Mosaics of Knowledge: Representing Information in the Roman World (Classical Culture and Society) 9780190632502, 019063250X

Table of contents :
Cover
Series
Mosaics of Knowledge
Copyright
Dedication
Contents
List of Figures
List of Tables
List of Plates
Acknowledgments
Plate
A Brief Orientation
1. Lists
Ordered Lists
Indexed Lists
Tables of Contents
Nested Lists
2. Tables and Tabular Organization
Actual Tables
Not Tables
Outliers
Conclusions
3. Weights and Measures
How Does Roman Measurement Work?
Standards and Standardization
Direct Standardization
Indirect Standardization
Complications
Conclusions
Chapter Appendix
4. Representing Three Dimensions
Perspective and the Theory of Space
The Corpora
Space in the Landscapes
Two Comprehensive Examples
Conclusions
5. Representing Two Dimensions
Data Graphics
Plans
What Is a “Map”?
Ancient Maps
Maps as Information Technology
Chapter Appendix
6. Conclusion
Where Are We Now?
Going Forward I: Power and Other Topics
Going Forward II: An IT Revolution in Late Antiquity?
References
Index

Citation preview

Mosaics of Knowledge

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Classical Culture and Society Series Editors Joseph Farrell and Robin Osborne Emotion, Restraint, and Community in Ancient Rome Robert A. Kaster Making Mockery: The Poetics of Ancient Satire Ralph M. Rosen Readers and Reading Culture in the High Roman Empire: A Study in Elite Communities William A. Johnson Apollonius of Rhodes and the Spaces of Hellenism William G. Thalmann The Captor’s Image: Greek Culture in Roman Ecphrasis Basil Dufallo Aratus and the Astronomical Tradition Emma Gee Gift and Gain: How Money Transformed Ancient Rome Neil Coffee Mosaics of Knowledge: Representing Information in the Roman World Andrew M. Riggsby

Mosaics of Knowledge Representing Information in the Roman World Andrew M. Riggsby

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1 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2019 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. CIP data is on file at the Library of Congress ISBN 978–​0–​19–​063250–​2 9 8 7 6 5 4 3 2 1 Printed by Sheridan Books, Inc., United States of America

For Mom and Dad

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CONTENTS List of Figures  ix List of Tables  xi List of Plates  xiii Acknowledgments  xv

A Brief Orientation  1 1. Lists  10 Ordered Lists  11 Indexed Lists  15 Tables of Contents  22 Nested Lists  29

2. Tables and Tabular Organization  42 Actual Tables  50 Not Tables  54 Outliers  70 Conclusions  73

3. Weights and Measures  83 How Does Roman Measurement Work?  85 Standards and Standardization  100 Direct Standardization  107 Indirect Standardization  115 Complications  120 Conclusions  125 Chapter Appendix  129

4. Representing Three Dimensions  130 Perspective and the Theory of Space  131 The Corpora  135 Space in the Landscapes  138 Two Comprehensive Examples  147 Conclusions  149

5. Representing Two Dimensions  154 Data Graphics  154 Plans  164

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What Is a “Map”?  172 Ancient Maps  180 Maps as Information Technology  194 Chapter Appendix  201

6. Conclusion  203 Where Are We Now?  203 Going Forward I: Power and Other Topics  210 Going Forward II: An IT Revolution in Late Antiquity?  216 References  223 Index  245

FIGURES 1.1 Supposed theater token from Pompeii  32 1.2 Supposed amphitheater token from Arles  33 1.3 Inscription on a theater seat from Verona; token from the amphitheater at Frosinone  35 2.1 Organization of status theory  43 2.2 Schematic diagram of Roman centuriation  50 2.3 Military duty roster from Egypt  53 2.4 Military duty roster from Egypt  54 2.5 Victorius, Calculus 63 4.1 Landscape from the columbarium of Villa Doria Pamphilj  142 4.2 Landscape from room 14, Villa A, Oplontis  143 4.3 Landscape from the villa under the Farnesina  145 4.4 Fall of Icarus 153 5.1 Roman portable sundial  156 5.2 Schematic illustration from a land-​surveying manual  158 5.3 More naturalistic illustration from a land-​surveying manual  158 5.4 Inscription detailing rights to draw water  159 5.5 Inscription showing plans for the funerary complex of Claudia Peloris and Ti. Claudius Eutychus  166 5.6 “Map” from Dura Europos  173 5.7 Population-​adjusted map illustrating the outcome of the 2016 U.S. presidential election  174 5.8 Stylized map illustrating the outcome of the 2016 U.S. presidential election 175 5.9 Network rendering of places named in Caesar  178 5.10 Schematic, two-​dimensional rendering of places named in Caesar  179 5.11 Forma Urbis Romae, detail  182 5.12 Forma Urbis Romae, detail  182 5.13 Scale of FUR implied by individual comparisons with modern measurement and magnitude of each measurement  183 5.14 Fragment of inscribed map depicting the centuriation at Arausio  187 5.15 Tabula Peutingeriana, detail  192 5.16 Tabula Peutingeriana, detail  192 6.1 Jerome, Chronicle 219

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TABLES 1.1 Early references to the supposed Arles amphitheater token  34 1.2 Supposed form of reference to a centralized catalog of Roman public statuary 39 1.3 Data about three American cities, arranged in tabular form  41 2.1 Varro illustrates linked proportions with numbers  52 2.2 Varro uses linked proportions to structure the declension of an adjective 52 2.3 Modern declension of the phrase hic Marcus 59 3.1 Multiple meanings of symbols used in systems of measurement  92 3.2 Variations in actual weights with respect to presumed standard values  103 3.3 References to measured lots of grain in TPSulp 117 3.4 Standard reference values for several Roman units of measurement  129 5.1 Concordance of Roman building plans  202

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PLATES 1 2 3 4 5 6 7 8

Fasti Amiternini, with color coding  Riot in the Amphitheater, Pompeii  Landscape from the columbarium of Villa Doria Pamphilj  Landscape from the villa under the Farnesina, walkway  Landscape from the villa under the Farnesina, cubiculum  Landscape from a villa at Boscotrecase  Landscape from the villa under the Farnesina, triclinium  Fragment of marble map of Rome (“via Anicia” fragment) 

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ACKNOWLEDGMENTS This project, at least some parts of it, dates back a long time. The seminar alluded to at the beginning of chapter 2 was offered in the late 1990s, and I suspect that some of the thoughts here probably first arose before I finished graduate school, while I was reading Edward Tufte’s books from my mother’s book shelf. I have acquired an unusually large number of scholarly debts over that time (and unfortunately have doubtless forgotten others equally important). I got particularly extensive assistance and commentary from Klaus Geus, Paul Keyser, Michael Koortbojian, Rabun Taylor, and the readers for Oxford University Press. Tony Corbeill, Serafina Cuomo, Tony Grafton, Joseph Howley, Nate Jones, Stephanie Frampton, John Clarke, Eric Orlin, Liz Robinson, Philip Stinson, and Tyler Travillian all read and commented on chapters in draft. I  have also gotten other help, particularly in the form of penetrating questions or advance access to work in progress from Dorian Borbonus, Alan Cameron, C. Michael Chin, Megan Goldman-Petri, Julia Hejduk, Alexander Jones, Duncan McRae, Reviel Netz, Carlos Noreña, Laura Novick, Dan-el Padilla Peralta, Tim Parkin, J.-B. Piggin, Phil Resnik and Jiesi Shi, Jane Sancinito, Josh Sosin, and a seminar which covered this material (Gabrielle Bouzigard, Timothy Corcoran, Eli Fleming, Vera Leh, Will Shrout, and Alain Zaramian). I  would also like to thank audiences at Brown, Chicago, Columbia, Duke, Johns Hopkins, Maryland-Baltimore County, Minnesota, NYU, North Carolina, Penn, Princeton, Texas Tech, Yale, and the Finnish Institute in Rome for subjecting various parts of the argument to friendly scrutiny. And, of course, I need to thank Joe Farrell, the series editor, and Stefan Vranka, the sponsoring editor, for their interest, encouragement, and assistance in transforming the “project” into an actual book. Finally, I would particularly like to signal the role in this project of my ongoing interaction with two younger scholars. Seth Bernard and Sarah Bond in their distinct, inimitable ways provided a stream of questions, prods, prompts, and problems and materials to work with. A project of this scope necessarily relies on the kindness of strangers to have any hope of reaching the necessary breadth, but even beyond that the constant presence of these two kept me honest and on my toes. While I have been working on parts of this project for many years, the core of the research and writing took place over two academic years, and I am more than happy to thank the funding entities that made that possible. In 2010–11, I  held the NEH/Roger A.  Hornsby Rome Prize at the American Academy in Rome. In addition to the scholars named earlier, I  must thank the Academy for both the

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xvi { Acknowledgments Fellowship and the atmosphere uniquely hospitable to scholarship. Then in 2013–​ 14, I  was the Stanley Kelley Jr. Visiting Professor for Distinguished Teaching at Princeton, a position which (perhaps ironically) carries quite modest teaching responsibilities and which in turn allowed me to take advantage of the remarkable research resources there. My thanks go to the University, the Classics Department, and to Andrew Feldherr, who brought it all together. I also need to thank several institutions which supplied other kinds of intellectual resources. The Soprintendenza Archeologia del Veneto and Dott.ssa Brunella Bruno, the director of its Nucleo Operativo di Verona, were kind enough to allow me direct examination of the two bronze map fragments found there (and discussed in ­chapter 5). The Bodleian Library in Oxford allowed me to inspect their manuscript of Jerome’s Chronicle (discussed in the conclusion). Bruce Barker-​Benfield, Senior Assistant Librarian in the Department of Special Collections and Western Manuscripts there, was particularly generous with his time and expertise in discussing the manuscript with me, and I hope to be able to publish further fruits of those discussions in due course. The Bibliothèque municipale d'Avignon provided images of an extremely rare volume on the antiquities of Arles. Finally, I (as every academic) must thank the library staff at my home institution, especially Shiela Winchester, the Classics bibliographer, and the InterLibrary Services Department for providing (and often finding) an endless supply of research materials. Kristina Schlegel did all the original drawings masterfully. Andrea Pittard provided assistance with the manuscript and bibliography. Khoa Tran did heroic work with image permissions. C. Berglie, the copy editor, had to deal with a rat’s nest of references. It would probably not have been possible for me to write this book a decade earlier. Modern information technology made it possible for me to gather the kind of scattered evidence it relies on and to move into several areas that were previously unfamiliar to me. At the same time, it relied on the serendipity provided by traditional library shelving, and I fear that in another decade or so it will again be impossible to write a book of this sort, where the objects of inquiry and sources of evidence were not givens from the beginning. My wife, Lisa Sandberg, once again brought her formidable editing skills to bear to grant this book such readability as it has, despite being subjected to the interminable process through which I brought the framework together. My father was a scientist with a strong amateur interest in premodern history, and was happy that he was able to read this whole book in manuscript before his death. And even before learning of her career as a computer programmer, one could spot my mother’s interest in data and design from the way she puts together a quilt. It is to them that this book is dedicated.

DeA Picture Library, licensed by Alinari

Plate 1   Fasti Amiternini. Color coding indicates categories of information



© Vanni Archive/​Art Resource, New York

Plate 2   Riot in the Amphitheater (Pompeii, now in the Museo Archeologico Nazionale, Naples)

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Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

Plate 3   Landscape from the columbarium of the Villa Doria Pamphilj (A/​XII)

Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

Plate 4   Landscape from the villa under the Farnesina, walkway F-​G (inv. 1233)

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Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

Plate 5   Landscape from the villa under the Farnesina, cubiculum D (inv. 1037)

© Marie-​Lan Nguyen /​Wikimedia Commons, used by permission

Plate 6   Landscape from a villa at Boscotrecase

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Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

Plate 7   Landscape from the villa under the Farnesina, triclinium C (inv. 1080)

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Plate 8   Fragment of a marble map of Rome (the “via Anicia” fragment) Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

A Brief Orientation

This book investigates information technologies in the classical Roman world—​ their invention, diffusion, and use, and the interactions among those processes. The focus is on conceptual developments—​e.g., “mapping,” “weighing,” “listing”—​ rather than material ones—​e.g., “codex,” “abacus.” (Within the area covered, however, the interaction of concepts with the materiality of their actual uses will be a recurring theme.) It also focuses principally on “high” technologies rather than, say, literacy or numeracy in general. Perhaps paradoxically, this will end up setting the book against most work to date on classical knowledge regimes. Scholarship has typically dealt with intra-​elite and largely discursive phenomena. As a result, we know a good deal about the intellectual history of antiquity’s formalized disciplines (e.g., rhetoric, philosophy, law, literature, grammar) and how they competed with and inflected one another. By contrast, my goal is to uncover an alternative set of regimes which were generally not theorized in antiquity, but which informed the practices of daily life, and did so in a broad variety of social locations (even if some had elite origins). These turn out to include relatively advanced technologies like complicated lists, tables, and textual illustrations. While most of the book will be about technologies that were “advanced” in their time, I want to begin with a brief narrative of the study of a more basic one: literacy. Until a few decades ago it was a commonly, if not universally, held view that the ability to read and write was widespread in the Roman world, not different at least in kind from advanced nations in the modern world. This changed dramatically with the publication in 1989 of William Harris’ Ancient Literacy. Harris deployed comparative evidence to argue that such mass literacy could only exist in contexts that met a number of social and institutional prerequisites—​systematic education, broad economic advantages that flow only to the literate, and the like—​then showed systematically that almost none of this was true anywhere in the classical world. On this basis he then projected rough literacy rates on the order of 1% to 30% at various times and places within that world. Much of the response to Harris has been accepting, if slightly more “optimistic,” at least on a local level. That is, scholars

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2 { Mosaics of Knowledge have been more willing to see social and institutional supports for literacy, even if they take different forms than modern ones and even if they only create larger pockets of literacy rather than universalizing it. But the real differences lie not in tweaking Harris’ numbers but in adding to his stock of questions and localizing their answers. There has been an increasing analytic interest in what might be called, in the plural of the title of Johnson and Parker’s 2009 book, Ancient Literacies. That is, with the basic quantitative picture already in place, interest has shifted to more qualitative questions of how reading and writing skills (and, to a lesser extent, numeracy) were employed by individuals in particular contexts. What kind of information, Woolf 2009 asks, would labels on commercial olive oil jars in their highly stereotyped format have been able to convey to “readers” in the industry, who might not be fully literate in general terms and might not even be Latin speakers? Or what, Beard 1991 considers, is the motivating effect of rituals that mediated access to the divine through writing? I tell this story, which will already be familiar to many readers, because it has multiple resonances with the unfamiliar story I will tell in the body of this book. First, I hope also to make modern states of affairs seem less natural. One reason (though not, of course, the only one) it was easy to accept a highly literate antiquity was the ease with which reading comes to individuals today. It does not then feel like a very strong claim to extend that across an entire society, though in fact it is. The information technologies discussed in this book—​things like numbered lists, numerical tables, or mechanical weights and measures—​offer a similar temptation. Their use comes so naturally to anyone acculturated in the modern world that we are likely to take it for granted that they were available in the ancient world as well. Most insidiously, something merely similar to a modern device can readily be taken for fully identical. Additionally, however, I would like to try to borrow some of the qualitative focus that characterizes much of the response to Ancient Literacy. That is, I ask not just how often Romans used various technologies but also when, how, and why. Those contextual questions are probably good historical practice in general, but they strike me as particularly urgent in this specific area of technology. As it happens, most of the information technologies discussed here were not huge successes that spread through the Roman world in the way, say, blown glass or concrete construction did. But the reason I can talk about them at length is that they were at least invented, unlike, say, stainess steel or stirrups. One need not (as most readers probably will not) believe in the necessary “progress” of technology to be puzzled by a lack of eagerness to adopt what were at least technically useful devices. “Why did the Romans use tables or scale representations differently than how we do?” for instance, is interesting because it will likely tell us as much about the Romans in general as about those tables or plans. Different people use technologies for particular purposes in particular circumstances. The question, thus, is almost never whether a particular technology is “good” or “powerful” or “elegant,” or anything else. The issue is whether particular people (or enough of them) find it worthwhile



A Brief Orientation }  3

to acquire that technology for some particular task before them. In a broad sense, we could make this point about any adoption of any technology, but I will argue that Roman cost-​benefit calculations in this respect were particularly strict and particularly local. While I  do not, I  hope, adopt a teleological view of technological change, I  should probably also point out that I  do not hold a purely culturalist view, either (even though the previous paragraph might have been read that way). I don’t think it is meaningful to describe any technology as “good” or “the best,” only good or best for some particular end (which might itself be defined by a complex of mechanical, social, and other aims). However, this does mean that to the extent that we understand those aims, we can say that some technologies are objectively better: they have a lower rate of false positives, they create less pollution, they are cheaper, the hardware is less likely to malfunction, they require fewer (or, if this is what circumstances demand, more numerous) human workers, they channel revenue to a politically powerful class. My account is also imperfectly culturalist because I believe that the invention and diffusion of inventions are path-​dependent. Devices do not simply arise whenever and wherever cultural circumstance might make them desirable. Various material preconditions and contingent discoveries are required. I don’t claim to have proven the truth of this point of view. Rather, I have sketched an approach which will stand or fall depending on how well it actually works throughout the body of the study. Though quite broad, the scope of this book will be limited in two important ways. Chronologically, it will extend, at least in principle, from the earliest Roman times to the year 300 (all dates will be ce unless otherwise noted). Any precise cutoff is of course arbitrary to some extent, but I have chosen this one for several reasons. As a practical matter, going substantially later would have expanded the available evidence too much to be able to handle (the reader will have to decide whether I have already bitten off more than I can chew). A cut-​off around 300 ce also corresponds to a fairly traditional sense of “classical” (that is, non-​Christian) Roman culture. That would not obviously be relevant in itself, but I  suspect that it is connected to another reason for the cut-​off. It appears to me, on the basis of evidence I have admittedly scrutinized less carefully, that there is an information technology revolution in Late Antiquity. There seem to be significant changes to the technologies described in most of my chapters (and the invention of at least one important new one) during roughly the fourth and fifth centuries. I will say a little more about both the shape and the possible reasons (some Christianity-​based) for this revolution in the last chapter, but the topic seems to me to require separate treatment. The end date of 300 will not be applied mechanically. First, evidence from later periods can sometimes be used to cast light on earlier ones. Second, I will be fairly generous in allowing myself to use evidence (especially inscriptions) that is not definitively datable to within my period. The other constraint will also be partial, perhaps even more so. Though I have been speaking (and will continue to do so) of “Roman” information technology, the

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4 { Mosaics of Knowledge focus of some of the chapters will be specifically on the Latin-​speaking world. That is hardly an obvious line to draw in a historical rather than, say, a literary context, so let me say a few words about why a linguistic distinction might be appropriate to the particular topic and in what ways in which this limitation will and will not be observed over the course of the book. Many of the technologies discussed here, especially in those first two chapters, can be seen as specialized forms of literacy. This seems to me to be the central insight of Jack Goody’s famous 1977 book, The Domestication of the Savage Mind, and its chapters on the cognitive operations enabled or encouraged by tables, lists, formulas, and recipes. My subject matter is deeper and narrower than Goody’s, but I also differ from him in one methodological emphasis. He tends to look more at what written technologies can do than what they actually do. The former was important for opening up a field of inquiry in a theoretical kind of way, but the historical specificity that I am aiming for seems to require the latter. Seeing these technologies as an aspect of literacy accounts for a restriction on the scope of this book. Though I will generally speak of “Rome” and “Romans,” my focus will be on the Latin world when the devices in question are used and transmitted by writing, and so we would not necessarily expect them to be constant across linguistic boundaries. Two examples might help show how this linguistic division clearly can work in practice (one is from outside the realm of this study and the other will be treated at length in c­ hapter 2). For the former, I offer the following observation on differences in substance between contracts surviving from Roman Egypt correlated with the language in which they are written (Alonso 2016, 65): [T]‌he contracts concluded by Romans in Greek are usually indistinguishable from those concluded by [non-​citizens]. Vain have been most attempts to identify “Roman” traits in these Greek contracts. Their Latin contracts, instead, which are rather scarce, do adhere to the Roman models both in form and content, even if occasionally with peregrine accretions. The contracts in question, even the ones in Greek, were concluded between Roman citizens. The difference is thus not one of culture in general or even legal culture but, rather, of language. Alonso suggests, plausibly enough, that the key factor was reliance on notaries among the less privileged classes to produce these kinds of documents. The second example has to do with tables (the organizational device, not the piece of furniture). These are not, as it turns out, particularly common in either the Latin-​or Greek-​speaking worlds, though they do appear in certain, very limited contexts. One of those contexts in the Greek world was the display of astronomical data of various sorts. Yet these do not appear in Latin. Roman authors either give (some of) the same information in continuous prose or in lists or, in the extreme case of Vettius Valens (second century), write in Greek themselves. These examples are not meant to show that Latin and Greek information technologies are entirely cut off from each other, a claim that would clearly be false. Rather, I  simply wish to illustrate that there are both theoretical and empirical



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reasons to suspect that there might be a significant level of separation. Nor do I mean to ignore the Greek-​speaking world all together. Most mechanically, there are at least a couple of cases where we have Greek texts that appear to be fairly direct representations of operations of the Roman state originally conducted in Latin (e.g., translations of senatorial decrees, labels on weights authorized by a Roman governor). Though they are rare, I will also record cases where I think direct influence from Greece to Rome can be established (e.g., the introduction of the chronological table). Occasionally, there will be points at which Greek evidence seems to provide an illuminating comparison, if not of a different sort than Mesopotamian cuneiform or Renaissance Italian evidence might offer. Finally, the technologies of c­ hapters 3 through 5 are less clearly tied to writing and so there is less call for a distinction. For instance, I look at weights and measures from across the Roman Empire. Even in those cases, however, the linguistic distinctions can resurface. The most “scientific” tradition of ancient (Mediterranean) mapping, for instance, is closely tied, even subordinate to, written geographical texts, and this may be reflected in broader practice. Greek and Roman practice in textual illustration overlaps in some respects, but contrasts in others. In addition to those restrictions of scope I  should mention what may seem a peculiar feature of many of the arguments. This book discusses devices that I presume will be familiar not only to every reader but also—​with the possible exception of “perspective” in c­ hapter 4—​to their school-​aged children. It may then come as a surprise that in many of the chapters I spend as much time as I do working out definitions of terms like “list,” “table,” and “map.” I will say a few words here about why that is. I do not intend to tease out “what we really mean” by these terms in the manner of an analytic philosopher. Nor do I intend a more historical or philological investigation of the possible semantic range of these English words, though for clarity’s sake I will point out ambiguities that I fear may mislead. Nor do I think that any of these technologies form a “natural kind” like, arguably, “dinosaur” or “proton” or “water.” Nor, finally, am I generally trying to reconstruct ancient Roman conceptual categories. Rather, I  am trying to capture features of Roman practice that line up only approximately with any language’s lexicon. In these cases I have decided that the easiest way forward is not to try the reader with frequent neologisms (“category 1 map,” “category 2 map,” etc.) or circumlocutions (“list-​ whose-​order-​conveys-​information-​to-​the-​intended-​audience” vs. “list-​with-​indices-​ permanently-​attached-​rather-​than-​created-​on-​the-​fly”). I  have chosen instead to use ordinary words that make the general area of interest clear, then to stipulate whatever additional properties are important for my local purpose. I do not defend these definitions as truer than any other. I intend them as useful, however, if they help express significant distinctions in Roman practice. For example, are lists of the types just mentioned restricted to specific use-​contexts? It is also true, however, that there is another, more specific issue at stake, and it is one that systematically results in more complex definitions. This arises from the relation of form and function in the technologies. When definitions have been

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6 { Mosaics of Knowledge offered in this area by others, they have typically been framed in terms of form. What, for instance, does a “table of contents” look like? In the last instance, I am more interested in function instead, but that cannot normally be observed directly. Fortunately, as a practical matter there are nonarbitrary connections between form and function, and in many cases the broader context can help us out. Different ways of organizing data facilitate different operations on those data, and it might be more or less plausible that anyone would need to consult a document in the ways that are theoretically possible. Thus I will integrate ideas of function into the “definitions.” That, however, will mean offering more elaborate specifications of form and context to stand in as proxies for direct observation of function. This is not, as I say, a way of giving a truer definition, nor do I suggest that people who use the words differently in other contexts thereby fall into error. Rather, it is a way of specifying the precise phenomena that I intend to investigate. I am interested, for instance, in which table-​like objects (in a broad, formal sense) serve the functions that are most typically associated with tables. (Those “associations” will generally be established by modern comparative and/​or experimental research.) Which formally map-​like objects can serve map-​related purposes? And so on for other key terms. In most cases, as it happens, the result is that I end up focusing on a narrower range of objects than might be expected, but occasionally (as with the case of maps) I will be arguing on the same basis for taking a broader view than is sometimes taken. For the reader’s convenience I conclude this introduction with a brief survey of the individual chapters.



1. Lists. While simple lists are ubiquitous in the Roman world, this chapter treats only specialized types: tables of contents, alphabetized lists, indexed lists, and nested lists. Each of these is rare and is largely or entirely restricted to quite specific contexts. For instance, tables of contents are used only for miscellanies with little inherent structure, nested lists for large and continuously expanding public records. (In passing, I demonstrate that a number of proposed listing schemes, such as the supposed numbering of theater seats, are mistaken.) These sophisticated list-​forms are used overwhelmingly to confirm or authorize information rather than provide it in the first instance. Moreover, they tend to arise in tandem with some physical process of collecting or sorting data, not merely contemplation of data in the abstract. 2. Tables and Tabular Organization. Tables (in the narrow sense of matrices with meaningful rows and columns) are also vanishingly rare. The chapter contrasts a variety of areas in which they might have been expected but are not in fact found (e.g., grammatical, arithmetical, or calendrical tables) to the few where they are attested (e.g., centuriation formae, military duty rosters). Tables tend to arise only in the context of a combination of circumscribed expert communities of users/​producers; constitution rather than recording of data; contexts in which priority









A Brief Orientation }  7

is given to organization itself over content; and/​or physical or enactive “scaffolding” for cognitive activity. That is, the surprising difficulty of building a table is eased by what cognitive scientists describe as the “off-​ loading” of processing from purely symbolic reasoning to bodily action, especially interaction with the physical world. 3. Weights and Measures. Serafina Cuomo has shown that at least some Roman thinkers about measurement harbored universalizing ambitions—​systems of formal equivalences between numerical quantities that would bypass the particularity of the various objects being measured. I argue that this regime emphatically failed to materialize. Measurement remained a (local) process, rather than a universal “black box” whereby numbers were allowed to stand in for objects. On inspection, many units of measurement turn out to be rough approximations, proportions (rather than absolute values), or not fully realized metonyms (e.g., a literal cup rather than a formally defined volume which shares that name). Neither state regulation nor the pressures of the market required adherence to universal standards, and in fact they would have rendered the notion almost meaningless. In turn, a wide variety of processes (in commerce, construction, recipes) are designed to be locally rather than globally predictable. 4. Representing Three Dimensions. Roman painting, it is rightly agreed, did not use single-​point or other formal perspectival systems. It has been influentially argued, then, that they lacked coherent spatial representation altogether. However, examination of three related sets of “sacro-​idyllic” representations show that they deploy a variety of spatializing tactics instead of a single system; for example, rough scaling and recession, encoding of distance by overlapping and differential shading, cuing by narrative content and by radically perspectival view of certain kinds of objects, and the physical height/​depth of plaster relief. The combination of these features creates a network of connections at a distance which gives three-​dimensional structure to representations even if they cannot be precisely or uniquely reconstructed. They are in this more topological sense “spatial,” even if not narrowly Euclidean. The fact that the sets of tactics overlap but are not the same in the various cases suggests that spatiality is a goal in itself rather than an epiphenomenon of other generic features. 5. Representing Two Dimensions. The chapter focuses on maps, but also examines (as background phenomena) data graphics, textual illustrations, and building plans. I consider issues such as reproducibility, social status, and representational minimalism. The notions of spatial representation developed in the previous chapter, combined with some of the specific features of the secondary technologies listed earlier, allow us to set expectations for what an ancient “map” should have looked like

8

8 { Mosaics of Knowledge



and thus to collect evidence for their limited (but indisputable) patterns of development and use. (The vast majority of the objects discussed in this chapter operate in the titular two dimensions, but there are a few exceptions.) 6. Conclusion. The first section attempts to tie together the content of the main chapters, particularly in terms of the themes listed immediately following. Then I sketch out several areas of related interest that I think are ripe for further inquiry in light of the conclusions of this book.

My subject matter is large and complex, so it should not be surprising that there is no monocausal explanation for the state of Roman information technology. As a result none of the following themes plays a role in every chapter. Still, all recur frequently, and the ensemble, I hope, binds the work together:





• Tolerance and context-​specificity. Roman information systems (e.g.,

volumetric measurement, records of land survey, representations of three dimensions) show in general a remarkable tolerance for error and/​or omission. The particular limits are a function of their use in the context of preconceived target-​tasks for which the information will be “good enough” and without regard for other possible uses or users. Those tasks, in turn, are themselves shaped so that poor-​quality information suffices to complete them. • Recording vs. constitution. Representations can, of course, be used to record facts which have some kind of prior existence (e.g., the list of distances in an itinerary). But they can also be used to bring facts into being (e.g., you cannot serve on a jury until your name appears in the praetor’s album; eligible soldiers are not in fact discharged until the relevant paperwork is completed). Romans are more comfortable in the latter mode than in the former. Moreover, the understanding of many cases hinges on recognition that what appears to be recording in fact hides constitution. So, for instance, Roman tables of contents serve poorly in a pure reference function, but make much more sense if they are read to create segmentation of the main text. • Text and paratext. Even in their most literary moments, Romans preferred imagining texts (at least potentially) as speech acts. This makes many informational devices (tables of contents, section numeration, tables, illustrations) problematic, insofar as they are inherently paratextual (and doubly so for items that cannot be linearized—​e.g., the last two examples). Problems of textual status discourage integration of formal data records with discursive texts. Conversely, the most sophisticated representations (fully realized tables, 3-​D spatial representations) tend to occur as stand-​alone objects, rather than being embedded in larger projects.





A Brief Orientation }  9

• Shared knowledge. These technologies require that producers and

consumers of individual representations (e.g., individual tables, maps, etc.) share at least some knowledge of the technology itself. This is particularly important to notice in cases where the general outline is common knowledge (use of weights and measures), but crucial details (objective values of those measures) are only knowable in extremely local contexts. In practice, the required knowledge seems to have been restricted to relatively small and isolated (if not always face-​to-​face) communities, a limitation which is self-​reinforcing.

As a consequence of all these interacting factors, Romans lived in a balkanized informational world. Persons in different “locations”—​whether those are geographical, social, or occupational—​would have had access to quite different informational resources, and the overall situation is thus not controlled by the needs of any particular class or group. Rather, there is a “tessellation” of contributions by intellectuals, bureaucrats, and tradesmen (hence the “mosaic” of the title).

10

1 }

Lists

Perhaps the most basic information technology made possible by writing is the list. Lists were ubiquitous in the Roman world, and I do not intend anything like a full account of them here. The scope of this chapter will be restricted in two ways. First, in keeping with the idea of “high” technology, I will be talking not about simple lists but about versions that have been augmented in various ways:  ordered lists, indexed lists, tables of contents, and nested lists. Second, even within most of those categories, I will not attempt an exhaustive survey of either themes or materials but, rather, make selected points. When I say that lists were “made possible by writing,” a reasonable objection might immediately be raised. Human beings have of course always talked about one thing, then another, then another. That is not just a matter of, say, the catalogs that figure prominently in the earliest poetry of Homer and Hesiod; it is the linear nature of human speech. But I want to insist that there is nonetheless something distinctive about writing down sequences of information. Here, I follow Goody’s classic discussion of lists, tables, and formulas as specialized technologies of literacy. He argues that writing transforms this oral discourse, giving the proper written list a variety of distinctive features: The list relies on discontinuity rather than continuity; it depends on physical placement, on location; it can be read in different directions, both sideways and downwards, up and down, as well as left and right; it has a clear cut beginning and a precise end. (1977.81)

10

These physical features in turn give rise to various practical consequences such as increased abstraction, increased attention to categorization, and an invitation to alternative arrangement or processing of the items listed. Not every written list takes advantage of all, or even any, of these opportunities, and—​as often—​the distinction could be framed as a spectrum rather than as a binary opposition. Still, Goody has identified a distinctive set of written forms, and convincingly connected them to important differences in use and power. Some of these advantages derive from literally having the kinds of written forms specified; others could perhaps attach to an

Lists }  11

oral list within a more broadly literate culture. My interest lies in texts that are not merely sequential but which also exhibit at least some of Goody’s “written” characteristics, whatever other specific additions (e.g., indexing, ordering) are the focus of each individual section of the chapter. (This same set of observations about writing down will be important to the next chapter, as well.)

Ordered Lists I begin with what I will call “ordered lists.” Of course, all lists have an order; that might even be considered their principal definitional feature (even if, as I mentioned earlier, readers do not have to respect that order). What I mean here is much more specific than that. “Ordered lists” will be shorthand for ones in which the order of the text itself is meant to inform the reader. This can happen in two rather different ways. On the one hand, a list can be organized by reference to properties of the words (or other individual entries) themselves (“word order”). Typically this helps a reader find out whether an item is on the list at all (sometimes to be used as an index). On the other hand, a list can be ordered in terms of some feature of the real-​ world entities that are referred to by its entries (“topic order”). This can in theory be used in the same way, but more often it is meant to convey something about that feature—​for example, “what is the fourth most populous city in Italy?” In principle, word order could appeal to the length of the words or some other feature, but in practice it normally means alphabetical order. Unlike the topics of the rest of this chapter and the next, alphabetization in the ancient world has already been the subject of an extensive and valuable basic study. In addition to various specific points which I will note individually, the basic narrative of the next two paragraphs will rely heavily on Daly 1967. With this framework in place it will be easy to move quickly to my own analytical remarks and in particular to some observations that will foreshadow many of the important themes of the rest of the book. Latin lists in deliberate alphabetical order appear to go back at least as far as a joke in a play by Plautus—​that is, the earliest extended Latin texts we have today (c. 200 bce)—​and continue through to the end of our period. (There are somewhat earlier Greek examples, and Plautus may well be adapting one such in his text.) The earliest examples, and perhaps the bulk of all those of our period, are alphabetized only with respect to the first letter of each word. Occasionally we see alphabetization through the second or later letters. (Full alphabetization appears occasionally in Greek, but seemingly not in Latin until after our period.) There is not, however, an overall trend over time toward more detailed arrangement. There seems to be something ordinary or matter of fact about Roman use of alphabetization. The joke in Plautus’ play does not call explicit attention to the ordering. Rather, a character starts reeling off a list of (otherwise unremarkable) names in alphabetical order. The humor seems to lie in having the audience

12

12 { Mosaics of Knowledge recognize on the basis of form that the list threatens to extend to the end of the alphabet (Asin. 864–​6). It is unclear what fraction of the audience could have gotten the joke—​we do not really know the fraction of the population that would have had the low requisite level of literacy—​but the fact that Plautus took the trouble to make a somewhat elaborate joke anyway suggests that many would have. It’s also true that authors who use alphabetical order either do not bother to explain what they are doing or use only a summary phrase to do so (“arranged by letters,” “in the order of letters,” etc.). This is in contrast to the use of some other devices we will see later. Alphabetization is also a common feature of school exercises, so it is not hard to see why it might be familiar to the general (literate) public.1 At the same time, as Daly has noted, it appears to be used principally in contexts which are anything but general or ordinary. He points out a number of scholarly uses; I would add only the case of Flavius Caper (Verb. Dub. 107–​12K)—​no later than Daly’s earliest example—​whose brief list of morphologically “doubtful words” is transparently in alphabetical order. Daly also notes administrative uses. He finds their number less than impressive, and that is a fair judgment, but I would note that subsequent scholarship (not focusing on alphabetization as such) has extended the roster of examples at least a bit.2 It is still not common in either realm, particularly in “outward-​facing” texts—​that is, those aimed at a reading public different from the producer(s). I am inclined to explain the gap between high accessibility and low actual use by another phenomenon that Daly 1967.52 had already noted:  alphabetization was inelegant. The contexts in which it typically appears (education, handbooks, internal state documents) are all relentlessly utilitarian. The two texts of some pretension which nonetheless use alphabetical order resort to it only in residual cases; it is how “the other” items in various categories are listed once more substantive categorization has been exhausted (Var. RR 1.1.9; Plin. HN 3.46, 26.164, 37.138). And at one point Pliny even apologizes as he begins a shorter group by noting that he is only alphabetizing peoples “who do not warrant closer attention.”3 Daly notes in this connection that the agricultural writer Columella, in borrowing two alphabetized lists of authors from Varro, re-​sorts one by birthplace and appears to invert two persons in the other simply to avoid alphabetical order.4 There is also a well-​known passage in the Aeneid in which Italian heroes are listed in alphabetical

1 Cribiore 1996.161–​7. Frampton 2018.62–​70. 2 Nicolet 1991.135, 173–​7; Salway 2012.200–​2. Tim Parkin points out to me that the alphabetical list of centenarians from Italy’s regio VIII preserved in Phlegon, Makrobioi (taken with Pliny the Elder’s access to a similar data set; HN 7.162–​4) could reflect some government document ordered on the same principle, though (as he also points out) alphabetization by praenomina seems very odd in such a context. 3 Plin. HN 3.130, quos scrupulosius dicere non attineat. 4 Perhaps also relevant here is the frequently made observation that Latin authors who receive a list in Greek alphabetical order often fail to rearrange it to maintain that order in Latin.

Lists }  13

order except for the intrusion of Messapus between Caeculus and Clausus. O’Hara 1989, however, has shown that Vergil tells Messapus’ story in such a way as to assimilate him to another well-​known hero, Cycnus. Cycnus’ name would be in correct first-​letter position here. Vergil, too, seems to be going out of his way to avoid alphabetization. There is also an exception which may prove the rule. The Augustan-​era scholar Verrius Flaccus wrote an extensive lexicon, perhaps closer to a modern encyclopedia than a dictionary. Our preserved versions have gone through some kind of editing at the hands of Festus (perhaps second century; very fragmentarily preserved), and large parts survive only via the subsequent epitome of Paul the Deacon (eighth century), but it seems likely that the basic structure is Verrius’. The work is organized by first-​letter alphabetization of the head-​words, and within each letter group there is a first section that is further alphabetized and a second one which is grouped more or less thematically. Glinister (2007.23–​4, 29–​32) has made a strong argument that alphabetization is not a pragmatic choice here. The work has no cross-​ references, and many discussions are attached to lemmata that are not necessarily obvious. The innocent reader would find it very hard to track down a particular bit of information, and even the expert might be daunted. Verrius, Glinister argues, uses alphabetization’s blandness to assert intellectual authority, the authority to distribute knowledge according to a system that is superficially objective, but in fact quite idiosyncratic. There are several patterns here that we will see throughout the book. First, alphabetization demonstrably exists in the Roman world, but its use and diffusion is perhaps surprisingly limited. This quantitative phenomenon also has a qualitative parallel. Romans do develop more “sophisticated” or powerful or (to put it less prejudicially) intensive alphabetization, but the more complex forms do little or nothing to displace the simpler ones. One should never cite technological progress as an explanation for anything, but from a modern perspective it is probably useful to point out that progress does not work even as a description here. In particular, in the variation between one-​letter, two-​letter, and so on alphabetization, we see a Roman tendency not to apply any more technology than is required by a particular situation. Second, the development is generally sparse, but also clustered. Alphabetization is relatively common in a few contexts and unknown in others where it could have been used. Additionally, I have mentioned an apparently aesthetic objection to alphabetization, and we will see other cases of resistance to formalism in data organization. The last pattern is slightly more complicated. Small 1997.63–​ 5 has hypothesized that the rarity of alphabetization is due (in part) to the instability at the time of the notion of the alphabet itself. Following her, Glinister 2007.22 has gone so far as to say alphabetization “is not an obviously useful means of arranging data in a world where ‘alphabetical order’ may fluctuate, where there appears to be no concept of the alphabet as a distinct entity.” Subsequent work by Frampton 2018.67–​70 has shown that the premise is false—​the alphabet was

14

14 { Mosaics of Knowledge very much reified by the period we are talking about—​but in any case, the evidence cited here for the ordinariness of alphabetization tells against such a deep cognitive explanation of the weakness of the technology.5 Cognitive factors will be significant throughout the book, but will rarely give simple, categorical answers to our questions. Here we should favor shallower and perhaps more diverse explanations. The other approach to ordered lists is by sorting the topics, not the words. In principle, the potential variety of topic orders is infinite; one could imagine, for instance, lists based on the date, location, or size of the items listed. There are many such lists surviving, at least at first glance, but it is often difficult to know that the objective order is meant to have (or in fact had) any informational value for the reader rather than being an artifact of composition.6 For instance, the list of canonical authors recommended by the rhetorician Quintilian (late first century) is at least roughly in chronological order within each genre (10.1.46–​131), but there are no absolute dates or even (for the most part) indications of gaps in time.7 Moreover, chronology applies only within genres, and those generic categories are in turn subordinated to a division between Greek and Latin texts. Chronology may have helped Quintilian pick an order, but it is so far down the organizational hierarchy that it could only help a reader find an author that she is nearly on top of already. Or take the lists of cities on the pocket sundials recently studied by Talbert 2017.147–​52, which instruct the user how to calibrate the timepiece for use at the local latitude. Many show rough clumping of nearby places, and some may reflect itineraries, but do not appear to follow these tendencies precisely, which means that the order is not in fact predictable. Nor is it clear what value the sundial reader would get even from knowing a correct order. All she really needs to know is her current position. For an author, though, ordering even a fairly simple list might make sense as a check for completeness. In the two cases just mentioned, there is good reason to think of the lists as not being ordered in my restricted sense, but more often there is little clear reason to guess one way or the other. However, I can suggest two sets of circumstances in which order is more likely than not to be important. On the one hand, we have a number of kinds of practical records such as financial accounts, rosters of military units (which are arranged by rank, then by year of enlistment), and various 5 More plausible is the notion (Glinister 2007.22–​3) that the syllable was more prominent in the Roman mind, and so may have made limited alphabetization more natural (cf. Frampton 2018.63–​4 on the status of syllables). However, the order of syllables seems still to depend on the order of the component letters. 6 Cf. Riggsby 2007.96–​8 for structure in HN that seems to be a residue of Pliny’s methods of composition, likely invisible to his original readers, who had neither the modern paratextual apparatus we do nor (I suspect) professional interest in reverse-​engineering Pliny’s working methods. 7 It might fairly be objected that what we have in Quintilian’s text is not really a list, since it fails in most respects to show the Goody features described a few pages ago. I imagine that Quintilian was working from an outline in the form of a much rawer list. If the end product was not really a list itself, that just suggests all the more strongly that the ordering was meant for the author not the readers.

Lists }  15

government registers. The registers record, for instance, births in the order received and note both the date and the position of the record within the sequential register. We will see all these document types again soon, but let me note here one feature they share (which itself will also be important later). In all of them the chronological order seems to be generated automatically, as the records in question are compiled over time. That is, for instance, a small business owner might list pay for his employees for a given day, then repeat the process on the same piece of papyrus the next day and the next, and so on.8 The fact that the individual records already in order in these cases are tagged with the date in question suggests that the order of composition was deliberately being harnessed to provide the user with chronological information. On a grander scale, the various state annals seem to have been constructed in the same way, with various kind of information (e.g., lists of prodigies) recorded in order at least yearly.9 I  separate these out because they point, at least by association and perhaps also causally, to the second set of contexts in which pointedly ordered lists are used. These are works of what might broadly be called scholarship. Most obviously there is Rome’s entire tradition of annalistic history, but we might also look at Cicero’s Brutus, which writes the history of Roman oratory mainly through a series of capsule biographies arranged in generations of orators. Unlike Quintilian, Cicero explicitly points to his chronological arrangement, and he uses it to make a point about what he sees as progress over time. In a less literary vein, we can point to the lists of officeholders, military triumphs, and calendrical information Romans carved into stone and which go under the cover term Fasti.10 We do not generally know who composed these, but the one exception (Fasti inscribed at Palestrina and composed by the first-​century bce scholar Verrius Flaccus11) is likely representative. The people who use topic-​ordered lists, then, look like roughly the same people as who use alphabetical lists. They are scholars and bureaucrats who frequently deal with information as such (without necessarily intervening in the management of whatever reality the data describe) and who interact intensively with each other more than speaking to a broader public.

Indexed Lists “Indexed lists” might include in principle any whose members are matched one to one with a set of indices—​numbers, letters, colors, and so on—​to help find material

8 For a specific example, see ­chapter 2, note 46. 9 For the Annales Maximi, see Cic. de Or. 2.52 and DServ. Aen. 1.373, with Frier 1979. For other magisterial (and thus annual) records, see the references cited at Riggsby 2006.134. Most or all of these will have been internal rather than published records (Riggsby 2006.140, 149–​50). 10 On Fasti, see further at ­chapter 2 “Appearance: Fasti”. 11 Suet. G&R 17.

16

16 { Mosaics of Knowledge within the list. As with the ordered lists, however, this type is dominated by a single sub-​type: the numbered list.12 The fact that labels are almost always based on numerical order creates a potential evidentiary problem when we do not have the entire list in hand. If we have a passing mention of, say, the fifth item on the list, does that mean that the whole list was fitted with numerical references (and so is a truly indexed list) or did someone just happen to count forward from the beginning on a particular occasion?13 This distinction will often not be a real problem, but it will be significant in at least a few cases that will come up in what follows. Thus I want to stipulate that for the rest of this section I mean only lists with built-​in indices, not ones generated on the fly and partially by a later user. Compared with most of the other technologies discussed in this book, numbered lists are fairly common. Here are some contexts in which they are used (most of these will be discussed at more length at various points in the book):

• sections of archives • segments of buildings • administrative regions of Rome and of Italy • military units of various sizes • milestones along roads • lots • units of time • segments of texts

In what follows I  want to argue for the existence of two limitations on numbered lists. One limitation is (like the items in the list) essentially a matter of genre or use-​context. The other is more functional, a way that numbering of lists is not exploited, even when it exists.

12 Two (or three) exceptions: the Roman market (nundinae) cycle divided an eight-​day “week” into days labeled A–​H; a work by Casellius Vindex (cited by Charisius 254.18, 312.24B) was arranged not in books 1, 2, etc., but A, B, though here the letters appear to be literal; each book discusses words that begin with the letter in question. Years were often identified by the names of (at Rome) the year’s consuls or (elsewhere) various other “eponymous” magistrates; Julius Obsequens’ book of prodigies is essentially a list structured in this way. But the unpredictability of these names, however, means that they cannot be used as an index in the same way as numbers or letters. 13 There are also at least a few cases that turn out to be neither. Roman legions were conventionally designated by numbers. At various points in the early empire there were two fifth legions, two sixth, two tenth, and (it appears) three third legions (generally distinguished by further epithets); the numbers are clearly not generated by counting, but because they are often repeated, they do not really work as indices at all. Also, probably, the tokens known today as spintriae. These feature large numerals on one side and erotic scenes or imperial portraits on the other. It has been hypothesized that they correspond in various ways to a catalog of sexual positions or the like, but Campana 2009 makes a strong case for regarding them as game tokens, with the numbers perhaps representing the value of the individual piece. The same is likely the case for similar tokens which match numerals on one side with counting gestures on the other (Williams and Williams 1995.590–​1).

Lists }  17

The last item on the foregoing list was “segments of text.” (I mean here individual texts; archives will come up later.) By the time we have longer surviving literary texts in Latin, they are divided by their authors into “books”—​that is to say, units that will notionally fit on a single papyrus roll—​which are then numbered.14 (I use “literary” here in a broad sense common in the Classics—​texts which were meant to be copied and circulated to an indefinite audience, not just those of some artistic ambition.) Given this nearly universal convention, it is then striking that smaller units of Latin texts are seldom if ever numbered. In principle, several such units were available. Today we refer to bits of Latin poetry by line number and (in the case of collections of short poems) the number of a given poem within its book. There seems to be no evidence for either practice in antiquity, whether directly in manuscripts or in external reference (say, in commentaries). This is despite the fact that lines were often counted in individual manuscript copies, apparently as part of the pricing process.15 Prose works were often thought of as being divided into capita, a word often translated as “chapters,” but perhaps closer to English “sections” or even “paragraphs” (there is a related, perhaps original, sense of “high points”).16 Not only do we have frequent reference to the general idea, but there is even some manuscript evidence for the marking out of such sections with ekthesis (reverse indentation) or even the letter k (for kaput, as the word was often spelled).17 Crucially, however, none of these divisions appears to come with reference numbers, not even in prose texts explicitly divided into units by rubrics. Latin also has a word pagina which can mean the same thing as the English word we derive from it: page. Before the rise of the codex, however, it typically refers to a field within a larger support medium—​say, a column of writing on an inscription or roll of papyrus. In no sense, however, are paginae used in our period as the basis for standard numeration of literary texts (we will see later that the case of archives is somewhat different).18 The lack of numerical references (other than book numbers) in commentary is particularly striking.19 The genre was a flourishing one already in antiquity, with subject texts including Vergil, Cicero, Terence, Homer, and others. In its modern form, the commentary is typically organized by numeration first (line numbers for verse, section/​chapter numbers for prose), then by rubric within any given numerical range. Ancient commentaries are generally organized by rubric alone. In

14 Moatti 1997.223. 15 Birt 1882.159–​209; Hall 1913.9, 13. 16 On the terminology, see Butler 2009.16–​7, 20. 17 Butler 2009.10–​5, 18–​9,  21–​3. 18 Grafton 1997.30 cites references to page numbers in an apparently standardized edition of certain legal texts, but this dates from the fifth century. Shafer 2017 has argued that certain effects in Vergil’s Georgics presuppose that certain words and phrases will fall at predictable points on the “page,” though for poetry this would only have required an early edition with a set number of lines to the page. 19 For possible (but still extremely scanty) Greek examples, see Barnes 2015.348–​50, Mansfeld and Runia 2009.199.

18

18 { Mosaics of Knowledge continuous reading, there is little difference, but if you pick up a literary text in the middle, it is much harder to find your place in an ancient commentary than in a modern one. For comparison, it may be useful to look at one very partial exception to the usual ancient practice. In the manuscripts of Asconius’ historical commentaries on several speeches of Cicero (first century), we have frequent (though not systematic) allusion to the position of his lemmata within Cicero’s text: around line 640 (10.10C) a little later (11.1) around line 800 (11.8) around the middle (11.19) around the middle (12.7) **** around the third part (23.21) around 160 lines from the last (53.5) This seems to be unique among commentaries. In fact, it has even been suggested that these headings were not part of the original text but, rather, were introduced by a later reader for his own benefit, then absorbed into the manuscript tradition. I will return to the reasons for this proposal in a minute. Whatever their source, these references obviously do not refer to standardized numerical labels. They are vague, they vary choice of units (lines, “parts,” none at all), and they count in whichever direction is locally convenient. The same approach seems to be visible in a text which is not literary even in the broad sense used here but also which bears on the more general issues of both this section and the last section of this chapter. In the early second century, a man named Vesbinus erected an inscription at Caere which recorded acts of the municipal government and subsequent correspondence with an imperial official authorizing him to set up a shrine. His inscription quotes extensively and with citations from the records (commentarius) of the municipality. The sections with the reference (as they are usually translated) are as follows: in which [commentarius] had been written this which is written below: In the consulship of L. Publilius Celsus and C. Clodius Cripinus [i.e., 113], on the Ides of April, in the [local] dictatorship of M.  Pontius Celsus and aedileship of C.  Suetonius Claudianus, the commentarius of the municipality of the people of Caere. From there (inde) page  27, sixth chapter. [provisional approval of the project subject to higher authority] From there page two, first chapter. [Letter to the relevant imperial official] From there page eight, first chapter. [Reply from that official] (CIL 11.3614.6–​18) In all three cases, the reference is to page and chapter. Birt 1882.158 takes the page and chapter numerations as running independently, but in parallel, so pages 2 and 8 would fall within c­ hapter 1, while page 26 lay somewhere in c­ hapter 6. This hypothesis ignores the fact that the three documents—​the initial decree calling for

Lists }  19

(inter alia) the approval from the curator, the letter making this request, and the curator’s reply—​are clearly in chronological order, as they would have been in the commentarius which is a running record.20 Birt’s scheme makes the initial decree the last of the three to appear in the commentarius. In fact, the same objection still applies even if we take pages to be individually broken down into chapters. I suggest that the page references have wrongly been translated as “page 27/​2/​8.” They should instead be read as “the 27th/​next/​eighth page” from the previous citation (an equally possible reading of the Latin). That is, inde (“from there”) doesn’t refer generally (and thus redundantly) to “from the commentary” but, more specifically, “from the last page mentioned.” The locations of the second and third documents are given by counting forward from the first and second documents, respectively. The first instance appears to count from a more public reference point marked out by the list of eponymous officials (perhaps some important date in the civic year). Note also that this material is placed after “what is written below” and so looks to be itself a quotation from the record. Moreover, the first date quoted (13 April) is very early if we take it to be the time of the original council decree, since the letter they ordered dispatched was not sent until 13 August (line 15). Rather, it is a reference point considerably before that decree, as represented by the twenty-​six-​page gap. It does not look as if this record had fixed numbers attached to its paginae, just ad hoc counting. In principle the capita could have been numbered, but that seems much less likely if there was no indexing at the higher level. This is made possible by the fact that there was, seemingly, only a single exemplar of the text. All that said, I  know of two circumstances in which texts do have numbered subsections: one in a particular text and the other an entire category. First, in the mid-​first century, Scribonius Largus wrote a collection of recipes for 271 medicines. The individual recipes are numbered, and the opening table of contents uses this numeration to direct the reader from symptoms to their proper remedy. I will say more about why this might be at the end of this section, after the other example and some of its implications. Second, though arguably not literary texts even in the broad sense I have offered, Roman statutes were often divided into numbered capita.21 For instance, Cicero takes for granted that he can refer to these capita by number even when speaking of a legislative proposal not yet passed: Why does it matter in ­chapter 3 you require the ratification of officials by the passage of a law by the curiae, when in ­chapter 4 the elected are given the same powers even without such a law. (Leg. agr. 2.29)

20 Riggsby 2006.138. 21 The tablets on which a few statutes are inscribed seem to be numbered, but this is almost certain to be for local use in placing the tablets, not a general reference system. The Flavian municipal law does not even show consistent formatting at lower levels, so it is unlikely the system assumed uniform carving (González 1986). In the enabling law for Gallia Cisalpina (CIL 11.1146) the (apparent) tablet numbers do not respect breaks in the chapter numbering. Cf. Butler 2009.16–​21.

20

20 { Mosaics of Knowledge Similar references appear sporadically in inscriptions and in the later juristic literature, and there is plausible reason to think that such numeration had at least appeared centuries earlier as illustrated by the three numbered capita of the lex Aquilia.22 Note, however, that in the Cicero passage I have just quoted, the reference to chapter numbers is not strictly necessary, since the relevant material from the cited source is paraphrased anyway. Looking up the proposal Cicero refers to could confirm what he says, but that appears to offer authority rather than information. This illustrates the second, functional limitation I alluded to earlier. There is a strong Roman norm against what I’ll call “obligatory cross-​reference.” That is, they do not like to force readers to look up a second text to be able to understand what they are reading in the first. Here is a modern example of an obligatory cross-​reference of the sort I contend the Romans avoid: AMERICAN DOCUMENTATION OF VESSEL REQUIRED. If 18 U.S.C. Section 1082 is repealed, the affirmative defenses provided by Section 47.09(b) apply only if the vessel is documented under the laws of the United States. (TxPC §47.10) This means nothing without consulting other sections of both the Texas penal code and the U.S.  federal code. This is entirely normal legislative drafting. Here is a Roman example, which I suggest is extraordinary: if there is no judgment within the time which is foreseen by ­chapter 12 of the recent lex Iulia on civil trials or the decrees of the Senate pertaining to this chapter. (lex Irnitana 91) There are several points to be made about the Roman example. First, it is the only obligatory cross-​reference to a numbered chapter in the surviving remains of Roman statute law. And I have not yet found another example in the ancient legal literature more generally. Again, a reference to provide authority is common enough, but not ones that must be tracked down to figure out what the immediate passage is saying. Second, the very text in which this reference appears would itself be difficult to refer to in the same way. It is an instance of the so-​called Flavian municipal law. The latter is a template for town charters in late first century ce Spain.23 We have fragmentary instances of laws based on the same template from other towns in which the chapters are numbered. At Irni, however, the only place where this quoted passage is preserved, the chapters of the law are identified by rubric, not by number.24 In fact, as a general matter, the chapters of inscribed laws are more often marked off by summary rubrics, by spacing, or by nothing at all rather than



Gaius 3.210, 215, 217; Rotondi 1966[1912].241–​2. González 1986. 24 González 1986.148. 22 23

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by numbers. The haphazard availability of numeration obviously discourages cross-​ references, but let me suggest that the reverse is also the case. I would suggest that it is helpful to think about this in terms of what we might call network effects.25 Telephones, for instance, are of little use if too few people have them. Hence, there can be a huge lag between the invention of a device and the bootstrapping needed for it really to take off. Numbering lists for obligatory cross-​ reference is a technology of this sort. We then see a kind of negative feedback or a vicious cycle. If you do not know anyone who cross-​references, why number your text? If numbered texts are not reliably available, why write a law that relies on their accessibility to be intelligible? Strong enough motivations of other sorts could, of course, overcome this kind of negative feedback (or, conversely, interrupt a virtuous circle), but all other things being equal, it is unlikely that these lists would simply drift into widespread use. That is particularly true if there is any truth to the idea that Romans tend not to deploy technology that is not locally necessary. I would also like to suggest, though I cannot claim to have examined every possible case, that the situation with the laws reveals a principle not of legal organization but of textual organization in general. I know of only one other clear example of obligatory cross-​reference by means of an index number (a sundial meridian which may have used indices to point to various astronomical events26). Ancient commentaries cite (at least) all the words of the target text they plan to discuss. The references in Scribonius’ medical text are arguably obligatory, but they are internal to the text. Book-​number references are common in the grammatical literature, but the sole relevant information is normally a word or phrase which is quoted anyway. Outside that grammatical literature, we see roughly the same in cases like this (an example picked because it happens to be cited by Bodel 2015.15 in a context to which we will return shortly): It is better therefore that during this season they should only prepare fruit which is required for use. It is the duty, however, of the shepherd to make cheese in the best possible manner and we have given him directions in the seventh book [7.8], which he should follow. (Col. 12.13.1) Here the passage in book 12 sets out instructions to the overseer’s wife vilica, while the book referred to gives instructions (as is noted explicitly) for the shepherd. The audience of passage in book 12 does not need any of the information found in section 8 of book 7 to give her orders to “make the cheese.” Similarly, grammatical citations universally give a reference for a form that has already been quoted.

25 For the term, see Shapiro and Varian 1999, esp. 173–​225. 26 Jones 2014.181. The object is reported, not surviving, so this reconstruction is somewhat speculative. Some complex Greek accounting documents contain index numbers that almost certainly refer to columns of text in another account, but it seems that the same information appears in both: P. Fay. 143 with de Ste. Croix 1956.35, BGU 1891 with Kortenbeutel 1937.2.

22

22 { Mosaics of Knowledge Now a possible reason for both the limited use of numeration and disinterest in the use of what numeration does exist for reference (as well as for the suggestion that the numbers in Asconius refer to an individual’s text) is the absence of standardized print editions in antiquity. Modern systems of reference, for prose works at least, often depend on such editions for their numeration, though perhaps at some remove. But the situation must be at least a little more complicated than that. The lack of standardized pages means numeration does not come for free, but it is hardly impossible. As we have already seen, non-​legal texts were segmented in other ways; those subdivisions were just not numbered. Here, we can again invoke the idea of negative feedback, and perhaps even more emphatically. Lack of numbered lists makes their use as standardized forms of reference in, say, literary commentary more expensive. Lack of such commentaries means there is one fewer reason to do even a little extra work to number texts. The self-​contained nature of Scribonius’ text makes it a natural exception. The specialized indexing system provides a built-​in reason for numbered sections. And, as I have argued elsewhere, Scribonius would have had an unusually precise sense of his audience and their needs, and so the table of contents itself would have been more worth constructing.27 (Tables of contents in general will also be the topic of the next section.) If that account is roughly correct, it leaves open the question of why any legal texts are numbered at all. In practice, as I  have noted, those numbers are cited in authorizing context. They guarantee that a quotation is correct. It makes sense that this is their purpose, and so a law might reasonably be “born with” numeration in anticipation of having its force propagated in this way. Individuals who subsequently had copies inscribed would have had varying commitments to this particular use, and so we see that the numeration is not reliably included in particular texts.

Tables of Contents For my purposes, a table of contents will be a summary of a work that lists its contents in abbreviated form and in the order of the original text.28 About a decade ago I  wrote a chapter about these, stressing their rarity in Roman texts. Rather than repeat most of that account, I want to do two other things here. First, I will respond to a claim in the subsequent literature that tables of contents are actually much more common. Doing so will, I think, vindicate my original claim, but will also give rise to some new insights into the character of the thing itself. Then I will offer some suggestions as to why objects of this sort are rare. I begin with two definitional distinctions. On the one hand, I distinguish “table of contents” from “index.” A table of contents is in text order, while an index is a

27 Riggsby 2007.92–​3, 103. 28 Riggsby 2007. Among other things, I discuss there the advantages and disadvantages of using the modern terminology in discussing the ancient phenomenon.

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summary ordered by some more generally available principle (typically alphabetization today) and then keyed back to the work by some diacritic feature (typically page or section numbers today). A table of contents may also include such keying, but it is not definitionally necessary. I introduce the distinction primarily to point out, I think uncontroversially, that there are apparently no indices in any classical Roman texts. On the other hand, I would also like to distinguish tables of contents from the rest of a broader category to which they do belong—​that of summaries in general. In particular, when I  say a table of contents “lists” its contents, I  mean that it operates as a list in Goody’s strong sense.29 The openings of two works by the little-​ admired second-​century writer Frontinus provide a convenient illustration of the distinction. Book II of his Strategems begins, after a general preface, with a full-​on table of contents:30 The categories (species) of things which pertain to battle are: on choosing a time for battle on choosing a place for battle on ordering the line-​of-​battle on disrupting the enemy line-​of-​battle on ambushes on letting the enemy escape, lest trapped he rejoin battle out of desperation on faking reverses on restoring [your] line of battle through perseverance. After the overall category is announced, we get a series of identically self-​contained prepositional phrases, well demarcated, and in principle subject to reordering. Note also that key terms like “battle” (proelium) and “line-​of-​battle” (acies) are repeated freely to keep the individual elements of the list self-​sufficient. By contrast, the third section of the same author’s On the Aqueducts of the City of Rome summarizes its contents as follows: Lest I appear to have missed anything relevant to the subject matter, I will first set out the names of the aqueducts which flow into Rome, then by whom, under which consuls, and in which year after the founding of the city each of them was built, then from what location and which milestone they arise and how much [of the course] is underground, how much along the ground, how much raised on arches; afterwards the height of each and their measures31

29 Russell 2005.268 seems to anticipate this distinction in the particular case of Quintilian. He finds that Quintilian tends to use asyndetic lists in contexts where they serve as local “tables of contents.” 30 The rendering as a single column may or may not be original to Frontinus, but on this kind of matter it does not appear that even early medieval manuscript evidence is of much value (see ­chapter 2, note 34). At any rate, it is significant this this list could be set in this format, which would be impossible in the following example. 31 There is some difficulty with the text at this point, but it does not affect the present argument.

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24 { Mosaics of Knowledge and what distributions are made from them: how much beyond the city, how much within the city each of the aqueducts provides proportionally to the individual regions; how many public distribution tanks there are and from these how much [water] is given to public works, how much to munera (as the more cultivated call them, how much to lakes, how much to the account of Caesar, how much for private uses by the generosity of Caesar; what law regulates constructing and maintaining these, what penalties established by law, senatorial decree, or imperial order enforce this. (typographic emphases mine) The topics proper are explicitly joined and ordered and supplemented by the bold-​ faced material. More subtly, the three series of separate questions I have underlined are each bound together (following a normal convention of literary Latin) by not repeating their words shared by parallel clauses (contrast the practice of Strategems). Finally, the pronouns (here italicized) only make sense as part of the broader text; the phrases that contain them cannot be detached and rearranged. This is a summary, but it lacks the list features that mark a developed table of contents. I turn now to the actual cases of Roman tables of contents, of which five are probably uncontroversial (in error, I omitted Frontinus in my earlier paper): Scribonius Largus, Compositiones Columella, On Rustic Matters Pliny the Elder, Natural History Frontinus, Strategems Aulus Gellus, Attic Nights In that earlier chapter I described the table of contents as a rare phenomenon, and if there are five, not four, that does not change the situation much. Bodel 2015.13, however, has subsequently claimed that the device would have been quite “familiar” to readers of the mid-​first century. In the course of his paper he cites, with varying degrees of conviction, a number of other classical works in which one might detect a table of contents. Frontinus, Aqueducts. Quintilian, Oratorical Training Statius, Silvae [Greek examples32]

Valerius Maximus, Memorable Deeds and Sayings Pliny the Younger, Letters Suetonius, Grammarians & Rhetoricians Varro, Rustic Matters I Florus, Epitome of Livy Cicero, Letters to Friends Solinus, Collection of Wonders

32 To the Greek examples should be added some tables of contents in the fullest sense pointed out to me by Alan Cameron in the Greek mythographic tradition (Parthenius, Antonius Liberalis). On his dating, the similar tables in the Latin Narrationes of Ovid would just fall within the scope of this study (Cameron 2004.13–​23), though I am not certain that is clear.

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We are both looking at the same evidence here; the difference is in interpretation, and there are two major points of disagreement. In analyzing the authors in the left-​hand column, we simply disagree about what counts as a table of contents. For the authors in the right-​hand column, the existence of a table of contents in some manuscripts is clear enough, but I  would argue that they are best understood as later accretions.33 I have already registered the sense in which I think Frontinus’ work on aqueducts does not have a table of contents, and the situation is the same for the other authors in that category. In fact, Frontinus’ summary seems to me closer to a table of contents than what we find in any of the others. For instance, this is the passage of Quintilian that Bodel has described as a table of contents (1.pr.21–​2): All the more must I be pardoned if I skip over not just minor matters, but ones necessary to the task I have set myself. For the first book will contain those matters that precede the job of the rhetoric teacher. In the second [book] we will treat the first elements in the rhetoric teacher’s domain and what may be said about the nature of rhetoric itself. Then five [books] will be given over to brain-​storming (for organization is subordinated to this topic), four to style (of which memory and delivery will be parts). One [book] will follow in which we must shape the orator himself, where we will discuss (insofar as limited capacity will allow) what character he should have, what approach to accepting, investigating, and pleading cases, what type of eloquence, what end to his pleading, and his activities after this retirement. (typographic emphases mine) This summary is not demarcated from the broader argument but, rather, is continuous with a previous argument about the imperfectability of rhetoric and following qualifications about the structure of the work. While there is less direct conjunction and use of pronouns than in Frontinus (bold-​faced and italicized material, respectively), we have the same omission of the verb in a series of repeated questions, as well as the omission of most instances of the word “book” (see underlined). Moreover, it is unclear how the parts introduced in subordinate clauses fit into the structure, and those clauses certainly do not stand alone. Finally, in a less formal respect, this passage mixes actual summary of the author’s choices with commentary on his agency (“I must be pardoned . . . ,” “insofar as . . .”). It is worth noting that these discursive summaries all have quite local rhetorical purposes within their works. I have just mentioned that Quintilian’s is part of a broader justification of imperfect rhetoric; Frontinus is justifying his utility to a very narrow audience; and Statius’ prefatory epistles appear to serve an authorizing, sphragis-​like function. (This, incidentally, seems to be the point of Bodel’s Greek

33 For the letter collection of Fronto we have a single, fragmentary late antique manuscript, so it is not really possible to decide any of these questions.

