Numbers and numeracy in the Greek polis 2021047066, 2021047067, 9789004467217, 9789004467224, 9004467211

Table of contents :
‎Contents
‎Acknowledgements
‎List of Illustrations and Tables
‎Abbreviations
‎Notes on Contributors
‎Introduction. Doing Things with Numbers (Sing, van Berkel and Osborne)
‎Part 1. Numbers in Society
‎Chapter 1. A Counting People: Valuing Numeracy in Democratic Athens (Kallet)
‎Chapter 2. The Appearance of Numbers (Osborne)
‎Chapter 3. Punishing and Valuing (Johnstone)
‎Chapter 4. Ten Thousand: Fines, Numbers and Institutional Change in Fifth-Century Athens (Blok)
‎Chapter 5. Numeric Communication in the Greek Historians: Quantification and Qualification (Rubincam)
‎Part 2. Communicating with Numbers
‎Chapter 6. Creative Accounting? Strategies of Enumeration in Epinician Texts (Sicka)
‎Chapter 7. Hidden Judgments and Failing Figures: Nicias’ Number Rhetoric (van Berkel)
‎Chapter 8. Performing Numbers in the Attic Orators (Sing)
‎Part 3. Conceptualising Number
‎Chapter 9. Numbers, Ontologically Speaking: Plato on Numerosity (Calian)
‎Chapter 10. Doing Geometry without Numbers: Re-reading Euclid’s Elements (Lee)
‎General Index
‎Index of Inscriptions
‎Index Locorum

Citation preview

Numbers and Numeracy in the Greek Polis

Mnemosyne Supplements history and archaeology of classical antiquity

Series Editor Jonathan M. Hall (University of Chicago)

Associate Editors Jan Paul Crielaard (Vrije Universiteit Amsterdam) Benet Salway (University College London)

volume 446

The titles published in this series are listed at brill.com/mns‑haca

Numbers and Numeracy in the Greek Polis Edited by

Robert Sing Tazuko Angela van Berkel Robin Osborne

leiden | boston

Cover illustration: IG i3 458A (EM 6738): the annual account of 446/5 for Pheidias’ statue of Athena Parthenos. © Acropolis Museum, 2010, photo: Nikos Daniilidis Library of Congress Cataloging-in-Publication Data Names: Sing, Robert, editor. | Berkel, Tazuko Angela van, 1979- editor. | Osborne, Robin, 1957- editor. Title: Numbers and numeracy in the Greek polis / edited by Robert Sing, Tazuko Angela van Berkel, Robin Osborne. Description: Leiden ; Boston : Brill, [2022] | Series: Mnemosyne. Supplements. History and archaeology of classical antiquity, 2352-8656 ; volume 446 | Includes bibliographical references and index. Identifiers: lccn 2021047066 (print) | lccn 2021047067 (ebook) | isbn 9789004467217 (hardback) | isbn 9789004467224 (ebook) Subjects: lcsh: Mathematics, Greek. | Numeration–History–To 1500. | Numerals–History–To 1500. | Greek language–Numerals. Classification: lcc qa22 .n86 2022 (print) | lcc qa22 (ebook) | ddc 510.938–dc23/eng/20211108 lc record available at https://lccn.loc.gov/2021047066 lc ebook record available at https://lccn.loc.gov/2021047067

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill‑typeface. issn 2352-8656 isbn 978-90-04-46721-7 (hardback) isbn 978-90-04-46722-4 (e-book) Copyright 2022 by Robert Sing, Tazuko Angela van Berkel, Robin Osborne. Published by Koninklijke Brill nv, Leiden, The Netherlands. Koninklijke Brill nv incorporates the imprints Brill, Brill Nijhoff, Brill Hotei, Brill Schöningh, Brill Fink, Brill mentis, Vandenhoeck & Ruprecht, Böhlau Verlag and V&R Unipress. Koninklijke Brill nv reserves the right to protect this publication against unauthorized use. Requests for re-use and/or translations must be addressed to Koninklijke Brill nv via brill.com or copyright.com. This book is printed on acid-free paper and produced in a sustainable manner.

Contents Acknowledgements vii List of Illustrations and Tables Abbreviations x Notes on Contributors xii

viii

Introduction 1 Robert Sing, Tazuko Angela van Berkel and Robin Osborne

part 1 Numbers in Society 1

A Counting People: Valuing Numeracy in Democratic Athens Lisa Kallet

27

2

The Appearance of Numbers Robin Osborne

3

Punishing and Valuing Steven Johnstone

4

Ten Thousand: Fines, Numbers and Institutional Change in Fifth-Century Athens 96 Josine Blok

5

Numeric Communication in the Greek Historians: Quantification and Qualification 131 Catherine Rubincam

58

78

part 2 Communicating with Numbers 6

Creative Accounting? Strategies of Enumeration in Epinician Texts Daniel Mahendra Jan Sicka

151

vi

contents

7

Hidden Judgments and Failing Figures: Nicias’ Number Rhetoric Tazuko Angela van Berkel

8

Performing Numbers in the Attic Orators Robert Sing

174

195

part 3 Conceptualising Number 9

Numbers, Ontologically Speaking: Plato on Numerosity Florin George Calian

10

Doing Geometry without Numbers: Re-reading Euclid’s Elements Eunsoo Lee General Index 267 Index of Inscriptions 277 Index Locorum 280

219

237

Acknowledgements All the papers in this volume were presented at the conference Numbers and Numeracy in Classical Greece, held at Leiden University on 2–3 September 2016. The conference was part of Tazuko van Berkel’s NWO Veni research program ‘Counting and Accountability’. The editors are grateful to Leiden University for hosting, and would like to thank the Netherlands Organisation for Scientific Research (NWO), and the Royal Netherlands Academy of Arts and Sciences (KNAW) for their financial support. The editors would also like to thank Angelos Matthaiou for his assistance in sourcing images, and are indebted to Giulia Moriconi and Millie Gall at Brill, and Paul Gruiters, for their advice and unstinting support.

List of Illustrations and Tables Illustrations 1.1

2.1

2.2 3.1 3.2 9.1 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12

IG i3 260–262: A portion of the three tribute quota lists for 453/2–451/0 on the Lapis Primus. (The rights on the depicted monument belong to the Hellenic Ministry of Culture and Sports (Law 3028/2002). The inscribed fragment EM 6870 (IG i3 260 vi, vii) of the first stele of the Athenian Tribute Lists belongs to the responsibility of the Epigraphic Museum. Hellenic Ministry of Culture and Sports/ Archaeological Resources Fund) 39 IG i3 460 (EM 6769): Fragment of the summary accounts of Pheidias’ statue of Athena Parthenos (438/7). © Acropolis Museum, 2010, photo: Nikos Daniilidis 66 IG i3 476 (EM 6667): Fragment of the accounts of the Erechtheion for 408/7. © Acropolis Museum, 2012, photo: Socratis Mavrommatis 67 Fines of officials in Greek cities valued in drachmae 86 Numbers used in fines of Greek officials 87 Knorr’s depiction of the formula for 2k+1 229 Geometry with numbers (Quantification) 240 Geometry with numbers (Calculation) 240 Geometry with numbers (Algebraisation) 241 Geometry with numbers (Geometrisation) 242 Diagram of Proposition i.35 247 Diagram of Proposition i.42 248 Diagram of Proposition i.45 249 Reproduced diagram for Proposition vi.1 254 Conversion map of the magnitude counting 254 Diagram of Proposition v.9 255 Diagram of Proposition v.10 255 Parabolic segments 262

Tables 4.1 5.1 5.2 5.3 10.1

Fines in Attic decrees of the fifth century bce 119 Types of number 142 Subject categories to which numbers may refer 142 Qualification of numbers 143 Figure counting after transforming figures 250

ix

list of illustrations and tables 10.2 10.3 10.4 10.5

Comparison of magnitudes 251 Visual magnitude counting 251 Inequality of two ratios 253 Analogy between number and magnitude

256

Abbreviations The names of ancient authors and their works are abbreviated in accordance with The Oxford Classical Dictionary, 4th edn., edited by E. Eidinow, S. Hornblower and A. Spawforth (Oxford: Oxford University Press, 2012), and abbreviations of journals follow L’Année Philologique. The following abbreviations are used for other reference works and editions of corpora: Agora xvi

Woodhead A.G. (ed.), The Athenian Agora. Inscriptions: The Decrees (Athenian Agora 16, Princeton: American School of Classical Studies at Athens, 1997). AIO Attic Inscriptions Online (https://www.atticinscriptions.com/). AIUK Attic Inscriptions in UK Collections (https://www.atticinscriptions.co m/papers/aiuk/). Corinth viii 1 Meritt, B.D. (ed.), Corinth, Volume viii Part 1, Greek Inscriptions 1896– 1927 (Cambridge, MA: Harvard University Press, 1931). DK Diels, H. and W. Kranz (eds), Die Fragmente der Vorsokratiker, 3 vols. (6th edn., Berlin: Weidmann, 1952). F.Delphes iii Fouilles de Delphes, iii: Épigraphie (Paris: Fontemoing → De Boccard for École Française d’Athènes, 1909–1985). FGrH Jacoby, F., et al. (eds), Die Fragmente der griechischen Historiker (Berlin: Weidmann → Leiden: Brill, 1923–). Gagarin and Gagarin, M. and P. Perlman (eds), The Laws of Ancient Crete: c. 650– Perlman 400bce (Oxford: Oxford University Press, 2016). I.Cret. Guarducci, M. (ed.), Inscriptiones Creticae, 4 vols. (Rome: La Libreria Dello Stato, 1935–1950). I.Eleusis Clinton, K., Eleusis. The Inscriptions on Stone. Documents of the Sanctuary and Public Documents of the Deme, 3 vols. (Athens: Archaeological Society at Athens, 2005–2008). IG Inscriptiones Graecae (Berlin: Reimer → De Gruyter, 1873–). I.Olympia Die Inschriften von Olympia (Olympia: Die Ergebnisse der … Ausgrabung), v (Berlin: A. Asher, 1896). IPArk Thür, G. and H. Taeuber, Prozessrechtliche Inschriften der griechischen Poleis: Arkadien (Vienna: Verlag der Österreichischen Akademie der Wissenschaften, 1994). I.Rhamnous Petrakos, B. Ch., Ὁ Δῆμος τοῦ Ραμνοῦντος: Σύνοψη τῶν ἀνασκαφῶν καὶ τῶν ἐρευνῶν (1813–1998), ii: Οἱ Ἐπιγραφές (Athens: Greek Archaeological Society, 1999). KA Kassel, R. and C. Austin (eds), Poetae Comici Graeci, 8 vols. (Berlin: De Gruyter, 1983–).

abbreviations LR LSAG LSJ ML OR PMG RE

RO SEG SLG Syll.3

xi

Leão, D.F. and P.J. Rhodes (eds), The Laws of Solon: a New Edition with Introduction, Translation and Commentary (London: I.B. Tauris, 2015). Jeffery, L.H., The Local Scripts of Archaic Greece (rev. A.W. Johnston, Oxford: Oxford University Press, 1990). Liddell, H.G., R. Scott and H.S. Jones et al., Greek-English Lexicon (9th edn., rev., Oxford: Clarendon Press, 1996). Meiggs, R. and D.M. Lewis (eds), Greek Historical Inscriptions to the End of the Fifth Century b.c. (2nd edn., Oxford: Clarendon Press, 1988). Osborne, R. and P.J. Rhodes (eds), Greek Historical Inscriptions 478– 404bc (Oxford: Oxford University Press, 2017). Page, D.L. (ed.), Poetae Melici Graeci (Oxford: Clarendon Press, 1962). Wissowa, G., et al. (eds), Paulys Real-Encyclopädie der classischen Altertumswissenschaft (Stuttgart: J.B. Metzler → Munich: A. Druckenmüller, 1893–1980). Rhodes, P.J. and R. Osborne (eds), Greek Historical Inscriptions 404– 323bc (Oxford: Oxford University Press, 2003). Supplementum Epigraphicum Graecum (Leiden: Sijthoff → Brill, 1923–). Page, D.L. (ed.), Supplementum Lyricis Graecis (Oxford: Clarendon Press, 1974). Dittenberger, W., Sylloge Inscriptionum Graecarum (3rd edn., Leipzig: Hirzel, 1915–1924).

