomposability Simon (1962) argued that most systems are partially decomposable, i.e., have parts that are integrated neither so tightly that they cannot be separated without great loss nor so loosely that they are independent. As progressive segregation descends the Lattice of Structures, a the constraint lost b at least initially is often small. The constraint in the overall system may not be much stronger than the constraint of a simpler structure, which is often an adequate approximation of the whole. Differentiation separates center and periphery. The center is the locus of unity; the periphery, of multiplicity. In centralization, the center tends to rigidify and the periphery to disintegrate. The asymmetrical relation between center and periphery may be complementary and reciprocal but may instead harbor unequal exchange, exploitation, and conflict.

a b

Figure 113 Segregation and systematization, p. 536 Note #13 Order, p. 332

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Differentiation may lead to fragmentation, resulting in new systems consisting of parts of the original whole. If the lowest levels are lost, the new system is bereft of foundation; if the highest levels are lost, it is bereft of horizon. If the new system consists only of higher levels, the benefits of being untethered are compromised by the hazards of being ungrounded. Progressive segregation, if uncontrolled, is not complexification but disintegration. The destruction of order occurs far more readily than its creation, and the danger of disintegration inheres in the relentless passage of time. 7.2.4.2 Systematization Development may exhibit not the descent of segregation but the ascent of 144 systematization, in which elements become increasingly constrained by higher ordinality relations. The system gains integrality, but the parts lose autonomy. Optimization becomes more difficult.

144. Systematization Progressive systematization (von Bertalanffy 1968) in which systems become more organized has already been introduced. a Systematization might alternatively label a process wherein relations encompass more attributes of the elements they link. b Stability is stratified, and higher levels of 145 The organization are generally possible. system can become more complex through the a b

Note #140 Two universal processes, p. 535 Note #4 Incompleteness, p. 306

542

NOTES

accretion and integration of pre-existing 146 but rarely does this avoid wholes, inconsistency.

145. Levels of structure and dynamics Previous discussion has offered at least two very different conceptions of “level”: (a) levels of stable equilibria of dynamic systems a (b) levels of composition and decomposition in the Lattice of Structures b To expand upon (a), logistic growth models can be cascaded. Figure 116 shows that this can also be done with the cusp catastrophe. c Catastrophe theory itself does not specify any control point path. Control factors for separate cusps could be different.) Joining Figure 116 to stages within a single cusp gives a dual – macro and micro – conception of diachronics. Figure 116 A hierarchy of cusp equilibria

OP5 OP4 OP3 OP2 OP1

a

Figure 105 Four patterns of growth and development (c), p. 517 Figure 113 Segregation and systematization, p. 536 c Notes #131 Cusp catastrophe, p. 520, and #152 Cusp of negation, p. 555. The Marxist theory of history has a structure that might be represented with Figure 116 A hierarchy of cusp equilibria, p. 542 (Zwick 1978a). b

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146. Integration of stable substructures The emergence of higher levels is analyzed by Simon (1962), who describes a complex system as typically assembled from stable substructures. Bronowski (1970), in his idea of “stratified stability and unbounded plans,” posits that the possibility of such a system (level) consisting of substructures pre-exists its instantiation, which may not in fact occur (like unfilled atomic energy levels). Similar ideas are discussed by (Platt 1970). The question arises whether the emergence of higher levels should be regarded as instances of system formation. a In the next note it is argued that not all levels have the same degree of integration and that the notion of “system formation” should be reserved for events that generate stronger and qualitatively distinct types of order. Even when stratification proceeds smoothly, there are limits to the scope of any organizing principle. Systematization proceeds spontaneously only so far. Barriers to development are encountered well before the limits of self-organization are reached, although special conditions may allow complexification to continue. Support may be provided by external factors. The chance emergence by fluctuation of a more encompassing order may stabilize structures that would otherwise be transient. A second process might augment the first and give it momentum. Or, systematization may be joined to segregation, ascent to descent, enabling both. Possible facilitating conditions are varied, but there is no guarantee that 147 complexity will increase or even persist.

a

Notes #32 Emergence, p. 363, and #120 System formation, p. 496

544

NOTES

147. Limits of complexification Increase of complexity is qualitative development, not mere quantitative growth. a The above selection from Essay summarizes a speculation (Zwick 1978c, Zwick and Fletcher 2014) on the limits of hierarchical self-organization. The idea is that complexification by stratification often occurs spontaneously via the self-assembly of lower-level units, but generation of higher – and qualitatively different – levels of organization by spontaneous processes occurs less readily. This idea asserts that this type of incompleteness is common in diachronic processes. To illustrate, consider the hierarchy of molecular structures within cells, built on the base level of atomic structures. The joining of atoms and molecules by bonded or non-bonded interactions generates complex structures – multimeric enzymes, ribosomes, etc. Small molecules readily react spontaneously under suitable chemical conditions to form larger (covalently bonded) molecules, macromolecules spontaneously aggregate (through non-covalent interactions) to form larger complexes. But molecules and complexes do not self-organize to form cells, regulated metabolisms enclosed by self-generated boundaries and capable of reproduction. System formation of cells does not occur spontaneously as does the self-organization of molecules. How life began is still a scientific mystery. Reaching still higher levels of organization depends on having achieved cellular organization. Once cells exist, selforganization is again possible. For example, tissues can selfassemble from constituent cells. But only up to a point. Complex eukaryotic organisms (or whole organ systems) cannot self-assemble from components. Under the aspect of similarity, the definition of system in terms of elements and relations suggests that levels of organization are equal in some sense. Under the aspect of difference, however, a

Note #125 Development vs growth, p. 510

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some levels are special, namely those that establish organizing principles which are qualitatively very different. The levels of atom, cell, and organism are special in this sense. Levels of molecular complexity that exist between atom and cell, and levels of tissue, organ, and organ system that exist between cell and organism are more ordinary. A transition to a level that reflects a radically new organizing principle is difficult; one might speak of a “barrier” to emergence of a qualitatively new organizing principle. These ideas are illustrated in Figure 117. Figure 117 Limits of self-organization (a) Hierarchical levels and the minor and major barriers to complexification; (b) the two organizing principles (OP) represented as two vertices of a shifted double cone. a The location of minor barrier and the number of levels organized by OP1 are only suggestive. The cones upward from OP2 and downward from OP1 are arbitrarily truncated. Their solid rendering represents the strong influence of the bottom-up and top-down organizing principles.

OP2

major barrier

concentration

minor barrier expansion

OP1 (a)

complexification (b)

In (a), the major barrier marks the shift to a new whole, to OP2. Transition across the major barrier establishes a qualitatively new order. This is system formation. b One might regard the a b

Figure 3 System as center, p. 49 Note #120 System formation, p. 496

546

NOTES

transition from any level to the next level as system formation, but major transitions, e.g., from molecular to cellular organization or from cellular to organismic organization, have greater significance. The inherent capacity of an organizing principle to elaborate complex structures is limited; only the emergence of a radically new principle allows complexification to continue. In (b), the vertices of the two double cones correspond to the primary levels of OP1 and OP2. The downward cone from OP2 and the upward cone from OP1 meet above but roughly near the minor barrier, which marks the transition from expansion to concentration. The minor barrier poses limits to spontaneous hierarchical ascent at a complexity less than the organizing limits of OP1. A common cause of this barrier is the combinatorial explosion of structures that can be produced by OP1. At some point, bottom-up self-organization allows a virtual infinity of possibilities and only a top-down mechanism can manage this potential variety. For example, a huge number of protein and nucleic acid polymers are possible via spontaneous covalent bonding. Formation of these polymers in cells cannot be left to spontaneous processes and must be governed by genetic information. Similarly, morphogenesis of complex organisms cannot rely on spontaneous self-organization of cells but requires programmed differentiation at the level of the whole. The minor barrier marks the emergence of individuality from combinatorial complexity, the meeting of top-down and bottomup organization, and the separation of different modes of organization. For example, lower subcellular levels are organized by covalent bonds and higher levels by non-covalent bonds, but this difference is not as substantial as the difference between molecular and cellular organization, below and above the major barrier. Transitions between ordinary levels proceed spontaneously, but specialized apparatuses are required to bridge barriers: for the major barrier, cellular and organismic

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reproduction; and for the minor barrier, protein synthesis for the cellular order and differentiation for the organismic order. In systematization, upward processes may need to be linked to downward processes. a Successful passage – not mere leakage – through the minor barrier presumes the prior, even if only transient, passage through the major barrier. The maximal realization of any organizing principle may be only possible after it has been transcended; that is, the minor barrier can be fully crossed only if the major barrier is at least provisionally bridged. A very complex order is never built by unidirectional ascent from a simpler order. This idea is depicted in Figure 118. A distinction thus must be made between complexification that exhausts the unfolding of an OP1 but does not launch a new OP2, shown in Figure 118(a), and complexification that completes the unfolding of an OP1 and launches a new OP2, shown in Figure 118(b,c). The latter includes a transformation of the organizing principle; the former does not. A similar distinction was made in the logistic models discussed earlier. b In single logistic growth and in growth-decline-disappearance, one OP unfolds but a second OP does not get initialized, but in double logistic growth a second OP is established. Figure 118 Spontaneous complexification via transient .

OP2 OP′2 '

OP1

a b

(a)

OP1

(b)

OP1

Note #140 Two universal processes, p. 535 Figure 105 Four patterns of growth and development, p. 517

(c)

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NOTES

In Figure 118(a), spontaneous complexification is blocked partially by the minor barrier and fully by the major barrier. In (b), through fluctuation, a transient precursor (OP′2) brings the minor transition under top-down influence. In (c) after this transient system formation, OP2 is consolidated and undergoes further complexification. Although (c) does not show any subsequent unfolding of OP2, this is implied by Figure 117(a). But the fluctuation to OP′2 which allows OP1 to reach full development may not occur, and the potential of OP1 may not be realized. This raises the question of a possible connection between limitation viewed in terms of logistic patterns and the major and minor barriers hypothesized here. Note first that this hierarchical model is speculative and non-mathematical, and thus hard to compare to a differential growth equation; also, the logistic equation was developed for quantitative growth, and not for the complexification of development, a so comparisons of these two models are not straightforward. This said, positive feedback producing exponential growth can bring difficulties for development from a combinatorial explosion, which is one interpretation of the minor barrier; also the shift to negative feedback that causes growth to level off might be viewed as establishment of a new OP (the process now being dominated by K, not by r). On the other hand, this new OP does not bridge the major barrier in a way that necessarily initiates a new process of complexification. The present model might alternatively be associated with the cusp catastrophe. b The minor barrier might be interpreted as entry into the bifurcation set, and transition across the major barrier might be exemplified by the jump to OP2 (although the cusp model depicts this as easy and not difficult). As noted above, the minor barrier delimits the downward influence of OP2; correspondingly in the cusp, entry into the bifurcation set a b

Note #125 Development vs growth, p. 510 Note #131 Cusp catastrophe, p. 520

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gives rise to the second equilibrium possibility associated with OP2. The hierarchical levels between OP1 and OP2 here correspond in the cusp to the numbered stages on the control point trajectory. The connections between the present model and both logistic growth and catastrophe theory are summarized in Table 18. Table 18 Aspects of limits of complexification

Aspects of the limits of complexification model Major Non-OP Minor barrier barrier levels Logistic growth

positive feedback

negative feedback

transient

Cusp catastrophe

entry into bifurcation set

change of OP

stages of trajectory

So far, complexification has been interpreted spatially as a (vertical) hierarchy of structures, but it can also be interpreted temporally as a (horizontal) sequence of stages (Figure 119). The development of OP1 is expansion; the completion of the process and the establishment of new organizing principle OP2 is concentration. a The above figure is simplified in the historical model presented in Commentary, which also discusses a different means by which the minor barrier can be overcome, namely by a second process which augments the first and, blending with it, bridges the barrier. b For more details about this model of complexification, see (Zwick 1978c).

a

In Chinese philosophy, expansion is yang and concentration is yin. As the neo-Confucian Zhou Dunyi (Wang 2005) asserts, “Heaven uses yang to produce the myriad things and uses yin to complete the myriad things.” b 6.1 A macro-historical model, p. 193; Note #166 Butterfly catastrophe, p. 570

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Figure 119 Divergent and convergent complexification This figure rotates earlier Figure 117 clockwise by 90° to show extension in time rather than space. In (a), lines are stages; barriers are shortened. In (b), two horizontal double cone diagrams are joined at their bases, a showing divergence (expansion) from OP1 leading to convergence (concentration) toward OP2. (The leftmost and rightmost cones are shortened.)

OP1

OP2

(a) time (b)

Ascent of systematization is sometimes too rapid, with new levels poorly integrated with those already present. Salience of new levels may undermine basic function. Through the emergence of higher levels, the system rises above lower level constraint. But lower levels are supplemented, not eliminated. What is transcended may be routinized or ignored but it persists and under adverse conditions it 148 claims its due. Only harmonious integration of levels, not transcendence of the lower by the higher, can endure.

148. Non-decomposability under stress Simon (1962) notes that although systems typically are partially decomposable vertically (as well as horizontally), with levels a

Figure 98 System formation; system as temporal center, p. 498, in Note #120 System formation

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partially sealed off one from another, lower-level constraints often become visible under limiting or adverse conditions. Systematization may increase connectedness without adding higher levels. Greater connectedness is a multiplier that can neutralize disturbance or amplify it and thus 149 can either increase or decrease stability. Some systems in their development move towards critical points where disruptive events at all scales become both unpredictable 150 and inevitable.

149. Connectedness for good and ill Mathematically, some forms of connectedness produce instability, but empirically in mature ecosystems (May 1974), connectedness is often associated with stability. Holling and collaborators (2002) describe overconnectedness in mature (K) ecosystems as causing instability and the destructive Ω phase. a Networks that are highly connected can survive loss of some paths between nodes since other paths are available but high connectivity also allows disruption to spread widely and rapidly. Hubs, i.e., high-degree nodes in scale-free networks, b are loci of vulnerability, while low-degree nodes can fail without adverse effects on the whole.

150. Self-organized criticality Bak (and Chen 1991; 1996) has proposed that many open systems driven far from equilibrium by a matter or energy flux exhibit “self-organized criticality” (SOC). They spontaneously reach steady states that are “critical points,” where because of connectedness small disturbances can cause sudden disruptions to occur at all scales. There is no typical size for these disruptive events, i.e., they are not described by a distribution such as a a b

Note #130 Trajectories of development, p. 517 Note #91 Scale-free networks, p. 450

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NOTES

Gaussian that has a central tendency. Instead, the frequency of these events has a power-law distribution. The number of events of size S varies with some negative power of S: N(S) = a S – b. On a log-log plot, the equation is linear: log N(S) = log(a) – b log(S). Figure 120 illustrates the idea of SOC. Figure 120 Self-organized criticality A state variable (e.g., the size of a sand pile) increases to a level at which a sudden perturbation causes a precipitous drop in its value. The magnitude of the drop is the size of the event. (Magnitudes are exaggerated to make the point visually clear.) This plot has a power-law distribution. Events with sizes of 1:2:4 have frequencies of 4:2:1.

state variable

time The paradigmatic SOC example is a sand pile, on which sand is continually dropped from above. The pile gradually grows until it reaches a steady state critical point. After this point is reached, continued dropping of sand causes avalanches that have a wide range of sizes. Small avalanches are frequent, and large avalanches are rare. It is impossible to predict when avalanches will occur or what their size will be. Avalanches are positive feedback events, in which very small causes such as a single grain of sand have big effects. (Amplification of small causes also occurs in chaos and catastrophe dynamics.) As noted in the discussion of local versus global causality, a the cause of the avalanche is not merely the falling grain of sand but also, and more fundamentally the poised state of the sand pile. Small causes can have large effects; both micro-randomness (size of a

3.4 Aspects of complexity and holism, p. 100

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an individual event) and macro-determinism (the overall powerlaw behavior) are true. Bak’s SOC resembles Holling’s adaptive cycle a in that the steady state reached in SOC is like the K phase, and disruptive SOC events are like shifts from K to Ω, but the return to the critical state in SOC may or may not be adaptive. Some possible instances of SOC, e.g., forest fires, may involve adaptation; others, e.g., sand piles, may not. In Holling’s model, adaptation occurs in the α phase, but SOC in its simplest form lacks this phase, and goes directly from Ω to r. Self-organized criticality is a type of complexity but Holling’s adaptive cycle applies only to complex adaptive systems b which are systems that adapt to, and are not merely being impacted by, their environments. Kauffman (1992) has argued that SOC occurs in ecological and evolutionary systems that are dynamically “at the edge of chaos” (Kauffman 1992), so being far from equilibrium and being at the edge of chaos may be linked. SOC processes may also generate fractal phenomena (Bak and Chen 1991), but fractal phenomena do not necessarily imply SOC. The presence of a power-law distribution also does not prove the presence of self-organized criticality. Such distributions are found in allometric relationships between properties of different organisms, which often result from dimensional considerations. For example, some properties of an organism vary with surface area, others with volume. Power-law distributions are also found in scale-free networks.

a b

Note #130 Trajectories of development, p. 517 5.1 No singular systems theory, p. 149

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NOTES

7.2.5. Internal opposition Notes: 151 152 153 154

page

Something intractable Cusp of negation Excess and overshoot Chance and necessity

554 556 559 560

Limitation may be internal and specific. Incompleteness and inconsistency engender development but also obstacles to development. As a response to incompleteness or as an intensification of inconsistency, there may emerge within the system a competing 151 order. Every system is flawed, and every flaw in a system is a potential nucleation site for an alternative organizing principle.

151. Something intractable A system can be as exhaustively provided as possible with information, with memory, with anticipatory and defensive mechanisms, even with openness towards events ... [but] ... there is something within that system that it cannot, in principle, deal with. Something that a system must, by virtue of its nature, overlook. And if history, especially modern history, is not simply a tale of development, the result of an automatic process of selection by trial and error, this is because “something intractable” is hidden and remains lodged at the secret heart of everything that fits into the system, something that cannot fail to make things happen in it. - Jean François Lyotard (1993)

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The alternative may derive from what was originally missing in the system. What is ignored or suppressed will eventually have its moment. The alternative may reflect the increased importance of function as a basis of identity, one not congruent with identity determined from within. Or the reverse: an internal order may emerge that competes with a previously dominant external function. More generally, every system is pulled in opposite directions by fundamental polarities. a If it is organized around one extreme, the other extreme is a potential challenger. Alternatively, difficulties of development may arise not from what was absent in the system in its formation but from what was present: not from original incompleteness but from original inconsistency. The system may contain two organizing principles: one dominant and the other subordinate. Confrontation of the organizing principle and its negation may grow into conflict, leading in some cases to ascendancy of the challenger. Usually, the system remains structured for a time in its earlier form, but continued shifts towards dominance of the alternative principle may finally make visible what has hitherto been latent. A crisis may ensue in which change accomplished in deep structure manifests also in surface structure. Finally, there may be transformation. The system may 152 yield to its negation.

a

Summary 1.1.9 and 7.1.9, pp. 23, 491; Notes #115 Binary oppositions, p. 492, and #116 Dyadic correlations, p. 492.

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NOTES

152. Cusp of negation The cusp catastrophe a shown in Figure 121 models a dialectical “struggle of opposites” in which one of the opposites is victorious (Zwick 1978a). By contrast, a struggle that leads to a synthesis of the opposites is modeled with the butterfly catastrophe. b 7.1.9 Summary lists several synchronic oppositions that afflict systems. Diachronic change is often a shift from one extreme to the other, or as Essay puts it, from one organizing principle to another. Figure 121(a) shows motion on the control surface from point 1 to point 7 that causes motion on the equilibrium surface from point 1 to point 7. Figure 121(b) shows the dominance of the alternative principle as latent at point 6 and manifest at point 8, after the system has shifted at point 7 from the lower surface (L) to the upper surface (U). The V(x) plots show that at point 6, the equilibrium state on L is inferior to the equilibrium on U, but the L equilibrium is actual (shown by the dot), while the U equilibrium is only potential. (Local and global optima are shown as low values of V; if V were some utility function, however, optima would be high values. Physicists minimize and economists maximize). Only when the equilibrium on L disappears at 7 does the victory of the new principle become possible. This is called “delay.” There is another possibility. If the system inside the bifurcation set is subjected to strong random fluctuations in the state, x, a shift from L to U could occur at 6, and could even occur with some probability earlier, e.g., before 5.

a

Note #131 Cusp catastrophe, p. 520; V(x) is potential in the dx/dt = dV/dx equation for the cusp. b Note #166 Butterfly catastrophe, p. 570

557

Chapter 7.2 Diachronics: Internal Opposition

Figure 121 Structural change as a cusp (a) Motion on control surface CS causes motion above it on the equilibrium surface ES; (b) V(x) at 8 locations of control point. BS=bifurcation set, U, L=upper, lower ES surfaces.