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26 { Mosaics of Knowledge examples as well.) These summaries do not explicitly purport to aid reference, as do the clear examples of tables of contents. Their discursive embeddedness actually discourages it, since it is harder for the reader to pick out items, and for the writer or later maker of texts to introduce supplementary organization of the page (indentation/​ekthesis, line breaks; perhaps post-​classically rubrication or numeration) that make consultation easier. Finally, literary propriety seems to set a tight cap on the length of the summaries. Now Bodel is not the only well-​informed scholar to look at passages like these and see a table of contents. König and Woolf 2013.52 cite not only the elder Pliny but also a passage in the Greek historian Diodorus (which is very much like the Frontinus and Quintilian examples we have already discussed) as instances of “an opening summary” designed to help readers of a range of encyclopedic works in both Latin and Greek. I  said in the introduction that the various definitions I would offer were designed to make my own investigation more precise, not question the validity of other projects. So what, if anything, is at stake in the different understandings here? First, as I  suggested in the last paragraph, there is a functional difference between tables of contents and more discursive summaries. The table of contents is by nature more accessible, especially in searching for a random bit of information, and because of other conventions it is likely to be much more extensive than an integrated summary. Second, in a moment we will have to ask whether certain other tables of contents were composed along with their respective works or were added later. The fewer the instances of tables of contents (in my strict sense) from the classical period are, the less support they provide for an early composition date for the others. I hope that I have been able to distinguish my tables of contents clearly enough from the broader category of “summaries” that examples of the latter do not automatically count as examples of the former (even if in other contexts the distinction is not important). For the second set of possible tables (in the right-​hand column), the conceptual issues are more straightforward, but the evidence is usually scantier than one would like. Did the authors provide these works with the tables of contents that we find in some of the manuscripts? Among these texts mentioned by Bodel, the most likely case seems to me to be the one that he is ultimately most interested in—​that of the younger Pliny’s letters. Only a few of the manuscripts offer tables of contents (they are attached to individual books), but they include some early ones. On the one hand, as he and Gibson 2014.38–​45 have both argued, the table of contents in the earliest manuscript fragment contains onomastic information that is not in letters themselves and therefore seemingly authorial. On the other hand, Kaster 1995.41–​ 2 has shown both that the same is true of the table of contents of Suetonius’ On Grammarians and Rhetoricians and that the table is nonetheless a later invention (it contains impossible errors). And even if we posit that the information is Plinian in origin, it is still scattered between the table of contents and the actual letters in the earliest substantial manuscript, making it unclear which is the origin. In fact, Robbins’ 1910.481–​2 reconstruction suggests that it is easier to imagine that the extra

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information began in the letters.34 Finally, if the fuller names are really important to the understanding of the letters, it seems at least a little peculiar that that information was not inserted in the letters themselves (as apparently happened for persons mentioned in the bodies of the letters35) or prepended to them.36 The problem is especially acute since, as we will see shortly, tables of contents are not carefully preserved in the copying of texts. This would be a terrible place to put important information. It is not impossible that the very few Plinian manuscripts that carry tables of contents represent the original state of affair, but it does not seem especially likely. In all the other cases, there is internal evidence that the tables of contents postdate the works themselves. I  have already just mentioned Suetonius. Similarly, Flach 2006.15–​7 demonstrates error and anachronism in the table of contents for Varro’s Res Rusticae. Halm 1865.97 notes that Valerius Maximus’ supposed table of contents reflects the state of text that already shows a significant lacuna.37 Jal 1967.xvii points out that Florus’ table of contents appears in only one manuscript, contains significant errors, and appears to reproduce caput divisions that are themselves not original. Solinus’ supposed table of contents contains errors that cannot plausibly be attributed to the author.38 The ad Familiares index is by definition post-​ Ciceronian since the collection itself is later than the author. It is harder to tell whether it is the work of one of the earliest editors, since we do not know who they were. Even Gibson 2014.39, after a systematic review of the evidence, concedes that these tables could be quite late. Rarity should not be surprising. As Doody 2001.2 has pointed out, the table of contents as we know it today is not a transhistorical given but, rather, “the product of a long history of scholarly methods” and evolution of book production. She actually avoids the modernizing term “table of contents” in favor of Pliny’s one-​ off description as summarium, but even this may reify too much. None of our authors really has a word for “table of contents” or even “list.” They name instead the elements to be listed: capita rerum (“headings” or “chief points”) for Gellius; argumenta (“topics”) for Columella; species (“sub-​categories”) for Frontinus; and

34 Barwick 1936.423–​7 offers an alternative account, but does not really argue for its greater plausibility. I would also note that the table of contents in the manuscript that Gibson and Bodel rely on makes organizational use of rubrication, seemingly a late antique feature. 35 Bodel 2015.28. 36 Moreover, Gibson suggests the point of the lists was to privilege an ordering other than his own—​ that is, to allow readers to follow individual correspondents they found particularly interesting. This would seem better accomplished by a single table of contents, not separate ones for the individual books. 37 There is also some evidence that is sometimes taken to show that our books 1–​9 were originally books 2–​10 of a 10-​book collection, and that the now lost book was a detailed index in the fashion of Pliny HN 1. Bodel flirts with this possibility. I think Wardle is right to dismiss these claims on their own terms, but in the present context I mainly note that this theory must posit a different (much longer) index than the one now preserved. That is, Valerius would have to have composed an index, which was subsequently lost then replaced by the present one. 38 Mommsen 1895.cii. Walter’s 1969.23–​4 attempt nonetheless to displace them onto someone else (perhaps an assistant) while maintaining their authenticity is not convincing.

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28 { Mosaics of Knowledge phrasal expressions for Pliny and Scribonius. Moreover, when Pliny mentions the device to Titus in his prefatory letter, he seems to allude to its rarity by citing a now-​lost precedent: Therefore you [the heir apparent and dedicatee] will give even others the chance not to read cover-​to-​cover but, as each one desires something, he may see this thing alone and know where he may find it. In our language, Valerius Soranus did this before me in his book entitled Women Initiates. This Soranus appears to be Q. Valerius Soranus (who held a magistracy in 82 bce), quite an obscure figure if the table of contents were really so common. And the rarity of the table of contents is also suggested by the fact that not only Pliny but also three of the other four surviving authors preface it with an explanation.39 That is to say, the authors do not just supply a list of topics; they also feel the need to explain its function in the most basic terms (contrast here the casualness with which alphabetical order is deployed).40 But even if it is true that the table of contents is a historically contingent form and that it’s quite rare in the Roman world, it still clearly exists. And the Romans who do use it explicitly assert its utility. So why the rarity? I think there are at least three important reasons. One is the same kind of negative feedback or vicious cycle I  described in the previous section. Tables of contents are rare, so readers don’t really expect to find them. Audiences don’t expect tables of contents, so writers are less likely to take the trouble to make them. Second, tables of contents are for miscellanies—​that is, for works that have no “structure of their own.” This is true both for the classical examples and even most of the works for which the tables arise only later in the manuscript tradition. There is a parallel here to what we have observed about alphabetical organization—​that is, that Romans construe it as a final fallback, used when you have to admit that you have not given any “real” shape to your data. The third factor in keeping tables of contents rare is more specifically textual or, rather, paratextual. “Paratext” is the term coined by Genette 1987 for material attached to a primary text, but marginal to it in terms of identity and even authorship: cover art and blurbs in the modern novel, prefaces, illustrations, indices, page numbers, and the like. Almost by definition the status of paratext is always already in question, but I  will argue throughout the book that Romans take a particularly skeptical view of its claim on membership in the host text. I will not

39 See further Riggsby 2007.90–​1. Each of the five lists in Frontinus’ collection is prefaced with a brief introduction such as the one quoted here. 40 It has been suggested to me that, given the paratextual nature of tables of contents discussed here, the “non-​authorial” tables of contents I have identified might nonetheless have arisen very close in time to the texts they are attached to. It is hard to prove or disprove this in most individual cases (though the Valerius Maximus table, for instance, must be considerably “downstream” from the original given the manuscript damage it assumes), but the need for explanation in the authorial cases suggests to me that the burden of proof is on those who would suggest generally early dates.

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immediately rehearse the whole argument, but I will point to some facts about the manuscript traditions of the various tables of contents. First, it is worth noting that at least some readers thought it was appropriate to add their own tables of contents to these works. Second, it may not be surprising that the nonauthorial tables of contents in texts like Suetonius, Valerius Maximus, Pliny’s Letters, and Cicero’s Letters to Friends do not appear consistently in the manuscripts, nor do they always fall in the same place when they are extant. More strikingly, exactly the same is true for the apparently authorial tables of contents for the Elder Pliny, Gellius, and Columella. 41 This suggests that there is something inherently optional about the form, perhaps just as much with respect to its presence or absence as to its location in the text. As a practical matter, the increased ephemerality of paratext aggravates the reliability issues that I  was just speaking of, for both readers and writers. Even if both parties happen to want a table of contents, the transmission of texts may intercept it. As a conceptual matter, the practical instability of tables of contents would make their conceptual separation from the “real” text self-​reinforcing.

Nested Lists My last type is the nested list—​that is, a list of lists or a list of lists of lists. The most basic form of this, the list of lists, is actually quite common and I will not treat these here. (They will, however, figure prominently in the next chapter. For clarity, let me stress that the limitation that I am about to introduce applies only to this section. Nested lists in general will feature in my later discussion of tables.) What I want to limit my attention to now are cases which share one or the other of two additional distinctions (though in fact it is nearly always both):  either the embedding goes three-​deep (that is, a list of lists of lists) or the individual lists are numbered. I will start by looking at several clear instances, then turn to three others that have been proposed, but which introduce various doubts and complications. The difference in situations in which nested lists are and are not used will prove illuminating. Finally, I will note one additional and somewhat bizarre example, which I take to be the exception that proves some of the rules I am proposing. Virtually all the examples I have been able to find involve the organization of documents in large archives. I  know of five sets of documents arranged in this way. These involve military discharge certificates, Egyptian composite rolls, birth registers, Roman senatorial decrees, and the roster of the grain dole of Rome. Diplomata. These are records of honorable discharge from military service. A  central record was kept, and the veteran was given a copy (often on bronze),

41 Doody 2001 on Pliny; Holford-​Strevens 2003.31 on Gellius; and Henderson 2002.111–​3 on Columella.

30

30 { Mosaics of Knowledge which could include a reference to the location of the original within the collection. For instance: Transcribed and verified from a bronze tablet set up at Rome on the Capitoline hill at the altar of the Julian clan on the right side in front of the statue of Pater Liber. Tablet 1, pagina 1, place 25. (CIL 16.10) The reference to tablet, pagina, and place (in that order) is typical both of these diplomata and these archives in general.42 The tablets are apparently numbered anew for each batch of soldiers released from service rather than, say, by year (Nesselhauf 1955.153).43 Birth registers. From the time of Augustus, the Roman government attempted to keep a register of citizen births. We happen to know something of how this actually worked in Egypt in the second century because we have papyrus copies of registrations surviving from there. Like the military diplomata, these record a place within the register. For instance, Declarations of children, accepted without confirmatory investigation. Tablet 4, pagina 5. (CPL 157)44 These declarations typically have only tablet and pagina, but not place.45 However, there seems to be a still higher level of effective organization by date, since the tabulae appear to be renumbered from 1 at the beginning of each year.46 Senatus consulta. The evidence here comes from the headers of a few inscribed copies of decrees, mostly found in the Greek world (in the areas to be affected by the decrees), one from Sardinia, and one from the historian Josephus, but they seem clearly to be translating reference information that existed in the original Latin. For instance:47 From the Senate’s record, tablet one, kheromata 4–​9, and the Quaestor’s files, p. 1. (SC de Aphrodisiensibus 1–​2; 35 bce)

42 The earliest, Neronian example omits the tabula, and one of seven later ones has only the tabula. 43 Because military units at several levels were identified by number, one could imagine a composite roster of soldiers made up of nested lists (“a soldier of X cohort in the Yth legion”), but I have seen no evidence for such a master list, nested or otherwise. 44 Also CPL 150–​3,  155–​6. 45 It appears that there were two entries, separated in time, for each birth. Sometimes we do not get a pagina reference for the first one. Sanders 1931.75 argues for the existence of a closely parallel copy, so that pagina would in fact have both senses (page and zone). There is little evidence beyond his reconstruction of an alternative term [char]to for pagina in one document. If he is right, there are probably no significant consequences for the present argument. 46 CPL 152.14–​15. Sanders 1927.409 and 1928.250 on the problems with determining just what year is being used as the unit (Roman, Egyptian, or years of the imperial reign). For our purposes the important point is that the reset seems well established. 47 In the first instance, see Sherk 1969.9–​11 and Williamson 1995.241–​4. Cf. RDGE 12. 20, 14.75, 23.58–​9; Josephus 14.10.10); Zollgesetz der Provinz Asia = Engelmann and Knibbe 1989, line 4. For possible lower level records, cf. CIL 10.7852 (first century): descriptum et recognitum ex codice ansato L. Helvi Agrippae proconsulis . . . tabula V ⊃ VIII et VIIII et X, where the backwards “C” seems to denote some kind of subsection. Mommsen (1885.279–​80) takes the backwards “C” to stand for cera

Lists }  31

These seem to follow a system similar to the birth records: organization by, at least, tabula and a term that appears to approximate pagina, both probably subordinate to the consular year (Reynolds 1982.65–​6). Tomoi synkollesimoi (composite documents). These are rolls created by literally gluing together a series of original documents (normally of a single sort—​say, petitions, tax lists, or official letters). These composite rolls are often themselves collected, and individual documents are then referred to by the number of the roll and of the document within (Clarysse 2003.347, 349). In at least one case (involving petitions) we even know that there are multiple numbered collections of rolls, and so individual documents are referred to by three digits instead of two (P. Ryl. II 220, 68–​89, including several examples). The surviving documents in question are all in Greek, and the practice seems to begin in late Hellenistic times, but the bulk of the examples are tied to administration in the Roman era. Grain allocation. Numerous texts record the inscription of persons into the Roman grain dole. They are regularly identified by the day of the month on which they draw, followed by either the number of the window at the Porticus Minucia from which they draw or a tablet on which they are listed. (I will go into the difference between the two in the next chapter.) On the one hand, listing by actual distribution window might seem more practical. But since the day comes first and the identity of the other parameter is not constant, I suspect that the list of days is the principal one, with tabulae/​windows listed under each possible day. If the lists were nested but independent, then we would have two separate lists of well over 100,000 individuals, and that seems even more unlikely. Moreover, even though we have inscriptions that leave blank spaces for these bits of data, we have no cases in which one value has been assigned, but not the other. As we saw with tables of contents, these nested list systems are not only fairly rare but also share a narrowly specific use context:





• They are all official records. • The records are nearly all quite large. It is worth comparing here the

structure of the commentarius of Caere, which appears not to use nested indexed lists. That record meets most of the other criteria, but was presumably much briefer than the other records from much larger communities. • They share a grow-​as-​you-​go system of ongoing construction. This will have been less dramatic for the grain rosters, but even those evolved over time as old recipients died and were replaced. • The systems are relatively concrete. The highest level of organization is typically a real thing (e.g., a year), and even the lower levels seem to refer

on the strength of the Greek parallels, but the Latin evidence from Caere seems to me to make that difficult, especially if (as Sherk 1969.10n20 notes) χρῶμα itself is ambiguous and can mean “column of text.” I know of no parallels for using this abbreviation for caput as CIL suggests ad loc.

32

32 { Mosaics of Knowledge

FIGURE 1.1  

Supposed theater token from Pompeii

After Romanelli 1811.136



to real and countable files or documents, rather than purely formal code numbers. • They obey the rule against obligatory cross-​reference. Documents that refer to the central registry do so for authorization, not for information. Hence references to the physical location of the discharge records (various points on and around the “altar of the gens Iulia”), and birth records (the “Atrium Magnum”). The location of the senatorial archives and the grain records may have been too well known to mention.

These features will turn out not just to be correlated but (I will argue) also have a causal role in determining when nested lists are used. Before I can make that argument, though, I need to finish looking at the other possible instances. There are three marginal cases that might not observe these generalizations, including one in which it has at least been claimed that nested organization is actually conventional. Two of these examples, as it happens, fall naturally together; they have to do with theaters and with collective burial sites. I will take them first, then turn to the odd man out—​a supposed system of registers for public art. The first instance comes from the world of seating in theaters and amphitheaters (from here on understand “and amphitheaters” wherever I say “theaters”). Modern works agree that seating was normally allotted on the basis of nested listing, in a form very familiar today: section X, row Y, seat Z. We know that various elements of theaters were identified by number in various places, and the standard handbooks state that these were in fact combined to locate individual seats.48 Scholars point to “tickets” such as the tokens in fi ­ gures 1.1 and 1.2, the former from Pompeii, the

48 Basic numbering: Golvin 1988.351–​4. X, Y, Z coordinates: Plattner/​Ashby s.v. Colosseum, Golvin 1988.353–​4, Fagan 2011.100–​1.

Lists }  33

FIGURE 1.2  

Supposed amphitheater token from Arles

After Jacquemin 1845.18

latter from near Arles. Though these are the only clear examples,49 their geographical distribution and use of precisely the same coordinate system have been found convincing. Let me suggest that there are several problems here. First, as I mentioned before, some parts of some theaters were identified by number—​entranceways, tiers, radial passageways, wedges, steps, individual places, and tabulationes (stories of wooden construction) are all individually attested—​but it is far from obvious apart from the tickets that any of these was individually typical, much less that specific combinations were the norm. More specifically, outside of these artifacts, our best direct evidence for numeration concerns either entrances or individual seats, neither pointed to on our tickets. It is important, then, that the tickets themselves are problematic. I hope you will indulge me in a little detective work here. I have given drawings of these objects, not photographs, but not because of the limits of publishing costs or uncooperative rights-​holders. As far as I can tell, no one has claimed to have seen either of these objects since the 1800s. In fact, as some nineteenth-​century scholars were already aware, no one had ever claimed to have seen the Pompeian example.50 It appears in Romanelli’s Viaggio a Pompeii as a reconstruction of what he thought theater tokens must have looked like (1811.136). The example from Arles appears first to see the light of day in slightly different forms (see table 1.1 for elements that vary) in four parallel accounts by two local historians of Arles, one of whom needed the text to support an otherwise doubtful claim about the structure of the amphitheater.51 Both locate it in the collection

49 There is also another set of tokens (e.g., Blanchet 1889), sometimes thought of as theater tickets, but perhaps better understood as game tokens. In any case, these do not have seat assignments. 50 Wieseler 1851.38, Blanchard 1889.232. Hirscheld lists it as a falsum at CIL 12.321* (1888). 51 Jacquemin 1835, 1845; Estrangin 1836, 1838, 1845. For the controversy in which Estrangin was engaged, see Gaujal 1840.295–​6.

34

34 { Mosaics of Knowledge TABLE 1.1  } Early references to the supposed Arles amphitheater token

Jacquemin 1835 Estrangin 1836, 1838 Estrangin 1845 Jacquemin 1845

“cun(eus) V”

“gladiatores” spelled out

shape

bibliographic reference

Y Y N Y

Y Y Y N

not given not given rectangle round

N N p. 435 N

of the local Chevalier de Romieu, though they are hazy about the source of their knowledge, and Estrangin (1845.439), in a different context, admits that the collection had long since been broken up and that this particular object was lost! He once cites the Chevalier’s own publication of local antiquities (de Romieu 1726), but in fact there is no trace therein of anything remotely resembling the token. At this point, the precise parallels in numeration between the two tickets seem to me to be more suspicious than confirmatory. As for the notation “Glad(iatores) Vela,” I would note that this could be a quotation from the Pompeiian inscription we know today as CIL 4.1194, originally published in 1764 and, as it happens, quoted earlier in Romanelli’s Viaggio (1811.48). I propose, then, that these “tickets” are of no evidentiary value and were created in part by retrojecting a modern mode of theater seating anachronistically. That said, we can look at two other proposed examples, less cited because they require aggressive interpretation to make them fit the pattern at all. I will give these first in the original Latin because their interpretation relies heavily on how one fills out various abbreviations (figure 1.3). The left-​hand text is inscribed directly on a theater seat from Verona (CIL 5.3456); the right-​hand one is another token, this one from Frosinone.52 The text on the seat has been read as (cuneus) I, loc(us) IIII, lin(ea) I = wedge 1, place [supposedly = “row”] 4, “line” [supposedly = “seat”] 1. For that to be correct we would need to assume that the bare “I” stands for the wedge (and indeed that it is a numeral in the first place) and to ignore the fact that it would be redundant since those large units were (and had to be) signaled already at the entrance. Moreover, unattested are both linea meaning “seat” rather than the dividing line between seats and locus, meaning a larger unit than “seat.” Finally, this complex inscription, whatever it means, is unique at a site where there are many examples marked instead with a single number. Whatever this text means, it is hardly typical of the theater as a whole. The token has been read as cun(eus) VI in(feriore), (gradus) X; (locus) VIII = wedge 6, lower level, step 10, seat 8. First, this requires us to assume that the punctuation mark was wrongly placed in the middle of a numeral VI, not after it.



52

Originally Gerard 1830.265. The reading referred to here is due to Mommsen 1849.286–​7.

Lists }  35

FIGURE 1.3  

(left) Inscription on a theater seat from Verona (CIL 5.3456); (right) Token from the amphitheater at Frosinone (Gerard 1830.265)

It also requires assuming the reverse text is a simple continuation of the obverse. Beyond that, it obviously involves some aggressive reconstruction (e.g., inferring inferiori “lower” from just IN), and finally, it leaves out the identifying units (step and place) in a way that is again otherwise unattested for these nested lists. Frankly, I am not sure what either of these objects are meant to say, but they hardly prove the existence of X, Y, Z coordinate seating. It is not even clear that we would want to read them as examples of such a system even if it were independently established. Now, there is one text that does genuinely suggest the use of some nested system in at least one place, and I suspect that it may be an inspiration for the two clearly fake tokens we saw a moment ago. A famous inscription records the award of several sections of special seating in the then-​new Colosseum to the priests of the Arval Brethren (CIL 6.2059):53 For the Arval Brethren. On level (maenianum) one, twelfth wedge, eight marble steps (on the first 5 15/​48 feet, on the eighth 5 15/​48 feet, total 42.5 feet. . . . On the top level, in the wooden seats of story (tabulatio) 53, 11 steps (on the first 5 19/​48 feet, on eleventh 5 45/​48 feet, total 63 23/​24 feet.54 There are almost certainly indexed lists here (the wedges and tabulationes). The case is less clear for the levels (which culminate in “top,” not “third”), much less the rows/​steps (where the counting may be within the assigned block, not an absolute reference). If there is nested listing here, it is different from what has been proposed for seating at other sites. First, it assigns not particular seats but a quantity of seating at an unspecified place within the indicated range. Second, it is not at all clear that seating in general was designated in a similar fashion. Most seating was not reserved in this fashion and so may not have been numbered in this fashion. Finally, it has been observed that to make the arithmetic of the top section work out, we seemingly have to imagine four rows at the length given for the first one and seven rows at the length of the last one.55 There is, however, no way to detect that

53 CIL 6.32363. It is universally agreed that there is an engraving problem which interferes with the middle part of the text (a section within my ellipsis). Nothing in my argument hinges on this fact or any proposed solutions. 54 fratribus Arvalibus maeniano I  cun(eo) XII gradib(us) marm(oreis) VIII gradu I  p(edes) V |(quadrantem) |(semunciam) |(sicilicum) /​grad(u) VIII p(edes) V |(quadrantem) |(semunciam) |(sicilicum) f(iunt) ped(es) XXXXII s(emis) et m(a)eniano /​II cun(eo) VI gradib(us) marm(oreis) IIII gradu I p(edes) XXII s(emis) et maeniano /​summo in ligneis tab(ulatione) LIII gradibus XI gradu I ped(es) V |(trientem) |(semunciam) grad(u) /​XI ped(es) V |(deuncem) |(sicilicum) f(iunt) ped(es) LXIII |(deunx) |(semuncia) /​summa ped(es) CXXVIII |(deunx) |(semuncia). 55 CIL ad loc.

36

36 { Mosaics of Knowledge arrangement without doing extensive calculations. This suggests to me an after-​ the-​fact description of an area that was originally laid out in the physical seating, not a prescription based on a preexisting seating grid. Whatever the details of the system here, I think there are functional reasons for the difference from a modern system, and I will return to them after looking at a related case outside the world of theaters. At least one example of nested listing can be found in the assignment of places, loci, in the collective burial monuments we call columbaria (lit. “pigeonholes”). Consider the early first-​century tomb from Rome called the monument of the XXXVI socii (“36 club-​members”) now attested only by inscriptional labels. The majority of these specify a burial location as in the following (CIL 6.11042; “lot” here in the context of casting lots): Property of Gaius Julius Aeschines, son of Gaius Lot 4, place 34 In the fifteen surviving texts, values for “lot” run from 1 to 5, and the highest “place” number is 36. Gatti 1882, who originally gathered the relevant inscriptions, argued for the existence of 180 niches, arranged in five rows of 36, corresponding to what we know from another inscription to have been the thirty-​six members of the club who funded the monument and were to receive equal shares in it (CIL 6.11034). There were then five lot castings to allot the individual places of each row among the various members, in line with the egalitarian principles of the introductory text.56 We also have numerical labels (single numerals) over some niches in the surviving Monument X on the Esquiline (of similar date), but Borbonus 2006.148–​9 has made a good case that space here was allotted an entire (numbered) column at a time, rather than distributing the loci of each row separately. That is, we have a numbered list, but not a nested one.57 There is also a less consistent use of numeration in the tomb at Rome associated with Lucius Abuccius and his freedpersons (CIL 6.8117–​ 72), undated and also attested only epigraphically. Most of these specify a quantity rather than a location, as in columbaria IX ollae XIIX “9 pigeonholes, 18 urns” (CIL 6.8122; two urns per niche was clearly the norm). When a location is referred to, it is in more concrete terms: “in a straight line,” “to the top,” “from the bottom,” “in this column,” “up from this label.” Two labels (CIL 6.8133–​4) mention a first and/​or second pigeonhole, where we might imagine numbered lists of columbaria within an ordo “column.” Given the isolation of these two instances, however, it is probably easier to read them as simply counting from the spot of the inscription rather than referring to an overall labeling system.

56 We have all five labels for one C. Rabirius Faustus, and he has a different locus in each lot. 57 The specific numbering system that Borbonus convincingly reconstructs is complicated enough that it could not be stumbled upon by mere counting. The painted labels are crucial.

Lists }  37

I have treated all the evidence I know of for labeling with nested lists in both theaters and columbaria. But this is far from all the evidence for labeling in those contexts, and that is important. The Arval inscription will be helpful to contextualize the distinction. The point of that text is not, of course, to facilitate the efficient reallocation of seats to each new spectacle audience but, rather, to highlight the permanent privileges of a few. And, in fact, this seems to be the point of the vast majority of inscriptions surviving from ancient theaters. They do not carry generic numbers. Instead, they bear the names of individuals or groups who are entitled to specific places. The inscribed name is a projection of honor at least as much as it is an identifier (Jones 2008, esp. 76–​92). What we know about theatrical seating from literary sources confirms that these kinds of honorific issues seem to have been at the forefront of Roman thinking.58 The best attested numeration, that of the entrances and wedges, might well have been needed to spread out the entrance in the context of a large theater or amphitheater, but it is not at all clear that anyone cared enough about the interests of a general audience spectator to go to the trouble of assigning individual seats for individual events. In fact, the very idea might have seemed problematic, since that ordinary spectator might not be thought to have “deserved” a reserved place.59 Similarly, we have an enormous number of labels from columbaria, and numbers of any sort are overwhelmingly absent. Instead, we get names and other information meant to project identity and/​or ownership by direct marking, rather than any kind of reference system (Borbonus 2014.106–​34). And even when numbers are used, they typically refer to a set of niches and rely in large part on direct deixis: “five seats here,” “the niches from floor to ceiling.” We happen to know that, perhaps surprisingly, individual niches in columbaria could change hands over time on the open market. In principle, then, one could imagine a columbarium that originally distributed niches in the manner of the monument of the XXXVI socii, but where that organization was lost over the course of generations of places changing hands or was simply not recorded as such by the original owners.60 While this is not impossible, the need for the nested system seems to stem from the elaborate attempts at egalitarianism at this particular site, and expressed on the inscription out front.61 More normally, however, this tendency struggles with a desire for clustering, not scattering, of individual plots, and that can be identified without the more complex system. In any case it would be significant that the hypothetical “new” owners do not refer to any system of nested lists.

58 Kolendo 1981, Rawson 1987. 59 It is generally, and plausibly, thought that the Arval Brethren are assigned seats in several zones to accommodate both themselves and various lower status dependents who might accompany them. Hopkins 1983.18, Fagan 2011.114. 60 Changing hands: Borbonus 2014.69, 75, 108. 61 Borbonus 2014.68–​9.

38

38 { Mosaics of Knowledge What the monument of the XXXVI socii actually provides, I  think, is not so much the tip of an iceberg of nested lists as a hint at the key to their rarity. The monument shares few of the features of the archives treated earlier, but it does have one. Its abstract organizational structure is closely tied to the actual physical organization of the thing itself. This, I want to suggest, is the most important determinant of the use of nested lists, and there are general cognitive reasons to believe this.62 Organization by simultaneous reference to multiple parameters is a real skill with significant cognitive demands, especially for a population that on any account did not do it regularly. But, as scholars of what is called “enacted cognition” are fond of pointing out, these kinds of abstractions usually do not arise simply from introspection but, rather, in the course of real-​world action. They do not become abstractions until a high threshold of repetition and context-​transposition is met. The various kinds of public records have both a particular purpose for nested listing (the need for authorization of crucial data) and a particular action substrate (the build-​as-​you-​go formation of the archive itself, and its actual physical components). Similarly, in the case of the columbaria, the actual process of allotment has both special requirements (the consideration of the whole structure at once) and special tools for handling them (the act of casting lots). The use of sors “lot” rather than, say, ordo “column” strongly suggests this kind of conceptualization was actually at work. Even in a relatively small data set, the act of processing can enable the structure as much as the other way around. But here or in any such tomb context, unlike the large archives, the activity is not ongoing, and so the potential structure is not reinforced. A somewhat different case takes us back in the direction of state archives. Adriano La Regina (1991) has recently posited the existence of a series of three registers of state-​owned sculpture at Rome beginning as early as the mid-​second century bce. He bases his claim on a series of cryptic inscriptions preserved on a certain number of statues and statue bases; he interprets these as reference numbers tying the works of art to the register.63 Examples of the three forms are given in table 1.2. At first sight, the various systems that La Regina posits seem to fit fairly comfortably with the others that I have just discussed.64 In particular, La Regina’s third, most advanced state has precisely the same tablet-​pagina-​place structure as the diplomata. Seen more closely, however, the parallels break down somewhat.

62 I  treat the cognitive aspects of the argument in greater depth in Riggsby (2018). The present chapter in its turn offers a more detailed historical/​philological analysis of the evidence than was possible in that paper. 63 Aside from the very fact of centralized recordkeeping, La Regina’s argument suggest that individual records were quite long and presumably included more (historical?) information than was strictly required for fiscal purposes. 64 It is perhaps worth noting that the top level is not, in any of the cases where we can tell, based on an imposed, abstract numeration (as seems to be imagined by La Regina).

Lists }  39 TABLE 1.2  } Supposed form of reference to a centralized catalog of Roman public statuary

LO CCXLIX L I XXVI L VI P L XXIIX

locus (“place”) 249 liber (book) 1, [item] 26 book 1, pagina 50, place 28

Taking the argument first on its own terms, there are parallels for roughly the context La Regina imagines, essentially an inventory of valuable state property. However, the parallels are all for very local inventories (say, the property of a particular temple), and there is no practical reason a similarly decentralized system would not suffice for the ends La Regina imagines for his single register. Also, we are asked to accept that the determiners “book” and “pagina” are regularly abbreviated, but that “place” is simply left out (except in two cases where it is actually unnecessary because the purported system of the time does not have embedding). Nor does he explain how the renumbering of individual works of art was avoided at the transitions between systems he proposes. And in any case the total number of data points is quite small, especially for an argument that requires the register to have been kept in at least three different forms over time (nine total, of which five display a single number). With those problems in mind, I’d like to point out that La Regina’s theory also runs against some of the recordkeeping trends I noted earlier. It not only relies on obligatory cross-​reference but in fact does nothing else. The works of art have only a bare reference number, while massive amounts of information can be found only in the register. Relatedly, and despite the apparent changes in system over time, the form of organization and the very existence of the archive are more closely tied than in the examples given earlier. The catalog of art could hardly have worked if it had not been designed for numerical reference from the beginning. In theory, one could have relied on descriptions, but in the absence of titles for works, this seems like a stretch. As with the theaters and columbaria, we obviously can’t say for certain, but the combination of philological and informational anomalies suggest to me that these registers, or at least their purported numbering scheme, are not real. And the very narrow set of occasions for nested lists seems to be confirmed. As with the extant theatrical evidence, I do not claim to know what these inscriptions mean, but I do not think it is even clear that they should be taken as a set. Finally, I promised one last exception to prove the rule, and in fact it will test nearly every rule I’ve offered in this chapter. It is a text called the Sortes Sangallenses. This divinatory text is preserved in a single manuscript from around the year 600, but internal evidence and comparison with a clearly related Greek text suggest that its basic structure goes back to the late third century at the latest.65 It appears to



65

Klingshirn 2005.

40

40 { Mosaics of Knowledge work as follows (the text of the instructions, if there ever was one, is now lost, but the reconstruction is uncontested).66 The diviner hears the petitioner’s question and interprets it to fit into a set of standard queries that have already been prepared (let us call it question number Q on his list). Then a random number R from 1 to 12 is generated whether by lot or by the petitioner’s choice. The answers are arranged in other lists; both the lists and the individual answers within each are identified by numbers. The diviner goes to list Q + R and reads off answer R, and this provides the resolution to the petitioner’s question. Thus we have a numbered list of numbered lists. It is unusual in several respects. Not only is it not part of the state apparatus but it also manages a fixed and fairly small amount of data (probably about 1,700 answers originally, though only a third survive). Moreover, it relies crucially on obligatory cross-​reference; you actually have to follow the numbers to get the information. The reason for all these peculiarities seems to lie in the peculiarity of the use context. It would have been simpler to have a list of questions, numbered or not, each followed by its own dozen answers. But picking an answer at random from a short and visible list would likely have seemed insufficiently magical. The function of the system as we have it is to interleave the answers to the various questions so as to conceal the fact that that is really all that was happening. (Note in this connection that you cannot actually get to some of the would-​be “answers” by following the method. The text nonetheless supplies dummy answers in these slots to give the impression of a solid block from which the appropriate information is miraculously pulled.) In strictly functional, informational terms, the system applied is inappropriate overkill. In the larger pragmatic context, it is intentional and valuable obfuscation. On the one hand, the numerical cross-​reference is made possible because there is really only one compound text; the reference is not really external. On the other hand, the numerical reference is desirable precisely because it helps conceal the relationship between question and answer, not because it facilitates information look-​up. Nested lists are close kin to another piece of information technology—​the table. It is in some respects (but not all!) a small step from



1. Austin a. population 931k b. area 272 mi2 c. founded 1839 2. Dallas a. population 1400k b. area 385 mi2 c. founded 1856

66

Dold 1948.9–​11.

Lists }  41



3. Houston a. population 2238k b. area 628 mi2 c. founded 1837

to what is depicted in table 1.3: TABLE 1.3  } Data about three American cities, arranged in tabular form

population (1000s) area (mi2) Founded

Austin

Dallas

Houston

931 272 1839

1300 385 1856

2238 628 1837

It is this latter form that will be the topic of the next chapter.

42

2 }

Tables and Tabular Organization

Status Rational Legal

Is it true? 3.6.66 3.6.70

Does it fit the definition? Is it wrong? 3.6.66 3.6.66 3.6.71 3.6.71

The table at the head of this chapter (in lieu of an epigraph) is one I drew up many years ago while making notes on a week’s reading in a seminar I  was teaching. Explaining what it means and why I  constructed it will help introduce the more general issues I  want to discuss. The text was by the first-​century rhetorician Quintilian, and it discussed what is called status theory.1 This is a heuristic designed to help advocates determine the essential issue in dispute in a legal conflict by offering a typology of the various possibilities. Different authorities give different versions, but all in the form of nested categories and subcategories. A typical version might be represented by something like figure 2.1 (though the graphic form of my “tree” diagram appears to be anachronistic2). In the first instance, each dispute falls into either the “rational” category or the “legal.” The rational is further divided into matters of fact (“Is it true?”; e.g., “Did Milo kill Clodius?”), of definition (“What kind of thing is it?”; e.g., “Is an accidental killing murder?”), and of higher justice (“Is it right?”; e.g., “Is time-​traveling to kill baby Hitler wrong?”). The legal questions, many of which I have omitted here, include how to pick between conflicting laws, between the letter and the spirit of a single law, or between competing jurisdictions. As is his normal practice, Quintilian begins his discussion of the topic with an exhaustive survey of previous opinion on exactly how to draw these distinctions, then announces what he takes to be the correct view. But unusually, Quintilian’s own conclusion in this case comes in three parts. The first possibility

42

1 IO 3.6. Holtsmark 1968 analyzes the structure of Quintilian’s three theories and their relationship to the prior tradition, but misunderstands (and devalues) the version I call “theory B” later, precisely because he does not detect the table nor (consequently) grasp that this allows Quintilian to resolve the problems of imbalance that Holtsmark correctly diagnoses in the other theories. 2 Piggin 2017. See also Bettini 1991.167–​83, Klapisch-​Zuber 2001, Corbier 2007, and Lima 2014.



Tables and Tabular Organization }  43 Status

Rational

It is true?

Does it fit defintition?

Is it wrong? Conflict of laws

FIGURE 2.1  

Legal Letter vs. Spirit

Organization of status theory

(let’s call it theory A) is one he says he no longer believes (3.6.63, 66–​7). The second option (let us call this one B) is technically correct for Quintilian, but he worries that it will be too complicated for students, the ultimate consumers of his theories. Hence, he offers yet a third theory (C), which, he says, will be close enough (3.6.83). Now, version B of status theory did not seem particularly tricky to me, and it has considerably fewer categories than many of the others Quintilian canvasses. But I did notice something else. As I had been reading along and taking notes, I had sketched out essentially the treelike diagram shown earlier to record theory A and a similar one for theory C. What struck me, however, was that for theory B, I’d drawn not a tree but—​for the first time that semester—​a table (in fact, the one now at the head of this chapter). Quintilian posits both two genera “types” of status (rational and legal; the rows of my table) and three template quaestiones “questions” (“Is it true?” and so on; the columns). Cross-​indexing each possible combination of one type and one question, we arrive at a total six forms of status. The three questions which had formerly been subcategories of the rational now cross-​cut both the rational and the legal types. In the table at the head of this chapter, the numbers indicate the sections of the text in which Quintilian discusses each of these six possible statuses. So, for instance, 3.6.70 reanalyzes what predecessors would have regarded as the legal status of jurisdiction, making it an example of a “legal” version of the question “Is it true?” (in this case, “Did court A have authority superior to that of court B?”). This suggested to me that the problem facing Quintilian’s potentially confused students was less the substance of his view and more its tabular organization—​that is, its use of cross-​cutting categories rather than hierarchically organized ones. If tabular organization was sufficiently unusual, maybe it presented an actual obstacle to understanding. In fact, a quick survey at the time seemed to support that idea. Roman tables appear to be vanishingly rare. What I propose to do in this chapter is first support that impression (in somewhat elaborated form), and then develop an account of what it means that the Roman table is such a rare creature. While the question of Roman tables has not really

44

44 { Mosaics of Knowledge been raised by classicists, more general claims have been made in broader historical surveys by scholars of information design and of cognition.3 These studies assert the universality of the table due, supposedly, to its utility as an organizational and even generative device. Tables give abstractions like contemporaneity or category membership a visible form and so make them easier to process (Novick and Hurley 2001.159). They encourage novel exploration of data sets (Marchese 2013.35, 56–​8; cf. Wainer 1997.3); within the universe of data they present, different users can focus different subsets and move in different directions. Finally, they bring out structural or relational aspects of their data sets (Novick and Hurley 2001.168–​9, Hurley and Novick 2010.278, Marchese 2013.35). After all, the whole point is to relate rows to columns. Of particular note here is the fact that the structure makes even “blank” space into meaningful negative information. My account in some respects runs counter to this scholarly trend. Granted, the more abstract mathematical and cognitive claims about the power of tables are well grounded. And it must be said that the earlier scholarship shows sound understanding of the individual pieces of evidence. I think, however, that the broader historical conclusions to be drawn from that evidence look very different if we examine context more carefully. First, it will become clear that the ancient examples cited are not representative of a much larger category; they are isolated outposts. Further, a closer reading of the particular cases will raise some theoretical questions about what a table is. Some things that look like tables are perhaps not. That, in turn, will lead us from the more or less empirical question of “How many tables?” to more historically complex questions of “Why?” and “For what?” When I speak of theoretical questions about what tables are, I do not propose to discover the “true” meaning of the word (much less any Latin term). Rather, as I noted in the book’s introduction, I mean to stipulate more carefully the kind of phenomenon that I want to study. Jack Goody (1977.53–​4) notes that the English word table has been used at various times to refer to almost any graphical display of information arranged in two or more dimensions. Among these, it commonly refers to a specific subset—​that is, to displays of information which are arranged in rows and columns and which Goody himself differentiates as “matrices.” I mean by “table” something both broader and narrower than Goody’s “matrix.” It is broader in that I  do not limit my discussion entirely to physical, graphic representations. Those will, to be sure, make up the great bulk of the evidence, but I will also be interested in “tabular organization” more abstractly. I  use that phrase to refer to material that is not arranged in graphic tables in a particular case but, rather, where there is reason to think that organization by cross-​cutting categories exists underlyingly, perhaps as a purely mental abstraction. This is of course what I just claimed for Quintilian. There is no trace of a formal table in the manuscripts, only

3 Novick and Hurley 2001.202–​3; Marchese 2011, 2013. Closer in style to my approach are Robson 2003, 2004 on cuneiform tables and Piggin 2017 on Romans’ tree diagrams, which, because of their more restricted subject matter, do not touch directly on Roman tables.



Tables and Tabular Organization }  45

evidence of the cross-​cutting organization across two independent axes. In most other cases, I  should note, I  will not be claiming to detect invisible tables. More often it will be a matter of confirming that the absence of visible tables in some case is not mere graphic accident. Is there any general way to detect tabular organization in the absence of an actual graphic table? We might compare here the nested lists of the previous chapter. None of those lists is actually preserved; we reconstructed them from the way indices were attached to single items. Fortunately, it will turn out here that we can use criteria developed for the seemingly opposite case, to which I will now turn. The sense in which my use of “table” will be narrower than “matrix” is more analytically significant. I  want to look not just at the shape of objects but also at whether they are actually being used to take advantage of at least some of the things tables have been found to be good for, especially the cross-​cutting of categories. Goody’s definitions are all framed in strictly formal terms. Mine does begin with a formal component, but I also integrate usage criteria. (Thus I have no quarrel with scholars who, asking different questions than I am, use the word more broadly, such as de Ste. Croix 1956.46, contrasting “tabular” accounting records to narrative ones, or Scappaticcio 2015, pointing out that some texts on papyrus shape grammatical paradigms into tavole, as opposed to the continuous text found in later manuscript traditions.) Formally, this means tables should not only have visible rows and columns but also have rows and columns that themselves convey information. They should be equipped, or at least equippable, with row and column headers explaining what is to be found in each. In some cases, the consequences of this criterion are fairly straightforward, in others less so. Clearly enough, a filled-​in crossword puzzle, magic word square, or Greek inscription carved stoichedon-​fashion (that is, in what we would today call a fixed-​width font) does not count as a table, despite letters arranged in rows and columns.4 The rows and columns do not mean anything. Over the course of this chapter, we will see a number of cases like this—​a gridlike structure that looks at a glance like a table, but upon closer inspection is better read otherwise. T i T B

H s a L

I N T E

S O A .

4 For actual examples of texts of this sort, see Benefiel 2012. Compare also, though it is somewhat later than our period, the pattern-​poetry of Optatian, wherein key phrases in a grid of letters take on significant shapes, such as the chi-​rho (Squire 2016).

46

46 { Mosaics of Knowledge A more subtle instance of essentially the same phenomenon is represented by lists like the following inscription of the second century, where the spacing between elements of the names has been arranged to create columns (CIL 11.3613): L Tuccius Cels[us viator con]sulum praet(orum) L • Arrunt[ius] L L C • Titiniu[s] C L M • Visinius M L Q • Pomponius Q L C • Sulpicius C L C • Calumeius C L L • Otius L L C • Oppius C L

Helenus Adiutor Philadelphus Urbanus Cthetus Erastus Communis Secundus

Those columns consist of the standard parts of formal nomenclature for Roman freedmen: abbreviated first name, clan name, abbreviation of former owner’s name, mark of manumission (“L”), and a family-branch name.5 Several of the columns are meaningful, standing for those standard components of the name. It is at least slightly odd that the column of Ls is entirely redundant, and even more striking that the (noninformational) punctuation after abbreviated first names is also pulled out into a column at the left of the text. At any rate, there is a deeper issue with the rows. They could be said to represent the individuals, but that would exhaust their content. That is, if this is a table, the rows are either all header or all data, but we cannot have both.6 That might encourage us to look back at the columns in a different light. Note, for instance, the clan-name column is left-justified, but the far right one of branch names is right-justified, actually making it harder to scan down.7 Two of the columns are, as just noted, entirely redundant. The text is clearly and deliberately spaced out, but it is not clear that this serves informational purposes. Instead, the design principles are aesthetic (the symmetry of the right and left justification) or at most concern for the clarity of individual lines. That understanding is also supported by the punctuation. In some cases, as apparently here, Latin uses dots to denote abbreviations, yet the writer or carver has separated them—essentially broken up single words from the abbreviated term—because of the formal distinction between alphabetic and nonalphabetic characters. Inscribed lists of names are common, and commonly disposed on the stone in this fashion. 5 One known statute (the municipal charter on the Tabula Heracleensis) specifies census records to be identified by praenomen, nomen, patron or father, tribe, and cognomen (CIL 1.592.146–7). Actual practice in other contexts varies, but only slightly. See also later on military records. 6 There are other problems, as well. Such structure as there exists is not consistently maintained. Extra information (Tuccius’ job title viator consulum praetorum in line 5) is not only allowed in (as a mark of special status?) but also permitted to disrupt the entire structure. 7 In many parallel examples, the last letter of short names is greatly delayed to double-justify the columns.



Tables and Tabular Organization }  47

In the sense used here, lists like this are merely that—​lists—​albeit ones that have been graphically tidied up, rather than tables.8 There is no real cross-​cutting of categories. That example, however, does not exhaust the problem of distinguishing lists and tables. Consider a document which opens as follows, giving students’ first names and their college majors: MARTHA ANDREW HESTON

Physics History Italian

This looks something like a table, and it would be hard to argue that name and major form a single unit in the way first name and last name often do. But what if the document continued like this? LISA Chemistry ELIZABETH Math JO Engineering Not only is this not a table (it has no clear columns), but it suggests that perhaps the previous one was not, either (in retrospect, the columns were clearly not intentionally designed). Rather, given the context of the second list, the first one resembles something more like the stoichedon/​crossword puzzle/​magic square case. The rows are deliberate, but the columns are a matter of happenstance, and so once again we have a list rather than a table. Clearly, this is a highly contrived example, but it illustrates an issue that will come up for a significant category of genuine evidence. That category, as it happens, is one that we have encountered twice already. At the very beginning of this chapter, I alluded to the common ancient practice of organizing material by nested categories and subcategories. At the end of c­ hapter 1, I discussed nested lists, which amount to the same thing. Nested structures like these often lend themselves to easy tabularization. Any data in a table can be put into nested lists; all you have to do is read off the rows or the columns (in any order). The reverse transformation (nested lists into tables) is possible when the sublists all have the same structure. This will automatically happen if you are recording stereotyped and therefore repetitive 8 I  am not the first person to find these definitional niceties (and especially the list–​table distinction) to be useful and important. As a historical matter, Robson 2004.138–​9 uses a similar distinction to describe the evolution from lists to tables in cuneiform culture. It took time for multi-​column documents to exploit their two-​dimensionality—​say, by summing numbers vertically and horizontally or by resorting columns for particular purposes. It took several steps for these to become full tables “cognitively distinct from well-​organized lists.” In an educational context, Gierdien 2009 argues that mastering a full multiplication table teaches different skills than a mere list of multiplication results, even though the latter could be said to have a (slight) horizontal extension in addition to its perpendicular length. Experimentally, Kessel 2008.21–​2 found that modern test subjects preferred tables over lists (and other devices) in just those situations that exploited the special properties of tables I have been talking about (e.g., negative information, lack of hierarchy between variables).

48

48 { Mosaics of Knowledge information: name, rank, serial number; name, rank, serial number, and so on. Even though this information was collected as a list, it can accidentally fall into tabular form. That is precisely what happened with the first list of students given earlier. How, then, can we tell something designed to be used as a table from something that merely falls into a similar shape? We will not always be able to tell for certain, but for clues we will need to turn to what is known about “use as a table,” and here we can look again to the modern, mostly experimental literature cited earlier. First, tables are nonhierarchical, allowing approach from both directions (Novick and Hurley 2001.169–​70, Marchese 2013.56). One can just as easily read the rows as the columns, and vice versa. Trees, by contrast, have a built-​in hierarchy among the parameters (Kessel 2008.22). We can sometimes see fairly direct effects of the underlying order when they are used in the form of a standardized order of variables. Because of their operational orientation, the labels for the Tomb of the XXXVI Socii list the lot-​casting (and thus rows) before the individual niches (= columns) rather than putting both dimensions on a par. The same is true of most of the archives we saw in the last chapter, where tablet always comes before pagina. In all those cases, we have a fairly precise reconstruction based on the meanings of “lot,” “tablet,” “pagina,” and the rest, but note that we could draw the same inference, if more cautiously, just from the invariable order of the variables; one depends on the other. On these grounds, one might deny the tabularity of a phone book or of a shopping list that lists quantities. These are two-​columned, but are designed to be read down (and indeed down a particular column), then across, not in cross-​cutting fashion. We will see a number of documents like this, which are perhaps better described as annotated lists rather than as tables. Second, indirect evidence of a hierarchy of parameters can come from the relative proportions of the dimensions of a purported table (cf. Robson 2004.116). The best Roman example we have seen so far (better will appear later) are the Sortes Sangallenses. We are assured by function, of course, that one always moves from questions to answers. But we would in any case suspect this just from the structure in which the list of questions is well over 100 long, but answers for each go only 12 deep. Third, rows and headers do not simply group information; they also mean something, as signified by the real or virtual headers I have mentioned. A table can, of course, reproduce some of this information in individual entries, but it is not necessary if one is imagining the layout as a table. Yet we will frequently see units of measurement (e.g., every amount of money being given its own $ or € or HS, rather than using one symbol for the whole column) or the names of things being counted (e.g., writing out “window 4” and “window 3”) instead of just placing “4” and “3” in the “window” column).9 This is highly redundant if you imagine that structure conveys information, but not if it is decorative. 9 In fact, in the Roman instances I have seen, it is always a would-​be column header. Presumably this is another reflection of the fact that what we are looking at are basically lists.



Tables and Tabular Organization }  49

Fourth, I began the previous chapter with Goody’s contention that the power of the list derives from disembedding its elements from normal discursive structure so as to deploy them for other purposes, perhaps unforeseen by the maker. Marchese 2013.56 has made precisely the same case for the table. This disembedding makes the elements available for the “novel uses” we have already seen as a benefit of tabular organization. But this does not happen in cases in which rows (and it is always rows rather than columns) are bound together syntactically, so we perhaps have not a table nor even a list of lists but, rather, a list of sentences or similar composite units. The grain dole inscriptions, for instance, typically do not just give the data (day and place of draw) but also spell out the formula “receives public grain” in every line. Finally, there are some cases in which we may approach a possible table by comparing its organization to that of texts with similar content. In some types of inscription we see a possible table or two amid a majority of texts that display exactly the same information in nontabular form. In general that would not be particularly meaningful, but two things can make it relevant. On the one hand, as we have already seen, aesthetic motives could lead to quasi-​tabular arrangement even absent informational concerns, so certain kinds of information can genuinely fall into a real table as if by accident.10 On the other hand, sufficiently narrow functional or bureaucratic context can suggest that none of the otherwise identical lists was “meant” to be tabular. None of these diagnostics is dispositive in itself (especially the last), but we will often have the benefit of several indications at once. Would-​be tables that are much longer than wide often also contain extra or redundant information and/​or are paralleled by similar texts with no hint of tabular form. In particular, I would note that almost all these criteria apply in the case of objects I have already described as annotated lists. At the same time, one has to admit that none of this is certain. Since I have moved away from a purely formal definition to one that brings usage into play, certainty will often not be possible. Indeed, in at least some cases there will be a real possibility that different readers used the same object differently. In the final section of this chapter I will return to the possibility of a reader “mistakenly” taking some list for a table.

10 Looking forward to the rest of the chapter, I note the following indications that data could fall, accidentally as it were, into tabular form for mechanical or aesthetic reasons, even if that shape were neither meant nor read to provide information. Clearly some inscriptions emphasized columns without any informational implications (e.g., columns with wholly redundant entries; words abbreviated or with the final letter delayed to clean up column edges), and even columns that broke up “natural” units of information (e.g., grouping letters apart from numerals, rather than keeping a price with its unit; or conversely entering credits and debits in the same column because of their formal similarity). Victorius’ description of his own work suggests that is precisely what happened in his case. The columns were deliberately produced to record a series of multiplications; it is an accident, and an effect that he appears not even to notice, that lining up parallel columns can appear to produce rows, as well.

50

50 { Mosaics of Knowledge The rest of the chapter will be arranged as follows. The first section describes the few clear cases of tables in the Roman world. Then we will examine a number of contexts in which one might expect tables to appear, show that they are not found there, and then consider a few especially ambiguous cases. Lastly, we’ll attempt some inferences about why tables do and do not appear where they do. This will not be a matter of necessary and sufficient conditions. Rather, as we will see, the (non)use of tables is affected by the weighing of several more or less independent factors.

Actual Tables Here I offer three clear examples of tables or categories of tables.

CENTURIATION Land allotments to individual settlers in new Roman colonies were commonly based on a division of territory into squares or rectangles called centuriae, or “centuries.” Surveyors marked out boundaries on the land and produced a maplike representation (called a forma), which might also list the original holders of land allotments (see figures 2.2, 5.14). The allotments, their size, block location, and ownership were then digested into a register (the liber), which could be reproduced and transported. Individual centuries were identified by their distance from two perpendicular axes—​the kardo and the decumanus. Thus, a block could be identified by coordinates—​say, two columns to the right (dexter) of the decumanus (DD II),

FIGURE 2.2  

Schematic diagram of Roman centuriation



Tables and Tabular Organization }  51

three rows this side of (cis) the kardo (CK III). The formae were often carved into bronze, valuable if melted down later, so we have only one other surviving example plus one in marble (Cavalieri Manasse 2004, Piganiol 1962),11 but the standardization of practice is well attested both by archeological evidence and by formal accounts in surveying manuals (Hyginus 165L, Siculus Flaccus 154L). Moreover, we have several dozen field markers from widely dispersed regions that give coordinates in terms of the system just described.12

VARRO The first-​century bce polymath Marcus Terentius Varro wrote a long and often highly theoretical account of Latin grammar (and indeed of language in general) called de Lingua Latina.13 He was particularly interested in the use of analogy (and of series of analogies) to describe the structure of Latin. This discussion does not literally contain any tables, but it does give instructions to the reader for how to construct two of her own:14 This will make what I am saying clearer. Let numbers be laid out as follows: in the first line there should be 1, 2, 4; in the second 10, 20, 40; in the third 100, 200, 400. . . . Similarly, in the declensions of words there is a “crossroads” because in one direction we go from subject form to subject form and in the other we go from subject forms to object forms, so as to make a similar shape, that is: in the first line hic albus, huic albo, huius albi; in the second haec alba, huic albae, huius albae; in the third hoc album, huic albo, huius albi. Clearly he is imagining—​and wants his reader to imagine—​figures essentially like ­tables 2.1 and 2.2. In the latter case, the columns represent grammatical cases, while the rows give different genders. We will return to the context of these tables later, but their existence seems clear even in the absence of being concretely rendered within the text.

11 There are also bronze fragments of two similar grid maps, but without coordinates recorded in Sáez-​Fernández 1990 and Cavalieri Manasse and Cresci 2015. It has been argued (Lucchelli 2015.74) that the lack of coordinates in the latter case shows the region was not subject to distribution described earlier, but see contra Buonopane 2015.59. Moreover, a number of texts make reference to the use of the formae to settle property disputes; see ­chapter 5, note 97. 12 Numidia, Africa Proconsularis; Gallia Narbonensis, Macedonia; and several regions of Italy. The most famous instance is the Gracchan marker CIL 1.640 = 10.3861. 13 Taylor 1978, Garcea 2008, Habinek 2009.133–​4. 14 Quod dico, apertius sic fiet. Esto sic expositos esse numeros, ut in primo versu sit unum duo quattuor, in secundo decem viginti quadraginta, in tertio centum ducenti quadringenti.  .  .  . Similiter in verborum declinationibus est bivium, quod et ab recto casu declinantur in obliquos et ab recto casu in rectum, ita ut formulam similiter efficiant, quod sit primo versu hic albus, huic albo, huius albi, secundo haec alba, huic albae, huius albae, tertio hoc album, huic albo, huius albi (LL 10.43–​4).

52

52 { Mosaics of Knowledge TABLE 2.1  } Varro illustrates linked proportions with numbers

1 10 100

2 20 200

4 40 400

TABLE 2.2  } Varro uses linked proportions to structure the declension of an adjective

Albus Alba Album

Albo Albae Albo

Albi Albae Albi

DUTY ROSTERS Figures 2.3 and 2.4 display images of two military documents, both roughly corresponding to what is called a “duty roster” today.15 Each displays the assignments of individual soldiers in a small unit over a series of days.16 The former is a papyrus of uncertain Egyptian provenance (PGenLat. 1, column V). It provides a record for elements of the legion “III Cyrenaica” and can be dated to the first days of October of an unknown year around 90. The latter is a sketch of a ceramic fragment from the Egyptian frontier mining outpost of Mons Claudianus (OClaud 308).17 Its context is much more fragmentary, so the unit is unknown and the date can be fixed only roughly to around 150.18 In both rosters there appears to be a distinction between fully blank cells (perhaps representing mere lack of an assignment) and ones containing a horizontal stroke (perhaps for men with exemptions).19 Given the parallels between these documents, they could represent a common type, as with centuriation. On the other hand, we possess a fairly substantial quantity of documentary records from the Roman military, including many that appear to record duty assignments, and I know of no other tabular examples, even in fragmentary form.20 In this last section of this chapter I will give an account (admittedly speculative) of how these two documents might have arisen independently, but in parallel. That would suggest that they are in fact more like the idiosyncratic table of Varro than the standard forms of centuriation.

15 Fink 1971 for texts and analysis; Phang 2008.205–​ 6, 2011.615–​ 6, for the particular texts mentioned here. 16 For a transcription of the texts, see appendix to this chapter. 17 For text and context, see Bingen and Cuvigny 1992. 18 On the date, see Bingen et al. 1997.510. 19 The earlier example also makes another distinction. Repeated assignments are generally represented by repeated notations, but in a few cases, a single assignment is written across multiple cells. We will see later that allowing information to cross boundaries usually disrupts tabular organization, but here it is harnessed to convey extra information iconically. 20 Thus also Phang, note 15, this chapter.

FIGURE 2.3  

Military duty roster from Egypt

Bibliothèque de Genève, BGE P. Gen. lat. Inv. 1. fragment 2, recto.

54

54 { Mosaics of Knowledge stip ue

ucsti . u.

aq .

a

u.p.

]q. . .

t]em

item u.p arm

item

sti ue item

u.p.

stip . u

u.p.

ucst

aq u

u a

arm

u

u

arm

u.p.

cibar . aq .

u

u FIGURE 2.4  

Military duty roster from Egypt (OClaud 308)

Not Tables My basic claim so far is that tables—​at least in the narrow sense of the term specified here—​are extremely rare in the Roman world. The rest of the chapter will be devoted to supplying the evidence to support that claim, noting certain exceptions and attempting to explain the resulting distribution of tables. This section will consider a series of contexts in which one might, from a modern perspective, expect the use of tables. In many of these contexts, there will be no hint of them. In other contexts, we will indeed see tablelike objects requiring further analysis, though most of these can be rejected with varying degrees of certainty. The “expectations” I have in mind are based on a variety of grounds: visual form (as in the case of the roster of names discussed earlier), modern custom in handling similar information today (e.g., grammatical or mathematical tables), or the habits of parallel modern institutions, particularly bureaucratic ones (e.g., governmental and military documents). I will go through a variety of examples, using these three rubrics (appearance, content, and institutional context) as an organizing device, but I do not mean them to have any particular analytical significance. I begin with cases based on appearance.



Tables and Tabular Organization }  55

APPEARANCE: FASTI For instances of Roman documents that look like tables, I will turn first to the several different kinds of record conventionally lumped together as Fasti.21 Although no two surviving examples are precisely identical to each other, all fall into one of three categories: calendars, lists of magistrates, and lists of official victory celebrations.22 Within each category there is considerable uniformity. To spare the reader’s patience a little, I will take up just one example of each type: a calendar from Venusia from around 20 (InscrIt 8), as well as the emperor Augustus’ slightly earlier lists of consuls and of triumphs now in the Capitoline Museum in Rome (InscrIt 1). These are among the best preserved examples of their respective types, and the forms are sufficiently well defined that further examples would be largely redundant.23 Modern accounts of the Roman calendar often take tabular form, and the ancient Fasti, typically very neatly arranged, certainly encourage that.24 This one provides several kinds of information in a fairly standard order (plate 1).





1. A cycle of letters running from A through H marking out the nundinal (market-​day) cycle (highlighted here in red). 2. The day of the month, designated in canonical fashion by either one of the three reference days in each month, KAL(ends), NON(es), EID(es, i.e., the Ides) or a numeral (or PR “day before”) showing the number of days until the next reference point (yellow). 3. The name of the month, but only on the first of each month (none shown in this image, but it is positioned roughly as NON or EID, but preceded by K). 4. Special festivals (green). 5. Notations such as F, N, and C for the civic/​religious status of the day (purple). 6. Miscellaneous information such as special sacrifices, astronomical events, or the number of days in the month, the last only on the last of each month (turquoise).

21 In general, see Feeney 2007, Rüpke 2011. Lists of magistrates and calendars, both common enough in the surviving remains, are clearly attested as “fasti” in antiquity (OLD, s.v.). We do not know the ancient name, if any, for the much rarer lists of triumphs (in addition to the principal example discussed below there seem to be only InscrIt 13.1.35 and 36). 22 There are also lists, in very similar form, of leaders of private associations (collegia). My remarks here apply to these as well. 23 The main difference, found primarily among the calendars, is that some exemplars display considerably more information than others. The sparser versions necessarily show less of the disruption of tabularity I will illustrate, but do not lack it. 24 For a list of these, see Rüpke 2011.6–​22, 44–​67 for general description and ix–​xii for catalog. A recently discovered instance from Alba Fucens (found subsequent to Rüpke’s book) confirms the patterns noted here (Letta 2014), as does an example from Taoromina found in the early 1960s, but only recently published more widely (most easily accessible in Ruck 1996).

56

56 { Mosaics of Knowledge Here the miscellaneous information is segregated at the far right and so does not interfere with the overall structure, and there are clear columns on the stones. Nonetheless, closer inspection reveals that most of the columns here do not represent any single variable, as the wandering of the color coding makes clear.25 If a given component is absent for a given day, notation for that category is omitted, and everything else on the line moves over one position to the left. So, for instance, the column that usually contains civic/​religious status instead registers festivals when they occur. (Additionally, on many calendars, KAL, NON, and EID are written wide enough to displace material to the right of where it would normally appear.) A few of the consular lists have the most nearly tabular form. For each year in the Capitoline example we have the names of the two chief magistrates plus numerical indications if either had held the same office previously. Every tenth year this information is preceded by the date from the founding of the city. In principle, this could give five columns (or six, if we include the date), but that is not really what we see. The first iteration of a consulship is not marked by a numeral, and is not even marked by blank space, since the main columns are right-​justified (as well as left-​justified). Even if we just ignore the iterations, we cannot quite read the table in three columns, either. On the one hand, there is a good deal of miscellaneous information interleaved into the basic consular list. Some bits of it are written across the entire field (holders of the censorship; interesting trivia about the consuls). Others are within one or the other of the visual columns (death in office and replacement; honorific titles). Yet others are written across the whole, but preserving the visual columns (abdication from office; holders of offices such as the military tribunate and the dictatorship that temporarily supplant the consulship). This means both that the content of the columns is unstable and that the “rows” are hard to parse, since they each take up a variable number of lines.26 On the other hand, even if all that “excess” information were stripped away, the remaining columns turn out not to mean much. There was, it seems, a standard order in which to list the consuls of a year (based on order of election), but Taylor (1951) has shown that the Capitoline Fasti sporadically (and without notice) violate that principle, perhaps as an honorific for the consul “promoted” to the first place. The reader, then, gets no consistent information from the two-​column structure. Most other magisterial lists are obviously not tabular at all, disposing their information as a single-​column list.27 A few of the others are like the Capitoline one—​ a roughly tabular framework broken up by the interpolation of other material such 25 This may be what Rüpke 2011.6 is referring to when he says the information is “partly in columns.” 26 The second and following lines of a given year are typically marked by indentation, but only if one is reading the left-​hand column. 27 On the ordering principles of these texts, see Bodel 1993, 1995. The closest case is probably the Fasti Antiates Maiores (InscrIt 3), in which censors are listed in the same columns as the consuls, but are written in a different color. They are not, however, distinguished from suffect consuls. The local magistrates of Emerita Augusta seem to have been disposed in two columns, but there do not seem to be other columns nor meaning to the ones we see, though the evidence is very scanty (Ventura Villanuova 2009).