Notes on Contributors Josine Blok is Professor Emerita of Ancient History at Utrecht University. Her research focuses on citizenship in ancient Greece, and comparative studies of ancient and modern democracies. The impact of religion and the meaning of gender in ancient Greek citizenship are key themes in her monograph Citizenship in Classical Athens (2017). Florin George Calian is a Research Fellow at the Institute for Ecumenical Research, Philosophy and Religious Studies Unit, Lucian Blaga University. He holds masters degrees in Medieval Studies and in Greek and Roman Archaeology, and received his Ph.D. from Central European University. Steven Johnstone is Professor of History at the University of Arizona in Tucson. A recipient of a Guggenheim Fellowship, he has written Disputes and Democracy (1999) and A History of Trust in Ancient Greece (2011). Lisa Kallet is Associate Professor of Classics at the University of Oxford and Cawkwell Fellow in Ancient History, University College. Her research focuses on Athens’ democracy and empire, and Attic epigraphy and historiography, especially Thucydides. Eunsoo Lee is Assistant Professor at the Korea Advanced Institute of Science and Technology. He received his Ph.D. in Classics from Stanford University. His research centres on the history of mathematics and the transmission of knowledge. Robin Osborne is Professor of Ancient History at the University of Cambridge and a Fellow of King’s College. He has published widely in Greek history, archaeology and art history. Catherine Rubincam is Associate Professor Emerita at the University of Toronto. Her current project is a database of quantifiable information on every number in the texts of the

notes on contributors

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major Greek historians, and a forthcoming monograph, Quantifying Mentalities: Numbers in Ancient Greek Historiography (2021). Daniel Mahendra Jan Sicka worked as Stipendiary Lecturer in Classics at St. John’s College, Oxford. His main research area lies in early and Classical Greek poetry, with particular interests in lyric metre, metatextuality, syntactic ambiguity, and the enactment of meaning through style. Robert Sing received his Ph.D. in Classics from the University of Cambridge. He has since published on the Demosthenic corpus and the Athenian system of pay for political participation. Tazuko Angela van Berkel is University Lecturer in Classics at Leiden University. She has published on Protagoras, Xenophon, friendship, ancient economic reflection and the rhetoric of numbers. Her 2020 monograph The Economics of Friendship was published by Brill.

introduction

Doing Things with Numbers Robert Sing, Tazuko Angela van Berkel and Robin Osborne

Numbers are ubiquitous and at the same time easy to overlook. Their presence tends to be taken for granted and we seldom reflect on how they constantly shape our daily experience—in the privacy of our homes and heads, and in the public realm, where we communicate and debate with people we do not personally know, when we contest facts, advocate causes and evaluate performances. Numbers serve two main roles in contemporary Western societies: to manage things and to persuade others. In both cases, a significant part of the control we achieve through numbers is due to the qualities that we attribute to them. The power of numbers comes from our assumption that they are normatively accurate and precise, that is, that they have been obtained through orderly and rigorous procedures that cancel out the subjective interests and idiosyncrasies of individuals.1 Numbers enable management because it is through numbers that we experience large-scale structures, from businesses to national economies and societies, as knowable and open to comparison and design. They allow us to understand decision-making as a form of calculation characterised by orderly and objective procedures, and we approach performance as something that can be enhanced with the use of targets, rankings and intelligence. Numbers are central to persuasion in part because of our expectation that they will be accurate, precise and reliable, and so they do well in the competition for public attention. That there are proverbially, of course, ‘lies,

1 Historically, modern statistics, originally called ‘political arithmetic’ in the Anglophone world, developed in tandem with the centralising tendencies of national bureaucracies. As T.M. Porter has shown in The Rise of Statistical Thinking, 1820–1900 (Princeton: Princeton University Press, 1986), standardisation of accounts and quantitative rigour are essentially adaptations to the demands of nation states for bureaucratic oversight, cf. his Trust in Numbers: the Pursuit of Objectivity in Science and Public Life (Princeton: Princeton University Press, 1995). Porter, ‘The Management of Society by Numbers’, in D. Pestre and J. Krige (eds), Companion Encyclopedia of Science in the Twentieth Century (London: Routledge, 2002), 97–110, observes at 97 how bureaucratic strategies for ‘managing populations and economies’ have in turn helped to define ‘what it means to be scientific’, arguing against a popular misconception that the push for quantitative rigour in management and politics originates in a vicarious desire to become more scientific.

© Robert Sing, Tazuko Angela and Robin Osborne, 2022 | doi:10.1163/9789004467224_002

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damned lies and statistics’ reflects our simultaneous awareness that numbers can all too easily be used in misleading ways.2 Selectivity is at the root of much of this persuasion, honest or not. Numbers that start off life as the calculations or estimates of experts, formulated within very specific parameters or probabilistic ranges, end up being rounded, misapplied or stripped of qualifiers.3 In a contemporary context of declining public trust in expertise and an increasingly siloed media landscape, the misrepresentation or outright fabrication of numeric information in public discourse has become a serious obstacle to forging agreement based on a shared foundation of fact.4 All this is to say that the ways we use and think about numbers are shaped not just by the pragmatics of what we are technically capable of counting, but by understandings about how numbers are produced, used and understood that are neither universal nor timeless. Until recently, the study of numbers in the ancient world has been concentrated in three areas: theoretical mathematics,5 philosophy,6 and the daily realia of the ancient world, especially the technology and expertise of counting

2 See D.N. McCloskey, Econometric History (London: MacMillan Education, 1987), esp. 41–60, and The Rhetoric of Economics (Madison, WI: University of Wisconsin Press, 1998), 100–111, on the rhetoric of statistics. 3 For the mechanics of the ‘social problems marketplace’ in which numbers compete, see J. Best, Damned Lies and Statistics (Berkeley: University of California Press, 2001), More Damned Lies and Statistics (Berkeley: University of California Press, 2004), ‘Birds—Dead and Deadly: Why Numeracy Needs to Address Social Construction’, Numeracy, 1/1 (2008), 1– 14. 4 For a satirical take on the fate of numbers in a so-called ‘post-truth’ America, see D. Maddox’s 2018 short film ‘Alternative Math’, 19 Sept. 2017, https://www.youtube.com/watch?v=​ Zh3Yz3PiXZw, accessed 1 Oct. 2018. 5 e.g. T. Heath, A History of Greek Mathematics, i: From Thales to Euclid (Oxford: Clarendon Press, 1921), 26–64 (Greek numerical notation and arithmetical operations), 65–117 (Pythagorean arithmetic); J. Klein, Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (Cambridge, MA: MIT Press, 1968; repr. New York: Dover, 1992); D.H. Fowler, The Mathematics of Plato’s Academy (2nd edn., Oxford: Clarendon Press, 1999). For the distinction between theoretical and ‘applied’ mathematics, see n. 51 below. 6 e.g. on Philolaus: M.C. Nussbaum, ‘Eleatic Conventionalism and Philolaus on the Conditions of Thought’, HSPh, 83 (1979), 63–108; C. Huffman, ‘The Role of Number in Philolaus’ Philosophy’, Phronesis, 33/1 (1988), 1–30. On Plato: D. Roochnik, ‘Counting on Number: Plato on the Goodness of Arithmos’, AJP, 115/4 (1994), 543–563; J.M. Moravcsik, ‘Plato on Numbers and Mathematics’, in P. Suppes, J.M. Moravcsik, and H. Mendell (eds), Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr (Stanford, CA: Centre for the Study of Language and Information, 2000), 177–195. Aristotle: T. Heath, Mathematics in Aristotle (Oxford: Clarendon Press, 1949), 206, 220–222; S. Gaukroger, ‘The One and the Many: Aristotle on the Individuation of Numbers’, CQ, 32/2 (1982), 312–322.

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3

and calculation.7 The numbers found in ancient writers have predominantly been taken at face value as data that are either true or false, realistic or unreliable, without sufficient sense of the pragmatic and communicative context in which they originally sat. The fundamental goal of the present volume is to demonstrate how social realities and cultural understandings shaped the production and use of numbers in the society of the Greek polis. ‘The polis’ is an abstraction that subsumes tremendous diversity. Just as Greek states visibly differentiated themselves from one another by using different ways of representing numerals, so they differentiate themselves for us through their different applications of number: more mercantile, democratic and militarily active poleis generated more numbers and used them to administer their financial resources and manpower. The source record for numbers, at its richest in the Classical period, is accordingly skewed towards Athens. The polis is, nevertheless, a meaningful frame through which to understand the societal and cultural embeddedness of numbers because it captures what is distinctive about Greek numeric practices. Every polis, at its physical heart, was a community of negotiated exchanges: a space where its inhabitants came together to transact and to participate, to give accounts and to be held accountable. The exchanges between self-governing and economically self-directed citizen equals invariably dominate our sources. Each of these citizens was a ‘valuing subject’ as well as a ‘valued object’8—one who, in both senses, counts. Numbers mattered in these interactions for their practical utility to quantify and to manage, but also for their power to communicate and persuade. The imbrication of numbers in the key institutions of the community, and the creation

7 On the abacus: M. Lang, ‘Herodotus and the Abacus’, Hesperia, 26 (1957), 271–288; ‘The Abacus and the Calendar’, Hesperia, 33 (1964), 146–167, ‘The Abacus and the Calendar ii’, Hesperia, 34 (1965), 224–257, ‘Abaci from the Athenian Agora’, Hesperia, 37 (1968), 241–243; A. Schärlig, Compter avec des cailloux: Le calcul élémentaire sur l’ abaque chez les anciens Grecs (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001). On notation: M.N. Tod, ‘The Greek Numeral Notation’, ABSA, 18 (1911–1912), 98–113, ‘Three Greek Numeral Systems’, JHS, 33 (1913), 27–34, ‘Further Notes on the Greek Acrophonic Numerals’, ABSA, 28 (1926–1927), 141– 157, ‘The Greek Acrophonic Numerals’, ABSA, 37 (1936–1937), 36–57, ‘The Alphabetic Numeral System in Attica’, ABSA, 45 (1950), 126–139; M. Lang, ‘Numerical Notation on Greek Vases’, Hesperia, 25 (1956), 1–24; L. Threatte, The Grammar of Attic Inscriptions, i: Phonology (Berlin: De Gruyter, 1980), 110–119; S. Chrisomalis, A Comparative History of Numerical Notation (Cambridge: Cambridge University Press, 2010). On Greek accounting methods: R.H. Macve, ‘Some Glosses on ‘Greek and Roman Accounting’ ’, History of Political Thought, 6/1–2 (1985), 233–264; R. Netz, ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321–352, at 329–334. 8 S. Johnstone, A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011), 10.