ES 8

U

1 2

(a)

7

6

5

4

L

x 1

CS 8

3

2

BS 7

6

5

8

3 4

V

1 2

7

(b) 6

4

5 L

3

U

x

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NOTES

The system is on L in most of its development. The jump to U at 7 is an event of restructuring. If the control point moves from point 8 to 1, there is a fall from U to L at 3; if the trajectory closes on itself, it could resemble Holling’s adaptive cycle. a But to the degree that the alternative principle is only a denial it offers no basis for a new order. What succeeds as negation never succeeds as affirmation. Negation, to supplant what is rejected, must be more than a corrective; it must offer a positive principle. But to be effective, negation yields to excess and distortion: excess in promotion of the 153 new, distortion in rejection of the old. No order was ever overturned while being granted its due. In the heat of conflict, no delicate titration of opposing principles can be accomplished. Means can never be calibrated precisely to ends. Every correction overshoots. In transformation there is no remedy for the lawful presence in all systems of incompleteness or inconsistency. Imperfections may be mitigated; they may be replaced with different deficiencies, but imperfection is an ineradicable condition. At the very moment when dominance of the new principle is finally established, when negation attempts to recast itself as affirmation, a price is exacted for the excess and distortion that brought victory. At that moment, the deficiencies of the new organizing principle are crystallized, and in this crystallization, the corruption of the new order begins.

a

Note #130 Trajectories of development, p. 517; see also Zwick and Hughes (2017).

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153. Excess and overshoot Just because something is flawed is no reason to prefer its opposite. – Theodor Adorno The opposing principle negates, and negation always suppresses some truth about what it opposes. Negation is an aspect of the dyad; reconciliation is possible only with the triad. To every action there is a reaction, and reactions typically overshoot. a Essay speaks about action and reaction, but these modes of behavior apply more generally to dynamic systems which have equilibrium points and negative feedback. It is not merely that any new order has imperfections. However flawed the old system was, it had attributes that were not deficient, that could be valuable to the new order, conceivably even to any order. What is essential and necessary or accidental and contingent are difficult to distinguish. In its excess of rejection, the new is inaugurated with incompleteness. And what is rejected in the struggle for dominance is not easily recoverable. The original principle may be vanquished and disappear. Or it may persist in the surface structure, while the deep structure has been transformed. The system may thus appear unchanged despite negation of its organizing principle. Every system has the capacity, through an unbroken line of development, to turn into its opposite without seeming to have done so. The struggle of principles may instead yield 154 the triumph of the original order, but its victory is never complete. Those aspects of a

Note #45 Feedback control, p. 386

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NOTES

the system that gained coherence by the opposing principle remain, and produce in the system a persistent strain. Recognition of the continued presence of this alternative is suppressed. But the success of this suppression cannot last forever; contradiction may be hidden for a while but not indefinitely.

154. Chance and necessity A triumph of the original order is not the result of a standard dialectical trajectory which, in the imagery of the cusp catastrophe, completely traverses the bifurcation set and transforms the system with a new organizing principle. Rather, it describes a path of the control point that reverses direction and exits on the same side of the bifurcation set that it entered. The standard dialectical trajectory may describe some phenomena in social systems, but there is no reason to accept the “necessitarian” aspect of early Marxist dialectics (Unger 1987). In the catastrophe-theoretic understanding of dialectics, the trajectory of the control point is not specified a priori but is contingent. However, the consequent motion of the behavior point is determined (though it may be partially stochastic), so catastrophe models can integrate chance and necessity, fusing the idiographic with the nomothetic. a Or, the struggle may lead to a synthesis b reflecting a third alternative. Conflict between opposing principles then shifts to conflict with this synthesis. Just as opposing principles enable and stimulate one another,

a

Note #129 History: idiographic or nomothetic, p. 516. Also see Zwick (1978a). b Note#166 Butterfly catastrophe, p. 570; Note #165 Two kinds of dialectic, p. 569; Note #20 Reconciling constraint and variety, p. 341.

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so too does a newly dominant center a incite both extremes. Those parts of the system ordered by the alternative principle may detach themselves or be expelled, and may form a new order. For the original system, inconsistency is resolved, but incompleteness remains. The problem is externalized but not thereby solved. Conflict with the new system ensues. The old and the new endanger one another. Partition leaves both marred. In the old system, the original principle is distorted; in the new system, aspects of the old are retained or the new order is incomplete.

a

The notion of “center” here is different from the notion of “center” in “center and periphery.”

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7.2.6 Texture Notes: 155 156 157 158 159 160 161 162

page

Environment is a limited source and sink Wastes are inevitable Closing the circle Limits to growth Temporal traps Growth as a PD Difficulty of reversing bad effects Destroying the environment that sustains

563 563 564 565 566 566 567 567

Limitation may be external and general. Only certain external substances are beneficial to assimilate; only certain internal substances are beneficial to retain. The environment, as a source for resources and a sink for wastes, is 155 Resources may be finite, not infinite. depleted; disorder or noxiants may hinder the capacity of the environment to support the system. The production of order for maintenance and development, for exchange, or for modification of the environment may or may not occur, but the production of disorder, either retained internally or expelled into the environment, is unavoidable. Wastes are a 156 necessary consequence of self-maintenance The wastes of the system are harmful to it and other systems of its kind and often to other kinds of systems. Only some wastes can be taken in by other systems and removed from the environment, but these other systems are not always present. The neutralization of harmful waste cannot be guaranteed. The 157 circle is not always or easily closed.

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155. Environment is a limited source and sink Any resource stock (dowry) acquired at system formation is limited. An internal stock may be depleted by external disturbance, a so a system ultimately depends for its persistence on a reliable flow of resources from its environment. No system can long endure if it extracts resources faster than they are replenished. Since dissipative systems tend to increase the flow that sustains them, b limits are typically encountered. c Excess of consumption over income is possible only as long as there is some dowry still available for consumption, but this dowry can be drawn upon only once; excess consumption can only be transient, not steady state, behavior. The same applies to noxiants. They can be neutralized by the environment at some definite rate – by their diffusion or inactivation or their uptake by other agents for which these noxiants are resources. No system can long endure if it pollutes its environment faster than this pollution can be neutralized.

156. Wastes are inevitable For concrete systems, this follows from the Second Law of Thermodynamics. The entropy of system + environment stays the same or, more commonly, increases over time. The production of wastes is thermodynamically mandated (although waste need not be internally retained). Functionally, generating useful products may be required by a superordinate order that embeds the system, but only the generation of waste is inescapable. And when useful products are produced, waste production is accelerated. Wastes and useful products are externalities, negative and positive ones, respectively. d

a

Rapid depletion of internal resources can occur, for example, if the environmental disturbance increases rapidly; see Figure 110 Failure of response to exponential danger, p. 526. b Note #42 Dissipative systems, p. 381 c Note #130 Trajectories of development, p. 517 d Note #60 Externalities, p. 412

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NOTES

Although thermodynamics does not apply to abstracted systems, “wastes” can occur in these systems as well, although this is rarely treated by any formal theory. One should completely refrain from applying thermodynamics to conceptual systems.

157. Closing the circle Figure 122 displays how wastes might be resources for other systems, thus increasing efficiency – the fraction of resources captured – of the flow process; it also shows how the circle can be closed, a which further improves efficiency and reduces overall waste. System products, as opposed to wastes, are not represented in the figure. Figure 122 Extending the path and closing the circle (a) A single system, S1, with resource inputs R1 and waste output W1. (b) Part of S1’s wastes, w1S, is utilized by system S2 as resource R2, so R1 is used more efficiently than it is in (a). (c) Some S2 wastes, namely w2S, are usable by S1 and are thus not wasted, thus closing the circle and further improving efficiency. w1E + w2E < w1E + W2 < W1, i.e., waste(c) < waste(b) < waste(a)

R1

S1

W1

(a) R1

R1 w1E

S1 w1S = R2 (b)

S2

W2

S1

w1E

S2

w1S = R2 w2E

w2S

(c)

In circumstances of limitation, the system 158 must shift from expansion to steady state. This shift may be difficult to achieve or come too late to prevent overshoot and collapse. a

Figure 75 Internalizing the external in decisions, p. 413

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Expansion inheres in an organizing principle that dictates the repeated priority of short159 term gain over long-term necessity. Uncontrolled growth of subsystems may 160 enlarge the system beyond sustainable size. It may be difficult to reverse the degradation of the environment already produced by such 161 growth. Even if the long term is considered, the future is an externality that is never fully encompassed. Moreover, a steady state, even if achieved, may not be sustainable. Systems often destroy the environments on which they 162 depend.

158. Limits to growth The limits to growth studies in the 1970s (Forrester 1971, Meadows et al. 1972) were the precursor of today’s concern with sustainability. However simplified these models were, and although growth that slows in one domain may continue in another, the principle popularized by these models is correct and still not fully appreciated. Indefinite exponential growth always encounters a limiting factor; positive feedback is always checked by negative feedback. The r-phase of expansion necessarily leads to a K phase of limitation. The result may be an S-shaped (logistic) growth pattern in which growth shifts to a steady state, but other patterns are possible. a At worst, growth overshoots the carrying capacity set by K, leading to collapse (Figure 123) by exhaustion of resources, accumulation of wastes, or other limitations. b Adaptations to r or K phases require different organizing principles; when a system needs to shift from OPr to OPK, it may not be able to do so in time. Collapse and recovery are modeled in the adaptive cycle. c

a

Figure 105 Four patterns of growth and development, p. 517 6.4.1 Sustainability and globalization, p. 248 c Figure 106 Holling's adaptive cycle model, p. 519 b

566

NOTES

Figure 123 Overshoot and collapse growth carrying capacity

159. Temporal traps John Platt’s “Social Traps” (1973) discusses the tendency in some systems to favor short-term gain over long-term interest. Addiction, an example of this tendency, is an iterated Prisoner’s Dilemma, where the game repeats over time. A player plays a virtual game with itself or a later generation. Call the players P(t1) and P(t2). P(t1) reasons as follows. “Either P(t2) will solve the problem, so taking a short-term view causes no long-term harm, or P(t2) will not solve it, in which case adverse effects of present action are insignificant in the long term.” P(t1) thus chooses the action motivated by short-term gain. The game repeats between P(t2) and P(t3). P(t2) again chooses the shortsighted action, and so on. The appropriate response is always deferred until tomorrow, but tomorrow never arrives.

160. Growth as a PD Growth of a system beyond optimal scale may be a Prisoner’s Dilemma, a i.e., the failure to act on the negative consequences for the system of unrestrained growth of its parts. Such suboptimization may be the consequence of insufficient centralization.

a

Note #78 Prisoner’s Dilemma, p. 433

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161. Difficulty of reversing bad effects A dependence on past history (path dependence) is an important property of many nonlinear systems. Reversing a cause often does not immediately reverse its effects. This is illustrated by hysteresis in the cusp catastrophe. a The control parameters are here not conflicting factors but rather normal and splitting factors, N and S, shown in Figure 124(a). (N and S are the p1 and p2 of the cusp equation, dx/dt = x3 – p1 – p2 x.) N represents the tendency toward the upper surface (high values of x) as opposed to the lower surface (low values of x); S governs how far apart the surfaces are, and thus how big the catastrophic jump is. The figure explains the irreversibility. Figure 124 Cusp catastrophe hysteresis In (a) control surface parameters are splitting and normal factors, N and S. The bifurcation set, BS, is the upside-down diverging V. If the control point first crosses the right edge of BS (where N is negative), causing the crash from high to low x in (b), this drop is reversed only if the control point moves all the way back to the left edge of BS (where N is positive).

(a)

(b)

N

x N

S control point motion

162. Destroying the environment that sustains Diamond’s (2005) discussion of societies that destroy the environments that sustain them has been introduced earlier. b

a b

Notes # 131 Cusp catastrophe, p. 520, and #152 Cusp of negation, p. 555 Note #134 Failures in meeting new challenges, p. 525

568

NOTES

7.2.7 Other systems Notes: 163 164 165 166 167

page

Natural selection The organized exploits the unorganized Two kinds of dialectics Butterfly catastrophe Butterfly of reconciliation

568 569 569 570 572

Limitation may be external and specific. When environmental resources are limited, there is a struggle for existence. The system may face 163 competition or predation. If it is large and complex, small and numerous antagonists may be difficult to counter. If it is small and simple, large and complex antagonists may overwhelm. No size or complexity is optimal for all situations of competition, predation, or conflict.

163. Natural selection When there is a population of similar systems competing for limited utility, only some will secure their interests; others will not thrive or even survive. Over the long term in any single functional niche, it may be that only one type of system will persist. Such “competitive exclusion” is the manifestation of positive feedback. Better adapted systems become more plentiful over time. This reduces diversity, needed for continued adaptability and for global as opposed to local optimization. Such movement toward unity (homogeneity) can however be counteracted by mechanisms that maintain niche multiplicity (heterogeneity). Different types can coexist because of extension in space (geographic isolation) or time (ecological succession).

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Systems suffer unequal exchange with larger 164 Unequal or more coherent systems. exchange drains resources, stunts development, and compromises autonomy. Even where there is mutual benefit, exchange also brings dependence and thus vulnerability. If dependence is extreme, determination becomes external rather than internal, and the system is partially absorbed into the more developed system on which it depends.

164. The organized exploits the unorganized Margalef (1963, 1968) argues that when a developed ecosystem borders upon an immature one, free energy flows from the immature system to the more developed one. The capacity of the organized to exploit the unorganized is also exemplified in games in which one player is a unity, while the other player is a multiplicity that can find itself stuck in a Prisoner’s Dilemma. Opposition between systems may be reconciled by a synthesis in which the system and its antagonist are integrated and harmonized. The dialectics of reconciliation are more demanding and subtle than the 165 dialectics of victory or defeat. Additional factors must balance and bind contending 166 If such factors are present, conflict forces. may be overcome, but the existence of these factors and the synthesis they enable may be transitory.

165. Two kinds of dialectic One can distinguish two kinds of dialectic: one where synthesis, the third stage of the dialectical triad, means a victory of one of the two contending forces and the other where synthesis means that a middle position emerges. The first can be modeled with

570

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the cusp catastrophe a; the second with the butterfly catastrophe, explained in the next note. b Politically the cusp models a polarization of left and right, while the butterfly models the emergence of a center at odds with both left and right. It must be admitted that, in this catastrophe-theoretic model, synthesis is captured only quantitatively as a simple compromise but not qualitatively as a creative fusion of opposites. (Making the metaphysics of dialectics exact c by giving it a catastrophetheoretic interpretation requires a sacrifice of content.) The cusp can evolve into a butterfly allowing the resolution of conflict. The butterfly can devolve into a cusp leaving conflict resurgent.

166. Butterfly catastrophe In the cusp catastrophe, there are two causal factors each favoring one of two equilibrium states. In the butterfly catastrophe, whose dynamics is given by dx/dt = p1 – p2 x – p3 x2 – p4 x3, there are two additional causal parameters (p3 and p4) known as the bias and butterfly factors, respectively. The butterfly catastrophe is is shown on the following page in Figure 125. For appropriate values of the parameters, especially the butterfly factor, a third intermediate equilibrium state emerges between the two cusp-like extreme equilibrium states. The butterfly factor is a mediating or reconciling factor, but this third equilibrium state is not merely a compromise. It arises at the expense of and in conflict with the extremes. If this parameter weakens to the point of vanishing, the intermediate state disappears, and the butterfly reverts to the cusp, with its two extremes. The fourth parameter, the bias factor, distorts the equilibrium surface to favor one of the extremes.

a

Note #131 Cusp catastrophe, p. 520 More detailed connections to the literature of Marxism are offered in (Zwick 1978a). c 2.3 A new conception of metaphysics, p. 54 b

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Figure 125 The butterfly catastrophe For c = 0, d > 0, (a) Control and behavior surfaces. α = lower equilibrim surface, β = upper equilibrium surface, γ = intermediate equilibrium surface (pocket) (b) one, two, or three equilibria at the various locations on the control surface.

(a)

γ

β

α

(b)

The cusp and the butterfly catastrophes roughly correlate with zero-sum and non-zero-sum games, respectively. In the cusp, the two equilibrium states of the system are mutually exclusive, just as in a zero-sum game one player must win and the other must lose. In the butterfly, the compromise solution represents the victory of neither extreme equilibrium state; this is

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analogous to a win-win solution of a non-zero-sum game. a These correlations of catastrophe theory, game theory, and dialectics are summarized in Table 19. Table 19 Catastrophes, games, and dialectics Catastrophe theory

Dyadic outcome cusp catastrophe

Non-dyadic outcome butterfly catastrophe

Game theory

zero-sum games

non-zero-sum games

Dialectics

victory or defeat

reconciliation

167. Butterfly of reconciliation Conflict in the cusp can be reconciled in the butterfly (Zwick 1978a); this can model the resolution of conflict. Consider a cusp where the struggle of opposites does not lead to victory of one over the other or where victory would not be optimal even if achievable. Compromise between the organizing principles is impossible because the middle equilibrium of the cusp is a repellor. Assume that the system has entered the bifurcation set, and thus has two opposing possible states. Suppose the singularity changes from a cusp to a butterfly, and the dynamics of the bias and butterfly control factors changes the bifurcation set so an intermediate equilibrium state comes to exist that did not exist before. If the butterfly factor is strong and the bias factor holds the conflicting factors in balance (or conflicting factors weaken), the system can move to this new state. This sequence is shown in Figure 126, which shows the motion of the control point over a two-dimensional section of the control surface.

a

Like all analogies, this analogy is imperfect. The compromise solution in the butterfly catastrophe doesn’t have a win-win utility interpretation. Dialectical reconciliation, however, might have a win-win character.

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Figure 126 From cusp to butterfly (a) plots an initial trajectory on the cusp. a In (b), shown larger, the singularity has changed to a butterfly after point 3. The trajectory might then move from point 4 where only the two cusp-like opposing equilibria are possible (αβ in Figure 125(d)), to point 5 where γ, the compromise equilibrium, is added as a possibility (αβγ in Figure 125(d)), to 6 where the compromise and only one conflictual state is available (αγ in Figure 125(d)), to point 7 where the compromise state is the only remaining stable state (γ in Figure 125(d)). If the state of the system at point 1 is α, then this state continues from 2 to 6, and only changes to state γ at point 7.

1

7 5

2

6

3 4 (a)

(b) This transition from cusp to butterfly is one interpretation of the idea, b that a process encountering difficulties of development can be facilitated by a second process. Here, the introduction of butterfly and bias factors is this second process. The first process is purely conflictual; blending of this second with the first transforms the catastrophe type from cusp to butterfly and allows synthesis or compromise. This is shown in Figure 127.

a b

Note #131 Cusp catastrophe, p. 520 6.1 A macro-historical model, p. 193

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Figure 127 Augmentation by a secondary process The stages here are the same as in Figure 126. The system remans in state α until reconciliation (γ) is reached at point 7.

butterfly and bias factors conflicting factors time

butterfly

cusp α 1

2

3

4

5

α

γ

6

7

The butterfly can be cascaded like the cusp a to yield a multistage macro-dialectical diachronic model, which an α-β opposition leads to a γ synthesis (and qualitative change) which gets transformed into a new α which generates a new α-β opposition, and so on.

a

Figure 116 A hierarchy of cusp equilibria, p. 542

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7.2.8 Embeddedness Notes: 168 169 170 171 172 173

page

Succession Punctuated equilibria Adaptation vs. adaptability When to change Generalized evolution Evolution of modeling subsystem

575 576 577 579 579 581

Limitation may be external and both general and specific. When a system is embedded in a more encompassing order, it is subject to constraints imposed by this order. If the order is itself only a transient in a process of 168 development, the system’s functional niche will eventually disappear.

168. Succession An example of a process of development is ecological succession. In succession, the species that constitute an ecosystem change until an ecological climax (mature) state is reached. Ecological processes are different from evolutionary ones in that in an ecosystem the species that are present are fixed, and while some may become extinct, new species are not introduced, except from neighboring ecosystems. What change over time are the relative proportions of different species. In evolutionary processes new species are introduced via genetic mechanisms. One can generalize notions of ecological or evolutionary change to social systems, although in such generalizations, one must be careful also to respect differences. Either sudden change or long-term gradual change in the embedding order can undermine the system. Sudden change following 169 prolonged stasis poses a special risk since

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170

successful adaptation inhibits adaptability. When an environment remains constant, adaptations rigidify and resilience degrades. Long-term gradual change may escape detection.