Tables and Tabular Organization }  57

as the holders of alternative or replacement offices.28 And even if this material were to be removed, it is not clear what the meaning of the remaining columns would be. The Capitoline triumph list similarly contains a variety of information which would be easy to reduce to a table: name of triumphing general, his official title, year, opponent, date of celebration. In fact it does not form a table, for some entries spill onto a second and even third line. Each first line begins with the triumphator’s name and ends with the year of the triumph, so one might try to pull those out and read them as a table. This, however, interferes with the organization in another way. To ensure that name and year frame the line, the triumphator’s office sometimes precedes and sometimes follows the date, and in a few cases it is even split across the date.29 Furthermore, there are other bits of information that are occasionally interpolated among the standard ones: for example, if the triumph was the first awarded under some special circumstances; if it was a lesser form of triumph such as an ovation or “Alban triumph,” and others. When these circumstances are not relevant, the phrases are simply omitted. Thus different entries are structured differently. While these various forms of Fasti could have been put into tabular form, none of them actually was, and perhaps a majority do not even come very close. The proximate causes for this are, on the one hand, the absence of symbols (such as blank space) usable as placeholders and, on the other, the addition of information that has some general thematic relevance but that does not strictly belong to one of the categories that might structure a table. The former may have seemed efficient and the latter generous or informative, but both break up the overall organization.

APPEARANCE: LATERCULI These are a relatively small and obscure group of texts, but their (highly standardized) form is a useful test of the identification strategies just suggested.30 They are partial rosters of military units, typically set up by soldiers as part of a collective dedication on the occasion of their discharge. We have examples from the legions in the provinces and from praetorian and urban cohorts from Rome, and they all look much like this segment from third-​century Rome (CIL 6.32639.9–​12).



M(arcus)

Aurel(ius)

M(arci)

f(ilius)

Pol(lia)

P(ublius) C(aius) M(arcus) M(arcus) M(arcus)

Ael(ius) Gavius Aurel(ius) Aurel(ius) Aurel(ius)

P(ubli) C(ai) M(arci) M(arci) M(arci)

f(ilius) f(ilius) f(ilius) f(ilius) f(ilius)

Ael(ia) Aur(elia) Fab(ia) Aur(elia) Cl(audia)

Aụ[-​-​-​] Iu[-​-​] Ru[-​-​-​] As[-​-​] Ad[-​-​-​] M[-​-​-​]

For placement of suffects, see especially Bodel 1995.295. For examples of these arrangements, see, respectively, the years 126, 120, and 122. 30 Benefiel 2001 catalogs and discusses the other known examples. 28 29

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58 { Mosaics of Knowledge This looks a lot like the list of names from the beginning of the chapter, but contains other information as well, such as (with examples from the first full line) marker of parentage (f here) instead of manumission (L in the earlier list), “tribe” or voting unit (Pollia), and place of origin (however we reconstruct Au-​). So is this a table? Perhaps not. As noted, filiation/​manumission and tribe of residence are part of formal Roman nomenclature in general (see note 5, this chapter). Moreover, at least in military contexts, the same appears to be the case for place of origin.31 It is used in this way not just here but also in virtually all rosters of this and other types (as we will see again later). In short, this document really is just like the donor roster—​a list of names in extended, formal fashion, spaced out for what appear to be aesthetic reasons. Like that earlier roster, it displays both a column of redundant information (the f meaning “son of ”). Many other examples, though not this one, unnaturally delay the final letters of words so as to justify both edges of the columns in which they appear. Moreover, as Benefiel (2001.222, 227–​8) has pointed out, at periods when only some soldiers are given tribes, their occasional introduction is allowed to disrupt the order, rather than leaving blank space when they are not given. The context of the laterculi also suggests we should not take the formal columns as informationally significant. Keep in mind that this is a list of now-​former soldiers. That is, it is not likely anyone was using a hypothetical “name column” as an index to find twenty-​year-​old cities of origin, much less using, say, the tribal column to find anything. This appears to be a list, if perhaps an annotated one, in “telephone book” fashion. Next I consider three areas in which the subject matter itself seems to invite the use of tables: grammatical morphology, arithmetic, and accounting.

CONTENT: GRAMMATICAL TABLES Latin is a highly inflected language; much of the meaning of a sentence—​the tense of the verb, the identity of the subject—​derives from the choice of endings attached to the individual words. Modern students of the language spend an enormous amount of time memorizing paradigm tables, and tables are displayed more sporadically to illustrate other aspects of the language as well. Of course, we have already seen the scholarly use of just such a table by Varro. It is striking, then, that the considerable ancient grammatical literature appears to not use tables to organize paradigms nor for other organizational purposes. To simplify a quite complex body of material, I will divide the evidence into two categories. The first consists of treatises of greater and lesser detail and sophistication. All these, however, are essentially lists of rules of morphology, syntax, and so on. These are preserved in both a robust medieval manuscript tradition (whose formatting unfortunately may have been changed in copying) and on papyrus (whose remains are quite scanty but nonetheless show some distinctive features). These will be treated here. The second category consists of Latin/​Greek bilingual texts. These

31

Phang 2011.613.



Tables and Tabular Organization }  59 TABLE 2.3  } Modern declension of the phrase hic Marcus

hic Marcus huius Marci huic Marci hunc Marcum O Marce ab hoc Marco

[hi Marci] [horum Marcorum] [his Marcis] [hos Marcos] [O Marci] ab his Marcis

are preserved in the same kind of contexts as the treatises. I will reserve these for the next section. There are numerous writers of formal treatises, but as with the Fasti, the individual instances are sufficiently similar to each other that a few examples will easily stand in for the whole body. For examples of inflection, I will look at “declension” of nouns and adjectives, which gives their singular and plural forms in the different cases (that is, different syntactic roles). There are two main traditions of how to do this. One, the numerically dominant one, will be represented here by the approach of the writer Charisius.32 His nominal paradigms inevitably start by assuming a particular gender and declensional class. He works through the possible singular forms (in a standard order of cases), then presents the plural forms in the same order:33 A masculine singular proper noun of the second declension is declined as follows in either number: singular hic Marcus [“this Marcus”], huius Marci, huic Marco, hunc Marcum, O Marco, ab hoc Marco, and so on to ab his Marcis. (GL 1.23.8–​10K) A modern text would probably arrange this as in table 2.3 (I have supplied the forms Charisius skips over with his “and so on” in my square brackets): It has been claimed that tabular organization of these paradigms (even in the broadest sense of “tabular”) was a late medieval invention, but I  would concede that the manuscript evidence simply does not tell us much one way or the other about the classical state of affairs.34 Varro’s case of course shows that tables were in some sense possible, but such organization is, in fact, belied by the broader structure of this work. Charisius has a standard order not just for the values of a particular variable (that is, here, an order for the cases) but also for the variables themselves: gender and declensional class, then number, then case.35

32 Also Diomedes, Probus, Donatus, Pompeius, Consentius, the fragmenta Bobiensa, and (though see later) Cledonius. 33 Nomen masculinum proprium singulare simplex declinationis secundae ita utroque numero declinatur, singulari hic Marcus, huius Marci, huic Marco, hunc Marcum, O Marce, ab hoc Marco et cetera usque ab his Marcis. 34 Dickey et al. 2013.182–​3. 35 See Dickey et al. 2013 for a more detailed accounting of the possibilities.

60

60 { Mosaics of Knowledge Recall that a table can by its nature be approached from different angles. Maintaining a rigid order of variables then suggests Charisius was not imagining a table. In fact, his order is so fixed that the formula et reliqua, literally “and the others,” always means specifically “and the other cases,” not, say, the other genders. Moreover, the plural forms are here in sequence with the singular, not in parallel with them, as is shown both by the word “up to” (usque) and by the fact that Charisius can omit all the plural forms but the last and still expect the initial ones to be filled in. This is a list rather than a table. In contexts other than declensional paradigms, we do very rarely see words arranged as if Charisius were reading across a modern table rather than down (that is, varying gender rather than case):36 There are nouns common to the masculine and feminine genders like hic and haec canis (“dog”) or masculine, feminine, and neuter, like hic and haec and hoc felix (“lucky person/​thing”). (GL 1.153.14–​6K) Note, however, the presence of the conjunctions here. These forms are not simply being “read off ” as a natural series, as in the declension of Marcus, but rather are treated as an arbitrary assemblage. The rarer model is found principally in the work of Priscian.37 Based on the order in which they are always listed, his declensions also exhibit an underlying hierarchy of declensional class, number, and case. At the bottom of the hierarchy, however, the standard order of cases breaks down. There is an underlying order, but if two or more cases are represented by the same form—​for instance, puellae, which serves as both the genitive and the dative singular of “girl”—​they are lumped together under the earliest relevant case. That means that between the various combinations of singular/​plural and the five basic Latin declensional patterns, we see a variety of orders of the cases (summarizing GL 2.284–​368K): 1st declension singular: nominative; genitive/​dative; accusative; vocative; ablative 1st declension plural: nominative/​vocative; genitive; dative/​ablative; accusative 2s: nom.; gen; dat/​abl; acc; voc 2p: nom/​voc; gen; dat/​abl; acc 3s: nom; gen; dat; acc; voc; abl 3p: nom; gen; dat/​abl; acc/​voc 4s: nom; gen; dat; acc; voc; abl 4p: nom/​acc/​voc; gen; dat/​abl

36 Sunt communia [sc. nomina] aut ex genere masculino et feminino, ut hic et haec canis, aut ex genere masculino, feminino, et neutro, ut hic et haec et hoc felix. 37 Also in Cledonius, though he also gives the more conventional form as well.



Tables and Tabular Organization }  61

5s: nom; gen/​dat; acc; voc; abl 5p: nom/​acc/​voc; gen; dat/​abl As with Charisius, there are no tables in the manuscripts, and Priscian’s hierarchy of variables suggests that his underlying organization is similarly nontabular. His difference from Charisius, the shuffling of cases, breaks down the possibility of organization into tables, even if we wanted to impose them on the text as it is ordered. In fact, we can see traces of the same lumping tendency in all the grammatical writers. In addition to categories such as declension and gender still used today, the ancient authorities divide all nouns into six formae (e.g., Diomedes, GL 1.308–​9K). That is, all nouns with four distinct singular forms (e.g., aper, Vergilius, res, canis, sidus) are taken together as quaternia, while all those with five distinct forms (e.g., pater, doctus) are quinaria, and so on. As a practical matter, division into formae discourages tabularization since, say, different quinaria do not have enough in common to combine their declensions, especially if singular and plural are both to be considered. Perhaps more important, it suggests an organizational principle shared not only with Priscian but also with the calendars. All appear to seek local efficiency by reducing the number of entries, even if this preempts the possibility of overall systematization. The papyrus texts that contain declensions of nouns (or conjugations of verbs) very much confirm what I have already suggested on the basis of the better preserved texts. Consider, for instance, P Louvre inv. E 7332, which holds several columns worth of declensions of nouns.38 This is very carefully written, and each new item is introduced in red ink (accompanied by a notice of the categories to which it belongs and a Greek translation). That is to say, some thought went into the mise en page of this text. The order of presentation is fixed. Feminine nouns are treated before neuters, and within each gender the author puts entries in alphabetical order of the ending of the nominative form (this and gender are the categories explicitly listed at the beginning of each entry). Each entry then proceeds in linear fashion through the singular and plural forms, rather than breaking the latter out in a second column.39 Moreover, the bulk of the plural forms are omitted in favor of “et cetera,” and the nominative singular form is normally not part of the list, since it has already been given in the header. A table would not permit such omissions, but if we take the list form at face value, such truncations are easy. Our other early texts on papyrus are much more fragmentary than this one, but none suggests even this level of organization.40

38 On this text, see Dickey et al. 2013, Scappaticcio 2015.184–​226. The papyrus is attributed to the fifth or sixth centuries. I  cite it here partly because the text could be classical and partly because it represents the upper limit of sophistication in any texts known to this point. 39 The nominative plural is generally marked with “Pl” beforehand. 40 See Scappaticcio 2015 for a full scholarly edition.

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62 { Mosaics of Knowledge

CONTENT: MATHEMATICS If not in grammatical paradigms, then one might still expect to find tables in mathematics, whether for pedagogical use or as a practical aid to computations.41 In fact, we encounter here more lists, though the evidence is somewhat circumstantial. Accounts of Greek-​language evidence from Egypt frequently refer to “tables” for addition, multiplication, and standard fractions, but as far as I  can tell, no parallel text has survived in Latin before roughly the fall of Rome. I  want to suggest, however, that what aids must have existed were likely not tables in the present sense. First, the Greek texts just mentioned are better thought of as lists. In the normal case, we have what are unquestionably lists of computations in one (or a few) columns, without headers. When “rows” across are roughly present, they do not always line up. Moreover, all figures are written out for each computation—​2 + 2 = 4, 2 + 3 = 5, 2 + 4 = 6, and so on—​rather than just the result at each intersection of row and column. And in many texts, each calculation is doubled up with its commutative pair, that is 2 + 3 = 5 is followed by 3 + 2 = 5. There are no matrices here, much less ones that contribute to meaning. Second, the first Latin example we have (Victorius’ Calculus of the late fifth century; figure 2.5) seems, despite its physical appearance, to be conceived on similar principles to the Greek lists. There are 100 columns (here I show the first six), each with forty-​five entries. Every other column, starting from the second, runs from 1 (in the center) up to 1000 by standardized increments and down through a similarly regular series of fractions to 1/​144. The other columns give the result of multiplying the adjacent list of standard values by 2, by 3, by 4, respectively, and so on up to multiplication by 50. The repetition suggests each pair of lists (or, perhaps better, list of pairs) stands alone, and that impression is reinforced by Victorius’ explicit instructions. In the preface he describes the use of his work in considerable detail, following a hierarchy of column (linea) first, then elements within columns (2.12–​9 Friedlein). Not only does he not move across rows, but there does not even appear to be a word for them. The repetitiveness of the task makes the rows line up, but actual use does not exploit that fact. This is not a table but, rather, a series of long lists, which are to be consulted (per the directions) in one direction only.

CONTENT: ACCOUNTING Bookkeeping might seem like another natural place to look for tables, and some scholars were once inclined to look for just that in ancient records, at least in passing.42 This happened in attempts to locate the double-​entry method in antiquity as part of a broader assessment of the sophistication of the Roman economy.

41 For reflections on the list–​table distinction in this context, see Gierdien 2009. 42 On Roman accounting in general, see Minaud 2005 (though with a curious lack of attention to documentary evidence) and LaGroue 2014.



Tables and Tabular Organization }  63

FIGURE 2.5  Victorius, Calculus, as recorded in Cod. Vat. Reg. Svecor, 1569

From Friedlein 1872.7

The debate over that question is not precisely the same as the one here, but the philological underpinnings are quite similar. Thus, the broad review of the evidence from an economic point of view by de Ste. Croix will give us a good headstart on the tables, as well. As part of a broadly “primitivist” account of the economy, de Ste. Croix (1956.46) finds that, in Roman and Greek accounting, records were typically “in narrative, not in tabular form.” Even in that minority case, however, he means “tabular” in a fairly broad sense: lists of entries, each typically formed of a

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64 { Mosaics of Knowledge name (of a person or product) paired with a number such as an amount of money. In some cases, this may be what I have described as “telephone book” or “shopping list” style, and sometimes it is even less organized than that.43 That is, the amounts of money may actually mean different things, mixing credits, debits, and totals. De Ste. Croix’s chapter has been far from the last word on the broader economic issues, but even the strongest contrary arguments (e.g., Rathbone’s 1991 study of the management of estates in third-​century ce Egypt) do not show that individual documents are much more sophisticated.44 Rather, the various accounts from his archive (and comparable ones) are composed of individually simple lists of various kinds of expenditures, purchases, and stocks; any additional complexity lies in their interaction. Annotated lists are perhaps more common than was previously realized, but that does not suggest they had been surpassed. On the other hand, it is also possible that the mismatch between the issue of economic sophistication and the specific form of bookkeeping could cut the other way. It might be possible that, for whatever reason, more complex records might have arisen in the context of some enterprise that as a whole was smaller and simpler. My survey of more recent evidence appears to confirm that this is not the case. Texts which show a clear columnar structure fall into one of two categories. A few maintain a rigorous shopping-​list form, like item, price; item, price; item, price. Documents which attempt to capture more complex information (and even some of those that do not) show breakdowns in the structure. Moreover, even when there are more than two items of information in each entry, the lists are almost never broken out into more than two columns. That this is the range of possibilities suggests to me that the graphic columns do not really represent a cross-​cutting variable of the same status so much as they do lines of text, and so the documents are properly called lists. There is too much evidence to review it all here, so I will offer two illustrations. One is an individual document that is an “exception” that tests the rule about only having two columns.45 The other is a set of related (and therefore mutually illuminating) accounts that has only come to light in the last few decades. The first document lists information about employment in a small weaving operation: date, job description, number of workers of that type for that day, and their total pay (POxy 4.737; I.7–​13; late first century bce). Graphically speaking, this falls into five columns (my translation removes some ambiguity in the preserved dates).46

43 Clear list: PVindob. L 111. Confused lists: PGenLat. 1, recto; Egypt; 80s ce = ChLA 7=RMR 68; PMasada 722; BM 1196. I treat instances from Vindolanda separately. 44 Bresson 2011 takes this later in date, but without additional refinements in terms of the issues discussed here. 45 See note 51, this chapter, for possible exceptions at Vindolanda. 46 ChLA 308. Excellent image at http://​library.case.edu/​digitalcase/​imsvr.ashx/​vga/​ksl/​oxyacc00/​ oxyacc00.jp2 (where the original is held)



Tables and Tabular Organization }  65

9 10 11 12

March weavers hired men March weavers hired men March weavers foreman March weavers

2 2 2 2 3 3

asses asses asses asses asses asses asses

7 8 7 8 10.5 6 10.5

Each line represents a particular category of worker(s) hired for a particular day. The date is only given for the first entry for any given day, and apparently no numeral is given if there is a single worker in a given category. While the matrix structure of this list is very clear, several features make it seem less tabular. The units are repeated anew in every row instead of being written or even just assumed as “header” information. In fact, they form a column of their own, rather than being part of the pay amount. Second, we have regular spillage from the first column into the second. More specifically, the verbal part of each date falls in the second column, while the numeric part of the date is left in the first.47 That is, for both the dates and the amounts of money, the columns are sorted by the distinction between numerals and alphabetic characters, not by the content of the data. (This is perhaps an even more extreme version of the noninformational use of columns for punctuation and the like we saw in the list of names at the beginning of the chapter.) Finally, the use of blank space is peculiar. It is possible this is meant to stand in for an implicit “1” in the next-​to-​last line of my example, but it seems more natural that blank space would mean (if anything) zero. Rather, the number is to be inferred from the singular ending on the noun, with the blank space not “meaning” anything at all. In that case, this means the text relies on reading elements across columns, not in the segregated fashion we expect of tables. And the spacing would then be another example of numeral/​letter segregation described earlier. The columnar structure might have arisen for greater legibility or simply for aesthetic reasons, but they do not provide informational structure. From the other end of the empire, there are a number of documents surviving from the Roman military encampment at Vindolanda in northern Britain (first–​ second centuries; Bowman and Thomas 1974–​2003). Among these are quite a few “accounts” (to use a very generic term) listing various commodities. Each of these is typically put on its own line and is followed by a quantity and/​or price. The numerical data are frequently pulled out into a column of their own, presenting a tabular appearance. Among these broadly similar documents, several can be ruled out as tables: some confuse different kinds of numerical data in the manner already discussed and some do not actually separate the numbers in their own 47 Technically, what we get in the second column is Idus or Nonas, not the name of the month. This is true for every preserved entry, except for the Nones, which then occupies the first column by itself.

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66 { Mosaics of Knowledge column.48 Nothing absolutely rules out the possibility that some of the others are tabular, but there are numerous reasons to doubt it nonetheless.49 The lists are normally organized by date and/​or by person (the giver or recipient of the objects), and the structure of the would-​be table is frequently interrupted by the interleaving of this other material. In fact, these are so frequent that they would have made sense as a header column if the writers were really aiming at tables. The hierarchy of parameters is the same in every document—​date, person, commodity, quantity, price—​suggesting a nested-​list structure. Sometimes nouns are listed in what appears to be a default usage of the accusative case, but all cases appear at least occasionally, assuming a syntax built around an implied verb. That is, the individual entries are construed as sentences.50 Finally, when there are two numbers in each line (i.e., both quantity and price), only the last is normally pulled out into a column.51 It is not impossible that one or another of these documents was meant as a table, but if so, that aspect seems not to have been valued at all, even in the immediate circumstance. What, then, of contexts where we might expect higher than average formalization of data collection? The state—​and in particular the army—​was both the largest organization in the Roman world and presumably the best able to require conformity with particular bureaucratic procedures, if so desired. Vegetius, a writer on tactics, even comments that legionary recruits needed not just physical strength but intellectual ability as well, because military recordkeeping was the most complex in the Roman world: The accounting of the whole legion, whether of duty assignments or secondments or financial matters, is entered into the records on a daily basis with greater diligence than the grain distribution or civil administration are recorded. (2.19) The other large-​scale projects the government engaged in included the distribution of various basic survival needs such as grain and water especially, but not exclusively, in Rome itself. This seems like a good place to look for tables.

CONTEXT: FASTI AND LATERCULI I treated both of these already for their graphic similarity to true tables, but they could just as well have been treated under this heading. That is, both come from environments in which one would expect both bureaucratic habits of mind and an ability to compel

48 Tab. Vindol. 181, 182, 185, 186, 190 (= 4), 192, 202, 581, 590, 596. 49 Tab. Vindol. 176, 180 (though here the right-​hand column is quite rough), 184, 207, 586. 50 Adams 1995.114–​6, 2003.547–​9. 51 The one seemingly clear exception is Tab. Vindol. 193, which consists of three lines of item/​quantity/​price. However, several longer texts (182, 186, 588, 596) have segments which maintain three-​column structure for similarly short stretches, but surrounding lines have different information and so different information structures. The spacing in the three-​column segments thus seems designed to separate items within the line more than to align columns vertically, and that might well be true of 193, as well.



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conformity with the bureaucracy’s notions of proper form. But, as we have seen, those circumstances do not give rise to tables in those contexts. Let me turn now to four different sets of examples emanating from other governmental contexts.

CONTEXT: ALIMENTA In the early second century, the emperor Trajan set up programs to provide financial support for selected youths (the motivation and precise selection are quite opaque).52 These were to be funded by making state loans to landowners, then directing the return payments to the subsidies (alimenta). We have a pair of inscriptions that record not the distributions themselves but the loans. For instance, a text of the early second century lists name of debtor, location of property used to secure the debt, amount loaned, and periodic payment on the loan (CIL 9.1455; Campania). This kind of stereotyped information would obviously lend itself to tabular organization, and since this is a state document, we might also expect bureaucratic pressure in that direction. Yet the bronze shows only two columns instead of the (at least) four we might expect from the information being displayed. Moreover, one of those columns contains only the monthly payment. Though there is very slight ekthesis, the names are buried in blocks of other information, so it is hard to use them to look up individual entries. Moreover, the rest of the text in these entries is written as a single chunk, breaking whenever the width of the column runs out, rather than at any point determined by the meaning. Each entry repeats a variety of “header” information—​not just HS (the standard monetary unit of account), but also words designating the assessment of the property, the value of the loan, and the name of the property itself.53 The names of the individuals are given in a case that marks them as recipients, syntactically connecting them to the rest of the entry, rather than the isolated form we would expect in a full-​on list or table. If this is a table, and it perhaps qualifies in purely formal terms, it makes little and poor use of that fact. The other document (CIL 11.1147; Emilia Romagna, early second century) gives roughly the same information, but dispenses with the vestigial second column; all information for each entry is contained in a single, continuous paragraph.

CONTEXT: MILITARY ROSTERS We have already seen the two duty rosters that are unambiguously rendered as tables, but there are other military rosters whose status is less clear.54 A number of 52 See, in general, Woolf 1990 with citations of the previous literature; and Criniti 1991 on the Veleia inscription. 53 Respectively, aestimati, in (with an implicitly accusative object), and fundus. Incidentally, the payment due in the exterior column is redundant, since it is always a set fraction (2.5%) of the loan amount. 54 In general, see the references in note 15, this chapter. There are a few additional instances on ceramic fragments including (beyond the one discussed here) OClaud 304–​6 and OAmst 8 (on the latter, see Clarysse and Sijpeseijn 1988).

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68 { Mosaics of Knowledge these survive on papyrus, most from an infantry unit known as the 20th Palmyrene cohort at Dura Europos in Syria. Most are broadly similar to the laterculi and to the simple accounting records discussed earlier. That is, the core of each is a list of members of the cohort, and many include no more than this.55 They are typically divided by subunit (infantry century or cavalry “wing,” denoted by the commander’s name), then within each the officers are listed, then rank-​and-​file soldiers ordered by year of enlistment. Unit names and dates are typically interleaved in the list rather than being put in the margins. Soldiers’ names are often divided into graphic columns in the standard fashion seen earlier. Additionally, however, a number of texts have verbal annotations giving rank, place or task of assignment, and/​or information about transfer. In some others, further information is conveyed by symbols, such as bars, arrowed bars, or dots. There is a typical, if not entirely uniform, order to these notations. From left to right we get: (in some entries) one or more dots of varying sizes, title indicating rank or pay grade, assignment (or a bar which seems to indicate a lack of assignment), then name (including place of origin). An arrowed bar sometimes appears, nearly always on top of a title, and seems also to indicate lack of assignment (Fink 1971.11). However, while the standard order tends to produce rough columns, the overall result is not a table. For instance, the arrowed bars sometimes come on top of indications of rank but sometimes precede them (e.g., #2.xxxvi.16; Fink 1971.2.xli), so they do not always preserve columnization. More significantly, rank and assignment, as well as some rarer information like transfers, often appear in a single column.56 This is because, like the Fasti, there is no systematic use of placeholders beyond the no-​assignment bar. There are also occasional idiosyncratic deviations from pattern—​for example, expressions of substitution off to the left in 1 Fink.57

CONTEXT: GRAIN DISTRIBUTION State grain distribution in the city of Rome was a huge operation; the numbers vary over time, but on the order of 200,000 persons received monthly allotments.58 Strictly speaking, the inscriptions we have are not a part of the administrative mechanism for this, but are private commissions of enrollees (as it happens, mostly guardsmen who left inscriptions at Ostia) who wished to advertise their status as rights-​holders. Still, the connection to what would seem to be a large bureaucracy, and the fact that many of these honorific inscriptions themselves arise from

55 On the formatting, see in general, Fink 1971.11–​7. 56 The substitution notations are rare enough that Fink describes them as intercolumnar rather than constituting their own column; moreover, they only appear in one of the rosters. 57 See, more fully, Fink 1971.13. 58 In general, see Virlouvet 1995, 2009.



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formal, military contexts, might lead one to expect a systematic use of tables such as likely existed in the case of centuriation. The relevant variables, as we saw in ­chapter 1, are name of recipient, day of draw, and either assigned window or tablet (presumably recording eligibility). Although we have a number of surviving parallel texts, most of them are clearly not tabular. There are two possible exceptions, one of which I reserve for the next section. The standard transcription of the other plausible candidate (CIL 6.220; Rome, early third century) suggests a tabular form, and in one place the carver appears to use blank space to preserve the integrity of the columns when information is lacking (line 19, no tribe given, for reasons unknown).59 In real life, however, the rightward drift of the lines and the sparing use of blank space make the table less clear than in the transcription. Moreover, much of the repeated information binds the lines together as syntactic units; each line repeats the formula “became a soldier on [date] under the prefect Magnus; received the public grain.” Furthermore, two of the main “variables,” the day of draw and the register of enrollment, do not actually vary; all these men draw on day 10 of the month and are recorded on tablet 144. While there are plausible, if ambiguous, formal reasons to see tabular organization here, it is not clear what purpose that form might serve. The other five texts recording allocation to groups of men are clearly nontabular for the kinds of reasons seen in other cases.60 For instance, in CIL 14.4500, we have roughly the same information as before, but the would-​be columns for, say, tribe, date, or window/​register, simply fail to line up. Additionally, there is a whole other set of texts in which some or all of the same information is recorded in formulaically similar language, but for single individuals.61 It is possible that this reflects multiple instances of mechanical borrowing from a tabular source, none of which transform that source, but it is simpler to imagine that the formula itself (roughly the individual row) is the basic unit here. Certainly, the repetition of redundant information in successive lines of longer texts would suggest this. This reinforces a nontabular reading of even CIL 6.220. Some published editions might suggest that another inscription, tied in a different way to the grain dole, is a table. Mommsen 1845.231 printed the fragmentary CIL 6. 10211 as a table of at least three columns: tribe, number of enrollees in the grain dole in each tribe, place where grain was received. Virlouvet 2009.234–​5 shows that this interpretation of the columns is unlikely, but the structure might still be tabular. While Mommsen prints the text in highly columnar form (even

59 The reproduction in CIL suggests a similar use of space in the previous line, where the date apparently did not require a numeral. It appears to me, however, from Virlouvet’s photograph, that in fact “ID” is centered in the column, so no full space is required beforehand. More broadly, though, this does suggest that the carver was thinking in informational terms (date) rather than formal ones (numerals vs. words), as we will see in other texts later. 60 CIL 14.4500, 4502, 4503, 4505, 4506. Cf. Virlouvet 2009.105–​94. 61 Collected at Virlouvet 2009.195–​270.

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70 { Mosaics of Knowledge lining up the numerals as if using some kind of place notation), other reports on the layout from the nineteenth century conflict with one another, and a very recently published photograph seems to settle the matter.62 The numerals indeed form a column (though without lining up place notation), but the prepositional phrases continue directly thereafter, rather than forming a separate column.63

CONTEXT: WATER DISTRIBUTION Our texts recording water distributions are fewer, more scattered, and more diverse than those attached to the grain distribution, but for our purposes, the basic idea is the same. They record similar information that could easily be tabular—​name, time(s) when water can be drawn, size(s) of allotment—​but in fact are not so. Again, I reserve one special case for the next section, but the remaining examples do not even break entries down into lines or rows, much less columns. Allotments are organized by place in a diagram (CIL 6.1261), by paragraph, and perhaps also diagram (CIL 14.3676), and seemingly (the text is broken) by paragraph (CIL 6.31566).

Outliers This section gathers several examples that are more ambiguous than those in the previous two. Part of that ambiguity lies in genre; they display information that we have already seen is not normally delivered in tabular fashion. The very fact that they would be isolated tables in their respective contexts where tables were not conventionally found is reason for some suspicion, but it would also make them particularly interesting if they do indeed turn out to be tables. The specific cases are:

• A water distribution text (CIL 8.4440/​18587) • A grain distribution text (CIL 14.4499) • A list of the victories of a charioteer named Teres (CIL 6.10053–​4) • A small set of bilingual texts apparently used for language instruction



I will treat the first three together, then come back to the language texts. The water distribution inscription (Lambasa, Algeria, early third century) is tabular, at least in formal terms, very much like the alimentary inscription discussed earlier. The columns give (in this order):  the name of the person drawing water at each site, the size (apparently) of the relevant property, and (as a single complex item) the times at which water could be drawn.64 That is, it dedicates an entire column solely to a number with no clear value as a reference index, then packs all the remaining data (several phrases giving the days and times when water might be



Minervini 1846, Mommsen 1845. Camodeca and Solin 2014.98 (SuppIt Imagines 4390). 64 On this inscription, see Shaw 1982 and Meuret 1996. 62 63



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drawn) into a single other column. The columns do little sorting, and the sorting they do is of no clear practical value. A grain distribution inscription, again formally tabular, records guardsmen enrolled in the public grain dole as a reward for a requisite number of years of service.65 After a brief preface, the columns of this document record name, date of enlistment, day on which grain could be drawn, the register on which the individual was listed, and an abbreviation (KC) of uncertain meaning.66 In some cases, the actual numbers are missing, but in general the text uses blank space to maintain the order of what is recorded. So much is tabular. On the other hand, not only does every line end with the seemingly redundant KC but each also includes the formulaic F(rumentum) P(ublicum) A(ccipit), or “receives public grain.”67 Additionally, the names of the two “variables” (day and table) are included in every line rather than being inferred from position, much less under a column header. Finally, the total effect of all this repeated material is to frame each line as a grammatically complete sentence. Teres’ inscription (Rome, early second century) lists the name of each horse, its origin or breed, and the number of victories won with it. The columns are clearly spaced out, though they are broken into a series of windows, rather than forming a single matrix. There is some difficulty in reconstructing the text as a whole. The text is divided, for reasons unknown, into two registers, and each register contains at least six columns; that is, the basic three-​column structure is replicated both horizontally and vertically. (Both original edges are now missing, so the overall layout is hard to reconstruct.) The columns in the two registers do not line up, so we have at least twice as many tables, if that is what they are, as needed for the data. The individual entries are listed in increasing number of victories. This combined with the extreme length of the whole (in contrast to its three-​column width) suggests a list. Other texts in the genre take on a variety of forms from continuous text to partial columniation, but none is comparably tabular.68 In all three cases, then, we have inscriptions that probably meet any reasonable formal test for tabularity, but which have other features that suggest this may in some sense have been the accidental result of recording repetitive data, including the fact that all are outliers in their respective fields, but are otherwise diverse from one another. I turn now to my last case, which is different is several respects. The section “Not Tables” discussed grammatical texts designed to lay out rules, particularly rules for the inflection of words. But as I mentioned then, there is another kind of grammatical text, albeit not as well preserved in our sources. This comprises a variety of bilingual texts—​glossaries, scenes from daily life in dialog form, and translations of literary works—​apparently all designed as aids for



On this inscription, see Virlouvet 2009.114–​20. On this inscription, see Virlouvet 2009.148–​69. 67 The tense of the abbreviated verb is uncertain. 68 The rest of CIL 6.10047–​56, 10063, 10067. 65 66

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72 { Mosaics of Knowledge language learners.69 Nearly all are in two-​column format, with the content typically extending over many pages.70 That is, they have the long and narrow shape typical of annotated phone-​book-​type lists. In the cases where there is evidence, they have a clear hierarchy of parameters (read down the left-​hand column, then across), because the left-​hand column is normally in some mechanical order (alphabetical or declensional) and only has one entry per line; the right column sometimes contains two translations of the same word or phrase. A number of the glossaries do not have either of these features, but there is no positive indication they would be used differently, either. There is, however, a closely related set of texts that might make more sense as tables. These are what Eleanor Dickey (2015) has described as columnar translations.71 At a quick glance, these look like the glossaries—​parallel lists of words in the two languages—​but there are two differences. The less important one is that the entries in these texts are often brief phrases rather than single words. The more important difference is that the columns can be read continuously as a single text. In some cases, the base text is an existing piece of canonical literature (Cicero, Vergil, or the like), and in other cases it is a simple composition, typically about some aspect of daily life. The latter seem to be designed as aids for beginning language students, while the literary texts are presumably aimed at somewhat more advanced ones. Dickey has shown that these texts were originally developed in the West to help Latin speakers learn Greek, but that the format was eventually borrowed for the benefit of Latin learners in the East. Like several of our list-​texts, they still have a clear directionality in the internal logic of the text and are much more extended in one dimension than in the other. And presumably the less advanced a reader, the more likely she would always simply read down and then across from native language to target (as with the glossaries). But there is another possibility. Some individual texts (of the elementary types) seem to have been transferred from the Latin context to the Greek more or less intact.72 This would mean that, at least over time, they were read both left column to right and vice versa. Moreover, unlike the glossaries, both columns would have a clear structure (whether narrative or argumentative), so either or both could be used by a given reader as the starting point. One could also imagine a reader working back up through the text to find some key word by remembering roughly where in the story it occurred. In short, it is not hard to imagine that at least some users “read” these texts in both directions, along both axes.

69 Fresura 2013; Dickey 2015; Ammirati 2015.39–​40, 48–​61, 65–​72. 70 There are some written in continuous text, and a very few that put a gloss in the same column as the lemma, but indented. These are not relevant here. 71 These appear to have been composed originally in roughly the second and third centuries, though many of the individual cases are complicated because the texts were clearly edited by users over long stretches of time (Dickey 2012.1.29, 50–​1). 72 Dickey 2010, 2015.1.39–​52; Ammirati 2015.41.



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Conclusions The most basic things I hope to have shown by this point are that tables are extremely rare in the Roman world, that many data sets the Romans saw fit to write down could easily have been put in tabular form, and that the tables that do appear are quite widely scattered, showing neither a geographical localization nor clear evolution over time. I have spent a lot of time on definitional issues because I think they illuminate the function(s) of tables, but I should stress here that they do not have much impact on the first, numerical claim I just made. Even on a broader understanding of “table,” we would still have only a few examples, given the breadth of time, space, and genre surveyed here. The reader has already seen every plausible category of example of which I am aware. The order of magnitude of the count does not change even if we judge everything I have called an annotated list to be a table instead. (And, in any case, one would then need an explanation of why such lists make up such a large fraction of all “tables,” which seems merely to rephrase the same question asked here.) Moreover, we have some ancient testimony that confirms the point. At the opening of the chapter, I speculated (and it does remain speculation) that Quintilian had avoided a particular theory because its underlying logic was tabular. But there are actually cases where we can see similar reasoning much more explicitly. That is, we know two authors who doubted their audiences’ knowledge of tables. We saw that Varro constructed an indisputable multiplication table to make a point about the analogical relationship between grammatical forms. For the present point, the important word in that sentence is “constructed.” He explains it step by step, with no hint that he expects his audience ever to have seen such a thing before.73 Moreover, while Varro’s table suffices to make his point about analogy, it would not be of any practical value, jumping from multiplication by 1 to 10 to 100 as it does. If his audience had been familiar with a more conventional multiplication table, it would presumably have been easier to point them to that instead.74 Somewhat later than our period, Jerome (in part translating Eusebius) expresses doubts about his audience’s familiarity with the table form. (See the last section of ­chapter 6 for more on Jerome’s massive, tabular Chronica of the late fourth century.) Eusebius spends two different paragraphs of his preface explaining what he is doing (8.16–​20, 18.14–​ 19.7H), much as Varro felt a need for explanation. Jerome reproduces all that, as well as additional instructions on color coding and warnings to copyists not to

73 Moreover, he offers the physical metaphor of a game board for additional guidance; I will return to this. 74 Among scholarly texts of Greek mathematics, Nicomachus has multiplication tables, but he has to construct them just like Varro does (Arith. 1.19.9, 1.24.2; cf. 2.3.4, 2.4.1). There is also a more specialized table earlier, which is also constructed explicitly, rather than by reference to more “standard” tables. No other attested author picks up on the tables, though there are not a lot of other number theorists.

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74 { Mosaics of Knowledge deviate from form (5.6–​16H), and even with all that, he worries about the difficulty of reading the new form (5.3–​6H). Tables turn out to be rare despite their utility in many contexts (as illustrated by the modern research cited at the beginning of this chapter). That would not sound in any way paradoxical if we were talking about technologies like cast iron or even Archimedes’ most sophisticated, calculus-​like discoveries. Casting iron and performing integral calculus are hard to do even if the results are valuable. Though it is probably less intuitive, I would suggest that we should think of tables in the same way:  they are harder than they look. Though reading and writing have become naturalized in some contemporary societies, illiteracy is historically the norm, and possession of literate skills turns on a complex array of social factors. To the extent that the use of tables is an advanced, specialized form of literacy, we would expect the same to be all the more true. We also need to look to factors that are more specific to tables. They are tools that, in the long run, make certain tasks relatively easier. Yet they require knowl­ edge of representational conventions (Novick and Hurley 2001.160). It is not a fact of nature that items in a row or column stand in any particular relationship to other items in the same row or column, much less all of them simultaneously. Nor is it self-​evident that the lines in a table are guides without any direct representational function (contrast the lines in a tree diagram which stand for relationships). Tables also seem to require an upfront cognitive investment when a given instance is first encountered. It is hard, for instance, to teach machines to interpret tables, especially if, as is the case for most Roman tables, they are imperfectly formed and underspecified in terms of row and column headers (Hu et al. 2001, Zanibbi et al. 2004). Ultimately, you can do more with tables, but it requires an investment. Today these difficulties are largely overcome by cultural saturation (Novick and Hurley 2001.201–​4). Whether or not children are formally instructed about tables as such, they encounter them (and often are required to use them) in classes on other topics in school, in administration there (e.g., class schedules, cafeteria menus), in the media, in posters in doctors’ offices, and so on. This leads to a virtuous circle. The evidence suggests the reverse for the Roman world; as with the specialized types of lists in the previous chapter, we see a vicious circle. The device is rare, so few expect an audience to be able to read it. Absent some specific institutional context, then, readers are not passively trained by the generic written environment, confirming the constraints on writers. In fact, the situation is slightly worse than that, since the “writers” are not really a special class actively choosing not to deploy tables. There is no reason to think that they are typically any more familiar with the table than their readers. It may be particularly important for the specific arguments of this chapter that tables present a cognitive difficulty that is absent in their close kin—​the nested lists or categories. The latter can be grasped piecemeal in a way that tables cannot. That is, a reader can understand that some element is a member of a given list or category



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without knowing or caring about how any given structure fits together. (Lakoff 1987 and others have even argued that this conceptual structure, modeled on intuition of physical containers, is one of the most basic and universal features of human symbolic cognition.) The point of a table, by contrast, is to locate each element simultaneously along both axes. You have to understand the table as a whole to read any given part of it. It is not surprising that there are more nested lists than tables, even when both would have been possible. There are also some more culturally specific issues that might further retard the development and/​or spread of tables. In the last chapter I argued that unease at relying on paratext constrained the use of some kinds of lists. That would be all the more true for tables, since they are more resolutely paratextual than lists. Lists are at least linear, and so they can slip back and forth from regular discourse to the disembeddedness that marks their distinctive status. Graphic tables are, by definition, two-​dimensional and so can never be fully embedded in a linear text. Moving away from factors we have noted already, we see that Romans are often stereotyped, not least by themselves, as a “practical” people, particularly by contrast to Greeks. Like many such stereotypes, this one is vague, tendentious, and not in itself explanatory, even if true in some sense or other. At the same time, the view does not come from nowhere, and I think I can point to two more specific cultural features that contribute both to that stereotype and to the situation I have been describing with respect to tables. First, there are local “improvements” like the “efficiencies” in the construction of Priscian’s grammatical declensions or, conversely, the redundant clarity of the repetitive columns of multiplicands in Victorius’ multiplication lists. They are locally practical, but globally they do not allow structure to do any work. Second, and I  think this is more than just a special case of local efficiency, is a horror vacui, the avoidance of using blank space to maintain structure, as in the Fasti and military rosters.75 One parallel outside the world of tables strictly defined might be found in the boards used for the board game today called Duodecim Scripta. In Greek-​ speaking areas, these boards are typically made up of abstract square or circular spaces. Latin versions are invariably made up of actual things, letters in words.76 This approach is also paralleled in (clearly nontabular) texts in which information will be inserted in a more abstract sense—​say, legal formulas into which the actual names of plaintiff and defendant must be inserted according to the needs

75 Cf. Kessel 2008.21–​2 on the importance of blank space. Several readers have suggested to me that the lack of placeholder notation in Roman numerals might be another instance of this phenomenon. I find the idea attractive, but I am hesitant to put much weight on the non-​use of a technology that they were likely entirely unaware of. 76 On these boards, see Schädler 1995.81. The principle is not absolute across all games. Latrunculi and some other games are played on a checkerboard (Austin 1934.26–​7), and for at least some games there is evidence that the pieces were placed in the blank spaces (Schädler 2007.361, though the Varro passage is an important part of his evidence). For others (Austin 1935.79; perhaps Schädler 2002), they are clearly placed on the intersections.

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76 { Mosaics of Knowledge of the particular case. In these cases, Latin prefers a dummy pronoun (e.g., ille, or “that guy”), pseudonym (e.g., Numidius Negidius, roughly “John Doe”), or tacitly exemplary term (e.g., a specific sum like HS 250 standing in for whatever the actual amount is). These have all been reasons for the rarity of Roman tables, but we do still find examples from time to time. Can we tell why they are distributed as they are? I think there is in fact no single explanation, but we can observe several factors that promote tabularization.

IDIOSYNCRATIC FACTORS Robson (2003, 2004, cf. 2007)  has studied the use of tables in Mesopotamian cuneiform texts and found a somewhat similar hit-​and-​miss pattern (though with clearer chronological patterning and narrower functional range than in the Roman record). The first great period of use even seems to be tied to the practice of a single administrator (2004.126, 138ff.). While I will sketch some factors of greater generality in a moment, I should make clear immediately that the Roman record also provides cases where tables seem to arise as a result of highly local contingencies. The grammarians, who eschewed tables altogether, were interested primarily in a specific and concrete subject matter, be it declension, or state officials, or whatever. Varro, however, was most of the way through a three-​book-​long discussion of analogy as a tool for understanding language. That is, he was working in a far more theoretical context to start with. For him, constructing a table is an extension of the principles of analogy. After all, constructing a simple analogy of the form A1:B1 ::  A2:B2 is, in effect, constructing a two-​by-​two table. Varro, or perhaps some predecessor also writing on the topic of analogy, also saw how to generalize that procedure by producing tables of larger size, a procedure he calls “conjoined analogy” (LL 10.48). Quintilian’s overall project is less theoretical than Varro’s, but there may still be an important local parallel. As I pointed out at the beginning of the chapter, Quintilian reached his conclusions after an extensive review of many other versions of the theory of status. And apparently, given his own three attempts, the topic was one he had given a lot of thought to over time. Yet, different theories of status are not really that different from one another. The various authorities were generally choosing from the same limited pool of elements and arranging them in similar kinds of patterns. While Quintilian was not working with such abstract categories as “analogy,” his immediate task was essentially one of (re-​)organizing the traditional substance of status, not of discovering new types (much less overturning the whole). Thus it would be less surprising for him to stumble onto an innovation in organization as such. But from his point of view, the informational novelty is a distraction, not an achievement. Hence, he hides it behind a more conventionally organized version of the theory.



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REPRESENTATIONAL VS. CONSTITUTIVE RECORDS It is striking that the vast bulk of what is represented on centuriation formae is text and the man-​made grid itself, not other features we would consider maplike (see further on this in ­chapter 5). I think there is a principle at work here that can be generalized to the two other cases where we may have more than a single table used for the same purpose. I would suggest that Romans are more comfortable in informational contexts with records that are constitutive rather than representational. That is, they record facts called into being by the table itself or as part of the same project as the creation of the table; they avoid registering independently existing facts. So, for instance, the centuriation records coordinates and land assignments that are made by the state and its surveyors, not, say, topographic features. The rosters give assignments for soldiers, not their height and weight. Even the parallel texts give what the writer stipulates is a translation, not an independently identifiable feature like a line number. The same can be argued for one of the more idiosyncratic tables. At a minimum, Quintilian is representing his own theory, not analyzing someone else’s who could dispute the reading. Additionally, I would argue that Quintilian is creating the individual elements of his table, not merely borrowing them. All the other rhetoricians differ in how they arrange some subset of the same pool of categories like “legal” and “definition.” For Quintilian, however, those are no longer the ultimate types but (to the extent that they still exist), rather, the row and column headers. The six types, which don’t have names at all, are defined instead by being at the intersection of two higher-​level categories. It is also worth pointing out a small but significant aspect of the phrasing here. Quintilian consistently exemplifies the three quaestiones with the indirect questions an sit, quid sit, and quale sit, or “whether something is, what it is, and what sort of thing it is.” He does so even when he is summarizing the work of someone else like Cicero (see IO 3.6.44, 80) who uses the more conventional formulations an fecerit, quid fecerit, and quale fecerit, or “whether he did it, what he did, and what sort of thing he did.” If these three questions are seen as varieties of rational question, then the choice of form is essentially arbitrary. But Quintilian is trying to generalize them, so he needs forms of esse, “to be,” rather than the more specific facere, “to do.” The rephrasing makes the questions applicable across what Quintilian calls “types.” Thus, like the traditional category names, they do not take up the role of placeholders, either.77

77 It might even be suggested that Varro does something similar in distinguishing identical strings of alphabetic characters if they are construed to represent different number/​case forms (Taylor 1978.71–​2 perhaps gets at the same point when he claims that in this passage a grammatical form is not defined by a string of characters but “in terms of the intersection between a vertical column and a horizontal row.”) But this is precisely what the normal grammarians did not or could not do. They read this words as—​in modern terms—​mere strings of characters. When they needed to make a similar distinction, or even when Varro does so outside of this table, they relied on phrasal expressions adding a preposition and/​or form of a demonstrative pronoun.

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DISTRIBUTED COGNITION Earlier in the chapter I mentioned cognitive psychological research about the value of tables, but also about the difficulties involved in learning their use.78 Now I would like to suggest that there are cognitive reasons why certain contexts are more hospitable to that use in the first place. It will be useful to return once more to Varro’s grammatical table. I noted earlier that he led into his declensional table with a numerical example. What I did not point out then was that there is another, preliminary step in Varro’s text. A few sections before, he had offered the reader a concrete physical analogy—​the checkerboard-​like playing surface for the game of latrunculi (LL 10.22).79 As far as we can tell, the rules of the game assign no significance to the rows and columns as such, so the board is not a table in itself. At the same time, though, it provides the reader with a “scaffolding” and in particular it frames the fully two-​dimensional extension of the eventual table.80 (This is all the more true for the formae produced in the centuriation process. After all, these simply reproduce a grid that has just been inscribed on the earth itself.81) If Varro’s first pass at the idea of a table of analogous forms takes advantage of a material substrate (albeit an imaginary version of a familiar object), his second engages with the physical world in a slightly different way. He does not actually display a numerical table, but asks his reader to construct it: “Let numbers be laid out as follows. In the first line . . . in the second . . . in the third.” The closely parallel language of the following description of the grid of adjectival forms invites the construction of this as well. I know of no parallel for such directions in the Roman world, but they are quite common in a different domain: Greek geometry. Proofs in this tradition are framed as the construction of diagrams with instructions like “Let the line AB be drawn” or “Let a square CDEF be set up.” In a penetrating analysis of the language of those mathematical texts, Netz 1999.68–​88 has shown that there is a complex fiction here. The actual reader, of course, typically had the full diagram before her in the text. And even in the production of the proof, it can be shown that the linear diagram must have been entirely in place before its labeling, which was generated in a complex process of framing the proof, whose written form was only fixed subsequently. That is to say, proofs were constructed in the context of

78 This section contextualizes Roman table use in light of modern cognitive theory. A parallel argument in Riggsby (2018) discusses the scientific aspects of the argument at greater length. In turn, this section (and this chapter more generally) provide a deeper philological analysis than is sketched in that paper. 79 On the shape of the board, see Austin 1934. Garcea 2008.81–​2, in an otherwise compelling analysis, appears to confuse this board with the more backgammon-​like one for the game of Duodecim Scripta. 80 While I do not mean to make any theory-​specific point by my use of the term “scaffolding” here, I  am very much influenced by the use of this notion by Clark 1997 and his later work. See further Riggsby (2018). 81 Sporadic use of other maplike features (such as representation of rivers) might reinforce the parallel between physical reality and abstract representation, but we will shortly see a limit to this.



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interaction with a physical diagram, and that interaction was then reproduced, if in different form, for the benefit of the reader. I raise this Greek parallel not as a direct source for Varro’s practice but, rather, to suggest that there is a common cognitive strategy at work.82 Contemporary researchers have shown the value of such physical interaction (typically real, but also imagined) in the learning of abstract mathematical concepts (Nathan 2008). In fact, this effect seems to be just a particular case of a much broader cognitive phenomenon. One of the principal insights of what is called distributed cognition is that much of that cognition is improved by or even requires “thinking with external objects” (Kirsh 2010).83 Interaction with external objects, including but not limited to formal representations, allows “off-​loading” not only of memory but also of actual processing from purely neural architecture. The generality of these scientific results seems to invite us to look for other traces of distributed cognition in our Roman material, and the military rosters lend themselves to just this kind of analysis. Many of these documents are straightforward lists, but a few start to take on characteristics that are more tabular. The ambiguity seems to result from the fact that what I have been reading as static objects were actually dynamic ones. That is, they typically show multiple hands and/​or erasures, suggesting they were working documents of some sort, not just file copies. At the heart of each was a list of names, with various other information attached more or less after the fact. The initial writer and subsequent individual annotators were likely thinking of them as lists, but the collective effort resulted in something more like tables. The physical necessities of annotating an already given list required the writer to commit to the informational value of disposing data in two dimensions at once. All this suggests a mechanism by which a full table might arise, and that may have been the context in which our two fully tabular duty rosters arose. It is true that we cannot draw a perfectly straight line between the two. If we were to force a tabular reading of most of these rosters, they cross-​index individual soldiers not with a series of dates but, rather, with a more diverse set of categories (implicitly set at one time or timelessly): rank, duty, and origin. Still, the assignment is the one most likely to be changed and is found at the outside edge of the core columns. Simple reuse of the same document without erasure would produce something very much like the tables we in fact have. But a more direct ancestor of the duty rosters might instead be found among some rarer documents preserved

82 Garcea 2008.80, on the strength of the parallels in Nicomachus (see note 74, this chapter), in fact argues that Quintilian is borrowing a standard mathematical technique. While Garcea must be right about the generally mathematical flavor of Varro’s use of analogy, Nicomachus is, as I’ve already noted, an outlier in the Greek evidence and seems to share precisely the same expectations of audience non-​ understanding that Varro does. 83 “Distributed cognition,” the idea that processes of cognition are not entirely confined to the nervous system, covers a variety of (not always mutually consistent) specifics, particularly the four Es (embedded, enacted, embodied, and extended cognition). At the level of abstraction to which I appeal here, I do not think there is any need to assess the merits of these subordinate notions, but for surveys, see Ward and Stapleton 2012.

80

80 { Mosaics of Knowledge in the vicinity of one of the full rosters. At Mons Claudianus, we have several lists of names with numerals appended, apparently to show to which watch individual soldiers would be assigned (OClaud 309–​36). These are on small, disposable ceramic fragments, and therefore do not lend themselves to expansion, but if an officer happened to start on a larger piece, he could make subsequent assignments to the right of what was already written, and the document would grow into almost exactly the form of the attested duty rosters. It may not be an accident that our two duty rosters arrange the names vertically, not horizontally; they descend from rosters, which are (vertical) lists of names. (I should note that this whole line of argument can be applied to the special indexed nested lists discussed in the previous chapter. As we saw already, virtually all those appeared in the context of databases that were the object of ongoing construction. Our evidence, mostly in the form of receipts of various sorts, gives primarily abstract numerical coordinates, but the clerks who produced them were sorting and creating concrete documents in physical archives. That form, also rare, seems to have benefited from physical enaction as well.) Two additional observations arise from this account, both of which can in turn be observed in the other material we have already seen: (1) physical manipulation is especially important for one of the most distinctive features of developed tables: the meaningful use of (blank) space; and (2) creative “mis-​”reading may have had a significant role to play in the evolution of Roman tables. If the duty rosters arose from more listlike structures, it makes sense of the way in which notations are (or are not) spread across columns in the roster of PGenLat 1.  As noted earlier, such spreading is the kind of thing that broke up tabularity in, say, some Fasti and accounting records, but here it is a sophisticated and expressive device integrated into the overall design. The interpretation of many of the abbreviations denoting assignments is uncertain, but if we accept almost any version proposed in the literature, it appears that iterated terms typically involve at most a formal removal to another unit—​for example, bath or sentry duty. Repetition over multiple days would in fact be iteration, not extension of a single, and so would invite multiple notation. By contrast, the tasks spread over two more columns seem to involve soldiers absenting themselves from base for an extended, continuous period—​for example, scouting, going to mines, or literally “departing from camp.” The difference in form is iconic of different functions without interfering with the structure of the table. It arises, however, in the context of a record in active use: literally writing several times over the course of days versus filling in several cells at once. A similar point can be made about the lists of grain recipients. In several cases, the information in the inscriptions is incomplete. We have names of several recipients, but space is sometimes left open for the day and place/​record of distribution.84 The 84 CIL 14.4499, 4502, and perhaps 4509. CIL 14.4505 overruns the ends of lines 5–​7 in a way that might suggest that an (insufficient) blank space was left originally, but then completely filled in.



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texts were originally carved to celebrate the completion of deployments to Ostia. At that time, the guardsmen had not necessarily completed the longer term required to gain citizenship and admission to the grain dole, or simply had not yet been formally enrolled because they had been away (Virvoulet 1995.274). So, despite being carved in stone, these texts are also working documents. Our most plausibly tabular example (CIL 14.4499, mentioned earlier) even shows a few of these numbers filled in by a second hand. Moreover, this text (unlike, say, CIL 14.4500) has the abbreviations for “day” and “tablet” already carved in each line, thus regulating the blank spaces for information to be filled in. Like the military duty rosters, these tablets resist the fear of blank space I noted earlier. In this case, it is because information was simply absent at the initial time of carving, but its eventual form was extremely predictable. In the rosters, soldiers are given particular tasks and so their spaces are filled in, though some will presumably remain empty. Retrospectively, blank space seems to represent, almost iconically, a lack of assignment, but it begins in anticipation of actual material. The closest parallel I know of for this use of blank space occurs in a context that has nothing to do with tables, but much with working documents. In the late first century, the major towns of Roman-​controlled Iberia were given charters in Roman form, now generally known as the Flavian Municipal Law or the lex Irnitana (the latter, strictly speaking, applies to a particular charter). The text of these charters seems to have been quite standardized except that various monetary amounts (e.g., qualifications for local office, limits to jurisdiction of local courts) vary from place to place. We happen to have a precious bronze fragment of a copy of one of these laws that has blank space in place of the numerical values.85 The instances are not numerous, but they do suggest what strikes me as a plausible clarification of the initial observation. Blank space is in fact avoided as an element unto itself, whether understood as a theoretical variable encompassing a range of values (like the x, y, and z of modern algebra) or as a null value like a modern zero (as might have been useful in a fully tabular calendar). But if blank space is necessary in an ongoing inscription, it can be grasped not just in abstract terms but also in operational ones. It is the physical point at which further writing will be inscribed. But in some cases that operational use (from the writer’s point of view) could be transformed into a symbolic role by readers. To the extent that we see tables in texts with columnar translation, they also seem to arise out of a certain kind of misreading. Here, unlike the army rosters, the changes seem to have more to do with a coincidence of small conceptual changes than with a physical operation. Substituting a continuous text, broken down into small segments, for a list of more or less random words requires no particular rethinking on the part of either composer or reader. But the structure built into the narrative or argument of the text is then imported into the structure of the



85

Fernández Gómez 1991.125–​6.

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82 { Mosaics of Knowledge columnar translation “for free” in both columns. That is, in the military case, we begin with a structured list in one dimension, then use of annotation builds up a second dimension. In the pedagogical case, the availability of structure in both columns encourages, or at least facilitates, moving back and forth between the two, making the dimensionality of a narrow list more real. They were then available to be misread as tables. It would not be hard to imagine tables evolving out of the various kinds of accounts that survive from Vindolanda. They have highly repetitive structure, and at least some of them appear to have been composed on an ongoing basis. On the other hand, they mostly seem to lack a “backbone,” a basic list which stabilizes one dimension until the other can arise. Nor is it clear that they would have been consulted in ways that would have made it important to be able to pick out random bits of data. Finally, the interleaved header information might have blocked misreadings of the sort we have just been discussing. Still, I would not be greatly surprised if one of the next slips recovered from the bogs turned out to contain a table after all. Tables, one might say, are merely rare in the Roman world. They are thus unlike technologies like stainless steel or the numeral zero that simply did not exist. But at the same time, they did not sweep the field like clay pots or simple lists. Nor are they even confined to particular periods or regions, or to a clear evolutionary path. They are not restricted to as narrow a set of uses as appears to be the case with the otherwise more sophisticated Babylonian tables. Such a complex set of facts suggests a multiplicity of causes, and I have attempted to articulate a number of these, as well as to consider to some extent how they might interact with each other. The many parallels between the use of tables and of complex lists have, I  hope, increased the plausibility of the accounts in both this chapter and the last. In the next chapter, however, I will move to a subject matter which does not have the same kinds of direct connections as these two have had. One thing that lists and tables share is an all-​or-​nothing quality: an item is included at a certain place or it is not. But we often need information with more gradations than that, and in the rest of the book I will turn to technologies that account for more continuous gradation and variation. The first of these topics will be quantitative measurements of space, time, weight, and so on.

3 }

Weights and Measures None of them should have coinage and weights and measures of their own. Let all of them use ours.

—​Dio 52.30.9

We move now to a very different set of technologies: systems for measuring quantities like weight and distance. There are traces in literary texts of great ambitions in this area. In an apocryphal anecdote, the first Roman emperor was advised to create universal standards for weights and measures throughout the empire (see chapter epigraph). A little closer to real life, Roman technical writers on metrology and related topics imagined a world that perhaps lacked universal standards, but in which all measurement could nonetheless be brought under control by a massive system of conversion formulae (Cuomo 2007a). In either case—​a single standard or a set of interconnected ones—​quantitative measurements take on a life of their own, valid beyond and without reference to the context in which they were originally made. By and large, these ambitions failed,1 and this chapter will offer an account of the prevalent metrological culture that explains that failure. Before I begin the detailed argument, I want to give a sketch of what I think that culture was like. Where, how, and why things were measured in the Roman world significantly affected the results. It was not just a matter of the weakness or lack of governmental standards, though that is an important feature of the landscape. No other persons or processes set weights and measures as predictably as we expect today (in a world in which, for instance, precise doses of powerful drugs and minute mechanical components are produced across the globe from where they are administered and assembled).2 Moreover, there was no expectation of that level of transparency, so a key part of this story is about the ways Romans found to get on with their lives without such predictable measurements. I should stress immediately that this does not mean that Romans did not measure things nor that their measurements were random or

1 For the associated standardization of coinage, which will not be treated in this chapter, see RPC I.26–​37, which shows a gradual and irregular convergence to Roman standards. 2 Geus 2014 makes a similar argument about the indeterminacy of the “day’s journey” in Herodotus, but uses it to hint at a broader metrological picture seemingly much like the one offered here.

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84 { Mosaics of Knowledge meaningless. The textual and archeological evidence for weighing and measuring is overwhelming.3 Rather, the exact meaning of numerical measurements was more often and more deeply tied to their local context than it was to universal and exact systems of reference. Roman measurements were (typically) good enough for their immediate purposes, but not necessarily for others. (In fact, the limited, local validity of measurements may well have led Romans to measure more often, not less.) Let me offer a specific example, slightly outside the scope of the main argument, just to suggest what kind of thing is at stake. Some years ago, Walter Scheidel (1996) published a statistical analysis of values for large private fortunes and for public expenditures recorded in ancient literary sources.4 The recorded values for all these different items showed a strong tendency to begin with the leading fi ­ gures 1, 3, and 4. There is no reason to think that either quantity (much less both of them) really falls into such a distribution. And the stylization here is not a matter of “mere” rounding (though Romans do that readily enough, too). Rounding works in from the less significant digits; this preference starts with the most significant. Also, rounding simplifies, but does not on average affect the distribution of a large set of numbers. A preference for 1, 3, and 4 gives a lopsided distribution. Presumably, among Roman texts that use “300,000,” some mean exactly that; after all, what it means to count to that number is not in doubt in normal cases. Other times, the same figure is likely an approximation, though how precise is hard to know, and presumably varies from case to case. Sometimes 290,000? 275,000? 250,000? But sometimes the same figure is essentially a figure of speech. Depending on context, 300,000 (or 30,000 or 3,000,000) can just mean “a lot.”5 Crucially, it is not necessarily clear to a reader which of these modes is being used. In individual passages, this is rarely a problem. However, it is a real issue for anyone (ancient or modern) who wants to take two such figures out of context to sum or compare or otherwise combine them. Suppose a single author in a single paragraph sets one fortune at HS 3,000,000 and another at HS 4,000,000. Both stereotypical numbers register a large but not unprecedented fortune. And, presumably, the author is claiming that the latter is (somewhat) larger than the former. But, given the conventionality of both figures, we cannot draw the same inference based on their appearance in two different passages, much less from two different authors. That is to say, I’m claiming that Romans sometimes do with seemingly specific 3 Richly illustrated in the contributions to Corti and Giordani 2001. 4 Scheidel 2016 revisits the issue both by revising his baseline expectations and by introducing a larger sample of recorded amounts of money. He ends up overturning the universality of the 1, 3, 4 preference (which my argument denies in any case), but not its relevance to particular contexts. Scheidel’s revised results reduce the preference in the original cases, but do not make it disappear (2016.815)—​“findings are not in need of revision”—​nor do they affect the extremely dramatic stylization of banquet costs pointed out at Scheidel 1996.230. My claim is simply the existence of digit preference in particular contexts. (The later paper notes some modest variation in the stylizations of different languages and genres of texts, but unfortunately aggregates all quantities regardless of what is being priced.) 5 For the last, most extreme possibility, compare also English “a couple” and Italian “un paio,” which need not mean precisely “two.”



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numerals what we might do in English with more obviously vague terms like “billionaire” and “multi-​billionaire.” Used in a single passage, the latter clearly suggests a larger fortune than the former. But if I call Donald Trump a multi-​billionaire at the beginning of an article, and then I go on to refer to Bill Gates as a billionaire several paragraphs later, that doesn’t mean I  am claiming Trump is richer.6 The main point of this example is to show a case in which identically phrased numerical claims might mean different things in different contexts, but a few other points need to be made. First, the context that matters for the American “billionaires” is the location of words within a text. More important to most of this chapter, however, will be contexts more like those we saw in the Roman example in which values for particular things (banquets, personal fortunes) were rendered in highly stylized forms. That is, the relevant “locations” will not be textual but, rather, any number of real-​ world social and geographical contexts. Do farmers in adjacent villages weigh grain the same way? In adjacent provinces? What about the farmer and the tax collector? The farmer and the fishmonger or the goldsmith? The farmer’s wife rationing out food to slaves versus cooking from a recipe? Second, I will argue that this context-​ dependency of measurement has consequences not just for modern interpretation but also for ancient practice. Persons in the ancient world would have faced many of the same ambiguities we do today. Thus they would have needed to learn the rules of individual contexts and/​or figure out how to get by in conditions of uncertainty. I will illustrate this point in detail at the end of the section “Standards and Standardization.” The chapter begins with a section describing various Roman ways of quantifying without general systems of reference. Three sections on standardization then follow:  one looking for standardization in practice, then two on formal and informal mechanisms that could have (but generally did not) produced standardization. Finally, I  note the limited circumstances in which Romans do appeal to broader standards, then try to tie together some general conclusions. (Two final notes on terminology and the scope of the chapter: First, for present purposes, I will refer to length, weight, volume, and so on as “dimensions” of measurement; I will also sometimes include price as one of these dimensions. Second, I  will treat here only measurements of quantities that vary continuously over a range. Counting devices like parapegmata and the census are not included.7)

How Does Roman Measurement Work? In what follows and especially in this section I will cite various specific pieces of evidence, but I will also offer a number of generalizations about how Romans measured.