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of persuasive performances with numbers and about numbers for audiences, are consequently among the features of the polis that distinguish it from other forms of ancient social and political organisation.9

1

Approach

Numbers are cognitive tools used in human cultures in relation to quantities.10 Typical uses of numbers are counting, measuring and labelling. There is, however, more to be read in a number than a valid or invalid correspondence with a quantity in reality. Numbers, first, enable the cognitive processes by which information is made intelligible and valuable. They provide precision, condense information, facilitate comparison, commensurate or integrate data. At the same time, the choices that are always involved in the creation and deployment of numbers mean that every use of number is invested with

9

10

The point has been made in relation to specific forms of intellectual inquiry involving numbers, e.g. mathematics: ‘early Greek mathematics … was a public activity, it was played out in front of an audience, and it fulfilled functions that were significant at a communal level’ (S. Cuomo, Ancient Mathematics (London: Routledge, 2001), 39). In particular, the open debate and persuasion involved in polis life has been linked to the importance of argument and deductive, demonstrable proof to Greek scientific inquiry, see G.E.R. Lloyd, Demystifying Mentalities (Cambridge: Cambridge University Press, 1990), 57–67, 77–79, 96–97; R. Netz, The Shaping of Deduction in Greek Mathematics (Cambridge, 1999), 292– 298, 308– 12. On the contested relationship between polis life and early Greek uses of writing, see e.g. R. Thomas, Literacy and Orality in Ancient Greece (Cambridge: Cambridge University Press, 1992); D.T. Steiner, The Tyrant’s Writ: Myths and Images of Writing in Ancient Greece (Princeton: Princeton University Press, 1994); C.W. Hedrick ‘Writing, Reading, and Democracy’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 157–174; A. Missiou, Literacy and Democracy in Fifth-Century Athens (Cambridge: Cambridge University Press, 2011). For the links between the writing of accounts and being accountable see J.K. Davies, ‘Accounts and Accountability in Classical Athens’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics, 201–212; D. Harris, ‘Freedom of Information and Accountability: the Inventory Lists of the Parthenon’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics, 213–225, and S. Cuomo, ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper (ed.), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278. For the contrasting uses of numbers in ancient Mesopotamia, see E. Robson, Mathematics in Ancient Iraq: A Social History (Princeton: Princeton University Press, 2008). We use ‘numbers’ to refer to verbal or lexical numbers, ‘numerals’ for symbolic notations of numbers. In the world of the Greek polis, ‘number’ (arithmos) usually refers to positive integers greater than one. The Greeks conceptualised numbers as discrete entities; the notion of an infinitely divisible continuous number line was not common currency.

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meaning beyond quantification: numbers can, for example, reflect notions of justice, consensus, expertise, accountability and transparency; they can be thought of as ‘democratic’ or ‘kingly’,11 as ‘religious’ or ‘magical’, as ‘scientific’ or ‘poetic’. As a result of this communicative resonance, counting and calculation can be directed towards bigger goals. Numbers, in short, carry meanings that are historically contingent and culturally variable. In the polis, they might help to forge social distinctions by ranking, to commemorate as part of a civic economy of honour, or to intimidate through the enumeration of resources. There is something counterintuitive about the context-dependency of numbers. Numbers were long taken to be natural and native concepts—essential and self-evident parts of the human cognitive toolbox. It is still debated whether the human concept of number is a by-product of our language faculty12 or whether it is pre-cultural and pre-linguistic.13 What is clearly innate and hardwired as a result of natural selection is the human ‘number sense’: a basic sense of approximation that helps us distinguish ‘a pair’ from ‘a handful’ or ‘a shipload’.14 To discriminate 12 from 11, however, we need to parse the world into discrete categories, and this requires symbolic means such as number words, tallies or notational symbols.15 These symbolic means are culturally variable, accounting not only for variation in number systems across cultures,16 but also for differences in how numbers are understood. Empirical evidence suggests that something as seemingly self-evident and fundamental as a mental ‘number line’ (where natural numbers are arranged on a one-dimensional

11 12

13

14

15

16

e.g. M. Christ, ‘Herodotean Kings and Historical Inquiry’, CA, 13/1 (1994), 167–202. See N. Chomsky, Rules and Representations (New York: Columbia University Press, 1980); H. Wiese, Numbers, Language and the Human Mind (Cambridge: Cambridge University Press, 2003). See K. McComb, C. Packer and A. Pusey, ‘Roaring and Numerical Assessment in Contests between Groups of Female Lions, Panthera Leo’, Amimal Behaviour, 47 (1994), 379– 387; K. Wynn, ‘Psychological Foundations of Number: Numerical Competence in Human Infants’, Trends in Cognitive Sciences, 2 (1998), 296–303; B. Butterworth, What Counts: How Every Brain is Hardwired for Math (New York: Simon & Schuster, 1999). See P. Damerow, Abstraction and Representation: Essays on the Cultural Evolution of Thinking (Dordrecht: Kluwer Academic Publishers, 1996); S. Dehaene, The Number Sense: How the Mind Creates Mathematics (Oxford: Oxford University Press, 1997). The hunter-gatherer Pirahã Indians are a striking example in the anthropological record of a culture with no number words apart from ‘one or a little’ and ‘a little more’. See C. Everett, Numbers and the Making of Us: Counting and the Course of Human Cultures (Cambridge, MA: Harvard University Press, 2017), 113–141. See Everett, Numbers, 60–110. On the history of numerical notation systems, see T. Crump, The Anthropology of Numbers (Cambridge: Cambridge University Press, 1990); Chrisomalis, A Comparative History.

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line, with small numbers on the left and large numbers on the right) is not hardwired, but a cultural construction.17 Numbers have a basis both in universal human cognition and in human cultures and societies. How are we to think about the relationship between number and culture? The sociological approach taken in this volume, that of social constructionism, has become widespread in the humanities over the last two decades.18 To say that numbers are subject to social construction is not to condemn them to the dark recesses of extreme relativism. It means neither more, nor less, than that numbers are part of the processes by which people assign meaning to the world and that such forms of meaning-making are social in origin.19 As Joel Best puts it: ‘Every number is a product of people’s choices (…) People have to decide whether to count, what to count, how to go about counting, and how to summarize the results of that counting process’ (emphasis added).20 We should add that there is also a who making these choices. Quantitative information, whether expressed as numerals, graphs or formulas, is a strategy of communication.21 Numbers have stakeholders: decision-makers who want the invisible to be visible, governments that need to keep track of and allocate resources, auditors who want figures to scrutinise, managers who aspire to compare and improve performance, and interest groups devoted to the advocacy of causes.22

17

18

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20 21 22

S. Carey, ‘Cognitive Foundations of Arithmetic: Evolution and Ontogenesis’, Mind and Language, 16 (2001), 37–55. On how nineteenth-century conceptions about evolutions of culture still inform our thinking about societies with an absence or paucity of numeral words as being ‘primitive’, see S. Chrisomalis, ‘The Cognitive and Cultural Foundations of Numbers’, in E. Robson and J. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2008), 495–518. On the constructionist approach in historical research, see J. Best, ‘Historical Development and Defining Issues of Constructionist Inquiry’, in J.A. Holstein and J.F. Gubrium (eds), Handbook of Constructionist Research (New York: Guilford, 2008), 41–64. Although mathematics as a scientific discipline is often believed to be immune to Kuhnian paradigm shifts, this ignores the degree to which the use of mathematical ‘truths’ varies from culture to culture. For further discussion, see Calian in this volume. On the relation between social systems and classification systems, see E. Durkheim and M. Mauss, Primitive Classification, trans. R. Needham (1905; 2nd edn., London: Cohen and West, 1970). In terms of the ‘6 gradations of constructionism’ of I. Hacking, The Social Construction of What? (Cambridge, MA: Harvard University Press, 1999), we commit to ‘historical constructionism’, 19–21. Best, ‘Birds’, 3. Porter, Trust, viii: ‘They [i.e. numbers] are intimately bound up with forms of community, and hence also with the social identity of the researchers.’ See P.M. Jackson, ‘Governance by Numbers: What Have We Learned Over the Past 30 Years’, Public Money and Management, 31/1 (2011), 13–26.

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The array of choices behind numbers is well illustrated by one of the most influential numbers in our world—Gross Domestic Product. GDP was devised by the economist Simon Kuznet in 1934 as a way to aggregate economic activity into a single number that followed simple and aesthetic criteria: it goes up when things go well and it goes down when things go badly. The number clearly has its merits. It has the obvious advantage of providing a uniform and standardised metric, and GDP per capita allows comparison of data between different countries. On the other hand, it relies on judgements about what is to be counted (consumption, investment, government spending, exports minus imports) and what is not to be counted (social inequalities and ecological impacts). There is also a who: since the invention of GDP, technical specialists—professional economists and central bankers—have become the key authorities in economic discourse and policy. Finally, there is an established practice of how (including when) to publish the results of the GDP calculation: as a decimal percentage on a quarterly basis. GDP is rather less than an objective measure of reality than the product of a contestable set of historically and culturally-contingent choices. Fundamental cultural predispositions also influence the terms in which GDP, or any performance metric, is subsequently discussed and applied in order to maximise its impact. Recent work in governance, management and public administration studies on ‘management by numbers’ indicates that the ranking of results has most effect in competitive individualistic communities, whereas targets work best in hierarchical communities that stress the importance of collective units and have high levels of trust in authority. Virtually any form of management by numbers will be ineffective in ‘fatalistic’ communities with strong distrust in authority and weak interpersonal bonds.23 Social and cultural context can shape not only individual uses of numbers but, at the most abstract level, the type of quantitative paradigm that dominates the collective imagination. Keith Hart has argued that statistical paradigms are one of the ‘forms’ through which we perceive cultural order.24 Whereas the prevalent statistical paradigm for the great part of the twentieth century was the Normal Distribution or the Bell Curve, characterised by symmetry, a continuous variable, and conformity to a central tendency, the latter part of the century witnessed the rise of the Power Law Distribution, premised on extreme

23

24

C. Hood, ‘Public Management by Numbers as a Performance-enhancing Drug: Two Hypotheses’, Public Administration Review, 72 (2012), 85–92, using the Grid/Group-classification from M. Douglas, ‘Risk as a Forensic Resource’, Daedalus, 119/4 (1990), 1–16. K. Hart, ‘From Bell Curve to Power Law. Distributional Models between National and World Society’, Social Analysis, 48/3 (2004), 220–224.