169. Punctuated equilibria Long-term evolutionary processes can exhibit extended periods of stasis interrupted by periods of major and rapid change. Such “punctuated equilibria” was proposed by Eldredge and Gould (1972) to account for sudden and massive extinctions in the evolutionary record. At least two quite different explanations are possible. Either punctuations were driven by sudden external events, e.g., asteroid collisions with earth, or they resulted from internal evolutionary processes, or both. Even if the well-known singular events in the evolutionary record resulted from external perturbations, it has still been demonstrated by many simulations that in nonlinear dynamic systems similar discontinuous events can be internally generated (Lindgren 1991; Ray 1991). The adaptive cycle and self-organized criticality a are among the possible models for punctuated equilibria. Ray's work suggests that there might be a natural progression through the environmental types defined by Emery and Trist. b The environment which embeds the system may change over time from being relatively undifferentiated (the subject of Texture in Synchronics and Diachronics), to one including other systems of same type and also other populations (the subject of Other systems), to structured worlds with developmental unfoldings and long-term evolutionary processes (the subject of Embeddedness).

a

Notes #130 Trajectories of development, p. 517, and #150 Self-organized criticality, p. 551 b Note #55 Environmental types, p. 404

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170. Adaptation vs. adaptability We know for example that any characteristic be it anatomical, physiological, or behavioral will, if it continues to be adaptive over considerable periods of time, be sunk deeper and deeper in the organizational structure of the system. That is, the constellation of causes which bring about the adaptive characteristic will gradually change in such a way that, when this process reaches its later stages, a gross disruption of the total system may be necessary to prevent the production of the previously adaptive characteristics. Moreover, the dilemma in which the system then finds itself will be formally comparable with what we call the double bind. It will appear to the system (again personifying) as if it can only achieve external adaptation at the price of internal disruption … Conversely, if it does not sink its adaptive mechanisms, these must be continually occupied in solving and resolving the old problems. - Gregory Bateson (1958) This is related to Waddington’s idea of “genetic assimilation” (also called the “Baldwin effect”). Once established temporarily, phenotypic adaptations that are successful for a long time tend to be assimilated into the genetic order. This is not Lamarckian inheritance; rather, behavioral adaptation creates the selective conditions under which random mutations, not more likely because of the successful behavior they facilitate, can introduce a genetic basis for this behavior, making its fitness benefits more reliable and more transmissible. Bateson (1958) has stressed that this is a general phenomenon. What seems to happen is that the longer an adaptive characteristic continues to have positive survival value, the more this characteristic becomes entrenched in the organization of the creature. I am not speaking of a crude inheritance of acquired characteristics, but of an analogy deeper than this between evolutionary process and individual learning... If repeated experience of a certain

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type of context shows that a certain type of response is regularly successful, this response becomes habitual, and there results an economy of mental process whereby the habitual response can be immediately produced without expenditure of effort upon those internal or external trials and errors ... The phenomenon of habit is an economical shortcut to adaptation. It sets free for the solution of other problems those parts of the mind which are most flexible and are, if you like, the organs of adaptive behavior. In the same sort of way there is evidently in the evolutionary process a progressive incorporation of adaptation... As it is more economical to hand over a behavior pattern to habit, so also it appears to be more economical to hand over an acquired anatomical peculiarity to the deep-seated corpus of embryological instructions contained in the chromosomes... Since evolution, the genomic adaptation of populations, occurs over longer time periods than learning, the behavioral adaptation of individuals, the two might be viewed as illustrating the dyad of rigidity and plasticity. Genetic adaptation illustrates rigidification, in von Bertalanffy’s (1968) terms, “progressive mechanization.” a Behavioral adaptation illustrates plasticity. But some fixed specializations (the cockroach, the shark) are robust. Isaiah Berlin, in The Hedgehog and the Fox (1953), discusses the relative merits of being a specialist, the strategy of the hedgehog who knows “one thing,” i.e., to roll up into a ball with spikes, or of being a generalist, represented by the fox, who knows “many things,” i.e., whose alleged craftiness reflects a diverse behavioral repertoire. b Change in the suprasystem requires change in the system’s adaptive strategy. The precise moment when an old strategy must be a b

Note #137 Mechanization (rigidification), p. 530 Note #44 Law of Requisite Variety, p. 384

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abandoned and a new one adopted is 171 The system may remain bound to elusive. an obsolete specialization, once optimal or at least viable, now harmful if not fatal. Or, the system may adapt by relinquishing ties to its organizing principle. It is then not the original system that persists. Viability is gained at the cost of identity.

171. When to change A system can be endangered by its own actions, especially when it has no adequate internal model that indicates when its interaction with its environment must change. a The system may be a population which adapts 172 Its to the suprasystem through evolution. lower-level constituent systems, untethered to fixed identities, undergo open-ended change; their multiplicity allows evolutionary innovations to be explored in parallel. Although the utility of innovations cannot be anticipated, selection allows beneficial innovations to be retained and harmful ones to be discarded.

172. Generalized evolution The biological concept of evolution properly applies to populations and not individuals. Individuals are tethered to genetic identities but populations may vary freely, with no aspect of populational identity necessarily held invariant. Darwin’s idea of evolution might be generalized and applied to entities that are not biological, such as social systems, which are similarly untethered, or to populations of such systems. In such applications, evolution means open-ended adaptation with the associated sacrifice of fixed identity, and the mechanisms of heredity, variation, and selection may be quite different from the a

Agency 1.1.6 and 7.1.6, pp. 13, 402, discusses such adaptive failures.

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mechanisms that operate in biological populations. In societal or technological evolution, it is sometimes possible to partially anticipate the utility (less reliably, the disutility) of innovations. Essay predominantly uses the organismic metaphor, in which systems are viewed as entities with internal structure and organization, as opposed to populations of entities, which are more loosely organized. This is a common convention in the systems literature, in which the “ideal type” is usually the individual, not the population. A notable exception is the work of Boulding (1978) for whom “system” often means population. To speak of an individual system, as opposed to a population, “evolving” gives the term a non-standard meaning. The population adapts in this way to the suprasystem. The rationality in adaptation via selection is extrinsic and at the level of the population. If, however, an evolutionary advance enables a system to estimate the utility of an innovation and adapt before the verdict of selection takes effect, the rationality inherent in this advance becomes intrinsic and at the level of the individual system. But estimates of utility cannot adequately consider all possible future actions and environmental states. In an additional advance, there may emerge within the system a subsystem that models the environment, the systemenvironment interaction, and the system 173 Such a modeling subsystem further itself. internalizes rationality. Long-term adaptation is superseded by short-term learning which empowers agency. But the modeling subsystem has its own deficiencies. New solutions generate new problems.

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173. Evolution of modeling subsystem Essay suggests a diachronic sequence for the evolution of the modeling subsystem, a as shown in Figure 128. Evolution first adds instrument, then goal, and then direction; in terms of types of information, first pragmatic, then semantic, and then syntactic. For the triune model mentioned in that earlier figure and note, first instinct and motor functions (reptilian brain) emerged, then emotional functions (paleo-mammalian brain), and then intellectual functions (neo-mammalian brain). Figure 128 Tetradic evolution GOAL semantic emotion critic 2 INSTRUMENT DIRECTION 3 syntactic intellect model

pragmatic instinct/motor 1 controller GROUND body controlled

This suggestion of a sequence for different types of information does not imply that early forms of life completely lacked semantic or syntactic modeling. Bacteria, for example, exhibit both semantic information (ATP levels are a measure of the “goodness of the situation”) and syntactic information (there are signal molecules whose meaning is not related to their structure); still, one can characterize their modeling subsystems as predominantly pragmatic in overall character. This sequence, namely instrument-goal-direction or pragmaticsemantic-syntactic, is one way b of ordering these components. a b

Figure 89 The modeling tetrad, p. 465 Table 14 Two syntactic-semantic-pragmatic hierarchies, p. 470

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In approximate dynamic programming (ADP), a evolution adds a controller, then a critic, and then a model. The critic internally evaluates the utility of the instrument’s action, so the system is not at the mercy of an environmental judgment of its viability; the model component is then advantageous and is selected for because of the needs of the critic to assess future utilities. For example, one might first get random regulators, e.g., genes, and natural selection then winnows out those regulators that do not achieve the goal of viability (“vicarious rationality”). This is regulation by trial and error; Ashby (1952, 1956) called this “hunt and stick” regulation. If the system gains the capacity to turn selective genes on or off based on internal signals about itself or environment, then the system is less at the mercy of external selection. Abstractly, if successful regulator actions are stored in memory together with the signals that evoked them, this instantiates Ashby’s cause-controlled regulation. b More advanced regulation awaits the development of a modeling subsystem that can select a controlling action based on a model of reality (which, e.g., stores strategies that have been successful in different contexts, and figures out which is applicable or can be adapted to a particular situation). This reflects a full shift from evolutionary adaptation to nervous system-based learning. Note that the ascending diachronic hierarchy implicit in this account, namely first instrument, then goal, and then direction, is different from the ascending synchronic hierarchy of the Parsonian tetrad, c namely first instrument, then direction, and then goal. This illustrates the point made earlier, d that even for systems of only four elements, there are many structural possibilities, each of which can convey a different meaning. e

a

Figure 89 The modeling tetrad, p. 465 Note #44 Law of Requisite Variety, p. 384 c Figure 33 Parsons’ tetrad of social systems, p. 253 d Note #5 Structure, p. 308 e Zwick (2018) b

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7.2.9 Impermanence Notes: 174 175 176 177 178 179 180

page

Things fade Thermodynamics vs. kinetics From being to non-being Failing all at once Dissolution Its effects may endure Decay is inherent in composite things

584 585 585 586 587 588 589

What flaws being is not remedied in becoming. Development, which negates incompleteness, is itself negated, as the limitations of the organizing principle reveal their consequences. The difficulties necessarily joined to any degree of successful development can be met only if these limitations are accepted. This may require deep change in the organizing principle, perhaps even its abandonment. Ultimately, all systems are composites and thus decomposable. Decomposability may be controlled and limited, and may be specified by the organizing principle, but decomposition may be uncontrolled and extensive, resulting finally in dissolution of internal order and the 174 system-environment boundary. Things fade, although the onset and rate of decay is not 175 prescribed.

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174. Things fade This refers to the first of Whitehead’s explanations of the causes of suffering: “Things fade and alternatives exclude.” a In terms of the earlier taxonomy of difficulties faced by systems b, “things fade” refers to internal and general difficulties, “alternatives exclude” to specific difficulties, either internal or external. Many mathematical and scientific interpretations of “things fade” might be invoked. The most obvious is thermodynamic. Things suffer the ultimate victory of entropy and reach an equilibrium that destroys the system-environment distinction. Or one might speak of the reversal of the disorder-to-order phase transformation invoked earlier to model system formation; or cast events in terms of the fold catastrophe, where change of the control parameter destroys the equilibrium state that was once possible; c or other catastrophe types (Thom 1975). That the fading of things is typically not instantaneous but takes time, is captured in this poem by Emily Dickinson (1998): Crumbling is not an instant’s Act A fundamental pause Dilapidation's processes Are organized Decays 'Tis first a Cobweb on the Soul A Cuticle of Dust A Borer in the Axis An Elemental Rust – Ruin is formal – Devil's work Consecutive and slow – Fail in an instant, no man did Slipping – is Crash's law. a

Note #132 Augustinian vs. Manichean devils, p. 522 See Limitation 1.2.3 and 7.2.3, pp. 26, 514; also Table 17 Limitation: internal/external, general/specific, p. 525 c Note #120 System formation, p. 496 b

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175. Thermodynamics vs. kinetics Thermodynamics is distinguished from kinetics. Thermodynamic laws speak about ultimate outcomes of processes but do not specify the rates of these processes, i.e., do not say when these outcomes will actually occur, or the path dependence these processes will exhibit. The systemenvironment distinction is only provisional, a and in the long run – for isolated concrete systems –disintegration is their lawful and unavoidable thermodynamic fate. Disintegration may be the sudden failure of a seemingly successful process of segregation or systematization that outstrips the capacity of the organizing principle to integrate. Decay may be protracted and for a long time indistinguishable from differentiation. Complexification may hide or neutralize the primal incompleteness or inconsistency, but it cannot produce an order that is forever sustainable. Confrontation with limitation 176 may be postponed but not indefinitely. 177 Order eventually succumbs to disorder.

176. From being to non-being As shown in Figure 129, system dissolution (a), the final shift from being to non-being (b), can be sudden, as in the fold catastrophe, which also models systems formation, b the transition from non-being to being (non-persistence to persistence). But dissolution might alternatively be extended in time, i.e., temporally fuzzy c and not crisp.

a

See Note #30 One, two, three, ten thousand, p. 359. Figure 99 Systems formation and the fold, p. 500 c Note #25 Fuzziness, p. 352 b

NOTES

586

Figure 129 System dissolution and the fold being

system dissolution time

(a)

non-being time

(b)

177. Failing all at once Dawkins (1995), writing on “God’s utility function,” makes the argument that most systems will fail “all at once,” because they are likely to be evolutionarily designed to do so, since failure comes from the weakest link, and there is thus no advantage in having stronger links. Spontaneous weakening of unnecessarily stronger links that distribute some of the energy for this unnecessary strength to the rest of the system will be advantageous. But in highly differentiated systems, such redistribution may not be so easily accomplished. Disintegration is the final victory of multiplicity over unity. Multiplicity does not differ intrinsically from disorder, and no system can be organized exclusively on the principle of multiplicity. A loss of necessary rigidity may set the stage for disintegration by destabilizing a complex or fragile order. Existence implies constraint, both internal and external. Modification of constraint is sometimes possible but never its complete absence. Existence implies distinction between system and environment. Modification of the distinction is sometimes possible but never its complete eradication. No means exist to assure the indefinite persistence of constraint and distinction. Loss of constraint and abolition of distinction is dissolution.

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The system may follow the archetypal route of organisms. Having achieved some measure of development, it suffers its preordained fate. It ages, and with the inevitable and irreversible weakening of its capacity to maintain order 178 It leaves and distinction, it passes away. behind its effects on its environment, which 179 may be considerable and may persist. The system is not, by reason of impermanence, unsuccessful, for how can permanence be a criterion of success? Decay is inherent in all 180 composite things.

178. Dissolution Whence things have their origin, Thence also their destruction happens, According to necessity; For they give to each other justice and recompense For their injustice In conformity with the ordinance of Time. - Anaximander a The proximal causes of the dissolution of the system may be excessive disorder or the extreme weakening or distortion of the organizing principle of the system; or excessive rigidification; or inability to maintain integrity of boundary and to regulate transactions with the environment; or dissolution due to action of other systems or an embedding suprasystem; or demise programmed as an adaptation in the population of such systems. To appropriate the language of Derrida (1982), it is not only the “différance” – the system-environment difference – which is deferred, i.e., never permanently established; the dissolution of this différance is also deferred. But eventually the moment of dissolution arrives. To recast the words of Anaximander in a poststructuralist and systems theoretic idiom, the unmarked a

Wheelwright (1966)

588

NOTES

(favored) state was “unjustly” seized by the system in its formation. This state really belongs to the ground, i.e., the environment, a which ultimately reclaims it “according to the ordinance of time.” System formation is “original sin,” which is the sin of having originated, b of disequilibrium, of arising from and disturbing the primal undifferentiated monad, the “apeiron.” The system does not pay for its disruption right away. Dissolution of order and the erasing of difference are deferred. But payment is finally exacted. The system is eventually overwhelmed by its environment. The fundamental disparity of power between system and environment is captured in Spinoza’s (1677) observation that “The force whereby a man persists in existing is limited, and infinitely surpassed by the power of external causes.” Spinoza means this to apply not only to human beings but to all modes of substance, i.e., to all systems.

179. Its effects may endure In the open systems view of system dissolution, the negation of structure is not necessarily accompanied by the immediate negation of function. The effects of the system on its environment are open-ended in both space and time. The magnitude of these effects attenuates or is amplified and their scope expands or contracts; their long-term impact is ultimately uncertain. In the closed systems view, dissolution is a simple terminus. This difference of conceptions is shown in Figure 130 which are mirror-reflections (reversals of the time axis) of the double cone, single cone, and single line representations of the system formation event. c Systems differ with respect to whether their dissolution is more a closed or an open event; or, from another perspective, some aspects of dissolution are closed in character, while others remain open to the future. a

Note #30 One, two, three, ten thousand, p. 359 For the opposite view, that systems formation is the gift of origin, see Appendix A.2.3 Euphorics, an antidote, p. 608 c Figure 98 System formation; system as temporal center, p. 498; Figure 100 System formation: difference in similarity, p. 501 b

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Figure 130 Two views of system dissolution (a) open systems view; (b) closed systems view; (c) alternative open systems view.

past (a)

similarity (c)

system future dissolution time

past (b)

system dissolution time

system dissolution system after-effects difference time

180. Decay is inherent in composite things The Second Law of Thermodynamics, as formulated by The Buddha, who added the following injunction as a corollary to his followers: Work out your salvation with diligence.

591

APPENDICES A. Auto-critique A.1 Structure A.1.1 Abstraction A.1.2 Inexactness A.1.3 Metaphor A.1.4 Rhetoric A.1.5 Scope A.2 Function A.2.1 Problematics A.2.2 Diagnostics, Therapeutics A.2.3 Euphorics, an antidote B. Lists of figures, tables B.1 All figures, tables B.2 Dyadic figures, tables B.3 Triadic figures, tables B.4 Tetradic figures B.5 Pentadic figures, table B.6 Hexadic figure

591 592 592 595 596 598 599 604 604 606 608 611 611 615 616 617 617 617

A. Auto-critique An attractive feature of an ontology of problems is that its concepts can articulate its own deficiencies. Self-criticism is not optional; it is part of any attempt to embrace the whole. Every doctrine needs to own up to its imperfections, include a warning insert about its possible “side effects,” try to recognize, assume responsibility for, and remedy its omissions and distortions. This is a specific application of a more general principle: It is an obligation of every system to try to put its own house in order. If it is the case that systems – not only concrete and abstracted systems but also conceptual systems – are unavoidably flawed, the central essay of this book must be so afflicted, as indeed it is. That which declares the imperfection of everything is of course also an irresistible target of attack. What follows is a critique of Essay, expressed in its own terms.

© Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7

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Although this critique doesn’t prove Essay’s assertions, it does provide some confirmatory satisfactions. The critique doesn’t exhaust the deficiencies of Essay; it just mentions some prominent ones. Some are remedied elsewhere in this book; some reflect flaws in the systems project itself. The deficiencies of Essay are both structural and functional. Its structural deficiencies include extreme abstraction and inexactness. Its use of rhetoric and metaphor is a kind of incompleteness; its excessive scope virtually assures inconsistency. Its functional deficiencies include its silence on how problems can be diagnosed and solved and its unrelenting focus on problems as opposed to opportunities. There are also deficiencies best understood diachronically, namely those arising from the multiple organizing principles that have guided this project over the course of its development. A.1 Structure A.1.1 Abstraction To generalize is to be an idiot. - William Blake (1798) Every generalization is false. - Peter Gay I am a specialist in generalizations. - Daniel Bell (2019) The abstraction of Essay is characteristic of systems theory. Situated between mathematics and philosophy and the theories of the sciences, systems theory seeks unity of the sciences through generality and abstraction. 1 Essay, which is an (i) exposition of systems ideas and a (ii) narrative about problems, is devoid of detail and is thus obscure. Notes, which unpacks the assertions of Essay, is an expansive treatment of (i) but does not remedy the deficiency of (ii), which is also only 1

Generalization and abstraction are not equivalent, but the generalization spoken of here is gained by abstraction.

Auto-Critique

593

partially remedied in 5.5 Metaphysician’s desk manual and Chapter 6 Science, religion, politics. The systems program’s concern with theory as opposed to fact reflects an incompleteness which is here acknowledged. Theory alone is insufficient for truth; it must mate with fact. But theory can be broadened in scope and deepened in subtlety, so that its union with fact, when it occurs, can be more fruitful. The pole of pure theory is complement to the pole of pure fact. Just as in both fiction and non-fiction there is a style of narrative that clings to the concrete, so too there is a style of theory, exemplified by Essay, that clings to the abstract. Each pole is an attractor. At these poles, generalizations from facts or exemplifications of theory are omitted because they weaken the unity of form. Although the extremes are attractors, neither extreme is fully satisfactory. Neither extreme can renounce the temptation of surreptitiously trying to encompass the other. Concrete narratives are often crafted with the expectation that appropriate generalizations will spontaneously occur to the reader without being articulated by the author. Similarly, abstract treatises are often crafted with the hope that appropriate examples will spontaneously occur to the reader without being explicitly advocated by the author. Such hope is implicit in Essay, although the examples in 5.5 Metaphysician’s desk manual and the short application of systems ideas in Chapter 6 Science, religion, politics are signs of this author’s insufficient confidence that applications of Essay’s abstractions will occur to the reader. These Commentary sections are attempts to prime the pump of imagining exemplifications of Essay’s abstractions. Facts are theory-laden; theories are fact-laden. This is a good thing, since fact without theory is incomprehensible, and theory without fact is undisciplined. Fact is incomplete without generalization, and theory is incomplete without exemplification. If these extensions are not provided, they will invariably be implicit. But the reliability of what is only

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implicit and not argued explicitly is limited. Devotion to fact leaves no interpretation untroubled, and respect for theory acknowledges difficulties of application. Essay is theory without exemplification, but its inherent incompleteness has compensating virtues. Abstract theory is non-aggressive. It does not compel application; it does not even insist on its best examples. This is more than stratagem; it reflects conservatism about the capacities of reason and thus disinclination to press home specific conclusions. 2 General theory makes ideas available to understanding. Use of these ideas is voluntary; they may or may not apply. Although the ideas themselves may appear grandiose, the optional nature of their use is a kind of modesty. In the uncertainty of applicability, there is also security. As Bunge (1973) notes, systems theories are only “vicariously testable.” Abstract theory has little to fear from fact, to which it can always disclaim connection, 3 just as concrete fact has little to fear from theory, being self-sufficient in its own domain. But it must be said that both strategies, in claiming immunity by embracing their incompleteness, are less than courageous. They evade the honest vulnerability of plain argument which is always a union of theory and fact. If a systems theory fits some empirical phenomenon, it may reveal the abstract essence of the phenomenon. If it does not fit, the theory remains ready for later use. In the meanwhile it can be appreciated for itself. Metaphysics, Edmund Wilson (1940) said, is the poetry of people who think in abstractions instead of images. 4 But it is poetry only at its best; at its worst, it is pompous or irrelevant. The risk of pomposity in the 2

To say again: the examples offered in 5.5 Metaphysician’s desk manual, p. 174, are intended only to illustrate how the ideas of Essay might be applied; they are not positions being intentionally and strongly advocated. 3 As Ashby (1956) notes of his Law of Requisite Variety, “... this law has nothing to fear [from any empirical findings].” The law itself, being mathematical, is just either correctly or incorrectly applied. 4 Heidegger wanted philosophy to read like poetry; Wittgenstein wanted his writings to be memorized.