Not a hypothetical case. See Mackler 2015. On parapegmata, see Lehoux 2007; on the census, see Nicolet 1991.

6 7

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86 { Mosaics of Knowledge The former will be cited in conventional form, but I should say something about the evidentiary basis for the latter. When I make claims about how measurement was actually conducted, I am looking at a set of numbers drawn both from inscriptional and from literary sources. (I take into account all specific figures; a modest fraction of the literary ones are fictional.) For most dimensions of measurement, my most important source has been the standard collection of Latin inscriptions, the Corpus Inscriptionum Latinarum (CIL).8 I  have also examined the whole of two corpora of special interest for preserving details of everyday transactions: the surviving tablets from the Roman military encampment at Vindolanda in England, and from the archive of the Sulpicius family near Pompeii. As for literary sources, I have largely restricted my attention to measurement-​rich authors: Pliny the Elder, Scribonius Largus, Cornelius Celsus, Cato the Elder, Columella, Apicius, Frontinus (on Aqueducts), Vitruvius, and the corpus of variously attributed land-​surveying manuals. When I have become aware of counterexamples to my claims, I have not excluded them just because they fall outside this corpus. For the convenience of the reader, I  have appended to this chapter a conventional list of units and conversions in the manner of a modern reference work or, for that matter, of the second-​century ce treatise by Volusius Maecianus that inspired Cuomo’s paper (e.g., 1 Roman pound = 12 Roman unciae = roughly 324 g). Those, however, are the “official” and/​or explicit rules. What I want to discuss in this section are instead strong tendencies of actual practice. These are (1) frequent, though often covert recourse to proportional measurement; (2) resistance to metonymic abstraction of units of measure; (3) frequent, though often also covert recourse to rough approximations; and (4) stylization of numerical values.

PROPORTIONS Many measurements in the Roman world were conducted not by any absolute standard but, rather, by proportion. The most famous examples are perhaps the blizzard of ratios in Vitruvius’ de Architectura.9 We also commonly find baroque examples in the division of estates in Roman wills (e.g., 1/​12 + 1/​5 of 1/​24—​that is, 11/​120; TPSulp 23). Proportional scaling was a standard part of the copying process in the fine arts, both for painting (method of squares) and or sculpture (e.g., pointing).10 And there are more isolated or idiosyncratic examples, like culinary or medical recipes explicitly framed in proportions, as well as the late coins marked with the numerical ratio of content (not absolute weight of silver).11 Use of proportions has practical virtues. It allows for flexibility in, say, the yield of a recipe

8 RIB even more helpfully gathers weights and measures together in fascicle II.2. For time spans in inscriptions, I have largely restricted myself to CIL 6, which records texts from Rome itself. 9 Riggsby 2016. 10 Painting: Clarke 2010, 2013. Sculpture: Wootton et al. 2013. 11 Recipes: e.g., Apicius 1.11.2, EV 2; Scribonius 57, 68. Coins: Howgego 1995.126–​7.



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or the scale of a building. More important in the present context, it grants independence to the user of that recipe. The use of ratios means your meter and gram (or your pes “foot” and libra “pound”) do not need to be the same as anyone else’s for the procedure to work (notwithstanding certain problems to be discussed in the section, “Complications”). What I would call attention to, however, are cases where measurement seemingly made by standardized units appears in fact to conceal the use of mere ratios. As will be discussed at greater length, a recipe collection circulating under the name of Apicius contains recipes that use not standard measures but, rather, concrete ones (equivalent to, say, a modern “coffee cup” or “wine glass”). That works in practice, as Grocock and Grainger 2006.83 point out, because in any given kitchen, it would maintain the proportions of ingredients: The ratio of one ingredient to another is more important than precise quantity when transmitting a recipe, particularly with liquids, and we find that this is often what the cook was trying to convey even when he used terms for specific quantities. But the same is true of nearly any recipe (or set of directions more generally) if it uses a single unit of measure, even if that unit appears to refer to a universal standard (see section on “Complications” for certain exceptions). Nearly all recipes in the medical texts and most in Apicius in fact use only a single unit of measurement even if that means having to use very high numerical values (e.g., 200 denarii in weight, more than 2 pounds). A preference for simplicity in units makes it easier to rely on ratios rather than count on absolute measurements. We can also see reliance on proportions in areas that go beyond recipes. One of the most consequential has to do with Roman water distribution. The central component of Frontinus’ treatise on the aqueducts of Rome is a comparison of the actual and official amounts of water flowing through various parts of the system. The odd thing about this, noted by all commentators, is that he gives his measurements in what are called quinariae. But this is a measure of the cross-​sectional area of pipes, not of the actual volume of water. The latter would depend on the velocity of the water as well, something Frontinus does not even claim to measure.12 Indeed, Romans do not seem to have formalized units for any kind of rate over time. Now, it has been argued that Romans were in fact capable of measuring water flow rates. Taylor 2000.35–​8 offers a series of experiments, each clearly within ancient technical capacity, through which this could have been calculated. Yet there is no textual or archeological evidence for the actual use of such means.13 What cross-​sectional areas capture well, however, are ratios of distributions, at least for the water coming from a given aqueduct at a given time. In fact, when we have inscriptions that record actual water allocations both in Rome and elsewhere, they rely on cross-​section

12 13

Though he is at least generally aware of its relevance: Aqu. 70.3, 73.6. Against such measurements, see Rodgers 1986 and Fahlbusch 1988.

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88 { Mosaics of Knowledge and/​or on the fraction of the day one is entitled to use the water supply.14 That is, proportion seems to be the norm, both in theory and in practice. Two further instances have to do with time. One is the use of the water clock to time courtroom speeches. Water clocks divided time in fixed ratios between speakers, but not uniformly between locales.15 The same is true of time measured by sundial. The Roman hour was 1/​12 of the period from sunrise to sunset (Vitr. 9.7.7); their length varies between roughly 45 and 75 minutes depending on the season (Hyginus 146.37–​148.7C), but the proportion remained fixed.16 While in certain technical contexts ancient scholars used a standard “equinoctial” hour (= 1/​24 of a day = 1 modern hour), this seems never to have been the default understanding of the word hora.17 In principle, it was possible to calibrate water clocks to each other or even to an external standard such as the hours of the solar day. But the evidence for the actual practice in the Roman (and, for that matter, the Greek world) is almost entirely limited to monumental and/​or theoretical showpieces (Lewis 2000.362–​3).

RESISTANCE TO METONYMY Many units of measurement in systems from around the world arise by metonymy from real things or events. The day is (in origin) the amount of time it takes the earth to turn once on its axis. The cubit (whether Roman, Near Eastern, or archaic Indian hath) stems from the human forearm. The Anglo-​American measure of volume we call the “cup” (i.e., 238.6 ml) of course derives from the capacity of an actual vessel of that name. Today most of the metonyms are fully conventional. If they were metaphors, we would call them “dead.” At the end of the process of abstraction, the day or foot or cup does not necessarily correspond to any particular event or person or object; they are standard quantities. In the Roman case, I will argue, the metonymy is often not as regular or as complete as we are used to. The concrete model often seems to remain very present in the minds of Roman measurers. And the mere possibility of ambiguity means that agents could not have assumed the abstract/​standard version of a given unit, even in cases where that happened in fact to be what was before them. Feeney 2007.156–​7 points out that the Republican Roman year is much harder to understand as a quantity than its modern counterpart. Julius Caesar introduced 14 CIL 3.14969.2 (time), 6.1261 (time), 8.18587 (time), 14.3676 (time and cross-​section of the openings into the main supply). 15 The only attested “practical” exception involves the use of water timing for military night watches, as suggested by an early Greek military writer called Aeneas Tacticus (Strat. 22.24–​5). But this is a circumstance in which the sundial would necessarily be unavailable, and at any rate the methods prescribed (tweaking the size of the vessel by adding and subtracting wax) are highly approximate. Such techniques might have been more useful for scholarly purposes. 16 These values are for the latitude of Rome. Two inscribed “menologia” (CIL 6.2305, 2306) give approximations of the length of day and night. One value is given for each month, and the smallest unit involved is the quarter hour. 17 Equal hours: Plin. HN 18.220–​1. Not the norm: Gibbs 1976.4, 10.



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essentially our modern calendar in 46 bce, but before then Romans had had short years interspersed with longer ones whenever a body of priests saw fit (355 vs. 377/​8 days).18 That is (and this is Feeney’s main point), the Roman celebration of “anniversaries” involved repetition of formal dates without what would today be the concomitant expectation that the original and the commemoration would be separated by a particular quantity of time. Moreover, the extra days were added as a month that did not even exist in “normal” years. In these circumstances, each calendar year was a distinct event, but their mutual dissimilarity discouraged collapsing them together to extract an abstract quantity. I would make a similar claim, though on different grounds, for Roman months and hours. Roman epitaphs often report a life span for the deceased, not infrequently in years, months, and days. I have examined all the instances from the city of Rome, and among them 301 give a number of days that is greater than 31—​ that is, more than a month’s “worth” of days. So, for instance, an epitaph now in Bologna gives a life span of “three years, 45 days” (CIL 6.12366). This set with 32+ days has two other interesting features. First, the great majority (255) show fewer than 63 days. Second, none of them lists any number of months. The pattern is not entirely clear, but this suggests to me hesitation in the Roman mind between the “month” as an event (that is, a calendar month) and the “month” as a duration (something that we could describe as being equal to so many days, minutes, or even seconds). For instance, someone born on, say, January 10 who then died on the February 24 immediately following her third birthday, had not obviously lived three years and one month, despite living 45 days more than three years. There was no named “month” through which she had lived beyond the three years. It is true that once one calendar month has elapsed, this effect disappears, but achieving that first month does seem to be important. Bailey 2013.168 observes that prices in Pompeian graffiti follow a similar pattern, with amounts often expressed as a large number of coins of a single denomination, rather than notionally “exchanging” some of these for a unit of higher denomination. Her explanation, for which she offers evidence beyond the fact itself, is that buyers and sellers tended to think of prices in concrete coins rather than abstract units of value. Hours, as noted, varied in length because they represented a fraction of the seasonal daylight. From day to day, the variation is quite small, but over the course of the year, the longest day is two-​thirds again as long as the shortest. That makes sense when the hour is seen as an event (“the fifth hour of the day”), but not if it is a unit of measurement for, say, roasting a chicken or paying a lawyer by the hour. The names of Latin’s smaller volumetric units (acetabulum, cyathus) derive from the names of actual vessels, as with English cup and spoon measures. These words

18 For fuller details, see Michels 1967, Bickerman 1980.47–​51, Hannah 2008.112–​22, and Rüpke 2011.68–​86. Technically, the added month was 27 or 28 days long, but replaced the last several days of February, yielding the net gains cited here (Michels 1967.145–​72).

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90 { Mosaics of Knowledge often appear in the recipe collection attributed to Apicius. Grocock and Grainger (2006.83–​6) have argued convincingly that they are often used there in their root senses; they do not represent a precise and reproducible quantity identical for all users. Apicius’ acetabulum explicitly comes in different sizes, which makes sense for actual cups, but not for a notional abstract unit of measure (6.8.4, 8.7.17).19 Moreover, the acetabulum and cyathus do not co-​occur in the same recipes. If both were just terms that meant something like “an actual cup from your kitchen,” then using both would be redundant. The fact that this non-​metonymic understanding is necessarily available then potentially affects all recipes. A reader doesn’t know from case to case whether a “cyathus,” for instance, is a certain number of (as we would say) milliliters or just an actual cup. In light of these general trends, we might also take notice of the (admittedly rare) use of diminutive forms of names for units of measurement—​for example, unicolam (“ounce-​let”) and sextariolus (“pint-​let”).20 These appear to take even the existing, formal measures back into concrete vessels, which can then be expanded or contracted. We have a similar ambiguity in the much different world of land surveying. Prior to distribution to settlers (see c­ hapter 2 on the process), surveyors conventionally divided land into large squares called centuriae. A centuria then came to be the name of a unit of area equal to 5,760,000 square (Roman) feet, the “normal” size of one of these plots. But in fact surveyors laid out squares (and rectangles) of other sizes at different times and places. Already in antiquity and even in professional circles, the fact that these were all centuriae (in the sense of basic distributional units) without necessarily being equivalent to the centuria (as a quantum of area) is known to have caused confusion.21 Though the evidence is more indirect, I think essentially the same kind of claim can be made about the passus, or “pace.” This is not a particularly common unit, mostly occurring as part of the phrase milia passuum, “thousands of paces” (what we typically call “Roman miles”). I will discuss that usage, but here I am interested in the restricted set of circumstances in which we see paces that are not components of miles. These uses of the passus fall into one of two categories. On the one hand, authors like Caesar and Livy conventionally use them in military contexts, and particularly in “tactical” descriptions.22 This framework is a two-​dimensional space, defined by the presence and extent of two opposed armies, and generally is small enough to be taken in at a glance by an observer in a realistically elevated position. On the other hand, Frontinus’ work on aqueducts gives certain measurements in paces.23 In his initial catalog of

19 So, apparently, also the one recipe (2.2.4) that uses “calix,” yet another type of cup, but one that lacked a value as an “official” measurement. 20 Juv. 1.40; Augustus apud Suet. Hor. 60. 21 Hyginus 126.6–​17, 136.28–​31; Frontinus 11.30–​34; Campbell 2000.377–​9. 22 Those other sources include, [Caes.] BA 18.3, BH 29.1; Cic. Fam. 10.30.3; Front. Strat. 2.2.5, 3.13.6; Plin. HN 11.19.2 (literally bees, but with an extended military metaphor); CIL 12.594, 8.8369. For a fuller account of “tactical space,” see Riggsby 2006.24–​5, 2009a.157. 23 Even half paces at §§7, 9.



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aqueducts, he uses passus for the distance of sources from the nearest road and for the lengths of various above-​and below-​ground segments. Both the military use and aqueduct construction are contexts in which we know Romans deployed professional surveying techniques, so it would be tempting to see the stand-​alone passus as part of the professional apparatus of the surveyor.24 But that is almost certainly not right. As a practical matter, the circumstances in the military narratives are precisely where one would least expect actual surveying: the heat of battle. And in at least one set of cases where we actually know military surveyors were at work, the subdivisions of the mile are in feet, not paces.25 As for aqueducts, measurement is practically feasible and we have a number of passing references to measurements in inscriptions of various sorts, but they are nearly all in feet (as with the military examples just cited). And feet are the measurement norm in the surveying handbooks. The pace is not, then, a trace of the work of measurement professionals. To get a better account, we need to look at three further peculiarities of how the passus is used. First, nearly all of Caesar’s passus measurements and a large fraction of Livy’s are qualified with circa, ferme, or the like (all meaning “about,” “around”).26 Second, nearly all these measurements are in round hundreds of paces. In Frontinus’ work on aqueducts, the use of the stand-​alone passus is similarly limited. All but a few of them are in round 10s and most are in round 100s. And in all these texts the range of measurements is nearly always between 200 and 1500 units.27 That is to say, they are not simply transcriptions of precise measurements (which, as we have seen, would likely have been in feet anyway). I would suggest that what we have here is another incomplete metonymy, this time with a “virtual” twist. The pace is used to hint at distances that “should” or “could” be measured, but generally haven’t been. As just noted, the passus is typically used in contexts where it is explicitly or implicitly approximative. Moreover, it occupies a realm between the scale of immediate human experience and that of geographical knowledge. The scale is too large to be directly apprehended (the way small numbers can be grasped without counting) or directly equated to a physical standard (say, the length of an arm or the height of a person). At the same time, these distances are not so large that they extend beyond any single human experience (as, for instance, the extent of a continent, at least before satellite photography). To come to the idea of 200 or 600 paces suggests an imaginary traverse of

24 Thus, it might be parallel with the pertica/​decempeda which was a specialist device both as a measure and as a piece of physical equipment. 25 CIL 7.1126, 1130, 1132. Cf. 6.29774ff. 26 This is perhaps more striking in Livy, who presumably did not have actual measurements available in the first place. This might be scrupulous recording of rounding the figures found in a source, but I suspect it is itself another feature of the standard military discourse. 27 The few longer examples prove to be an artifact of adding or subtracting a precise short measure in passus to/​from a large, rounder one, thus producing a falsely “precise” large result—​e.g., 1.6 (779 + 221), 1.7, 1.9 (528 + 6472), 1.11 (22172 + 358), 1.14, 1.15 (609 + 6491).

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92 { Mosaics of Knowledge the space (as the etymology of the word itself would support). And the imaginary nature of the traverse would explain why passus measures are so often meant as approximations. It is used in cases both where one could not have measured and where one simply had not. In the circumstances I have been describing so far, metonymy is simply incomplete. In other cases, there is a more complicated relationship between the material thing and the abstract unit. Consider the modius, one of the important measures of dry capacity (almost 9 liters). Duncan-​Jones (1976a, 1976b) has shown that there were at least five standards for this, ranging in modern terms from about 8.5 to 13 liters. Occasionally, adjectives were added to distinguish versions (viz. modii italici, cumulati, and castrenses), but there are fewer terms than standards, and in any case the words are used only sporadically. Hence, any given case is ambiguous. The root meaning of modius is simply “measuring vessel,” and the word is in fact well attested in just that sense. The fact that the root sense was always available means that differing “standards” could and did arise repeatedly and independently. Thus there was always potential ambiguity between any of the putative standards and the more generic idea of measurement. The existence of different modii points to a more general source of ambiguity—​ homonyms, or the existence of several standards under the same name. The next section will treat the question of “official” standards more generally, but here I note only the fact that metonymy might interfere with their establishment. Most of the units notionally based on body parts had different local instantiations which coexisted over long periods of time, in part perhaps because no particular standard foot or cubit was more authentically a foot or forearm than any other.28 For instance, in addition to the standard Roman foot, the general Drusus seems to have introduced (or at least codified) an alternative foot in Germany in the early first century that continued to carry his name; it was longer than the Roman standard by 1/​8 (Hyginus 90.8–​9. Note also his immediately preceding comments on difficulties caused by differences between the Roman and Ptolemaic foot).

28 More generally, see Luciani and Lucchelli 2008.141n88. While it is not really a case of failed metonymy, another form of ambiguity may deserve mention here. Standard symbols for various Roman fractions were also polyvalent, as shown in table 3.1. TABLE 3.1  } Multiple meanings of symbols used in systems of measurement

—​ ⊃ S £

1/​12, 1/​10 1/​40, 1/​100, 1/​288; sextarius 1/​2, 1/​24; quinarius 1/​20, 1/​24

Of course, a few of these usages (especially the numerical vs. unit readings of ⊃ and S) will be more or less automatically disambiguated in context, but not the majority of them.



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APPROXIMATION Modern measurement systems can be extremely specific because (a)  they use combinations of units (e.g., feet plus inches, cups plus teaspoons29), (b) they have very small base units (e.g., gram, millimeter), and/​or (c) they can employ the small numerical fractions made easy by decimal notation. In principle, Roman metrology allows for both small and combined units, at least for some dimensions of measurement, and while there is of course no decimal notation, Romans did have available a rich system of standard words and symbols for fractions down to 1/​288 (a scripulum) of any given unit. In practice, however, actual Roman measurements tend to draw on a greatly impoverished repertoire compared to the rich specificity theoretically available. Failure to use and to combine units (especially the small ones) and failure to use available numerical values show that their measurement practice employed more approximation than it might appear to. Some of this simplification can be seen just by observation of large numbers of measurements. Take prices. We know that a grossly disproportionate number of them are denominated in asses and denarii (rather than any of the other available coins), most often one or the other of the two. Moreover, Bailey 2013.154 has shown that the numerical values of these prices are normally “low, round, repetitive, or all three.” Now, it might be objected that prices are choices, not external facts; the fact that so many American prices end in .95 or .99 does not tell us much about expectations for more uniform distribution of other quantities. But, in fact, in most contexts of actual measurement, Romans still preferred particular units from those available in any particular dimension of measurement; they preferred not to combine even the favored ones; and, frequently, though less uniformly, they also preferred integer values of these units. Looking at units first, we regularly get linear measurement in miles or feet or digiti, but not the various possible combinations, weight in pounds or denarii, not in combination; pricing in asses or denarii or sestertii, not combinations; labeled container volumes in sextarii, cyathi, or heminae, not, once again, in combination; and most time spans (except life spans) similarly. As for numbers, the elaborate system of fractions also only comes into play in limited circumstances as we will see later. None of these rules is absolute (see later for some particular areas of exception), but all are strong tendencies. There are even ancient references to a preference for simplicity of units. The mid-​first-​century moralizing philosopher Seneca talks about the worthlessness of worldly learning without correct moral values in this way:30

29 Less important in the SI metric system than other modern versions. 30 Quid mihi prodest scire agellum in partes dividere, si nescio cum fratre dividere? Quid prodest colligere subtiliter pedes iugeri et conprendere etiam si quid decempedam effugit, si tristem me facit vicinus inpotens et aliquid ex meo abradens?

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94 { Mosaics of Knowledge What good does it do to know how to divide a little plot into parts, if I cannot share it with my brother? What good to compare in detail (subtiliter) every foot of an acre and capture even what might escape the official measuring rod, if the rowdy neighbor who scrapes off a little of mine makes me unhappy? (Ep. 88.11.3) Slightly later, and less seriously, the epigrammatist Martial describes a highly practiced lover this way:31 Whenever Marulla has weighed an erect penis with her fingers and measured it for a long time, she tells the pounds, scruples, and sextules; after the deed and the work-​out, when it lies like a loose strap, Marulla tells how much lighter it is. Therefore, that is not a hand, it is a scale. (10.55) In Seneca’s case, an overly “subtle” measurement is exemplified by one that descends from iugera (very roughly acres) to individual feet. In Martial’s poem, Marulla’s precision is almost literally inhuman; her hand is “actually” a scale, but this has already been signaled by the use of not one or two but three different units.32 I take it that these forms of expression are something like a rhetorical equivalent for modern phrases like “to the last decimal place.” The mere combination of units sent the Roman audience a clear message of punctiliousness that is at best the realm of professionals and at worst counterproductive in its narrow focus. We should note that the single-​unit tendency is local rather than global. That is, we cannot just say that there was one “real” system of measures that was less diverse than the theoretical handbook version. For instance, we have two large Latin collections of medical recipes, one by Scribonius Largus and the other by Cornelius Celsus (both first half of first century). The vast majority of individual recipes (in both collections) do not mix weights in denarii with those in pounds, even though both collections have both types of recipes. Similar observations can be made about, say, the recipes in Apicius, the use of cubits versus feet in different anecdotes in Pliny the Elder, or the measurements in the first-​century architectural treatise by Vitruvius, or even those in preserved inventory lists from the Roman military encampment at Vindolanda in northern Britain a century later. Such diversity as we see in the whole texts stems from the fact that they collect information from different sources (e.g., different authors for Vitruvius, different daily reports digested into



31

Arrectum quotiens Marulla penem Pensavit digitis diuque mensa est, Libras, scripula sextulasque dicit; Idem post opus et suas palaestras Loro cum similis iacet remisso, Quanto sit levior Marulla dicit. Non ergo est manus ista, sed statera.

32 That the pound is one of the units suggests the kind of over-​the-​top exaggeration which animates the poem.



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longer-​term summaries in the camp). For instance, Pliny the Elder’s encyclopedia generally uses Roman units like feet and miles, but occasionally switches to Greek cubits and stadia for groups of items which seem to derive from Greek sources (e.g., HN 2.85, 247–​8, 7.21–​31, 73–​76).33 Again, we are not looking at a contrast between (complex) theory and (simple) reality. Rather, there is a multiplicity of real systems, depending on person or context, and one feature the systems share is a preference for simplification of units. I have already noted that this tendency leaves open the possibility of hidden use of ratios, but even if particular readers do not take that option, the writers have still impoverished the individual systems of measurement. Our second source of fine distinction in modern systems is the existence of small units like the gram, millimeter, and second. The small units of Roman measure, however, tend to be sources of ambiguity and/​or approximation. The smallest unit of volume is the cochlear, a word which originally means “snail,” and from there comes to refer to a spoon (presumably reminiscent of a shell), and finally to a particular measure, like the modern teaspoon or tablespoon. For instance, in a recipe for improving the shelf life of grape must, the agricultural writer Columella measures it thus:  “A heaped spoon [cochlear] of must (or something like this vessel), that is, the fourth part of a cyathus.”34 The conversion seems clear enough—​four cochlearia to the cyathus, the next smallest measure—​but it becomes problematic on closer reading. After all, the “heaping” option makes it unclear how fixed the cochlear is. Moreover, Columella admits that other, similar vessels would work as well. In fact, other sources give the conversion quite differently. Isidore, the late collector of etymologies, in line with a number of earlier but Greek sources, calculates 8 cochlearia to the cyathus (Hultsch 1864.29). The pseudo-​Plinian treatise On Medicine (pr.9) and other anonymous Latin metrologers give 20 to the cyathus, and the ratios in the Poem on Weights (78) yield 24 cochlearia to the cyathus. To some extent, this may be another case of incomplete metonymy as described earlier. Different real spoons give rise to different measures. But the fact that even deliberate attempts at standardization are so diverse suggests a more general caution about precision here. Even when the cochlear is not literally a spoon, it still has a force closer to the English “pinch” or “dash” than to the kind of “tablespoon” specifiable as a precise number of milliliters. Medical writers used the weight of a coin, the denarius (usually defined as 1/​ 84 of a Roman pound), as a standard for the fairly small measurements that their recipes often demanded. This despite the fact that 1/​84 is not a standard fraction, and the more conventional sextula (i.e., 1/​72) was available at essentially the same value. The origin of this practice presumably lies in the earlier medical tradition

33 As a secondary tendency, it does seem that compound units are somewhat less rare in cases where there are clear concrete sources for the measures (say, years, months, days, feet, digits, cubits) as opposed to the more arbitrary units of weight or volume (or the hour or longer units of length like the league or stadion or mile). 34 Musti cochlear cumulatum vel simile genus poculi huius, quod est quarta pars cyathi (12.3).

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96 { Mosaics of Knowledge that measured based on a similar Greek coin, the obol. Moreover, both the denarius and the obol share an advantage in their ready physical availability. Denarii were ubiquitous, while balance weights less than an uncia (1/​12 pound) seem to have been rare. This is probably another instance of failed metonymy, but whatever its origins, the use of the denarius has an interesting consequence. The usual claim that denarii weighed 1/​84 of a pound turns out to be too loosely phrased. Crawford (1974.592) emphasizes that the actual ancient framing of this ratio (and of all such others) is that there were 84 denarii to the pound. The technology used to produce coins would have made it much easier to control the weight of whole batches than of individual coins. Direct observation verifies considerable variation. To take some random examples from the standard catalogs, among Spanish issues of the imperial period, 1 as coins weigh 7–​15.5 g, with the middle half in the range 10.5–​12.5 g. For 1/​2 as coins, those ranges are 3.5–​8.25 g and 5.5–​6.5 g, respectively.35 That is, the rough weight of a denomination was a given, but any particular coin was unlikely to be a precise match for another. A denarius is a reliable order of magnitude, but no more precise than that. The same is also likely, if impossible to show with certainty, for the minute. Modern “minutes” derive from a Latin term for small units of angle measurement. For astronomers, observing the rotation of the stars every 24 hours, these fractional angles were naturally equivalent to small fractions of time. Neither the geometrical nor the chronometric version is clearly attested at our period.36 But if they did already exist, their value may not have been fixed from the beginning. Isidore of Seville says there are 10 minuta to the hour, rather than the later 60 minutes. Under normal circumstances, it would have been very difficult for Romans to measure such small units of time directly, and this may have discouraged a unified definition. Perhaps more basically, Wright 2000.184–​5 has pointed out that Roman sundials are not normally marked with units smaller than the hour. This is particularly relevant for portable models, where distance along the scale is not simply proportional to the passage of time. Anything less than the hour is something of a guess. (It is true, however, that professional astronomical and geographical texts measure angles in degrees and multiple small fractions of thereof, showing both small units and combination of units—​e.g., E.E.S. inv. 79/​1 (l)b. But this is ultimately a measurement of a fraction of a circle—​that is, a proportion.) Other approximations involve numerical values rather than choice of units. The main instance has to do with fractionation and in particular with halving. The half

35 RPC 64–​5. RRC 594 gives Republican examples of this extreme variability. RPC I.30 points out more generally that the variation within individual issues is great enough to make it difficult to detect (or refute) patterns among issues. 36 Fractions of the hour itself are extremely rare. We have halves at CIL 6.3558, 12532, 37540, 16467, 8152, 10794, 29067, 23008, 3855, 13252; 8.4440, 18419. Less than this only at Plin. HN 2.58 and 18.325 (both astronomical); CIL 11.1513 (perhaps); and Aur. Fro. 1p.142 (31N) (probably figurative). Jones (forthcoming) shows that there was a trend over time to more precise (though not necessarily more accurate) measurements in Greek professional astronomy, though even then from 1 hour to 15 minutes.



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is far and away the most commonly used Latin fractional expression (even though the system is formally duodecimal). It is also the only fraction used with units that are not otherwise divided (the mile, most units of time) and the only one used in certain contexts where fractionation is not otherwise used (tomb frontage, lengths and areas in survey). Additionally, halves are deeply embedded in the Latin language. Beyond a word for “half ” itself (semis), there are specialized terms for “one and a half ” (sesqui-​) and units like the semuncia (1/​2 uncia), dimidia sextula (1/​2 sextula), selibra (1/​2 pound), and semodius (1/​2 modius). There is a particular significance to using “halves” expressed verbally rather than numerically, which differs from modern expressions like “.5” or even “1/​2.” A “.5” suggests a certain level of precision because it creates a strong expectation that the quantity being measured is less than .6 and more than .4. Similarly, “1/​ 2” automatically creates the possibility of other terms: 1/​2 is more than 1/​3, more than 2/​5, more than 3/​7, and so on. A “half ” can be used as a synonym for these arithmetically more precise expressions, but on its own it extends more broadly. More children can be described in English, for instance, as being “a year and a half ” old than “18 months.” Halves have an inherent capacity for approximation, a sign of mere in-​betweenness.37 So it makes sense that we see the semi-​ prefix used in contexts where there is no sense of literal or precise quantification in the same way as the English “half-​baked” or “half-​assed”: semicoctus “half-​cooked,” semiconspicuus “half-​visible,” semiermis “half-​armed [with weapons].” In all these cases, semi-​means nothing more than “partial.” My claim, then, is that there exists what might be called a pseudo-​numerical usage of “half.” What seems to be distinctive about the Roman case is that Latin has so many areas in which the half is cut off from the rest of the numerical system and thus allows for this freer play—​ instances where the “half ” could have been literal, but is not.38 Moreover, the phenomenon is not strictly tied to the lexeme semi-​. There are at least a couple of other forms of measure that at first appear to be precise measurements, but that are in fact just manifestations of the approximating “half.” For instance, looking at the number of months recorded as part of life spans recorded in epitaphs, we find a disproportionate number of instances of 6—​that is, about half a year. The seeming measurement conceals what is really an approximation—​much as is done a little more obviously when ages are rounded to multiples of 5 and 10 years—​and it just means somewhere between one integer value and the next. Another instance has to do with the passus, and here I return to its use as a component of the Roman mile. Measurements in miles are normally given in whole numbers, but a few are made more precise by the addition of some number of paces. The vast majority of these

37 This might even explain the occasional use of the symbol S to mean not 1/​2 but a sesuncia—​ i.e., 1/​2 of an uncia = 1/​24. Halving is seen as a function rather than a specific number, a means of approximating a unit smaller than some reference value. 38 Note here that the sign for half is an abbreviation of the word, not an arbitrary symbol like I, V, X, etc. (with the possible exception of M). See further in the next paragraph.

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98 { Mosaics of Knowledge in fact add 500 passus—​that is, half a mile. There is of course no reason that a random set of real measurements should turn up more distances of 500 units than of 400 or 600. This, I would suggest, is because the “500 paces” generally has little to do with the formal pace or even the rough approximations constituted by 400 or 600 of them (discussed earlier); it is a way of suggesting “half a mile” in the sense of “less than a mile, but more than nothing.” Finally, Keyser 1988 has shown that the Roman numeral notations for 5, 50, and 500 were derived from those for 10, 100, and 1000, even though there was no linguistic reason for them to be picked out for this special treatment. I would suggest that we take this historical fact more literally, as well. Of course, for purposes of arithmetic, V must really be 5, not just “half-​10-​ish” (and so on for L and D). But the preexisting importance of halving explains why these numbers were picked out for special treatment, why the symbols were derived by halving larger units rather than doubling smaller ones, and why the original derivation was (apparently) by the literal halving of the symbol for the higher number.

STYLIZATION I noted instances where standard values (say, ages given in 5-​or 10-​year increments or distances of 500 paces) were not to be taken literally but, rather, as approximations. At the same time, these usages stand as examples of another phenomenon. In purely formal terms this is described as “heaping”—​that is, the disproportionate appearance of certain numerical values with respect to an expected distribution. A classic case that does not involve rounding or approximation is found in certain Chinese birth data which show spikes at twelve-​year intervals, apparently corresponding to a favorable point in the astrological cycle of years.39 In other cases, the heaping is caused by stylization of the numbers themselves without any reference to what is being represented. So, for instance, not only is there a preference for “rounded” ages in low-​literacy populations but also there is a secondary preference for even values over odd ones (Duncan-​Jones 1977; Mukhopadhyay 2015). To illustrate with a minor Roman case, the various standard sizes of Roman pipes are named in numerical terms (e.g., quinaria, denaria, centenaria) denoting their size, generally in round numbers.40 But Frontinus (Aqu. 31–​32) tells us that the 12-​, 20-​, 100-​, and 120-​gauges do not in fact live up to the sizes implied by the etymology; the first is “too large” and the others are smaller than expected. That is, the watermen preferred a neat numerical sequence to measures known to be more correct. I have already briefly mentioned Bailey’s (2013.156) observation that prices recorded at Pompeii, mostly in graffiti, tend to use at least whole numbers of coins for

39 Jowett and Li 1992.431. In this case, the heaping may be “real.” That is, the timing of actual births might be affected by the good omen. 40 Precisely where these numbers come from was disputed in antiquity. Frontinus Aqu. 25 prefers the diameter in quadrantes to the width (in digiti) of the sheet to be wrapped to form the pipe.



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small (single-​digit) transactions and rounded values (multiples of 10) for anything beyond that. In principle, it is possible that prices, which are set intentionally, rather than conforming themselves to some outside given, are a special case. They might well be more subject to various kinds of heaping than true measurements. In fact, however, the exception, if there is one, is at most a matter of degree. I also mentioned at the beginning of the chapter Scheidel’s (1996) findings on digit heaping (in favor of 1, 3, and 4) in evaluations of whole fortunes, composite expenditures on large projects, and various state budget figures. To that list of contexts we have added measures of middling distances. The “halving” effect creates a disproportionate number of figures with a leading 5. In the epigraphic and papyrological records, 3, 6, and 9 hours are overrepresented, perhaps because they become a proxy for the coarser division of the day (and night) into watches.41 Distances recorded in Roman itineraries show a preference for even numbers over odd, with special favor for multiples of 10 and against figures ending in 1.42 As a crude, but at least more general approach, I have also done a database search to find all instances in classical Latin of 20, 30, 40 . . . and 300, 400 . . . written out as words.43 These include instances where the words are part of a composite numeral, picking out, for instance, both parts of “two thousand three hundred.” That inclusiveness, as well as the combination of numbers from different contexts, might be expected, if anything, to smooth over local stylization effects. In general we would expect some decline in leading figures—​that is, from number of 2s to number of 3s to number of 4s and so on.44 Our data obey that very general rule, but it does not account for more specific features we see. First, instead of a steady decline, there is a sharp drop in frequency of digits greater than 5.45 Second, the number of 4s is actually less than that of 5s. Finally, 9s are much rarer than anything else. The missing 4s and 9s are perhaps a matter of rounding, and the extra 5s may also stem from a halving effect. As a whole, however, the sharp drop from 2–​5 to 6–​9 seems to be a stylization phenomenon in its own right. This is, to repeat, a very crude measure, but it does suggest that there is some kind of pervasive stylization going on. It is

41 Epigraphic (mostly funerary): Ehrlich 2012.39–​40, 64–​7. Papyrological (from military contexts): Birth 2014.408. 42 This is based on a composite of figures found in the Peutinger Map and Antonine Itinerary, as collated by Talbert 2010. Moreover, these sources are themselves composites. The double level of composition could conceal additional but competing stylizations in individual documents. For instance, distances ending in -​9 are strongly dispreferred (except for simply 9). Of course, some of these effects could be real. So for instance, the fact that 12 miles is the most common distance recorded may well be a feature of settlement patterns as much as it is of measurement. 43 For reasons that I suspect are largely editorial, Livy accounts for about half the total sample, but his pattern does not seem very different from the overall picture. I did not count instances of 200 because of the difficulty of disambiguating the homonymous verb form. 44 Spoorenberg 2007.847, Scheidel 2016 (with reference to earlier work by Benford and followers at his note 2). Note, however, that my data include non-​leading digits and so should be more uniformly distributed. 45 Despite the importance of 7 as a “magic”/​symbolic number in certain literary contexts, these multiples of 7 do not seem particularly common.

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100 { Mosaics of Knowledge also clear from the specific cases cited here that stylization takes on different forms in different contexts, and more granular research is clearly called for in the individual cases. However, I will now move to the question of standardization of units of measure.

Standards and Standardization The first section was about the widespread use of measurement procedures that produce results that are useful for their immediate users, but could not necessarily be handed to anyone else for other purposes—​measurements without reliance on standards that are available broadly and in detail.46 But what if someone wanted to appeal to such standards? How available would they have been? Intuition suggests that length would be the easiest quantity to standardize, and in fact that seems to be the case. We have a number of portable measuring rules, inscribed tables of measures, and artistic representations of rulers, seemingly at full scale. They vary among themselves over a range of about 6 millimeters, but point to a Roman foot of just shy of 300  mm (Duncan-​Jones 1980.127–​8, Röttlander 1996). A  single monument from Libya gives standards for several measures of length, both Roman and otherwise. Each is represented not by a single line but by a rough rectangle where two parallel sides should both exemplify the unit. However, Ippolito 1967 shows that supposedly equal longer segments vary by 1% to 3% with respect to each other and shorter ones by up to 8.6%. Such magnitude of variation would be irrelevant in many contexts (say, buying lumber or fabric by the yard), but might be significant in, say, carpentry, where you cannot, for instance, tolerate a crossbar precut a few millimeters too short to extend across the chair it is supposed to support. The archeological and epigraphic records for weights are quite rich and we even have some evidence of weights that claim official status for themselves. As Gatti (1881.181) pointed out, some mention a place of standardization, while others cite more personal forms of authority.47 In the former case, we have weights and balances marked with forms of the phrase “confirmed at (exactum ad) [place].” The places include the Capitolium (likely the temple of Jupiter on the summit of the Capitoline hill), the temple of Castor (in the Forum, at the foot of the Capitoline),

46 This section and the next overlap in various ways with the topics of three interesting recent papers: Berrendonner 2009 (focusing on the role of local officials); Pérez Zurita 2011 (public administration in general), and Rizzi 2013 (legal questions, also treating Athens along with Rome). All three are exemplary for their clarity and their careful compilation of primary evidence, but they seem to me (with the partial exception of Berrendonner) to assume rather than argue for a quite modern metrological culture. The same is perhaps all the more true of discussions of metrology in exhibition catalogs, where many of the physical objects are most easily accessible. I will cite the individual papers as warranted. 47 Also sometimes both in combination, as, e.g., ILS 8627 citing both the Capitolium and the urban prefect Simonius Iulianus.



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the temple of Ops (also on the Capitoline), and perhaps (the exactum language is missing) temples of Augustus and of Trajan and various military camps including the Praetorian camp outside Rome.48 Persons are referred to by an individual name and/​or official title.49 Typically lumped in with the person-​based standards are several devices marked exacta ad Articuleian(um?), probably meaning “confirmed according to the standard of Articuleius.” Articuleius was one of the aediles of 47, the year in which several of “his” weights are explicitly dated.50 The details of some of these weights suggest questions about their use. We have something like seventy weights that claim to be exactum ad Castoris, most seemingly in good condition.51 Many of them were produced in sets of nested, bowl-​shaped weights. Modern measurements show that most of these deviate individually from their labeled values. Of the 55 where we can judge, 38 are off by at least 2%, 18 by at least 5%, 10 by at least 10% and 8 by 20% or more with a maximum deviation of 53%.52 The smaller weights typically show larger deviations. When we have relatively complete sets, the individual weights do not appear to be more precisely calibrated to each other than to examples from other sets. As is typical of previous scholarship, I  have calculated deviations from the presumed standard, but perhaps more important than the average deviation is the potential range, since weight can be “high” or “low.”53 Given the ranges just mentioned, it would be common for two supposedly equal weights to differ from each other by 10% and hardly surprising for them to be 20% apart. Your certified weight and my certified weight might be virtually the same, might be slightly different, and might be quite a bit different, but there would be no way to tell without direct comparison nor any obvious way to tell which to prefer in the case of differences. (The deviations of apparently official weights from Bithynia/​Pontus that we will see later are of similar or greater magnitude.)

48 Capitolium:  Carm. de Pond. 61–​2; ILS 8627, 8632; Meadows and Williams 2001, Pérez Zurita 2011.128. Castor:  Gatti 1881, Pérez Zurita 2011.128. Ops:  ILS 8637a, b.  Temples of Augustus and Trajan: Gruter 1616.221 (the apparent absence of these objects from any later source might be cause for suspicion). Praetorian camp: ILS 8639. Provincial military camps: Pérez Zurita 2011.131. 49 Offices appealed to include those of the aediles and later the urban prefect, and individuals include Q. Junius Rusticus (in fact, urban prefect in the 160s) and Rutilius Lupus (prefect of the grain supply under Trajan). AE 1940.38. Pérez Zurita 2011.127n11. 50 Gatti 1881; Pérez Zurita 2011.125n5. These campaigns are well enough attested to suggest that we are not missing a lot of other, similar ones because of random failures of evidence. 51 These have just been cataloged in the useful paper by Luciani and Lucchelli 2016. 52 There are potential problems with a few of the most extreme cases, but it is hard to see how the maximum deviation can be less than 40%. Găzdac and Wright 2009 claim the last of these to be a forgery. There is no apparent evidence for this beyond the discrepancy, but the condition of the weight is not as good as many of the others. In fact, I would be more suspicious of the two examples (AE 1982.818) that purport to agree with the “official” weight to the 100th of a gram. 53 As is also conventional, I have used 327 g as the “true” value for the Roman pound. The deviations shown here can be reduced very slightly by assuming a lower value than is typically reconstructed on other grounds (perhaps 320 g). Berrendonner 2009.361–​2, in fact, suggests this is the Articuleian average, as well as the weight of the (possibly official) RIB 2412.99. See further note 59, this chapter.

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102 { Mosaics of Knowledge If even the ad Castoris weights alone offered something of a moving target, what could Roman users have made of the multiplicity of other standards available? It is possible, of course, that the diversity we see in the inscriptions is superficial, and that the various standards (ad Castoris, Articuleius, etc.) were coordinated with each other. Yet there is no evidence for that either in practice or aspirationally, and there might even be some trace of mismatches. The ad Castoris weights just discussed imply on average a pound of about 320 g. Modern estimates based on precious metal coinage, where one might imagine the state would have an interest in a conservative position, have put the pound at more like 327 g.54 That would be a fairly small difference in many practical contexts, but it is certainly one the Romans themselves would have been able to detect.55 That suggests that there may have been genuinely different official standards, rather than multiple locations housing exemplars of a single standard. If so, then the end user confronts an entirely new layer of uncertainty when faced with a weight claiming to be valued at so many pounds, without referring to a source. She knows neither whether it hits the target nor, most of the time, what that target is. A somewhat different issue is raised by a pair of official weights from Roman Egypt (De Romanis 1998.37). These come from different sites (Coptos and, probably, Alexandria), but can be dated to within a year of each other. Both are labeled in an irregular number of Roman units and seem to define standards for an indigenous Egyptian unit. The two, however, explicitly represent slightly different (Roman) weights, suggesting that the authorities allowed the underlying unit to vary from place to place.56 The sample is too small to tell if the textual labels and actual weights correspond, but we have direct evidence for the spatial locality of the standard. Variation in labeled weights that do not appear to claim official authority is quite similar to this. For instance, Pink 1938.83–​7 collected all the labeled Roman weights in museum collections in Austria. We also have similar collections of weights from Pompeii/​ Herculaneum (CIL 10.8067/​857) and from Britain (RIB 58 2414 ). Table 3.2 gives their variation in the same ranges as for the ad Castoris weights (the percentage within each collection is followed, in parentheses, by the raw number).59 The last row gives the largest single deviation in each sample. 54 Hultsch 1882.155–​61, following Boekh. 55 Holland 2001 and Jenemann 2000.120–​9 on the sensitivity of ancient balances. 56 De Romanis 1998.37–​8 also notes evidence for variation over time. 57 There is similar variation in objects, apparently meant to be identical, made from precious metals and recorded at CIL 10.8071; see also notes 63, 69, 92, this chapter. Duncan-​Jones 1994.214, working from the larger stone weights now preserved in Naples, gets an average of 322.8 g to the pound, and somewhat less variation than in other samples. However, he trims a large number of outliers from his sample before the computations, giving at best a poor sense of what would have been knowable by an ancient user. 58 See full discussion at Frere and Tomlin 1991.1–​4, and note that they omit outliers from their computations. They suggest a bias toward vendors in their sample. See also more generally on standards of weight, Crawford 1974.591–​2. 59 In all cases I have counted only weights without recorded damage. I have used 327 g as the norm, though a lower value does not clearly have even the small advantage it has for the ad Castoris weights. I have omitted weights where the unit of measure is unclear (say, uncia vs. solidus), unless one alternative is a (question-​begging) “provincial” version of a unit.



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TABLE 3.2  } Variations in actual weights with respect to presumed standard values

% Variation from “standard”

Britain

Austria

Pompeii

ad Castoris

20+ 10+ 5+ 2+ Maximum

1.3 (1) 15 (12) 42 (33) 65 (51) 22%

2.3 (1) 9.3 (4) 23 (10) 58 (25) 49%

3 (2) 9 (6) 34 (23) 58 (39) 25%

14 (8) 17 (10) 31 (18) 67 (38) 53%

These figures, however, overstate the degree of standardization in a number of ways. Most important, I  have omitted unlabeled weights, which are quite common. Their intended value is often impossible to guess from nearness to assumed standards, and so would increase the range of variation dramatically. The collections from Pompeii/​Herculaneum and from Austria have a high number of very large (20–​100 lbs.) stone weights—​presumably less subject to loss and destruction—​which tend to be more precise than day-​to-​day measures. Moreover, the same points I made about the official weights apply here as well. Individual weights fall both above and below standard, so the range is essentially twice what is suggested, since actual individuals can only compare two existing weights, not a weight and the imaginary standard. To put things more concretely, among the British weights, for instance, there is little danger of mistaking 1-​and 2-​or 3-​and 5-​pound weights for each other, even without looking at the labels. However, what scholars have not been able to resolve decisively, despite specific attention and modern equipment, is whether they are keyed to a single standard, to multiple versions of what is meant to be a single standard, or even perhaps (in Britain) to a combination of Roman and native “Celtic” units. That is, a pound or ounce weight would presumably have been recognizably pound-​ish or ounce-​ish to a Roman user. But at the same time, the relationship between any two different pound weights, much less that between a given pound and a given ounce, would have been quite unpredictable. The evidence for volume is trickier to handle than that for weight. An early statute supposedly defined the largest normal liquid measure—​the amphora—​as the volume of 80 pounds of wine. Because of varying interpretations of the pound and variability in the density of the calibrating substance, modern estimates of “the” amphora range from 25.7 to 27.84 liters. This is not a big enough range to affect the identification of, say, an amphora versus a “congius” (1/​8 amphora), but it already suggests that the Romans themselves might have experienced considerable technical difficulty in establishing a consistent standard. We in fact have only three labeled objects that could be described as official Roman volumetric standards. One cannot be reliably measured owing to damage (Haverfield 1916), and the other two create problems when set against the official

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104 { Mosaics of Knowledge definition.60 The easier case is a long-​known vessel with an inscription claiming to contain 10 pounds as verified on the Capitoline. According to the definition of the lex Silia, that should make it a congius. Modern measurements make it out as 3.38 liters (implying an amphora of just over 27 liters). The difficulty is that, based on the standards of the same law, that implies a heavier pound than anyone imagines in any other context. Hultsch 1882.124 points out that the elaborate double-​truncated-​cone shape of the vessel could not have been constructed with considerable precision. Because he is interested in the “true” value of the congius, he then looks for other ways to calculate it. I would suggest, however, that the very mutual inconsistency of the law, the volume of the vessel, and the weight of that capacity is the important thing to observe. It is not at all clear that “true value” would have any straight-​forward meaning for an actual Roman user. More difficult to interpret is another vessel, likely a military measure for grain, discovered a century ago in Britain.61 It claims both to be calibrated (exactus) to 17.5 sextarii (a sextarius is a dry measure about 1/​6 of the congius) and to “have” (habet) 38 pounds. The weight plausibly refers to the vessel itself; it seems a little light, but no more so than many of the ad Castoris weights. Rivet holes near the top may also suggest a small component is missing.62 The peculiar number of sextarii has been explained as a week’s worth of rations (at 2.5 sextarii/​day/​soldier; Mann 1984). The measured volume of the whole would give a sextarius much greater (c. 20%) than would be expected from calculation. However, if the component indicated by the rivet holes was a “gauge mark,” then filling it to this point brings the vessel within 3% of the calculated value (RIB 2415.56, with important qualifications). This would actually be quite a good fit compared to some of the other standards we have seen, but it involves a fairly speculative reconstruction. Though “national” volumetric measures were rare, we are much more plentifully supplied with local measuring tables.63 These are large slabs of stone with series of roughly conical or hemispherical concavities of various sizes carved into

60 See also note 78, this chapter, for a later fourth-​century example with similar problems. 61 Haverfield 1916; RIB 2415.56. 62 Lange 2010.107–​16, 2011 argues that both figures give the capacity of the vessel as calibrated with olive oil. The weight is supposedly fixed in terms of special pound used only for oil. There are traces of special measures for oil, but none that then works out into the measure of other things, and some reason to believe that they are essentially volumetric rather than weight-​based in the first place (so, explicitly, Galen, in Hultsch 1864.210–​11; in general, Hultsch 1864.78–​80, 1882.120). The sextarius, in this supposed system, is not a single unit but means the volume of several (18 or 20 or 22 or 24) ounces of oil or water, sometimes modified by an additional multiplier (25/​24 or 7/​8 or 35/​36). On this account, the volume is both redundant (from the point of view of the maker) and unintelligibly ambiguous (from the point of view of the end user). Berriman 1956 had already sketched a roughly similar, though water-​ based, argument. It should also be pointed out that the vessel was probably not watertight in the first place (Haverfield 1916; RIB 2415.56). 63 In principle, one might also study individual, labeled ceramic measures, but damage means this is possible only very rarely. It does appear, however, that they show the same kind of variation as the “unofficial” weights. For examples, see Féret and Sylvestre 2008, Kütter 2008, Trapp 2005.



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their tops, sometimes with outlets cut through the bottom of the slab.64 Some carry inscriptions that tell us what we might have guessed anyway—​that these are meant as standards for measurement, a use also indicated by their frequent position in or near identifiable market places. Thanks to a recent and exhaustive study of Italian examples, we know the actual capacities of 72 cavities from 21 tables.65 As Lange 2010 demonstrates, the measured capacities show very little relation to any reconstruction of the system of volume measures. Nor is it even typically clear how the different cavities of any single table are meant to relate to one another.66 If the state offered a centralized standard, these do not reproduce it.67 Lange’s own view, however, is that beneath the chaos, there is actually a system of quite precise measurements, which involve identities not between volumes in the abstract but, rather, between weights of standard substances. A  given container, for instance, might be calibrated to hold some number of pounds of olive oil where that number was picked so that the volume would then also hold a round number of pounds of wheat. I do not find this account convincing, but for present purposes it does not matter.68 These devices would still be hyper-​local, each cavity designed to measure a particular quantity of a single substance for a particular market. Absent labels for individual cavities, and they are always absent, one would never know what any of them “stood for” without local insider knowledge. Moving to unofficial measures, we do not have many labeled items (as we did with the weights), but we do have some studies of the capacity of standard shipping containers called amphorae. This is an attractive object of study for our purposes because the same word amphora is carried over to the world of weights and measures as the name for a standard unit. Olmer 2001.230–​3 notes “extreme variability” in amphora capacity, while Wikander 2008.763 settles for “significant” variation. Relatively stable series of vessels can vary by up to 20% among one another, and even then an ancient user might not be able to recognize which ones were (relatively)

64 The precise method or methods of use are unknown. The ones with outlets could of course have been used to release a calibrated amount of liquid into another vessel. Some have speculated that the stone cavities were designed to hold removable metal vessels into which actual commodities were poured. On the issues, see Lange 2010.30–​2, 86–​90, 139–​42; Cioffi 2014; Rezkallah-​Boussaid 2014. 65 Lange 2010. Some, like the Pompeiian example mentioned earlier, are explicitly public, but generally we do not know the ownership. Supplemental argument in Lange 2011 and additional data in Lange 2014. 66 Lange 2010.104–​6, 147; 2014.83–​4. 67 For very similar results in a North African context, see also Rezkallah-​Boussaid 2014.72–​3. 68 There are so many free variables—​substances to be weighed, different approximations for the density of each substance, different “standard” divisions of units (e.g., 10 and 12 uncia pounds, several different base versions of the sextarius), as well as several optional multipliers (6/​5, 25/​24, 95/​96) that can apparently be appealed to ad lib., that it is hard to take the proffered coincidences as anything but just that. More generally, the approach makes the whole system of volumetric measure a clumsy gloss on the system of weights. This may well have been the form the root definitions took, but given the wide usage of volumetric terminology, as well as the need to be able to measure a wide variety of different substances, it is not possible that these units did not take on a life of their own. See also note 62, this chapter.

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106 { Mosaics of Knowledge precise (Olmer 2001.233).69 Some transport vessels appear to have been marked with empty and loaded weights, but this is largely restricted to a particular (though large) subset of olive-​oil amphorae—​the “Dressel 20” form (Olmer 2001.230–​1, 236; Edmonson 2014.685–​7). The same vessels often record a check on the total weight, but it is not clear how secure this would be, since the empty weight could not be checked. At any rate, the procedure would at most displace the issue of standardization in this class of vessels from volume to weight. Ancient time-​telling, as modern scholars have noted, distinguishes two different activities (and their associated devices) far more sharply than we do today.70 Water clocks were the primary means of measuring duration of time (“you may plead for four turns of the hourglass”). Sundials, by contrast were used to synchronize activity (“arrive for the trial at the third hour”). Both devices might be owned or produced by the state, but there is no evidence of any state attempt at coordination or standardization of either, and in fact it is not clear, as we saw in the discussion of approximation, to what extent the hour was really a unit of duration.71 Of course, even without state intervention, there is a “natural” standard at any given latitude once it is accepted that each day (sunrise to sunset) is divided into 12 equal hours. In principle, Greco-​Roman stationary sundials could have done this extremely accurately, but in practice builders preferred less accurate types (Gibbs 1976.4, 79). Portable models had a built-​in approximation with errors varying by latitude, season, and time of day (Wright 2000.182–​3, Talbert 2017.141–​3). I would suggest again that the maximum possible error is at least as important to actual use as the average. At any rate, Wright 2000.184–​5 goes on to point out that ancient sundials virtually always marked only whole hours, indicating little expectation of precision.72 How big a deal is the variation visible in these various dimensions? As I suggested in the introduction to this chapter, persons in the ancient world would have needed to learn the rules of individual contexts and/​or figure out how to get by in conditions of uncertainty. To take an extremely local set of examples as an illustration, let us turn back to weights. If you asked a particular vendor for three pounds of apples, you would likely know roughly what you would get, but would you be sure enough

69 Although outside the scope of the present chapter, observed variabilities in the capacities of earlier Greek amphorae show similar variability: there were clearly notional standards, but there was so much variation over time and space that we cannot tell whether the makers were merely unable to meet those standards or whether they themselves varied (Wallace 1986). Wallace’s emphasis is on the degree of standardization, and certainly his evidence shows that the notion existed, but the position he can refute is an extremely skeptical one. 70 Birth 2014.396. 71 The markings of a sundial need to be calibrated for latitude, particularly if it is to be used to track the progress through the seasons in addition to hours (Gibbs 1976.8–​11 with n25). Yet we happen to have evidence that an early sundial taken from Sicily was prominently displayed at Rome for nearly a century before anyone realized it was not properly set for the more northerly location (Plin. HN 7.213). 72 ideatur, et non amplius paene ab omnibus nisi quota sit solum inquiri festinetur. . . nam omnes fere, sicut supra memoratum est, quota sit solum requirunt (29, 40). Jones (forthcoming) shows that even professional astronomical contexts were not wildly different.



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about the quantity to agree in advance to pay the same price for this order from two different vendors? To set a price in advance even with a single vendor? To be confident that this amount would be enough to fill your pie? All these possibilities would be routine today, but a fairly modest variation in measurement could disrupt trust in numbers separate from the things themselves, and we have seen evidence that there would have been plenty of variation. It might also be asked whether the level of variation I’ve described isn’t just a matter of the limits of ancient technology in areas like metalworking. Weights and measures could only be made so uniform. Given the greater regularity of larger weights, there should be something to this, but that is hardly the whole story. First, the technological explanation hardly accounts for the numerous extreme cases, as Lieb 2004.134 has pointed out. Second, part of the supposed “problem” is self-​ inflicted. The fact that Romans liked the convenient but presumably harder to calibrate shape of nested weights suggests that precision was not their highest value. Similarly, the standard measures of large volumes are truncated cones or even pairs of them, and the hemispherical and conical cavities in most measuring tables would have been much harder to calibrate than cubes. More generally, audiences seem to have demanded regularity of form in weights and measures. This may have been a matter of aesthetics and/​or to avoid post-​manufacture tampering, but it also prevented finer calibration at the time of making. Romans could have measured these dimensions more precisely than they did. More important, though, intention is not the only issue here. Whatever the causes, Romans would have known that different weights or rulers or containers produced different results. All the variation recorded and discussed earlier would have been easy to observe in practice. Differences in length of whole millimeters are visually obvious. Similarly, pouring the contents of one exactly full container into a supposed equal one will reveal slight inequality at a glance. Differences in weight are not directly visible, but in fact the balance scales used during this period could detect them with ease. The most rough-​and-​ready Roman scales would have had a resolution of better than 1:100, and for the best available equipment it would have been around 1:5000.73 It would be strange for anyone to ignore this fact and act as if a more idealized system were in fact in place (especially as the idealization seems more ours than theirs). Rather, actual agents would just never presume that two similarly labeled measures were necessarily equal in practice.

Direct Standardization Standards available for weighing and measuring varied, sometimes with clear chronological or geographical patterns, sometimes seemingly at random. In this section



73

Jenemann 2000, Holland 2001.

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108 { Mosaics of Knowledge and the next, I will set that diversity into context by looking at pressures or—​more often—​their absence toward and away from standardization. This section will focus on direct commands from various state actors; the next section will then look at incentives built into the structure of the marketplace (broadly construed), whether that involves private parties interacting with one another or with the state. The first trace of direct action occurs quite early in Roman history. This is the lex Silia, seemingly of the mid-​third century bce. The statute, attested only by Festus (288L), defined three measures of liquid volume and perhaps one of dry measure, all in terms of various weights of wine.74 No definition of the unit of weight is offered. The statute did not, however, require or even encourage the use of these units by individuals, whether in specific acts of measurement or in the construction of measures. Rather, it forbade state officials, on pain of a massive fine, from unilaterally changing or tampering with official “weights, measures, and vessels”—​that is, a limited set of physical objects. As it turns out, the lex Silia is essentially sui generis. Subsequent public law on the matter is much narrower. The offense of falsum was originally concerned with falsification of wills and coinage, but it was eventually extended to cover those who “corrupt publicly approved measures” for various commodities (D. 48.10.32.1).75 As with the lex Silia, there are no rules about general usage of measures, or even their original construction. The crime lies in physically “corrupting” or “adulterating” state-​owned or state-​certified measures.76 Falsification seems to be a particular concern in cases in which obligations to the state grain supply (annona) were at stake (D. 47.11.6, 48.19.37). As perhaps befits an essentially political offense, the penalties are stiff, typically exile. Attempts at standardization by several late-​fourth-​century emperors will highlight, by way of contrast, the weakness and absence of earlier state intervention. Ammianus Marcellinus tells us that in the 360s the urban prefect Praetextatus “established weights throughout all regions.”77 Also connected to Praetextatus’ name is a provision to require (it appears) measurement rather than estimation of the weight of pork sold in the marketplace (CTh 14.4.4). Given his office, these rules were presumably both local, urban ones. The Theodosian Code, however, also records imperial edicts from the 380s that required the distribution of public standards of measurement in every community of the empire (CTh 12.6.19, 12.6.21pr). Punishment was explicitly to be inflicted on anyone who failed to follow this norm, not just, for instance, those who might be trying to cheat the state. It

74 On the law, see Cloud 1985. 75 This provision sounds a great deal like one said to have been introduced by Trajan and enhanced by Hadrian (D. 47.11.6.1–​2). If so, it may have been limited (at least only originally) to cases where the victim of the tampering was the state itself. Cf. D. 48.19.37 for another connection of “false” measures and the annona (and, in fact, to the same geographical context mentioned in 47.11.6pr). Cf. Robinson 1992.133–​4; 1995.37, 89. 76 D. 48.11.6.1 corruperit and 47.11.6.1 adulterinae respectively. 77 ponderaque per regiones instituit universas 27.9.10.



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does not seem that any of these attempts at projecting standards were successful, but the point here is simply that even the attempts stand out.78 We see nothing like this earlier. The state could conceivably also have encouraged standardization by making its use a practical necessity for specific interactions—​say, basing a tax on the square footage of real estate or import duties on pounds of goods.79 Taxation is a huge topic owing to the diversity of Roman practices over time and space, but one can make some reasonable generalizations.80 The Roman state collected a variety of taxes, some in cash and some in kind, often taking over systems that existed before conquest. In a few of these cases, the assessment must have required a calibrated measurement, at least at some point. Egyptian landowners were typically required to pay a set volume of grain per unit area under cultivation. In a few other cases, we know of taxes in cash based on acreage. Now land area is a special case I will discuss later, but in general I  would point out that for present purposes it’s not clear that the ancient state was answerable to a uniform standard in the way that many modern ones would be. That is, it’s not clear that the citizen can require consistency in the state’s measurements. In any case, however, the bulk of taxes were computed in ways that avoided having to do any kind of standardized measurement. In some cases, communities or whole provinces were simply charged a set sum of money. Customs duties, while typically ad valorem, could also be collected by count (OGIS 2.674; IGRP 3.1056). (De Romanis 1998 does point out that in at least one known case in Roman Egypt, notionally ad valorem taxes were actually computed by multiplying measured weights by standardized valuations.) Tithing (or, more generally, proportional taxation in kind) of produce was also common. Five percent is 5%, whether the state gets one cup or one barrel of each twenty. In some areas, there were poll taxes, based by definition on simple counting. Finally, there was a wide range of taxes based on some fraction of an already assessed cash value: inheritance, most customs duties, manumitted slaves, or simply direct taxation of the worth of pieces of land.

78 Pérez Zurita 2011.131 tries to move the date back a little (to c.  370), referring to a potential standard measure of volume found in Spain (AE 1915.75). The required reading of the inscription on the object is highly speculative and in any case Curchin 2014.291–​2 (who is broadly sympathetic to seeing an attempt at standardization) notes that the vessel deviates significantly from its expected capacity if it was meant as a standard. There is a superficially similar vessel from roughly a century earlier (ILS 8627), which the Urban Prefect had sent to the “regions,” presumably of the city itself. This is both local and, if Coarelli 1987.446–​7 is correct to connect it the mechanisms of state food distribution, more specifically for the internal use of the state. 79 Rizzi 2013.19–​20 can even point to a few cases of Greek laws requiring the use of specific measures in similar contexts. There are a few Imperial enactments granting privileges to persons who participated in certain favored trades to the extent of so many modii per day or per ship (e.g., Gaius 1.32, 34; Scaevola D. 50.5.3), but it is not clear, how these composites could have been measured with any precision. 80 This remainder of this paragraph and the next rely heavily on the information collected by Jones 1974.151–​85 and Duncan-​Jones 1990.187–​98, where primary sources may be found. See also Erdkamp 2005.206–​37.

110

110 { Mosaics of Knowledge Intriguing in this context is an inscription from around 200 which preserves a dossier of official acts in a matter touching on the public grain supply (CIL 3.14165.8).81 Considerable parts of the text are missing, and so some of the circumstances are unknown, but we can glean enough to draw an important conclusion. There was a dispute between shippers belonging to a guild based in Arles and the parties receiving the grain that they were carrying to Rome. It apparently hinged on the question of whether the quantities of grain delivered were the same as the quantities recorded as having been loaded. The first item of the official response was to require the shippers to bring with them marked iron measures and appropriate personnel to reproduce the measurements on arrival in port. That is, the solution is not to appeal to a universal standard but, rather, to say “bring your own and show your work.” This is particularly striking, given the relatively late date of the dispute and its official context, both in terms of the forum for resolution and because the state itself is at least an interested party. If the central state did not directly impose a system of weights and measures, it might still have achieved the same end in two other ways. One is by setting the terms of the commercial law which governs interactions between private parties. The salient legal category in private law is not “false” measures but, rather, ones that are iniquum, which I  translate provisionally as “dishonest,” though we will have to return to the issue shortly. As would be expected, the issue is with measures that are in some sense “too” big or small.82 Even among the small number of texts we have, there are a variety of legal analyses of the situation, but the stakes are typically much lower than with the falsum cases: the authorities sometimes destroy the offending measures and/​or the injured party is made whole, but no one is executed, exiled, or even fined. We have a few literary reports of destruction, and at least as it is represented to us, this smashing seems more of a theatrical gesture of support for fair exchange than any kind of systematic monitoring.83 For example, as Persius writes in his first satire (1.126–​30; A.  S. Klein’s translation, slightly modified):84 I want readers with cleansed ears, not . . . [a man] who thinks he is something, full of provincial importance because at Arretium, as aedile, he shattered heminas . . . iniquas.

81 =ILS 6987. On the text in general, see Rey-​Coquais 1993. On the point at issue here, Corti 2001.144 and Pérez Zurita 2011.126. 82 D. 4.3.18.3 maiora, minora; 19.1.32 minoribus; 47.2.53.22 maiora. 83 Juv. 10.99–​102, Persius 1.129–​30. Cf. Ulp. D. 19.2.13.8 and (assuming a speculative, but not unlikely supplement to the text) CIL 14.2625 for more neutral instances. Pace Pérez Zurita 2011.133, that is not clearly the point of the phrase aere fracto describing the source of the measures labelled thus CIL 12.1377, and certainly not for the use of the same phrase in AE 2003.1279. 84 inde uaporata lector mihi ferueat aure,/​non hic qui in crepidas Graiorum ludere gestit/​sordidus et lusco qui possit dicere ‘lusce,'/​sese aliquem credens Italo quod honore supinus/​fregerit heminas Arreti aedilis iniquas.