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inequality, and exponential rather than continuous growth. Is this indicative of a larger paradigm shift from an egalitarian and atomistic worldview to a physics of complexity and interconnectivity? We may see an analogue in ancient philosophical discussions of ‘geometric’ and ‘arithmetic’ models of equality and justice, where geometric and proportional equality is used to model an aristocratic world view, and arithmetic and numerical equality is used to express a democratic value system.25 The influence of culture on numbers is not one way. Numbers can exert their own force on society, institutions and interactions. Critics have often pointed out how the GDP metric seriously warps our understanding of well-being and progress, while others, accustomed to the policies and assumptions that GDP has engendered, continue to advocate its value.26 These relationships of historical cause and effect can sometimes be difficult to untangle. Werner Sombart famously claimed that the invention of double entry bookkeeping, one of the ‘finest inventions of the human mind’,27 was driven by the needs of the capitalism that emerged in the trading cities of Renaissance Italy.28 Jane GleesonWhite argued just the reverse, that the economic transformation of early capitalism was predicated on the advent of double entry bookkeeping.29 The model of causality behind both views has been attacked as too narrow.30 Michael Hobart, abandoning the language of direct causes, suggests that the seemingly

25

26

27

28 29 30

See, for example, Isoc. 7.21–22; Arist. Eth. Nic. 1131a20–b24, Pol. 1301a19–1302a15, 1318a3– 27; Archytas 47B3 DK. See F.D. Harvey, ‘Two Kinds of Equality’, C&M, 26 (1965), 101–146; C. Huffman, Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King (Cambridge: Cambridge University Press, 2005). e.g. ‘We are Stealing the Future, Selling it in the Present, and Calling it GDP’ (P. Hawken, Commencement Address to the Class of 2009 at the University of Portland, Portland, OR, 3 May 2009). See further, L. Fioramonti, Gross Domestic Problem: the Politics Behind the World’s Most Powerful Number (London: Zed Books, 2013). Goethe’s Werner in Wilhelm Meisters Lehrjahre, i.10 (Berlin, 1795; Stuttgart: Philipp Reclam, 1982), 35: ‘Welche Vorteile gewährt die doppelte Buchhaltung dem Kaufmanne! Es ist eine der schönsten Erfindungen des menschlichen Geistes …’. The first printed explanation of the principles of double entry bookkeeping occurs in a small section of Luca Pacioli’s 1494 Summa de Arithmetica, geometria, proportioni et proportionalità. W. Sombart, Der Moderne Kapitalismus, ii.1 (Munich & Leipzig: Duncker & Humblot, 1924), 118–119. J. Gleeson-White, Double Entry: How the Merchants of Venice Created Modern Finance (New York: W.W. Norton & Co, 2012). Against Sombart, see B. Yamey, ‘Scientific Bookkeeping and the Rise of Capitalism’, Economic History Review, 2/1 (1949), 99–113; M. Power, ‘From the Science of Accounts to the Financial Accountability of Science’, in M. Power (ed.), Accounting and Science: Natural Inquiry and Commercial Reason (Cambridge: Cambridge University Press, 1996), 1–35. Against Gleeson-White, see K. Hoskin, D. Ma and R.H. Macve, ‘A Genealogy of Myths

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small and isolated innovations of the Renaissance, such as the business contract, the polyphonic motet, perspective drawing and clocks, all ‘betoken’ a larger shift in information technology. For Hobart, there was a movement from the impulse to ‘name, identify and group’, in short the ‘classifying temper’ of the European Middle Ages, to a relational numeracy—a science of patterns, instigated by the adoption of Hindu-Arabic numerals, positional counting, and double entry bookkeeping.31 In the case of ancient Greece, we may also detect shifts in which numbers catalyse changes, both in themselves and in tandem with related social technologies such as literacy, epigraphic practice, listing and tabular formatting.32 Money is another, particularly important, example. Money made everything theoretically reducible to numbers, and fractional denominations of coinage allowed individuals to conduct exchanges by the comparatively quick and simple act of counting coins.33 It was consequently through money that numbers became critical to the organisation of daily life for many Greeks, and a great deal of work has been done on the role coinage played in the wider cultural and ideological formation of the polis.34

31 32

33 34

about the Rationality of Accounting in the West and in the East’, SSRN, 27 Nov. 2013, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2389309, accessed 24 Mar. 2021. M.E. Hobart, The Great Rift: Literacy, Numeracy, and the Religion-Science Divide (Cambridge, MA: Harvard University Press, 2018). On the complex relationship between ‘public literacy’ (the epigraphic habit) and political culture and organisation, see R. Thomas, Literacy, and R. Osborne, ‘Introduction. Ritual, Finance, Politics: an Account of Athenian Democracy’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 1–21. On Greek literacy more generally, see C. Pébarthe, Cité, Démocratie et Écriture: Histoire de l’ alphabétisation d’Athènes à l’époque classique (Paris: De Boccard, 2006). On monetisation and the cultural history of numbers, see T. Crump, ‘Money and Number: the Trojan Horse of Language’, Man, 13 (1978), 503–518, see further n. 34. On the continuities and differences between lists in oral and literate cultures, see A. Kirk, ‘The List as Treasury in the Greek World’, Ph.D. thesis (University of California Berkeley, 2011) and E. Minchin, ‘The Performance of Lists and Catalogues in the Homeric Epics’, in I. Worthington (ed.), Voice into Text: Orality and Literacy in Ancient Greece (Leiden: Brill, 1996), 3–20. On numbers and tabular formatting, see Cuomo, ‘Accounts’. Netz, ‘Counter Culture’, 329–334. See, most importantly, S. von Reden, Exchange in Ancient Greece (London: Duckworth, 1995); L. Kurke, Coins, Bodies, Games, and Gold: the Politics of Meaning in Archaic Greece (Princeton: Princeton University Press, 1999) with J.H. Kroll, review of L. Kurke, Coins, Bodies, Games, and Gold: the Politics of Meaning in Archaic Greece (Princeton, NJ: Princeton University Press, 1999), in CJ, 96 (2000), 85–90; D.M. Schaps, The Invention of Coinage and the Monetization of Ancient Greece (Ann Arbor: University of Michigan Press, 2004);

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To identify the constraints and choices behind a number is to open up a latent dimension of meaning and influence. Numbers, once defamiliarised in this way, are often unintentionally communicative. In some performances, numbers are supporting actors, suggesting the pragmatics of numeric practice and the unconscious cultural assumptions of the calculator. At other times, numbers and their meanings are purposefully front and centre. The interpretation of cultural meaning, consciously intended or not, is always to some degree context-contingent (a fact which necessarily applies to the present volume as well). Greeks themselves could interpret the numeric behaviours of non-Greek societies in terms of the wider opposition they drew between the autonomy of the polis and the hierarchy of eastern monarchical states: non-Greeks did not participate in counts but were the counted objects of their rulers, and such quantification was a strategy of despotic control and conquest, never a rhetorical tactic to win audiences to a cause.35 Within Greece, an Athenian might understand an inscribed catalogue of confiscated property primarily as a demonstration of the transparency of the public officials involved; elsewhere, it might more easily be seen as a bid to encourage law-abiding behaviour through evidence of punishment.36 While keeping in mind the limits of our interpretative reach, it is just as important to be open to the inherent ambiguity and mutability of meaning in many numeric performances. The reticence of numbers can enable them to support multiple, non-exclusive readings, sometimes intentionally. Moreover, if the calculator lacks control over the future context of the communication of their counting, the constellation of possible meanings will shift according to the precise historical moment and the individual. Whether the columns of numbers on the Athenian ‘Tribute Lists’ proclaim piety, power, transparency or (more plausibly) ‘all of the above’ depends, then, not just on Greek (specifically Athenian) cultural understandings, but who is looking and when.37 The difficulty of pinning down one message or even mapping out the possible messages of some numeric performances is another reason for the importance of numbers as a tool of communication in the polis.

35 36 37

R. Seaford, Money and the Early Greek Mind (Cambridge: Cambridge University Press, 2004). See van Berkel and Sing in this volume. On the ‘Attic stelae’, see W.K. Pritchett, ‘The Attic Stelai: Part i’, Hesperia, 22/4 (1953), 225– 299; W.K. Pritchett and A. Pippin, ‘The Attic Stelai: Part ii’, Hesperia, 25/3 (1956), 178–323. On the Athenian Tribute Lists and their function, see R. Thomas, Oral Tradition and Written Record (Cambridge: Cambridge University Press, 1989), 60ff., and Kallet in this volume pp. 52–53.

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Scholarly attention in classics has come relatively late to the social construction of numbers, largely because the subject has fallen through the cracks of traditional disciplinary divides. Several important studies have appeared in recent years, and they fall into two broad groups. The first is primarily concerned with exploring how the production and conception of numbers was embedded in everyday social life. Quantification is a ‘social technology’38— something that is used by people to do things in the real world. As such, when Greeks engaged with numbers, they did so with a certain amount of shared knowledge about numbers in their society, an awareness of their own level of numeracy (‘the ability to count, keep records of these counts, and make rational calculations’)39 and that of others, how different numbers were generated, and what information a given number was actually providing. The first study to foreground explicitly the embeddedness of all Greek numeric practices in the public context of the polis was Serafina Cuomo’s Ancient Mathematics (2001). Cuomo departs from the traditional template of the historiography of science by offering what is essentially an ethnography of mathematics up to the sixth century ce. As such, the survey synthesises the development of scientific and philosophical knowledge with the everyday numbers of commercial exchange and the work of skilled professionals like surveyors and architects. These diverse practices are set within their social, cultural and political contexts, focusing on the people involved: their practical purposes, communicative aims, and ideological agendas.40 Cuomo’s volume was followed by Reviel Netz’s avowedly programmatic 2002 article ‘Counter Culture’. Netz calls for a ‘cognitive’ history of numeracy: a history of the culturally-specific ways that the mental and physical operation of calculating shaped the conception of what numbers are. For Netz, this had wide implications in Greece. He sees a ‘coherent pattern of cultural activities’ stemming from the practice of calculating by manipulating physical counters across a flat surface, not by writing out abstract values on a page.41 The Greek conception of numbers as discrete and tactile, rather than continuous and visual, helps to explain, for example, why argument takes written form but calculation does not, and the nature of that peculiarly Greek phenomenon of coined money.42

38 39 40 41 42

Porter, Trust, 49. R.J. Emigh, ‘Numeracy or Enumeration? The Use of Numbers by States and Societies’, Social Science History, 26/4 (2002), 653–698, at 653. Cf. Netz, The Shaping of Deduction, 271–312, on the elite backgrounds and concerns of Greek mathematicians. Netz, ‘Counter Culture’, 324. See p. 9.