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discourse of pure theory parallels the risk of triviality in the discourse of pure fact. Pomposity can be avoided by mathematical language at the price of obscurity and potential irrelevance. So an exact and scientific metaphysics must also be expressible in natural language. Ordinary metaphysics, however, grounded neither in mathematics nor in science, runs the risk of being both pompous and obscure, and when it is imperial in its ambitions, it is a fundamentalism. Finally, it must be acknowledged that a narrative of pure theory or pure fact is always inspired by an agenda governed by value. Essay reflects an agenda; really, multiple agendas. A.1.2 Inexactness A man with one theory is lost. - Bertolt Brecht (1920) Consistency is the last refuge of the unimaginative. - Oscar Wilde (1885) Essay offers an account of the difficulties afflicting many systems. For breadth of coverage, this account is verbal, not mathematical, so exactness is not attained. Nevertheless many of the ideas of Essay have mathematical sources in graph theory, set theory, information theory, dynamic systems theory, decision and game theory, and other systems theories. Formal integration of all these theories would be a formidable task, so Essay’s metaphysics is exact only piecewise. Where Notes unpack Essay’s mathematical references, the explanations are mostly short; to do more would require extensive treatises on multiple mathematical theories. Essay is not restricted, however, to mathematical ideas. There are in it ideas from the natural and social sciences, some of which are strictly verbal, and philosophical concepts. In Essay’s narrative, ideas that have mathematical interpretations are not distinguished from those that do not. Also, the mathematical interpretations of Essay offered in Notes are not necessarily the only way that the assertions of Essay could be made exact.

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Essay overreaches the domain over which formal consistency can be attained. But conceptual coherence is provided structurally by a framework of general categories and functionally by the theme of an ontology of problems. 5 Integrality is also furthered by the organizing idea of “system,” by relationships among relevant mathematical theories, and by the continuity and plausibility of the story being told. The abstraction of Essay helps unify the narrative, but it is not the case that there is oneness in heavenly theory and “ten thousand things” in earthly fact. To our dismay or delight, the Platonic realm is populated by many ideas which coexist with as much mutual disharmony as afflicts multiplicity in the material realm. Although abstraction is normally associated with monism, Essay reveals its intrinsic pluralism, more visible when unpacked in Notes. Phenomena viewed abstractly are not necessarily unified since they require explanation by multiple abstract theories. A.1.3 Metaphor Metaphor is not an indulgence. It is a way of reaching essence. - Edward Rothstein (1995) A metaphor is always a failure. – Northrop Frye (1957) Exactness is an ideal, standard for any mature scientific metaphysics, but Essay makes use of the full continuum (Zwick 1978a) from limited metaphor to rich analogy to isomorphism (exact analogy) to formal theory. Although the important ideas in Essay are mathematical, metaphor and analogy are also included. A focus on the organism played an important role in the development of systems theory, which in part crystallized around attempts to explain biological phenomena, such as selfreplication and purposeful action, which were difficult to accommodate within Newtonian mechanics; biological notions were then often extended to systems in general. Beyond the organismic metaphor, Essay sometimes yields also to 5

5.3 Categories of complexity, p. 160, and 5.4 Ontology of problems, p. 167

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anthropomorphism, sociomorphism, or mechanomorphism. It is difficult to generalize without utilizing a morphism of one sort or another. Ideally, analogies should be restricted to being candidates for mathematical treatment, but they are too rich to be disallowed in a metaphysical essay. Moreover, one might argue that mathematics itself is not free of metaphor and analogy; they are just deeply hidden. In metaphor and analogy, there are hazards – intellectual, aesthetic, and moral; intellectual, because analogies are not only incomplete but imprecise; aesthetic, because metaphors are often mixed; and moral, because pernicious ideologies always deploy simplistic analogies and hateful metaphors. 6 These hazards are at least partially mitigated by the detail offered in Notes. But even extensively developed theories, if they are sufficiently general, cannot escape being reduced to simplistic notions. Levins and Lewontin (1985) write: Every theory of the world that is at all powerful and covers a large domain of phenomena carries immanent within itself its own caricature. If it is to give a satisfactory explanation of a wide range of events in the world in a wide variety of circumstances, a theory necessarily must contain some logically very powerful element that is flexible enough to be applicable in some many situations. Yet the very logical power of such a system is also its greatest weakness, for a theory that can explain everything explains nothing. It ceases to be a theory of the contingent world and becomes instead a 6

The moral hazard implicit in the use of analogies is illustrated by the obvious dangers of applying the concept of an “invasive species” outside the realm of ecology. Social Darwinism is a classic example of the dangers of undisciplined analogizing. Such hazards are partially mitigated if analogies are required to meet ESM standards of formal precision and empirical validity. Formal precision converts analogies into isomorphisms which by rigorously defining what is similar in two systems sharply indicate also what is different, namely everything else. At least indirect empirical validation is also required of any argument by analogy.

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vacuous metaphysic that generates not only all possible worlds but all conceivable ones. The narrow line that separates a genuinely fruitful and powerful theory from its sterile caricature is crossed over and over again by vulgarizers who seize upon the powerful explanatory element and, by using it indiscriminately, destroy its usefulness. These authors are speaking of Marxism, Freudianism, and Darwinism. 7 A similar vulnerability to caricature afflicted systems theory in its classical phase (general systems theory, cybernetics) and continues to afflict its contemporary phase (complexity, complex adaptive systems). A.1.4 Rhetoric Today only exaggeration can be the medium of truth. - Theodor Adorno But if one were not allowed to exaggerate, why should one write at all? - Gustave Flaubert (1853) Abstraction, unfettered by the discipline of exactitude, yields not only to the temptation of analogy but also to the lure of rhetoric. Essay is rife with hyperbole. It speaks of all systems being subject to particular laws, of systems necessarily encountering difficulties or tensions between opposites, etc. This is rhetoric. If metaphysics is intellectual poetry, as Wilson (1940) suggests, then rhetoric might be justified as poetic license. In Essay arguments are simplified for clarity and force, and care is not always taken to distinguish between what is 7

The Levins-Lewontin quote displays the fear of metaphysical taint, anathema to Marxists, Freudians, and Darwinists alike. It is also a clear statement of the dialectical – and metaphysical – principle that the greatest strength of any system is also its greatest weakness. Metaphysics is a tarbaby; the more one tries to get away from it, the more one sticks to it. No philosophical task is more compelling in this “post-metaphysical” era than the recovery of metaphysics, but it needs to be both exact and scientific.

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necessary, what is typical, and what only sometimes occurs. There is more than one way that things can go, but Essay exaggerates for effect. This should not be surprising, given the principle that in every polarity, it is always the extremes that are compelling and easily communicable. Extremes are the attractors of thought, 8 and especially of expressions of thought. In the dyad of logic and rhetoric, logic is the unmarked 9 (favored) term for philosophical discourse. Essay succumbs to some extent to rhetoric. A few entries in Notes even indulge in the language of the mystical. Why not? The rational and the mystical can be – and should be – friends. But finally, the systems project must reject the plasticity of rhetoric in favor of the rigor of logic. Between Habermas and Heidegger, between “communicative reason” and obscure and ethics-ignoring ontology, the choice (to favor Habermas) is plain. The rhetoric of Essay may give the impression that it is a deductive system of assertions. It is not. It is rather a metaphysical narrative that progresses through a sequence of propositions, like the postures of a philosophical t'ai chi. The propositions are archetypal truths that may or may not apply to any specific phenomenon. From them, a subset might be drawn and applied to some phenomenon at hand, just as the postures of t’ai chi can be applied to various martial-arts situations. A.1.5 Scope Essay is flawed not only in its unremitting abstraction and in its failure to satisfy the demand of exactness but in its insistence on addressing concrete, abstracted, and conceptual systems. In mixing ideas from the natural sciences (primarily the realm of concrete systems), the social sciences (primarily the realm of abstracted systems), and the purely conceptual realm of mathematics, Essay merges domains which for the sake of consistency and clarity ought to be kept separate. 8 9

Note #118 The extremes are attractors, p. 494 Note #8 Incompleteness vs. inconsistency, p. 320

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This is in fact a difficulty intrinsic to the epistemological niche which systems theory seeks to fill. Located midway in abstraction between mathematics and philosophy and the theories of the various sciences, systems theory finds itself, insofar as it is exact, within the realm of mathematics where ideas need not refer to the world of fact, and insofar as it is scientific, within the realm of descriptions of actually existing systems. Bridging two worlds, one suffers the strain of existing in both. But the separateness of these worlds should not be overstated. To make a sharp distinction between the two and restrict discussion to one or the other is to ignore possible connections between these worlds. “Distinction is perfect continence” (Spencer-Brown 1972), yes, but perfect continence is sterile. Moreover, there is no intrinsic difference between mathematical ideas that correspond to the world we inhabit and mathematical ideas that for now only satisfy the truth criterion of coherence. 10 Ideas that apply to a merely possible world might at any moment gain application to our actual world. For example, Gödel’s undecidability result which proved the incompleteness of sufficiently rich formal systems appears to apply only to certain conceptual systems. The statement that Gödel proved to be undecidable does not seem to have relevance to real-world phenomena, despite attempts to apply it to consciousness and free will. Still, it is not only the statement constructed by Gödel, which at a meta-level asserts its nontheoremhood, that is undecidable, but all assertions whose truth depends upon this statement or have a form similar to it. The influence of Gödel’s proof extends to other domains of mathematics, Diophantine equations for example. But beyond the domain of formal systems, the Halting Problem of automata theory has a close relation to Gödel’s result, and automata are widely used to model real-world phenomena. In recent years, mathematical undecidability has been found to be relevant to the 10

This echoes the thesis in Essay that systems which possess the capacity to represent internally aspects of themselves and their environment have no foolproof means to distinguish between reality and illusion.

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dynamics of systems of nonlinear differential equations, 11 which are extensively used to model the world. Applications in game theory have also appeared. So the case for relevance of Gödel’s proof to concrete and abstracted systems becomes stronger. Similarly, Shannon entropy, a measure of uncertainty, has no necessary a priori connection with the entropy of physics, which applies to the matter-energy aspects of concrete systems. Still, the connection between these two concepts is not superficial but is rather a deep isomorphism that has spawned a substantial literature on the foundations of physical concepts. Nevertheless, obscuring the distinctions between concrete, abstracted, and conceptual systems poses dangers. For example, the terms “incompleteness” and “inconsistency” used in Essay are normally used for formal systems, and applying them to worldly phenomena requires alteration of their meanings. This alteration is explained in Notes, 12 but some of the discussion there bears repeating. In a formal system inconsistency is unacceptable, since it allows one to prove any proposition whatever. What is meant by this term in this book, where it is applied to both concrete and abstracted systems, is not formal inconsistency but rather (i) contradiction arising from aggregation, i.e., ignoring locations, times, or instances where the contradictory facts exist, or (ii) contradiction in a dialectical sense, i.e., coexistence of opposing needs, forces, or tendencies. Perhaps a different word should be used, but there does not appear to be a better word that suggests the complementarity of the generalized incompleteness and generalized inconsistency that is asserted in this book. Still, the use of “inconsistency” and “contradiction” in multiple and unconventional ways might be seen as sacrificing exactness for the sake of a richer metaphysical narrative. This criticism is a fair one.

11

N. Baas, personal communication Notes #4 Incompleteness, p. 306, #6 Inconsistency, p. 311, #8 Incompleteness vs. inconsistency, p. 320. 12

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While excessive scope generates inconsistency, inadequate scope reflects incompleteness. This book is incomplete in part because a systems theoretic ESM is mainly about “everything” as viewed from a world-centered (ontological) stance 13; “everything” viewed from a human-centered (epistemological) stance is not adequately explored. For example, only minimal exposition is offered of the experiential relevance of systems ideas. 14 Since the systems project is first and foremost science, which inherently assumes the world-centered stance, this limitation should perhaps be taken for granted. But the incompleteness of this book goes well beyond limitations of the world-centered stance. Incompleteness is simply inevitable for any undertaking that seeks transdisciplinary connections between mathematics, science, and philosophy. It is worth identifying at least a few salient omissions in Essay, Commentary, and Notes. First, Synchronics stops at the level of complex organisms. Aside from not doing justice to the subject of cognition, it does not extend to the Boulding (1956) level 15 of social organizations or ecosystems, or the biosphere. This does not mean that this book is silent about these domains but rather that the systems ideas and methods applied to them are not specific to these levels, but apply as well to – since they were developed for – lower-level systems. 16 For example, networks are widely applied to social systems but the analysis of networks is at or near the most general type of analysis that can be applied to any system whatever. Luhmann, a major theorist of social systems, makes extensive use of the idea of autopoiesis. This idea is applicable to the simplest of organisms and is not specific to the level of social systems. Ideas about feedback in dynamic systems offer insights into how socioecological systems undermine the carrying capacities of their 13

Table 1 Ontological vs. epistemological stances, p. 57 But see 6.2.5 Personal knowledge, p. 221. 15 5.2 Hierarchy of system types, p. 154 16 See the discussion of this point in 5.3 Categories of complexity, p. 160, especially comments on ideas of Kurzweil and Wolfram. 14

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environments, but this type of analysis is extremely general. There are, or at least there ought to be, systems ideas and methods that uniquely apply to social organizations, ecosystems, and other high-level systems, and it would have been desirable for Essay and Notes to include such level-specific approaches. Second, while mathematical and scientific ideas of Essay are unpacked in Notes, only a few ideas are concretized – and in a limited way – with real-world examples. Some examples are given in Commentary in 5.5 Metaphysician’s desk manual and Chapter 6 Science, religion, politics. This book is incomplete in the limited examples it offers of applications of systems ideas. Third, the mathematical ideas in Essay and Notes mostly privilege discreteness. An exact and scientific metaphysics should include adequate treatment of continuum concepts. Fourth, the whole that is the systems/complexity field is itself too big to embrace, not even to speak of the enormously larger fields of mathematics, science, and philosophy that systems thought ambitiously seeks to connect with. The systems project in general and this book in particular cannot autopoietically generate a boundary 17 for itself, and the untapped but relevant literature is quasi-infinite. The author is limited by the range of his interests and knowledge, and by the merciless finitude of time. This book gives greater emphasis to older work that carried the systems or cybernetics label than newer work done under the banner of “complexity,” but even the older literature on general systems theory and cybernetics is too big to do justice to. To give just one example, Second Order Cybernetics 18 is not discussed in this book.

17

Note #47 Autopoiesis, p. 393 Second-order Cybernetics seeks to encompass observation of a system along with the system being observed. This is appropriate and indeed necessary for modeling social systems, where self-reference is an objective phenomenon with causal significance. In the author’s view, however, this is inappropriate for modeling systems in general, where it in effect tries to 18

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Fifth, although Commentary insists 19 that many systems cannot be understood without considering their historical dimension, it offers only the most abbreviated remarks on the historical development of the systems field itself. There are undoubtedly many other omissions in this book. Awareness of incompleteness is necessarily incomplete. Even if it were complete, it would be of no avail. “Books are never completed; they are only abandoned.” (The original quote by E. M. Forster is about art, here replaced with the word “books.”) A.2 Function A.2.1 Problematics This is the way we are made, the perception of the malum is infinitely easier for us than the perception of the bonum; it is more direct, more compelling, less given to differences of opinion or taste…An evil forces its perception on us by its mere presence, whereas the beneficial can be present unobtrusively and remain unperceived, unless we reflect on it. - Hans Jonas (1984). The horrorific vision is not a Gnostic whimsy, or as Nietzsche would have it a sign of a spiritual weakness of those who cannot endure the exigencies of life; it is not even an accusation directed against the Creator but a necessary vehicle of semantic orientation. - Agata Bielik-Robson (2007) That good is fragile is no grounds for despair; evil is fragile as well. - Judith Shklar (1985)

fuse the world-centered and human-centered views, which are best kept apart. Also barely discussed in this book is semiotics. 19 3.5.2 Adding history, p. 116

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Essay achieves a degree of integrality by being organized around the problems faced by many kinds of systems. It proclaims the lawfulness and interconnectedness of these difficulties, and the impossibility of completely evading them. It thus links the philosophical and scientific enterprise of systems theory to the practical concerns of systems analysis. But the result of this exclusive focus on problems is a narrative that is pessimistic and somber in tone. The precariousness of some systems actually inspires hope, and the destruction of these systems is welcomed and not feared. Also, Essay discourses about the perils of being and becoming but not about its pleasures. hough it does not preclude the harmonization of contradictions, it says little about such reconciliations. It mentions but does not explore the possibility that the part, in grasping its partness, might achieve a glimpse of a larger whole. Some problems have solutions; Essay does not speak of them, except to note that solutions generate new problems. But why frame the discourse this way – as problem-solutionproblem. Why not let the affirmative, the positive, the optimistic (!) frame the narrative? Every problem is an opportunity; why focus on one and not the other when the two are in fact inseparable; why not a metaphysics of opportunities? The quote above from Jonas gives one possible answer. The orientation of Essay has some affinity with Stoicism, with its acceptance of the limitations intrinsic to the natural order, Gnosticism, with its defiant complaint that creation is flawed, and Buddhism, with its idea of “dukkha” (unsatisfactoriness). From the perspective of an ontology of problems, there is indeed a rent in the fabric of existence, and it is cosmological in the systems sense. The appropriate response to it is the human effort of fixing (tikkun), correcting, harmonizing; or, in the language of a meta-physician, healing.