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More fundamental, though, is the question of just what it is these officials were enforcing, however sporadically. Literary and epigraphic texts agree with the legal ones that it is not false or counterfeit measures but, again, ones that are iniquum, so we need to turn to the precise meaning of that term.85 Etymologically, iniquum is of course in-​ + aequum, “not level.” Historically it can retain this root meaning or take on various metaphorical senses like “unequal” or “unfair.” Legal scholars have generally assumed that in this context it means “not equal [to the official standard],” but no text actually says as much. Moreover, this assumption presupposes an infrastructure that would make the implied comparison possible. Evidence we’ll see later calls the existence of that infrastructure into question, but for now let us just look at some explicit features of the law itself.86 Most important, nonstandard “standards” are explicitly protected both specifically and generically. We know that as a general rule, the parties to a transaction were entitled to pick a regional standard, or in fact any measures to which they mutually agreed (D. 18.1.71). And such a contractual term agreeing to use a particular set of measures is still valid, even if the measures are later admitted to be problematic (D. 4.3.18.3).87 Moreover, there are oddities in the position of a third party who provides weights and measures that turn out to be dishonest.88 One of our texts goes out of its way to protect the lender if she did not know her weights were dishonest. Another notes that the borrower of dishonest weights is liable to the lender (apparently for the value of the equipment) if the authorities confiscate them, regardless of what the lender knew.89 The suggestion I would make to account for all this is to take iniquum in a vague and local sense as “dishonest.”90 As noted, the parties can clearly opt for any standard, specific or general, that they wish, so no weights and measures can be inherently iniquum. This would explain the law’s solicitude for the provider of “bad” measures. If there is no master standard, then this circumstance is quite likely to arise. The owner/​ lender cannot, as a general matter, know that her equipment isn’t what a third party promises it is. It also explains why the owner of these measures might hope to be compensated by someone who borrowed them if they are subsequently confiscated

85 CIL 11.6375, 14.2625, AE 1935.49, 1999.1120 (speculative), CIL 9.2854 (doubtful). Cf. lex Irn. 19. 86 Lamberti 1994.368n21 has rightly already called this assumption into question. 87 The disappointed party might still have recourse to the residual actio de dolo, as emphasized by Watson 1991.299. 88 D. 4.3.18.3. Such an owner would presumably be in the same position in the scenario in another passage (D. 47.2.52.22), but that text does not bring attention to the issue. 89 D. 19.21.3.8. Lamberti 1994 offers a different reading of the passage, but it relies on supplying a word for which there is no real evidence. It also claims to explain the previously undernoted fact that only the borrower’s liability is at issue; her scenario (in which the hire is of a scale-​maker, not a scale) does not really explain the reverse asymmetry. Not all scholars have even grasped the basic point (correctly made by Rizzi 2012) that the basic issue is who will pay for the lost measures themselves, not liability for some potentially fraudulent transaction made with them. 90 Cf. also Lange’s argument (see note 91, this chapter) on exaequare as a local act (“calibrate”) rather than a global one (“standardize”).

112

112 { Mosaics of Knowledge by the authorities. The measures would not automatically be improper for other purposes, for which they could still have been hired out. Even though there were not really “national” mechanisms of standardization, one could imagine that the Roman authorities might try to harness local authorities to accomplish the same end or that those local authorities might take up the task of their own accord. Now, it is certainly the case that the Roman state sometimes harnessed local governments to administer “national” programs, most notably taxation. But the provision of weights and measures does not appear to be one of these. There are weights and measures from the provinces that claim verification with respect to the Capitolium or the Temple of Castor, but they are not among the (quite numerous) local dedications. Even a famous object from Pompeii, whose inscription commends a set of measures that are sometimes said to replace a local “Oscan” standard with a Roman one, says merely that the measures were to be aequum and cites no authority beyond the local council (CIL 10.793). (It is not actually clear that the narrative as reconstructed is even true.91) It is known that the officials with “marketplace” jurisdiction—​aediles at Rome and elsewhere, agoranomoi and especially metronomoi to the east—​often exercised notional supervision of weights and measures therein.92 And there is, in fact, a great deal of epigraphic evidence for the provision of public weights and measures at the local level.93 The texts recording the gifts do not refer to external standards, so let us look at how they are framed.94 They are sometimes given by the aediles and sometimes by other magistrates who do not necessarily have markets or weights and measures in their official portfolios.95 Indeed, they are sometimes given by wealthy private citizens, so “publicly available measures” are not necessarily the same as “publicly provided” ones. Often these gifts are, as far as we can tell, freestanding,

91 Mancini 1871 (note that citations of this article often have both the volume and page number wrong). However, Lange 2011.61–​3 suggests that there is considerable circularity in this account, pointing out that the item is not securely dated and shows that the key word in the text (exaequare) more likely means “calibrate” than “standardize.” 92 Pérez Zurita 2011.127, Berrendonner 2009.357–​ 8, Rizzi 2013.13–​ 15; Lex Irn 19; Robinson 1992.132–​4. Bresson’s 2016.239–​42 account of the Greek situation is rhetorically very positive/​maximalist, but I don’t think the substance of his position is necessarily so far from that expressed here (as is also the case with Wallace and Cioffi cited later, this note). Supervision is local to cities or even to particular markets and/​or commodities. Nearly all supervisory officials had non-​metrological duties. There remains very little evidence for intervention in the production of weights and measures. Moreover, direct inspection of weights and measures shows loose standardization. See, for instance, Wallace 1986 (amphorae), Cioffi 2014 (sekomata—​i.e., tabulae mensoriae), and especially Lang and Crosby 1964 (weights from the Athenian agora). 93 Frayn 1993.110 points out that most inscriptions referring to weight standards cite local authority. Further, see Frayn 1993.110–​11, 114. Cf. also the next note and the African examples quoted by Cagnat 1905.492. 94 Berrendonner 2009.362 is surely right to take SC iussu (AE 1977.168) as reference to the local council of Tuder, not the Roman Senate, and the same should be said of CIL 10.6017 (Minturnae). On the terminology of governance, see Kübler 1901.2319–​22. On the use of exaequare in the latter inscription, see note 91, this chapter. 95 Pérez Zurita 2011.135–​8, 140–​2; Berrendonner 2009.359–​60.



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but sometimes they are explicitly part of broader campaigns of euergetism that do not focus on weights and measures.96 Not only is its execution local but it also is quite haphazard. No particular category of persons was broadly responsible for providing weights and measures, and it is not even clear that weights and measures were distinct from a broader set of “public goods.” This could hardly have been an effective way to impose highly technical standards of the purported variety, even if that had somehow been intended. Sometimes, in fact, we know that local and regional officials supported multiple measurement standards. Barresi 1991.481 points out that public authorities even in the third century appear to have been publishing length standards that explicitly supported multiple systems: not just the Roman foot but also the Egyptian cubit and a Punic cubit.97 Similar are a series of weights that have recently been identified from Bithynia and Pontus (provinces in modern Turkey). These date from the mid-​ second to the late-​third centuries, and typically bear the names of the governor and of a local official concerned with weights.98 On the one hand, this presumably lends some kind of state authority to these weights. On the other hand, they explicitly refer to at least two different standards—​the Roman pound and the local litra. That is, even the Roman state did not assume the naturalness of its own units. There is, however, one area in which commonly available standards are generally assumed—​measurement of land. From very early times, land could be sold by means of a procedure called mancipatio. Mancipatio has a variety of legal consequences, but the one that is important to us is a guarantee built in for the buyer’s benefit. If the seller specified the area of the land at the time of sale and the plot turned out to be smaller, the buyer was entitled to a proportional refund (doubled, if the case had to be taken to trial).99 There is no reference to how this would be measured, which itself suggests that the area was assumed to be an inherent property of the plot of land and that any survey ought to come up with the same result. There is also another, later action available to a party to a sale harmed by a “surveyor who reported a false measure (falsum modum).”100 For our purposes, the interesting point is the word falsum. It uses the term we have seen for counterfeiting, not that for mere mismeasure. As earlier, the term appears in a context in which measurement is understood to be comparable to an independent standard—​there the state

96 Pérez Zurita 2011.127, 129 reads CIL 6.282 to show vici magistri at Rome not only donating weights but also returning to office years later to adjust them to standards. Much more plausible is Panciera 1978.318–​9, who shows that the later magistrates are different people and that what they provide is ongoing expenses, not revisions. This is a Roman example of the same kind of euergetism we see in the municipalities. Baratta 2012.70–​2 records a couple of cases in which a single gift includes metrological standards of different sorts. 97 They are not aligned with each other on the stone, so they are apparently not meant for easy conversion between systems, pace Berrendonner 2009.361. On the ongoing use of all these measures, as well as ad hoc compromises between them, see Camporeale 2014. 98 Summary of the finds at Haensch and Weiss 2014.540–​6. 99 Paul Sent. 1.19.1, 2.17.4; Watson 1965.81ff. 100 D. 11.6.

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114 { Mosaics of Knowledge specification, here the supposedly transparent “fact” of the matter. It is perhaps not surprising that the measurement of land should stand out in this way. These are measurements that would not be carried out by the general public, but by a small set of professionals operating within what seems, from the later textual evidence, to have been a well-​defined tradition.101 Their equipment, moreover, seems to have been fairly precise even by modern standards.102 The state was directly interested in such measurements both for distribution of land and for allocating responsibilities later.103 Measurements, then, might well have been reproducible enough in this domain to become taken for granted. (And the amount of money at stake might well have encouraged people to looks for such standards.) The cases in which measurement did play a role in taxation, however, are then worth a closer look. They are overwhelmingly land taxes, so that measurement at least can be done once and does not need to be constantly reenacted. Moreover, this might have been predicted given the special status of land measurement suggested earlier. In Egypt, the grain itself would also have had to be measured in each case, so this makes for a much more metrologically ambitious program. It also seems to be a peculiar holdover of the Pharaonic regime, but more important, it (and, for that matter, the land survey) could just as well have been imposed on a local basis. That is, even when taxes were calculated on the basis of measured amounts, it is not clear that the measurement was indeed uniform from place to place. I have already noted what appear to be explicitly different official weight standards at different locations in Roman Egypt. And, while we do not have direct evidence for the relevant measurements in Roman Sicily, we do seem to have grain measures from the earlier Greek system they took over. Even in the small sample we have, we see variation of at least 15% among what seem to be meant as equivalent vessels.104 Similar considerations apply to water distribution. A modern industrial user of water might require fixed quantities. A modern urban planner might want to measure absolute usage over time to determine whether new capacity was needed. Or a secondary market involving longer-​term storage of water before redistribution would presumably require a measurement in amphorae or the like. But for the task we have outlined—​allocation of shares of a given supply of water—​ratios of cross-​sections suffice. The state does not need to know absolute totals or to be able to compare the allotments of two distant users (drawing from different sources). The obligations are simply never framed in those terms. In this respect, water distribution is simply the reverse of taxation.

101 Robinson 1992.115–​6 points out that the action was eventually extended, though most of the specific examples are either still land surveying (of components, rather than whole lots, D. 11.6.5.2) or do not involve measure at all and respond rather to the need for an action against members of liberal professions who are not technically subject to employment contracts (D. 11.6.7.3–​4). 102 On the precision of Roman survey instruments, see Lewis 2001. On the results, see Duncan-​Jones 1980.127. 103 CIL 1.593.39. See ­chapter 5, this volume, for more on the informational aspects of these rules. 104 Walthall 2011.



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Indirect Standardization If the Roman state (and other governmental bodies) did little to compel standardization, the market more broadly could well have created incentives for the cooperative adoption of some standards. I mean “market” in a broad sense, including not just commercial exchange but also interaction in a variety of instrumental contexts. As with taxation, I can hardly be exhaustive, but I do want to point to several indications that the kinds of practice I  have described are fairly typical. In other words, if we ask whether Romans engaged in practices, commercial or otherwise, which required reproducible abstraction of measurements, the answer is generally no. One area in which precision might seem necessary is in construction. How else could Roman buildings of such seeming regularity have been built?105 On the one hand, in some respects the premise is false; Roman construction is perhaps less regular than it appears (Wilson Jones 2000.71–​2). I have already mentioned that the feet inferred from construction are statistical averages rather than clear units, and so are not evidence of even local uniformity. And on-​site improvisation seems to be common (Taylor 2003.26–​9). On the other hand, for some procedures, such as the fluting and tapering of columns, there were analog methods of producing effects that did not require difficult numerical measurements. Semi-​circular fluting, for instance, can be produced by trial and error, attempting to rotate a right-​angle rule through the cut channel. A circular colonnade can be designed by setting out equal angles rather than attempting equal linear measures, or an amphitheater can be given a desired number of fixed-​width bays by experiments with compass and model ellipses.106 But the crucial point is much more general than these geometric tricks. What this kind of construction requires is at most precise internal correspondence, not accurate conformity to some external standard. Take, for instance, the famous Maison Carrée temple in Nîmes. Wilson Jones 2000.71 points out that the exterior lengths of its two flanks correspond to each other within a single millimeter. But if the builders had tried to do this simply by specifying a number, and having teams of builders work on the two sides guided by that measure, it would have been impossible. As we saw, “standard” foot measures do not agree with each other closely enough to achieve this result. Such a project would either need an in-​house standard foot that workers could use as a reference or it could build out one side of the structure, then fit the other to that (effectively making the first side the “in-​ house” standard). Construction-​site graffiti recently found under the Flavian-​era

105 Taylor 2003.16 notes the extreme metric specificity of the building contract preserved at CIL 1.698, and also the seeming rarity of this phenomenon. I would add two inscribed building plans to be discussed in the c­ hapter 5, but note that all these items are forward-​looking. That is, because they prescribe lengths rather than describe them, they can be read in proportional terms; they do not need a standard foot to work. 106 Wilson Jones 2000.7–​8, 60–​1; Taylor 2003.40, 42.

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116 { Mosaics of Knowledge temple in Brescia may provide direct evidence for the first possibility in the form of what appear to be assorted fractions of the foot,107 but what we know about improvisation suggests a combination of strategies might have been the norm. This explains the inconsistency between projects, and even between segments of single projects, that have already been observed in the secondary literature. Scholars have made further study both of land surveying (as just suggested) and of monumental architecture, which we know often to have been designed around systems of multiples based on a single “module”—​that is, a basic measurement—​ which would often have been chosen in simple, whole numbers of feet.108 These studies suggest the expected basic unit of a little less than 300 mm, but with variation in the precise value, just as one might expect if the rulers themselves were not exactly equal.109 It should also be noted that these values for modules are statistical abstractions; whether because of error, approximation, or something else, the inferred values of the various modules ensure the best fit of a set of data with internal discrepancies. That is, it is not clear how important the precise standard was to the builders. The same question is raised in a more specific way by the construction of the Pantheon in Rome. Experts who have studied the metrology of the building agree that the porch and the rotunda were constructed according to slightly different modules.110 The actual difference is minute (about 1 mm), but it is nonetheless striking that a single standard may not have been a matter of course for a single project. It has been suggested in the modern literature that Roman stone quarries kept inventories of components (columns, capitals, etc.) in conventional sizes.111 If these were cut to precise lengths without any particular customer in mind, that would suggest a considerable degree of standardization. Russell (2013), however, has shown that this view is likely mistaken. He examined remains found in quarries and noted that, despite some rough clumping of column lengths around round figures such as 20, 30, or 40 feet, neither these nor the other elements come in objectively standard sizes (2013.221–​4). Moreover, he suggests that the columns tend to run “long” since they would in any case have to be finished at the construction site (221). In fact, we have clear cases of more dramatic trimming of various elements when the total size of a composite form was found, on site, to be excessive (248). Perhaps most important for present purposes, he also argues that builders did not simply send in orders but, rather, dispatched agents and even whole teams to the quarries (208–​11). At

107 Dell’Acqua 2014.341–​5. The measurements, if that is what they are, are marked off along both sides of a long rectangle, exactly as the case of the Libyan inscribed measuring table. 108 Duncan-​Jones 1980, however, points out the difficulties of using this method to discern the differences between similar standards. We encountered the same issue above with weight standards. 109 Hecht 1979.107–​8, Duncan-​Jones 1980.127, Dilke 1971.85. Dilke and Hecht also detect a slight downward drift over the first three centuries ce. 110 Amy and Gros 1979.I.85. Cf. Wilson Jones 2000.233n7 for similar observations at other locations. 111 E.g., Ward-​Perkins 1980a.327, 1980b.25.



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least some of these seem to have brought models with them (209), but in any case they would have been able to use their own measures rather than relying on some standard that was simply “out there.” Now some of these individual instances will seem unsurprising, but a similar argument can be made for a seemingly harder case: the grain trade. At long distance, the uncertainty of shipping would have discouraged reliance on any particular measurements. I have already mentioned the order that the shippers from Arles should transport their own measures along with the goods, rather than submitting to some kind of “neutral” measurement. More generically, measurement seems to be a genre feature of artistic representations that depict the loading of ships, as we see in paintings from Pompeii and from Ostia and in mosaics from Sousse in Tunisia (see book cover) and Ostia. This remeasurement as part of the ship-​loading process suggests the same kind of step-​by-​step use of quantification (cf. Rickman 1980.121–​2, 133; Corti 2001.144–​5). But we even see hedging at the destination. Consider a set of contracts from the archive of the Sulpicius family that record commercial lots of grains and legumes. (These documents were written on wax tablets preserved by the eruption of Vesuvius; they are referred to here by their numeration in the standard edition called TPSulp.) These record the goods in a variety of combinations of volume, location, and number of storage containers, as shown in table 3.3. “Location” appears to be the key property; that specifies what lot is legally in question. “Volume,” sometimes absent and sometimes approximate, is merely one type of supplemental information. Moreover, TPSulp 51 and 52 fairly clearly refer to the same lot of grains and give the same figures. But this means that the stated volume in 52 is in fact an approximation, as the same figure in 51 is explicitly described (plus minus, “give or take”). This leads one to wonder how precise the measurements in 46 and 79 are. Other documents in the archive reveal other localized procedures. One, which gives a volume in modii but not a number of sacks, tells us that the receiving party would carry out the measurement himself (TPSulp 46). In another, a weight of pledged silver is explicitly approximate, but is certified by the seal of one of the parties (55). Measurement is secondary, but when it is needed, it is not outsourced.

TABLE 3.3  } References to measured lots of grain in TPSulp.

Number Location Sacks Modii

45 • •

46 • •

51 • • • (explicitly approximate)

52 • • •

79 • •

118

118 { Mosaics of Knowledge We have already noted the lack of actual standardization of time, so it will not be surprising that there was not a lot of call for it. The object of the water clock was to give the two sides of a debate equal time to speak. For this, the clock only needed to match itself; that is enough to establish the desired ratio. The same is true of the sundial. Sundials aimed to establish times for starting and ending business, both public and private, such as when court hearings would start or when men and women were allowed into public baths.112 The length of the hour and even the actual time from dawn to a given appointment were immaterial so long as the parties agreed. Since the occasions on which this would be relevant were all face-​ to-​face meetings, a single sundial would often have been used, and the divergences with other devices would have been largely immaterial. And, in fact, this is directly attested. Cetius Faventinus, an amateur writing on the construction of sundials in (perhaps) the third century, twice suggests that no great precision is required because virtually no one cares about anything more precise than the hour: In their haste, practically no one asks anything beyond the hour. . . . Nearly all (as was noted above) ask only what the hour is. (29.2, 4)113 Seneca comments in passing that horologia (whether water, sun, or both is not clear) disagreed more than philosophers (Apocol. 2). The fact that anyone would even notice suggests that that comparison could at least be imagined, but in practice might not have been relied upon. There are also cases in which, at least in the ancient view, the conflict was probably not even visible. Let me return to the sundial and the water clock. The solar hour varied over location and season, while clepsydra turns were at most loosely connected to the hour (see at notes 15–​17, this chapter, for the very limited professional exceptions). The conjunction of the two systems would have required both to be standardized, but that was never required by actual Roman use of either individually. As we noted, the sundial was used to answer the question “when?” The clepsydra, by contrast, was used to answer “for how long?” Moreover, that duration is almost always prescriptive, relating to a single, localized time and place (Riggsby 2009b). Each device is reasonably well adapted to its particular purpose. Absent a theoretical commitment to a single “time” measuring device, there is little reason to bring them together. If they do not need to be linked to one another, they do not need to be individually standardized. In fact, the differing uses may have been an actual obstacle. If the variable solar hour was, for purposes of scheduling, the “real” time, then the regularity of the water clock would have been a disadvantage.114 To 112 For a comprehensive account, see Laurence 2007.154–​66 (for the baths, see CIL 2.5183). 113 non amplius paene ab omnibus nisi quota sit solum inquiri festinetur  .  .  .  omnes fere, sicut supra memoratum est, quota sit solum requirunt. 114 There are scattered exceptions. Julius Caesar reports investigation with water clocks to establish that (winter) nights were actually shorter on the Isle of Man than farther south (BG 5.13.4). Yet this could be measured without complicated calibration. In fact, the simplest thing would simply be to take a single device northward, measuring as you went.



Weights and Measures }  119

close this section I want to look at one more feature of Roman commercial law. The issue here is a little more abstract than in the earlier cases. The question, in essence, is the extent to which the Roman law of sale recognized what we think of as a “commodity.” Obviously, the more interchangeable merchandise is, the simpler it is to coordinate commerce in it. If you have generic commodities, it makes commerce more efficient. Now, just in general the Roman contract of sale (emptio venditio) required that an object being sold had to be specifically identified before the agreement could become binding. In cases of unique objects, this was simple: in modern terms, a baseball team could trade one of their players for “Bryce Harper” or even for “that guy” if the general manager pointed at someone in the room, but not for “a player to be named later.” What is less obvious is how that principle should be applied in the case of what we think of as commodities. Apparently it was taken to mean that you cannot sell an abstract quantity of something. More specifically, Gaius tells us: In things that depend on weight, number, or measure, like grain, wine, oil, and silver, the sale is not considered completed, even when the price is agreed unless the goods are measured, counted, or weighed. . . . If wine is sold at a certain price per the amphora, oil per the metreta, grain per the modius, or silver per the pound, it is asked when the sale seems to have been completed. . . . Sabinius and Cassius think the purchase is completed then, when they are counted, measured, or weighed.115 That is, an agreement to sell “that wheel of cheese” is binding immediately, but one to sell “10 pounds of cheese” is not. It takes effect only once a specific 10 pounds of cheese have been weighed out.116 The dispute among legal scholars has been about whether this can actually be correct. This feature of the law has been described (perhaps correctly) as a primitive relic in the contract of sale. So much so that some scholars have attempted to avoid the plain reading of this text (and of a few others) because they find the result too archaic. They want to carve out

115 In his quae pondere numero mensurave constant, veluti frumento vino oleo argento, modo ea servantur quae in ceteris, ut simul atque de pretio convenerit, videatur perfecta venditio, modo ut, etiamsi de pretio convenerit, non tamen aliter videatur perfecta venditio, quam si admensa adpensa adnumeratave sint. nam si omne vinum vel oleum vel frumentum vel argentum quantumcumque esset uno pretio venierit, idem iuris est quod in ceteris rebus. quod si vinum ita venierit, ut in singulas amphoras, item oleum, ut in singulos metretas, item frumentum, ut in singulos modios, item argentum, ut in singulas libras certum pretium diceretur, quaeritur, quando videatur emptio perfici. quod similiter scilicet quaeritur et de his quae numero constant, si pro numero corporum pretium fuerit statutum. Sabinus et Cassius tunc perfici emptionem existimant, cum adnumerata admensa adpensave sint, quia venditio quasi sub hac condicione videtur fieri, ut in singulos metretas aut in singulos modios quos quasve admensus eris, aut in singulas libras quas adpenderis, aut in singula corpora quae adnumeraveris (Gaius D. 18.1.35.5). 116 The category of things “that depend on weight, number, or measure” appears elsewhere in the law. In mutuum (12.1.2) and return of dotal property (23.3.42pr), the situation does not come into being until an initial measuring out, so there is no room for the kind of dispute we see in sale. It is also possible to leave property by measure in a will, likely because advance measurement is simply not practical. We have no information on what would happen if the legatee challenged the measure of his legacy.

120

120 { Mosaics of Knowledge exceptions:  if at least the source of the measured good is specified, they say, the contract goes into effect immediately: If some of the wine (say, 100 metretae) is sold from a vat, it is true (and apparently agreed upon) that before the measurement all risk falls on the seller. (Gaius D. 18.1.35.7)117 On their reading of this second passage, the contract comes into being at the time of general agreement (note that it doesn’t actually say that), but the risk of damage to the goods passes from seller to buyer, later, at the time of measurement.118 But, normally the shift in risk comes with the creation of the contract. And the passage I just quoted says that creation of the contract comes at the time of measurement. So they are claiming that this passage violates both those rules. But it’s so much easier to read if we just admit that it doesn’t violate either: measurement, formation of contract, and transfer of risk all just happen at once. There is no deal until you measure out the goods. Moreover, Johnston 1999.80 has pointed out an important additional fact that he regards as a surprising oddity. In theory, if you really wanted to do a generic sale, you could use a different kind of contract which doesn’t have the same technicalities I’ve just mentioned. A far as we can tell, however, this rarely if ever happened in practice. But that makes sense if what we’re looking at isn’t just a technicality that fell between the cracks but, rather, reflects a real Roman belief or value. They really thought this is how things should work. What both legal theory and actual individual parties reject here is the idea that a numerical measurement has a transparent, transferable meaning. The parties are of course welcome to use measurement systems as heuristics to decide how to bargain. That bargain, however, is not fixed until it has been reduced to a trade of some unique thing for a price.

Complications To this point I  have concentrated on what seems most distinctive to me about Roman metrology: the locality and context-​sensitivity of weights and measures. It would be a mistake, however, to take this tendency for the entire picture. In part, theoretical concerns encourage us to expect at least some diversity; it is hardly obvious that every “locality” or “context” should be of the same size. And so we

117 Sed et si ex doleario pars vini venierit, veluti metretae centum, verissimum est (quod et constare videtur) antequam admetiatur, omne periculum ad venditorem pertinere: nec interest, unum pretium omnium centum metretarum in semel dictum sit an in singulos eos. 118 See, e.g., Zimmermann 1996.236–​7, Birks 2014.71, Du Plessis 2015.264. At any rate, there is little debate that fully generic sale of quantities was never valid (Abatino 2012.xvii–​xx). For exhaustive discussion of all related issues with full bibliography, see Abatino 2012 (esp. 89–​105 on the passages just cited). Cf. Seckel and Levy 1927.137–​8 for a theoretical workaround.



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find things in fact. There are areas in which Romans in fact relied on numerical measurements free from the act of measurement, and others in which they might at least seem to have done so. We have already discussed the case of land survey, but in this section I want more generally to look at real and seeming exceptions to the general principles, both for the sake of completeness and because the contrasts will be informative. That is, locating more precisely where Romans aspired to more generalizable measures will give us a clearer idea of why they did so.

CONSTITUTION VS. MEASUREMENT At the end of the previous section I  noted that the law of sale was much more anxious about measuring out the thing being sold than the price. The former actually had to be carried out; the latter had only to be calculable.119 And in fact, there are other financial areas in which Romans were willing to perform complex and precise calculations on amounts of money conceived of as simple numbers. In particular, these involve the division of estates and computation of interest, both by means of the ponderous apparatus of Roman fractional arithmetic.120 Weight and length and so on are descriptive claims and so could be wrong, thus requiring caution when tools for measurement and communication are not reliable. Assigning a value is not a description; it is more performative. In the case of contract, we see that directly. In the other cases, such an assignment is either presumed to have happened (estates) or involves operation entirely within the world of values (interest on loans). Of course, descriptive information might be useful in arriving at certain assessments (e.g., what did the last horse sell for?), but once a price is agreed to, it simply is a fact. In fact, one might say the same of the measurements by proportion whose importance was stressed in the first section of this chapter. Each user imposes his or her own foot or pound or cyathus on the project at hand, rather than being constrained by some external version. But let me turn now to an example I have not yet mentioned—​the late antique system of taxation that today usually goes by the name of capitatio.121 The system broke down both the population and the land of the empire into units of tax liability, called capita and iuga, respectively. We have traces of formulas to convert various quantities of land of various quality into the appropriate number of units, and that looks like a stand-​in on the grandest possible scale. But while on one side of the equation we have concrete iugera, on the other we have purely notional units of fiscal accounting. Moreover, the “conversions” vary

119 This is fairly clearly the case from other texts on the law of sale. 120 Bailey 2013. On Roman fractional arithmetic, see Maher and Makowski 2001. 121 Grey 2007.368–​70; 2011.189–​91, 194, 214–​5. He notes (2007.369) that there was an appeal procedure, but that the attested cases are all holistic and typically have to do with changed conditions after the original assessment. That is, we have no evidence for technical challenges alleging measurement errors.

122

122 { Mosaics of Knowledge regionally, suggesting that the target is (necessarily) rough fiscal equivalence rather than any formal, metrological equality. The state did not measure iuga (or capita); it brought them into being. In all these cases, we have numbers, but not really measurements. Hence, the rules of measurement do not apply.

SYMBOLISM As I have said, most measurements fall into quite simple and even stylized patterns, but there are a few exceptions that might suggest considerable attention to and concern for the quantification. One class involves the weights of objects made of precious metals. This is often inscribed on the objects themselves, but the most elaborate case I know of is a dedication of a (now lost) silver statue of Isis supposedly weighing in at 121 209/​288 librae (that is, a roughly 40 kg object purportedly measured to within 1.5 g; CIL 2.3386).122 The second and somewhat more common class involves life spans (but not other time spans) in epitaphs. These regularly count years, months, and days, and not infrequently hours as well. Third, the charts of latitudes found on pocket sundials are frequently rendered with greater precision than could actually help the users, since the tiny devices can only be roughly calibrated. The situations have several things in common. First, there can be symbolic value to the precise accounting. Neither the dedicator nor the deceased is to be cheated out of the tiniest fraction of her gift/​life.123 In the case of the sundials, the value more likely lies in the owner’s access to “high technology” and projection of worldliness. Second, the measurements appear in contexts that are nontransactional. No one need take any action based on the purported life span. The recorded weights are redundant when they are on the objects themselves and ambiguous when (as quite often; CIL 10.8071) the labeled weights are for an entire set, not the individual object. Fixed sundials are not expected to agree with one another, so there is no reason to think mobile ones would, either. Finally, there seems to be considerable fiction. Evidence from digit heaping shows that there is fabrication in the age data, and the weights recorded on the silver objects apparently bear only a tenuous relationship to the actual figures.124 The latitudes on sundials are often simply wrong or attached to such large areas as to be meaningless. One might describe this phenomenon (with Talbert 2017.143–​6 speaking specifically of the sundials) as “an imperative to precision without accuracy; it hardly requires trust or consistency in

122 Other examples at CIL 10.7939, 8071. 123 Rounded age spans are frequently marked as approximations by the standard phrase plus minus. The other common context for this expression is in land area, one of the domains in which Romans did expect transparent measurement. 124 Weights: CIL 10.7939, 8067, and 8071.



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measurement, and might even discourage it.” More briefly, we might call this insistence, in quite specific contexts, of highly specific, but often fictitious measurements as “precisionism.”

REAL EXCEPTIONS Finally, I turn to what I would call real exceptions. Most of these turn on what I will call allometry, borrowing a term from comparative anatomy. Allometry is a phenomenon in which, for functional reasons, parallel parts of a system do not scale up or down in linear proportion to each other. For instance, in both evolution and engineering, there are a number of constraints based on the fact that the volume and surface or cross-​sectional area of a given object cannot scale together. Larger animals of a given type (say, tigers) are proportionally more stocky than smaller ones of the same type (say, house cats) so that, among other things, the strength of their muscles (proportional to the cross-​sectional area) can keep up with their weight (proportional to their volume). For reasons of chemistry and physics, one cannot triple quantities of chemical leaveners or alcohol in baking in the same way as one can increase the butter, flour, or eggs.125 Sometimes, in short, natural law means simple proportionality is impossible. Romans’ recognition of these phenomena seems to be rare. They did not have many processes that involved precise chemical proportions, as in the baking cases. Their engineers must have had some awareness of cube-​square issues, but they do not make an appearance in our sources. We do, however, see other, more specialized constraints in Vitruvius’ architectural manual.126 Most of his prescriptions are framed in ratios—​in fact, in complex sets of ratios built around a single modulus for each building. But absolute measure creeps into the description of optical effects, to the scaling of certain secondary rooms, and to the application of drills. The drill issue is a simple question of physics, but the others seem due to the presence of a hidden fixed term, the size and other properties of the human users of buildings. The first section of this chapter argued that many recipes in the Apicius collection could be read as giving proportions rather than standardized measures. This, however, is not always possible. There are cases where Grocock and Grainger 2006 concede that terms like acetabulum must be used as precise measures as when a particular ratio of liquid to egg is required for the structure of the dish.127 In fact, we can generalize the situation somewhat. Allometry becomes potentially important not just when an abstract system of proportions collides with a concrete object (a person, an egg). It also happens when two different proportional systems interact. Recipes which measure ingredients solely by weight or solely by volume require no specific units. Using

125 The scaled-​up cake will fall and will not have burned off enough of its alcohol. 126 For a more detailed account of this aspect of Vitruvius, see Riggsby 2016. 127 Apicius 7.5.4, 8.6.5, 8.6.7, 8.7.17. The last is one of the recipes that calls for two sizes of acetabula, a tension noted but not explained at their 84n2.

124

124 { Mosaics of Knowledge both—​say, cups and ounces—​in the same recipe, requires a fairly specific sense of what those terms mean. The converse of the argument that single units free users from standards is that unit conversions require standards. It is important, then, to look at how much conversion Romans did. In principle, this could be done by mechanical devices or with mathematical formulas. We have a few standards for length and a few balance scales that incorporate more than one system.128 I have already had reason to mention the Libyan inscription which offers standards for three different linear measures (Barresi 1991). We also have a couple of steelyard scales which, depending on how they are hung, could measure weight in different units.129 None of these devices lends itself to comparison. One could do two different measurements in any given case, but none is designed to display two different values at once (in contrast to, say, a ruler with metric and imperial markings set parallel to each other). As for texts, I have already quoted or referred to a number of such texts, but it is worth pulling them out as a group. (I will call these conversion tables, though, as it happens, we never have a true “table” in the sense described in ­chapter 2.) They fall broadly into two groups. One group consists of explicitly metrological, or at least definitional, works, typically converting between measures of the same dimension (e.g., feet and digits). A treatise by the second-​century jurist Volusius Maecianus is the only dedicated work of the sort. Agricultural and encyclopedic writers (Varro, Verrius Flaccus, Columella) and the land surveyors have passages which record various conversions. These generalized conversion texts are either tied to a very limited, professional audience (jurists, surveyors) or are embedded in much broader encyclopedic projects. In the professional case, their reach is by definition limited and thus also their projection of interchangeability effects. In the encyclopedic case, the actual audience may have been larger, but the dilution of metrological material by so much else would undercut any implication of measurements systematically transposable across contexts. The other set treats conversions that require contact between different kinds of measurement (e.g., pounds and gallons). These have very limited scopes and very limited target audiences. They always appear ad hoc in works that are not metrological as such. For instance, Vitruvius offers two sets of complex equivalences, as well as a one-​off weight:volume conversion for mercury. One conversion set gives moduli for the construction of catapults designed to hurl projectiles of various weights (given in pounds); the figure used by the builder to calibrate the device is the diameter (measured in digiti) of the torsion springs. The other set is a list of weights (in pounds) for 10-​foot lengths of water pipes of various standard diameters (in digiti). Frontinus (Aqu. 35–​63) offers an even more elaborate accounting of pipes, listing diameter and perimeter (in digiti) and cross-​section (in quinarii) for twenty-​five

Table: Barresi 1991. Scale: Savio and Lucchelli 2003. Radic and Jurisic 1993.133; Savio and Lucchelli 2003.

128 129

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different gauges.130 There are a few things to note here. First, the list is short; these are all the explicit conversion texts I know of. There are also more numerous texts which record specific facts, such as a military unit’s consumption of rations, in multiple units. But in these retrospective cases, the measurements are essentially independent of one another and so do not presuppose any particular relationship between the units. Second, except for the Cato passage, these texts all have highly localized audiences, not in the geographical sense we’ve seen before but in a professional one:  the military engineers and the state water-distribution apparatus. Within limited circles, standardization to the point of substitution is possible.131 I close this section with a fascinating, if likely unusual, case discovered by De Romanis (1998). In a papyrus recording Roman collection of import duties in Egypt, he noted that part of the calculation involved converting the weight of the goods from talents to Roman pounds, then back into talents. The second conversion was done at a slightly different rate from the first, resulting in a slight reduction in the notional weight. In form, this is clearly a conversion, but in substance that is less clear. After all, the method is to give two different values for what is notionally the weight in the same units of the same object. De Romanis argues convincingly that the function of the double conversion was to slightly reduce the effective tax rate that was being paid. It is not entirely clear why this was the method chosen; perhaps the local authorities could adjust the weights but not the notional rate? Whatever the details, I would suggest that this fiscal context explains the manipulation. What is ultimately being adjusted is not a weight that might be relevant elsewhere but, rather, the cash assessment. Thus we are back in the territory discussed at the beginning of this section. Assessment is not really measurement and so is not restricted in the same way.

Conclusions In the cases of lists and tables given in the previous chapters, my first question was whether the Romans used those technologies at all. For weights and measures, the question has rather been “how”? How did they use them, and what did they think they were doing in the process? The particular question I asked along those lines was to what extent various parts of the Roman system of weights and measures could be interchanged between one context and another. Modern measurements of these kinds of quantities normally have a “black box” quality to them. I do not really know how (or even whether) the contents of cans of food I buy are made to

130 There is also a passage of Cato (Agr. 57) that correlates quantities of wine rations to units of time and a similar, if briefer accountings of actual consumption in the context of the military encampment at Vindolanda in Britain (TabVind. 6.205). The lex Silia de ponderibus seems to set an equation of one quadrantal of volume with 80 librae of weight (of wine). 131 Radic and Jurisic 1993.133; Savio and Lucchelli 2003.

126

126 { Mosaics of Knowledge correspond to the quantities printed on their labels, much less whether I have actually just put 10.2 gallons of gasoline in my car. At the beginning of the chapter I mentioned the technical treatises (both surveying and juristic) in which Cuomo had already found some of this detachment of numbers from the act of measurement. Similarly, the “conversion tables” I  have just discussed appear to put into practice the same kind of free play of numbers that she saw in the more theoretical texts. I also suggested a special status for land surveying even beyond the theoretical works. The “acreage” of a piece of land seems to have been treated as a knowable independent of any individual measurement. Finally, there is cash. One of the most basic premises of the Roman (or perhaps any) monetary system is the equivalence of two amounts assigned the same formal denomination. If you offer to buy a bicycle for $300, it would not make sense for anyone to ask which $300 (assuming it is agreed they are all at least “real”). At the same time, I hope to have shown that these examples do not represent the Roman norm. Though measuring things was certainly an everyday occurrence, we need to distinguish “measurements” as the end result of that process (values that might then be transmitted, transformed, and transposed on their own) from the processes themselves (actions that necessarily take place at particular times and places, typically in face-​to-​face contexts). The features of Roman metrological practice I detailed in the first section of the chapter all emphasize the local and/​or concrete at the expense of the universal and abstract:







• Proportionality. Measurement by proportion floats free of standards. If

you and I both make a pound cake based on a proportional recipe—​equal parts eggs, flour, butter, sugar—​both are likely to come out equally well, even if we have different measuring cups. But at the same time, I cannot go to my neighbor and ask to borrow “one part flour” to complete my cake. • Resisting metonymy. This is the tendency that most directly operates against the transposition of measurements. Whenever a “cup” or “pace” or “month” is a reference to a particular thing, counting those things does not, by definition, produce a result that can be used for comparison out of context. It is, however, locally convenient, since to a particular audience, even if just an audience of one, there is no question what the standard is. • Approximation. Approximation makes it hard to “borrow” measurements between contexts. A measurement that is “close enough” in one context may not be so in another. And if there is a series of “approximately equal” quantities, later instances can drift farther and farther from the earlier ones. • Stylization. When Romans show a preference for certain numbers, regardless of what is notionally being measured, it operates as an extreme form of rounding (and thus of approximation), but with even more unpredictable results.



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Moreover, in all these cases we need to observe an important feedback effect. Sometimes particular Romans intended measurements to represent precise numbers of abstract units, while others did not. A second party, especially one not in a habitual or face-​to-​face relationship, would not know whether to expect that none of the four listed phenomena was in play in any given case. This is all the more true since many of the approximations, proportions, and non-​metonyms are hidden. That is, they take the same form as more specific and abstract measurements. Moreover, as I have tried to show, these phenomena (or at least the first three) were not failures of standardization; they were alternative strategies of measurement in their own right. Their absence, then, need not have been felt as a lack at the time. “Modernization” and standardization would not only have required considerable effort but also for many there would have been no incentive for the project. This argument implies that, in a sufficiently narrow local context, the broad ambiguities about what kind of measurement was intended could be overcome. Long experience of your neighbor or cheesemonger could tell you this. But how broadly could such circles be extended? To go reliably beyond face-​to-​face relationships, you would need some kind of infrastructure (both technological and administrative) to make standards available to interested parties. This seems to have been largely nonexistent. Provision of standards at the universal or empire-​wide levels seems both impossible in practice and not even an aspiration of the central government. Many local municipalities did at least aim to make common standards available, though these were not a given (at least if we take literally the rhetoric of the dedications). Nor were these necessarily appropriate for all purposes. They are almost always attached to the physical location of the local marketplace; there is no trace of “consumer” or even “industrial” standards.132 Standards for different dimensions (weight, length, etc.) seem to have been provided independently of one another. The magnitude of each was at least sometimes chosen with very specific purposes in mind (e.g., the salt trade) and so may not have been convenient for other purposes.133 Finally, the variations between local sets would have made them, at best, suspect for trade involving at least one nonlocal party. I have noted already the order to the shippers from Arles to bring their measure with them and the Pompeian contract specifying who would make the measurement. These are fairly isolated examples, but the clear legal rule allowing agreement of the parties to any measures they wished suggests that something like this, if arranged more informally, might well have been common. If I know what my local fruit vendor and my butcher call a “pound,” it does not much matter if they agree with each other, much less with a standard on the Capitoline. It might be claimed that particular Roman accomplishments imply the use of standardized measurements, particularly in construction, even if we do not know

Berrendonner 2009.364–​5. Pérez Zurita 2011.130; Berrendonner 2009.356, 366; CIL 6.282.

132 133

128

128 { Mosaics of Knowledge how it was accomplished. Thus, standardization must at least have been broadly available. I have touched on the relevant facts here, but it may be worth addressing more generally. Modern scientific usage distinguishes between “accuracy” (closeness to truth) and “precision” (repeatability) of measurements. A cleanly engineered 990 mm long “meter” stick can be precise—​it will reliably give the same results in the same context—​but it is not accurate. I would suggest that what these Roman accomplishments require, at least the vast majority of them, is not accuracy but, rather, precision. Precision, though, is by definition a local characteristic. But if measurement was not globally convincing, it could still be quite useful locally.134 Proportional recipes are enough to make recipes work in a hyper-​local context—​that is, in one’s own kitchen or workshop. Measures were clearly of value in commercial contexts as well, so long as they were denaturalized as part of the process. We need to distinguish again between measurement as result (a bare number or the like) and measurement as process (the physical application of a scale or ruler or the like). A Roman might not necessarily trust a number attached to some set of goods, but observing (or even performing) the measurement him-​or herself, and seeing the measures as well as the thing measured, could provide useful information. In a few cases trust might extend beyond one’s direct experience. Certain professional communities may have been able to maintain some standards across time and space. Astronomers’ equinoctial hours, the irregular pipe sizes of the state water supply, and the whole field of land surveying seem to provide examples. And, as we have also seen, state officials sometimes aspired to standardize specific measures in local contexts. But this seems largely to have been in contexts of considerable face-​to-​face familiarity and of physical proximity to a set of measures. Trust need not extend beyond what one could, at least in principle, have measured oneself. This, presumably, was why mensores—​that is, of people whose job was to measure land or grain or whatever—​loom so large in Roman commercial life.135 It is not because measurement as result is reliable, or even strictly meaningful, but because it is not. You can only know, and therefore only rely on, measurement as process. The pessimistic reading of all this is that a rational Roman actor would not rely too heavily on quantitative measurements without knowing where they came from. The optimistic reading is that in a world of various overlapping metrological communities, you can get by fairly well without that trust. The structure, then, of those communities would tend to reproduce itself, keeping social worlds fragmented along the economic path of least resistance.136

134 Cf. the notion of “communities of measurement” offered by Saliou 2014.11–​12. 135 For a general account of the evidence for mensores, see Baratta 2006. 136 For trust in measurement (and the lack thereof) in a parallel Athenian context, see Johnstone 2011.35–​61. This question could reasonably be framed in terms of the New Institutional Economics’ emphasis on structural features that affect the distribution of transaction costs and so (de)form particular economies. See also “Going Forward I” in c­ hapter 6 for further discussion and references.



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Chapter Appendix Here are some rough equivalents for Roman units of measure. Given the argument of this chapter and because these are only intended to given an order of magnitude impression, I will ignore controversy about precise figures. TABLE 3.4  } Standard reference values for several Roman units of measurement

ROMAN

MODERN

Pound (libra) Sextarius modius Foot (pes) Pace (passus) Mile (mille passus) Hour (hora)

327 g 560 ml 8.5 l (or more, depending on type) 296 mm 1.5 m 1.5 km (.92 English miles) 45–​75 minutes (varies seasonally)

130

4 }

Representing Three Dimensions

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The masterpieces of ancient sculpture are undoubted works of the highest craftsmanship. As a matter of taste, one might or might not enjoy them, but it is hard to argue that they were not executed with extreme skill, whether in realistic or more idealized modes. The same might be said less readily of ancient painting, much of which seems a little crude to modern eyes, especially ones that have not studied it attentively. Perhaps the main reason for this, well known to specialists in the field, is a lack of skill in or attention to perspective, particularly when compared to, say, works from the Renaissance forward. Even paintings which show anatomically plausible persons and “correctly” drafted objects of other sorts tend to scatter them around the painting in ways that seem odd or even “illogical.” Now, the actual situation is much more complex than I have just described it. Even to the casual viewer, there is obvious variation among Roman paintings (and some among their early modern counterparts, as well), and there is a long history of sophisticated scholarly analysis of how best to characterize the situation. My interest in all this is of course less about “art” than previous treatments’. The questions at stake here seem to me to lend themselves to formulation in terms of information technology. What information about spatial relationship did Roman artists convey and by what means? Given that question, the treatment I propose in this chapter is twofold. First, even just at the descriptive level, I want to offer a more precise characterization of what is going on in certain Roman artworks, and in particular one not defined by what might be thought to be lacking. Once that is done, a more historically specific and more genuinely causal explanation may be possible. Why are these tactics of spatial representation the ones used? In principle, there is no reason that these questions need be restricted to the study of painting. They are really questions about the organization of visual fields, not about painting in particular. At a minimum, they could also be asked of relief sculpture, and I intend to extend my inquiry in that direction as well. On the other hand, a general inquiry into all aspects of all such visual fields would be an almost inconceivably large undertaking. What I have in mind here is much more modest: a triple case study largely restricted to particular works of a single genre in different media: landscape representations in fresco and in stucco relief.



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The overall shape of my chapter will be as follows. The first section will lay out the theoretical issues that are at stake here. In particular, it will address the foundational issue of what we mean—​or could or should mean—​when we speak of “space” in these contexts. The second will introduce the sets of artworks that will underlie my principal case studies. The third and longest section will analyze the spatial strategies adopted in these works. Finally, I  will wrap up with two analyses of individual works from two other corpora and some general observations about how the specific cases contribute back to the theoretical discussion.

Perspective and the Theory of Space At least in outline, there has been agreement over decades of scholarship (which I do not mean to question) about the substance of the history of perspective in ancient painting, but there remains a question of terminology. The general notion of perspective is centuries old and widely applied, but (perhaps just because it ranges so far across time and space), usage of the term varies, even in didactic contexts. As a result, I begin with definitional concerns again, albeit more briefly than in the previous chapters. On the one hand, “perspective” can refer to any attempt to represent a three-​dimensional reality in two dimensions (e.g., Carr and Leonard 1992.54). Elsewhere it is restricted to formalized, mathematically regular systems such as were developed in early modern Europe and are a hallmark of Renaissance painting (e.g., Berger 1972.16, Taylor 1981.74). Panofsky’s 1991.27 great essay on the topic begins with what looks initially like an intermediate position: We shall speak of a fully “perspectival” view of space when not mere isolated objects, such as houses or furniture, are represented in “foreshortening,” but rather only when the entire picture has been transformed . . . into a “window,” and when we are meant to believe we are looking through this window into a space. (His subsequent discussion, however, goes on in practice to restrict the term to roughly the same set of paintings as the explicitly narrow one.) As a matter of definition, I will be using the broadest sense of the word—​the representation of three dimensions in two—​but much of the argument could be paraphrased as claiming that the Roman works of art studied here should be considered perspectival under Panofsky’s definition (taken at face value) as well. When I  want to refer to the narrowest, mathematical sense of “perspective,” I will describe it as “formal.” The ancient ability to render the three-​dimensionality of objects and scenes in two-​dimensional media (and/​or interest in rendering it) developed only over time, and even then in a fitful and piecemeal fashion. Phenomena like foreshortening and three-​quarter views appear earlier for some kinds of subjects than others and even

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132 { Mosaics of Knowledge in certain subcomponents before others (so, for instance, the wheels of chariots before other parts).1 The details of this development are not particularly important here, since most of it seems already to have taken place by the time of the works I will be discussing. Somewhat more relevant and also more controversial are two other questions. First, what was the “peak” of this development? That is, just how regular a system (say single-​point or any such formal perspective) was ever available in antiquity? Second, what approach(es) to perspective became the norm? On the first point, both sides cite, pro and con, mostly the same sets of paintings and the same passages from authors like Vitruvius as evidence for, respectively, the practice and theory of formal perspective.2 The deniers of formal perspective seem to me to have had largely the better of the argument, at least on the practical side, though the fact that debate remains possible is, I will suggest, significant in itself. As for the second question, even the most aggressive advocates of ancient formal perspective would admit that single-​point perspective never became an ancient norm. Instead, the most characteristic Roman development for treating complex compositions is what is often called “mixed” perspective. The classic, though not the first, formulation is that of von Blankenhagen and Alexander 1990.43:3 that form of perspective which most of these previous representations share [is] the so-​called bird’s eye perspective. The term is unfortunate because the objects represented are not uniformly seen from a high eye level. In fact each appears in its own perspective, namely, that which is most informative and in which its shape and volume may be comprehended most easily. Within the frame of frieze or panel the objects thus represented are arranged according to the convention that “above” means “behind” or “distant.” Buildings therefore appear as seen from different, but usually high, points of view while people and smaller objects seem to be represented at much lower eye levels. There is, necessarily, no consistent scale—​the representation of reality as it appears to the eye takes second place to the desire to give the fullest possible information about the things selected for representation.

1 Richter 1970. 2 Pro: Beyen 1939, White 1956, Sinisgalli 2012. Con: Panofsky 1991, Richter 1970, Tybout 1989, Gros 2008, Stinson 2011. Note that many of these scholars make important contributions not limited to precisely the issue in question here. Valerio 1998, seconded by LaRocca 2008.34, claims that observation of the physical evidence is moot because there is no evidence for an awareness of projective geometry in classical times. But in fact modern projective geometry postdates the entire discovery and diffusion of single-​point perspective in the early modern period. What is lacking in antiquity on his theory, then, is a way of thinking about perspective that is so narrowly defined as to be of little interest for most purposes (including the present ones). Hinterhöller-​Klein 2015 offers individual readings of an enormous corpus of examples and takes into account a wider array of forms of formal perspective than is usual, finding that they are often in evidence in regions of individual works, if not systematically governing any as a whole. Despite the breadth of her study, however, she does restrict her attention essentially to perspective in the narrowly mathematical sense I find inadequate in this chapter. 3 See also especially Panofsky “an aggregate space . . . never . . . a systematic space.” Also Lehmann 1953.148–​51.



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So for instance we have the famous painting in Naples of a riot in the Pompeiian amphitheater (plate 2). The high-​angle view of the amphitheater gives us a good idea of its form. But if we saw the people from the same position, they’d be considerably smaller, and greatly foreshortened, as well. As a result, they’d be nearly illegible. Hence, they are painted as if from lower down and closer in. Moreover, the view of the amphitheater is itself divided. A near-​bird’s-​eye view is adopted for the interior, but the exterior is seen more frontally. Other scholars speak of “partial,” “inconsistent,” or non-​”unified” perspective, but the general idea seems to be the same. These writers usually try to avoid progressivist accounts in which classical painters were simply unable to reach a set of absolute standards; rather, they could well have had an entirely different aesthetic; I too will try to remain at least neutral on this.4 While this is the more or less agreed-​on core, some have expressed more extreme views on the incoherence or even lack of perspective in Roman art. That is, there is what might be called a “primitivist” tendency to stress the distance between classical and (early) modern practices. A conventional form of this is the claim that Roman painting sacrificed representation of space in favor of the solidity of represented objects. Early last century, Panofsky 1991.41–​3 had already spoken in zero-​sum terms of this trade-​off between space and corporeality in classical art, and I think a similar framing is implicit in most primitivist scholarship. However, the most extensive, the most explicit, and the most recent treatment is that of Eugenio La Rocca’s 2008 Lo spazio negato. He examines largely the same corpus of paintings I will look at here, and, as the title says, speaks of their “denial” of space (35, 42). What is the “space” that he says is being “denied”? At one point he speaks of it as an “infinite continuum,” but for the most part we have to piece a definition together by looking at specific features that are supposedly being denied.5 [It] is not constructed according to a unitary mathematical logic, nor agglutinated into an ensemble, nor does it seem to extend beyond the spectator’s field of vision. All the objects that make up the image . . . account for the effects of light and atmosphere in refined fashion, but not in a gradual and organic manner from foreground to background. Rather, they are distributed in the field of the painting according to different scales, but without a coherent system of reduction towards the horizon, a symptom of the lack of a consistent relationship between size and distance. In practice, every picture is composed of objects that live more or less individually and more or less isolated from the others in a space continually denied as unifying element. (35, emphasis mine)

4 Panofsky 1991.40, Lehmann 1953.149, Richter 1970.61, Ling 1977.12, Stinson 2011.423–​4. 5 He takes a somewhat more nuanced position at 34 “tale assenza . . . spazio infinito,” but it doesn’t really seem to be reflected in his readings.

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134 { Mosaics of Knowledge Many of the specific points (“regular,” “mathematical,” “coherent,” “consistent”) are just different ways of saying that La Rocca is looking for a fully predictable system. The essential claim is that this is necessary for space to serve as an organizing device (“unifying element”). Thus the supposed replacement of continuous regression by division into a pair of horizontal bands, more or less discontinuous with each other, is seen more broadly as a symptom of the absence of space in this sense (36, 43, 44). I’ll have much more to say about this in concrete cases (especially the first part of the section “Two Comprehensive Examples”), but for now I’ll stay at the theoretical level. Definitions like this smuggle in some very specific (and to some extent presentist) assumptions about what “space” is. Space, that is, is more or less explicitly equated with the quite specific mathematical phenomenon of Euclidean space (in geometrical terms) or even Cartesian (in algebraic ones): infinite, homogeneous, infinitely divisible, and susceptible to uniform measurement. These are common expectations in our highly mathematized world, but not necessary, even in that context (as I will try to show shortly). Moreover, when single-​point perspective (a system clearly “spatial” in La Rocca’s sense) did arise, it carried the field so successfully (in the relatively recent past) and is so deeply embedded in our visual common sense (even now) that it is hard to imagine alternative systems with similar but not identical functions.6 Yet, as I have argued elsewhere, this notion of space should be seen as a particular case, even a limit case, of the category.7 There has been quite a bit of scholarship on theories of “space” (and the related notion of “place”), but there are considerable continuities, and I prefer to frame the distinction as follows: A “space” is in the first instance a range of possibilities—​the individual “places”—​a set of objects that are distinct, but at least comparable with one another. The space is given a structure defined by the relationships between its component places. Spaces, that is, are the context in which we can give meaning to properties like proximity, relational orientation, presence/​absence, and partitioning. But the degree of complexity and regularity of this structure can vary greatly. On the one hand, the most highly articulated spaces would include precisely the Euclidean/​Cartesian space I’ve mentioned. The least articulated, on the other hand, would include, say, the Greek division of the world into oikumene, antipodes, and so on (that is, a quartering of the earth defined by the northern/​southern and eastern/​western hemispheres). In some of the cases I have discussed previously, the spatial structures are similarly rudimentary. But there are also vastly more complex cases like the images I  will discuss in this chapter and the complex networks and maplike objects which I will treat in the next chapter. The problem with the modern model is not so much that it is too mathematical but, rather, that it is limited to a very particular mathematics.



More or less explicitly argued by Richter 1970.3. Riggsby 2009a.

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I will be arguing for spaces that lack uniformity and regularity of measurement, but which still have a meaningful topology. In this view, formal regularity is not a definitional characteristic but an extra option. At a minimum, this theoretical perspective makes it easier to see something important that is nonetheless true independently; regularity is a characteristic that can be possessed in degrees rather than simply being present or absent. After all, one might say that a Claude Lorrain landscape or Paul Cezanne still-​ life “manipulated” space, but not that it “denied” it for failure to precisely meet Renaissance requirements. The other supposedly diagnostic features of space—​ “gradual” transformation and infinite extension—​seem similarly optional to me. Gradualness is a special case even within the already special case of mathematically predictable systems. Gestures at infinite extension are important in certain kinds of type-​scenes that were dear to Renaissance Italian painters, but were rather less so for Romans. That distinction is not entirely arbitrary (as I will discuss at the end of this chapter), but it does suggest the formal feature is more contingent than necessary. By contrast, the other features I take to be “spatial” (that is, proximity, relational orientation, presence/​absence, and partitioning) will all play important roles in our paintings. Now, obviously it is entirely legitimate for La Rocca and others to focus on the more specific phenomenon of Euclidean space, and the demonstration that it is absent (or nearly so) in classical antiquity is an important result. But we still need to avoid the implicit confusion of “uniform” (which Roman painting is not) with “unified” (which, I will argue, it sometimes is). I worry that if we confuse the differently spatial with the non-​spatial, if we define Roman art simply by what it (supposedly) lacks, we will fail to attend to how it actually operates.

The Corpora My investigation will focus on three sets of objects:  a group of paintings originally from a columbarium found on the grounds of the Villa Doria Pamphilj in Rome, another group from the walls of the suburban villa found under the Villa Farnesina, also in Rome, and some stucco ceiling reliefs again from the “villa under the Farnesina.”8 It is a fortunate coincidence that all three are currently displayed virtually next to one another on the same floor of the Palazzo Massimo museum in Rome, but there are substantive reasons to take them together as well.9 On the one hand, they share similar date, location, and subject matter. They all seem to date from roughly 20 bce. All involve stereotyped rural landscapes of fairly broad scope,

8 Thus these works are all clearly Roman in both their physical location and their patronage. The artists might well have been Greek in some ethnic or even linguistic sense, though it is worth noting that the one attested painter of the genre has a seemingly Italian name (Ling 1977.2). 9 Silberberg 1980 catalogs the corpus of sacro-​idyllic paintings as a whole. For analytic studies, see Ling 1977 and Bergmann 1992. See also Peters 1963, Salvatori 2008, and Croisille 2010 on landscape.

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136 { Mosaics of Knowledge punctuated by trees, buildings, people, and animals, but without any central subject. The particular types of buildings and the postures and activities of the staffage figures draw from a quite limited repertoire. Despite these generic similarities, there are interesting contrasts between the members of the set. The Pamphilj paintings are less complicated and, to all appearances, the work of less skilled artists. The Farnesina works, both in themselves and because of their context, appear to be works of top artists, thought by some to have been working for members of the imperial family. Moreover, the stuccos obviously differ in medium from both sets of paintings. While just these observed similarities are enough, I  think, to ground a useful analysis, that choice comes close enough to some controversial questions about the genre(s) of the paintings that I should say a few words about them directly. The works I have just pointed to clearly belong to a network of landscape paintings, mostly from the vicinity of Rome and from Campania, the next region south along the coast, that dates back to around 40 bce and extends beyond the eruption of Vesuvius. Some or all of these (depending on one’s precise scholarly inclinations) are instances of what is called “sacro-​(or sacral-​) idyllic” painting. In addition to the direct evidence of the paintings themselves, we have two pieces of literary testimony which appear to refer to this type of painting (Vitr. 7.5.2, Plin. HN 35.116–​7). The controversial issues today include how (if at all) to divide these up into subgenres and what development (if any) over time we can observe.10 In that light, it is important to stress that I have picked my particular set of images for purely formal reasons. The topic here is representation of complex spatial relations, so I have taken paintings which each include a variety of different subjects of different sorts (human, animal, architectural, natural) without any of them necessarily being central. I will try to give a very brief description here of the three major bodies of evidence, then I will analyze them in specifically spatial terms in the following section. (As is the norm for ancient works of art, none of these appear to have titles. In what follows I will identify individual panels by their museum inventory numbers.)

VILLA PAMPHILJ COLUMBARIUM Most of the objects in each painting fall into one of two fairly well-​defined tiers (see plate 3).11 (I will discuss later the one panel with three tiers.) Across the bottom (apparently “forward”) stretch of each panel are placed people, animals, trees, architecture, and a few natural hills or rock outcroppings. At least some of these items are tall enough to reach nearly to the top of the field.

10 My general inclination is to see neither a clear development nor sharp divisions between subgenres, but neither position is important to the argument that follows. 11 Discussion at Ling 1993.



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The figures in the lower tier sit on or just below a simple ground line.12 This is formed by a single band of color (different ones in different paintings)13 across the bottom of the field. It is generally level across the field, though the line does tend to slant toward the bottom edge of the paintings at the ends. The second tier begins roughly halfway up the field. It consists solely of buildings and those are restricted to the space left between the first-​tier figures, to the right and left of the central temple and trees. Individual buildings at this level sometimes sit on a small, secondary ground line, but this appears only sporadically, not across the whole work. Sky is represented by the plain white of the plaster background. Figures and setting are very roughly in naturalistic scale to one another in the foreground, though obviously one cannot make precise claims in the absence of any real referents. When there is a demonstrable mismatch, it consists in the buildings being too small; their width is sometimes barely more than the height of a person. Buildings in the upper tier are consistently (if necessarily) smaller than those below, suggesting recession, though in the absence of human figures for comparison (in the upper tier) it is again impossible to make precise claims about distance and scale.

VILLA DELLA FARNESINA FRESCOS The composition of these paintings is more fluid than that seen in the Pamphilj paintings (see plate 4). Humans and animals are generally distributed through the bottom third or half of the field. Trees and buildings often start at that same level, but can reach most of the way to the top of the frame. There are also other buildings that begin at higher levels. In most such cases, these buildings are explicitly put on significantly elevated ground. In other cases, it seems to be a matter of recession of more distant objects. We can sometimes validate the latter interpretation by noting the use of atmospheric perspective. The buildings that appear to be “up = back” are rendered in lighter and less saturated tones (as the temple above and to the left of the central scene). Of course, these structures could plausibly be elevated as well as distant. The ground is not restricted to a uniform band at the bottom, but extends as much as halfway up the field in places (it also does not generally reach all the way down to the purely uniform green strip that serves as a lower border for all the paintings). Moreover, it is differentiated by color, with brownish rock outcroppings, blue water, and green vegetation-​covered ground. People are perhaps slightly too large in comparison to nearby buildings, but this is less clear than in the Pamphilj paintings.

12 Exception: MAN 517351, a painting that is unusual in many respects (cf. note 18, this chapter). 13 In MAN 571966, a switch from brown to blue represents the pool in which one of the figures is fishing.

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VILLA DELLA FARNESINA RELIEFS The stucco reliefs from the ceilings of three rooms were not as numerous as the paintings to start with, nor are they as well preserved (see plate 5).14 Hence, one must be a little cautious about claims that this or that feature is rare or common; the sample size is quite small. In broad outline, however, there does appear to be a fairly standardized structure. The architecture generally forms a band that takes up most of the center half or two-​thirds of each field. In several cases, that band veers up or down at one end (and in one case does both, producing a Y configuration15). People, animals, and small plants are scattered below the central band, and there are also often people among (and even in) the architecture. The buildings and trees are often based on what looks like bare rock, and there are also a few outcroppings that are not specifically attached to anything. Smoother ground lines are traced between many of the constructions. The existence of fishermen and bridges suggests that we should imagine some rivers or other water features, but these are barely (if at all) represented directly. The end passages that move upward apparently also move “back” (as here on the right; the buildings are distinctly smaller). As in the two sets of paintings, the buildings are in general probably slightly too small with respect to the people. This is exaggerated in MNR 1072, where the towers are smaller due to their recession from the front, but the people nearby are at virtually the same scale as any others. By contrast, the livestock at the far bottom of two other panels (1069, 1074), are conspicuously large, presumably representing a forward position.

Space in the Landscapes To turn now to the analysis, let me repeat my general question: What spatial relations are encoded in these works and how? I won’t demonstrate the pervasive use of certain familiar tactics such as use of relative size and the general “up = back” equation (though a particular version of this will be important). The general principles are familiar today, and there will be (indeed have already been) examples in passing. What I want to look at with greater deliberation are some more peculiar strategies, some perhaps unique to individual artists.

STACKING The simplest device used to create depth is superposition, or stacking. If one object obstructs the view of another, the blocking object is “nearer” the viewer than the blocked one. In and of itself, this is not a particularly powerful or subtle device. All



14 15

Discussion at Mielsch 1975 and Blanc 2008. MNR 1037, 1072, 1074.



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it can show is order of recession, and only for the items directly superimposed. If we have two neighboring “stacks,” it is difficult to read correspondences at any particular level of depth, much less an absolute scale, even an approximate one. But this is true only for superposition by itself. In combination with other features, however, it can add to the spatial complexity and rigor of a scene. For instance, in plate 4 the central building is in front of both the bridge to its left and the tree to its right. In each pair of men pulling the net (lower left), the man who is slightly behind is also slightly farther away from the viewer. Plate 5 offers a more layered example. In order (receding from the viewer in the central complex), we have a woman slightly bent at the waist, the slanted-​roofed building, a tree, a pillar topped with a statue, and perhaps a tower of some sort.