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Netz’s demonstration of the cultural ramifications of calculation have informed the subsequent research agenda. Cuomo (2013) reframed problems of authorship and readership with respect to inscribed fifth-century Athenian accounts by reappraising the influence of their political and cultural setting. Cuomo concludes that while ordinary citizens (not slaves or professionals) were the most likely calculators, the problematic combination of openness and impenetrability that we find in the content and layout of the documents—their ‘transparent opaqueness’—cannot be understood solely in terms of democracy.43 Rather, we must look to Athens’ identity as both democracy and empire, simultaneously demanding accountability as well as control. The pivotal influence of social and economic realities on numbers with respect to measuring and valuing has been demonstrated by Steven Johnstone in A History of Trust (2011). Practical obstacles and information uncertainties meant that exact valuing with numbers was sometimes not possible, and consequently numeric measurements are not the accurate, precise, and objective figures that we might assume them to be. The impracticality of always using universal, standard measures meant that measuring and tracking consumption in the oikos was done through the non-standard but consistent measurement of containers. Similarly, the difficulty of establishing clear market values for land, and the impossibility of knowing if an individual had made a full declaration of their assets, meant that numbers expressing wealth ultimately derive their transactional validity from social agreement, not empirical verification.44 Here numbers are valuable not because they are impersonal but the reverse: they proceed from and signify personal agreement. Since numbers carry meaning in addition to their value, they can be used to do more than organise and convey information. The other focus of social constructionist research has been the understanding of how, on the level of individuals and their audiences, texts reproduce and reshape the cultural meanings of numbers for persuasive ends. These performances ranged from the silent numbers displayed in inscribed accounts or monuments of athletic victory, to the verbalised calculations of orators and actors. The societal production of meaning, and its persuasive reproduction and interrogation are not, of course, separate topics of study. The scholarship of Catherine Rubincam45 on numbers

43 44 45

See also Davies, ‘Accounts’; Harris, ‘Freedom’. Johnstone, A History, 35–80 on measuring, 81–110 on valuing. See further Sing in this volume, pp. 207–209. C. Rubincam, ‘Qualification of Numerals in the Constitution of Athens’, Phoenix, 33/4 (1979), 293–307, ‘Casualty Figures in the Battle Descriptions of Thucydides’, TAPA, 121 (1991), 181–198, ‘The Topography of Pylos and Sphakteria and Thucydides’ Measurement

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in Greek historiography has shown how important it is to keep one eye on the practical constraints and conventions of quantification not only when using figures as historical evidence, but when analysing persuasive intent. Rubincam’s stress on the danger of anachronistic assumptions about numbers in ancient texts has helped to effect something of a ‘communicative turn’ in the literary analysis of their function and presentation. For example, Matthew Christ46 and Alex Purves47 show that characters in Herodotus who are preoccupied with measuring and counting invariably have imperial projects in mind: they use numbers for self-aggrandisement and the demonstration of power, draw false comfort from numbers, and understand conquest through practices of quantification and measurement. For Herodotus and Thucydides, Emily Greenwood has instructively compared interpretations of numbers on character level with those on the authorial or narratorial level.48 Valeria Sergueenkova argues that engagements with large numbers throughout Herodotus’ work are not merely rhetorical strategies to bolster the narrator’s credibility or authority, but historiographical techniques for visualising power and comprehending immense timescales.49 Finally, the study by Athena Kirk of poetic catalogues and epigraphic inventories has brought to light a paradoxical trait of such lists. Their presentation of numbers does not facilitate but effectively discourages precise calculation: they seem to be invested in visualising or evoking ‘boundlessness’ rather than quantifiability.50

The Papers The volume is the first to be dedicated to numbers in the ancient world not solely in terms of mathematics or as epiphenomena of monetisation, ac-

46 47

48 49 50

of Distance’, JHS, 121 (2001), 77–90, ‘Numbers in Greek Poetry and Historiography: Quantifying Fehling’, CQ, 53/2 (2003), 448–463, ‘Herodotus and His Descendants: Numbers in Ancient and Modern Narratives of Xerxes’ Campaign’, HSPh, 104 (2008), 93–138. M. Christ, ‘Herodotean Kings’, cf. D. Konstan, ‘Persians, Greeks and Empire’, Arethusa, 20 (1987), 59–73. A. Purves, ‘The Plot Unravels: Darius’s Numbered Days in Scythia (Herodotus 4.98)’, Helios, 33/1 (2006), 1–26, Space and Time in Ancient Greek Narrative (Cambridge: Cambridge University Press, 2010), 143–144. E. Greenwood, ‘Surveying Greatness and Magnitude in Herodotus’, in T. Harrison and E. Irwin (eds), Interpreting Herodotus (Oxford: Oxford University Press, 2018), 163–186. V. Sergueenkova, ‘Counting the Past in Herodotus’ Histories’, JHS, 136 (2016), 121–131. Kirk, ‘The List’.

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counting or time keeping, for example, but as objects of study in their own right. Its papers continue the work of teasing out the impact of societal realities and persuasive communication on the use of numbers while making plain that both lines of inquiry are essential to recapture the framework that patterned Greek numeric practices and thinking. By doing so, the history of seemingly disparate things and practices—coins, casualties, ritual libations or trierarchies— can be seen together as drawing some of their meaning from their employment of numbers. What is offered up here is not a comprehensive survey of all numeric practices. While there is, to be sure, much discussion of Classical Athens, the individual papers span a range of Greek material from the sixth to the third centuries bce and collectively demonstrate both the fruits of an interdisciplinary approach and the tremendous scope for further work. Part 1, ‘Numbers in Society’, explores how social, political and economic activity shaped the way numbers were generated and used. Here, the focus is on documents that shed light on the use of numbers in daily life and political organisation. Relevant to many papers across the volume, but central here, is the question of the level of numeracy of ‘ordinary’ Greeks.51 We begin by trying to build a clearer picture of the upper end of the spectrum of numeric activity by focusing on Athens, the most prolific producer of numbers in the Greek world. Lisa Kallet, touching on many of the numeric practices that are explored in subsequent papers, argues that the prevalence of numbers at Athens must be understood in terms of the churn of transactions and calculations within the uniquely Athenian complex of democracy, empire and monetised exchange. Moreover, the democracy not only depended on but generated a numerate citizenry, through the collective numeric education of mass political participation and the group working that took place on official boards. Going further, Kallet draws on the evidence of popular culture in Old Comedy to demonstrate that the ubiquity of numbers, in turn, produced a quantifying mentality among Athenians. As ‘a counting people’, the importance of money to public and indi-

51

On the divide and distinction between ‘practical’ (sometimes referred to as ‘applied’, ‘amateur’ or ‘folk’) mathematics and ‘theoretical’ mathematics in the Greek world, see M. Asper, ‘The Two Cultures of Mathematics in Ancient Greece’, in E. Robson and J. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2009), 107–132. On the professional numeric skills of ‘practical’ practitioners, like surveyors, architects and bankers, see J.J. Coulton, Greek Architects at Work: Problems of Structure and Design (London: Elek, 1977), 58–68; E.E. Cohen, Athenian Economy and Society: A Banking Perspective (Princeton: Princeton University Press, 1992), 72–75, 83–84; selected papers in K. Verboven, K. Vandorpe and V. Chankowski (eds), PISTOI DIA TÈN TECHNÈN. Bankers, Loans and Archives in the Ancient World: Studies in Honour of Raymond Bogaert (Leuven: Peeters, 2008).

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vidual well-being meant that Athenians came to conceptualise power, as well as the good life it enabled, in terms of number, and valued that which was counted. As Kallet recognises, the evidence of numbers in public inscriptions is central to any discussion of everyday numeracy. Robin Osborne traces the changing way that Athenian inscriptions display numeric information, and reassesses the communicative intentions behind the inscribing of numbers. The use of numerals as workaday notation in trade helps to explain why numerals are invariably used to express monetary sums, as well as the apparent fifth-century ‘prejudice’ against inscribing numerals outside accounts. By contrast, in the fourth-century, numerals appear in a far wider range of inscriptions and are more likely to be embedded in continuous text, rather than highlighted through devices like columnar formatting. Osborne suggests that choices about the presentation of numbers were never principally about the clear communication of detailed information. The trend towards the more widespread, embedded use of numerals instead reflects an intensification of the Athenian view of numbers as quotidian, and reduced interest in the overall visual impact of numbers in a post-imperial setting. Steven Johnstone similarly finds new meaning in patterns of numeric usage, showing how in contexts of punishment and reward relationships between the citizen and the polis were symbolically evaluated and constructed through numbers. As such, quantified monetary penalties often do not derive from market values, but instead carry symbolic meaning. Fines in lawcodes can articulate the proportional relationships between different offences, criminals and victims, and the clustering of fines (and the value of honours) for poleis officials around specific amounts shows them being used to effect status changes in orders of magnitude (i.e. ‘some’ or ‘more’ (dis)honour). Johnstone posits that a similar process of commensuration took place in court when Athenian juries chose how large a fine to inflict. Astronomical fines and unquantified punishments (like exile), on the other hand, express the ‘incommensurability’ of punishments that excluded the citizen from the polis. Josine Blok brings another perspective to the high Athenian fines considered by Johnstone. Blok demonstrates that the immense fines sometimes specified in fifth-century decrees for non-compliant citizens and officials are part of a wider increase in the maximum level of fines in the 430s. Fines rose from maxima of 50–100 drachmae to 1,000 drachmae, and sometimes 10,000. Blok rejects the explanation that their primary purpose was to expedite public business. Rather, the fines can be linked to the political climate of the last third of the fifth century; they are expressions of the determination of a vindictive demos in the throes of war, egged on by populist leaders, to demonstrate