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A.2.2 Diagnostics, Therapeutics But even if one accepts a focus on problems as legitimate and useful, Essay only surveys difficulties that might afflict systems but does not provide resources for deciding, for any particular system, which difficulties are actually present and of those present which are most important. Systems suffer tensions, flaws, etc., but how are the salient issues to be identified in concrete cases? A metaphysician’s desk manual needs a section on diagnostics that tells the practitioner what the symptoms are of these diseases, so one might be able to detect which difficulties best account for the problems manifested in any particular system. Although problems may arise from single imperfections, they are usually multiply determined. They may reflect an improper balance of openness and closedness, impossibility of predicting the future, tension between individual and collective rationality, parasitism of informational levels, etc. It may not be apparent which if any metaphysical flaw is more important than the others, and it may be difficult to integrate multiple flaws. Although Essay (specifically Synchronics) facilitates the diagnosis of problems by proceeding (roughly) from more general to less general causes of dysfunction, it is not evident how generality or specificity bears on the effectiveness of the conceptualization of a problem. Nor is it clear how diagnosis might include an estimate of the severity and corrigibility of any particular dysfunction. Moreover, problematics must be supplemented not only with diagnostics but also with therapeutics, the instrumentalities of tikkun. 20 Given a fundamental analysis of problems and the capacity to identify difficulties in particular situations, there is always the query, “what is to be done?” How are fundamental problems to be dealt with, ineluctable contradictions harmonized, opportunities latent in problems detected and seized; these issues are not taken up in Essay. Joining the 20

5.4 Ontology of problems, p. 167

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metaphysics of systems theory to the pragmatics of systems analysis 21 dictates that solutions, however uncertain, impermanent, and partial, must nonetheless be sought. About therapeutics, Essay has nothing explicit to say. Therapeutics is always concrete, specific, and short-term; there are no general and permanent solutions to “metaphysical evil.” 22 Problems are universal, but solutions, at least to deep problems, are unique. In part this is due to the multiplicity of abstract principles that converge in any particular phenomenon; in part this is due to every phenomenon being saturated with a multiplicity of brute facts. (These are two different kinds of complexity). Still, solutions, however conditioned by the particular, also reflect the universal. And for problems whose scope is limited, solutions do exist. There are solutions to linear problems; there are ways to design stable feedback controllers, even ways to use chaos for the purposes of control; there are good (satisficing) though not perfect methods of global optimization for some specific problems; 23 there are remedies to dilemmas of collective rationality; there are modes of adaptation that accommodate the unpredictability of future events; there are ways to enhance hierarchical integration; there are strategies that reconcile the needs of closedness and openness; and so on. One might imagine tying together these limited solutions in a narrative that would be an inverse of the problematics orientation of Essay. It would be desirable to set out the therapeutic solutions already available and to explore new ones, but this is beyond the scope of this book. Doing so might even be counterproductive. It might obscure the need for therapeutics to be rooted in the 21

4.5 Systems theory and systems analysis, p. 141 6.3.1 Secular Theodicy, p. 226 23 The “no free lunch theorem” (Wolpert and Macready 1997) illustrates the claim made here that problems are general but solutions are specific. It says that there is no algorithm that performs best on all optimization problems but one can have better or worse algorithms for specific types of problems. This theorem might apply also to non optimization problems. 22

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concrete, by fostering the illusion that general problems can be universally and permanently solved by equally general solutions. 24 It might reinforce the superficial assumption that problems are anomalies that by will or foresight can be prevented or eliminated. This is an assumption not conducive to an intelligent search for remedies. A rush to therapeutics will often involve avoidance of problematics, a reluctance to probe deeply into the underlying causes of problems, understanding of which is necessary for effective solutions, however partial and temporary. This said, a meta-physician’s desk manual 25 should certainly have information about both diagnostics and therapeutics and also special section on emergencies and triage. Unfortunately, with therapeutics there comes iatrogenics. Solutions, even when they are effective and don’t aggravate the problems they are intended to solve, create new problems. It is impossible to do only one thing, 26 and only a small portion of the consequences of any action can be foreseen. But this is no justification for stopping at problematics, for intellectualizing disease without seeking its cure. Understanding is for doing, not merely for knowing. A.2.3 Euphorics, an antidote There is a crack in everything; that is to let the light in. - Leonard Cohen (1992) For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose. - Ralph Waldo Emerson (2005) Finally, beyond therapeutics, there is – let it be called – euphorics. In contrast to disease there is health, even flourishing (Aristotle’s “eudaimonia”), whose significance is undiminished, 24

A tight coupling of some problems and their solutions characterizes Operations Research. 25 5.5 Metaphysician’s desk manual, p. 174 26 Note #59 Multiplication of effects, p. 411

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perhaps even enhanced, by lack of permanence. In contrast to malfunction and stress there is efficacy and felicity. Indeed, “problematics” and “euphorics” are two sides of the same coin. Incompleteness, negation, and hazard are problems from one perspective. But from another perspective, it is because of incompleteness that there is the possibility of relation. One might even say that because of incompleteness – more generally, finitude – there is the possibility of love, an emergent in the realm of life that depends on both uniqueness and universality, openness and closedness, however much these polar opposites war upon one another. Because of inconsistency there is the possibility of change, i.e., becoming. Polarity as a source of tension is simultaneously polarity as a source of dynamics. Only the opposition of order and disorder allows an escape from the tyranny and absurdity of extreme order or extreme variety. Hierarchy is a ladder between different orders of existence, and on such ladders, not only devils but also angels ascend and descend. Distillation of information refines materiality and stretches the ladder ever upward. All problems flow from limitation, yet the limited also inherently implies the unlimited: Finitude is the absence of infinity, but absence is a mode of presence. In fact, the infinite itself is also flawed – by the absence in it of finitude, and all that is only possible in finitude. System formation is not a disruption in the apeiron, 27 but its beneficent creation; not original sin but original blessing. Gratitude for existence is the natural response of being. The dissolution of some systems is cause for celebration. Only in the disappearance of the old is there space for the new. Problems present opportunities and fundamental problems present fundamental opportunities. Vulnerability – even transience – is a key to creativity and meaning. Life and mind need to be poised between frozen order and random chaos.

27

Note #178 Dissolution, p. 587

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All of the ideas of the central essay of the book might have been cast in light of euphorics, but this too would have been only a partial truth. A balancing of problematics and euphorics might have been attempted – remaining poised between the two has some of the virtues claimed for “the edge of chaos” – but where is that intermediate point and how is one to remain poised there and avoid a banal compromise between opposite perceptions of reality? Essay might have been constructed to move from problematics to euphorics, as this section has done; to begin with negation, enter a realm of contradiction where both negation and affirmation coexist, 28 and move to some ultimate victory of affirmation. But, as Essay itself declares, 29 affirmation cannot be accomplished as an unfolding of negation; it needs its own independent source. Negation hints at affirmation, as absence hints at presence, but hints are insufficient. Affirmation, to be effective, requires development. To embrace both problematics and euphorics is difficult; one pole needs to be privileged. Essay’s choice has a logic to it: to privilege what arouses thought, 30 namely the existence of problems, since in bliss the mind rests. This choice is also dictated by Levinas’ (1989) injunction, which here is accepted, that ethics should precede ontology.

28

The bifurcation set in catastrophe-theoretic models; see Note #131 Cusp catastrophe, p. 520 29 What succeeds as negation never succeeds as affirmation (1.2.5.4.2). 30 See the Jonas quote that opens A.2.1 Problematics, p. 604

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B. Lists of figures, tables B.1 All figures, tables TO THE READER Figure 1 Structure and function of the systems project

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COMMENTARY Figure 2 Structure of Commentary 40 Figure 3 System as center 49 Figure 4 An exact and scientific metaphysics 55 Figure 5 Coherence and correspondence 61 Figure 6 Between math/philosophy and scientific theories 64 Table 1 Ontological vs. epistemological stances 57 Figure 7 Systems theories and specific scientific theories 65 Figure 8 Transdisciplinarity of some systems theories 67 Figure 9 Intersection of math, philosophy, scientific theories 67 Figure 10 ESM as aim and source 69 Table 2 Some general phenomena (systems themes) 71 Table 3 Epistemological hierarchy 72 Figure 11 Isomorphisms 74 Figure 12 Model derived deductively 75 Figure 13 Substance and form 80 Figure 14 Concrete, abstracted, and conceptual systems 85 Figure 15 Triad of matter, energy, and information 88 Figure 16 Utility as a 4th fundamental category 94 Table 4 Some categories and systems theories 97 Figure 17 Isomorphism vs. emergence/reduction. 98 Table 5 Some aspects of “complexity” and “holism” 101 Figure 18 Lineal, mutual (feedback), branching causality 104 Figure 19 Structure, function, and history 117 Figure 20 Creation, Destruction, Maintenance 119 Figure 21 Hexad of synchronics and diachronics 120 Table 6 Systems theories are not simply mathematics 123 Figure 22 Object theory in a Pythagorean university 128 Figure 23 Systems theory and systems analysis 142 Figure 24 Models in systems theory and systems analysis 144 Figure 25 Tetrad of problem solving 146

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Table 7 Organizing principles for integrating systems theory154 Table 8 Boulding’s hierarchy of system types 156 Table 9 Levels of autonomy and information 158 Figure 27 Process model 194 Figure 28 Macro-historical processes of complexification 197 Figure 29 Systems project assisting development of science 207 Figure 30 Metaphysical, natural, and moral evils 231 Figure 31 Pareto-optimality 233 Figure 32 Modification of the triple sustainability concept 252 Figure 33 Parsons’ tetrad of social systems 253 Figure 34 Four fundamentalisms 257 Figure 35 Separation of powers and the Arrow theorem 265 Figure 36 Tetrad of culture 267

NOTES Synchronics Wholeness Figure 37 Alternative representations of a neutral system 298 Figure 38 Hierarchy of Janus-faced systems 299 Figure 39 A minimal system S with environment E 301 Figure 40 Adding attributes to elements and relations 302 Figure 41 A triadic non-decomposable relation 305 Figure 42 Representations of (directed) triadic relations 306 Figure 43 Incompleteness involving attributes and relations 307 Figure 44 Lattice of (specific) structures for neutral system 308 Figure 45 Specific and general structures; loops 309 Figure 46 Lattice of (general) structures for 4 elements 310 Figure 47 Inconsistency involving attributes and relations 313 Figure 48 Four level logic 315 Figure 49 Varieties of dyadic links 319 Constraint Figure 50 Uncertainties of relations and elements Figure 51 Coupled and uncoupled dynamic systems Figure 52 Elementary cellular automaton Figure 53 An iterative graph Figure 54 Plateau of viability

326 328 328 329 342

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Distinction Figure 55 Two depictions of system and environment Figure 56 External relation Figure 57 Tetrad of number; pentad of system

346 355 359

Persistence Figure 59 Negative and positive feedback Figure 60 Stabilizing and destabilizing loops Figure 61 Homeostatic plateau Figure 62 The fold catastrophe Figure 63 Flux is the basis for order Figure 64 Cause-controlled (feedforward) regulation Figure 65 Error-controlled (negative feedback) regulation Figure 66 Thermostat feedback control system Figure 67 Modes of negative feedback

374 375 375 377 382 377 386 387 387

Identity Figure 68 Syntactic, semantic, pragmatic information 391 Figure 69 Information from matter-energy via utility 393 Figure 70 Autopoiesis; additional information input 394 Figure 71 Phenotype determined by genotype, environment 396 Figure 72 Inconsistent internal and external identity 398 Agency Figure 73 Environmental types Figure 74 Externalities Figure 75 Internalizing the external in decisions Figure 76 Indirect effects can cause counterintuitive results Figure 31 Pareto-optimality (figure from Commentary) Figure 77 Arrow impossibility triad and tetrad Figure 78 Stability and resilience Figure 79 Tetrad of purposeful action Figure 80 Eating and being eaten Figure 82 Autonomy vs. heteronomy Table 10 Decision under risk Table 11 Two-player game Table 12 Prisoner’s Dilemma Table 13 The game of Chicken

405 412 413 414 419 421 425 426 428 438 407 430 433 435

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Complexity Figure 83 Scale-free networks Figure 84 Macro- and micro-heterogeneity Figure 85 Two conceptions of three levels of analysis Figure 86 The highest is not the whole Figure 87 Informational parasitism

450 452 454 456 460

Cognition Figure 88 The modeling subsystem Figure 89 The modeling tetrad Figure 90 Pragmatic, semantic, syntactic Table 14 Two syntactic-semantic-pragmatic hierarchies Figure 91 Multiple subselves Figure 92 Codependence of modeling of self and other Figure 93 Embeddedness of cognition Figure 94 Temporal triad; space-time tetrad Figure 95 Cognition and autopoiesis Table 15 Sensitivity and specificity Figure 96 Sensitivity vs. specificity (ROC) Figure 97 Levels of operation of the modeling subsystem

463 465 468 470 473 474 475 476 480 485 485 488

Diachronics Origin Figure 98 System formation; system as temporal center Figure 99 Systems formation and the fold Figure 100 System formation: difference in similarity Figure 101 System formation, a time-space tetrad Figure 102 Phase transition

498 500 501 501 503

Development Figure 103 Progress and Pareto-optimality

511

Limitation Figure 104 Nucleation, expansion, limitation Figure 105 Four patterns of growth and development Figure 106 Holling's adaptive cycle model Figure 107 The cusp catastrophe Figure 108 Being1 vs. being2 Table 16 Devils, catastrophes, and games Table 17 Limitation: internal/external, general/specific

515 517 519 521 523 524 525

Lists of figures, tables

Figure 109 Tetrad of adaptive failures Figure 110 Failure of response to exponential danger

615

525 526

Complexification Figure 111 Critical paths among multiple processes Figure 112 Optimum path determination Figure 113 Segregation and systematization Figure 114 Coupling of entropy increase and decrease Figure 115 Differentiation on the cusp Figure 116 A hierarchy of cusp equilibria Figure 117 Limits of self-organization Figure 118 Spontaneous complexification via transient Table 18 Aspects of limits of complexification Figure 120 Self-organized criticality

532 533 536 538 540 542 545 547 549 552

Internal Opposition Figure 121 Structural change as a cusp

557

Texture Figure 122 Extending the path and closing the circle Figure 123 Overshoot and collapse Figure 124 Cusp catastrophe hysteresis

564 566 567

Other systems Figure 125 The butterfly catastrophe Table 19 Catastrophes, games, and dialectics Figure 126 From cusp to butterfly Figure 127 Augmentation by a secondary process

571 572 573 574

Embeddedness Figure 128 Tetradic evolution

581

Impermanence Figure 129 System dissolution and the fold Figure 130 Two views of system dissolution

586 589

B.2 Dyadic figures, tables Figure 1 Structure and function of the systems project Figure 3 System as center Table 1 Ontological vs. epistemological stances Figure 5 Coherence and correspondence Figure 13 Substance and form

xi 49 57 61 80

616

Appendices

Figure 19 Structure, function, and history 117 Figure 23 Systems theory and systems analysis 142 Table 7 Organizing principles for integrating systems theory154 Figure 26 ESM organizing principles 154 Figure 30 Metaphysical, natural, and moral evils 231 Figure 31 Pareto-optimality 233 Figure 33 Parsons’ tetrad of social systems 253 Figure 55 Two depictions of system and environment 346 Figure 70 Autopoiesis; additional information input 394 Figure 82 Autonomy vs. heteronomy 438 Figure 84 Macro- and micro-heterogeneity 452 Figure 87 Informational parasitism 460 Figure 88 The modeling subsystem 463 Figure 98 System formation; system as temporal center 498 Table 16 Devils, catastrophes, and games 524 Table 17 Limitation: internal/external, general/specific 525 Figure 103 Progress and Pareto-optimality 511 Figure 114 Coupling of entropy increase and decrease 538 Table 19 Catastrophes, games, and dialectics 572 Figure 130 Two views of system dissolution 589

B.3 Triadic figures, tables Figure 1 Structure and function of the systems project xi Figure 3 System as center 49 Figure 4 An exact and scientific metaphysics 55 Figure 9 Intersection of math, philosophy, scientific theories 67 Figure 14 Concrete, abstracted, and conceptual systems 85 Figure 15 Triad of matter, energy, and information 88 Figure 19 Structure, function, and history 117 Figure 20 Creation, Destruction, Maintenance 119 Figure 30 Metaphysical, natural, and moral evils 231 Figure 35 Separation of powers and the Arrow theorem 265 Figure 41 A triadic non-decomposable relation 305 Figure 55 Two depictions of system and environment 346 Figure 64 Cause-controlled (feedforward) regulation 377 Figure 65 Error-controlled (negative feedback) regulation 386 Figure 68 Syntactic, semantic, pragmatic information 391 Figure 69 Information from matter-energy via utility 393

Lists of figures, tables

617

Figure 71 Phenotype determined by genotype, environment 396 Figure 77 Arrow impossibility triad and tetrad 421 Figure 82 Autonomy vs. heteronomy 438 Figure 89 The modeling tetrad 465 Figure 90 Pragmatic, semantic, syntactic; regulatory triad 468 Table 14 Two syntactic-semantic-pragmatic hierarchies 470 Figure 94 Temporal triad; space-time tetrad 476 Figure 97 Levels of operation of the modeling subsystem 488 Figure 98 System formation; system as temporal center 498 Figure 104 Nucleation, expansion, limitation 515 Figure 125 The butterfly catastrophe 571 Figure 130 Two views of system dissolution 589

B.4 Tetradic figures Figure 16 Utility as a 4th fundamental category Figure 25 Tetrad of problem solving Figure 32 Modification of the triple sustainability concept Figure 33 Parsons’ tetrad of social systems Figure 34 Four fundamentalisms Figure 35 Separation of powers and the Arrow theorem Figure 48 Four level logic Figure 57 Tetrad of number; pentad of system Figure 79 Tetrad of purposeful action Figure 77 Arrow impossibility triad and tetrad Figure 89 The modeling tetrad Figure 94 Temporal triad; space-time tetrad Figure 101 System formation, a time-space tetrad Figure 109 Tetrad of adaptive failures Figure 128 Tetradic evolution

94 146 252 253 257 265 315 359 426 421 465 476 501 525 581

B.5 Pentadic figures, table Figure 2 Structure of Commentary Figure 16 Utility as a 4th fundamental category (c) Table 4 Some categories and systems theories Figure 57 Tetrad of number; pentad of system Figure 80 Eating and being eaten

40 94 97 359 428

B.6 Hexadic figure Figure 21 Hexad of synchronics and diachronics

120

619

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ACKNOWLEDGMENTS Writing Elements and Relations has been a solitary experience, but the book itself is the result of many past interactions with mentors, colleagues, students, friends, and family. These categories of course overlap, so I’ve sequenced my acknowledgments roughly in the order that the people I want to thank have come into my life. I mention many names, but I’m sure I’ve missed some people who have been important to my professional life. I ask for forgiveness! The story of the book begins with my elementary and high school education at the Yeshivah of Flatbush (YF), a Jewish day school in Brooklyn, NY, at which I studied both religious and secular subjects. It begins there because my scientific career, initially in biophysics but for most of my professional life in systems theory, has its source in the interest in mathematics implanted in me by the math teacher, Israel Wallach. I owe thanks to Max Blatt, a social studies teacher, whose inspiring course on world history is the source of my interest in models of history. Among the Jewish studies faculty, the teacher who had the greatest impact on me was Rabbi David Eliach, may his memory be a blessing, who imparted to me a love of Judaism and confidence in my critical faculties. While this book is about systems theory, a fusion of science, math, and philosophy, it also reflects my interest in religion, which traces back to my YF education. I went to college at Columbia and was a physics major and math minor. In my senior year, I shifted to electrical engineering and took courses in information theory, feedback control theory, and network analysis. This was my introduction to the systems field. I was in NROTC, and after graduating in 1960 became an Ensign in the Navy. To my great fortune, I was assigned to the Physics Branch of the Office of Naval Research. I owe a great debt to my mentors at ONR, who made it possible for me to advance my scientific education while in the military. Jack Soules nourished my interest in physics and gave me helpful © Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7

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personal advice. Wayne Gruner demonstrated how one penetrates to the gist of scientific questions. Martin Garstens encouraged my interest in biophysics and in the philosophical issues at the heart of the difference between life and non-life. At ONR, I heard about advances in all of the sciences, which made me forever fascinated by breaking discoveries even in fields distant from my own. After military service, I went back to school as a graduate student in the MIT Biology Department. Guided by my PhD advisor, Cyrus Levinthal, my research on macro-molecular structure introduced me to computer modeling and simulation. My graduate studies in molecular biology gave me a secure base of discipline-specific scientific knowledge which later helped to ground my transdisciplinary interests. My mathematical and computational knowledge was also broadened at MIT by exposure to AI research directed by Marvin Minsky. After a post-doctoral year at Stanford, I joined the faculty of the Biophysics Department of the University of Chicago. I learned from and much enjoyed friendships and collegial relationships with Paul Sigler, Elmar Zeitler, and Robert Haselkorn in my department, and with my student and later colleague David Bantz. Another student and friend Jane Koretz helped me recognize that my interests were broader than the structure of molecules. They encompassed structure in general, which reflected a systems theory orientation, and they also ranged beyond science. University of Chicago faculty colleagues Richard Lewontin and Richard Levins introduced me to dialectical thought and William Wimsatt to philosophy of science. My years in Chicago, a time of countercultural and political ferment, were for me also a period of personal spiritual exploration; in an unexpected linkage of my personal and professional lives, a teacher I was much influenced by made the observation to me, “You like to structure knowledge.” I took my position at Portland State University in 1976 and fully transitioned from biophysics to systems theory. I cannot sufficiently thank my Systems Science Program faculty

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colleagues: Harold Linstone, George Lendaris, Andy Fraser, and Wayne Wakeland. Harold Linstone, the first program Director, wrote a job description consisting mainly of a list of major systems theorists – this unusually substantive advertisement encouraged me to apply for the position; I thank him also for his theory of “multiple perspectives” which has made the irrationality of university politics comprehensible. George Lendaris enabled me to grasp the distinction between the different projects within the systems field that I have come to label “systems theory” and “systems analysis.” Andy Fraser, whose work on chaos and information theory was a jewel of research creativity, was an exemplar of scientific rigor; his leaving PSU for Los Alamos National Labs was a big loss to the program. I owe a huge debt to Wayne Wakeland. His efforts on behalf of the Systems Science Program were and continue to be nothing short of extraordinary; over the last many years my teaching and research activities would have been impossible were it not for his skillful and self-sacrificing labor on behalf of this unique program, which has been continually threatened by university budgetary crises. I’m also much indebted to Dawn Sharafi, administrative assistant for the program, longtime friend, and the center of our systems community life for many years. Felix Gurley-Rimberg, a senior auditor and great fan of our program, encouraged me to develop a data mining course which became an important addition to the program’s curriculum. Thanks are due as well to Nancy Perrin and Beatrice Oshika who provided the program with excellent leadership for many years, and to Bill Feyerherm, a rare administrator who understood the significance of systems thinking. I also thank Todd Rosenstiel, now dean of the College of Liberal Arts and Science for his long support of the systems program. Systems Science graduates who became adjunct faculty also contributed greatly to the program and to my own professional activities. Jeff Fletcher was an outstanding faculty member in both Systems Science and University Studies, PSU’s general education program. One of my biggest disappointments at PSU was our missing the opportunity to retain him as