COLOR I’ve already mentioned in passing the notion of “atmospheric perspective.” Under that convention, widely known but perhaps most famously used in Chinese landscape paintings, a reduced, paler, and bluer palette is used to mark background figures in contradistinction to the foreground. Such shading does in the Farnesina paintings roughly the work done in the Pamphilj paintings by the division into upper and lower tiers. My main observation here, however, is a more distinctive phenomenon. Within the tiers in the Pamphilj paintings, color effects are sometimes used to articulate local spatial relations. When two figures overlap or nearly so, the one in “front” is typically rendered in a dark red, while the one “behind” is in a less intense and usually bluer hue, as with both pairs of figures in plate 3. This principle applies to people, animals, and inanimate features of the landscape. Moreover, it seems to operate on buildings; the closest face of a structure can take on the “foreground” coloration, while the rest has the “background” (thus the faces of the statue base on the left). Note that this device makes a different use of a very similar coloring than atmospheric perspective does. Normal atmospheric perspective is used to relegate material to the generic background in a global sense. In the present cases, the distinction being made is between adjacent figures, not between overall foreground and background. So in plate 3, the red woman on the far right is forward with respect to her overlapping companion, even though she appears to be “even with” the non-​overlapping statue base (and compare the two women clearly in front of the portico in scene F/​XIX).

PHYSICAL DEPTH Obviously the Farnesina reliefs do not have color effects, but we can look at a different resource that the artist had that was not available in fresco: the actual depth of the plaster. So the woman behind the column near the center of plate 5 is in lower relief than the woman in front of it. Functionally, this tactic seems to be used for the same ends as shading in the Pamphilj paintings—​that is, to register local

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140 { Mosaics of Knowledge rather than global spatial relations. An object in higher relief is closer to the viewer than a nearby or overlapping object in lower relief, a distinction which can often be confirmed by stacking relations. Thus both square towers (center and right) are of similar depth, even though the one on the right (again, smaller and higher) appears to be farther away. The items coded “behind” by low relief are the juncture of the short colonnade with the tower on the right of the central tower and the columns behind the steeply sloped building on the left. (Note also that on the left, the column edges are incised. The existence of this option gives the artist a little more depth to work with.) This gradation, combined with the pronounced slant of the structure, suggests that the colonnade extends out from the rear square tower toward the viewer from far back in the picture.

SPECIAL OBJECTS My next device is found in both the paintings and the reliefs of the Farnesina. There are compositions that feature distant (i.e., reduced scale) architecture set apart on a hill or other platform, but also then joined to the core by a bridge (e.g., plates 4, 5). The general compositional formula is, again, “up = back,” but in the absence of systematic perspective, the precise relationship is in principle underdetermined. But in both media from the Farnesina, the artists seem to make up for this by having the elevation serve double duty. The bridge constrains the possible distance between the two points it connects, and its angle shows that it goes both “back” and “up.” So the viewer is spared total aporia. At the same time, that viewer can see different precise combinations of elevation and distance as he or she sees fit. The flexibility makes it less likely to be forced to admit a contradiction (we will see other strategies with similar effect). Moreover, at least this last strategy—​using distinctive perspectives on individual elements to structure the whole and exploiting connections that are “real” in the world of the painting—​is spatial in a more general sense. It simultaneously connects two elements and holds them at a distance. It does not create (or rely on) the existence of infinite and continuous space, but it does, at a minimum, yield a network, a “space” in the broader sense discussed. Taking a cue from this particular case, we can trace other features used to structure the space of the paintings and reliefs. Some habits of local representation—​that is, stereotypical forms of individual buildings—​are best explained in the context of a global concern for spatial arrangement. I spoke of the bridges and will turn later to a similar use of porticos, typically shown in high-​angle perspective, but first I will talk about a more specialized case. The most striking of these is the porta sacra, as is found in the upper right of figure 4.1, on the raised ground.16 This is almost never shown face-​on or even in a normal



16

Evidence collected by Dall’Olio 1989.



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three-​quarter view. Rather, it is viewed almost—​but not quite—​end-​on. Why the dramatic foreshortening? “Mixed perspective” would locate this in the most “informative” view available, but that fails to answer the question: What kind of information is it that is being maximized here? The gate itself is harder to see than if a broader angle were taken. If we see the gate nearly edge-​on, the only component privileged is the nearer column, but these objects—​simple cylinders and rectangular prisms—​would look the same from any direction. Nor do we have a clear idea of the individual components or of the width of the gate. What we do know is that the width projects back from the viewer. What is clarified is not the structure of the gate itself but its disposition in space.17 It extends almost straight back into the distance. The extreme foreshortening makes a “real” width hard to infer in strictly formal terms, but the type of object (a gateway) is standard enough that the viewer can project its depth on pragmatic grounds.

GROUND The most important connecting object, however, is less specialized: the ground. The ground line of the Pamphilj paintings binds together all the people and buildings in the foreground. The connection tends to be formal, in that the ground is generally level and monochrome.18 Still, even this connection encourages the viewer to read the proximity of the features and their roughly plausible relative scale in fairly literal terms. The ground of the Farnesina paintings does the same thing, of course, but it also has a more active role. First, the ground has considerable two-​dimensional extension, rather than being the one-​dimensional line on which the Pamphilj figures perch. It can extend far from the bottom of the frame (though the distance varies considerably from case to case), rising behind figures and buildings. In some cases, it also represents three-​dimensional variation, as when shading is used to mark one face of an outcrop as being nearer the viewer. (One might note that placing such hills back from the bottom of the composition creates and yet limits the up–​back ambiguity in the same way as the use of bridges discussed earlier). Another way in which the ground operates is by division into types. Color plays a role here as well; it frequently distinguishes grass and bare rock, and occasionally we also see water and paved surfaces (plate 4). In the first instance, these are

17 The standard view of these gates is not only oblique but also from below. It may be relevant that this common trope may be just a single (if far the most common) instance of a more general phenomenon. The view from below is shared not just by the sacred gates but also by most of the open structures in the Farnesina frescos. This view is likely to be more “informative” in the straightforward sense that it allows us to see through the buildings, something that would not be a consideration for closed structures. 18 We should, however, note the shadows cast by figures in a number of paintings, and the much more complex ground in MNR 517531, which works much more like the Farnesina paintings. The subject matter of this painting is also distinct, both for the unusual thatched-​roof buildings and for the distinctively rural (not just nonurban) setting.

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FIGURE 4.1  

Landscape from the columbarium of Villa Doria Pamphilj (F/​XX)

Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

qualitative distinctions; the different surfaces are experienced and/​or used differently. But, as I have noted elsewhere,19 the quantitative and the qualitative interact. A  partition driven by difference of qualitative characteristics is still a partition. A ground divided up into patches of different surfaces is not a Renaissance-​style checkerboard pattern, but it is still an articulated space. It exhibits the dynamic of connection-​at-​distance noted earlier but extends it beyond simple dyads. Indeed, it brings all the elements of some of these works together. For instance, in the lower center of plate 4, to the left of the central building, the different colors mark off different zones of land (at the very bottom), water, the landing, and then water again behind the landing.

CUEING A more general strategy has to do with the role the human figures play in the compositions. Past readings of particular works have focused on how these figures are situated with respect to the background of larger architecture and trees. But they do not merely inhabit the space; they also help shape it by what I will describe as “cueing.” In fi ­ gure 4.1 the man on the rise is clearly making an offering at the small altar in front of the gate, while the woman on the right prepares to do the



19

Riggsby 2007.93, 2010.154.

FIGURE 4.2  

Landscape from room 14, Villa A, Oplontis

Photo Paul Bardagjy. Courtesy the Oplontis Project.

144

144 { Mosaics of Knowledge same from the patera already in her hand (a reading also made easier by the limited behavioral repertoire of these works). In any case, the three figures and the complex structure (mound, tree, gate altar) are all bound together by the action. In plate 5, from the door of the central tower and working uphill to the right, we have two pairs of characters interacting directly. The pointing gesture is vague, but it is enough to establish a small separate-​but-​connected network over space. Here the tower on the right and the pillar in the center are also bound in, if more loosely by the location of the uppermost woman in the doorway and the direct overlap of two women with the pillar. Some viewers might even continue this chain to the building on the left, whose door the woman on the left could just have exited. Note that there is also an effect here more specific than “connection.” The implicit narrative, however vague, constrains the possible readings of scale. That is, the kinds of interactions shown here encourage us to take the relative sizes of the people and objects fairly literally. In fact, it may not be necessary to appeal to implicit narrative. In some cases mere adjacency can create the required grouping.

TIERS A particular version of “up = back” that requires extended discussion is the division of subjects along two or more discrete horizontal tiers. I now want to return to the notion that Roman painting offered that arrangement because it could not conceive of disposition through a continuous space. First, I’ll just register briefly the observation that even if a sharp division into tiers was descriptively correct, such disposition would still be spatial in the more general sense. That is, the fact of recession confirms that the up and down grouping codes a (back–​front) spatial relationship, however crude, rather than something non-​spatial, like hierarchy of importance. Second, it seems to me that in many cases, the descriptive claim relies on somewhat strained readings. Take another example from the Farnesina reliefs (figure 4.3). On the one hand, this is a clear manifestation of mixed perspective. The three towers are seen from different points of view, and even components do not show uniform construction. So, for instance, the half-​walls supporting the central porch, presumably meant to be parallel in “reality,” diverge, and the presumably level surface on the left side appears to slope down to the inside. And in the left tower, the farther wall projects too far to be plausibly combined with the nearer one (assuming that they are meant to be of equal length). It is possible that one could analyze this or the other Farnesina stuccos as tiers, with a minimal foreground tier of animals and/​or human figures, then a second tier containing the architecture and more people. (Though here, it is perhaps problematic that the background tier, if it is such, runs diagonally from lower left to upper right. Moreover, it is not clear that we really want to separate the “foreground” pair and altar from the “background” temple so close to each other on the surface.) At any rate, such a division should at least raise the question of how much depth is contained within the supposed “background.” If we start from the basic “up = back” principle and the orientation of



FIGURE 4.3  

Representing Three Dimensions }  145

Landscape from the villa under the Farnesina, cubiculum B (inv. 1072)

Su concessione del Ministerio dei beni e delle attività culturali e del turismo—​Museo Nazionale Romano

the left tower (whether based on the tower itself or the porch), then the front plane of the central tower is behind the tower to the viewer’s left and the orientation of its porch suggests that the structure projects nearly straight back from the viewer. The right tower is in turn behind the central one, as shown both by its elevation and its somewhat reduced scale. Moreover, there is a tree clearly behind each of these towers, taking the viewer farther back across the whole width of the composition. Yet the notion of division into tiers did not, of course, come out of nowhere. It is a reasonable analysis, for instance, of many of the Pamphilj paintings. And, in fact, there are more dramatic examples of tiering than those. Consider the images from Villa A in Oplontis (figure 4.2) or the one we have already seen from the Villa Doria Pamphilj columbarium (figure 4.1), the largest and most complicated of the images there. They dispose their subjects not in two tiers, but in four and (roughly) three, respectively. This would seem to make La Rocca’s point, if anything, more forcefully. The “up = back” convention is presumably still in effect, but the other forms of coding can’t really handle the more complex situation. Read in terms of its other conventions, the Pamphilj painting simply has two foregrounds. This is made the more jarring by the lower scene’s naturally lighter tones and slightly smaller size, which could elsewhere have been read as signs of atmospheric perspective and so as of greater distance. In this already incoherent context, the fact that the background buildings are not at the same level makes them all the more “floating.” In the Oplontis painting, there is at most modest recession and no color effects. In both cases the artificiality of the division into tiers is obvious.

146

146 { Mosaics of Knowledge The Pamphilj painter clearly lacked skill and/​or interest in a smoothly continuous recession, but in most of his paintings this is not particularly striking. Almost everything is in the foreground. The background is sufficiently limited in subject matter and sufficiently isolated (horizontally as well as vertically) that it is clear specific relationships to the foreground are not crucial to the image. It is only in the three-​tiered image that this approach does not work; there is too much vertical space to fill. Hence, the awkward combination of two foregrounds. The same holds for the four-​tier formula in the Oplontis paintings.20 Elsewhere, when a more conventional space is available in the villa, we get representations more in line with the norms of the Farnesina paintings. The differences in aspect ratio, I think, are not accidental. Throughout the entire sacro-​idyllic corpus, the tall forms are vastly outnumbered by the broad ones—​so much so that this must reflect an active preference. (There are also a few more square images that will be discussed.) I  would explain that preference in terms of the spatial issues. That is, spatially coding and decoding tall images was hard or even nonsensical, and this seems to have been a problem for at least most artists and patrons. In some cases (Farnsesia stuccos and an image from Boscotrecase to be discussed in the section “Two Comprehensive Examples”), more elaborate devices than simple tiering were deployed to allow viewers to develop their own spatial solutions. But even in the absence of such technique, the problem was largely avoided by controlling aspect ratio (Pamphilj and Farnesina paintings).

CONCEALMENT If this last point is correct, then it suggests something else important. While there was clearly no audience expectation of formal perspective, a certain level of spatial coherence does seem to have been a desideratum, at least among the patrons of these corpora. And, in fact there are a number of other devices that make the same point—​devices that have been said by some to “conceal” the lack of a unified perspective in these paintings. One technique involves setting the line of the horizon (typically “too high”) behind buildings or other elements of the principal composition.21 Another is the use of a limited palette which artificially unites passages whose formal spatial syntax would otherwise be confused.22 One might also see a similar effect as a second function of the stereotyped porticos in their high-​angle perspective, discussed earlier. Seen from this angle, they take up more of the field than they would otherwise and so “paper over” gaps between other objects which they connect.23 Again, if there were no expectation at all of spatial coherence, there would be no reason to “conceal” its (partial) absence.

20 Clarke 1996.86–​8 (catalog 2–​8). 21 La Rocca 2008.35, 41. This is a particularly strong tendency in the paintings from the Temple of Isis in Pompeii. There, cliffs or other high virtual walls rise sharply in the medium-​distance background. 22 Ling 1977.13; La Rocca 2008.35, 36–​7. 23 Von Blanckenhagen and Alexander 1990.23–​4.



Representing Three Dimensions }  147

To summarize the argument to this point:  The creators of these works of art signaled spatial relationships between objects (potentially of different sorts) on a local basis by means of variety of different devices. The very variety of these devices, however, means that the groups organized locally on different bases can overlap one another, and so the organization grows outward into larger units. Assigning notional measurements to people or objects (or the spaces between them) is not automatic but not impossible. Rather, it involves the viewer in making approximations (in a manner that is perhaps less surprising given the results of the previous chapter about approximation in real measurement). But as in the previous chapter, the fact of approximation does not mean that the spatial information provided by the works of art is meaningless. It just means that, within some locally defined range of possibilities, there is no unique way to parse a given image.

Two Comprehensive Examples Having examined a number of spatial strategies individually, I  want to take extended looks at two related paintings from sets we have not yet considered. The first (plate 6) comes from an Augustan-​period villa at Boscotrecase (near Naples), and I bring it up particularly because it has been discussed as a two-​tier painting by von Blankenhagen and Alexander 1990:22.24 In the landscape paintings from this villa, they argue: foreground and background scenes have no representational connections with each other. The given view does not lead the eye gradually into farther and farther distances; on the contrary, the view comprises two distinct stages. They are differently painted, differently designed, differently seen. The way the viewer is asked to read the foreground setting is not the way he reads the background scenery. Here we might first want to look at the amount of depth within each supposed tier, as in the case of the Farnesina stuccos. On the left, for instance, the lone traveler is seemingly nearer than the (smaller and perhaps lighter) pair to his right. They in turn are in front of the shorter tower, which is in front of the taller tower, which is in front of the tree, which is in front of the rock formation. Lumping them all together as a single “tier” begs the spatial question it is meant to settle. But more fundamental objections to the anti-​spatial reading might be made. How separate is that background and how is it to be processed differently? Von Blankenhagen and Alexander (14, 24) pick out the clusters of buildings, figures, and cliffs to the right and left, and say of the portico on the right that “it establishes a link with the foreground which resists literal interpretation.” Now this is certainly



24

MAN 147501. Sampaolo and Bragantini 2009.212, 216–​7 (#78).

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148 { Mosaics of Knowledge true if we use “literal” to smuggle in the rules of single-​point perspective; the scale and point of view of the portico do not match that of surrounding objects. But that seems to be a blinkered view. The same waters seem to lap at the shore facing the shrine (roughly to the left) and the shore below the portico, and at any rate there’s an intelligible front-​to-​back progression of land–​water–​land. That is, there is a step-​by-​step series of distinct zones that are to be read as in direct contact with one another. The near end of the portico is perhaps indicated by the red band on the far left side, but even if this is the case, the back corner seems to be hidden behind the tree trunk. Thus, in order of recession from the viewer, we have the column at the near end of the shrine, the tree, the opposite end of the shrine (details concealed by the trunk), then the near end of the portico. This is likely at somewhat greater distance than the other intervals, if we take the relatively small scale of the portico as a sign of distance. But it need not be vastly farther, especially since there is a lot of horizontal space available behind the central shrine. The distances of the various intervals are not strictly governed by the perspective and so are conjectural, but they can easily be conjectured. The portico as an individual object is governed by somewhat different rules from those of surrounding objects (though, as discussed, this stereotyped form is used to signal depth to the viewer). But none of this prevents the viewer from integrating it with both the “foreground” and the rest of the “background.” On the other side, we have the foreground figure (with the dog), then the traveler marked by his lighter color, followed by the two women in front of the square building, doubly marked by color and reduced scale. Von Blanckenhagen and Alexander suggest there is no way to integrate front and back. I’d say, rather, that there is no unique way to do so. The space is not rigorously constructed, but that does not mean it cannot have forms of coherence. The other example (plate 7) is from the villa under the Farnesina again, but a different room, a dining room where it is one of a number of fairly similar pictures. The walls all around are divided into zones by slim painted columns and have scenes painted directly onto the background, without any further notional “frame.” Many of the panels are significantly worn, but as far as we can tell they seem to use roughly the same repertoire of images as the other landscapes in the other areas of the building. The background is obviously black rather than white, and the image zone is squarer than most we have seen (except the painting from Boscotrecase). These (and similar black-​ground images from Boscotrecase) are generally taken to be particularly lacking in overall sense of space. The individual images are commonly said to “float” independently on the sea of black which, in itself, represents nothing.25 This is a reasonable description of the panels as wholes, but fails as an account of their internal construction. We do not need a “real” background to establish a reasonably clear spatial system.



25

La Rocca 2008.43; Ling 1977.12; von Blanckenhagen and Alexander 1990.12, 41.



Representing Three Dimensions }  149

Consider the buildings disposed from the center left diagonally up and to the right. These all share similar scale and a three-​quarter view from far above; unlike the “riot in the amphitheater,” this does come close to being a real bird’s-​eye perspective. The recession could provide another example of the ambiguity of “up = back” previously discussed, but here we have two other cues. The ladder from the top of the first building to the middle of the second suggests that moving up the representation counts as both up and back in the represented world. Moreover, many of the horizontals in the buildings drift slightly lower as they move from left to right. The series of three buildings climbs an invisible slope, then the temple/​ statue/​worshiper complex starts to move across the surface of the same slope, while other structures now hard to decipher seem to continue this. The rough location of this hypothetical plane is confirmed by the groups of small figures to the right of the second building and what I believe is a goat farther below. They mark out a parallel path up the slope. The distance from the view suggests we should not expect much diminution as we go back, and in fact the buildings on the third level are only slightly smaller than that on the first. Turning to the porta sacra and altar in the lower right, we see a configuration much like the sacrificial scene with column and altar discussed earlier. This one creates the same local pocket of space, but it also interacts with the larger composition. The plane defined by the face of the gate does not precisely cut the ground along a line of equal elevation (the angle with the line of vision is a little too acute), but it runs fairly close. This is not a matter of the presence or absence of naturalism. The gate could presumably be “built” at any angle. The point has to do with the way the viewer’s attention is directed. The upper left half of the painting constructs a fairly uniform plane tilting up and to the left as it moves away from the viewer. The placement of a combination with such clear—​if only roughly complementary—​ directionality in the lower right anchors the scheme for the whole image. As I have stressed in the other cases, there is no demonstrably correct unique spatial reading here, but the viewer is clearly being nudged in certain interpretive directions.

Conclusions Before outlining my positive conclusions, I would like to clarify where I differ from and where I agree with the previous work referred to in the discussion to this point. On the one hand, there are only a few points at which I have challenged (or wish to challenge) the individual readings of particular works. And I don’t think that there can there be serious doubt of the general, descriptive validity of the idea of “mixed perspective.” On the other hand, on a practical level, the unit of spatial organization in these paintings can clearly be larger than the paradigm cases typically pointed to, such as components of objects (Richter) or individual people or buildings (von Blanckenhagen and Alexander). The strategies I’ve discussed (stacking, cuing,

150

150 { Mosaics of Knowledge typological partitioning, and the like) are also in a sense local, but crucially the local unit is always a pair (or more) of entities. But once we’re talking about fixing relationships among objects, their effects can be cumulative. As long as we do not look for perfect mathematical rigor, it is immediately clear that groups (of people, of buildings, of both) can be and are spatially coordinated. Much of a picture may be structured by the particular way its elements are combined, even if it is not made by inserting elements into a structure that preexists them. It is important to observe that the works we have been examining show not just a variety of treatments but also a variety of systems of treatment. The Pamphilj paintings show rough division into tiers (though with other restrictions on the background). The Farnesina reliefs have a strong central focus, with a reduced foreground, and a much weaker division between levels. The Farnesina paintings have almost no tiering at all. The Pamphilj paintings and Farnesina reliefs both have special conventions (though, notably, unrelated ones) for rendering superimposed figures. The Pamphilj paintings have an essentially one-​dimensional ground, the ones from the villa under the Farnesina prefer a two-​dimensional one (though here there is some variation). The Farnesina reliefs have their particular approach to hollow buildings. These artists are concerned about encoding spatial relations in individually consistent ways, even if they differ from one another. I could also point here to Stinson’s 2011 recent analysis of second-​style architectural vistas. These generally show rough convergence of orthogonals to one or a few points in an upper register and a separate system of coordinated parallels below that. The function of this system remains a little unclear, but it is impossible to deny that it is a system. The commonality of all these works is precisely at the level of seeking some form of spatial coherence, not any particular way of doing so. That argues that spatiality is directly at issue, not (for instance) the side effect of particular generic conventions. This much is consistent with something I’ve been arguing in non-​artistic contexts for some years now.26 Attempts to identify “the” ancient or even “the” Roman sense of space are misguided. Romans, like presumably all humans, operate with a rich repertoire of spatial schemata, deploying different ones in different contexts. This is an important reason why I  felt it useful to pursue a fairly limited case study here (unlike the more comprehensive approach of earlier chapters). It is true that comparisons I’ve drawn from other sites such as Oplontis and Boscotrecase suggest that other sacro-​idyllic paintings operate in very similar ways to the ones that are my principal focus. And one could make similar arguments about painting from the House of Livia on the Palatine, the Villa of the Quintilii just outside Rome, or the Temple of Isis in Pompeii. Still, each also shows its own particularities of style. The paintings from the temple, for instance, show a particular fondness for rocky hills that rise in a way that obscures where the “horizon” might be taken to lie. Second-​style wall painting works differently in detail (described by Panofsky



26

Riggsby 2003.185, 2009.



Representing Three Dimensions }  151

1991.38–​9 as “fishbone” perspective and worked out more precisely in the work of Stinson just cited), but it still shares the broader interest in a structured approach to spatial representation. My claim here has essentially been that a certain approach to space was possible, not that it was typical. More diverse evidence could only possibly show greater diversity of forms of spatiality.27 At the same time, that does not mean the choices are infinite or arbitrary. Particular schemata can be better adapted to particular contexts, whether because of their overall complexity or simplicity or because of more specific features. I’ll return to the notion of adaptation to context in a second, but first I should note one respect in which the present results are potentially less obviously congenial to my broader project. The earlier chapters of this book have generally taken what might be described as a minimalist view of Roman information technology. In this chapter, I  have taken a somewhat more expansive view of its power, so I want to explain how these conclusions might nonetheless fit into that broader picture. First, I should reiterate that I am not talking about the extreme regularization of space characteristic of formal perspective but, rather, the improvisation and approximation we saw in ­chapter 3’s discussion of metrological systems. Second, my sense is that the works I’ve been looking at, at least those from under the Farnesina, are near the limits of the usually available technology. That is, they represent what Roman artists could do rather than what they typically did do, not so unlike the occasional use of tables or nested lists. But why such high-​tech here? The minimalism and localism I  have found in other technologies are probably not values in themselves. They are epiphenomena of an underlying context-​specificity. The Roman asks “What do I  need to bring to bear to solve the particular problem before me?” In some cases, such as with the stereotyped porticoes and gates, I  have suggested this question has a fairly straightforward answer. But in decorative paintings more generally, the definition of “problem” and thus of “solve” is presumably a complex one. That is, we must move at least briefly back to the world of art as art or art as social practice, not just art as information technology. One relevant context is very concrete: location within the decorative contexts into which these works are embedded. What we have here are not stand-​alone masterpieces, nor even the focal images of a room or a wall. All are parts, often small parts, of elaborate decorative ensembles. Many sit outside the natural line of sight of a standing viewer. On the one hand, it might be argued that this environment warns against overreading. Secondary images would have been required just to give a general impression. On the other hand, that still means that a particular kind of impression was required. And the tactics described here are quite elaborate for images that are in various senses marginal. That argues that conveying spatial information was in fact quite desirable.

27 If one were to pursue this diversity, it might be best to go not to yet another form of painting, but to look at something more different like architectural depictions on coinage, for which see Hefner 2008 and Elkins 2015.

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152 { Mosaics of Knowledge Another, more general, context is genre. Many observers have commented on the “idyllic” or “dreamlike” quality of many of these scenes, and in particular the contribution of perspective to that quality. The idea seems to be that the lack of a systematic perspective makes it hard to pin down the “reality” of what’s being represented. Here the role of perspective is paralleled by frequently limited color palettes and the limited repertoire and generic sketching of the staffage figures and their actions.28 Let me suggest, however, that there is another side to the “dreaminess” so many have seen. It is not just the fact that these images are not fully naturalistic, but also the fact that they are not purely stylized or generic either. The detail and color of a surveyor’s diagram underdescribe reality, but it would never be described as dreamlike. While the figures in our works (human, natural, and architectural) are generic enough that no real referent would be imagined, they are diverse enough that individual paintings (and frescos) are all individuals, not just types. Similarly, the “dreaminess” of the perspective lies not just in the lack of system but also in the presence of a substantial degree of spatiality. That “in the middle” character leads me to my final point in this chapter. Earlier I referred to the opposition set up by Panofsky between (supposedly) an ancient emphasis on corporeality versus early modern attention to space. I think this is a false choice. The paradigm cases of the early modern spatiality are architectural. There may be human figures, but they are unnecessary and often minor ornaments. After all, human bodies’ lack of straight lines makes them poor vehicles to show off the precise, continuous transformations that porticos, paving stones, and the like display so well. But these are again the properties of a specific system. In the looser binding characteristic of Roman spatial strategies, the characters become important or, rather, the interactions between characters and their “settings” (including each other, animals, plants, landscape, and architectural features) become important. These interactions establish certain connections across space, divide regions elsewhere, and resolve potential ambiguities. Admittedly, these Roman strategies of combination will not always work, but even observing the circumstances of failure can illustrate the same point as the successes. On the one hand, if figures are grouped too densely it is impossible for them to interact coherently in constructing space, as with, say, battle scenes in high relief like those on the Portonaccio sarcophagus. Space there is largely abandoned in favor in individual forms and, as far as the ensemble goes, sheer activity. On the other hand, Romans do not commission or view many paintings like this Fall of Icarus (figure 4.4), outside of this one specific subject. A subject isolated in the sky cannot be located. That might be described as an avoidance of space, but it is more precisely described as an avoidance of empty space. Roman painters claim space by the act of occupying it, not by populating something already projected. The works

28 Panofsky 1991.43 (perspective); Ling 1977.12 (perspective), 13 (color); Nodelman 1971; Salvadori 2008.26–​7 (figures), 32–​5 (color).



FIGURE 4.4  

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Fall of Icarus

BM 1867,0508.1355, © The Trustees of the British Museum

we have seen occupy a middle ground of density and variety of figures. In this middle ground, we can see that Panofsky’s opposition need not be an opposition. In fact, corporeality and “space” can work together, rather than against each other. That artistic preference for the middle ground implicates a relatively small number of artists and patrons in the kind of spatiality I have discussed. In the next chapter, however, we will see that the same theoretical apparatus will help us trace similar patterns among much wider groups and in at least somewhat more practical contexts.

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5 }

Representing Two Dimensions

After the artistic turn and somewhat narrow focus of the previous chapter, this one returns (for the most part) to more utilitarian objects and to an attempt at more general coverage. It does, however, remain with graphic images, and (again, for the most part) with graphic images read as spatial representations of real things. The bulk of the chapter (and its analytic center) is devoted to maps; individual sections will discuss competing definitions of the term, review the resulting evidence, and set that evidence into a broader information technology context. But before I get to that, I  want to touch on three other kinds of representations:  data graphics, textual illustrations, and architectural plans. All these, of course, count as information technologies in their own right, but my main interest in them is how they cast light on important questions in that core area of mapping, such as reproducibility, the interaction of social status and technology, and the depth and breadth of public understanding. There will be considerable overlap of material between the categories here. “Illustration,” for instance, cross-​cuts all the other categories. Plans, in my rough-​and-​ready categorization, record objects, while maps record in the first instance an area and then only incidentally the objects within. In any case, I intend these categories more for organizational convenience than analytical significance. In fact, the functional overlaps between these types are one of the useful observations one might make about this material. (The objects studied here do not literally all represent the titular “two dimensions,” but the overwhelming majority do, and even the exceptional cases do not seem to be concerned with a third dimension in the manner of the art discussed in the previous chapter.)

Data Graphics

154

This section will be very brief, since much of its purpose will be to note that most types of data graphics we know today did not exist in the Roman world. This category includes devices such as the scatterplot, pie chart, bar graph, “thematic” map, timeline, and musical staff notation. What they have in common is that



Representing Two Dimensions }  155

they are much more symbolic or conventionalized than the other kinds of visual representations treated here—​that is, the paintings, plans, maps, and the like. That conventionalization is made necessary because of abstraction. Selected features of a situation (e.g., temperature, population, magnetic field) are quantified, then represented by the length, area, and/​or position of some abstract graphic element (e.g., lines, bars, bullets). With marginal exceptions, the devices I  have listed are inventions of the seventeenth century or later.1 The value of most data graphics (in contrast to, say, tables) hinges on the ability to (re)produce them fairly precisely, so it is perhaps not surprising that they do not generally appear until after the rise of printing technology. But it is also important to note Beniger and Robyn’s 1978.2 observation that most data graphics arose at a time when a whole new range of data-​collecting devices were being invented:  the thermometer, the barometer, the pendulum clock, and others. There were more numerical data to organize and communicate. By contrast, as the previous chapter argued, Romans were suspicious of reducing real-​world situations to disembedded numbers and operating only with the latter, and this is precisely what data graphics do. There are two striking exceptions, though neither is much considered in the literature on more modern data graphics. One is the sundial face (as in figure 5.1).2 Fortunately, Greco-​Roman sundials have been well studied on their own, so I can be brief here.3 The shadow cast by the pointer (gnomon) of the sundial moves across a field of crossing lines and curves (the precise pattern varies with the shape of the sundial). At any given time of year, the tip of the shadow traces a predictable curve across the surface (in this case, key instances are represented by the arcs within the circle). Thus the time of day can be discerned by following its progress through that arc (here marked out by the radial lines). The great difference between sundials and the other data graphics is that the sun (and geometry) “naturally” translate between abstractly quantified time and a graphic representation without an intervening numerical stage. The original design of the device would in principle have required formal computations, but it is not clear that individual cases normally involved such recourse to first principles. In fact, as c­ hapter 3 noted, actual use seems not to have demanded any particular precision in design.4 In particular, as was also argued in c­ hapter 3, the likely uses of sundials were much more local than those of a modern clock, and so the question of the “accuracy” of the underlying data was perhaps not really at issue. Thus a sundial, at least a classical one, largely avoids the

1 Beniger and Robyn 1978; Tufte 1983.28–​34, 43–​6; Friendly 2009; Rosenberg and Grafton 2010, esp. 18–​10, 112–​22. 2 Though see Vaccaro 2015 for essentially the same insight on sundials. 3 For overviews and bibliography, see Gibbs 1976, Houston 2015, Schaldach 2016, Talbert 2017. 4 That is, many sundials were very sloppily constructed; there was a preference for shapes that were in fact harder to calibrate; and sundials were, to judge from findspots, often used far from the latitude for which they were calibrated. See further Talbert 2017.191–​201 for the possibility of a template used by a sundial maker.

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FIGURE 5.1  

Roman portable sundial

Inv. 51358. © Museum of the History of Science, University of Oxford.



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issues of reproduction and of data measurement which would have rendered other data graphics both difficult and unnecessary in their original context. The other, similar type of data graphic is the anemoscope, a wind rose with a rod projecting from the center point, flying a pennant to show wind direction.5 As in the case of the sundial, the graphic quantification is produced directly, not through a numerical intermediary. And here the basic device is even simpler, requiring only a series of equal angles. Measurement of winds was used to suggest the timing of agricultural activities, but great precision was presumably not necessary, nor certainly was global accuracy.

TEXTUAL ILLUSTRATIONS Here I want to look just at illustrations that were originally included with some verbal text to clarify or extend that text’s meaning.6 The fine vignettes in the fifth-​century Vatican codex of the Aeneid, for instance, are not an example since they were not part of Vergil’s composition. Nor, ordinarily, would an author’s portrait (like a modern dust jacket photo) count, since it is not explanatory, nor finally a painter’s pattern book, since the illustrations were presumably the whole of the content.7 In collecting examples I have also chosen to draw an admittedly subjective line between what I think of as illustrated texts (included) and captioned images (not). I have ignored, for instance, paintings, graffiti, and parapegmata (time-​keeping pegboards) which label characters with names. I will begin just by working quickly through the short list of examples for which we have visual evidence, then discuss the not much longer set of cases attested but no longer visible. Most of the illustrations are built into utilitarian objects of various sorts, but we will start with the ones embedded in long, more or less literary texts. The surviving illustrations in Latin texts (I will refer to the somewhat different Greek case later) are from a single body of them—​the Corpus Agrimensorum, a collection of manuals on various aspects of land surveying. The illustrations appear to be integral to the texts. There are passing references to the illustrations in two of the authors within the corpus, and when already in Late Antiquity a commentator arranged many of the illustrations in a separate volume, the stylistic differences among them show his work is almost certainly a compilation rather than an original composition.8 The bulk of the texts themselves were composed in the late first and second centuries ce, but others date close to the time of the earliest surviving manuscript, from the

5 See Bond 2014 for examples and further references. 6 Zimmermann and Hammerstaedt 1996 and Small 2003.118–​54 survey illustrations, integral or not, in a variety of ancient texts. I will cite specific points as applicable. 7 On author portraits, however, see Small 2003.129–​31. For pattern books, see Clarke 2009. 8 Campbell 2000.xxv, xxxiv. The reference in Hyginus is admittedly doubtful, but I see little reason for Campbell’s concerns about translating Frontinus’ similitudo as “illustration” at 3.11, 13C.

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FIGURE 5.2  

Schematic illustration from a land-​surveying manual

Herzog August Bibliothek Wolfenbüttel, Cod. Guelf. 36.23A, fol. 42r.

FIGURE 5.3  

More naturalistic illustration from a land-​surveying manual

Herzog August Bibliothek Wolfenbüttel, Cod. Guelf. 36.23A, fol. 42r.

sixth century.9 The images range from quite schematic diagrams (e.g., figure 5.2), to diagrams decorated with more naturalistic landscape detail (e.g., figure 5.3), to a few pure landscapes. Carder (1978.167–​204, esp. 183–​6) has made a good case that, at least in general, we should imagine the diagrammatic illustrations to represent the early state of affairs, and take the naturalistic elements as later (both, that is, as copyists’ embellishments in the earlier texts and original features in the later ones.) As I said, however, most of the illustrations that survived antiquity are not part of extended texts. Rather, they are integrated into a variety of objects, often of seemingly utilitarian design. We may begin with a pair of inscriptions both containing maps centered on water-​distribution systems. As it happens, neither of the water inscriptions is still extant today, but consistent drawings from the early modern period give us a clear sense of what they looked like.10 One (from Rome; CIL 6.1261;

9 The other major manuscript is from the ninth century. On the illustrations in general, see Carder 1978 and Campbell 2000.xxiii–​xxvi. On the dating of individual texts, see Campbell 2000.xxvii–​xliv. 10 CIL 6.1261, 14.3676. For detailed discussion of both, see Rodríguez-​Alemeida 2002.23–​36, though his circumstantial reconstructions are speculative.



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FIGURE 5.4  

Inscription detailing rights to draw water (CIL 6.1261)

figure 5.4) displays text explaining when several parties will be allowed to draw water from the system. Then there are two undulating pairs of lines that seem to represent aqueducts or canals.11 In addition to the basic courses of water, there are features I will refer to as “bridges” (breaks in the canals), “draw-​points” (thin, triangular offshoots), and “settling tanks” (offset rectangles), though the actual meaning is not clear in any of these cases. The other diagram (CIL 14.3676, from Tivoli; not shown) has slightly more elaborate text and lacks the offshoots and tanks, at least in its recorded portion. Both are quite schematic, and in particular they represent only parts of the water-​distribution system itself, not other built or natural features. Moving into an even more utilitarian realm, we may turn to the stamps that imperial Roman brick-​makers impressed on their products to control various aspects of their production and distribution. These typically involved text, but some used images as well. What I want to consider here are the “speaking signa” studied by Bodel 2005, which were used to indicate that a particular person was involved in the production of the labeled brick. These signs could be “literal” (a wolf for a man named Lupus), metonymic (a caduceus for a person named Hermes, after the god who carried that object), or, apparently, purely conventional (pine cones, clubs). Depending on the particular brick-​making firm, such images were used to designate persons in different roles in the enterprise. Most interesting for our purposes is their use to indicate that the owner of the firm was also the supervisor of a particular lot, in contradistinction to employee or contracted supervisors who were identified by their initials. That is, the illustration is not just a clarification but also the sole bearer of some of the meaning of the stamp as a whole. To whom was that meaning



11

One of these is broken in two by cross-​cutting lines that could represent a bridge.

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160 { Mosaics of Knowledge being conveyed? There seem not to have been industry standards for the usage of these images, and indeed, even the same firm’s usage might not be consistent over time. This fact and the relative opacity of both the images and the texts suggest that the intended audience was internal to the firm or, at most, also included a limited and specialized set of potential buyers. Last among the surviving illustrated texts are small objects called defixiones.12 These are tablets that were written on and buried as part of magical rituals. All contain words and/​or sacred names, some also contain specialized symbols (characteres), and a few have representations of recognizable figures. Some are crude human figures, often named, and likely or certainly representing the targets of the spells. Others are supernatural entities, often partially zoomorphic. These appear to be the powers called upon to bring about the results of the spells. One could imagine the human figures being (notionally) used in the manner of a modern wanted poster—​simply to inform the spirits whom to target. However, we know that parallel rituals often used images of the target in more engaged performative fashion, as with a voodoo doll, and that kind of use might well be imagined for the drawn version as well.13 Naming of the spirits involved so as to bind or activate them was an extremely important part of ancient magical ritual,14 and it seems likely that the graphic illustration played a parallel performative role there, too. Turning to illustrations now completely lost, we find that there are a number nonetheless securely attested. We have the text of Vitruvius’ architectural manual (late first century bce), which refers to ten illustrations at various points, but they are all lost to us in the manuscript tradition.15 In some cases, the image would have been of a complex geometric figure that the reader could in theory have constructed by following the verbal directions in the text.16 The others are curves which could not have been described precisely in words, images of complex mechanical devices, or in one instance a diagram from music theory whose precise form remains unknown.17 Pliny the Elder’s encyclopedic Natural History did not, so far as we know, have illustrations of its own. It does, however, speak at some length on works that do, and expresses conflicting opinions of them.18 On the one hand, Pliny is impressed by what he reports as a late first-​century bce fad for imagines, in this case likenesses of persons (HN 35.11). He cites instances by the polymath Varro and perhaps by Cicero’s correspondent (and minor scholar in his own right) Atticus.19 He is 12 Audollent 1904.lxxv–​lxxvii. 13 Graf 1997.138–​46; numerous specific examples at Ogden 2002.245–​60. 14 Graf 1997.95, 129, 201. 15 Vitr. 1.6.12–​3; 3.3.13; 3.4.5; 3.5.8; 5.4.1; 5.5.6; 8.5.3; 9.pr.5, 8; 10.6.4. 16 Vitr. 1.6.12–​3, 9.pr.5, 9.pr.8, 10.6.4 (in part). 17 Curves: Vitr. 3.3.13, 3.4.5, 3.5.8. Devices: 8.5.3, 10.6.4 (in part). Diagram: 5.4.1, 5.5.6. 18 On these passages, see already Small 2003.131–​8. 19 The two cases are typically lumped together as publishers of images. Pliny says in Atticus’ case addito de eis volumine, which should mean “about” images rather than “of ” them. Nepos (Att. 18.6) would, by himself, more naturally be read to describe illustrations as part of the work, but could conceivably be read as referring to verses that could be used with real portraits elsewhere. The Pliny passage,



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particularly impressed that Varro was able to grant both immortality and worldwide fame to the seven hundred men recorded in his collection. On the other hand, he has grave doubts about Greek botanical writers who seem to have organized their works in the same way—​that is, with images of the various plants accompanied by commentary on their medical uses (25.8). Lifelike images are hard enough in the first place, he says, and the problem is compounded by generations of copying. I will return to the disjunction shortly, but first I have one more example of illustration to recount. Though it is not entirely certain, there is a good possibility of illustrated sex manuals. The clearest evidence is from Suetonius’ early second-​century biography of the emperor Tiberius. In his secluded villa, the emperor adorned his bedrooms (which were everywhere) with paintings and statuettes of the most lascivious images and equipped them with the books of Elephantis, lest anyone lack an instance (exemplar) of the required position (schema) in doing the deed.20 Schema has been taken to mean illustration (as it does elsewhere), but Small (2003.140) is surely right that here it takes on another attested sense—​“sexual position.” Nonetheless, that philological issue may be a red herring. The question is actually what “instance” (exemplar) refers to. The paintings and statuary are clearly visual, and exemplar seems to suggest the same for the books of Elephantis.21 Moreover, if the books are solely verbal, then they are anticlimactic in Suetonius’ display of vice. Thus we seem to have illustrations of schemata. This passage may then be connected with a less discussed one, a slightly earlier poem from an anonymous collection known as the Priapeia. A brief epigram describes a woman dedicating “obscene tablets from the books of Elephantis” to the phallic god Priapus if she is allowed to bring the painted figures (pictas . . . figuras) to life. Here there are clearly images. In principle, they could have been inspired by the text rather than already being found in it (as perhaps for the spells discussed earlier), but that seems to introduce an unnecessary complication. If we have two attestations of illustrations in the text, then that makes it more likely that they were part of the author’s original design and not a later embellishment.

up to the point where Atticus and Varro appear, is about galleries of artistic portraits, which would naturally have involved a fairly generic set of figures (from Homer on down), which canon could then be captured in verse independently of any particular set of actual sculptures. 20 Suet. Tib. 43.1. Cubicula plurifariam disposita tabellis ac sigillis lascivissimarum picturarum et figurarum adornavit librisque Elephantidis instruxit, ne cui in opera edenda exemplar impe[t]‌ratae schemae deesset. 21 The name is likely a pseudonym. Both passages cited here, as well as the one other that mentions the work (Mart. 12.43), describe its content in terms of a list or typology of positions, something that seems to be a genre feature of sex manuals. See Vessey 1976, Parker 1992.

162

162 { Mosaics of Knowledge In considering all these types of illustrations as a set, I want to point out three cross-​cutting issues: their stylistic minimalism, problems with their reproducibility, and the interaction of social status with the use of illustrations. Most of the illustrations are minimal in stylistic terms or in their intended audience (or both). I mentioned the narrow focus of the water-​distribution diagrams—​ they represented nothing but the water-​distribution system itself. Similarly, the original diagrams in the surveying manuals seemed to include almost nothing but the demarcations that would be created by the surveyors themselves. Neither the targets nor the agents of magical spells are set in any kind of context (a few are given a nonrepresentational frame). We cannot really judge the merely reported illustrations in this respect, but none of them (particularly those in Vitruvius) would have lent itself to elaboration. The ones based on geometrical construction, in particular, seem to have had a similarly narrow focus. Even within the limits of what is being represented, these texts are economical about how they represent it. The Corpus Agrimensorum and the water-​distribution inscriptions rely on schematic line drawings. The defixiones are slightly more elaborate, but only a little. One of Vitruvius’ lost illustrations was of a surveying instrument called a chorobates—​a long beam with legs on either end plus plumb lines and a water trough for leveling.22 The device is simple enough that an elaborate diagram does not seem necessary (in fact, it is a little strange that he felt the need for a drawing at all). Vitruvius’ other illustrations seem to be geometrical in the broad sense, even if not compass-​ and-​ straightedge constructions. Given their apparent focus on overall positions, even the sex manuals need not have used more than schematic representations. That is not to say that they would have avoided more naturalistic versions like the ones found in Pompeiian wall paintings, but the details of these embellishments could have varied from copy to copy without damaging their informational value. The clear exceptions to this norm are the two kinds of text mentioned by Pliny, and the particular cases suggest that reproducibility may have been one of the constraints on the more normal case. On the one hand, there are the botanical illustrations.23 Such manuscript evidence as exists seems to confirm some of Pliny’s assertions, both in that the illustrated texts are all Greek (that is, it would appear that Latin authors like Pliny simply did not use such images) and because it suggests that (re)producibility is at least one source of the problem with these non-​schematic images. Images vary considerably from manuscript to manuscript, a real problem for identifying species that were supposedly medically potent. On the other hand, Pliny positively celebrates the presumably non-​schematic imagines in Varro’s work. Small 2003.133 has pointed out that what Pliny specifically praises appears to be



22 23

Grewe 2009 on the use of the device, though the argument does not affect the present point. Zimmermann and Hammerstaedt 1996.957–​8.



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a technical innovation: “the images . . . were inserted by means of a most fruitful invention.”24 This is hardly clear, but the most straightforward reading would seem to take this literally. One way or another, we should imagine the imagines being produced before the “book” (roll) as such, then being inserted into it or even bound together to construct the book. This would in principle help both by taking the art out of the hands of scribes (in favor of more professional artists) and by eliminating the constraints of working with a whole roll at a time. (The fact that Vitruvius’ illustrations were typically left to the end of their respective books was presumably a more pedestrian attempt to address the former problem.) It would not help with reproduction, but might well serve as a means to produce a luxury edition, whose further reproduction might well not have been desired. Pliny makes a further comment about Varro’s work which is interesting because it is almost certainly wrong. Varro has given his subjects a literally supernatural gift because he did not “permit their forms to perish nor for the passage of time to have force against men.”25 We know only a fraction of the seven hundred illustrious persons commemorated by Varro, but no one alive during Varro’s lifetime is attested. They go back as early as Homer, Hesiod, and Pythagoras, and at least one entirely mythical figure (Daedalus) was included, and likely many others such as the pre-​Roman “Alban kings” (Geiger 1998.306). That is, however much Varro may or may not have contributed to the immortal fame of these already canonical figures, transmitting their actual likenesses was not an important part of the process. If likeness to real persons was not really a goal, there is no reason that likeness across an edition would have been important, either. Many of the other illustrations also do not answer to reality, though for a different reason. The diagrams in Vitruvius, the land-​surveying manuals, and the sex manuals are all “models for” rather than “models of.” That is, the reader is meant to make the world conform to the text (including illustrations), rather than the author’s bringing his text into conformity with the world. The images on defixiones are seemingly “models of,” but at least those depicting divinities are not constrained by reality. Even for images of the target, they seem to be better identified by the name inevitably attached as a caption than by any physical features. The images on the bricks need only be comprehensible to a very limited audience of those who know the limited possible range of meanings; they need only hint in the same direction. The illustrations on the two water-​distribution inscriptions are likely true models of their subjects, though they need to be only very roughly accurate to serve as indices to the text. They just need to be in the correct linear order. Besides reproducibility, social status seems to play a role in choosing where illustrations are used. Pierre Gros 1996 has pointed out that the number of illustrations in Vitruvius is strikingly low both by contrast with modern architectural

24 Plin. HN 35.11. benignissimo invento insertis . . . imaginibus. 25 non passus intercidere figuras aut vetustatem aevi contra homines valere, inventor muneris etiam dis invidiosi.

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164 { Mosaics of Knowledge writing (not least translations of this very work) and with the work practice of ancient architects as Vitruvius himself describes it. Gros goes on to argue that the issue of practice is the actual key to the sparse use of textual illustrations. Elite discourse took the form of just that—​discourse modeled as oral utterance. Recourse to drawing was a practical matter and thus of lower social standing. Vitruvius only resorted to it in this text when he felt he had exhausted his ability to describe something in words (14). It can hardly be an accident, then, that Frontinus, who speaks very strongly of the utility of maps to the management of Rome’s water system (1.17.3), includes none of them in his treatise on the topic.26 The text has a different and more literary agenda than literal management.27 I would suggest that we might want to extend Gros’ point about the rarity of illustrations in Vitruvius. He connected that to an issue of social positioning. Diagrams are workmanlike in a world in which elites value speech above manual labor. All these images except the portraits of famous men fall into that category, and in general they appear in contexts where there is less need to apologize for practicality than Vitruvius seems to have felt. Whether the underlying activity was obviously suspect (sex manuals, defixiones), or the texts seem to have been confessedly professional documents (surveying manuals, herbals, perhaps the official records of the water supply), or the texts were functionally anonymous (water inscriptions, sex manuals, defixiones), there was little to lose by offering a “practical” form rather than more polished words. This might also explain, or at least reinforce, the Greek/​Latin split that appears to exist in the world of illustrations. In addition to the herbals mentioned (and other illustrated ones, such as Dioscurides’), mathematical works frequently included diagrams, and we know that a number of Aristotelian works refer to illustrations (now lost), and others found in other technical texts.28 Greek culture had its own set of prejudices concerning labor and technical skills, but it had (especially under Roman rule) more room for a middling ground of respectability for those skills at an appropriate level of systemization and abstraction (Cuomo 2007b.7–​40). Thus there was more opportunity for a work to advertise itself openly as technical by including illustrations.

Plans This section considers architectural plans.29 As was alluded to earlier, the architect Vitruvius mentioned the use of various kinds of drawings in his line of work: floor

26 Nostrae quidem sollicitudini non suffecit, singula oculis subiecisse; formas quoque ductuum facere curavimus, ex quibus apparet ubi valles quantaeque, ubi flumina traicerentur, ubi montium lateribus specus applicitae maiorem adsiduamque tuendi ac muniendi rivi exigant curam. Hinc illa contingit utilitas, ut rem statim veluti in conspectu habere possimus et deliberare tamquam adsistentes. 27 König 2007. 28 Zimmermann and Hammerstaedt 1996.956–​8 for classical examples. 29 In general, Hülsen 1890, Heisel 1993.184–​ 218, Haselberger 1997, Rodríguez-​Almeida 2002, Brodersen 2003.225–​36, Autori vari 2006.26–​37, Corso 2016. Though it is sometimes included in these



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plans, elevations, and something like perspective views.30 He ties these to actual stages of design, so they seem to be a component of the process itself. A century and a half later, the miscellanist Aulus Gellius incidentally mentions walking into a consultation between a patron and his architects in which the latter are offering a variety of plans on parchment to choose from for a bath complex (19.10.2–​3). These might have been working design documents (like Vitruvius’) or ones prepared specially as advertisements. At any rate, Gellius seems to assume casually both that this is something architects might do and that a nonprofessional patron might find it useful to examine such documents. The matter-​of-​factness of both the literary reports seems to support what we would think of as the “commonsense” position that architects would make systematic use of such drawings. Moreover, one would have expected them typically to be drawn on perishable materials, as is explicitly attested by Gellius. It is not surprising again that this specific type of drawing seems not to survive.31 There are, however, other kinds of plans Romans inscribed more permanently. There are enough of them, most falling into one of a few categories, that I will not attempt to discuss all the extant examples. (However, all instances I am aware of are listed in the appendix to this chapter. Though the studies listed in note 29 cover similar bodies of material to mine, there is no standard corpus of plans, nor can all be found in any single, larger epigraphic corpus. Hence I will use the numeration of my own list in the chapter appendix to refer to individual objects: “inv.” plus number.) The most basic distinction to be made, it seems to me, is between plans that focus their attention—​often by means of labeling—​on the subcomponents of a structure (I will call these “part-​oriented”), those that are more interested in structures as totalities (I will call these “building-​oriented”), and those that model only particular components of a building. These last, at least as we know them, are carved into building materials near construction for which they are meant as a “blueprint.” The most dramatic example is a life-​size elevation of the Pantheon façade found carved into a pavement outside the Mausoleum of Augustus (Haselberger 1994; inv. 14). We also have reduced-​scale forms for a series of archways in Capua and apparently for stucco ornamentation there as well (inv. 13).32 Recently, profiles of the cornice of an early imperial temple in Brescia were found traced in wall plaster from the remains of an earlier temple on

discussions, I will omit CIL 14.607, agreeing with Schädler 1998.17 that it likely represents a gameboard for duodecim scripta rather than a floor plan. The shape does not match known boards precisely (for the shapes, see c­ hapter 2), but the squares in the lower field seem unmistakably to be dice. I also omit a city plan from Auguntum, which is widely thought to be a forgery (Heisel 1993.197, Brodersen 2003.231–​2). 30 Vitr. 1.2.2. Cf. 1.1.2 on why architects need to be draftsmen. 31 A possible exception is a plan preserved from Egypt (POxy. 2406), though its original use context is unknown. It is perhaps also worth noting that surviving building contracts seem neither to contain nor to refer to such plans (in contrast to the role of surveyor’s maps in land disputes, for which see note 97, this chapter). 32 Arches: Inglese 2014.95–​108 (with earlier lit.). Stucco: de Francescis 1983.

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FIGURE 5.5  

Inscription showing plans for the funerary complex of Claudia Peloris and Ti. Claudius

Eutychus © Giovanni Dall’Orto /​Wikimedia Commons, used by permission.

the same site, and other possible instances have been found at other sites (inv. 15).33 These are not particularly numerous, but it is possible that archeological discoveries will change that. It was presumably easier to inscribe plaster than stone, but much of this would then have been lost to us. The category of part-​oriented plans comprises only two floor plans of entire buildings, each featuring written measurements of the internal rooms. One of these is a carefully inscribed plaque indicating the ownership of a tomb, and mostly taken up by plans for the monument itself plus two floors of an associated service building (inv. 6; figure 5.5). The other, now mostly lost, is a mosaic from the floor of a bath complex in Rome, apparently giving the layout of that very complex (inv. 9). In addition to the basic floor plan and dimensions, this mosaic appears to have color-​coded features such as pools, water channels, windows, and heating vents.34 The last and largest set of plans all show segments of urban fabric, in at least one case of Rome itself (inv. 1; plate 8).35 Most of these carry numerical indications that appear to be measurements of building frontage and/​or names that probably indicate the owners. The first shared feature of these plans is one we already noted in the case of the water-​distribution inscriptions: the narrow focus on the built environment. Of course, plans by definition will center on this, but the striking thing is the extent

33 Brescia: Dell’Acqua 2014.341. Others: Inglese 2014.138–​51. 34 Albertoni 1987, Bouet 1998. 35 The illustrations of watercourses discussed earlier might also be fit into this category but are not nearly as similar to the other instances as all those others are to each other.



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to which any other kinds of features are excluded, such as specific streams, woods, or the broader topography of hills. A plan of a funerary complex appears to show beds of vegetation and trees, but only because they have been planted for the purpose, as shown by their rigidly geometric disposition (inv. 5).36 In plate 8, the line across the bottom must relate to the Tiber, and Rodríguez Alemeida 2002.47 takes it as the low-​water mark. But even this might be a human construct—​for example, the border between street and riverbank; note that we have straight line segments, not a curve. At any rate, this seems to be the only candidate for a truly natural feature in any of the plans. A second shared feature is that, while the mode of representation is largely iconic, there are crucial symbolic/​conventional features as well. In some respects this is a feature of virtually any floor plan in any context. They are normally not pure sections cut parallel to ground at a single level; rather, they compress multiple levels into one. For instance, an architectural blueprint conventionally shows both outline of the floor/​foundation and the situation of the walls that are literally above that level. In plate 8, the steps in front of the temple are obviously on different levels, and the line (with attached rectangles) that cuts across the lower third of the figure appears to be the edge of the coverage of a portico.37 Beyond this basic fact, however, these plans rely on a variety of other conventionalized representations. Simple dots appear to represent trees in inv. 5, and they are used elsewhere to represent columns. The double lines that represent walls in most of these cases are conventional in that they do not actually show the space between as solid, nor do they obviously correspond to the thickness of actual walls (we will return to more general questions of scale later).38 In addition to the monumental steps of the temple just referred to, the plan makers also have conventional signs for internal stairways—​extended triangles, with or without lines across them that might represent steps. Two or three of the plans appear to use a rectangle with drawn diagonals, set in or next to a wall, to indicate a window in that wall (e.g., in the temple in plate 8). A recently discovered fragment which depicts part of the Forum of Augustus appears to use a similar convention to depict an archway that opens between two spaces (inv. 4).39 Plans like these, then, are not simply reproductions of what the drafter has seen, nor simplifications of what he has seen, nor even (given that at least some of them are forward-​looking plans) composites of the kinds of things he has seen. The particular configurations of present and absent elements were never visible at the same

36 CIL 6.29847 with Autori vari 2006.30–​1. 37 In the funerary complex from Urbino, the square podium of the tomb proper is likely high enough that the cut-​out arcs of the internal figure would be much higher than anything else in the diagram (Hülsen 1890). 38 Reynolds 1996.71–​3. 39 Meneghini 2006.166 (the same symbol is standard on the Forma Urbis Romae to be discussed later).

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168 { Mosaics of Knowledge time. These plans are necessarily works of imagination, however much observation may have gone into them as well. A third shared feature, in a general sense, is that these plans all appear to be to scale, in that one could certainly imagine buildings built in precisely their proportions. Measured lengths in the part-​oriented plans are at least roughly consistent with the numerical labels, though sloppily.40 It might, however, be pointed out (as scholars have long done) that the three different plans in an inscription in Perugia (­figure 5.5; inv. 6), including two for different floors of the same building, are at significantly different scales from one another without any explicit warning.41 In most cases it is hard to assess the scale, if any, of the building-​oriented plans. Most of them do not correspond to known remains. In the recently discovered plan of the Forum of Augustus (inv. 4), direct comparison with remains shows a scale of about 1:250, but precision is lacking.42 It is rarely even clear precisely what frontages the numerical labels correspond to within the representation.43 In one exception (plate 8), comparing labels to measured intervals on the stone implies an intended scale of 1:250, but there is no way to know how uniformly that was applied.44 On the other hand, the two private roads in inv. 7 are accompanied by numbers which appear to be lengths. If these are meant to correspond to the length of the displayed segments, then the figure is not drawn to uniform scale, no matter how neatly executed it appears.45 For reasons to be discussed in the next section, many scholars have suggested a scale of 1:240 for most or all of the building-​oriented plans. This is not implausible given what is being depicted, but there is no way to confirm any particular level of consistency among or even within plans. What are these “plans” for? The role of the on-​site component “blueprints” seems clear enough. The answers for the part-​and building-​oriented varieties are less obvious and, I think, differ from each other, but in both cases my approach will be through an examination of their labeling.46 40 Hülsen 1890.50–​2, Bouet 1998.854, Carettoni et al. 1960.209. 41 Carettoni et al. 1960.210. All are quite different in scale from the other component-​oriented plan, CIL 6.29845. 42 Meneghini 2006.159, 161. 43 Strictly speaking, it is not really known that they correspond to street frontage at all. It has been suggested to me that some could be connected to, say, water distribution somehow. 44 Lugli 1992.24. All scholars doing computations of this sort assume the numerical measures represent Roman feet and that the standard length of that foot is known and consistent. The former seems secure; the latter is probably close enough for most purposes (though the issues raised in ­chapter 3 suggest it may be harder than is usually thought to distinguish 1:240 from 1:250). 45 Moreover, the buildings appear to be far too large to fit with the scale of either road (Hülsen 1890.55). 46 To the extent that we imagine the part-​oriented plans as being drawn to scale, the labeled measurements are seemingly redundant. But this is perhaps true more in a formal sense than for any actual viewer. At least for the three plans on the plaque in fi ­ gure 5.5, there is no guide to scale. That is, the viewer gets neither a formula (e.g., “one part in 240”) nor an example (e.g., a short line segment labeled as some large number of feet). (In fact, no surviving plan has such a scale, though only the plan from Urbino [inv. 5] is complete enough for this to mean anything at all.) That makes the calibration of the plan less redundant, at least for the reader, if not the creator. Arnaud 1989.12 suggests that the same



Representing Two Dimensions }  169

The part-​oriented plans could be practical guides to construction. They are prescriptive and each uses a single unit of measurement—​precisely the conditions for which we would expect numerical measurement on the basis of the arguments of ­chapter 3. But I think these plans are in fact doing something else. Consider the mosaic depicting the plan of a bathing complex. The medium is typically meant for ornamentation; our particular mosaic presumably postdates the construction of the fabric of the building, and, of course, the object cannot be moved from its original location. This was clearly not a plan from which to build. One could imagine pragmatic uses for a map after the fact, such as a guide to users and staff, but the dimensions would be irrelevant to them. Much better, then, is the suggestion of Bouet 1998.889 that the patron of the building has here reproduced an original functional or marketing plan in the more permanent medium on site as part of the advertisement of his euergetism, in much the same way that verbal inscriptions list benefactions in considerable detail.47 A similar kind of explanation, it seems to me, makes sense for the three plans of the funerary complex of Claudia Peloris (figure 5.5; inv. 6).48 The medium could certainly be used for data storage, but often also (additionally or instead) focuses on display or advertisement. Inscriptions with the kind of wording of this one are external and (like the mosaic) after the fact. They are used both as memorials (identifying the dead) and to assert ownership. The person who commissioned this inscription, then, could have stumbled across the same strategy as the bath patron—​reproducing working sketches as a way to advertise the relative grandeur of the complex. The reproduction of all three plans on a stone of this size (.55 m x .77 m) seems to have made accurate scaling impossible, but it does nothing to harm their display value. Both the (seeming) scale and the specific numbers in these derivative works are essentially another form of the precisionism discussed in c­ hapter 3. And if this usage is essentially secondary or derivative of working plans (on perishable materials), it is not surprising that these part-​oriented plans are relatively rare. The building-​oriented plans have been the object of considerable scholarly inquiry, usually in the context of a much larger plan/​map called the Forma Urbis Romae (which we will take up in the next section), but here I want to take them first on their own. The consensus view, which at some level must be accepted, is that they are “cadastral” documents. Cadastral surveys are ones “that create, mark, define, retrace, or reestablish” information about the “ownership of land” (both by individuals and by political entities).49 The case for this is based principally on the redundancy was required of cadastral formae by a law of Trajan. He misreads the passage in question (33.25–​7C), which is inter alia descriptive rather than normative. It is not clear in practice how far individual allotments were graphically indicated on the formae. They are not on the (perhaps unusual) stone example from Orange (inv. 12). 47 On the textual expression, see, for instance, Horster 2015. 48 A somewhat similar argument at Brodersen 2003.236, but he takes this display function to be the principal one for all plans. 49 http://​www.blm.gov/​wo/​st/​en/​prog/​more/​cadastralsurvey.html.

170

170 { Mosaics of Knowledge two kinds of information included in the textual labels on these plans.50 At least five out of nine attach personal names to individual structures; these would be easy to interpret as showing ownership or something similar even if it were not the case that (wherever we can tell) those names are given in Latin’s possessive form. At least five out of nine (overlapping the other set of five just mentioned) place numerals outside some buildings or on other features.51 The numbers seemingly appear only along road frontage, and that has led scholars to connect them with a Roman law that made property owners responsible for the maintenance of public streets on which their buildings fronted and, in particular, calculated their liability in proportion to the length of that frontage.52 The interpretation of the names and numerals as owners and frontages seems secure enough. If ownership is one of the only kinds of information broadly recorded, then these documents are cadastral in the broad sense of recording that information. However, the word cadastral usually also carries with it the implication of a systematic investigation by the state, typically a geometric survey producing a graphic output, though a register like the Domesday Book would also qualify. Certainly the state is the mostly likely collector (or at least owner) of records that include multiple owners. But the likelihood of an actual survey, while not logically out of the question, is greatly exaggerated when scholars conflate the various surviving examples with each other and with the (seemingly later) Forma Urbis Romae. Let me point out some points of variation in the surviving evidence (while reminding the reader that most of the examples we have are fragmentary, and perhaps greatly so). First, two of the three frontages in the plan from Urbino (inv. 5)  are along private roads, and so the argument about legal responsibility has no purchase.53 It might be better to read this plan along the lines of the component-​oriented ones—​ that is, as a display piece rather than a strictly informational device. That might also account for its other “hidden” irregularities of scale; they appear to show off architectural features at the expense of empty or planted space. Second, the water-​ distribution inscriptions appear to be tied to ownership both literally (of the land) and more loosely (of the water rights), but are also clearly part of a different administrative project than what is imagined for the other inscriptions, and presumably a much more limited one. Third, at least one plan does not have “enough” names to fit the supposed pattern. Found in a necropolis near Rome’s port city, it does not

50 The mere fact that they are ground-​floor plans may also be a sign of this. Roman law does not distinguish ownership vertically, but could allow for essentially any partition at ground level. We know from archeological work at Pompeii that the internal configuration of blocks or “houses” (as defined by doorways) can change over time, so a complete floor plan might be desirable to track ownership. 51 On the assumptions built into the interpretation of these numbers, see note 44, this chapter. 52 The legal provision cited is at CIL 1.593.38–​9. For the legal situation more generally, see Robinson 1992.59–​73. For discussion in the present context, see Nicolet 1987, Rodríguez-​Almeida 2002.43–​4. 53 Cf. Frühinsfeld 2013 on the distinction (more complicated than it looks) between public and private roads. Nonetheless, the “private” roads here appear to be internal to the property, and so likely private in any sense.