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its power and enrich itself. The approaches taken by Johnstone and Blok are exemplary: while making a case that numbers do more than signify quantities, neither dismisses the figure of 10,000 as an empty threat. Their complementary analyses of social and political meaning highlight the need for the contextual or ‘thick’ description of numbers. Catherine Rubincam again brings us closer to the original context in which numbers were used and understood, this time by Greek historians and their readers. Rubincam’s decades-long project of systematically coding the numeric expressions in the six earliest Greek historians (surveyed in an appendix) has produced a database that can be used to analyse statistically the type, subject and qualification of any particular number in terms of the text as a whole and Greek historiography more generally. The selected case studies not only provide salutary warnings about the pitfalls of imprecise or anachronistic readings and translations, but reveal the extent to which numbers that look problematic to us can be explained as the products of both the practical limits of knowledge and the numeric practice of a particular historian. Parts 2 and 3 focus on numbers in persuasive communication. Part 2, ‘Communicating with Numbers’, showcases the diverse ways numbers can be used to persuade: the presentational choices of poets, prose writers and speakers reproduce and reshape numbers’ cultural meanings in order to make their numbers rhetorically effective, that is, compelling and trustworthy. On occasion, we encounter explicit meditation on the complexity of persuasive numeric speech itself. Daniel Mahendra Jan Sicka examines how epinician poetry can present numbers in ways that exploit the epistemological limitations of the audience. Studied linguistic ambiguity and the manipulation of attribution are used by Pindar and, as Sicka shows, other epinician media, to enable the interpretation that a patron won more victories than was actually the case. Additionally, a less impressive tally can be enhanced by attributing exceptional qualities to it, or excused through counterfactual suggestion. The poets, however, nearly always stop short of outright fabrication, in part because the effectiveness of their misleading praise would only grow as the distance in time and space increased between each reperformance and those with independent knowledge of the actual record. Tazuko Angela van Berkel shows how close study of Thucydides’ Sicilian Debate reveals the disingenuous rejection and suppression of numbers, as well as misunderstandings about how others use and interpret figures and qualifiers. For Thucydides, these epistemological failures stem from the agonistic context of democratic decision-making itself, which makes it impossible to arrive at agreed, accurate understandings of numeric information. This flawed ‘demo-

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cratic numeracy’ contrasts with the ‘critical numeracy’ of Thucydides’ himself, characterised by the careful evaluation of numbers, transparency and qualification. Van Berkel reads Thucydides’ occasional reluctance to state all of his own figures when calculating as a way of underscoring the need to acknowledge uncertainty, and of inviting readers to calculate for themselves. With Robert Sing we move from debates in historiography to the individual speeches themselves. In Athens, audiences in the assembly and courts were all too aware that speakers might try to mislead them using numbers. Verbal calculations could also be very different to follow. Sing surveys the ways that numbers were, consequently, performed by fourth-century orators to manage anxieties and maximise their persuasive power. Strategies like the exposition of calculations were used to make numeric claims appear credible—more like the kind of transparent, verified numbers used in the administration of the polis. Given how difficult it ultimately was to verify a numeric claim, numbers were most credible for Athenians when they were integrated into a compelling portrayal of character (ēthos). Skilled speakers understood the cultural associations of different kinds of numeric behaviour, and took care to portray others in ways that made allegations about their conduct sound plausible. Equally, speakers could self-characterise as valuable advisors by exhibiting the praiseworthy handling of numbers. Part 3, ‘Conceptualising Number’, considers persuasive performances of numbers in front of smaller, specialised, reading audiences, where numbers are approached not only as instruments to think with, but as entities to think about. It has often been observed that the Greek lexeme ἀριθμός does not signify ‘number’ (German: Zahl) but ‘a number of [things]’ (German: Anzahl, Old English: Tale), that is, a numbered assemblage or a quantity of things rather than a concept.52 However, this did not preclude reflection on number as a concept, an entity or a force in its own right. It is significant that numbers themselves became an object of cultural and intellectual reflection in fifth and fourthcentury Greek societies: featuring in several Kulturentstehungslehre, numbers were seen as important inventions with an active, transformative force on human social life.53 Florin George Calian offers a reappraisal of Plato’s metaphysical number theory. In a close reading of the argument for the generation of numbers in

52

53

Klein, Mathematical Thought, 46–60. The (modern) mathematical notion of number is ‘metarepresentational’, i.e. it mentions numbers (‘five is more than four’) rather than using them (‘I have seven apples, five are red’). See D.R. Olson, The Mind on Paper: Reading, Consciousness and Rationality (Cambridge: Cambridge University Press, 2016), 65–84. e.g. Aesch. PV. 343–378; Eur. Phoen. 541; Gorg. Pal. fr. 82 B11a30 DK; Pl. Alc.i 126d2.

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Parmenides (142b–144a), Calian challenges the view that Plato’s conception of numbers is a ‘Platonist’ one. In line with common Greek parlance, in which ἀριθμός refers to natural numbers starting from two, Plato’s argument states the ontological primacy of two over one; moreover, ‘oddness’ and ‘evenness’, typically understood as properties of numbers in modern conceptualisation, behave as species in which numbers participate. Throughout Plato’s attempt to understand multiplicity we see how he does not envisage numbers as organised along a linear number line; rather, his is a hierarchical conception of numbers—a conception ontologically rooted in the One-Multiple dichotomy, but premised historically on broader developments in Greek conceptions of cardinal and ordinal numbers. The final paper, by Eunsoo Lee, tackles the surprising absence of numerals in the geometric proofs of Euclid’s Elements. Lee sees the geometer as setting forth a different method of quantification by measuring a figure (line, shape or area) in terms of another figure, through ratio and proportion. With this ‘visual magnitude counting’ we come full circle, for this conception of number as magnitude is shaped by the everyday practice of measuring an object by comparing it to an agreed standard. Moreover, it is suggested that a key reason for why this numberless strand of mathematics persisted was the competitive, performative intellectual tradition of Greece; the absence of number, in mathematical treatises, enabled the wondrous, suspenseful revelation of proof.

Bibliography Asper, M., ‘The Two Cultures of Mathematics in Ancient Greece’, in E. Robson and J. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2009), 107–132. Best, J., Damned Lies and Statistics (Berkeley: University of California Press, 2001). Best, J., More Damned Lies and Statistics (Berkeley: University of California Press, 2004). Best, J., ‘Birds—Dead and Deadly: Why Numeracy Needs to Address Social Construction’, Numeracy, 1/1 (2008), 1–14. Best, J., ‘Historical Development and Defining Issues of Constructionist Inquiry’, in J.A. Holstein and J.F. Gubrium (eds), Handbook of Constructionist Research (New York: Guilford, 2008), 41–64. Butterworth, B., What Counts: How Every Brain is Hardwired for Math (New York: Simon & Schuster, 1999). Carey, S., ‘Cognitive Foundations of Arithmetic: Evolution and Ontogenesis’, Mind and Language, 16 (2001), 37–55. Chomsky, N., Rules and Representations (New York: Columbia University Press, 1980).

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Chrisomalis, S., ‘The Cognitive and Cultural Foundations of Numbers’, in E. Robson and J. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2008), 495–518. Chrisomalis, S., A Comparative History of Numerical Notation (Cambridge: Cambridge University Press, 2010). Christ, M., ‘Herodotean Kings and Historical Inquiry’, CA, 13/1 (1994), 167–202. Cohen, E.E., Athenian Economy and Society: A Banking Perspective (Princeton: Princeton University Press, 1992). Coulton, J.J., Greek Architects at Work: Problems of Structure and Design (London: Elek, 1977). Crump, T., ‘Money and Number: the Trojan Horse of Language’, Man, 13 (1978), 503–518. Crump, T., The Anthropology of Numbers (Cambridge: Cambridge University Press, 1990). Cuomo, S., Ancient Mathematics (London: Routledge, 2001). Cuomo, S., ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper (ed.), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278. Damerow, P., Abstraction and Representation: Essays on the Cultural Evolution of Thinking (Dordrecht: Kluwer Academic Publishers, 1996). Davies, J.K., ‘Accounts and Accountability in Classical Athens’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994) 201–212. Dehaene, S., The Number Sense: How the Mind Creates Mathematics (Oxford: Oxford University Press, 1997). Douglas, M., ‘Risk as a Forensic Resource’, Daedalus, 119/4 (1990), 1–16. Durkheim, E. and M. Mauss, Primitive Classification, trans. R. Needham (1905; 2nd edn., London: Cohen and West, 1970). Emigh, R.J., ‘Numeracy or Enumeration? The Use of Numbers by States and Societies’, Social Science History, 26/4 (2002), 653–698. Everett, C., Numbers and the Making of Us: Counting and the Course of Human Cultures (Cambridge, MA: Harvard University Press, 2017). Fioramonti, L., Gross Domestic Problem: the Politics Behind the World’s Most Powerful Number (London: Zed Books, 2013). Fowler, D.H., The Mathematics of Plato’s Academy (2nd edn., Oxford: Clarendon Press, 1999). Gaukroger, S., ‘The One and the Many: Aristotle on the Individuation of Numbers’, CQ, 32/2 (1982), 312–322. Gleeson-White, J., Double Entry: How the Merchants of Venice Created Modern Finance (New York: W.W. Norton & Co, 2012). Goethe, J.W. von, Wilhelm Meisters Lehrjahre, i (Berlin, 1795; Stuttgart: Philipp Reclam, 1982).

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Greenwood, E., ‘Surveying Greatness and Magnitude in Herodotus’, in T. Harrison and E. Irwin (eds), Interpreting Herodotus (Oxford: Oxford University Press, 2018), 163– 186. Hacking, I., The Social Construction of What? (Cambridge, MA: Harvard University Press, 1999). Harris, D., ‘Freedom of Information and Accountability: the Inventory Lists of the Parthenon’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 213– 225. Hart, K., ‘From Bell Curve to Power Law. Distributional Models Between National and World Society’, Social Analysis, 48/3 (2004), 220–224. Harvey, F.D., ‘Two Kinds of Equality’, C&M, 26 (1965), 101–146. Hawken, P., Commencement Address to the Class of 2009 at the University of Portland, Portland, OR, 3 May 2009. Heath, T., A History of Greek Mathematics, i: From Thales to Euclid (Oxford: Clarendon Press, 1921). Heath, T., Mathematics in Aristotle (Oxford: Clarendon Press, 1949). Hedrick, C.W., ‘Writing, Reading, and Democracy’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 157–174. Hobart, M.E., The Great Rift: Literacy, Numeracy, and the Religion-Science Divide (Cambridge, MA: Harvard University Press, 2018). Hood, C., ‘Public Management by Numbers as a Performance-enhancing Drug: Two Hypotheses’, Public Administration Review, 72 (2012), 85–92. Hoskin, K., D. Ma and R.H. Macve, ‘A Genealogy of Myths about the Rationality of Accounting in the West and in the East’, SSRN, 27 Nov. 2013, https://papers.ssrn.com/​ sol3/papers.cfm?abstract_id=2389309, accessed 24 Mar. 2021. Huffman, C., ‘The Role of Number in Philolaus’ Philosophy’, Phronesis, 33/1 (1988), 1–30. Huffman, C., Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King (Cambridge: Cambridge University Press, 2005). Jackson, P.M., ‘Governance by Numbers: What Have We Learned Over the Past 30 Years’, Public Money and Management, 31/1 (2011), 13–26. Johnstone, S., A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011). Kirk, A., ‘The List as Treasury in the Greek World’, Ph.D. thesis (University of California Berkeley, 2011). Klein, J., Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (Cambridge, MA: MIT Press, 1968; repr. New York: Dover, 1992). Konstan, D., ‘Persians, Greeks and Empire’, Arethusa, 20 (1987), 59–73. Kroll, J.H., review of L. Kurke, Coins, Bodies, Games, and Gold: the Politics of Meaning