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Systems Science faculty. In my earlier work with him as his PhD supervisor, our research meetings on the evolution of cooperation had often started with him posing a research question and ended an hour or two later with our having worked out a good answer – a repeated experience that was sheer intellectual bliss. David Hall helped me to appreciate the relevance of indigenous culture to systems thought and to the challenges of the present historical moment. Joe Fusion has been critical to my research and teaching program in discrete multivariate modeling (DMM), and to the OCCAM software that is central to it. Rajesh Venkatachalapathy has personified for me the insatiable intellectual curiosity that characterizes many who are attracted to the systems field; I know of no one who knows more about more things than he does. Other faculty colleagues at PSU assisted me in this book project in direct or indirect ways. They include Tim Anderson, Brad Berman, Judah Bierman, Sue Danielson, Avram Hiller, Ladis Kristof, Gary Langford, Niles Lehman, Robert Liebman, Alan Mishchenko, Thomas Kinderman, Thomas Luckett, Bart Massey, Melanie Mitchell, Marek Perkowski, Thomas Seppalainen, Vivek Shandas, and Neal Wallace. My diverse intellectual interests were shared and validated in collegial relationships with Robert Liebman, Thomas Luckett, and Marek Perkowski. Ladis Kristof inspired my study of systems ideas on “center and periphery.” Melanie Mitchell broadened my traditional systems science orientation with the more contemporary complex systems perspective, and, along with George Lendaris, introduced me to neural networks. Bart Massey gave valuable help to my DMM software project. Thomas Seppalainen, after reading part of an early version of this book, said to one of my students that it made him think of “Spinoza on steroids”; I took this as a compliment, realizing only later that it might have been a criticism; either way I embrace it. In classes, seminars, research, and informal discussions, my students have taught me a great deal. Many of them have

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become faculty members at various universities or have taken professional positions at other public or private organizations. Among these students, I thank Eran Agmon, Dan Akins, Athena Aktipis, Heather Alexander, Anas Al-Rabadi, John Anasis, Douglas Anderson, Mohsen Attaran, John Balwit, Chris Bartlo, Erik Bass, David Burke, Renato Carletti, Nancy Carney, Alistar Chan, Guy Cutting, Naghmeh Daneshi, Michael Dejardin, Shane Dicks, John Driscoll, Ike Eisenhauer, Saman Fatma, Jeff Fletcher, Henry Foresman, Parker Foresman, Keith Forman, Dale Frakes, Cecily Froemke, Joe Fusion, Peter Geissert, Nick Gilla, Ben Grad, Michael Gray, Carla Green, Allen Grimm, Brad Gross, Stanislaw Grygiel, Dave Hall, Marcus Harris, William Herzberg, Lars Holstrom, Jamshid Hosseini, Cyrene Howland, Joshua Hughes, Cory Johnson, Martin Jetton, Michael Johnson, Richard Jolly, Erin Kenzie, Sai Kiersarsky, Grant Kirby, Robert Kramer, Greg Lankenau, Dave Lawrence, Laura Lazorski, Longjun Liu, Byrne Lovell, Richard Lockwood, Steve Malen, Shawn Marincas, John Maxwell, Marty McCall, Lindsay Mico, Ruth Miller, Scott Mist, Catherine Moore, Heather Moore, Alex Nielson, Nathan Nifong, Andey Nunes, Barry Oken, Peter Olson, Kruti Pandya, David Percy, Ed Ramsden, Dora Raymaker, Andreas Rechtsteiner, Peter Roolf, Rolando Salazar, Roberto Santiago, Meme Samkow, Teresa Schmidt, Terry Schumacher, Daniel Schwartz, Tad Shannon, Steve Shervais, Fazlollah Shirazi, Richard Smith, Tatiana Snyder, Gary Sotnik, Ryan Spangler, Kevin Stoltz, Jonathan Straus, Trevor Thiess, Rajesh Venkatachalapathy, Kevin Vixie, Mehmet Vurkac, Bronson Wacker, Michael Weisdorf, Don Wilcox, Ken Willett, Jusug Yang, Jessica Yates, Alex York, Joe Zenisek, and Amanuel Zimam. Although this list is long, it is still incomplete. I’m sure that I’ve omitted some students who have significantly influenced my systems thinking. I’ve used early drafts of Elements and Relations in the Systems Philosophy class which I have taught for many years, and many of the students whom I list above took this class. They helped me develop and refine the ideas in the book and transformed it into a continuing source of intellectual

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stimulation and pleasure for me. Steve Shervais’ high spirits made the class – and everyday life in Systems Science – especially enjoyable. He along with Michael Johnson, Tad Shannon, and Ken Willett once serenaded me with a song they composed about the challenge of integrating the multiple theories that constitute the systems project, a theme that I address in Chapter 5 (Commentary). I also treasure the comment of another Systems Philosophy student whose name is now lost to me who was surprised to find that the Essay part of this book reminded him of the Tao Te Ching; needless to say, I couldn’t have been rewarded with a more welcome compliment. Many other students in the Systems Philosophy class contributed to this book project in ways too numerous to identify. I owe thanks to friends and colleagues in the larger communities of systems science and adjoining fields, including Yaneer Bar-Yam, Mark Bedau, Mario Bunge, Roger Conant, Peter Corning, Doug Elias, Francis Heylighen, Cliff Joslyn, Stuart Kauffman, George Klir, Klaus Krippendorff, Marcus Locker, George Mobus, Chrystopher Nehaniv, William Tastle, Len Troncale, Uri Wilensky, and Robert Wright. Of these acknowledgments, Mario Bunge is the one person with whom I never actually interacted, but I must express my deep thanks to him here because his notion of an (exact and) scientific metaphysics is central to my understanding of the systems field. I am especially grateful to George Mobus for adopting Elements and Relations for his Systems Science series published by Springer Publishing Company; his support and encouragement provided me with the energy that I needed to move it forward. George Klir was a long-time systems friend from whom I never ceased learning; every one of his talks that I attended began with my feeling that I was familiar with his topic and ended with my gratitude for having been taught new things. From George Klir and Klaus Krippendorff I learned about reconstructability analysis, a.k.a. discrete multivariate modeling (DMM), which has been central to my systems research program; its core ideas play an important role in this book. I’ve valued my collegial friendship with Cliff Joslyn, once a student of Klir’s, and the

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partnership he has fostered between PSU Systems Science and the Pacific Northwest National Labs. I am very grateful to Nancy Carney, whose grants helped to fund my DMM work, and thank other OHSU researchers – Arie Barratt, Patricia Kramer, Shawn Westaway, and Beth Wilmot – with whom I’ve interacted, along with PSU students and graduates, on varied DMM projects. Excursions into the systems field of Artificial Life led to productive and pleasurable collaborations with Mark Bedau, Reed faculty member, and for years also Systems Science adjunct faculty. Many other systems theorists and practitioners whom I met at conferences helped me in direct or indirect ways in this book project. After coming to PSU my first sabbatical was spent in the Philosophy of Science Department at Boston University, led by Marx Wartofsky and Robert Cohen. It was their seminar series that introduced me to Spinoza and Goethe as philosophers of science. And it was in the intellectually stimulating environment that this seminar series created that I wrote “Incompleteness, Negation, Hazard: On the Precariousness of Systems” which later evolved into the Essay part – and the intellectual heart – of Elements and Relations. More recently in Portland, I’ve been a member for many years of the Philosophy-Religion Discussion Group (PRDG), which now includes Doug Donkel, John Hammond, Stephen Jolin, and Kirke Wolfe. PRDG once included Hugo duCoudray, Richard Hartman, Palmer Pardington, and Alice Simpson, all of whom have passed away and are much missed. My friends/colleagues in this group have taught me a great deal about philosophy and religion. Doug Donkel introduced me to continental thought, especially Heidegger and Derrida, and gave strong support to my book project. John Hammond helped me develop thoughts on secular theodicy. Stephen Jolin consistently demonstrated the synergy between intellectual openness and critical thought; my friendship with him predates his joining PRDG. It was many years ago that he enabled me to understand that the unique was as important as the universal. Kirke Wolfe gave me useful comments on my manuscript and, through his interest in

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Buddhism, supported my conceptualization of the “inner sciences.” Hugo duCoudray was a systems-oriented psychology professor who influenced me to engage more fully with the work of Gregory Bateson and whose intellectual framework resonated with mine. Richard Hartman deepened my interest in continental philosophy and German Idealism. Palmer Pardington acquainted me with process thought, which broadened my conception of what a systems perspective might encompass. Alice Simpson always kept us grounded by bringing us back to the fundamental question of “What is philosophy for?” Levinas, for whom “ethics precedes ontology,” would have found an excellent emissary in her. My interests in philosophy and religion and their relations to systems thought have been nourished by conversations with Steve Wasserstrom of Reed College, who enhanced my awareness of the intersection of religion and politics. Sylvia Frankel at the Institute for Judaic Studies encouraged me in my studies of Jewish themes. Among distant colleagues who have influenced my thinking in these areas are Yossi Chajes, Irene Eber, Michael Gormann-Thelen, Zev Harvey, Andreas Leutzsch, and Benjamin Pollock. My interest in religion has not been solely intellectual. I’m not sure if or how what I have learned from my mentors in spiritual matters manifests in this book, but I suspect that their influence is pervasive. Among the guides I’ve encountered in this realm, the teachers who have had the greatest impacts on me – in different ways – were Christopher Fremantle, Rabbi Aryeh Hirschfield, and Don Nickerson. My gratitude to these three men is deep and vast. I’ve had very many stimulating discussions with Anthony Blake on the philosophical, religious, and scientific ideas of John G. Bennett, ideas that play an important role in the book. I also thank David Seamon for our exchanges about Bennett and for stimulating my interests in Christopher Alexander’s pattern language and Goethe’s science. John Dale, also very

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knowledgeable about Bennett’s writings, is in a league of his own in his extraordinarily generous and professional assistance in editing this book and in his appreciation, despite the book’s flaws, of what I am trying to accomplish in it. His review of my manuscript addressed the full range of issues from fundamental conceptual questions to technical copy-editing. Unfortunately, the press of time has prevented me from making use of more than a small fraction of his suggestions; many flaws that remain in this book are undoubtedly ones that he marked up as needing correction. Interactions with other Portland intellectuals have also assisted me in this project. I thank Terry Bristol not only for the exceptional Science, Technology, and Society lecture series that he organized for many years but also for stimulating discussions about the significance of engineering, thermodynamics, and the history of philosophy. Todd Duncan helped me appreciate the significance of systems ideas not only for education in science but more broadly as components of a new scientific worldview that was connected to all aspects of human culture. My personal and family friendships have also supported this undertaking. I’ve enjoyed and have been intellectually stimulated by many conversations I’ve with Allen Hunter on scientific, political, and other matters. My religious interests have been deepened by conversations with Steve Engel. The late poet Peter Sears inspired me to try to express some ideas through narrative structure rather than conventional argument. I’ve treasured my conversations with Gary Smith, who also expanded my understanding of psychology and psychoanalysis; and Rachel Greenwald Smith, his daughter, in her book on the politics of affect in contemporary fiction, helped me recognize the place of neoliberalism in recent political history. Lastly and most significantly, I have been shaped and supported by family. My mother, Aida Hodas, reminded me always to keep my eye on tachliss, the moral bottom line. My father, Abraham (Al) Zwick, taught me that doing what I enjoy

678

Acknowledgments

was the key to being able to do what was meaningful to me. My sister, Arlene Zwick Leventhal, and my late brother-in-law, Ed Leventhal, always supported me with unconditional affection and respect. My son, Michael, has been a constant spur to me to get on with the task I’ve undertaken and a source of joy and energy and optimism. Finally, I must single out one person, whose importance to me in every aspect of my life exceeds all others, and whose help in this project in countless ways – encouraging, sympathizing, editing, and enduring my interminable expositions – has been far beyond what I could possibly have hoped for or expect: my wife and soulmate, Elinor Langer.

679

INDEX Some words are used too frequently to index, e.g., attribute, conflict, constraint, diachronics, distinction, environment, growth, hierarchy, multiplicity, order, relation, synchronics, system, systems theory, stability, and utility. However, some of these words are included with modifiers in the index. For example, “relation” as a general term is not indexed, but “relation:external” is. “Incompleteness” and “inconsistency” are not indexed, nor are “completeness” and “consistency,” but “incompleteness vs. inconsistency” is. “Dynamic system” is not indexed, but “dynamic system:discrete” is. A colon denotes a subcategory of the indexed term. Essay is not indexed, but its contents which are repeated in Notes are indexed there. The References and Acknowledgments sections are also not indexed. An index is, of course, a system and thus unavoidably imperfect.

A abstracted systems. See concrete, abstracted, and conceptual systems abstraction, x, xv, 64, 65, 75, 76, 151, 175, 219, 222, 223, 242, 278, 351, 366, 470, 592, 593, 594, 596, 598, 599, 600 Ackoff, Russell L., 513, See systems analysis active vs. passive, 88, 89, 90, 157, 368, 401, 404, 411, 426, 427, 479, 523 actual vs. possible (potential), 161, 162, 185, 195, 196, 211, 213, 239, 282, 307, 313, 322, 329, 331, 332,

355, 476, 498, 509, 520, 522, 556 adaptation, 71, 92, 173, 183, 189, 216, 253, 404, 458, 553, 565, 578, 579, 582, 587, 607 adaptive cycle model, 76, 450, 518, 519, 553, 558, 565, See also Holling, Crawford Stanley:and Gunderson, Lance H. Adorno, Theodor W., 80, 247, 559, 598 agent-based modeling, 141, 145, 165, 367, See also computer simulation aggregating preferences, 230, 266, 276, 420, 422, See also Arrow, Kenneth alchemy, 239, 240

© Springer Nature Switzerland AG 2023 M. Zwick, Elements and Relations, IFSR International Series in Systems Science and Systems Engineering 35, https://doi.org/10.1007/978-3-030-99403-7

Index

680

Anaximander, 587 Angyal, Andreas, 60, 125, 304, 307, 313, 357 anthropic principle, 47, 235, 236 antisemitism, 163, 202, 219 Aristotle, 56, 80, 253, 522, 608, See also causation:material,efficient ,formal,final Armstrong, Karen, 196, 199, See history:model of human Arrow, Kenneth, 215, 230, 264, 265, 266, 276, 420, 421, 422, 486, 492, See also aggregating preferences Artificial Intelligence, 52, 92, 115, 139, 140 Artificial Life, 53, 85, 92, 98, 114, 139, 140 Ashby, W. Ross, 63, 64, 75, 77, 134, 139, 152, 219, 318, 339, 351, 378, 384, 385, 388, 393, 463, 481, 534, 582, 594 attribute intrinsic vs. extrinsic, 302, 317, 364, 370 link between element and relation, 72, 301, 302, 303, 307, 313 Augustine, 340, 522 Augustinian vs. Manichean devils, 520, 522, 523, 524, 584 automata, 51, 65, 66, 68, 78, 83, 84, 124, 127, 139, 149, 151, 153, 165, 320, 327, 339, 357, 367, 443, 600, See also dynamic system:discrete

cellular, 78, 135, 165, 328, 395, 503 theory, 51, 52, 55, 66, 68, 78, 83, 92, 151, 152, 153, 320, 367, 384, 600 automatic, sensitive, and conscious levels of cognition, 487, 488, 489, 490, See also modeling subsystem; consciousness autonomic. See hyponomicautonomic-hypernomic triad autonomy, 157, 158, 184, 240, 256, 314, 399, 400, 403, 438, 439, 491, 492 vs. heteronomy, 438 autopoiesis, 89, 109, 157, 159, 236, 255, 350, 352, 354, 393, 394, 397, 401, 463, 480, 502, 503, 513, 602, 603, See also Maturana, Umberto and Varela, Francisco Axelrod, Robert, 238, 434, See also game theory:Prisoner's Dilemma Axial period, 196, 197, 199, 200, 206, 245, See also history:model of human

B Baas, Nils, 98, 321, 367, 601 Bagley, Richard J., 97, 140, See also generalized:metabolism; Artificial Life Bak, Per, 76, 551, 553, See also self-organized criticality Barabási, Albert-Laszlo, 450, See network:scale-free

Index

Bar-Yam, Yaneer, 149, 152, 174, See complex systems; systems analysis Bateson, Gregory, 100, 139, 351, 379, 390, 484, 487, 512, 577, See modeling subsystem; pragmaticsemantic-syntactic triad Bayesian approach, 483, 484 Bedau, Mark, 366, See also emergence; Artificial Life; agent-based modeling Beer, Stafford, 149, 446 behaviorism, 114, 165 Bell, Daniel, 592 Bennett, Charles, 444, See also logical depth Bennett, John G., 40, 94, 111, 145, 146, 158, 166, 238, 280, 313, 329, 361, 397, 428, 487, 494, 512, See also dyad; triad; tetrad; pentad; hexad; hyponomicautonomic-hypernomic triad; hierarchy:of categories in Synchronics; Blake, Anthony Bentley, Arthur, 455 Berlin, Isaiah, 170, 273, 274, 275, 578 Berlinski, David, 149 Bible, 61, 170, 228, 239, 244, 497 Bielik-Robson, Agata, 604 binary oppositions, 115, 233, 322, 323, 334, 337, 340, 348, 356, 359, 360, 361, 391, 457, 512, 599, See also dyad; marked vs. unmarked terms; yin and yang binding the future, 180, 417, 472

681

Blake, Anthony, 88, 161, 361, See also Bennett, John G. Blake, William, 122, 164, 211, 350, 592 Bohm, David, 338 Bohr, Niels, 47, 273 Boltzmann’s constant, 86, 134, See also entropy Boulding, Kenneth, xv, 51, 63, 75, 143, 156, 157, 159, 162, 164, 165, 197, 238, 239, 246, 254, 327, 351, 397, 427, 440, 446, 447, 531, 580, 602, See also hierarchy:of system types; great chain of being boundary, 167, 177, 189, 303, 344, 346, 348, 350, 351, 352, 353, 354, 380, 381, 394, 400, 401, 412, 415, 419, 437, 443, 497, 503, 583, 603 conditions, 111 subsystem, 350, 393, 401, 503, 587 bounded rationality. See satisficing Brecht, Bertolt, 283, 595 Brinkman, Richard, 510, See also growth:vs. development Bronowski, Jacob, 543 Buber, Martin, 404, 406 Buddhism, 201, 227, 315, 475, 478, 589, 605 Buddhist logic, 314 Bunge, Mario, 43, 55, 63, 64, 68, 71, 72, 75, 77, 83, 84, 97, 144, 151, 594, See also metaphysics:exact and scientific; vicarious:testability; stufffree perspective

Index

682

Burke, Edmund, 413 Butler, Samuel, 260, 277, 494 butterfly effect, 107, 410

C Cage, John, 358 capitalism, 187, 204, 257, 259, 260, 262, 269, 270 Capps, John, 61 carrying capacity, 188, 518, See also sustainability catastrophe theory, xiii, 126, 375, 520, 584, See also Thom, Rene; Zeeman, Erik Christopher butterfly catastrophe, 76, 194, 199, 276, 343, 376, 410, 514, 528, 549, 556, 560, 570, 571, 572, 573, 574 cusp catastrophe, 76, 107, 258, 314, 332, 343, 376, 493, 495, 500, 509, 514, 516, 520, 521, 523, 524, 528, 531, 540, 542, 548, 549, 556, 557, 560, 567, 570, 572, 573, 574, 610 fold catastrophe, 164, 376, 377, 425, 499, 500, 520, 524, 528, 584, 585 categorical imperative, 436, See also Kant, Immanuel; Golden Rule category theory, 129 causation, 103, 105, 107, 220, 318 causal loop diagrams, 375 lineal, 101, 103, 104, 309

material,efficient,formal,fi nal, 80, 146, 253, 331, 468, See also Aristotle center and periphery, 83, 185, 213, 269, 296, 357, 384, 396, 438, 529, 540, See also Wallerstein, Immanuel central tendency, 451, 552 central vs. fundamental, 48, 49, 50, 51, 57, 79, 104, 111, 136, 237, 283, 538 centrality, 371 graph-, 317, 318, 529 of biology to systems theory, 39, 95, 135, 169, 281 centralization, 71, 266, 447, 448, 529, 531, 566, See also progressive centralization Chaitin, Gregory, 92, 125, 395, See also information:algorithmic chaos, 48, 53, 65, 66, 78, 85, 92, 103, 125, 126, 130, 135, 151, 171, 229, 336, 338, 609 anti-chaos, 337 edge of, 98, 214, 224, 239, 339, 443, 444, 448, 505, 528, 553, 610 Chicken. See game theory: Chicken Christianity, 184, 200, 243, 245 Chuang Tzu, 239, 337, 457, See also Taoism Churchman, C. West, 238, 348, 497, See also systems analysis climate change, xi, 203, 225, 278, 526