Representing Two Dimensions }  171

display any names, even though the placement of three numerals in the surviving fragment suggests that we have at least large parts of whatever units are being measured (inv. 7).54 The fact that we do not have even parts of names suggests that they were likely not there at all. Conversely, a different fragment, now known only from sketches, has “too many” names.55 Its main block is a series of narrow, multistory structures arranged in townhouse fashion. Each is given a name, and all appear to open out onto a portico and thence to a street. There is only one structure whose frontage survives entirely, but there we can see that there is no numeral in front of the building and there is some other writing that cannot be a numeral out in the street proper.56 Finally, and more subtly, the numerals on the inscription in plate 8 do not actually attach to buildings proper but, rather, to portions of the portico in front of them, as is made clear both by the division of the edge line of the portico into distinct segments and the assignment of a separate number to the apparent gate between the first and second segments on the left.57 This diversity within a broad family resemblance extends beyond the labels to the details of the representational conventions used. Internal stairs are represented by similar designs, but not always quite the same—​right versus isosceles triangles versus rectangles; cross-​strokes present versus absent.58 (External stairs are represented by the more, though not entirely, literal rectangular form referred to earlier.) Columns are sometimes dots, sometimes circles, and sometimes circles surrounded by squares apparently representing their bases. There are also distinctions between circles and squares which may be conventional or may represent the actual cross-​section of pillars. Conversely, as noted, the same dot that is a column in one inscription represents a tree in another (Heisel 1993.202). In place of the parallel lines generally used to denote walls, one plan uses single lines and another uses, in the case of buildings that abut each other, triple lines.59 And different plans appear to have different conventions for how many sections they compress into the single layer. For instance, Pedroni 1992.228–​9 has argued that some have a special form (fully closed rectangles) for areas that are functionally on a given level, but are literally

54 Calza and Squarciapino 1962.18. Good images at Rodríguez-​Almeida 2002.58 and tav. VI. 55 Rodríguez-​Almeida 2002.51–​6, Autori vari 2006.35–​6; inv. 8. 56 Another fragment, recently discovered in the Forum Transitorium in Rome (inv. 3), carries no numerals, but given the disposition of buildings depicted on the stone, no inferences can be drawn from that lack. 57 Pace Brodersen 2003.234, they cannot record the distance along the river itself, which is rendered (if at all) by the next line down. Note also that the numbers appear to measure the length of some externally visible units, not abstract units of ownership. 58 Pedroni 1992 argues that the number of cross-​strokes indicates the number of stories in the building. If so, this would be an extraordinarily abstract information graphic in the Roman context. It would also give the building of “Cornelia and her partners” in plate 8 something of the shape of New  York City’s Flatiron building, and in general (including the FUR) there seem to be too few instances with a single cross-​stroke. 59 Single: CIL 6.29847. Triple: CIL 6.29846.

172

172 { Mosaics of Knowledge slightly elevated over the adjacent rooms (e.g., some of the rooms in the upper part of ­figure 5.12). It is clear, then, that all these plans share at least a family resemblance in form, and most of them have at least generally similar ends. At the same time, it is not at all clear that any two of them belong to the same administrative project or even share exactly the same functions across projects.60 Our surviving fragments cannot come from a single grand survey. The diversity would allow for a series of smaller surveys, but it also fits well with a suggestion made by Nicolet 1987.15–​25. He points out that the same law which allots responsibility to frontage holders also speaks at some length about declarations (professiones) that apparently were to be filed with the authorities by all property owners in and around Rome. The law as a whole covers a wide variety of subject matter, so we cannot be sure the two issues are related, but it is certainly plausible. Nicolet also points out that Julius Caesar is known to have tried to improve the urban census by working street by street to get information from property owners (rather than summoning whatever citizens would appear to register themselves, as in the past).61 I  am less confident than Nicolet that there was a single, generalized professio any more than a single survey. Aside from the unlikeliness that we would have no direct evidence of this, it conflicts both with Nicolet’s own evidence62 that there were different kinds of professio and with the diversity of the material evidence here. (I will say more about the collation of such diverse data.) Nonetheless, the general mechanism is very attractive as an explanation for the origin of our data. Not only could the authorities have asked at various points for the different kinds of data more or less attested (ownership and value of property) but perhaps even for the plans themselves. That information, after all, would have been much more easily accessible to individual owners than to the state. Just as, for instance, Rome’s criminal justice system relied on citizen denunciations, so other administrative functions could operate by harnessing those citizens rather than by creating a professional bureaucracy.

What Is a “Map”? We turn now to the central subject of this chapter—​maps. Maps have probably been the subject of more intense scholarly scrutiny of late than any other category treated in this book. It is universally agreed that a very small circle of professional geographers, mostly Greek, could and did make world maps,63 but much attention

60 The two water-​drawing inscriptions are the most likely exception here. 61 Suet. Div. Jul. 41.5: Recensum populi nec more nec loco solito, sed vicatim per dominos insularum egit. This was apparently part of a move to revise the rolls of those entitled to grain at public expense. 62 Especially the material drawn from Cicero’s letters (Nicolet 1987.16) 63 The culmination of this tradition lies in the various works of Ptolemy. The claim is separate from the question of whether such maps circulated with manuscripts of Ptolemy’s text from the beginning. A closely related tradition could and did also make star charts, occasionally used as the basis for artworks, but in this chapter I treat only terrestrial maps.



Representing Two Dimensions }  173

FIGURE 5.6  

“Map” from Dura Europos

After Cumont 1925, pl. 1

has been directed to the question of whether anyone else made or even used maps. For much of the 1990s and the beginning of the 2000s, the orthodox answer was no.

1. Greco-​Roman maps did not exist. In their stead were, if anything, various kinds of linear forms; moreover, 2. Their absence was a symptom of a general cognitive difference in spatial cognition between antiquity and modernity.

The more current view, which focuses on other issues, admits the high proportion of linear to cartographic representations in antiquity, but insists that the latter do exist.64 I am very much in agreement with this, but I also think it will be worthwhile to take a closer look at how the absolutist version could have arisen in the first place, and that involves addressing a question that the more recent literature has not really faced head-​on: Just what do we mean by the term “map?”65 What was typically said to rule out possible ancient maps is that the known candidates were supposedly “one-​dimensional” and/​or that they were not precisely to scale. The two objections converge when a would-​be map is described as “merely schematic.” So, for example, the graphic representation from Dura-​Europos in Syria (figure 5.6) has been said to register stages of a coasting journey, not the genuinely “two-​dimensional” disposition of towns in space. Or take the famously elongated Tabula Peutingeriana (see later, fi ­ gure 5.16), which is clearly not to scale.

64 Sherk 1974; Dilke 1985; Podossinov and Chekin 1991; Hänger 2001; Talbert 2004, 2009, 2012, 2017. Salway 2012, Boschung et  al. 2013, and much of the Common Sense Geography project as represented by Geus and Thiering 2014 (most relevant to the specific claims here are Poiss 2014 and Ilyushechkina et al. 2014; Dan et al. 2014.22–​3 dismiss maps on similar grounds to those quoted here, but I think my broader understanding of “map” actually fits their general research agenda better, a sort of “common sense” cartography.). Kolb 2016 admits of maps but then falls back on an almost entirely linear vision. 65 For a very similar historiographical sketch, see already Rathmann 2013.11–​5. However, when he asks “what is a map?” he is making an inquiry into ancient genres, not our own theory, as I will.

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174 { Mosaics of Knowledge

FIGURE 5.7  

Population-​adjusted map illustrating the outcome of the 2016 U.S. presidential election

M.E.J. Newman, licensed CC BY 2.0.

And when Livy describes an inscription recording a military triumph as being in the shape of Sardinia (site of the conquest), Brodersen 2003.158 dismisses it as schematic, presumably with both criteria in mind. It is certainly incomplete and not necessarily to any particular scale. Two-​dimensional continuity and regular scale are both important tools in the kit of the modern cartographer, and it is a fair question when they arose. But I would suggest that equating the notion of “map” in general with these particular features of particular maps does more harm than good for two reasons. First, and as a matter of practice, many modern maps, such as the population-​biased one (figure 5.7) and the stylized one (figure 5.8) would not count as maps on this account. In fact, no “map” ever sketched on an envelope or paper napkin would qualify. If so many modern maps must be labeled as imposters, yet are seemingly also quite interchangeable with the “real” thing in casual usage, it calls the original categorization into question. Second, and this will be the core of my argument in this section, the very narrow view of what counts as a cartographic representation of space stems from an unduly narrow take on what counts as space itself.66

66 Put another way, the old view was of direct correspondence between map and reality. My version also allows us to take into account the crucial mediation of mental models, whose importance Geus and Thiering 2014 and Thiering 2014 rightly insist on.



Representing Two Dimensions }  175 AK

ME VT WA

MT ID

OR CA

ND

MN

WY NV AZ

SD CO

TX HI FIGURE 5.8  

IL KY

AR LA

NY

IN

MO KS

OK

MI

IA

NE

UT NM

WI

TN

MS

OH WV

PA

MD

VA AL

NH MA

NJ

RI

CT

DE NC

DC

SC GA FL

Stylized map illustrating the outcome of the 2016 U.S. presidential election

The individual space-​articulating tactics discussed in ­chapter 4—​effects of color and scale, superposition, appeal to pragmatic knowledge, stereotyped gestures, and so on—​are perhaps specific to paintings, but I  want to offer three broader generalizations from that discussion that are important for thinking about maps. First, while none of the specific devices has anything like the power of single-​point perspective to organize a painting, the compositional effect of different constraints can still create coherence. Second, and relatedly, that coherence is achieved by situating chunks—​in the paintings, buildings, ponds, people—​with respect to one another, not to a predefined but invisible framework. That is, the compositionality starts at the local level and builds outward, a practice we will see in Roman maps.67 Third, any attempt to attach particular distances or sizes to objects represented was necessarily an approximation. That third point, approximation, is relevant to mapping in several ways. Most directly, I’m suggesting that precise scale should not be a defining feature of “map-​ hood.”68 Take, for example, the Forma Urbis Romae. This is a colossal, early third-​ century plan of the whole city of Rome inscribed on marble (a fuller description can wait until the next section). Brodersen 2003.235 objects that its scale varies by up to a factor of slightly more than 2 from place to place (with concomitant distortions of orientation), and it is therefore not a map at all. Much of this variation actually has to do with the limits of carving accuracy. However, and this is importantly a more general point, even if we take the variation at face value, the

67 Klaus Geus points out to me that even Ptolemy’s practice, though in theory based on a universal grid, must have followed the same pattern. Only a limited number of sites could be located by his preferred, astronomical methods. The bulk were then traced to one of these sites by less reliable terrestrial measurements. See especially Geog. 1.4. 68 Some useful remarks on this point may be found at Parker 2008.244.

176

176 { Mosaics of Knowledge viewer who does not know the “real” scale of some segment of the map is still not completely ignorant of spatial relations. Though Brodersen is right about the most extreme possible cases, it is still the case that a building depicted as one-​eighth the size of the Circus Maximus on the map will normally be roughly one-​eighth the size in real life. And these kinds of approximations only get better over longer distances. Moreover, the relatively stable scale means the map also generally preserves (rough) orientations. Northwest on the map means, roughly, northwest in real life. Perhaps this is not an excellent map, but it seems strange to deny that it is a map at all. And if, as appears to be the case, a map of land distribution at Orange (which we will revisit) is systematically compressed along one axis, the viewer would have understood still more. Given these kinds of approximations, we can say the visual representations in this chapter work exactly as one would expect from the numerical representations studied in c­hapter  3. They are “good enough” approximations. They probably resemble the numerical case in another way as well. None of our complete representations gives a standard scale to convert represented length into actual distance. What these images are best suited to give the reader, then, is a sense of proportional relationships. Moreover, the patterns of approximation suggest yet another way in which the visual representations of reality here work in the same way as the fictional ones studied in the previous chapter. I argued there that artistic representations of space did not allow for unique reconstructions of the “original” scenes they represented, but that this did not mean they allowed no reconstruction at all. They were not impossible to read, just ambiguous. Similarly, the fact that scholars cannot agree on the reconstruction of particular ancient maps is not an argument that there is nothing to reconstruct (pace Brodersen 2003.269–​ 72). The representational conventions used in mapping would not have produced a unique (and therefore precisely reconstructable) image, but that does not mean there were no conventions at all. At any rate, the general relevance of approximate measurements to cartography seems clear. Less obviously, I would suggest that my other two generalizations—​ compositionality and the locality of that composition—​mean that one can approximate not just scale but also two-​dimensionality. The most important cases here are networks and schematic patchwork constructions.69 As a technical mathematical fact, even a simple network has a higher dimension than its linear components have individually.70 Perhaps more important for present purposes, there is experimental evidence that networks are also cognitively distinctive. Experiments on types of diagrams have shown that those with multiple pathways among pairs of

69 Pace Brodersen 2003.59–​65. 70 Daqing et al. 2011. In fact, if the network has certain additional properties, its dimensionality can be higher than that of the embedding space, but that doesn’t seem to be the case with any of the ancient objects to be discussed.

Representing Two Dimensions } 177

points are harder to process than those with only unique paths.71 This should be all the more true for a space-filling, if still schematic image like the stylized U.S. map (figure 5.8).72 Sets of lines and configurations of boxes are more like full maps than they are like individual lines and boxes.73 So while something like the Dura-Europos image (figure 5.6) might reasonably be thought “merely” linear, the same is not true for a network like a modern subway map or the road network of the Peutinger map (on which more later). So how does this affect the questions we started with? We can immediately rebut the claim that Romans lacked any kind of cartographic consciousness. Let’s look at the triumphal tablet I referred to earlier. Livy says a tablet was set up in the temple of Mater Matuta, inscribed74 Under the command of Tiberius Gracchus the army of the Roman people conquered Sardinia [and did other deeds]. . . . Because of all this, he gave this tablet as a gift to Jove. It was the shape of the island Sardinia, and on it were painted images of battles. (Liv. 41.28.8) Focusing on Livy’s characterization by means of an outline, Janni and Brodersen take this as evidence of a linear imagination, but it actually shows that the framing as “one-dimensional” is misleading.75 From the point of view of a traveler on the route, any outline, whether shaped like a triangle, circle, or violin, is identical. They should experience all segments as just more forward and backward. But our texts don’t take that perspective. They frequently characterize shapes as if seen from above precisely by seeing a shape disposed across two dimensions. The phrase “the

71

Hurley and Novick 2010.287–8. In fact, we can probably see this cognitive distinctiveness in the Roman evidence. Benet Salway 2012 has made an exhaustive study of the organization of Roman collections of itineraries in various formats. He makes a number of important observations (one was already noted), but the most general is their “atomization.” That is, there is no representation of the fact that a particular landmark might be a node in a network. Each point simply reoccurs in however many itineraries happen to pass through. (Interestingly, this remains the case even for the one text Salway can show with fair certainty to have been based on some kind of map.) The itineraries do not note the existence of nodes, I take it, because the two forms (itinerary and network) are not in fact the same thing. The nodes exist only in the latter, more sophisticated structure. 73 Klaus Geus (personal communication) has expressed discomfort with the language of “onedimensional” routes, pointing out that, at least at junctures, there is not just forward and back but also left and right. I think this is precisely correct, and it is the clearest case of the distinction I am drawing here. A network composed of one-dimensional segments is not itself one-dimensional, any more than a segment made up of zero-dimensional points is itself zero-dimensional. 74 ‘Ti. Semproni Gracchi consulis imperio auspicioque legio exercitusque populi Romani Sardiniam subegit  .  .  .  cuius rei ergo hanc tabulam donum Ioui dedit.’ Sardiniae insulae forma erat, atque in ea simulacra pugnarum picta. 75 Janni 1984.125–7 and Brodersen 2003.39–40 point out the frequency with which ancient authors described some territory by characterizing its silhouette. Cf. Arnaud 1989.22. Similarly, the “bodily” directions Arnaud cites, even if they evoke the experience of an actual traveler, do so in a way that implies two-dimensional awareness: “turn this way” or “look in that direction.” Much closer to my position is Lebreton 2010.79–80. 72

178

178 { Mosaics of Knowledge Ocean

Ocean Rhone

Aquitani Garumna

Galli

Belgae Matrona/ Sequana

Pyrenees FIGURE 5.9  

Germani Rhine

Rhine

Network rendering of places named in Caesar, BG 1.1

shape of the island” clearly points in that direction; in the case of Sardinia, convention dictated the shape of a footprint.76 Placing the battles within that frame reiterates that it is a container and a partitionable space (however unrealistic the interior content doubtless was). That inscription was a map in a minimal sense, but it suffices to demonstrate that Romans had a two-​dimensional imagination. Other examples can show that there are more complex cases, as well. To take a well-​known example, at the beginning of Julius Caesar’s de Bello Gallico, not only is “all Gaul divided into three parts” but also the author goes on to tell us quite a bit about how those parts fit together.77 The river Garumna divides the Gauls from the Aquitani; the Matrona and Sequana separate them from the Belgae. . . . Of these, one part, which they say the Gauls hold, begins from the river Rhone and is enclosed by the Garumna, the [Atlantic] Ocean, and the territory of the Belgae, and across from the Sequani and Helvetii it touches the Rhine and turns north. (6) The Belgae begin from the end of the territory of Gaul and run to the lower part of the river Rhine; they look to the northeast. (7)  Aquitania reaches from the Garumna to the Pyrenees and the part of the Ocean near Spain. It faces northwest. One could try to construct an account of this in terms of linear routes as long as the names of rivers are read as metonyms for the points at which some route crosses that river (figure 5.9).

76 See McGushin 1992.186 for the evidence, both Greek and Roman. 77 BG 1.1.2, 5–​7. Gallos ab Aquitanis Garumna flumen, a Belgis Matrona et Sequana dividit.  .  .  . Eorum una pars, quam Gallos obtinere dictum est, initium capit a flumine Rhodano, continetur Garumna flumine, Oceano, finibus Belgarum, attingit etiam ab Sequanis et Helvetiis flumen Rhenum, vergit ad septentriones. 6 Belgae ab extremis Galliae finibus oriuntur, pertinent ad inferiorem partem fluminis Rheni, spectant in septentrionem et orientem solem. 7 Aquitania a Garumna flumine ad Pyrenaeos montes et eam partem Oceani quae est ad Hispaniam pertinet; spectat inter occasum solis et septentriones. Cf. also Ilyschechkina et al. 2014 (esp. 257) for the spatial complexity that can be extracted by a cognitively sensitive reading of linear text.



Representing Two Dimensions }  179

Ocean Spain

Aquitani

Galli

Helvetii FIGURE 5.10  

Belgae

Germani

Schematic, two-​dimensional rendering of places named in Caesar, BG 1.1

But there are any number of problems with this approach. First, this is at the least a network of routes, and that is already a more complex object than any individual route. Second, let us think about those rivers again for a second. The “Rhine” (and “Ocean”) are construed to have multiple parts, so their names don’t really look like codes for crossings. And, after all, we have a good imaginative understanding of what a river looks like, very much like the cases of the portico and gateway in the paintings of the previous chapter; it’s easy to imagine they have their own extension. Third, consider specifically the description of the territory of the Galli. On a linear reading it’s not clear how the Belgae “contain” a region that they (with the Matrona in between) are not even adjacent to, but on a three-​dimensional view it is quite straightforward. Moreover, the very meaning of continetur (“is enclosed”), as well as the fact that its action comes from multiple directions, suggests that the territory of the Galli is indeed an area. Moreover, and this is the fourth problem, all three zones are said to face in certain directions, and so each must have more structure than being a simple point. Finally, and this really gives away the game, those directions are defined in terms of cardinal directions.78 That is, there is a two-​ dimensional framework which can govern the entire construction. Taking that together with the various adjacency pairs, the multiple instances of bodies of water, and the directional evidence, the passage describes something like that shown in figure 5.10 (using “up” arbitrarily for north):79 78 Uncharacteristically, Brodersen 2016 admits similar arguments in favor of the “geographical” consciousness of Solinus. 79 Nor is an extended vision restricted to passages (such as the two just discussed) which are perhaps self-​consciously “geographic.” Even passing spatial descriptions are often hard to reduce to simple linear paths. Consider the path, which goes “between the Iura mountain and the river Rhone” (1.6.1). The actual geography of the region shows us that Caesar must mean the river was on one side of the route (roughly the north) and the mountain was on the other. Should we then imagine that Caesar’s “between” means that there is a hypothetical route from the mountain to the river with a road untaken as a point in between? It is hard to see how either the road or the river could be construed as a point. Or consider a description such as “the Iura mountain, which divides the territory of the Sequani from the Helvetii” (1.8.1). Here one can imagine a notional path from the territory of the Sequani to the mountain to the Helvetii, each conceived of as points. Yet to say that the mountain “divides” the two

180

180 { Mosaics of Knowledge But supposing even that I am right about those examples, at least descriptively, am I really answering my own original question? That is, is it really fair to describe these objects and mental conceptions as “maps”? In their History of Cartography, Harley and Woodward 1987.xvi define maps as any “graphic representations that facilitate a spatial understanding of things, concepts, conditions, processes, or events in the human world.” This expansive definition clearly made sense in the context of their project; a groundbreakingly comprehensive history of world cartography would obviously suffer if it allowed preemptive exclusion. The data needed to be collected before they could be sorted. I am not sure, however, whether such a generous understanding is desirable everywhere. If our question is how to characterize a particular corner of antiquity, it does matter exactly how different devices “facilitate a spatial understanding.” But if we do not accept Janni and Brodersen’s strict constraints, are there to be any at all?80 For most people, I suspect that the essential feature of what makes a map a map is that its “facilitat[ion of] spatial understanding” is related to its iconic character, and that is the criterion I wish to stipulate here. A map describes some physical space by establishing parallels, piece by piece, between elements of the map and of reality. A map, that is, needs in some sense to “look like” the world. One way to achieve that, of course, is to establish a systematic, mathematical projection between map and reality, but that is hardly the only way.

Ancient Maps The maps of this section will differ from the objects in the section “Plans” in covering more territory and in the very fact of being defined by a territory rather than by the objects therein, though (to repeat an earlier point) I do not mean to propose either a sharp or an explanatory distinction between the two. In particular, the three smallest “maps” here could also reasonably be described as giant plans. The examples in this section will be ordered on the mechanical principle of amount of territory represented (from smallest to largest), though I will have considerably more to say about some of these cases than others. As I lay out these data, I will also be discussing the categorization of the individual instances as maps in light of the theoretical discussion in the last section. The next (and final) section of the chapter will review this material more analytically, and in particular will try to address some territories is, after all, to make a more specific claim than that it is “between” them. “Divide” seems, rather, to draw a line cutting an area into two parts. This suggests that the territories of the Sequani and Helvetii are seen as areas with two-​dimensional extent, and that in turn suggests Caesar’s “between” can be two-​dimensional, as well. 80 I have also restricted myself to planlike maps of a given surface area. We also have some representation of cities in profile, but these seem unlikely to have conveyed information to any likely audience, certainly not about spatial relations (even if individually iconic buildings were depicted). See Favro 2006.



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standing issues about map use by setting them in the broader context of information technology. Let us turn now to the specific cases. We have already seen several of the directly attested maps. At least the less text-​heavy of our two water-​distribution inscriptions (figure 5.4) appears to be a map of a general area, rather than a pair of annotated schematics of the waterways. Not only are there two separate watercourses, but even the land between the two appears to be divided into at least two registers, as defined by the texts marking the individual estates. Moreover, one should note the sharp bend in the right-​hand fork and the double-​bend in the left-​hand fork in the lower channel. These would be pointless if we read the inscription as just the conjunction of two separate representations of waterways. We have no idea what actual area is being “represented” here, and so no idea what kind of scale or precision is used, but it is hard to see how this image is not meant to be read in maplike fashion. The other water-​distribution inscription has much less detail, but given its double channels, similar style, and similar textual content, it would not be surprising if it had been similarly maplike. Also surviving on marble is a map I have already alluded to twice, but which can now get the extended discussion it deserves. The object was a very large plan of much of the city of Rome (originally about 18 m x 13 m). Today it is called by the (modern) Latin name Forma Urbis Romae, or “Map of the City of Rome” (henceforth FUR; examples at figures 5.11 and 5.12). This was originally displayed on a wall inside a temple in the heart of Rome.81 The contents of the map and its archeological context allow it to be dated securely to the first decade of the third century, during the reign of the emperor Septimius Severus (early third century). We have something on the order of 1200 fragments, which make up about 12% of the original surface area. The general style is quite close to that of the building plans already discussed, though there are some differences, most notably the use of single lines for most walls and a much more minimal program of labeling (both of which will be discussed at more length). Like the plans, it appears to record only features of the built environment. There are no topographical indications, and at least in surviving fragments, the Tiber is “represented” only by blank space.82 Like the plans discussed earlier, this is the kind of object whose modern analogs would be drawn at consistent scale. Unlike those other plans, there are enough instances in which we can compare the graphic representation to the remains of actual structures that we can confirm our intuition is at least generally correct. There have, however, been disagreements as to what that scale might be and how uniform it is. Following those leads will, I think, have important results beyond the technical

81 Almost universally taken to be the Temple of Peace, though Freyberger 2013.180–​5 reads it into a possible, adjacent Temple of Rome. The choice does not affect the arguments that follow. 82 Najbjerg and Trimble 2006.93. Fragment 32f could be read as suggesting an outline for the Tiber Island (see Carettoni et al. 1960.93 for the location), but this is hardly clear. The line visible on the fragment could be architectural.

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FIGURE 5.11  

Forma Urbis Romae, frr. 11f–​h

FIGURE 5.12  

Forma Urbis Romae, fr. 10g

question of arriving at a numerical ratio for the scale. The normal scale of well-​ known buildings on the FUR is clearly something like the 1:250 or so found on the smaller plans. Around the turn of the twentieth century, scholars made a number of different proposals that various buildings or areas were artificially enlarged to increase their visual prominence. Some of these claims were refuted in the monumental publication of the fragments in Carettoni et  al. 1960, but the authors of that work went on to assume regularity of scale even in places where evidence was lacking. They also preferred a specific scale of 1:240, which they supported both by observation of actual remains in some places and by the convenience (from a Roman point of view) of a scale defined by a multiple of 12. Among experts on the



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y = 0.0744x + 239.31 R2 = 0.005

300

scale

250 200 150 100 50 0

0

10

20

30

40

50 60 distanze (m)

70

80

90

100

110

Vertical axis: scale of the Forma Urbis Romae implied by individual comparisons with modern measurement. Horizontal axis: magnitude of each measurement FIGURE 5.13  

From Fabiani 2009.4.

FUR today, consensus has largely converged on both ideas—​uniformity and the particular value of 1:240—​even though little or no additional evidence has been adduced. Moreover, many scholars have gone on to attribute the same 1:240 scale to the smaller plans discussed in the previous section, in moves that are almost entirely circular.83 By contrast, Brodersen 2003.235, as we saw, emphasized the wide range of scales that have been inferred for various elements—​from 1:189 to 1:413—​ and deviations from the “standard” orientation up to 21 degrees.84 Recently, however, an Italian team has subjected all these questions to new scrutiny, including fresh scientific measurements of actual distances and the use of modern statistical techniques to analyze the resulting range of numerical values.85 The most striking result is that, although the range of scales implied by various measurements is quite broad, it narrows dramatically as the absolute length of the distances increases, especially beyond about 40 meters. We can plot a graph of the scales at which various known distances are represented (vertical axis) against the actual value of those distances (Fabiani 2009.3; figure 5.13). The average scale is calculated as about 1:246. There are modest variations among areas along the general

83 For instance, Conticello de Spagnolis 1984.49–​56, discussing the scale of the via Anicia plan, simply accepts the assertion that the others are to this scale. The overlap between this plan and a surviving fragment of the FUR suggests both were to at least roughly the same scale, but we do not know independently what that was, nor is the overlap precise enough, it seems to me, to distinguish between, say 1:240 and 1:250 scale. 84 In fact, he says “over 25” degrees from reality, but the source he cites only measures angles between pairs of buildings, rather than picking a normative orientation. It does not give values over 21. 85 Fabiani 2009, Crespi et al. 2011.

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184 { Mosaics of Knowledge lines proposed by earlier scholars, and one area (around the Theater of Marcellus) appears to have suffered special disruption (as had also been suspected).86 The combination of all this evidence suggests to me the following. There was an intended scale of 1:240 or 1:250 or conceivably both, since (as we will see) the individual segments of the map may derive from different sources. The number 246 (= 2 × 3 × 41) is after all only a statistical average and is too irregular to have been a deliberate choice. Instead it seems to be the result of a combination (to be detailed) of (a) slightly inconsistent systems along with errors both (b) random and (c) systemic. In general, I will be arguing, we are in the same situation here as with many of the local metrological standards. That is, it is clear that standards in some sense existed, but it is impossible, even with modern techniques, to infer exactly what they were, and so it is unlikely that an ancient observer could have readily inferred them, either. Additionally, whatever the notional standard, there were divergences, both intentional and otherwise. There are at least three different factors that seem to have caused these divergences. First, the engraving technique of the map does not allow for precision over short distances. So even scholars who claim that known buildings all conform to a single scale admit that the same cannot be said for components of those buildings. Incidentally, in this light, the scaling of a plan fragment like figure 5.11 actually seems fairly precise, contrary to Brodersen’s claims. Second, there do seem to be a few cases where the orientation and perhaps even the size of a building have been adjusted for deliberate effect, such as (wrongly) aligning the Circus Maximus with the vertical axis of the map. Similarly, Hülsen’s 1914.109 early claim that structures on the Palatine were expanded for emphasis still seems plausible. Finally, there appear to be effects from the composition of incompatible component maps to create the whole. I will say more about this, but to give an example, it is likely that the slant of the row of narrow structures in figure 5.12 is not real, but reflects a systematic distortion needed to fit the structures into a space left on the stone slab before the adjacent component map. (I note an important technical consequence of this phenomenon. These effects appear to be clustered in obscure, private buildings. If so, they would be largely invisible to the recent analysis of scale cited, which relies on identification of map features with surviving remains. Thus the actual variation in scale across the map is presumably greater than has been measured so far.) To understand how this composition worked, we need to look at one other feature of the map. The time it represents is curious. As I noted, the artifact itself can be securely dated to a fairly narrow period in the early third century. Archeologists, however, have been able to show that the architecture depicted on the map is not a snapshot of the actual state at the time it was carved, nor in fact of any one time.87 For instance, it depicts a monument called the Septizodium, built at most a decade earlier than the map was made, but other areas are shown in forms dating from

86 87

Contra Carettoni et al. 1960. Trimble 2008.76–​8.



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various points in the course of the first century. This has been taken to demonstrate that the map was not based on a single survey but was instead pieced together from several surveys. We are now in a position to put chronology, scale, and composition of the map together. Even before the systematic and scientific study by Crespi et  al. 2011, scholars had noted differences in the map’s accuracy at long versus short distances. As just mentioned, buildings as wholes are more exactly scaled than their subcomponents, and distances between major monuments are perhaps more precise still (Carettoni et al. 1960.75–​8). Framing the question in terms of orientation rather than distance, Rodríguez-​Almeida 1977.223 measured the angles between the axes of major monuments and found that deviations from reality are generally smaller the farther apart the buildings are.88 He proposes that the precision of the long-​distance measurements is the key to understanding the composition of the map; they are not just a symptom but also a mechanism of construction (225–​6). The first step, on his account, was to pick a central reference point. This would presumably be somewhere on the Capitoline hill, a location both elevated and at the center of the eventual map. Then the distance and direction of peripheral landmarks were established in reference to the central point. Regions of the city were then surveyed independently, working outward in each case from the local landmark. The final form of the FUR was created by assembling a “mosaic” of the individual surveys. Incompatibilities in the conduct of the local surveys were then resolved not by resurvey (which would presumably just have displaced the conflicts) but, rather, by ad hoc adjustments on the part of the designers of the map (like the row of slanting rooms). In fact, the adjustments may have been left to men who were artisans (stonecutters) rather than surveyors or even administrators used to dealing with surveys. Most of the steps of this reconstruction make sense to me, but I would like to direct more attention to the supposed local surveys. The focus of the FUR is on public buildings.89 They are the only ones labeled, and many of them are drawn according to special graphic conventions such as rendering walls with double lines and/​or in color. They seem to be the subject of the deliberate manipulations (as of the scale of the Palatine complex or the orientation of the Circus Maximus). And they likely even provide the elements for the network of landmarks that form the backbone of the map. One might have imagined that the state would have found access to these buildings more convenient than to private ones. Yet our evidence for the diversity of the FUR’s sources comes precisely from that very public architecture. Instead of fresh measurements, whatever plans happened to be at hand were

88 Note that, as a mathematical fact, if not only individual buildings are drawn to scale but also the space in between, then orientation will necessarily be preserved at any scale. If any (noncircular) building rotates, it will distort the shape of adjacent open space, thus violating its scaling. 89 See especially Trimble 2008.79–​88; the qualifications at 94–​5 are of considerable interest in themselves, but are not significant for the present argument.

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186 { Mosaics of Knowledge used even for those public buildings. It seems unlikely that the private property would then have been surveyed more systematically than the public property. We should also think back to the smaller plans discussed in the previous section. It has reasonably been suggested that these represent at least the kinds of preexisting data stores that could have been used to construct the FUR. But as we saw, these earlier plans certainly do not represent a single document or survey, or even a single kind of document or survey, despite their broad stylistic similarity.90 Furthermore, it was at least a possibility that they (or at any rate some of them) derived from the declarations of landowners rather than from a survey conducted, even locally, by standardized means. A convincing case has been made by others that the FUR was constructed for ideological rather than informational purposes.91 It lacked much of the textual information of the smaller, earlier plans and at any rate was displayed so high on the wall (from 4 m at the bottom to 17 m at the top) that most of the graphic detail would have been invisible to most viewers. In this context it made sense to patch the map together from whatever materials were at hand, even if they were not entirely compatible. It is not impossible that some survey was conducted for the purpose. Perhaps some areas had somehow escaped the imperial records, especially if they did not front on any public road. But there is really nothing in the fabric of the proj­ ect to suggest that a comprehensive survey project or even a comprehensive archive lay behind it. This is a map, but that does not mean that it arose from an individual act of mapping. We may now turn briefer attention to maps of larger areas, starting with the centuriation records that were discussed in c­hapter  2. Recall that surveyors inscribed squares (or rectangles) on the ground, then recorded the land allotments, century by century, in corresponding blocks on a map, typically inscribed on bronze (though our single best-​preserved example is in marble).92 A plot of land that was in reality X blocks from the main axial road and Y blocks from the perpendicular one was recorded on the corresponding grid square in the representation. Brodersen 2003.223–​4 objects that these do not amount to evidence for accurate mapmaking, since real-​life squares of land are represented by rectangles on some plans. Then he goes on to suggest (anticipated here by Arnaud 1989.17) that—​even setting aside the issue of scale—​such objects do not give evidence of map literacy, since the various squares could be referred to by their coordinates, by recourse to the register instead of the map.

90 The evidence is not conclusive, but I  would still go further than Trimble’s 2008.75 agnosticism on the view of Rodríguez-​Almeida 2002 and Freyberger 2013.178–​80 that our non-​FUR fragments represent the remains of similarly grand maps. The evidence against a single survey also tells against Freyberger’s 2013.179, 189 view that the FUR is a copy of a bronze cadastral map. 91 Reynolds 1996.124–​34, Freyberger 2013.189. 92 See ­chapter 2, notes 11 and 12 for the objects. The monument actually preserves records of three different surveys, each apparently conducted in slightly different ways.



FIGURE 5.14  

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Fragment of an inscribed map depicting the centuriation at Arausio

After Piganiol 1962.fig. 33

For reasons discussed in the previous section, I am generally less concerned with scale than is Brodersen. But in this particular case, I think the facts actually have a force quite the reverse of what he claims. The size of the rectangles in the inscription is consistent enough that we can say that the image has simply been vertically compressed. (The ratio is 6:7, as Piganiol 1962 had already noted.) The horizontal and vertical scales are unequal, but not therefore nonexistent.93 Now, if this inscription merely gave a grid and text, one might object that compression need not amount to a scale at all. These objects could in principle be read, by coordinates, as tables. On this reading, there would be no representation of space at all. Chapter 2 has already argued that a tabular reading is itself dependent on the spatial one (rather than the other way around), but we can also make a more specific point here. Unlike many of the other maps and plans, this one also represents a few natural features, mostly rivers. These are prominent and not merely schematic (consider, for instance, the island in the river at Piganiol 1962.fig. 33; figure 5.14). Again, we do not (and cannot) know whether these representations are accurate, but they are clearly meant as geographical representations. The fact that the island crosses the surveyed dividing lines suggests at least a general sense on the part of the mapmaker of where it “should” go, and in fact observing how the material river interacted with the material grid would have kept the representation close to reality. There would have been a natural check at each boundary. This is, after all, essentially the operation of the

93 Compare the even more sophisticated used of differing horizontal and vertical scales to produce models of entasis for columns. Wilson Jones 2000.128.

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188 { Mosaics of Knowledge “method of squares” painters used to scale images up or down.94 That does not in itself prove a perfectly applied scale, but it does require at least an approximation. As for the possible redundancy of map and register, I think that, too, tends to argue for the opposite of Brodersen’s and Arnaud’s inferences. The textual register may well have been the more practical reference for some purposes, but it was in the hands of the state and would have been accessed directly only by professionals. The display object (if any) was the map.95 This suggests that the graphic form was the more generally legible one. And two of our three bronze versions appear not in fact to have listed the coordinates. These may reflect surveying beyond centuriation in the narrow sense, but that would merely explain why the maps are not redundant with the registers, not refute the fact.96 I would also repeat the point that, though we only have one extensive example of the survey maps (and the three tiny fragments of bronze ones), there is excellent evidence that they were in fact fairly common. Beyond the extant examples, we have a number of other cases in which we know for certain that the formae required in theory were actually produced. The second-​century historian Granius Licinianus (10F) recalls the nationalization and redistribution of land in Campania in the mid-​ second century bce. The distribution naturally involved a survey, and a forma was published in the capital. We also have about a half-​dozen inscriptions recording the resolution of various border disputes by reference to the preexisting formae.97 I have been speaking of formae produced in the course of centuriation or comparable state allocation processes, since that is where most of the evidence is. However, Siculus Flaccus tells us that possessors in more remote regions made their own formae, even though these documents lacked, he says, legal status (104.31–​33C). This suggests that not just the cognitive principles but also the practice of mapmaking penetrated beyond professional circles and perhaps also below even their social level of modest respectability. In principle we have no way of telling if any of our fragments arise in this context, but I would not want to rule out, for instance, inv. 5. Moving on to larger areas, we have already seen an example of a province-​level map (from Livy), and we owe another (and clearly more sophisticated) one to the combination of a recent archeological discovery and the brilliant interpretation of

94 Clarke 2010, 2013. 95 Aside from the monumental character of the Orange maps, we may note the apparent mounting hole on the top of Verona A, presumably to be hung on a wall (if not a free-​standing monument) rather than being filed away. For the libri in the Corpus Agrimensorum, see 35.11–​26, 37.12–​38.14, 48.20–​25, 51.1–​29, 84.8–​26, 102.9–​15, 118.16–​119.6, 165.10–​166.2Th. 96 Cavalieri Manasse 2004.60–​1, Lucchelli 2015.74; contra Buonopane 2015.59–​60. 97 See Elliott 2004, and in particular his catalog items 16, 22, 31, 66, 67, 87, and perhaps 56. I do not think that Rodríguez-​Almeida 2002.5–​8 has identified another instance. The motion described in his text is literal, not projected onto a map. Boundaries could, in principle, be fixed in purely verbal terms, but since we know that the normal output of surveys included a graphic component and that that component was called a forma, it is very hard not to see maps in all these cases. Presumably they have suffered in terms of preservation for being inscribed on valuable bronze or on perishable materials (citations in note 95, this chapter and at note 12, ­chapter 2).



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its inscribed text by Salway.98 The monument is a statue base dating from the mid-​ first century and found at Patara on the southeast coast of modern Turkey. The base is covered with text describing itineraries among important communities in the province of Lycia. The individual routes are ordered by systematic exhaustion of the paths in a given direction, and once a given tree has been exhausted, move on in a clockwise order to the next path out of the original starting node. As Salway shows, this is not necessarily a useful arrangement for the reader as traveler, but it is natural and easy to generate if the composer of the text is in fact working from at least a sketched network. Networks, as I have argued, are maps. And in this case (dealing with built infrastructure, not just a swath of territory), it is not hard to imagine that state officials would have access to at least a rudimentary survey of distances and the like.99 We might also consider in this context a controversial passage from the military writer Vegetius (3.6). In discussing the advance planning that a prudent general should carry out, he refers to the need for itineraries which account for distances, the quality of roads, and the placement of shortcuts, mountains, and rivers. The truly clever general, however, will use itineraries that are “not only written down (adnotata), but also drawn (picta) . . . so that he may pick out a path not only by the mental planning, but by visual inspection.” It is true (as we saw in the section “Textual Illustrations”) that the illustrations in the surveying manuals acquired a certain amount of ornamental decoration, but in places where there was already drawing in the first place. It is much harder to imagine that kind of accretion taking place around textual itineraries of the sort we have surviving, even before considering a military context. Moreover, such illustration would be manifestly useless for the purpose Vegetius specifies.100 More likely, then, Vegetius refers to a network or even a slightly more elaborate schematic diagram. It may be best to imagine such maps as dating from late in our period, when Roman armies were fighting principally on their “own” territory, not invading unfamiliar lands.101 At any rate, this appears not only to be a map (in the present sense) but also a whole category of them. Diagrams of the continents and of Euboia found in many manuscripts of, respectively, Sallust and Lucan are certainly two-​dimensional schemata (though they may not be ancient).102 Similarly, the conventional division of the earth into four

98 Salway 2007, 2012. Lebreton 2010.108–​9 has a different reading which doesn’t really account for Salway’s basic observation, but in any case is crucially two-​dimensional. 99 I agree with Lebreton 2010.98 that it is, however, highly unlikely that the inscription represents the results of a de novo survey by the new Roman government. 100 It has been suggested that Vegetius has no knowledge of actual practice in this respect (and indeed others). Even if true, that is more problematic for military history than for the present discussion. In fact, it would be of great cartographic interest if Vegetius (and his audience) were familiar enough with maps to mistakenly attribute them to generals. 101 Lebreton 2010.80n65, however, argues for greater time-​depth. One might see Plin. HN 6.40 as additional evidence on this point, though the passage is not clear enough to bear much weight. 102 They are clearly not authorial illustrations of the sort discussed in the section on “Textual Illustrations,” but even Arnaud 1989.25–​6 is sympathetic to the idea that they are at least late antique.

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190 { Mosaics of Knowledge zones (dividing by what we think of as northern vs. southern and eastern vs. western hemispheres), as described in elaborate detail by the surveying writer Agennius Urbicus (19.23–​41C), is a simple but still geographic schema, not just a symbol of “the world” or “power” that a bare globe admittedly can be.103 That last example takes us to the realm of world maps. Pliny the Elder cites Agrippa, the friend and minister of the emperor Augustus, for many pieces of geographical information—​in particular for many distances. Only one passage, however, gives us much sense of the form of Agrippa’s work. After giving the length and breadth of the province of Baetica, Pliny continues: Who would believe that Agrippa (and with him the divine Augustus) made a mistake in this respect . . . when laying out the world (orbem) for the city to see (urbi spectandum)? For he [Augustus] completed the portico which held it in accordance with the plan and notes of Agrippa after it had been begun by his [Agrippa’s] sister. (HN 3.17) Most readers have taken the “world to be gazed at” to mean a map painted on the wall of the portico. Arnaud 1989.21 and Brodersen 2003.275–​8, however, have challenged this on a variety of grounds, suggesting instead that Agrippa’s monument consisted rather of a text listing place names and perhaps distances.104 Other passages are found in which the verb spectare (“gaze at”) is purportedly used with a text as its object. Virtually all the information explicitly derived from Agrippa consists of distances—​precisely the kind of information we might expect from an itinerary-​like text. Finally, it is pointed out that destinatio (“plan”) need not refer to more than a general intention and that commentariis (“notes”) are by definition textual. But this interpretation ignores the crucial phrase “which held it.” There is some object here which is equivalent to the “world” (orbem), but not to the notes (commentarii). Moreover, commentarii in Latin are typically notes on something else.105 They are textual, but that again leaves another entity unaccounted for. The “gazing” passages cited do not actually involve looking at a textual representation. Rather, they all describe, however metaphorically or hyperbolically, seeing the world itself. It seems very likely that there is a text involved here, whether in addition to the map (as a separate commentary) or superimposed (as in the case of the Peutinger map), but that does not refute the existence of a graphic object. But is it cartographic? The accompanying text contained a lot of information about provinces, and it is not hard to imagine that the map itself was organized similarly. If so, they would have been forced into a network of adjacency pairs, since it was known which provinces adjoined which. If the individual provinces were even remotely to scale (and we know that the map had a set of plausible

103 See Geus 2013 for discussion of the passage, including several convincing emendations. I suspect that roughly the same is true for the chorography mentioned by Vitruvius (8.2.6), but proof is lacking. 104 Arnaud 2007–​8.88 seems to have moderated this position somewhat. 105 Riggsby 2006.135–​6.



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measurements for them), then this would have forced an at least recognizable configuration of the whole along the lines of traditional scholarly reconstructions.106 Here, as in Caesar’s case earlier, we see a parallel with the artworks I discussed in ­chapter 4: space constructed not as a single framework but, rather, as a series of smaller but interlocking armatures. And also like Caesar’s case, it is not hard to imagine the whole being organized on the basis of cardinal directions. Again, this would presumably not meet modern standards of regularity, and might be regarded as somewhat schematic, but there is every reason to think that it had meaningful scale, and it surely went beyond the linear. Whatever the sources of information that underlay Agrippa’s project, the map itself was displayed in a crowded, public place. It likely did not serve any administrative purpose. Most of the associated information, at least as far as we can tell from what survives, would not have been obviously useful to a viewer planning a trip or the like. Too many of the measurements were of relatively abstract entities, like provinces. Rather, as scholarly consensus rightly holds, it seems more likely designed as a gesture of authority, both Roman political authority over much of the land displayed and a more general human capacity to comprehend and appropriate the oikumene as a whole.107 A few years before the end of our period, we get an extended description of what appears to be another world map. The orator Eumenius appealed to the emperor to be allowed to restore various parts of a school at Augustodunum (modern Autun) that had been sacked during a period of civil strife a few decades earlier. The climax of the facilities to be restored is another decorated portico. This was to contain (among other things): the sites, extents, and intervals of all places, with their names attached, where each river arises and ends, how the shorelines bend, and how Ocean both circles the earth and intrudes on the land. Some of this information could have been conveyed verbally, and some of it perhaps was (the distances are a likely candidate), but sites and the origins of rivers and bends in the seashore are hard to imagine in anything but pictorial form. This seems very much like Agrippa’s map in form and context. Beyond the explicitly educational purpose, the appeal to the emperor may suggest that this, too, had symbolic value as a gesture of authority. The last map I will discuss is also at the margins of this study. The Peutinger map (figures 5.15, 5.16), named after an early modern owner, depicts the Roman Empire plus considerable territory to the east, as far as India. The object we have dates from

106 Presumably along the lines of the attempted reconstructions collected at Brodersen 2003.271–​2. 107 That Mettius Pompusianus could be accused under Domitian of treasonous ambition under for having a world “map” in his possession strongly supports this kind of reading, though it is less clear from our evidence how cartographic the representation (depictum orbem terrae) in question was. See Arnaud 1983.

192

192 { Mosaics of Knowledge

FIGURE 5.15  

Tabula Peutingeriana

http://​digital.onb.ac.at/​rep/​access/​open/​10002029 (section 7, detail) © Österreichische Nationalbibliothek

FIGURE 5.16  

Tabula Peutingeriana

http://​digital.onb.ac.at/​rep/​access/​open/​10002029 (section 7) © Österreichische Nationalbibliothek.

very roughly 1300, but powerful arguments have been advanced that it is a copy of an original composed between the early second and early fourth centuries.108 The 108 I follow here the account of Talbert 2010, esp. 83–​4, 133–​6, and see also Salway 2005.119–​35. Talbert goes on (2010.142–​57) to argue more specifically for a date around 300. Contra Albu 2014 (medieval date) and Rathmann 2011–​12 (Hellenistic, albeit with later revisions); on the arguments of the latter see note 111, this chapter.



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map has two very striking features. The first and most immediately apparent is its extremely elongated shape. Even though the far western segment is missing, the surviving part measures nearly 7 meters long but only about 33 centimeters high.109 The second distinctive feature has to do with the information inscribed across the various land masses. In addition to landmarks represented by various standardized icons, the map presents an enormous network of roads denoted by single red line segments. Moreover, the map lists distances between the major landmarks just mentioned or minor ones represented by name and a jag in the road (as in the highlighted circle). Both of these features have led some commentators to suggest that the Peutinger map is not properly a map after all.110 On the one hand, the elongated form and near elimination of open water mean there is no uniform scale. For instance, Italy is spread across a third of the panels and runs essentially east–​west (see figure 5.16). The image here covers roughly the southern half of Italy. By contrast, farther lands like India take up only fractions of the far right panel, and all open water is compressed into narrow streams. There is no correspondence between the labeled lengths of road distances and the measurement of those segments on the map itself. The prominence of roads, landmarks, and associated distances is strongly reminiscent of the written itineraries that survive in both inscriptions and manuscript collections. Hence it has been claimed that the object is nothing but another collection of such itineraries, distinctive only for the decoration that surrounds it. On this account, the Peutinger map is another piece of evidence for the dominance of a route-​oriented worldview; its seemingly maplike figures are irrelevant ornamentation such as grew up around the diagrams in the land-​surveying manuals. This view is at least misleading. It would be bizarre to deny a connection to the itinerary tradition, but to collapse this very different form of document with those lists based on (partially) shared content begs the question. Obviously, both are geographical representations in some broad sense, but what kind of spatial structures do they imply? The shape of a list matches naturally with the linear/​route form, but this object is at least a network. As we have already seen, networks are not routes. Moreover, Talbert has argued forcefully for an even stronger claim in this case. The peculiar shape of this map is possible only if we imagine a mapmaker who already had a reasonably “correct” (from a modern point of view) geographic vision in mind. The mapmaker compressed and expanded the various landmasses in idiosyncratic ways, but he preserved their basic topological structure including, importantly, the ways the coastlines, rivers, and mountain ranges are arranged relative to one another. Moreover, at least some of the human landmarks must have been part of this base before the routes were fitted in; just following the lists of itineraries could not by chance reproduce the right topological relationships in the

We have eleven panels; at least one is missing, but more likely up to three. Janni 1984.61–​2; Arnaud 1989.12, 15; Brodersen 2003.179–​80, 186–​7.

109 110

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194 { Mosaics of Knowledge placement of all the other landmarks. Finally, Guckelsberger 2015 has pointed out that the map is surprisingly regular in representing longitude; pairs of sites that are north–​south of one another in reality tend to remain so on the map. The Peutinger map must have been produced by transforming, at least mentally, a roughly correct model of the Roman world.111 It is too complex to have arisen from the formless data of itineraries and still come as close to “reality” as it actually does. In fact, we have already seen transformations of this sort—​though much less extreme in both magnitude and irregularity—​in the Orange survey maps (inv. 12) and the FUR. Also like the FUR, the Peutinger map is not temporally coherent. It includes, for instance, both towns destroyed by Vesuvius in 79 and routes through Roman Dacia that did not exist until the second century. Its extreme shape and density also make it hard to read at a distance (especially if it were not mounted at eye level). These features significantly reduce the value of the map for actual travel planning. It is not surprising, then, that Talbert 2010.142–​57 has also proposed a similar display purpose for it. The map illustrates the notional range of Rome’s power and apparently goes to some cartographic lengths to center Rome and Italy in the empire and the world. The road network thus becomes less a practical guide and more of another graphic illustration of the extensive and intensive reach of Roman power.

Maps as Information Technology If we take comparative evidence seriously, it suggests that we should be suspicious of claims that linear routes were “the” Roman way of imagining space. While the route/​map distinction is widely important, it hardly exhausts the possibilities of human spatial cognition. In earlier work I have argued that a crucial step in understanding the Roman conception of space is to appreciate its internal diversity. I  have tried to demonstrate this in some detail in the contexts of both domestic space and historiographic writing.112 Talbert and Salway have made independent, parallel arguments in the geographical realm.113 For instance, although preserved

111 Rathmann 2011–​12 may be right that the background map is essentially Hellenistic in form, but on this account the itineraries need (mostly) to have been plotted before the compression took place, so the composition of the map needs to postdate most of the data collection. This is all the more true if, as Guckelsberger 2015 has suggested, an even distribution of names across the map face was one of the designer’s desiderata. Rathmann’s more general claim to bolster his theory—​that the Peutinger map and the diagram on the recently discovered Artemidorus papyrus are examples of an always already compressed form of “chorographic” map—​relies too heavily on (a) just two examples; (b) interpreting all ambiguities in the papyrus in favor of similarity with the map; and (c) reading Ptolemy’s sharp, prescriptive distinction between geography and chorography as descriptively valid across Greco-​Roman culture. The last point is demonstrably false (Prontera 2006). 112 Riggsby 2003, 2009a. 113 Most generally, Talbert 2008.22, Salway 2012. See also more tentative remarks by Whittaker 2002.101.



Representing Two Dimensions }  195

itineraries obviously show the importance of route-​based thinking, the way they are grouped and captioned in some collections also shows at least a general two-​ dimensional awareness of how Roman provinces were grouped. If we then expect Romans to have had multiple models for spatial understanding, we will not be surprised if they also have multiple graphic modes of spatial representation, and the different forms will be used for different, specific purposes. This is more or less what we in fact see. Thinking about the cognitive issues makes it harder to ignore what all but the most skeptical scholars admit to be (exceptional) ancient maps. So, for instance, Janni does not take seriously the maps produced by survey (much less building plans), in part because for him they are merely the reproduction of “an area embraced by a single act of perception.”114 But the seeming naturalness of these large-​scale representations is primarily an artifact of our extensive experience with such things. (One might compare here the observation, mentioned in passing in ­chapter  4, that mere faithful observation will not lead a painter to stumble into single-​point perspective. In fact, it is a conventionalized form of representation.) The discussion of plans in the previous section showed that the same applies emphatically there. Some of the individual symbols used are purely conventional, but more important, so is the basic procedure of taking and then combining notional sections of buildings. This is an imaginative process; it does not reproduce anything the drafter had ever seen or even could have seen. It is possible that the same process was simply never applied on a different scale, but it seems to me that the burden of proof is at least shifted. We would need some specific explanation of why the difference in scale was relevant. Romans used a variety of maps, with a variety of degrees of formal rigor and for a specific set of purposes. The two principal uses we have seen are recording property rights (land survey, but also the water inscriptions) and individually or nationally aggrandizing display (FUR, map of Sardinia, map of Agrippa, Peutinger map). If we ignore the (largely arbitrary) distinction of scale, these are also the most prominent uses of the plans we saw. It might be tempting to reduce this to a single function by arguing that the display function was an epiphenomenon of recording possession. I have already suggested nearly as much in the individual cases, and the same could be said of numerous other geographical (but non-​cartographic) representations.115 On the other hand, other interpretations (such as advertisement of euergetism) are possible in several of these cases. More seriously, the display maps appear to be much richer than those that clearly regulate possession, especially in

114 Janni 1984.57 and also more generally 63–​5 distinguishing “mere” perception from abstract transformation. Cf. also Arnaud 1989.25 and Rambaud’s 1974 division of Caesarian representations by scale. 115 For instance, Pliny’s Natural History as a whole (cf. Murphy 2004), city personifications in triumphal processions (cf. Holliday 1997), or the placement, across the empire, of honorific statues as ordered in the tabula Siriarensis (CIL 6.40348; cf. Rowe 2002).

196

196 { Mosaics of Knowledge their depiction of natural features. At the same time, they seem to allow for a much wider range of regularity in scale and the like, perhaps in parallel with the special metrological regularity of land survey we saw in c­ hapter 3. I would prefer to think, then, that the display maps, at least those of large areas, either exist as independent type(s) or, more likely, depend on other “real” ones that are less well attested, and may be transformed in various ad hoc ways. We do have enough evidence to suggest where some of those “real” ones could have been used. Eumenius’ map was educational. Articulated globes and the maps that accompany texts of Lucan and Sallust are similar in expressing a theoretical, but not thereby merely symbolic, geography. They explain in outline how the world is put together. More practical, presumably, would be whatever map lay behind the Patara inscription (presumably some sort of administrative document) and such military maps as eventually developed. And we can almost certainly add the smaller, building-​oriented plans, which seem to have sprung from official functions, whether or not they are state documents. And, while we do not know that graphic representations ever captured the kind of provincial and road-​network structures that Talbert and Salway have found, it is not clear that we would expect any of them to be preserved, either. Utilitarian documents would be more likely to require editing, and so would more likely be on perishable materials, and at any rate would be discarded once obsolete. It is the “useless” display versions that will have been preserved. As noted previously, we are almost certainly missing an enormous quantity of survey maps and architectural plans. At the same time, some skepticism has to be admitted: Roman maps and uses for them seem genuinely to have been quite rare by modern standards.116 Individual navigation and city planning, for instance, are unattested and seem unlikely. Mapping at the provincial level is rare, if not entirely unattested, and perhaps never done in the rigorous manner of smaller-​scale land surveying or larger-​scale scientific geography. So what to make of the contrast? Twenty years ago, Richard Talbert 1997.177 rightly asked (reviewing the first edition of Brodersen’s monograph): Could landowners’ very familiarity with [survey] maps in fact have reinforced their inability to see the potential for comparable smaller scale representations of larger areas? Did it make a difference, too, that the men who drew survey maps ranked socially below the Roman upper classes and even the local elites? To take his last point first, I  think there are clear status issues, though I  would describe them somewhat differently. I have argued that this kind of status distinction restricted the use of illustrations in texts. Elite discourse preferred the verbal; drawings were for craftsmen. Both Vitruvius and the archeological remains suggest

116 Arnaud 1989.16 and Brodersen 2003 stress, fairly enough, the lack of textual references to the use of maps in particular cases. It might, however, be pointed out that by the same measure, we would have great doubts of the use of itineraries as well.



Representing Two Dimensions }  197

that they were in fact widely used among a certain set of craftsmen. But, in contrast to some of the other information technologies discussed in this book, there is also evidence for their broader intelligibility (whether or not nonspecialists generally produced such plans). The display value of maps and plans, whether for private patrons (as in the case of the tomb plan and the baths mosaic) or for public ones, including the state (say Agrippa’s map or the FUR) hinges on the average viewer being able to grasp that a map or plan is a representation of a certain kind of space, whether or not that viewer understood or cared about the details. Yet that same evidence also cuts the other way. If those maps were being used because they were accessible to persons of lower status, they are still being used by elites to assert higher status. Given that apparent contradiction, I would like to reframe the analysis slightly, using terms that have already come up in a couple of the earlier chapters. Let me suggest that the inelegance of textual illustrations is not strictly a consequence of their being graphic rather than verbal but instead lies in the combination of the two modes. Elites have no generalized problem with self-​presentation through artistic means—​paintings, sculpture, and architecture—​ whether as representations of the subject (at least in the first two media) or as objects in their own right. But illustrations are inherently paratextual, and as ­chapter 2 argued, paratext raises issues for Romans even in purely verbal forms. In fact, I have argued elsewhere (2007.92) that the entries in Latin tables of contents were phrased to gloss over just this gap between the segmentation of a list and continuous discourse. In parallel, Netz 2013.237–​40 has independently argued that Greek literary works lack illustrations and some other paratextual elements117 because their (written) texts are construed as tools for (notionally oral) performance.118 Elite discourse is linear; illustrated texts are discontinuous. A  stand-​ alone map is much closer to an art object than it is to a textual illustration. There is no danger it will be mistaken for broken speech; it is a different form of representation of its own.119 Be that as it may, let me return to Talbert’s first question and see if we can make some progress there. That is, again, “could landowners’ very familiarity with [survey] maps in fact have reinforced their inability to see the potential for comparable smaller-​scale representations of larger areas?” I think this is on the right

117 His list of features includes word divisions and punctuation that are present in classical Latin texts, but I suspect that just these features could have been seen as an aid to performance in contradistinction to his other items, such as font size or color. 118 Exceptions are either very marginal types like picture and isopsephic poems (for which see Luz 2010) or imagistic graffiti (for which see Kruschwitz 2008.256–​7, Maulucci 1993). For the former the term technopaignia explicitly denotes their technical character and their unseriousness. Graffiti, whatever the undeterminable status of their writers, represent a form that claims no status for itself. 119 This seems to be true even if the map is captioned, since captioning seems acceptable even on highly “artistic” representations. A similar argument should, I think, be made about tombstones which offer both text and images that describe the life of the deceased. These are neither illustrated text nor captioned images, but in the first instance are monuments ornamented with both text and image.

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198 { Mosaics of Knowledge track, but I’d like to change perspective. “Comparable smaller scale representation of larger areas” is descriptively clear, but it strikes me as too broad a category to attribute, even potentially, to Roman agents. The general trend we have seen throughout this book is to deploy particular technologies, even the relatively “easy” ones, in quite particular contexts and for quite particular aims.120 We have also seen this in this chapter. The practices of drafting plans, surveys, the Peutinger map, and (as far as we can tell) most of the lost-​but-​remembered maps are clearly different. But even within those categories, there may well have been diversity. For instance, I argued that the various building plans, which have sometimes even been taken as fragments of the same stone, show at best a general family resemblance. Plans made at different times for different purposes take on different forms. The same is true of the three fragments of bronze survey maps. Only one lists grid coordinates. Two of the three depict graphic features other than the grid boundaries, and two give both names and figures for individuals, while the other has collective information. At least the group/​individual distinction must reflect some difference in function, and it has been argued that features of one of the fragments from Verona take it out of the realm of centuriation stricto sensu (see note 96, this chapter). We can see the same kind of use-​driven diversity of spatial representation at the cognitive level even in a single author. Rambaud 1974 argued that in Caesar’s war commentaries, space was conceived in very different ways depending on the scale of what was being described. I later argued that his typology is not descriptively incorrect, but probably does not get at the origins of the distinction. Even in ordinary language, speakers vary the perspective from which they describe spaces, taking “perspective” in both its concrete and expanded metaphorical senses. The choice of perspective in either sense is driven by utility for local purposes. Differences in scale, I  would then suggest, are another effect stemming from the same cause (differences in local use context). (2009a.156, citing Tversky et al. 2000 for the “ordinary language” claim) What was true of Caesar is true of Roman mapping in general. What we need to ask, then, is not what the Romans might have been able to do with small-​scale maps but, rather, what particular use among the many possibilities might have been so valuable as to justify by itself the considerable effort that would have been required to produce them? What map would be so irresistible as to be what a decade or so ago would have been called a “killer app”? That is a high bar, but related considerations suggest that it still understates the obstacles to broader map use. I have just argued that context-​specificity meant that a particular use would need to be highly desirable to justify expending effort on



Cf. Guckelsberger 2014.41 for geographical representations as “fit-​to-​purpose.”

120



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creating a new map, even if the new use were a conceptually straightforward extension of existing technology. But the notion of context-​specificity might suggest that at that conceptual level there might not even be a single technology to “extend.” It has been noted that there is no standard Latin equivalent of “map,” and for some scholars this is at least emblematic of the absence of the thing itself. I would suggest a different version of the same basic intuition.121 What, we may ask, is “the” Roman practice that was putatively never extended? While particular practices like land surveying could have provided models for extension, it might be wrong to group together all the forms of mapping discussed here. Such a grouping was likely not a Roman category, as we can see both institutionally and formally. Consider the institutional location of some of the objects we have discussed. If, for instance, the aediles held the records of street frontage (since they were in charge of the streets), it is not clear that those records would be available to different officials (much less to the general public). Additionally, the incompatibility would be formal. Different maps varied in scale, orientation, units of measurement, and content. Moreover, we know of no cases in which any of those features were formally specified, so there would be no straightforward way to “translate” maps that were not initially compatible (or even to tell reliably whether they were compatible in the first place). Does that square really mean a square pillar or just a major one? Is the street outside your house actually as wide as the one outside my house? And if we extend our view to other kinds of objects, like the maps painted on walls, there is seemingly much greater diversity in form. The most optimistic histories of Roman mapping have suggested that existing surveys could or even did serve as the basis for a general mapping of Roman territory in the manner of the U.S. Geological Survey or the British Ordinance Survey. This apparently did not happen, and in fact it could not have happened, for both kinds of reasons just discussed. Institutionally, surveying was tied to the establishment of colonies or other occasions for the distribution of land by the state to individuals. So the map of Campanian properties was in the hands of the censors only because the state had originally given out that land in the first place.122 In principle these records should have been gathered and stored centrally by at least the time of Hyginus (158.28–​30C; second century?), though with unknown effectiveness.123 At any rate, this is clearly a bottom-​up process. Julius Caesar’s project to “measure the world,” if not entirely legendary, was too small to do anything but resurvey selected communities (if it was not, in fact, to locate particular sites on the globe).124 There is no general practice of

121 Keeping in mind that arguments that “lack” of a word implies lack of a concept are never conclusive in themselves. 122 Granius Licinianus p10F. The passage makes it clear that there had been no such map prior to the nationalization and redistribution of what had been in private hands. 123 The one known appeal to this archive failed. See CIL 10.7852 with Mastino 1993. 124 See Nicolet and Gautier-​Dalché 1986.

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200 { Mosaics of Knowledge purely descriptive survey. Formally, surveying was carried out by standardized methods, but produced results that were not always precisely equivalent. The size of the plots produced clearly varied from place to place, and there are some hints that the units of measurement may have varied. (We can compare here the variety of units actually used in placing Roman “mile” stones.) Even in theory, there were many options for the orientation of the survey grids, and still more are found in practice. Finally, as a practical matter, even where centuriation was at its densest, not enough land was surveyed to make combination practical. Essentially the same thing can be seen in textual form (again in Caesar): the different levels of organization are so different from one another in structure as to be incommensurable with one another.125 But what, one might ask, would happen, if a single individual of sufficient power and vision—​say, an emperor—​were to try to overcome these barriers and build up a composite representation? In the case of turning centuriation into a basis for broader mapping, probably nothing. No amount of vision could make up for the incompleteness and mutual incompatibility of the records with which his staff would have had to start.126 Nor would it change the fact that standard Roman surveys would have nothing to say about uninhabited territory. A better case—​in fact perhaps the best case—​is represented by the FUR. This combines existing resources and, perhaps, also some novel work to move, as far as we can tell, from one order of magnitude to the next one. But it does so at the cost of giving up most informational value. Textual data seems to be stripped from the original sources. In the big picture, the graphic representation was probably fairly reliable, but in matters of any detail it was much less likely to be correct or even visible. My general view of Roman map use, then, is as follows:  Most of the maps Romans used were less predictably constructed than modern ones, whether in terms of scale, full two-​dimensionality, or both. They showed variability in more specific features, as well. Romans used fewer maps for fewer purposes than modern Western societies do. Nonetheless, there do not seem to have been generalized cognitive obstacles to their use. Not only have we seen specific graphic and textual instances, but it also seems that maplike objects were legible enough to make them a suitable form of display both by the state and by more modestly situated individuals. Reproducibility issues probably had some constraining effect, but were not, I think, likely to have been decisive. If, for instance, herbals were hard to copy reliably, then one might expect problems with maps. Ptolemy worries that overcrowding could spoil even a well-​planned map. And the apparent evolution

125 Riggsby 2006.25. 126 It has been suggested to me that gaps might be made up by recourse to other kinds of records: details attached to the road system, army camps and troops, tax lists. It seems to me that this simply multiplies the problem of incompatible and quite incomplete data sets, and even then assumes a lot about the central collection of these other types of information.