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in Archaic Greece (Princeton, NJ: Princeton University Press, 1999), in CJ, 96 (2000), 85–90. Kurke, L., Coins, Bodies, Games, and Gold: the Politics of Meaning in Archaic Greece (Princeton: Princeton University Press, 1999). Lang, M., ‘Numerical Notation on Greek Vases’, Hesperia, 25 (1956), 1–24. Lang, M., ‘Herodotus and the Abacus’, Hesperia, 26 (1957), 271–288. Lang, M., ‘The Abacus and the Calendar’, Hesperia, 33 (1964), 146–167. Lang, M., ‘The Abacus and the Calendar ii’, Hesperia, 34 (1965), 224–257. Lang, M., ‘Abaci from the Athenian Agora’, Hesperia, 37 (1968), 241–243. Lloyd, G.E.R., Demystifying Mentalities (Cambridge: Cambridge University Press, 1990). Macve, R.H., ‘Some Glosses on ‘Greek and Roman Accounting’’, History of Political Thought, 6/1–2 (1985), 233–264. Maddox, D., ‘Alternative Math’ [video], 19 Sept. 2017, https://www.youtube.com/watch​ ?v=Zh3Yz3PiXZw, accessed 1 Oct. 2018. McCloskey, D.N., Econometric History (London: MacMillan Education, 1987). McCloskey, D.N., The Rhetoric of Economics (2nd edn., Madison, WI: University of Wisconsin Press, 1998). McComb, K., C. Packer and A. Pusey, ‘Roaring and Numerical Assessment in Contests between Groups of Female Lions, Panthera Leo’, Animal Behaviour, 47 (1994), 379– 387. Minchin, E., ‘The Performance of Lists and Catalogues in the Homeric Epics’, in I. Worthington (ed.), Voice into Text: Orality and Literacy in Ancient Greece (Leiden: Brill, 1996), 3–20. Missiou, A., Literacy and Democracy in Fifth-Century Athens (Cambridge: Cambridge University Press, 2011). Moravcsik, J.M., ‘Plato on Numbers and Mathematics’, in P. Suppes, J.M. Moravcsik and H. Mendell (eds), Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr (Stanford, CA: Center for the Study of Language and Information, 2000), 177–195. Netz, R., The Shaping of Deduction in Greek Mathematics (Cambridge: Cambridge University Press, 1999). Netz, R., ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321– 352. Nussbaum, M.C., ‘Eleatic Conventionalism and Philolaus on the Conditions of Thought’, HSPh, 83 (1979), 63–108. Olson, D.R., The Mind on Paper: Reading, Consciousness and Rationality (Cambridge: Cambridge University Press, 2016). Osborne, R., ‘Introduction. Ritual, Finance, Politics: An Account of Athenian Democracy’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 1–21.

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Pébarthe, C., Cité, Démocratie et Écriture: Histoire de l’alphabétisation d’Athènes à l’époque classique (Paris: De Boccard, 2006). Porter, T.M., The Rise of Statistical Thinking, 1820–1900 (Princeton: Princeton University Press, 1986). Porter, T.M., Trust in Numbers: the Pursuit of Objectivity in Science and Public Life (Princeton: Princeton University Press, 1995). Porter, T.M., ‘The Management of Society by Numbers’, in D. Pestre and J. Krige (eds), Companion Encyclopedia of Science in the Twentieth Century (London: Routledge, 2002), 97–110. Power, M., ‘From the Science of Accounts to the Financial Accountability of Science’, in M. Power (ed.), Accounting and Science: Natural Inquiry and Commercial Reason (Cambridge: Cambridge University Press, 1996), 1–35. Pritchett, W.K., ‘The Attic Stelai: Part i’, Hesperia, 22/4 (1953), 225–299. Pritchett, W.K. and A. Pippin, ‘The Attic Stelai: Part ii’, Hesperia, 25/3 (1956), 178–323. Purves, A., ‘The Plot Unravels: Darius’s Numbered Days in Scythia (Herodotus 4.98)’, Helios, 33/1 (2006), 1–26. Purves, A., Space and Time in Ancient Greek Narrative (Cambridge: Cambridge University Press, 2010). Reden, S. von, Exchange in Ancient Greece (London: Duckworth, 1995). Robson, E., Mathematics in Ancient Iraq: a Social History (Princeton: Princeton University Press, 2008). Roochnik, D., ‘Counting on Number: Plato on the Goodness of Arithmos’, AJP, 115/4 (1994), 543–563. Rubincam, C., ‘Qualification of Numerals in the Constitution of Athens’, Phoenix, 33/4 (1979), 293–307. Rubincam, C., ‘Casualty Figures in the Battle Descriptions of Thucydides’, TAPA, 121 (1991), 181–198. Rubincam, C., ‘The Topography of Pylos and Sphakteria and Thucydides’ Measurement of Distance’, JHS, 121 (2001), 77–90. Rubincam, C., ‘Numbers in Greek Poetry and Historiography: Quantifying Fehling’, CQ, 53/2 (2003), 448–463. Rubincam, C., ‘Herodotus and His Descendants: Numbers in Ancient and Modern Narratives of Xerxes’ Campaign’, HSPh, 104 (2008), 93–138. Schaps, D.M., The Invention of Coinage and the Monetization of Ancient Greece (Ann Arbor: University of Michigan Press, 2004). Schärlig, A., Compter avec des cailloux: Le calcul élémentaire sur l’abaque chez les anciens Grecs (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001). Seaford, R., Money and the Early Greek Mind (Cambridge: Cambridge University Press, 2004). Sergueenkova, V., ‘Counting the Past in Herodotus’ Histories’, JHS, 136 (2016), 121–131.

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Sombart, W., Der Moderne Kapitalismus, ii.1 (Munich & Leipzig: Duncker & Humblot, 1924). Steiner, D.T., The Tyrant’s Writ: Myths and Images of Writing in Ancient Greece (Princeton: Princeton University Press, 1994). Thomas, R., Oral Tradition and Written Record in Classical Athens (Cambridge: Cambridge University Press, 1989). Thomas, R., Literacy and Orality in Ancient Greece (Cambridge: Cambridge University Press, 1992). Threatte, L., The Grammar of Attic Inscriptions, i: Phonology (Berlin: De Gruyter, 1980). Tod, M.N., ‘The Greek Numeral Notation’, ABSA, 18 (1911–1912), 98–113. Tod, M.N., ‘Three Greek Numeral Systems’, JHS, 33 (1913), 27–34. Tod, M.N., ‘Further Notes on the Greek Acrophonic Numerals’, ABSA, 28 (1926–1927), 141–157. Tod, M.N., ‘The Greek Acrophonic Numerals’, ABSA, 37 (1936–1937), 236–258. Tod, M.N., ‘The Alphabetic Numeral System in Attica’, ABSA, 45 (1950), 126–139. Verboven, K., K. Vandorpe and V. Chankowski (eds), PISTOI DIA TÈN TECHNÈN. Bankers, Loans and Archives in the Ancient World: Studies in Honour of Raymond Bogaert (Leuven: Peeters, 2008). Wiese, H., Numbers, Language and the Human Mind (Cambridge: Cambridge University Press, 2003). Wynn, K., ‘Psychological Foundations of Number: Numerical Competence in Human Infants’, Trends in Cognitive Sciences, 2 (1998), 296–303. Yamey, B., ‘Scientific Bookkeeping and the Rise of Capitalism’, Economic History Review, 2/1 (1949), 99–113.

part 1 Numbers in Society

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chapter 1

A Counting People: Valuing Numeracy in Democratic Athens Lisa Kallet

κᾆτ’ ἐπειδὰν ὦ μόνος, στένω κέχηνα σκορδινῶμαι πέρδομαι, ἀπορῶ γράφω παρατίλλομαι λογίζομαι and in my solitude I sigh, I yawn, I stretch myself, I fart, I fiddle, scribble, pluck my beard, do sums aristophanes, Acharnians 29–311

… What people chose to count and measure reveals not only what was important to them, but what they wanted to understand and, often, what they wanted to control patricia cline cohen, A Calculating People: the Spread of Numeracy in Early America2

∵ In his visit to America in the nineteenth century, Alexis de Tocqueville observed a people with a calculating mentality and a penchant for statistics that were a source of pleasure.3 This was a new-enough conception as to be self-conscious,

1 All translations of Aristophanes are those of J. Henderson, Loeb Classical Library, unless otherwise noted. 2 P.C. Cohen, A Calculating People: The Spread of Numeracy in Early America (New York: Routledge, 1999), 206. 3 A. de Tocqueville, Democracy in America, J.P. Mayer and M. Lerner (eds), trans. G. Lawrence (New York: Harper & Row, 1966), 508–510; see also R. Lerner, ‘Commerce and Character: The Anglo-American as a New-Model Man’, William and Mary Quarterly, 34 (1979), 3–26.

© Lisa Kallet, 2022 | doi:10.1163/9789004467224_003

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one deriving from an explosion of commerce and facilitated by an egalitarian society. These reflections have much to offer to a study of counting and calculating in Athenian culture, one that Reviel Netz has termed a ‘counter culture’.4 In her discussion of accounts and accounting in fifth-century Athens, Serafina Cuomo considers a high level of numeracy likely among its citizens, regarding this as a function of both Athens’ political system and its empire. Drawing comparisons with Mesopotamia, with its highly educated scribal class, and Rome, where many public slaves might be employed for keeping accounts, she notes that Athens’ direct democracy required numeracy of its citizens at a level beyond mere counting. Indeed, she posits that because of the need for accounts and accounting, prima facie it was ‘inevitable that every citizen, in order to be a good citizen, ought also to possess some specialised knowledge’.5 Cuomo’s study highlights much about the ways in which Athenian democracy made numeracy a desideratum or even a necessity in the context of making accounts. I would like to build on her discussion by examining more fully the practical mechanisms and fora in which numerate skills (also here referred to as ‘financial literacy’, a term that recognises the need for writing in, for example, making accounts) were fostered, taught and learnt in the absence of formal education. Numeracy was a fundamental tool in the administrative bureaucracy of the democracy, as well as the empire, which increased significantly the need for financial literacy.6 In an earlier discussion on politicians as repositories of and experts on financial information, which

4 R. Netz, ‘Counter Culture: Toward a History of Greek Numeracy’, HS, 40 (2002), 321–352. Netz is writing about Greek culture generally, looking at the widespread use of pebble counters and the abacus, the largest concentration of which have been found in Athens. 5 S. Cuomo, ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper (ed.), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278 at 263–264. With it, Cuomo rightly insists on a citizenry capable of producing their own accounts at their euthynai. A nice illustration of the conspicuous recognition—and anxiety?—that the audit will come round at the end of a magistrate’s term is the fifth-century calendar of sacrifices from Thorikos (OR 146), which explicitly refers to the audit required of magistrates, and connects it to an oath, to be sworn by the magistrates and their assistants (paredroi) (ll. 57–65, cf. OR 107A.6, B.7–21, a decree of the deme Skambonidai, which also refers to the euthynē); see also, below, p. 34. On accounts and accountability, see the important discussion of J.K. Davies, ‘Accounts and Accountability in Classical Athens’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 201–212. 6 Numeracy, like literacy, was unrestricted among the inhabitants of Athens. A study of numer-