683

Index

closed system. See also isolated, closed, and open systems; thermodynamics; open vs. closed systems views closing the circle, 188, 249, 319, 412, 564 cognition. See modeling subsystem Cohen, Leonard, 608 Commoner, Barry, 188, 249, 412 complex adaptive systems, 47, 48, 53, 92, 139, 142, 152, 163, 461, 598 complex systems, ix, 53, 70, 93, 103, 135, 150, 152, 170, 174, 446 complexity, 48, 53, 106, 125, 142, 150, 151, 157, 161, 172, 238, 598, 603 combinatorial, 445 computational, 99, 122, 230, 366, 422 irreducible, 219 computer simulation, 53, 84, 123, 124, 125, 132, 141, 145, 165, 366, 367, 459, 479, 576, See also agentbased modeling; systems dynamics; Tierra boids, 141, See also Reynolds, Craig Conant, Roger, 463 concrete, abstracted, and conceptual systems, xii, 85, 86, 87, 174, 306, 321, 322, 334, 351, 363, 378, 379, 398 Confucianism, 200, 549 consciousness, 217, 235, 240, 242, 487, 488, 490, 600, See also automatic,

sensitive, and conscious levels of cognition consilience, 138, 209 constructivism, 56, 57, 219, 478 continental philosophy, 56, 57, 87, 163, 312, 347 control theory, 51, 52, 59, 66, 78, 82, 97, 173, See also regulation; feedback Copernican principle, 44, 198 counterintuitive effects, 105, 172, 179, 224, 279, 367, 411, 413, 414, 415, 416, 433, See also Watzlawick, Paul; Taoism Crutchfield, James, 78, 99, 443 cybernetics, xiii, xvii, 48, 52, 53, 55, 57, 59, 60, 66, 114, 133, 142, 150, 351, 388, 393, 598, 603, See also Wiener, Norbert; general systems theory; Second Order Cybernetics

D Darwin, Charles, 113, 118, 137, 169, 579, 598 Davis, James, 318, 414 Dawkins, Richard, 586 de Saussure, Ferdinand, 391, See also semiotics de Tocqueville, Alexis, 116 decision theory, xiii, 406, 408, 429, 484, See also game theory decomposability, 101, 133, 304, 305, 333, 453, 467, 528, 539, 550, 583, See also Lattice of Structures; reconstructability analysis;

684

mereology; hierarchy:whole-part partial, 255, 335, 348, 358, 457, 540, 550, See also Simon, Herbert A. deconstruction, xvi, 220, 322, 457, 473, See also continental philosophy democracy, 202, 256, 258, 259, 261, 262, 265, 266, 273 Derrida, Jacques, 322, 361, 492, 499, 587, See also continental philosophy Descartes, Rene, 56 Deutsch, Karl, 238, 246, 388, 399, 417 dialectics, xiii, 60, 202, 205, 231, 312, 314, 315, 323, 493, 512, 514, 556, 560, 569, 570, 572, 574, 598, 601, See also Hegel, Georg Wilhelm Friedrich; Marx, Karl; Engels, Friederich Diamond, Jared, 189, 525, 567 Dickinson, Emily, 378, 584, 585 différance, 361, 587, See also Derrida, Jacques difference, 97, 303, 312, 345, 347, 356, 359, 361, 390, 391, 401, 484, 539, 587, See also similarity vs. difference differential equation, 65, 83, 124, 126, 330, 357, 365, 442, 503, 601, See also system dynamics discount factor, 188, 307, 409, 410, 417, 499, 534 disequilibrium, 195, 196, 344, 349, 381, 507, 508, 509, 537, See also equilibrium;

Index

force and flux; thermodynamics dissipative system, 381, 401, 502, 504, 509, 563, See also thermodynamics; force and flux; Prigogine, Ilya disturbance, 102, 185, 373, 374, 383, 384, 385, 386, 387, 396, 408, 440, 449, 469, 492, 551, 563, See also stability; regulation amplification and deamplification, 185, 387, 449, 509, 551, 588 Dobzhansky, Theodosius, 116 Donkel, Doug, 164, See also continental philosophy; Heidegger, Martin Donne, John, 237 double cone diagram, xi, 48, 49, 110, 296, 300, 358, 391, 470, 476, 498, 537, See also structure:and function; RosenstockHuessy, Eugen; support variable dukkha, 227, 605, See also Buddhism dyad, 56, 62, 79, 80, 87, 88, 90, 94, 99, 110, 119, 125, 135, 161, 163, 164, 254, 255, 256, 265, 266, 276, 297, 298, 299, 301, 304, 305, 306, 308, 310, 312, 314, 316, 317, 320, 322, 323, 325, 334, 340, 345, 347, 356, 360, 362, 364, 369, 396, 405, 427, 429, 454, 467, 473, 491, 492, 494, 497, 512, 520, 524, 537, 559, 578, 599, See also binary oppositions;

685

Index

marked and unmarked terms; yin and yang dynamic programming, 533 approximate, 467, 582, See also Lendaris, George G. dynamic system, xiii attractor, 70, 115, 158, 215, 303, 329, 331, 334, 337, 339, 362, 373, 424, 443, 494, 516, 527, 528, 538, 593 basin of attraction, 215, 329, 330, 339, 354, 355, 373, 424, 509, 516 deterministic, 82, 83, 106, 126, 171, 327, 329, 334, 338, 378, 379 discrete, 83, 84, 164, 328, 337, 339, 442 gradient, 330, 332, 376, 424, 442, 500, 508, 509, 521 meta-dynamics, 528, 538 nonlinear, 65, 66, 77, 86, 120, 121, 134, 152, 171, 209, 218, 321, 329, 330, 338, 339, 340, 366, 367, 376, 413, 443, 504, 576, 601 trajectory, 328, 355, 373, 410, 514, 515, 518, 522, 549, 557, 558, 560, 573

E earthquakes, 83, 186, 224 education, 52, 93, 183, 184, 221, 225, 226 Eigen, Manfred, 503, 529 Einstein, Albert, 47, 105

Elsasser, Walter, 135, 136, 160 Elster, Jon, 404, 405, 418, 534 emergence, 50, 53, 59, 78, 79, 90, 93, 97, 98, 99, 100, 137, 138, 141, 155, 184, 199, 209, 212, 214, 215, 231, 236, 237, 239, 267, 302, 324, 354, 363, 364, 365, 366, 367, 370, 393, 415, 434, 441, 458, 470, 471, 502, 518, 543, 545, 546, 570 downward, 364, 371 of attributes, 164, 318, 324, 363, 364, 365, 370, 497 ontological vs. epistemological, 99 Emerson, Ralph Waldo, 417, 608 Emery, Frederick E. and Trist, Eric L., 404, 405, 440, 474, 475, 525, 576, See also environment:types Engels, Friederich, 60, See also Marx, Karl entropy, 334, 335, 378, 379, 380, 381, 383, 442, 443, 452, 563, See also uncertainty; Boltzmann’s constant; thermodynamics; statistical mechanics environment, 347 internal, 316, 339, 348, 356 relevant, 240, 307, 316, 349, 355, 414, 463 types, 347, 404, 405, 427, 440, 484, 525, 576 epistemological, 63, 68, 75, 91, 96, 101, 128, 390, 461, 600, See also ontological vs. epistemological

Index

686

hierarchy, 71, 74, 77, 176, 190, 278, See also Bunge, Mario equality, inequality, 180, 184, 215, 266, 274, 275, 277, 458 equilibrium dynamic, 116, 260, 328, 329, 330, 365, 376, 377, 424, 447, 507, 512, 521, 549, 553, 559, 570, 571, 572, 573, 585 dynamic vs. thermodynamic, distinguished, 328 thermodynamic, 59, 87, 98, 120, 121, 131, 132, 214, 328, 335, 381, 383, 504, 507, 508, 537, 538, 551, 584 essential variable, 303, 384, 385, 386, 488, 534, See also regulation eternity, 313, 329, 355, See also dynamic system; Bennett, John G. evil, 170, 227, 229, 604, See also theodicy; ontology of problems; Neiman, Susan metaphysical, natural, moral, 227, 228, 231, 232, 280, 281, 522, 607 exchange, 181, 185, 254, 406, 427, 436, 437, 540, 562, 569, See also thermodynamics; isolated, closed, and open systems matter-energy, 352, 380 value, 115, 116 exploitation, 172, 175, 185, 249, 269, 436, 458, 460, 540

exponential growth, 188, 208, 224, 225, 248, 423, 429, 518, 526, 548, 563, 565, See also growth extension, 81, 150, 302, 346, 357, 384, 464, 476, 508, 550, See also support variables externalities, 188, 249, 259, 260, 262, 263, 412, 434, 563, See also suboptimality

F Fallacy of Composition, 422, 434, See also game theory:Prisoner's Dilemma; aggregating preferences; Arrow, Kenneth Farmer, J. Doyne, 97, 140 feedback. See also control theory control, 51, 59, 78, 96, 156, 159, 386, 388, 446 negative, 114, 216, 224, 267, 386, 387, 413, 415, 447, 517, 549, 565 positive, 266, 269, 414, 517, 518, 548, 549, 565 feedforward control, 59, 195, 384, 396, See also regulation:cause-controlled Feibleman, James K. and Friend, Julius W., 309, 322, 454, 512, 531 Feigenbaum’s constant, 86, 134, See also chaos Festinger, Leon, 509 Fichte, Johann Gottlieb, 315, 473 fires, effects of oversuppression, 179, 224

687

Index

Firstness, Secondness, Thirdness, 161, 323, 359, 360, 361, 473, See also Peirce, Charles S. Fletcher, Jeffrey, 229, 236, 408, 484, 544 flocking and schooling, 99, 141, See also isomorphism Fodor, Jerry Alan, 115 Fontana, Walter, 97, 529, See also Artificial Life force and flux, 255, 271, 362, 381, 504, 507, 509, 551, See also disequilibrium; dissipative system; Prigogine, Ilya; thermodynamics Forrester, Jay, 107, 248, 415, See also system dynamics Forster, Edward Morgan, 604 Foucault, Michel, 118, See also structure:function, and history fractals, 82, 126, 263, 339, 367, 467, 553, See also Mandelbrot, Benoit Freud, Sigmund, 59, 113, 169, 235, 478, 598, See also Jung, Carl; Lacan, Jacques; psychoanalysis Friston, Karl, 480, 483 frozen accident, 101, 121, 137, 262, See also Gell-Mann, Murray; history:ideographic vs. nomothetic views of function, 113, 183, 330, 390, 401, 424, 440, 446, 448, 459, 491, 504, See also structure:and function; structure:function and history

fundamentalism, 47, 220, 244, 257, 258, 264, 269, 270, 457, 595, See also central vs. fundamental; reductionism systems theoretic, 164, 165, See also ontological:vs. ontic fuzzy set theory, 60, 63, 126, 213, 314, 315, 352, 353, 499, See also Zadeh, Lofteh; Kosko, Bart; set theory

G Gaia, 166, 249 Galileo, 211 game theory, xiii, 51, 52, 55, 65, 66, 76, 77, 78, 83, 96, 97, 149, 150, 152, 172, 215, 218, 286, 321, 322, 365, 384, 404, 405, 432, 433, 502, 595, 601 Chicken, 75, 250, 434, 435 coalition theory, 322, 365, 405, 406, 431, 504 n-person, 435, 504 Prisoner’s Dilemma, 75, 78, 138, 172, 225, 279, 422, 431, 433, 486, 566, 569 zero-sum vs. non zerosum, 83, 322, 405, 419, 430, 431, 432, 433, 523, 571, 572 Gay, Peter, 592 Gell-Mann, Murray, 47, 106, 121, 152, 155, 212, See also frozen accidents; complex adaptive systems; complex systems

Index

688

general systems theory, 52, 138, 142, 149, 150, 598, See also von Bertalanffy, Ludwig; cybernetics generalizations, 63, 66, 68, 92, 134, 166, 247, 304, 335, 353, 424, 592 generalized evolution, 66, 71, 82, 120, 121, 137, 424, 579 genotype, phenotype, 162, 396, 438 incompleteness vs. inconsistency, 601 mechanics, 75, 135 metabolism, 71, 97, 124, See also metabolism genetic algorithm, 66, 78, 424, See also optimization:global Gerard, Ralph, 51, 117, 139, See also structure:function, and history Gleick, James, 65, 141, 151, See also chaos; flocking and schooling global warming. See climate change globalization, 182, 185, 199, 245, 250, 252, 271 Gnosticism, 170, 604, 605 God, 49, 58, 160, 226, 228, 229, 234, 236, 239, 241, 243 -World-Human triad, 56, 120, 202, 227 Gödel’s Theorem, 63, 230, 320, 338, 367, 600 Golden Rule, 440, See also categorical imperative Goldstein, Herbert, 75, 135, See also generalized:mechanics

Gould, Stephen J., 243, 576 graph theory, 66, 126, 129, 329, 444, 503, See also hypergraph; centrality:graph Gray, William, 471 great chain of being, 246, See hierarchy:of system types; Boulding, Kenneth Greimas, Algirdas, 315, See also semiotics; tetrad growth and form, xv, 531 logistic curve, 224, 374, 502, 517, 518, 519, 542, 547, 548, 549, 565 vs. development, 70, 510, 511, 517, See also Brinkman, Richard

H Habermas, Jurgen, 236, 599 Hall, Arthur D. and Fagen, Robert E., 301, See system:defined halting problem, 320, 367, See also Gödel’s Theorem Hamburger, Henry, 419, 436, 504, See game theory Hardin, Garrett, 411, 421 Hartley, Ralph, 326, See also uncertainty Hayles, N. Katherine, 218, 340 Hazony, Yoram, 61, 495 Hegel, Georg Wilhelm Friedrich, 60, 118, 197, 202, 233, 258, 315, 323, 609 Heidegger, Martin, 60, 163, 594, 599, See also continental philosophy

Index

Heraclitus, 170 Hesse, Hermann, 241, See also isomorphism; metaphor hexad, 119, 120, 161 hierarchy different kinds of, 108 epistemological. See epistemological:hierarc hy in tetrad, 359, 530, 582 nomic. See hyponomicautonomic-hypernomic triad of categories in Synchronics, 158, 160, 161, 162, 163, 164, 232 of categories of Peirce, 359, See also Peirce, Charles S. of sciences, 43, 66, 80, 136, See also reductionism of scientific categories, 90, 97, 183, 394, 458 of system types, 154, 155, 159, 160, 161, 165, 197, 239, 327, See also Boulding, Kenneth of types of information, 158, 159, 216, 391, 463, 470, 487, See also pragmatic-semanticsyntactic triad vs. network, 445, 446, 447, 448, 451 whole-part, 108, 457, 549, See also mereology; limits of spontaneous complexification Hillman, James, 242, See also Jung, Carl

689

history. See also structure:function, and history historical materialism, 204, See also Marx, Karl ideographic vs. nomothetic views, 120, 121, 122, 211, 516, 522 model of human, 122, 193, 194, 196, 244, 267, 268, 269, 278, 501, 549, 573, See also PI,II,III processes; Armstrong, Karen Hobbesian dilemma, 434, 504, See also game theory:Prisoner's Dilemma holism, 60, 79, 100, 101, 102, 103, 106, 130, 305, 441 Holling, Crawford Stanley, 425 and Gunderson, Lance H., 76, 107, 450, 518, 519, 553, 558, 565, See also adaptive cycle model homeopathic intervention, 416, See also counterintuitive effects; Taoism homogeneity and heterogeneity, 266, 332, 335, 341, 452, 453, 568, See also similarity vs. difference, universality vs. uniqueness Hoos, Ida, 149 Horgan, John, 78 human-centered perspective. See world- vs. humancentered perspectives Hume, David, 54, 94 Huntington, Samuel, 204, 245, See also history:model of human

Index

690

hypergraph, 125, 304, 311, 317, See also graph theory hyponomic-autonomichypernomic triad, 90, 166, 231, 280, 282, See Bennett, John G.

I Ichazo, Oscar, 240, See triad; consciousness; technology ideal types, 257, 456, 516 immune system, 82, 121, 179, 181, 401 incompleteness vs. inconsistency, xiii, xv, 229, 286, 295, 304, 306, 311, 316, 320, 321, 322, 331, 333, 431, 490, 601, See generalized:incompleteness vs. inconsistency information algorithmic, 92, 125, 159, 213, 395, 396, 397, 442, 534, See also Chaitin, Gregory; Kolmogorov, Andrey N. mutual, 325, 333, 483 information theory, xiii, 51, 52, 55, 65, 66, 77, 78, 82, 86, 92, 94, 97, 125, 126, 132, 134, 149, 150, 152, 153, 159, 209, 218, 301, 326, 333, 335, 341, 342, 384, 395, 468, 470, 595 and meaning, 341 quantum, 135 informational parasitism, 171, 183, 264, 266, 458, 459, 475 intelligent design, 219, 244

Internet, 81, 82, 87, 93, 239, 271, 451 Islam, 184, 200, 245, 246, 258 isolated, closed, and open systems, 131, 348, 352, 378, 379, 380, 383, 452, 504, 510, 523, 537, 538, See also thermodynamics isomorphism, 64, 73, 76, 97, 98, 99, 129, 237, 238, 240, 242, 471, 481, See also metaphor

J Jacobs, Jane, 261 Jakobson, Roland, 322, See also semiotics Janus-faced, 82, 299, 363 Jonas, Hans, 99, 135, 137, 217, 231, 388, 604 Judaism, 50, 184, 241, 281, See also Kabbalah; Mussar Jung, Carl, 240, See also Freud, Sigmund; Lacan, Jacques; psychoanalysis

K Kabbalah, 168, 228, 229, 231, 232, 233, 656, See also Judaism; tikkun; tsimtsum Kalton, Michael C., 149, 152 Kant, Immanuel, 47, 48, 56, 58, 61, 70, 157, 216, 357, 434, 436, 440 Kauffman, Stuart, 98, 110, 118, 136, 332, 444, 450, 505, 553, See also actual vs. possible (potential); dynamic system; edge of chaos;

691

Index

generalized:evolution; emergence; Artificial Life Kellert, Stephen H., 70, 135 Kepler, 72, 230 King, Martin Luther, 187, 280 Klir, George, 57, 152, 285, 297, 298, 301, 352, See also reconstructability analysis Knoke, David and Kuklinski, James H., 317, 351 Koestler, Arthur, 82, 230, 299, 363, 406, 530, See also self-assertive vs. integrative tendencies Kolmogorov, Andrey N., 92, 125, 159, 395, See also information:algorithmic Kosko, Bart, 63, See also fuzzy set theory Krippendorff, Klaus, 298, 326, See also reconstructability analysis Kronecker, Leopold, 160, 359 Kuhn, Al, 446, See also system:uncontrolled vs. controlled

L Lacan, Jacques, 468, 470, See also Freud, Sigmund; Jung, Carl; psychoanalysis Langton, Christopher, 84, 98, 334, 337, 339, 443, 505, See also edge of chaos; Artificial Life Lanier, Jaron, 458 Lao Tzu, 164, 239, 362, See also Taoism Laplace, Pierre-Simon, 45, 46 Lattice of Structures, 101, 258, 308, 311, 323, 326,

333, 337, 358, 510, 538, 540, 542, See also hypergraph; reconstructability analysis Law of Requisite Variety, 77, 342, 384, 385, 386, 408, 594, See also regulation:causecontrolled; Ashby, W. Ross leading part, 104, 257, 317, 529, See also von Bertalanffy, Ludwig; fundamentalism Leibniz, Gottfried Wilhelm, 231, 232, 362, 559 Lendaris, George G., 300, 467, See also dynamic programming:approximate; systems analysis Lenin, Vladimir I., 606 Leontief, Wassily, 510, See also growth:vs. development Levenson, Jon, 228, 239, See also Bible Levinas, Emmanuel, 168, 610 Levins, Richard, 449, 597, 598 Levi-Strauss, Claude, 210, 323, See also structuralism Lewontin, Richard, 597, 598 Libchaber, Albert, 70 liberty, 274, 275, 276, 277 Lilienfeld, Robert, 144, 149, 219 limits of spontaneous complexification, xiv, 45, 75, 108, 193, 194, 198, 513, 544, 548, 549 Lindgren, Kristian, 576, See generalized:evolution; Artificial Life

Index

692

Linstone, Harold, 455, See also systems analysis living systems theory, 401, See also Miller, James G. logic, 63, 78, 281, 311, 314, 315, 347, 599 logical depth, 395, 444, See also Bennett, Charles logistic equation continuous, 517, See also growth; logistic curve discrete, 339, See also chaos Lovell, Byrne, 408, See also decision theory Luhmann, Niklas, 125, 263, 532, 602 Luria, Isaac, 228, 229, 231, 232, See also Kabbalah; tsimtsum; tikkun Lyotard, Jean-Francois, 554

M MacLean, Paul D., 467 Mandelbrot, Benoit, 353, See also fractals Margalef, Ramon, 189, 459, 569, See also exploitation marked vs. unmarked terms, 322, 323, 334, 337, 340, 347, 356, 359, 361, 446, 457, 492, 524, 537, 587, 599, See also Jakobson, Roland; binary oppositions; dyad; yin and yang Marx, Karl, 118, 122, 204, 233, 247, 542 Marxism, 200, 219, 254, 257, 272, 314, 560, 598 Mattesich, Richard, 99, 142