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of the illustrations for the Corpus Agrimensorum might well demonstrate a more general split between the goals of mapmakers and those of the artisans who made later copies. On the other hand, many of our maps, most obviously the engraved ones, seem to be one-​offs. And more personal maps would not have had to survive as many generations of copying as manuscript texts, since their utility would be more closely bound to particular times and places. Most important, the relatively schematic nature of many ancient maps is presumably an advantage here. It would be easier to preserve the topological structure of an original than its precise scaling; the most “distorted” illustrations in the Corpus appear to manage at least this. Why were more kinds of maps not used for more ends? First, we should expect no general answer to that question. The issue should always be why maps were not used for individual purposes. Second, “map” was probably not as obvious a solution to any problem in a Roman context than it would be for us, for such a gen­ eral category may simply not have existed. At best, inspiration for a new form of mapping would have had to come from something more specific, like survey forma. Finally, neither these general considerations nor most of the subordinate details have purely to do with maps as such. The occasional, ad hoc character of Roman maps is just another case of the stubborn specificity of Roman information technology in general.

Chapter Appendix CONCORDANCE OF ROMAN BUILDING PLANS This chapter discusses all Roman building plans known to me, but very similar sets of material have been gathered in a variety of earlier studies. Since there is, however, no standard reference system that includes the entire set, I provide here a basic numeration plus page references to treatments of the various plans in the earlier literature (columns 3–​7). These objects are typically referred to by modern place names (column 2), typically based on their find spots. For items 12–​15, not included in most of these lists, I have also given an original or major publication.

via Anicia colle Oppio/​via della Polveriera* Foro Transitorio/​di Nerva Foro di Augusto Urbino* Perugia Isola Sacra/​Porto necropolis Amelia Baths/​via Marsala Priorato di Malta/​Aventino Tivoli Orange (Piganiol 1962) Capua (De Francescis 1983; Inglese 2014) Pantheon (Haselberger 1994) Brescia Capitolium (Dell’Acqua 2014)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

43–​9 41–​3 61–​6 —​ —​ 37–​41 56–​9 51–​6 —​ 23–​33 33–​6 —​ —​ —​ —​

ALMEIDA 2002

2006

26–​7 27–​8 28–​9 29–​30 30–​1 31–​4 34–​5 35–​6 36–​7 —​ —​ —​ —​ —​ —​

RODRÍGUEZ-​

AUTORI VARI

*Both no. 2 and no. 5 are occasionally associated with the via Labicana. † Rodríguez-​Alemeida wrongly assigns this to CIL 6.

LOCATION

#

—​ 207 —​ —​ 207–​8 208 208 208–​9 209 —​ —​ 207 —​ —​ —​

ET AL. 1960

CARETTONI

—​ 198–​9 —​ —​ 186–​8 188–​91 198–​9 —​ 191–​3 185–​6 —​ —​ 210–​1 —​ —​

HEISEL 1993

—​ 6.29846 —​ —​ 6.29847 6.9015/​29847a —​ 11.4419 6.29845 6.1261 14.3767† —​ —​ —​ —​

CIL

5.5 —​ —​ —​ 5.4 —​ 5.7 —​ —​ —​

plate 8 —​ —​ —​

VOLUME)

FIGURE (THIS

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6 }

Conclusion Where Are We Now? While the discussion of maps in the last chapter started to bring together many of the themes of the book as a whole, it may still be helpful to do so a little more explicitly and systematically before I move on to two suggestions about where to proceed from here. I surveyed a variety of advanced Roman information technologies: nested numbered lists, tables, specific measurement systems, maps, and others. Use of these technologies ranged from the merely limited to the nearly nonexistent. In one sense, of course, that is simply a reflection of the very selection of “advanced” technologies; if there had been chapters on simple lists or counting or itineraries, the situation would have been different. But that does not explain why the rarer forms are rare. In this first section I want both to review some factors that appear to be relevant to the distribution of information technologies and to offer a more precise characterization of their use than “rare.” I begin with some negative observations. In formal terms these technologies are somewhat more sophisticated than their more common counterparts, but not overwhelmingly so; as I mentioned in the book’s introduction, most of these devices are familiar enough to schoolchildren today. Nor do they generally rely on difficult-​to-​ acquire mechanical sophistication. (The major exceptions to this point, treated at length later, have to do with precise reproduction of images.) Nor, finally, are they strongly associated with environments of great wealth or bureaucratic culture.1 The point about bureaucracy requires a little nuance, since I certainly do not mean that there is no connection. State archives were home to nearly all of the nested lists. 1 See the section “Going Forward I,” and c­ hapter  5, notes 122 and 123 on state archives, which could contain considerable quantities of material, but rarely collected systematically and not organized well for later use. Hopkins 1991.141–​2 speaks of the use of “alphabetical files, file numbers, [and] page numbers” in Roman Egypt because “knowledge had to be stored in such a way that it could effectively be recalled.” This exaggerates the frequency of any of these devices in the records (see, for instance, ­chapter  2 on alphabetical lists), but perhaps just as important, it overstates their value. His specific examples (which I think are in fact representative) are all about verifying an already known or suspected piece of information, not novel research or combination. These records are more about authority than recall.

203

204

204 { Mosaics of Knowledge Most tables, the most generalizable measurements, and a significant fraction of suspected maps arose in the context of complex land surveys. But there is also a large element of coincidence here. The nested lists and tables arise, I argued, from the concrete practices of making and maintaining specific kinds of records, not from the broader context of “bureaucracy.” Precision measurement and mapping seem to have more to do with other specifics of the task (the practical and ideological importance of land ownership; the relative ease of standardizing measurements of length). It is telling that, by contrast, the numeration of chapters of laws does not give rise to either numbered subsections or obligatory cross-​reference, despite complete government control over their composition. Romans’ limited ability to make precise reproductions might have been expected to limit the use of some technologies, and that did turn out to be true. Difficulty in reproduction seems to have played a role both in limiting the use of illustrations in texts and in creating a preference, when illustrations were used, for relatively schematic ones. A similar explanation might be one reason that architectural plans were apparently a more routine tool than maps. (I refer here not to sheer quantity, which is irrecoverable and might at any rate be biased toward the more numerous buildings. Rather I contrast the near-​silence of our narrative sources about maps with their matter-​of-​fact reference to plans.) Among the maps that were produced, issues of reproduction may have encouraged the same looser, more schematic form that we see in textual illustrations. On the other hand, the precise mechanisms and circumstances involved did not always turn out to be so obvious. Technical limitations would have made it impossible to produce weights and measures as precisely standardized as we have today, but in the cases where we can best tell (weights, sundials), there don’t seem to have been attempts to push the limits even of the available technology. Issues of reproducibility played a part in another tendency, though without fully explaining it. Conveyors of information were cautious about relying on specialized formal conventions. The most general instance of this caution regards the various kinds of material I have described as “paratextual.” Under that heading we can include whole blocks of material—​tables, tables of contents, entire illustrations—​that did not fit into the linear flow of a text. It also includes things like standardized segmentation of texts, whether by pagination or by numeration of sections. Reading these properly relies on knowledge of conventions beyond mere literacy. Beyond paratext we may think, among the (near-​)tables for instance, of both the redundant use of classifying terms (symbols for measures and costs) and the unwillingness to recognize blank space as meaningful in the specialized context. That is, composers of texts do not ask the user to read “header” information into individual entries on the basis of their position within the structure. In plans, owners’ names are typically given in the possessive form, rather than a neutral reference form. Simple lists, though not directly studied here, seem also to cling to the syntax of imaginary sentences. Moreover, though the evidence is very limited, it may be the case that building plans relied on numerical labels for lengths, rather than on scale,

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even in cases where effort seems to have been devoted to drawing to scale. And the more elaborate quantification that would have been necessary for information graphics seems not even to have been attempted. Recall that in the two “exceptions” (sundials and wind gauges), the variable graphic component is literal rather than conventional. Even where texts are broken into numbered segments, obligatory cross-​reference is avoided. In part, as I suggested, this may stem from practical concerns. All the forms of paratext cited require precise reproduction of at least page layout. The problems are often more acute for the specific devices. Will users be able to measure a line segment correctly or, indeed, will the scribe or engraver get that length right in the first place? Will the reader find a numbered copy of the same text for reference? But there are also cultural preferences at work. In ­chapter 5, I argued for the conceptual conflation of texts, especially prestigious ones, with oral discourse or performance. This collapse of categories militates against use not just of paratext (as I  have already argued) but also of most of these other devices just listed. In the case of tables, it would break down linearity if the reader were forced to refer up or across to get information on units or be able to interpret blank cells at all. Obligatory cross-​reference is by definition nonlinear. But the caution seems to be generalized even beyond cases where this is directly an issue. Preserving the syntax of a more fully imagined utterance in map legends or in lists—​rather than falling back on a default case—​presumably does not make them vastly easier for a reader to process linearly. It can, however, reflect the producer’s inability or disinterest in thinking outside the normal world of oral discourse. A very different set of constraints that we have also seen involves what might be described as avoidance of answerability to reality. Two aspects of metrology fall under this rubric. On the one hand, the localized standards recognized by law limit the possibility that outsiders can check measurements. The same is true of more implicit localization, such as the common use of unlabeled (and not discernibly standardized) weights or of sundials which, through sloppy construction or relocation, were not calibrated for their location. On the other hand, implicit and explicit reliance on proportions means that there is no question of the “right” amount for many recipes and other procedures. The same is true of the one kind of quantification that is freely practiced—​the assignment of monetary values. Tables, we noted, are more likely to be used to bring facts into being than to record observations. One factor in the predominance of plans over maps is that the former are prescriptive, the latter descriptive. And among maps, the seemingly most common type (centuriation formae) are themselves largely prescriptive, assigning ownership more than tracking features of the terrain. Most of the textual illustrations we saw were not answerable to reality: prescription in Vitruvius and the sex manuals, nonrepresentational symbols in the brick stamps, pictures addressed to a (for us) fictional audience in the defixiones, essentially fictional content in Varro’s collection of portraits. It may not be an accident, then, that the spatially sophisticated paintings we examined in ­chapter 4 belong to a fictional genre. The most prominent

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206 { Mosaics of Knowledge counterexamples are probably the illustrations in herbals, and we saw that those were both criticized by Pliny and seemingly avoided in Latin more generally on precisely the grounds of likely error. All these tendencies are merely that—​tendencies rather than absolute rules. One context in which they are less likely to operate (or, perhaps, one countervailing tendency) is in tightly closed environments. The one indexed table of contents we saw was for the most specialized work: a set of drug recipes. Tables were used within individual military units or in professional land-​surveying circles. (Survey maps were sometimes publicly displayed, but reference to coordinates was actually more important to the in-​house registers held in state archives.) Similarly, only professional clerks would normally have needed to navigate the use of nested lists. Scale representations and standards were used on individual construction sites. That last set of considerations leads me back to the general characterization of the use of advanced information technologies. While it is correct to describe them as “rare,” it may be more informative to say “local” or even in some cases “hyper-​ local.” Across the empire, people used overtly different units (e.g., feet vs. cubits), homonymous but still clearly different units (e.g., various kinds of cubits, modii, and feet), and (apparently in practice, if not in theory) different standards for the “same” units from town to town, market to market, or even stall to stall. The situation is striking similar to that in two other areas I have only touched on in this book, but which have been studied carefully by others. Phang 2011.324–​7 notes the un-​“modern” character of the Roman military bureaucracy, deploying across time and space both differing types of documents and different forms of individual types. Among the several rosters and reports by which the Roman army kept track of its soldiers, only one (the annual pridianum or unit strength report) “was intended to be read by superiors not already familiar with the daily operation of the unit” (330). Moreover, examples of these do not take on fully standard form even in our quite limited sources (329). In another realm, LaGroue 2014.119–​20 observes that, at least in the republican period, accounting records were praiseworthy for being neat and presentable, rather than following any formal principles or practices. As with weighing and measuring in the marketplace, these forms of recordkeeping presumably have a serious informational purpose, but it tends to be localized. What does this commander want to keep track of ? In what order does this landowner want to see things? What do they want in those respects this month? Before returning to general conclusions, I  would like to note two further points about these combined examples (that is, weights and measures, the army, accounting). First, the observed diversity is, of course, not unconstrained. There are clear “family resemblances” among weights and measures, among military documents, and among accounts. On the one hand, this suggests that there could be some interoperability even in the absence of universal standards. One pound or document might be “good enough” to take the place of another for some purpose. On the other hand, it increases the possibility of confusion and mistake. In the absence of universal norms, the choice an individual would have to make would be

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just to accept the risk, or to do extra work to remeasure or redocument for the new purpose. Second, the term “local” requires some clarification. In many cases, it is a reasonably straightforward geographical term—​pertaining to a particular province, or valley, or community. In other cases, it may refer to a geographically diverse professional community, such as those of soldiers or land surveyors or physicians. But most strikingly, it can seemingly often mean a micro-​community of approximately two. A commander and his clerk, a customer and a vendor, a pater familias and his son—​such dyads can produce their own micro-​standards, especially in cases where there is an ongoing relationship. In fact, as I argued before, measurement by proportions can be seen as creating local communities not even of two people, but of one. Local variation is easy to see in the case of weights and measures because the basic practice of weighing and measuring is essentially universal. For some of the specialized technologies treated here, it is a little more difficult to distinguish between the simply “rare” and the “local” in any more specific sense. Still, we have seen traces. Even within the quite narrow temporal and generic range of landscape paintings, we observed three overlapping but distinct systems of spatial representation. Individual workshops have their own conventions. The surviving building plans all look alike at a glance, but present different kinds of information and rely on differing representational conventions to do so. This could represent different workshops and/​or simply different projects. Tables and nested lists appear only in quite specific locations defined by profession, and show signs of having arisen independently in those locations. The most cryptic illustration types, the speaking signa, appear to circulate within or only just beyond individual firms. That is, when we have more than a few examples of any of these kinds of information technologies, we can distinguish specific forms among them or at least point to very specific environments that host them. The fact that at least some of these devices seem to have been invented multiple times points to a second characterization. In discussing tables, I alluded to Romans’ self-​image as a practical people. One side of that image focuses on prioritizing deeds over words. But that does not mean that is a pure ethos of striving; it is an ethos of getting the particular job done. Greek speculative philosophy and natural science were the canonical targets of mockery from this point of view, but I suspect that fully modern bureaucratic regularization might well have seemed similarly superfluous. Thus we have seen no attempts at deliberate technology transfer from one area to another (though I would not rule the possibility out altogether). Nor do we even see much in the way of regularizing technologies that already share that “family resemblance.” On this point, too, it is hard to prove that any particular factor is relevant in cases where a technology simply does not appear. It might, among other things, simply be unknown. But there are hints of particular cases in which minimizing effort seems to be a principle in its own right. “Depth” of alphabetization is chosen on an ad hoc, project-​by-​project basis. Most paintings simply do not try to organize as much space as the type of landscape we examined. Land

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208 { Mosaics of Knowledge surveying is apparently never carried out for descriptive purpose but only for (re-​) assignment of possession. This is the context in which I  think it makes sense to speak of “negative feedback loops,” as I did in several chapters. You don’t have to presuppose a tendency toward technological progress to observe that local cost-​ benefit calculations can be very local, indeed. Agents will accept little or no cost to themselves to make their work useful for someone else’s project. That refusal may create more work in the aggregate; in a world where recorded weights and measures are ambiguous or untrustworthy, many more measurements need to be taken (hence the robust availability of professional mensores). What is “practical” for the individual may be a burden for the collective. The net result of all these choices is a fragmented or, as I  described it in the “Brief Orientation,” a tessellated informational landscape. Information technology varied from place to place, time to time, profession to profession, and so on and so actual information would not flow easily across those boundaries. In one respect, however, the mosaic metaphor does not adequately capture the complexity of the situation. As the individual chapters have shown, the divisions operate in several dimensions and at different scales. Hence, the homogeneity of individual tesserae is somewhat misleading here. Virtually every individual would have belonged to a different set of overlapping informational communities. It’s worth contrasting the situation I have described for “advanced” technologies with that for more basic literacy. Woolf 2009.673–​95 makes a compelling argument that, at least at the most basic level, Roman society was not home to multiple “literacies” but, rather, to a more or less generalized single skill. But, as he also points out, this is very much a contingent fact about literacy. In Rome, which lacked a comprehensive educational apparatus, that unitary skill arose from the interaction and overlap of multiple mileux for learning and using literacy. For our more advanced technologies, the required critical mass never existed, and of course there was even less of an educational apparatus in the background. All this has been framed rather negatively, so it may be worth reiterating that using the most powerful or most sophisticated options available in every case is not obviously beneficial. The Romans were, of course, right that doing so would require foresight and advance planning. This would require both more total effort and a redistribution of effort away from the ultimate beneficiaries. Scholars of ancient travel have frequently noted the near total lack of evidence for the use of maps as a means of way-​finding. Instead, itineraries seemed to have served that purpose (in various combinations with appeal to local informants). But that is hardly an irrational choice even from a modern point of view. An old American Automobile Association TripTik (i.e., a strip map of a highway route) or modern GPS directions discard unnecessary cartographic information to focus on the navigational task at hand. A precision-​scaled two-​dimensional map is useful for more speculative purposes or, more generally, for a user whose goals are unknown, but not for one just getting from known A to known B. Selling stone columns that are a little longer than notional standard length means there is less danger of a nasty

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surprise when a component is not large enough to fit into the building you are constructing. And general systems, whether of measurement or paperwork, which do not presuppose a high degree of regularization are much less subject to chain-​ reaction failures if there is an error somewhere. Few documents or measurements would have been passed from hand to hand to hand, anyway. But my central point was not that Roman information technology was primitive (though that is not an entirely unfair description); it lay, rather, in the specific contours of the system. I conclude this section with a methodological observation that relates to that focus. I warned in the book’s introduction that there would be a lot of attention to the definition of various phenomena (tables, maps, etc.). Readers of drafts of individual chapters of this book were generally accepting of that, but when I laid out the whole argument for the first time (to a seminar I was teaching), several students pointed out a tension, if not strictly a contradiction, in the role definition played in different parts of the argument. For “tables of contents” and “tables,” I was generally trying to narrow the scope of inquiry. That is, while the various English terms were useful signals to the reader, I wanted ultimately to discuss more specific phenomena in each case. But for “space” and “map,” I  wanted to expand on some existing usages. I think that this is not a problem—​at least as a matter of the strict logic of the individual arguments—​but my students were nonetheless right to seize on the distinction. The dichotomy between exclusive and inclusive definition arises from a premise I did not fully recognize until completing most of the study. That hidden premise is embedded in the brief sketch, in the introduction, of the history of literacy studies. Stepping back to take in the broadest perspective, I would describe their trajectory schematically as moving through three stages:

1. A more or less unreflective equation of antiquity and today. Literacy was common. 2. Recognition that the equation was false. The apparatus that supports modern literacy was absent and so literacy must have been rare. 3. Consideration on their own terms of ancient phenomena that are not precisely like modern parallels, but are still broadly similar. Granting the general correctness of (2), attention has been redirected to more specific questions of use in particular contexts. While qualitative considerations are at the fore, the more ecumenical view tends to increase quantitative estimates of literacy at least a little.

In the very general sense in which any such schema can be valid, it appears not just in the study of literacy but in many other historiographies, as well. The scholarship on cartography cited in ­chapter 5 traces a similar path:

1. Unreflective equation. Roman maps were common. 2. Recognition of difference. Maps did not exist. 3. Focus on local specifics. Maps in various forms made up a small (but real) part of a package of ancient ways of negotiating space.

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210 { Mosaics of Knowledge Outside the scope of this book, one could see a similar pattern in the development of studies of the economy or of oratorical persuasion. The details vary—​cutting-​ edge views of the economy are more modernizing than in other areas, for instance—​ but the broad pattern seems clear enough. I point this out not just to describe it but also to advocate for making the move to the third stage. This kind of culturalist approach is almost invariably productive in the study of antiquity. We limit our vision too much if we ask strictly if this or that phenomenon—​as defined in modern terms—​existed in the ancient world. Much of what is both true and interesting lies in a zone of broad similarity or likeness, not in absolute identity or absence. The main reason that definition plays different roles in different parts of the book is that the existing historical discourse on different topics is at different points along the trajectory I just outlined.2 When I spoke of “space” in artistic representations and “maps,” I  was in large part responding to scholars who represented the second stage of my schema. They noted the near absence of precisely modern manifestations of those two things in the ancient evidence. Those are reasonable and valuable observations, but they should not (I argued) distract us from the existence and even the prominence of broadly similar practices that are nonetheless specific to the ancient world. Moving from the second stage to the third requires, in relative terms, opening up definitions. The situation with “tables” and “tables of contents” is different. There is little to no previous scholarship on these topics, but the default position seems to be that of the first stage. That is, scholars who label some artifact as a table or table of contents typically feel no need to justify that or even remark on it; the unspoken assumption is familiarity. (The notable exception among these cases, Doody’s 2001 paper on tables of contents, is perhaps a particularly smart and self-​aware example of the second stage.) My ultimate object here is still to get to the third, culturalist stage—​hence my own modest differences with Doody—​but the more immediate task is to separate the ancient from the modern, and that typically involves isolating technologies that are common today but rare or nonexistent in antiquity. Hence, the importance of exclusionary definitions.

Going Forward I: Power and Other Topics While my main hope in writing this book was to open up a (largely) new field of inquiry, the results also have implications for other areas of research. I don’t mean, of course, that longstanding scholarly issues will suddenly be resolved if we merely reframe them in terms of information technology. Rather, knowledge of Roman information technology practice will, I hope, prove to be a valuable and surprisingly flexible new tool in concert with others and in a variety of domains. In some

2 Secondarily, there may be a distinction between binary and analog technologies. In tables and lists, bits of data simply are or are not in particular places; weights, measures, and drawings (including maps and paintings) offer continuous variation.

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cases, this will involve fairly mechanical application of observations about specific technologies. For instance, in the course of the book I showed that informational considerations should make us suspicious of the standard understanding of how Roman theater seating worked, but confirm a strict interpretation of the Roman law of generic sale. I’ll mention another potential example from beyond the book. Roby 2016.9–​10 discusses the difference in descriptive style between ancient “ekphrastic” directions for construction and the much simpler style of modern Ikea assembly instructions. This hinges in large part, as she points out, on the fact that Ikea can off-​load many potential difficulties onto “a complicated infrastructure of manufacture and distribution which, for example, allows me to make sense of what is meant by a part called ‘102509.’ ” What I would add is that that infrastructure includes not only precision milling and containerized shipping but also the reference system that allows an arbitrary number to stand in for a concrete piece of hardware. Here the mechanical issues are presumably sufficient to cause the ancient–​modern difference, but it is not hard to imagine cases in which the informational component could be more important. My argument also participates in a much more general discussion that cuts across many substantive areas of historical research—​the degree and kinds of differentiation or homogeneity of the Roman world in a number of different dimensions. None of these is strictly (or even mostly) an informational issue, but all will have informational aspects or constraints. In the remainder of this section I want to offer three quite different examples of such more complex phenomena. For decades now archeologists and historians have argued about how (and in fact whether) to speak of the “Romanization” of the provinces. At a minimum, it is agreed that we need to break down all the implicit categories; that is, neither “Roman” nor “provincial” is a homogeneous category, nor are they necessarily exclusive of each other.3 Consider an example from the recent legal literature. In a series of papers, Ari Bryen has laid out an important model for the ways provincial subjects in the East (where the relevant evidence exists) came to inhabit the Roman legal system.4 He traces the ways in which subjects mixed and matched a variety of originally Roman legal materials in attempts to harness the immense power of the government to advantage in their (mostly) local disputes. At first sight this looks like what one might call an “oppositional” practice, especially by contrast with what Haensch 1992.240–​4 has argued were the archival practices of the state itself. He claims that by an early imperial date each provincial archive systematically collected a standardized repertoire of legislation and other documents, including items not originally directed at the province itself. Yet there is only one document in his evidence that seems a plausible example of this systematic collection (P Oxy. 2104, a letter of Alexander Severus to the “koinon of the Greeks in Bithynia,” found in

3 For the status quaestionis, see the multiparty discussion in issue 21.1 (2014) of Archaeological Dialogues. 4 Bryen 2012, 2014, 2016.

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212 { Mosaics of Knowledge multiple copies in Egypt), and Martín 1981 has pointed out that it could easily have come to the attention of the officials precisely in being offered as evidence by a party to a particular dispute. This suggests at least the possibility that what we see is not a radical clash between subalterns and the state but, rather, variations (whose range needs to be investigated) on a shared legal style, with both litigants and the state taking a catch-​as-​catch-​can approach to legal documents. Refining and testing that hypothesis would not only be a question of discovering what went into the state archives but also how they were organized. Haensch also argues that over time the state developed topical and other organizational schemes to make this mass of material accessible (at least to itself). The evidence does show multiple persons entering multiple kinds of documents into the governor’s commentarii, but not that any of that diversity reflects organizational principles. Rather, like so many of the shorter records discussed in c­ hapter 2, these commentarii are most easily read as purely sequential records, in which documents are essentially filed under the date on which they were used or received for some particular purpose (which is indeed precisely the normal sense of the word; Riggsby 2006.137–​40). This would also fit well with the picture developed in ­chapter 1 of archives that are indexed to facilitate confirmation rather than discovery of individual documents. If this is the case, then the mere possession of large quantities of documents by the state is less important. Without good search and indexing capabilities, officialdom would be back in a similar position to that of private parties, though with much greater opportunity for windfall discoveries and with more depending on the expertise of individual keepers of the files. Clearer knowledge of how these records were, in fact, kept would thus help us understand the nature of legal culture(s) in the provinces. Beyond this example and more briefly, we might also ask whether advanced information technology might give any kind of party a practical advantage in other intercultural interactions.5 Would anyone, for instance, have had a large enough collection of documents that an index would be significantly more valuable than human memory? And wouldn’t that be even more likely in the case of larger collections of simpler data than the legal material just discussed—​for instance, financial or landholding records moving back and forth between local authorities? And, at any rate, whether or not we want to say anyone has been made more “Roman,” the new shape of such records, negotiated implicitly or explicitly between the various authorities, would make life under the new regime at least a little different. Informational questions are certain to be important to contemporary study of the Roman economy. Consider, for instance, the discussion recently framed by Temin 2006 and Kessler and Temin 2008 vs. Bransbourg 2012 on the integration of the Roman economy. Temin argues for a strong and simple correlation of 5 Many kinds of information, of course, do not lend themselves to this type of manipulation and capture. Styles of pottery and of religious rituals, for instance, were not written down in the first place. The question, however, is not how many things can’t be analyzed this way but, rather, how many can.

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prices at Rome and those elsewhere in the empire, suggesting all are part of a single price-​setting regime. Bransbourg does not deny this altogether, but sees a more complexly segmented market. There are a number of informational angles to this debate. How, for instance, could this price information be transmitted or even be standardized enough to allow for transmission? The localized cultures of documentation and measurement outlined in c­ hapters 3 and 5 would work against unified markets. More generally, the shape of informational culture surely constitutes one of the “institutional arrangements” which mediate and shape the possible behav­ ior of individual agents according to the increasingly popular framework of the “New Institutional Economics.”6 This would again include traditions of measurement and documentation, but also, say, internal accounting and recordkeeping (see ­chapter 2).7 Moreover, there are questions of information availability. Different information structures make it more or less easy to answer certain questions, and agents attend disproportionately to the variables they can see most easily.8 So, for instance, the accounts from Vindolanda make it increasingly more difficult to sort information by date, by counterparty, and by commodity. Building plans were seemingly much easier to come by for the ground floor than for above (in addition to other sharp but idiosyncratic restrictions on their content). How would these kinds of systematic information constraints affect transactions in their respective sectors?9 Finally, I  want to propose a yet broader issue. An old observation, found in many traditions, holds that “knowledge is power.” As it is most widely understood, the proverb is about individually useful objective facts. The more one knows about the emperor’s rescripts, or the motives of one’s competitors, or how to build machines, or when the rains will come, the more powerful one becomes. In recent decades, classicists (as humanists more generally) have devoted considerable energy to exploring a different equation of knowledge and power. This approach, following more and less closely in the footsteps of Foucault, is more concerned with systems of knowledge than with individual facts. Specifically, it is interested in the ways regimes of power and knowledge mutually constitute each other. That is, roughly,

6 The bibliography is already large, but for some initial approaches see Scheidel et  al. 2007 (with the review of Maucourant 2011), Kehoe 2012, and Kehoe et  al. 2015. Erdkamp 2014 worries that “[w]‌hile Temin establishes which formal and informal institutions potentially could have contributed to lowering transaction costs and enhancing the performance of the market, the question remains as to what extent they actually did contribute to the functioning of the market. Assuming that institutions are beneficial because that is what they are for, Temin takes the constructive role of Roman ‘firms’ and collegia more or less for granted.” This seems to me to reflect a more general trend. Practitioners of NIE within ancient history sometimes assume, to a lesser extent than Temin but more than the theory itself requires, that the institutions they study facilitate (not just affect) economic performance. 7 For precursors of this discussion, see the works cited in c­ hapter 2 at notes 42–​4. 8 For some of the cognitive roots of this kind of availability bias, see Kahneman and Miller 1986.144–​5, Kahneman 2011.ch.12. 9 See Terpstra 2013 for an extensive account of the systemic consequences of informational problems. The cases he discusses, however, do not hinge on the forms in which information is stored.

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214 { Mosaics of Knowledge how do the very shapes of categories of knowledge reflect and promote ideologies? So, for instance, Serafina Cuomo’s 2007 essay (mentioned in ­chapter 3) discusses the creation by imperial writers on metrology of abstract systems of measurement designed to make all the things of the empire accessible and accountable for imperial administration. The actual equivalence of things measured as equal is not a natural fact, and I even argued that the metrologers failed to impose their regime in practice. But by creating those specific (and genuine) forms of useful knowledge, such an imposition would not only have been an act of power (that is, something that required power to impose on the population) but also an empowering act (that is, one that enabled future control of material resources by the state). Both these approaches are valid and in fact quite useful, but I would like to suggest taking a third as well, combining the systemic orientation of the more recent “Foucauldian” work with a somewhat more objectivist, workaday understanding of “knowledge” as in the traditional sense. In doing so, I also want to direct more attention to the other term in our aphorism—​power—​and in particular to Anthony Giddens’ remarks on the subject.10 Giddens’ own presentation is embedded in a complex, deeply theoretical account of human action in general (his theory of “structuration”), but I think the relevant points for my purposes can be put more simply. “Power” in this system is “ ‘transformative capacity,’ the capability to intervene in a given set of events so as in some way to alter them.” Transformation is effected through dominion over persons and/​or over things. In either case “both sources of power depend in large degree upon the management of time-​space relations” (1987.7). That is, both presuppose the ability to plan and arrange for the actual and desired locations on things and people over time and across space. The precise ways in which this planning and arrangement can be carried out are dependent on the nature and distribution of information, and thus of information technology. “Surveillance as the coding of information is an essential element of such power, because the mnemonic and distributional advantages it allows over purely oral culture are immense” (47). That is, the collection and storage of data are prerequisites for the supervision of actual behavior. A couple of important observations about power arise immediately. First, even if an institution (say, a modern corporation or the Roman army) possesses considerable power, that power is not necessarily at the disposal of any individual agent within the institution. More specifically, there are a variety of possible relationships between the “scope” of a leader’s authority (how widely can he exert influence across time and space?) and its intensity (how powerful are the sanctions she can employ at a particular place and time?). The high intensity of the rule of an ancient absolute monarch does not guarantee “a wide scope of actual mastery over

10 In particular, Giddens 1984.28–​ 34, 256–​ 62; Giddens 1987.7–​ 16, 35–​ 60. While I  have found Giddens particularly helpful, I would not argue that his treatment is definitive. I am fully convinced, however, by the likes of Noreña 2006 and Slootjes 2011, that “power” requires much more explicit theoretical attention than it is usually given to be a useful term of analysis. See also following note.

Conclusion }  215

the conduct of the subject population” (1987.10), especially by contrast with what is possible in a modern nation-​state. That is because of the second point. An extended scope of control requires surveillance, both the collecting and the keeping of information on individuals and their activities. In premodern states, the units for which this is possible (Giddens’ term is “containers”) are small. He speaks in terms of cities (as opposed to nation-​states, in the modern case), and even that generally seems optimistic to me. The fragmentation of information technology seen in this book suggests a fragmentation of information—​there are few or no large containers—​and thus sharp limits on total available power. Giddens’ view of the premodern world—​that as a category ancient states had vastly less power than modern institutions, and ancient agents, even rulers, had less control than their modern counterparts—​probably bears repeating, even if it is not in itself original to him.11 But to get full value from his theoretical apparatus we need to think about the level of generality at which we are to operate. The mere fact of literacy suffices for the intensity of surveillance that allows Giddens to describe early states as “states,” and that’s all he really needs to know. His own detailed research interests are principally about how exactly the intensive power practices specific to the modern state arise and operate. At this level of abstraction, there is little need to look at the details of any particular literate state, which lacks more modern technologies. The value of Giddens’ perspective, then, lies in using his analytical framework to consider specific features of the Roman world in detail. In essence, this is yet another iteration of the move from what I’ve called a “second-​stage” interpretation of history (“the ancient state is not the same as the modern”) to a third, culturalist one (“what are the specific operations of this ancient state?”). A variety of questions arise naturally within this framework, even without direct reference to individual information technologies of the sort described in this book, and I offer here three quick examples. Roman provinces grew considerably smaller in the later empire as the state’s information-​gathering capacities seem to have grown. Is it possible that these “reduced” provinces could have evolved into power containers in a way that was impossible earlier? How much could a (supposedly) uniform civil law contribute to widespread surveillance by regularizing at least certain parameters for describing daily life? And more generally, the less power, that is, the less “transformative capacity,” we imagine to have existed in Roman society, should that not be a correspondingly conservative force? If there is less transformative capacity, then almost by definition there is less opportunity for its unforeseen applications. The more specific idea I’m suggesting here, however, is that it would be particularly fruitful to bring the results of the present book (and parallel future research)

11 The contributors to Ando and Richardson 2017 (and especially Ando himself) explore this by means of Michael Mann’s notion of “infrastructural power.” While this gets at a lot of the same issues I raise here, it seems to me not to take on board the informational issues as naturally as Giddens’ framing does.

216

216 { Mosaics of Knowledge to bear within this framework. The goal would be to construct a more fine-​grained picture of what information the state (or other entities) could collect and act on over what kinds of ranges of time-​space. This would involve combining research on the content of information collected and stored by various Roman institutions with inquiry into the forms in which that information was held and thus how it could be accessed. There is already a substantial body of work on the content side, especially for the state, but also in some other areas such as estate-​level accounting.12 Form is less well studied and generally only in passing,13 so I hope this book helps provoke a more deliberate approach in this direction. At a minimum, less “advanced” technologies (say, simple listing) will need to be taken more systematically into account. I suspect many of the features of advanced technology I have discussed here—​for instance, the fact that nonstandardization of form makes combination of records difficult—​will be found more broadly; but ultimately these are empirical questions. Then, combining form and content, we can begin to ask questions like how hard it would be to detect a false claim of citizenship, whether an estate owner could compare labor costs across properties, or whether even experts could have had ready access to the “correct” answer to a subtle question of contract law. The present book does not, of course, settle the kinds of questions raised in this paragraph, but it does aim to raise and to frame them.

Going Forward II: An IT Revolution in Late Antiquity? When offering an end date for this study of around 300 ce, one reason was my suspicion that considerable changes lay just a little beyond that date. Establishing (or disproving) that would require another book, and one that I’m not well equipped to write. Still, I’d like to close this book by pointing to the traces that led me to that suspicion, a number of which have already come up, if only in passing. I’ll simply list these, then treat in more detail a single case from the fourth century that I think could be important both as a model (for the kinds of trends we should be looking for) and as a resource (for ancient technological adapters):

• The graphic counterpart of a nested list is a “tree” diagram, such as

I used to illustrate status theory or might be used to illustrate family relationships. There is textual evidence that has been interpreted as showing these existed (in the familial context) during the period of this book, but I am convinced by Piggin’s 2017 argument that we should not

12 State: for instance, Nicolet 1991; Demougin 1994; Moatti 1998, 2011. Accounting: see c­ hapter 2, note 42. 13 Just a few examples: the references in ­chapter 1, note 47, on cataloging of Roman legal materials, or Hopkins 1991.141–​2 on the organization of documents in Roman Egypt. The danger of such passing observations is that they tend to overgeneralize organizational features that are actually observed only in very limited contexts.

Conclusion }  217













assume their appearance until an anonymous stemma of Jesus’ ancestry, probably dating to the early 400s. Approximately a century later we find trees used (by Boethius) to show category structure. This is a major development in the area of data graphics. • Two of the world maps already discussed appear to date very close to the cutoff of 300. There is textual attestation of a similar project under Theodosius II (mid-​fifth century), and some hint that this court-​ sponsored map was part of a broader cultural trend.14 Perhaps most dramatically, there seems to have been a map included in the text of Macrobius’ Commentary on the Dream of Scipio (2.9.7; early fifth century). There is not enough evidence here to say anything about broader cartographic trends, but we might think of the consolidation of at least one kind of map. • The same work of Macrobius has four diagrams in the form of loose geometric constructions.15 The instructions are explicit in the text; it is less clear whether the images were nonetheless also supplied in the original, as in Greek mathematical texts. In either case, the striking thing is the transfer of this technique from a very restricted Greek/​technical context to an elite Latin one. • At the same time as these graphic devices appear to be expanding their range, interest in the kind of complex spatial representation discussed in ­chapter 4 appears to fall. • In the fifth century we have traces of standardized and numbered pagination in certain legal textbooks. Slightly earlier (and as part of a project I’ll say a little more about later) we have separate systems of numeration for the Gospels and for the letters of Paul.16 Not only do these represent an extension of the types of texts divided into numbered sections, but all are apparently created to support obligatory cross-​reference. • Those last two points also show an increasing level of comfort with paratext.17 The same can be said of the invention of rubrication and the rise of illustrations and tables of contents. One might make particular note of willingness to retrofit classical texts with this kind of apparatus. • In ­chapter 2, I argued that surviving simple accounting documents were better read as lists, if annotated ones, than tables. The main issue was that none of them ever developed a clear second dimension of columns disposed across the page. Beginning in the fourth century and on into

14 Traiana 2013. 15 Macrob. 1.21.3–​4, 1.22.11–​2, 2.5.13–​17, 2.6.2–​7, 2.7.4–​12. 16 Aland and Aland 1995. 17 See also studies of late antique paratext, such as Wallraff 2012, Fioretti 2015 (also including classical material), and Lang and Crawford 2017.

218

218 { Mosaics of Knowledge the fifth and sixth, we start to see possible exceptions, albeit highly scattered ones. The case I  want to examine in more detail, however, takes us back to tables. The clearest table from the Latin-​speaking world is not a mere illustration but also constitutes the entire second book of the Chronicle of St. Jerome, a work in which he correlates historical events from across the known world.18 The rows of the chart represent years from the notional birth of Abraham to the year 378 (almost 2,500  years). Each two-​page spread is then divided into columns to represent chronologies of various geographical areas (e.g., Rome, Greece, Egypt) as represented by the regnal years of their respective rulers.19 There are also columns for dates by year from Abraham and by Greek Olympiads, as well as a center space for text describing important events. (The number and choice of theaters varies over time, eventually converging in a single column for the Roman Empire.) I give only a sample as rendered in a seventh-​century manuscript now in Bern (figure 6.1). Here, from the left, we have Olympiad years, then regnal years for Medes, Jews, Romans, Macedonians, Lydians, and Egyptians. The central display-​space then records specific events of the relevant years—​here principally Cyrus’ activities in Judea—​and a secondary open column records famous individuals. We happen to know exactly where Jerome got the idea of the table (as well as most of its content):  a closely similar table in Eusebius’ Χρονικοὶ Κανόνες, translated and augmented by Jerome. Grafton and Williams 2006 trace those origins further back not just to Eusebius but also to his predecessor, Origen. Origen produced a tabular edition of the Bible called the Hexapla. The rows of this work were headed by a Hebrew text, broken down word by word. The following columns give a Greek-​letter transliteration of each word, followed by the respective versions of four different Greek translations, very much as in the language-​learning texts we encountered in c­ hapter 2. Starting from that basic narrative we can point to a variety of different factors that led to the creation and success of this table. In terms of Jerome’s (and Eusebius’) work itself, the intellectual task is essentially an informational rather than a substantive one. That is, the main point of these chronicles is not to inform readers of events and persons they didn’t know or couldn’t discover otherwise; it was to set them in a unified framework to enable comparisons and computations. There was dispute, for instance, over the relative dates for Moses and the Trojan War, and so:20

18 On the mechanics of dealing with Jerome’s text, see Burgess 2002. On the broader historical context (to which I well return below), see Burgess and Kulikowski 2013. 19 When the number of columns drops sufficiently, Jerome goes over to a single-​page format. 20 Necessarium [Eusebius] duxi veritatem diligentius persequi, et ob id in priori libello quasi quandam materiam futuro operi omnium mihi regum tempora praenotavi, Chaldaeorum, Assyriorum,  .  .  .  In praesenti autem, stylo eadem tempora contra se invicem ponens, et singularum gentium annos dinumerans, ut quid cuique coaetaneum fuit, ita curioso ordine coaptavi.

Conclusion }  219

I judged it necessary to seek the truth more diligently and so in the earlier book I wrote out the times of all the kings (the Chaldeans, the Assyrians, etc.) for myself as “raw material” for future work. . . . In the present book, however, placing equivalent times one next to the other in columns, and counting out the years of the individual peoples, I have put it together in careful order so that each item will be with its contemporaries.

FIGURE 6.1  Jerome, Chronicle, as arranged in Burgerbibliothek Bern, Cod. 219, f. 45r

Photograph: Codices Electronici AG, www.e-​​​codices.ch)

220

220 { Mosaics of Knowledge This is just as true of Jerome (who, after all, reproduced the passage) as it is of Eusebius. Thus even if Eusebius and Jerome were not interested in information technology in the abstract, the specific needs of the project would lead them in that direction, just as they seem to have led Quintilian down a similar road. The ideological content of the work had similar effect.21 Eusebius’ zeal for synchronism was driven by new theological imperatives, and those too were shared by Jerome. As Burgess and Kulikowski 2013 have pointed out, this was at least threefold:



1. Priority: Demonstrating the priority of, and so in some sense the superiority of, Christianity, broadly construed, in comparison to seemingly older traditions. 2. Eschatology: Addressing the theory that the world would end 6000 years after creation—​that is, fairly soon. 3. Teleology: Illustrating the divine plan for the world by showing the convergence of the manifold past into the single narrative of the (Christian) Roman Empire.

One might add that the centralized authority of the one God might also underwrite such a project in a more general way. Finally, as we have seen in several other cases, the physical activity involved in producing the texts was integrally involved in their shaping. Here, however, there seem to have been at least two distinct material influences. One of these is tied to the theological imperatives just discussed. The literary culture of antiquity was always richly intertextual, but the Christian ideology of divinely inspired scripture gave a unique impetus for precise verbatim comparison of passages that had not previously existed, and which are mechanically quite difficult to carry out with books written on rolls. Sharing this broad emphasis, but going beyond both the strictly religious imperatives and the specific form of Origen, Eusebius also developed a characteristic style of composition by mosaic of primary source quotations. This was used in writing not only about scripture but about human history, as well.22 The physical processes involved in collating texts before the comparative devices were invented, especially (though not exclusively) if the texts to be compared were still in that roll form—​sorting, aligning, rearranging—​are extremely intensive.23 Unfortunately, we do not know how these were produced, but one wonders if there was not some system of slips or note cards with individual data points that Eusebius and his staff could then rearrange and manipulate directly as part of the compositional process. At minimum, though, these works must have arisen from a physical sorting of

21 In fact, as Grafton and Williams 2006 have shown, Eusebius was something of an IT revolutionary more generally, using tabulation, color, and other formal devices to structure both historical and scriptural work. See also Wallraff 2013. 22 Grafton and Williams 2006.199–​200. 23 Grafton and Williams 2006.205–​6 on preserved evidence of Origen’s notes.

Conclusion }  221

manuscripts, not just the recollection from memory that seems to have underlaid so much classical literature. Eusebius, who worked in a library that included Origen’s Hexapla, as well as many later acquisitions by the collector Pamphilus, adopted the general form to a variety of purposes including the chronological table we have already seen, as well as tables coordinating the contents of Psalms and (most successfully) the Canon of parallel passages in the Gospels.24 Finally, though the narrative I just sketched begins in the world of the book roll, it takes place during the rise of the codex as the principal book form.25 It has been observed that the rise of the codex (both its potentially large format and its regular demarcation of units—​i.e., page spreads) makes tables of this sort much more practical.26 Moreover, the mere fact of the transition may have shaken up book production enough to encourage formal experiments. Again, the same feature helps both Eusebius and Jerome in the same way. As with the classical examples of tables, and perhaps even more so, the creation of the Chronicle was highly overdetermined. But it is different in at least three important respects. First, at least some of the components are quite general and lasting. The same ideological concerns would have motivated readers, as well as these specific writers. (Perhaps it is not accidental that the first preserved tree displays Jesus’ lineage.) Second, we get not just one table, however huge; the same system also produced the Hexapla (fairly clearly tabular itself), canon tables, and their associated systems of numeration and reference. Third, these artifacts did not just sit in the workshop where they were invented; they were projected across the world. The Chronicle was an enormous success, and the canon tables even more so.27 This is the kind of development that could break through the negative feedback loops I have spoken of frequently. Christianity could serve both as a context for new information technologies and as a vector to bring those technologies into other parts of life. Scholars of Late Antiquity have (as my notes here can only hint at) studied a number of these developments—​most notably the co-​evolution of the codex and Christianity and their respective corollary effects, but certainly others as well. Many of these individual lines of inquiry are, in fact, more advanced than discussions of the classical period, and I don’t pretend to control the existing literatures. Nonetheless, it appears to me that what is still lacking is a more comprehensive study of the sort represented by this book—​that is, one that groups all these different devices together under the rubric of “information technology.” I see three advantages. First is attention to potential interconnections among different technologies. For instance,

24 The evolution from Hexapla to Chronicle would look very much like an extension of the trajectory from glossaries to columnar translation I hinted at earlier (and which may well have be an origin point for the Hexapla itself). 25 Haines-​Eiten 2013 for a very concise guide to a huge topic. 26 Grafton and Williams 2006.10–​2, citing earlier literature. 27 Burgess and Kulikowski 2013.126–​7.

222

222 { Mosaics of Knowledge do different kinds of paratext “bootstrap” each other and does this affect their status as “authorial” or not? Is there some connection between the rise of relatively abstract diagrams and the decline of complexly spatial art? Second, it would facilitate attention to cultural contexts that are less commonly invoked in informational contexts. For instance, and just to pick among factors that are already topics of discussion in their own right, we have already seen signs of the late antique world’s ambitions to greater universality with informational consequences in things like the Price Edict, taxation by capitatio, and attempted standardization of weights and measures. Does this go further? Elsewhere, might self-​conscious “belatedness” and the narrowing of the literary canon not encourage technologies to consolidate and organize existing knowledge?28 And perhaps some of the social constraints based on elite subordination of text to performance were loosened or dissolved in the late antique world.29 Third, as I have tried to do for the classical period, using information technology as a category of analysis would warn us not to segregate elite literary activity from the broader (and, in informational terms, potentially more sophisticated) stream of day-​to-​day practices. If anything, the late antique world will likely provide a much richer supply of this kind of documentation.30 The late antique version of this book would be a larger project than the original, perhaps multiple larger projects, but it’s one worth pursuing.

28 On the canon, see Netz (in press). 29 On late antique textuality in general, see Formisiano 2007; for some very general effects, see Gaddis 2009. 30 I would note here, for instance, the enormous ratio of postclassical to classical texts gathered in volumes of Chartae Latinae Antiquiores.

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INDEX Tables, and figures are indicated by an italic t, and f following the page numbers accounting, 21, 45, 62–​66, 67–​68, 80, 121–​22, 206–​7, 212–​13, 215–​16,  217–​18 aesthetics, 13, 46–​47, 49, 58, 65, 107, 133 alimenta, 67 allometry,  123–​24 alphabetization, 11–​14, 22–​23, 28, 61, 71–​72,  207–​8 annotation, 48, 49, 58, 62–​64, 68, 71–​72, 73, 79–​80. See also labels answerability, see constitution Apicius, 85–​86, 87, 89–​90, 94–​95, 123–​24 approximation, 84–​85, 87–​88, 91–​92, 93–​98, 106, 117, 122–​23, 126–​27, 134, 135, 147–​48, 151, 152, 175–​77, 187–​88 Arausio, see inscriptions discussed: Orange survey maps archives, 16, 29–​32, 38–​39, 48, 62–​64, 80, 117, 186, 199–​200, 203–​4, 206, 211–​12. See also governmental documents army, see military, Roman artworks discussed Dura Europos “map”, 173–​74, 173f, 177 Fall of Icarus (BM 1867,0508.1355), 152–​53,  153f Landscape (Columbarium of Villa Pamphilj A/​XII), 136–​37, 139 Landscape (Columbarium of Villa Pamphilj F/​XX), 140–​41, 142–​44, 142f, 145 Landscape (MANN 147502), 147–​48 Landscape (MNR 1037), 138–​40, 144 Landscape (MNR 1072), 138–​39, 144–​45,  145f Landscape (MNR 1080), 148–​49 Landscape (MNR 1233), 137, 140,  141–​42 Landscape (Oplontis A 14), 143f, 145 Peutinger map (see Peutinger map) Riot in the Amphitheater (MANN 11222), 133 Asconius, 17–​18, 22   board games, 73–​74, 75–​76, 78, 164–​65 capita in taxation, 121–​22, 221–​22 in textual organization (see segmentation) cartography, see maps

centuriation, 50–​51, 68–​69, 77, 90–​91, 186–​88, 197–​98, 199–​200,  205–​6 chronological order, 14–​15, 212 codex, 1, 17, 220–​22 cognition, 3–​4, 13–​14, 38, 43–​44, 46–​47, 74–​75, 78–​80, 173, 176–​77, 178, 188, 194–​95, 200–​1,  212–​13 coins, 83–​84, 86–​87, 89, 93, 95–​96, 102, 108,  150–​51 color, 56–​57, 73–​74, 137, 139, 145, 147–​48, 152, 166, 175, 185–​86, 220 columbaria,  36–​38 Columella, 24, 28–​29, 85–​86. See also individual passages discussed commentarius, 18–​19, 31, 190, 212 compositionality, 147, 149–​50, 152–​53, 176–​77, 179,  190–​91 concealment, 146, 150–​51 constitution (of facts), 77, 121–​22, 163, 205–​6,  212–​13 construction, 90–​91, 115–​17, 127–​28, 165–​66, 169, 206 contracts, 4, 111–​12, 113–​14, 115–​16, 117, 119–​20, 121, 127, 164–​65 conventions, 74, 133, 139, 145, 150, 154–​55, 159–​60, 167–​68, 171–​72, 176, 177–​78, 185–​86, 191–​93, 195, 204–​5, 207 conversion (of units), 95, 113, 121–​22,  124–​26 Cornelius Celsus, 85–​86, 94–​95 corporeality, 133, 152–​53 Corpus Agrimensorum, 157, 162, 188, 200–​1. See also individual passages discussed counting, 16, 18–​19, 35–​36, 85, 91–​92, 109, 126, 203 cross–​referencing, 13, 20–​22, 32, 39–​40, 203–​5,  217 cueing,  142–​44 culturalist interpretation, 210, 215 cuneiform texts, 4–​5, 43–​44, 46–​47, 76, 82   data graphics, 154–​57 definitions ancient, 96, 103–​5, 108, 124 (see also standardization) modern, 5–​6, 11, 22–​23, 26, 29, 45–​49, 73, 131, 133–​35, 172–​80,  209–​10

245

246

246 { Index defixio, 160, 162, 163, 164, 205–​6 depth,  139–​40 diagrams, 42–​43, 70, 74, 78–​79, 151, 157–​59, 160, 162, 163, 164, 176–​77, 189–​90, 193–​94, 210–​11, 216–​17,  221–​22 dimensionality (outside of chapter 4), 44–​ 45, 48–​49, 72, 75, 78, 81–​82, 90–​91, 173–​74, 176–​79, 188–​90, 194–​95, 200–​1, 208–​9,  217–​18 Diodorus, 26 dishonest measures, 110–​12 distance, see length   economics, 62–​64, 128, 210, 212–​13 Eumenius, 191, 196 Eusebius,  218–​21   falsum, see forgery family resemblance, 55, 67–​68, 149–​51, 171–​72, 197–​98,  206–​8 Fasti, 15, 55–​57, 66–​67, 68, 75–​76, 80 feedback loops, 21, 28, 74, 127 Florus, 27 forgery, 108, 110, 113–​14 Forma Urbis Romae (FUR), 167, 169–​71, 175–​76, 181–​86, 193–​94, 195–​97,  200 formae in grammar, 61 in surveying, 50–​51, 77, 168, 188, 205–​6 (see also Forma Urbis Romae) fractions, 62, 89, 93, 95–​97, 99–​100, 109, 115–​16,  121 Frontinus, 24, 25–​26, 85–​86, 87–​88, 90–​91, 98, 124–​25, 157–​58, 163–​64. See also individual passages discussed   Gellius, Aulus, 24, 28–​29 goats, 149 Goody, Jack, 3–​4, 10–​11, 14, 23, 44–​45, 49 governmental documents, 12, 14–​15, 29–​31, 38–​39, 56–​57, 170–​71, 188–​89, 196, 199–​200, 204, 206, 211–​12, 214–​16. See also archives grain, 31, 49, 68–​70, 71, 80–​81, 84–​85, 100–​1, 104, 108, 109–​10, 114, 117, 119, 128, 172 grammar, 12, 21, 45, 51, 58–​61, 71–​72, 75–​76. See also individual passages discussed Greek, 3–​5, 11, 12–​13, 17–​18, 21, 24, 25–​26, 30, 31, 39–​40, 58–​59, 61–​64, 72, 73–​74, 75–​76, 78–​79, 87, 88, 89, 94–​96, 105–​6, 109, 112–​13, 114, 134–​35, 137, 172–​73, 177–​78, 197, 207–​8, 217, 218 ground lines, 137, 138, 141–​42   heaping (of digits), 84–​85, 91, 98–​99, 122–​23 Hexapla, 218, 220–​21 homonyms, 92, 92t, 206 hours 88, 89, 96, 98–​99, 106, 118, 122–​23,  128   illustrations, 70, 157–​64, 189, 196–​97, 200–​1, 204–​6, 207, 217 iniquum, see dishonest measures

inscriptions discussed CIL 2.3386, 122–​23 CIL 3.14165, 110 CIL 5.3456, 34, 35f CIL 6.220, 68–​69 CIL 6.1261, 70, 87–​88, 158–​59, 201 CIL 6.2059, 35 CIL 6.8117–​72, 36 CIL 6.8122, 36 CIL 6.8122–​4, 36 CIL 6.9015 (= tomb of Claudia Peloris), 166,  168–​69 CIL 6.10053–​4, 70, 71 CIL 6.10211, 69–​70 CIL 6.11034, 36 CIL 6.11042, 36 CIL 6.12366, 89 CIL 6.32639, 57 CIL 8.4440/​18587,  70–​71 CIL 9.1455, 102, 118 CIL 10.793, 112 CIL 10.8067, 102 CIL 10.8068, 103 CIL 10.8071, 122–​23 CIL 11.1147, 67 CIL 11.3613, 11 CIL 11.3614, 18 CIL 14.3676, 70, 87–​88, 158–​59 CIL 14.4499, 70, 71, 80–​81 CIL 14.4500, 80–​81 CIL 16.10, 30 FUR (see Forma Urbis Romae) IGRP 3.1056, 109 IscrIt 1, 52 IscrIt 8, 52 Lex Irnitana, 20, 81 OGIS 2.674, 109 Orange survey maps, 175–​76, 187–​88,  193–​94 Patara monument, 188–​89, 196 RIB 2414, 102, 104 SC de Aphrodisiensibus, 30 Verona A and B, 59, 188, 197–​98 Via Anicia plan, 166–​67, 168, 170–​72 itineraries, 14, 98–​99, 176–​77, 188–​89, 190, 193–​95, 196, 203, 208–​9   Jerome, 73–​74,  218–​21 Julius Caesar, 88–​89, 90–​91, 119, 172, 178–​79, 190–​91, 198, 199–​200. See also individual passages discussed Juristic passages discussed CTh 12.6.19, 12.6.21pr, 108–​9 CTh 14.4.4, 108–​9 D. 4.3.18.3, 111–​12 D. 18.1.35, 119, 120 D. 18.1.71, 111–​12 D. 47.11.6, 108 D. 48.10.32.1, 108 D. 48.19.37, 108   labels, 1–​2, 4–​5, 16, 36–​37, 48, 78–​79, 93, 100–​1, 102–​5, 107, 122–​23, 157, 159–​60,

Index }  247 165, 168–​71, 181, 185–​86, 191–​93, 200, 204–​5. See also annotation Late Antiquity, 3, 108–​9, 215, 216–​22 laterculi, 57–​58,  66–​68 length, 88, 90–​92, 93, 94–​95, 97–​99, 100, 115–​17, 123–​24, 166, 168, 169–​71 lex Irnitana, see Inscriptions discussed lex Silia, 103–​4, 108, 124–​25 lists in general (outside chapter 1), 44–​45, 46–​49, 62–​64, 79–​80,  215–​16 nested, 29–​40, 44–​45, 47–​48, 65–​66, 74–​75, 80, 151, 203–​4, 206, 207, 216–​17 literacy, 1–​4, 10, 11–​12, 74, 98, 204–​5, 208, 209, 214, 215 Livy, 90–​91, 99–​100, 173–​74, 177–​78, 188–​89. See also individual passages discussed localism, 1–​3, 14–​15, 18, 19, 21, 39, 61, 73, 75–​76, 88, 92, 94–​95, 102, 104–​5, 106, 108–​9, 111–​13, 114, 115–​16, 117, 118–​19, 124–​28, 139–​41, 147, 149–​50, 155–​57, 159–​60, 162, 172, 185–​86, 198–​201,  206–​8   magistrates, 55, 56–​57, 100–​1, 108–​9, 110, 112–​13, 198–​200 maps (outside chapter 5), 50–​51, 77, 78, 98–​99, 134–​35, 203–​4, 205–​6, 208–​9,  217 materiality, 10 mathematics, 62, 73–​74, 78–​79 measuring tables, 104–​5, 112–​13 mensores, 83–​84, 128, 207–​8 metonymy, 88–​92, 95–​96, 126 military, Roman, 14–​15, 29–​30, 52, 65–​66, 67–​69, 75–​76, 90–​91,  206 misreading, creative, 81–​82 Monument X (Esquiline), 36 natural features, 157–​58, 162, 166–​67, 187–​88,  195–​96 nundinae, 15–​16, 55 Origen, see Hexapla Ostraca discussed OAmst 8, 67–​68 OClaud 308, 52 OClaud 309–​36,  79–​80   painting types sacro–​idyllic,  135–​36 second style, 150–​51 paintings, see artworks discussed Panofsky, Erwin, 131, 133, 152–​53 Papyri discussed CPL 157, 30 Fink 1 (P Dura 100), 68 Fink 2 (P Dura 101), 68 P Gen. Lat. 1, 52, 80 P Louvre inv. E7332, 61 P Oxy. 737, 64 P Oxy. 2104, 211–​12 P Ryl. II 220, 31 parapegmata, 85, 157, 158–​59

paratext, 14, 28–​29, 75, 197, 204–​5, 217,  221–​22 passages discussed. See also Juristic passages discussed Agennius Urbicus 19C, 189–​90 Apicius 6.8.4, 8.7.17, 89–​90 Caesar, BG 1.1, 178 Cetius Faventinus 29, 118 Charisius 1.23.8–​10K, 59 Charisius 1.153.14–​6K, 60 Cicero, Fam., 27, 28–​29 Cicero, Brutus, 15 Cicero, Leg. Agr. 2.29, 19 Columella 12.3, 95 Columella 12.13, 21 Dio 52.30.9, 83 Diomedes 1.308–​9K, 61 Eusebius, Chron. pref., 73–​74 Festus 288L, 108 Flavius Caper, Verb. Dub. 107–​12K, 12 Frontinus, Aqu. 3, 23–​24 Frontinus, Aqu. 17, 163–​64 Frontinus, Aqu. 35–​63,  124–​25 Frontinus, Strat. 2, 23 Gellius 19.10.2–​3,  164–​65 Granius Licinianus 10F, 188 Hyginus 90C, 92 Hyginus 146–​8C, 88 Hyginus 158C, 50–​51, 199–​200 Livy 41.28.8, 177 Macrobius Somn. 2.9.7, 217 Martial Ep. 10.55, 94 Persius 1.126–​30, 110 Plautus, Asin 864–​6,  11–​12 Pliny HN praef. 33, 27–​28 Pliny HN 3.17, 190 Pliny HN 25.8, 160–​61 Pliny HN 35.11, 160–​61 Priapeia 4, 161 Priscian 2.284–​385K, 60 Quintilian 1.pr.21–​2, 25 Quintilian 3.6, 42–​43, 77 Quintilian 10.1.46–​131, 14 Seneca Apocol. 2, 118 Seneca Ep. 88.11, 94 Siculus Flaccus 104C, 188 Siculus Flaccus 121C, 50–​51 Suetonius, G&R, 26–​27,  28–​29 Suetonius, Tib. 43.1, 161 Varro LL 10.22, 78 Varro LL 10.43–​4, 51 Varro LL 10.48, 76 Varro RR, 27 Varro, RR 1.1.9, 12 Vergil, Aen. 7.691, 12–​13 Vegetius 2.19, 66 Vegetius 3.6, 189 Vitruvius 8.2.6, 189–​90 Vitruvius 9.7.7, 88 perspective in general, 131–​33, 134 “mixed”, 132–​3 3, 140–​4 1, 144–​4 5,  149–​5 0

248

248 { Index Peutinger map, 98–​99, 173–​74, 177, 190, 191–​94, 195–​96,  197–​98 plans, 115–​16, 154, 164–​72, 181, 184, 185–​88, 196–​98, 204–​6, 207,  212–​13 Pliny the Elder, 12–​13, 14, 24, 27–​29, 85–​86, 94–​95, 160–​61, 162–​63, 190, 195–​96, 205–​ 6. See also individual passages discussed Pliny the Younger, 26–​27, 28–​29 power,  210–​16 precision, 94, 97, 103–​4, 106–​7, 113–​14, 115–​16, 118, 122–​23, 127–​28, 155–​57, 168, 181, 184, 185, 203–​4. See also approximation precisionism, 122–​23, 169 prices, 49, 64, 65–​66, 84–​85, 89, 93, 98–​99, 106, 119, 120, 121, 125–​26, 206, 212–​13,  221–​22 progress, 2–​3, 13, 133, 207–​9 proportionality, 86–​88, 96, 109, 113–​14, 115–​16, 121–​22, 123–​24, 169–​70, 176,  205–​7   Quintilian, 25–​26, 73–​74, 76, 77. See also individual passages discussed   redundancy, 46–​47, 48, 49, 58, 67, 69, 71, 75–​76, 104, 122–​23, 168, 188, 204–​5 representational conventions, see conventions reproducibility, 50–​51, 78, 89–​90, 104, 110, 113–​14, 115, 155–​57, 162–​63, 200–​1,  203–​5 rosters, 14–​15, 46–​47, 52, 54f, 57–​58, 63f, 67–​ 68, 75–​76, 77, 79–​82, 201–​31  rounding, see heaping routes, see itineraries   scaffolding, 38, 78. See also cognition scale. See also proportionality absolute, 165–​66, 167, 168–​69, 170–​71, 173–​74, 175–​76, 181–​84, 185–​88, 190–​ 91, 193, 195–​96, 198–​99, 200–​1, 204–​5, 206,  208–​9 relative, 123, 133, 137, 138–​39, 140, 141, 144–​45, 147–​48, 149,  204–​5 Scribonius Largus, 19, 21, 22, 24, 85–​86 seating, theater, 32–​36 sections, see segmentation segmentation, 17, 18–​19, 20, 22, 27–​28, 30, 31, 38–​39, 48, 204–​5 sekomata, see measuring tables social status, 1, 46–​47, 68–​69, 163–​64, 188, 196–​97, 217,  221–​22 Solinus, 27, 179 Sortes Sangallenses, 39–​40, 48 space blank, 31, 43–​44, 52, 56, 57, 65, 68–​69, 71, 75–​76, 80–​36, 181,  204–​5

specific instances, 90–​92, 167, 170–​71, 173–​74, 187–​88,  196–​97 theory of, 133–​35, 138–​47, 148, 152–​53, 174–​80, 187–​88, 190–​91, 194–​95, 198, 207–​8, 209, 210 stacking,  138–​39 standardization. See also scale effects, 17, 18, 22, 55, 56, 59, 60, 83–​84, 87, 92, 94, 100–​20, 123–​25, 127–​28, 159–​60, 183–​84, 185–​86, 191–​93, 203–​7, 208–​9, 210–​13,  217 processes of, 50–​51, 81, 88, 92, 95, 100–​14, 124, 127, 185–​86, 199–​200 Statius,  25–​26 stereotyped objects, 140–​41, 146, 149 sundials, 14, 21, 88, 96, 106, 118–​19, 122–​23, 155–​57, 156f,  204–​6 surveying, 85–​86, 90–​91, 96–​97, 113–​14, 116, 124, 125–​26, 128, 152, 157–​58, 162, 163, 164, 169–​71, 172, 184–​86, 189–​90, 193–​94, 195–​200, 201, 203–​4, 206, 207–​8. See also centuriation   tables (outside chapter 2), 4–​5, 124, 125–​26, 151, 154–​55, 187–​88, 203–​6, 207, 209, 210, 217, 218–​21 tables of contents, 19, 22–​29, 206, 210 Tabula Peutingeriana, see Peutinger map tabulae mensoriae, see measuring tables Tabulae Pompeianae Sulpiciorum, 86–​87, 117, 117t Tabulae Vindolandenses, 65–​66, 82, 94–​95, 124–​25,  212–​13 Temple of Castor (as weight standard), 100–​2,  112 tiers, 134, 136, 144–​46, 147–​48 time, 88–​89, 93, 94, 96, 106, 118–​19, 122–​23 tokens, 16, 32–​35 Tomb of the XXXVI Socii, 36, 37–​38, 48 tree diagrams, 42–​43, 48, 74, 216–​17, 221   Valerius Maximus, 27, 28–​29, 30 Valerius Soranus, 28 Varro, 51, 58–​59, 73–​74, 76, 78–​79. See also individual passages discussed Verrius Flaccus, 13, 15 Victorius, 49, 62, 75–​76 Vindolanda, see Tabulae Vindolandenses Vitruvius, 85–​87, 94–​95, 123–​25, 131–​32, 160, 162–​65, 196–​97,  205–​6 volume, 87, 88, 89–​90, 92, 93, 94–​95, 103–​6, 108, 110, 113, 117, 119, 120, 123–​24 Volusius Maecianus, 86, 124   water, 70, 87–​88, 90–​91, 98, 114, 124–​25,  163–​64 weight, 87, 93, 94–​96, 100–​3, 108–​9, 113, 117, 119, 122–​23, 124, 125