Maturana, Umberto and Varela, Francisco, 100, 157, 393, See also autopoiesis and Uribe, Ricardo, 503 May, Robert, 143, 144, 449 McNamara, Robert, 168, See also systems analysis Meadows, Donella H. and Dennis L., 248 meme, 87, 239, 475 mereology, 69, 107, 108, See also whole vs. parts; hierarchy:whole-part Mesarovic, Mihajlo D., 321 metabolism, 90, 393, 503, See also generalized: metabolism meta-narratives, 205, 220, 283, 284 metaphor, 84, 89, 131, 138, 174, 215, 232, 240, 249, 320, 368, 395, 396, 500, 575, 580, 592, 596, 597, See also isomorphism metaphysician’s desk manual, xv, 2, 154, 173, 174, 190, 279, 593, 594, 603, 606, 608 metaphysics, exact and scientific (ESM), x, 39, 43, 55, 58, 59, 61, 63, 65, 66, 69, 70, 71, 73, 76, 78, 92, 123, 127, 137, 139, 140, 141, 143, 144, 149, 150, 151, 153, 155, 162, 165, 191, 209, 219, 226, 239, 244, 282, 283, 351, 595, See also Bunge, Mario Midgley, Mary, 43, 217, 221, 234 Mill, John Stuart, 94

693

Index

Miller, James G., 85, 89, 139, 152, 350, 378, 383, 401, 446, See also living systems theory Milsum, John H., 400, 425 Minsky, Marvin, 472, See also Artificial Intelligence Mitchell, Melanie, 54, 78, 149, 152, 424, 483, See also genetic algorithm; metaphor; complex systems; computer simulation; network:neural Mobus, George E., 149, 152, See also systems science; systems engineering modeling subsystem, 57, 96, 113, 115, 162, 165, 183, 303, 316, 438, 461, 462, 463, 464, 465, 466, 471, 472, 473, 474, 475, 477, 478, 481, 482, 483, 486, 488, 489, 490, 498, 501, 580, 581, 582 modernity, 177, 196, 201, 202, 204, 206, 245, 246 modernization, 245, 246, 247, 256, 269, 270, 271 monad, 111, 161, 164, 312, 345, 347, 359, 360, 362, 473, 497, 524 Morinis, Alan, 241, See also Mussar Murdoch, Iris, 62, 344 Mussar, 206, 241, See also Pirke Avot; Morinis, Alan

N natural selection, 96, 113, 137, 336, 478, 582, See also generalized:evolution Needham, Joseph, 240

Neiman, Susan, 231, See evil; theodicy neoliberalism, 187, 258 network. See also graph theory; hypergraph neural, 140, 467, 480 scale-free, 83, 104, 450, 451, 529, 551, 553 small world, 450 theory. See graph theory Newton, Isaac, 58, 61, 75, 122 Nietzsche, Friedrich, 118, 338 nominal variables, 83, 126, 296, 321, 326, 327 nominalism vs. realism, 213, 350

O ontological, 49, 168, 237, 461 parity, 49, 50, 97 vs. epistemological, 44, 48, 91, 99, 173, 390 vs. ontic, 163, 362, 376, See also Heidegger, Martin ontology of problems, xi, xii, xiii, xiv, 39, 168, 169, 171, 173, 174, 175, 190, 191, 226, 227, 232, 273, 279, 281, 295, 591, 596, 605, 606, 607, 608, 609, 610 open systems, 59, 101, 125, 156, 240, 369, 381, See also isolated, closed, and open systems; thermodynamics; Prigogine, Ilya far from equilibrium, 87, 98, 132, 214, 383, 504, 538, 551 open vs. closed systems views, 111, 112, 211, 298, 299,

Index

694

300, 301, 306, 307, 319, 323, 327, 345, 348, 356, 363, 370, 397, 454, 498, 499, 588, 589 operating system, 161, 166, 271, 459 Operations Research, 141, 145, 608, See also systems analysis optimization, 82, 145, 172, 216, 264, 277, 322, 404, 408, 424, 434, 459, 483, See also Pareto-optimality; suboptimality global, 383, 424, See also genetic algorithm; simulated annealing order through fluctuations, 214, 510, See also dissipative system; Prigogine, Ilya organizing principle, 39, 45, 135, 147, 153, 154, 160, 169, 178, 186, 191, 194, 259, 295, 303, 306, 311, 316, 340, 341, 349, 351, 356, 369, 377, 381, 394, 396, 397, 398, 445, 448, 456, 502, 508, 514, 516, 517, 522, 535, 545, 546, 547, 549, 555, 560, 583, 587 original sin, 169, 229, 588, 609 overshoot, 188, 387, 413, 415, 518, 559, 565

P Padulo, Louis and Arbib, Michael A., 149 panarchy, 519, See also Holling, Crawford

Stanley:and Gunderson, Lance H. pandemic, 178, 179, 182, 185, 186, 203, 225, 244, 526, See also viruses paradox, 216, 399, 415, 416, 523, See also counterintuitive effects Pareto-optimality, 233, 280, 419, 420, 427, 430, 433, 511, See also suboptimality; optimization Parisi, Giorgio, 70 Parsons, Talcott, 114, 125, 145, 252, 253, 254, 257, 263, 266, 268, 269, 276, 428, 448, 466, 492, 530, 582, See also tetrad Pascal, Blaise, 141 path analysis, 319, 413 path dependence, 420, 567, 585 Pattee, Howard H., 392, See also boundary:conditions; pragmatic-semanticsyntactic triad Peirce, Charles S., 55, 161, 164, 323, 359, 361, 471, 473, See also Firstness, Secondness, Thirdness; metaphysics, exact and scientific (ESM); semiotics pentad, 40, 96, 161, 266, 428, 429, 512 phase transition, 132, 376, 443, 502, 503 PI,II,III processes, 197, 203, 207, 244, 245, 250, 254, 256, 258, 259, 264, See also history:model of human

695

Index

Piaget, Jean, 114, 470, 480, See also modeling subsystem Pinker, Steven, 115 Pirke Avot, ix, 206, 281, See also Mussar Planck’s constant, 133, 134, 335, See also quantum theory Plato, 46, 80, 81, 86, 129, 230, 478, 522, 596 Platt, John, 270, 543, 566 polarization, 540, 570, See also catastrophe theory:cusp catastrophe; feedback:positive Popper, Karl, 61, 78 population human, 199, 248, 251, 271 vs. individual, 65, 96, 138, 157, 159, 166, 213, 302, 311, 325, 331, 343, 385, 396, 399, 408, 441, 446, 447, 462, 505, 517, 568, 576, 578, 579, 580, 587 post-modernism, 87, 202, 205, 219, 220, See also continental philosophy post-structuralism, 220, 356, 499, 587, See also continental philosophy Pouvreau, David, 168 power law, 354, 450, 451, 553, See also selforganized criticality; edge of chaos pragmatic-semantic-syntactic triad, 62, 109, 391, 392, 393, 465, 468, 469, 470, 471, 479, 484, 581, See also Weaver, Warren;

hierarchy:of types of information Prigogine, Ilya, 125, 132, 383, 504, 508, See also forces and fluxes; dissipative systems; disequilibrium; order through fluctuations Prisoner’s Dilemma. See Game theory: Prisoner's Dilemma process description, 159, 395, 534, See also state vs. process description progressive centralization, 448, 530, 540, See also von Bertalanffy, Ludwig progressive segregation, 536, 537, 539, 540, 585 progressive segregation vs. systematization, 535, 537, 538, See also von Bertalanffy, Ludwig progressive systematization, 541 psychoanalysis, 118, 219, 474, See also Freud, Sigmund; Jung, Carl; Lacan, Jacques punctuated equilibria, 224, 576, See dynamic system; generalized:evolution purpose, xiv, 49, 59, 90, 109, 114, 142, 145, 146, 195, 197, 216, 217, 231, 239, 296, 351, 371, 388, 426, 465, 596 Pythagoras, 81, 170, 237

Q quantum theory, 44, 45, 46, 59, 78, 83, 106, 121, 133, 210, 235, 237, 314, 358,

Index

696

See also information theory:quantum Quine, Willard Van Orman, 63, 174

R racism, 187, 202, 220, 258, 271 Rapoport, Anatol, 52, 63, 139, 432, See also game theory and Chammah, A.M., 433 Ray, Thomas, 459, 576, See also Tierra; Artificial Life reconstructability analysis, 60, 326, See also Ashby, W. Ross; Klir, George; Krippendorff, Klaus; Lattice of Structures; decomposability reductionism, x, 44, 48, 80, 101, 107, 108, 111, 114, 130, 136, 164, 200, 227, 232, 236, 258, 272, 282, See also fundamentalism regulation, 71, 81, 104, 114, 150, 183, 254, 260, 261, 453, 458, 459, 464, 465, 467, 469, 530, 582, See also control theory; feedback; stability cause-controlled, 104, 384, 385, 388, 396, 479, 582 error-controlled, 104, 384, 386, 388, 447, 479 hunt and stick, 388, 582 relation as constraint, 92, 102, 159, 299, 301, 321, 324, 325, 364, 442, 453, 497 defined set-theoretically, 331

external, 355, 356, 364, 370, 371, 398 higher vs. lower ordinality, 101, 105, 233, 304, 305, 333, 334, 369, 442, 495, 536, 539 internal, 348, 356, 365, 371 nonlinear, 53, 101, 102, 103, 326 static vs. dynamic, 156, 308, 327, 512 resilience, 102, 186, 423, 424, 425, 519, See also Holling, Crawford Stanley; stability Reynolds, Craig, 141, See also computer simulation:boids Rheingold, Howard, 458 rhetoric, 1, 592, 598, 599 risk, 178, 180, 377, 406, 408, 423, 469 Robertshaw, Joseph, 418 Rosenstock-Huessy, Eugen, 476, See also double cone diagram Rosenthal, David, 487, See also consciousness Rosenzweig, Franz, 56, 119, 202, 205, 227, See also God:-World-Human triad; hexad Rosenzweig, Michael, 415 Ross, Don, 116 Ross, Stephen David, 49, 97 Rothstein, Edward, 596 Rutherford, Ernest, 130

S Sacks, Rabbi Lord Jonathan, 50 satisficing, 180, 404, 408, 607, See also optimization;

Index

bounded rationality; Simon, Herbert A. Sayama, Hiroki, 152 scale, 49, 50, 107, 108, 112, 114, 117, 157, 167, 195, 210, 224, 240, 254, 262, 263, 266, 267, 299, 300, 319, 335, 347, 351, 353, 354, 362, 368, 415, 421, 439, 440, 453, 519, 531, 551, 553, 566 -free networks. See networks, scale-free multi, 98, 101, 107, 152, 336 Scholem, Gershom, 228, See also Kabbalah Schopenhauer, Arthur, 58 Schrödinger, Irwin, 335 Second Law of Thermodynamics, 131, 132, 133, 378, 379, 504, 523, 563, 589, See also thermodynamics Second Order Cybernetics, 133, 461, 603, See also von Foerster, Heinz, See also cybernetics self-assertive vs. integrative tendencies, 363, See also Koestler, Arthur self-organization, 53, 71, 99, 124, 128, 141, 157, 173, 195, 314, 401, 502, 503, 543, 544, 545, 546 self-organized criticality, 76, 83, 98, See also Bak, Per self-reference, 133, 314, 320, 463, 486, 487, 603 semiotics, 92, 218, 220, 315, 391, 392, 471, See also de Saussure, Ferdinand;

697

Jakobson, Roland; Peirce, Charles S.; structuralism Senge, Peter, 145, See also system dynamics; ontology of problems; systems analysis set theory, 126, 129, 325, 337, 353, 595, See also fuzzy set theory Shannon, Claude, 86, 132, 335, 395, 601, See also information theory and Weaver, Warren, 52, 65, 92, 342, 468 similarity vs. difference, 50, 79, 80, 90, 93, 97, 100, 111, 135, 144, 155, 171, 211, 212, 215, 231, 283, 303, 353, 359, 362, 390, 427, 452, 500, 544, See also universality vs. uniqueness Simon, Herbert A., 47, 53, 107, 125, 139, 145, 150, 348, 457, 532, 540, 543, 550, See also satisficing; bounded rationality; decomposability:partial Sims, Karl, 141, See Artificial Life; computer simulation simulated annealing, 132, 383, 424, See optimization:global Smale, Steven, 321, 367, See also dynamic system:nonlinear Smith, Adam, 94 Snow, Charles Percy, 48, 131, 268 special relativity, 44, 59, 68, 134 Spencer, Herbert, 411

698

Spencer-Brown, George, 59, 215, 314, 322, 345, 347, 358, 361, 600, See system:environment distinction; logic Spengler, Oswald, 122 Spinoza, Baruch, 47, 81, 105, 110, 157, 167, 168, 214, 219, 226, 481, 588 stability, 71, 172, 173, 249, 373, 374, 376, 379, 444, 447, 449, 499, 500, 512, 534, 543, 551, See also dynamic system; regulation meta-, 313 structural, 375, 425, See also catastrophe theory state description, 159, 395, 442, 444 vs. process description, 92, 125, 308, 327, 365, 395, 532 statistical mechanics, 86, 92, 97, 98, 130, 132, 133, 134, 150, 335, 366 Steiner, George, 46 Stoicism, 200, 605 structuralism, 92, 114, 218, 323, See also Levi-Strauss, Claude; semiotics structure, 89, 185, 308, 371, 397, 404, 405, 442, 448, 454, 491, 510, 512, 577 and function, xi, xiv, 49, 106, 109, 111, 114, 115, 116, 118, 119, 120, 122, 158, 161, 162, 171, 193, 212, 220, 232, 285, 295, 298, 300, 316, 319, 345, 346, 356, 358, 369, 370, 397, 398,

Index

453, 454, 464, 470, 476, 491, 501 function, and history, xiv, 48, 60, 100, 101, 109, 116, 117, 118, 122, 136, 193, 210, 285, 467, 499, 516 loops, 309 stuff-free perspective, 79, 83, 84, 85, 89, 92, 93, 135, 140, 141, See also Bunge, Mario suboptimality, 180, 423, 434, 566, See also optimization; Pareto-optimality superadditivity, 365, 431, 505, See whole vs. parts; game theory:coalition theory support variable, 297, 302, 311, 312, 327, 357, 476, 539, See also extension sustainability, 188, 199, 247, 248, 249, 250, 251, 252, 565, 585 symmetry, 79, 135, 318, 347, 457 breaking, 50, 106, 130, 135, 322, 323, 347, 436, 504 synergy, 305, 341, 538, See also game theory:zero-sum vs. non zero-sum system and 'being', 163, See also Heidegger, Martin as order, 295, 344, 496, 497 defined, 108, 295, 296, 297, 303, 313, 351, 357, 444, 454, 491, 496, 502, 544 directed vs. neutral, 297, 305, 309, 311, 317,

699

Index

327, 334, 396, 414, 532, 533 -environment distinction, 161, 296, 316, 344, 345, 346, 348, 350, 353, 363, 367, 491, 496, 497, 585 formation, 71, 167, 194, 198, 200, 201, 206, 222, 228, 239, 285, 463, 496, 497, 498, 499, 500, 502, 505, 527, 543, 545, 546, 548, 550, 563, 584, 588 uncontrolled vs. controlled, 263, 388, 446, 447, 510, 539 system dynamics, 107, 145, 248, 375, 415, See also computer simulation systems analysis, 141, 142, 143, 144, 145, 149, 151, 167, 168, 171, 219, 351, 497, 533, 605, 607 systems engineering, x, 141, 174, 533 systems science, 151, See also general systems theory; systems analysis, Operations Research

T t'ai chi, 240, 599 Taoism, 201, 229, 240, 314, 361, 362, 416 technology, 68, 92, 131, 141, 208, 221, 240, 264 Teilhard de Chardin, Pierre, 87, 239, 271 tetrad, 94, 95, 96, 109, 145, 146, 161, 253, 254, 256, 257, 266, 267, 272, 276,

304, 310, 316, 385, 386, 405, 420, 426, 465, 466, 467, 472, 512, 525, 536, 582 theodicy, 174, 226, 227, 228, 229, 231, 234, 281, 607, See evil; ontology of problems; Neiman, Susan theory of everything (TOE), ix, x, xiii, 39, 46, 47, 49, 57, 58, 79, 130, 131, 136, 208, 209, 282, See also metaphysics, exact and scientific (ESM) thermodynamics, xiii, 66, 78, 86, 91, 93, 95, 97, 115, 116, 121, 130, 131, 132, 133, 134, 218, 260, 329, 334, 335, 336, 348, 349, 350, 352, 366, 378, 380, 381, 504, 507, 508, 509, 563, 564, 584, 585, See also Prigogine, Ilya; statistical mechanics Thom, Rene, 375, 514, 523, 584, See also catastrophe theory; Zeeman, Erik Christopher Tierra, 459, See also Ray, Thomas; Artificial Life; computer simulation tikkun, 168, 233, 238, 241, 280, 605, 606, See also Kabbalah Toulmin, Stephen, 43, 61 Toynbee, Arnold, 122, See history:model of human transdisciplinarity, 63, 65, 123, 127, 602, See metaphysics, exact and scientific (ESM) transformation

Index

700

matter, energy, information, 87, 91, 93, 131, 161, 183, 188, 210, 390, 458, 515 system, 117, 161, 244, 272, 502, 505, 513, 514, 547, 555, 558, 584 to modernity, 196, 201, 204, See history:model of human; Armstrong, Karen; PI,II,III processes triad, 56, 62, 79, 88, 90, 91, 93, 94, 117, 119, 145, 161, 163, 164, 166, 202, 239, 256, 266, 276, 285, 297, 299, 301, 303, 304, 305, 308, 315, 316, 360, 361, 362, 369, 396, 427, 454, 466, 467, 471, 473, 494, 519, 559, 569 Troncale, Len, 155, 174, See also ontology of problems; isomorphism truth, conceptions of, 60, 61, 78, 190, 600 tsimtsum, 228, 362, See also Kabbalah

U uncertainty, 132, 134, 325, 326, 327, 332, 333, 334, 335, 336, 341, 352, 361, 364, 378, 385, 395, 403, 442, 453, 601, See also entropy Unger, Roberto Mangabeira, 178, 560 unintended consequences, 105, 273, 413, See also counterintuitive effects

uniqueness, 97, 121, 441, 445, See also universality vs. uniqueness unity of science, 44, 45, 47, 52, 151, 208, 209 unity vs. multiplicity, 172, 239, 295, 302, 323, 340, 491 universality (as a principle of physics), 84, 132 universality vs. uniqueness, 137, 144, 241, 283, 427, 441, 445, 495, 609, See also similarity vs. difference

V Varela, Francisco, 314, See also Maturana, Umberto and Varela, Francisco; autopoiesis; logic variety and constraint, 222, 314, 331, 334, 341 vicarious rationality, 96, 582 testability, 62, 77, 594, See also Bunge, Mario virus, 78, 172, 181, 429, 458, 459, See also pandemic; informational parasitism vitalism, 100, 244 Voltaire, 233 von Bertalanffy, Ludwig, 52, 63, 66, 75, 104, 121, 139, 143, 149, 168, 351, 448, 529, 530, 539, 541, See also general systems theory; leading part; progressive centralization; progressive segregation, systematization

701

Index

von Foerster, Heinz, 133, See also Second Order Cybernetics von Goethe, Johann Wolfgang, 60, 61 von Neumann, John and Morgenstern, Oskar, 52, 94, 95, 139, 403, 429, See also game theory; decision theory

W Waddington, Conrad H., 534, 577 Wakeland, Wayne, 145, 180, See also systems analysis; systems engineering; computer simulation; system dynamics; agentbased modeling Walker, Crayton C. and Ashby, W. Ross, 339, See also Ashby, W. Ross; chaos Wallerstein, Immanuel, 185, 269, See also center and periphery; exploitation; Marxism Watts, Duncan J., 450, See network:small world Watzlawick, Paul, 416, See also counterintuitive effects Weaver, Warren, 52, 53, 62, 65, 92, 342, 391, 443, 469, 470, See also hierarchy:of types of information; Shannon, Claude Weinberg, Steven, 110, 113, 130, See also reductionism

Whitehead, Alfred North, 68, 127, 230, 327, 378, 522, 584 whole vs. parts, 102, 176, 305, 364, 505, See also mereology; superadditivity; hierarchy:whole-part Whyte, Lancelot Law, 118, 273 Wiener, Norbert, 52, 59, 63, 139, 325, 388, 522, 523, See also cybernetics; control theory; purpose; Augustine:Augustinian vs. Manichean devils Wieseltier, Leon, 243 Wigner, Eugene, 62 Wilde, Oscar, 595 Wilson, Colin, 475, See also informational parasitism Wilson, Edmund, 594, 598 Wilson, Edward O., 138 win-win outcomes, 280, 432, 572, See also Paretooptimality Wittgenstein, Ludwig, 315, 594 Wolfram, Stephen, 84, 125, 127, 151, 164, 327, 339, 443, See also automata, cellular; chaos, edge of; fundamentalism:systems theoretic world- vs. human-centered perspectives, 56, 57, 87, 227, 282, 283, 462, 602, 604, See also Rosenzweig, Franz Wright, Robert, 212, See also synergy; emergence

Index

702

Y yin and yang, 314, 323, 340, 361, 549, See also dyad; binary oppositions Yovel, Yirmiyahu, 202, 315

Z Zadeh, Lofteh, 63, 314, 352, See also fuzzy set theory

Zeeman, Erik Christopher, 107, 514, See Thom Rene; catastrophe theory Zwick, Martin, xiii, 60, 108, 193, 205, 226, 229, 234, 236, 240, 253, 320, 326, 341, 342, 471, 482, 490, 514, 544, 549, 556, 560, 570, 572