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they communicated to the demos, I argued that expertise at the top was crucial to citizens’ ability to make decisions on complex financial issues, especially those concerning the Athenian empire. I also argued that these leaders shaped and reinforced the notion that monetary revenue from the empire was essential to those citizens’ security and well-being, thereby instilling this notion over time as a virtual fact, not tied to any one particular individual or viewpoint.7 Yet while it is true that politicians were expected to have a range of knowledge in order to be persuasive to the majority of voters in the assembly, it does not follow that the demos was clueless. Indeed, the study of numeracy among Athenian citizens who participated in the democracy reveals the expectation that they be numerate because that skill was required in order for the administrative bureaucracy to function competently. From a cultural standpoint, numeracy both influenced and conditioned how Athenians thought about and expressed what mattered to them and how, as Cohen puts it, they wanted to control their world through quantification and statistics. And what mattered to Athenians was the good life due to their power. Moreover, power was not some abstraction incapable of definition and representation. Power was counted, quantified and measured in concrete forms (in a similar vein, Thucydides has Pericles represent power as something concrete, measured by signs and evidence, witnessed and acknowledged, 2.41). Numeracy was embedded in Athenian culture and spawned a quantitative mentality that determined value in terms of number.8 My focus here is the fifth century, because of two interlinked phenomena from the mid-century: significantly increased, paid democratic participation, and a naval empire that both required a large, paid political and military presence in the tributary cities, and funnelled monetary resources from those citizens to Athens annually.9 These linked phenomena, democracy and empire,

acy among the whole community, including female citizens, metics, and slaves, would be ideal, but is beyond the scope of this chapter, as is the distinction between numeracy in urbanised and rural Athens. 7 L. Kallet-Marx, ‘Money Talks: Rhetor, Demos and the Resources of the Athenian Empire’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 227–251, cf. Arist. Rh. 1359b8; Xen. Mem. 3.6.5–6; see also H. Yunis, ‘How do the People Decide? Thucydides on Periclean Rhetoric and Civic Instruction’, AJP, 112 (1991), 179–200. 8 Cohen, A Calculating People uses the term ‘quantitative mentality’ in her study of the spread of numeracy in nineteenth century America, in which statistics were socially valued. 9 Neither the democracy nor the empire were spun out of whole cloth in the early fifth century: the navy had already started to be developed on a large scale, see J.K. Davies, ‘Corridors,

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formed part of what made Athens exceptional; and numeracy was a significant, unappreciated part of that exceptionalism. I begin with a brief word on the latter.

1

Athenian ‘Exceptionalism’

Like other cities, Athens had a harbour/emporion, mines, coinage,10 a monetised public and private economy,11 and democracy.12 What, then, made Athens so remarkable? It was not simply a matter of size—or a greater abundance of evidence. It was both the scale and the combination of factors that have no comparison in the rest of the Greek world. In particular, Athens’ large, natural harbour and emporion at the Peiraieus became a magnet for merchants from around the Aegean, Black Sea, and Mediterranean, while Athens’ mining district in southern Attica at Laureion produced a staggering quantity of excep-

10 11

12

Cleruchies, Commodities, and Coins: The Pre-history of the Athenian Empire’, in A. Slawisch (ed.), Handels- und Finanzgebaren in der Ägäis im 5. Jh.V.Chr./ Trade and Finance in the 5th c. bc Aegean World (BYZAS, 18; Istanbul: Ege Yayinlari, 2013), 43–66; L. Kallet, ‘The Origins of the Athenian Economic Arche’, JHS, 133 (2013), 34–60; H. van Wees, Ships and Silver, Taxes and Tribute: A Fiscal History of Archaic Athens (London: I.B. Tauris, 2013), 63–81. At the same time, we should not overlook the importance of businesses, manufacturing, and retail markets for their role in advancing numeracy, see E.M. Harris, ‘Workshop, Marketplace and Household: the Nature of Technical Specialisation in Classical Athens and its Influence on Economy and Society’, in P. Cartledge, E.E. Cohen and L. Foxhall (eds), Money, Labour and Land: Approaches to the Economies of Ancient Greece (London: 2002), 67–99, focusing on the Classical period. Knowledge of the quantity of fractional coinage that existed from the beginning of silver coinage has revolutionised the understanding of early coinage and its implications on questions like numeracy, see H.S. Kim, ‘Small Change and the Moneyed Economy’, in Money, Labour and Land, 44–51. Gillan Davis and Kenneth Sheedy are in the process of assembling a corpus of Athenian Wappenmünzen from roughly the third quarter of the sixth century that includes a heretofore unappreciated quantity of fractional coinage. See below (n. 11) on small change and its implications. L. Kallet and J.H. Kroll, The Athenian Empire: Using Coins as Sources (Cambridge: Cambridge University Press, 2020), 39–88. Small change, normally difficult to account for (collectors tend to covet the large denominations), is an unequivocal marker of a monetised, market economy. Precious evidence from a representative small polis comes from a hoard found in the Ionian city of Kolophon containing enormous numbers of fractional coinage (up to millions of pieces) the lowest denomination of which is the ¼ obol, see H.S. Kim and J.H. Kroll, ‘A Hoard of Archaic Coins of Colophon and Unminted Silver (CH i.3)’, AJN, 20 (2008), 53–104 at 58–59. E.W. Robinson, Democracy Beyond Athens: Popular Government in the Greek Classical Age (Cambridge: Cambridge University Press, 2011).

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tionally pure silver and made it the largest exporter of silver, whether as coin or bullion, in the Greek world from the sixth century through to the fourth.13 Laureion was not just another mine.14 Athens’ naval empire, founded in 478 when the city created a naval alliance that Greeks joined thanks to the spectre of Persia, was exploitative at its core.15 Athens controlled its members primarily by making them pay tribute, which was funnelled into enlarging and strengthening what became a formidable Athenian navy; but Athens’ techniques of exploitation also included the appropriation of mines and emporia, and the seizure and renting out of land.16 By mid-century, the city was by far the wealthiest in the Greek world, with a massive influx of revenue obtained in diverse ways from the cities and regions subsumed under its power. The year 454 was a milestone. At that time, the reserve that had accumulated on the island of Delos (the ritual centre of the empire) was moved to Athens. It is not idle to speculate that the sight of an extraordinary quantity of silver coinage, however it was transported, was visually powerful.17 It appears, moreover, that the annual tribute, or a portion of it, that was conveyed annually to Athens at the time of the Great Dionysia

13

14

15 16 17

Xenophon (Vect. 2.7), writing in the 350s in the aftermath of the Social War, advised merchants that Athenian silver, always available, could be exported as a commodity (whether coined or as bullion). He notes that the resource is not as productive as it could be and sees slaves, not technical innovation, as the answer. J. Ober, Democracy and Knowledge: Innovation and Learning in Classical Athens (Princeton: Princeton University Press, 2008), 72–73 emphasises the role of the state in assessing productivity using the fifth-century mines as a model. On the mines see further Kallet and Kroll, The Athenian Empire, 21–22, 50–52, 78–81, 102. There is no better way to take in the sheer scale of the monetised economy of Athens in the fifth century in relation to other wealthy cities than to consider the output of tetradrachms in the mid-fifth century relative to that of the perhaps two other best-known wealthy minters in the fifth century: Syracuse and Corinth. The ‘Tehran hoard’, mid 450s– c. 440 bce, suggests a production per annum of c. 2,000,000 Athenian silver tetradrachms or just under 1,400 talents. Corinth minted 20–30,000 staters per annum, Syracuse no more than 20,000 tetradrachms per annum, see J.H. Kroll, ‘What about Coinage?’, in J. Ma, N. Papazarkadas and R. Parker (eds), Interpreting the Athenian Empire (London: Duckworth, 2009), 195–209 at 198 (provisional, with earlier calculations). That estimate of production excludes coins from the drachma on down (the small change)—to account for those we would need to add millions upon millions more. Davies, ‘Corridors’; Kallet, ‘The Origins’. Kallet, ‘The Origins’, 44–52, 56–57; L. Kallet-Marx, Money, Expense and Naval Power in Thucydides’ History, 1–5.24 (Berkeley and Los Angeles, 1993), 198–201. On the amount of the reserve, Thuc. 2.13.3 gives the figure of 9,700 talents at its height; see further L.J. Samons ii, Empire of the Owl: Athenian Imperial Finance (Historia Einzelshriften, 142; Stuttgart: Franz Steiner, 2000), 93–112.

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from 454 onwards, was paraded on the stage at the Theatre of Dionysos during the opening ceremony.18 What this means is that the Athenians made use of their wealth for visual, even ritual, display as a sign of the city’s power. It needs emphasising that no Greeks in the fifth century, or ever, had seen—literally seen—money displayed and circulating in their economy and society on this scale. Athens’ domestic output of silver and the silver coin paid by Athens’ subjects, while expended in large quantities, also accumulated and resulted in a mid-fifth-century reserve of near 10,000 talents (Thuc. 2.13.3). Athens’ unique store of explicitly monetary wealth signified, as well as funded, its extraordinary naval power. The city’s wealth conjoined with its power was expressed numerically and was critical to the meanings and functions of number in the polis.

2

Democracy and Numeracy

2.1 Pay—the emmisthos polis Plato’s Socrates notoriously criticises Pericles for corrupting the Athenians by introducing jury pay, making them greedy and lazy.19 Though this was likely a typical aristocratic attitude, Pericles’ response will have been that financial recompense was essential, given the increasing number of administrative duties that the polis needed citizens to perform. A passage in the Aristotelian Athenian Constitution (Ath. Pol. 24.3) is key: [The Athenians] provided abundant maintenance for the many … so that more than 20,000 men were supported from the tribute, the taxes and the allies. There were 6,000 jurors, 1,600 archers, and also 1,200 cavalry; 500 members of the boulē; 500 guards of the dockyards, and also 50 guards on the Acropolis; up to 700 officials at home and about 700 overseas. In addition to these, when the Athenians later went to war they had 2,500 hoplites; 20 guard ships; other ships sent out for the tribute … employing 2,000 men selected by lot; also …. the jail guards. All these were paid from public funds.20 We should not take this evidence (which in any case contains round figures) strictly at face value, but there is no reason to reject the overall point of the 18 19 20

Isoc. 8.82, cf. Ar. Ach. 505, 643; A. Raubitschek, ‘Two Notes on Isocrates’, TAPA, 72 (1941), 356–362. The Athenians are philarguroi, lit. ‘silver-lovers’ (Pl. Grg. 515 E). Author’s translation.

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passage, which is to emphasise the extent of the democratic and imperial bureaucracy, its military needs and, as a result of both, pay.21 Historical factors help to explain the spread of public pay. The political reforms of Ephialtes in 462 expanded the duties of the popular courts, manned annually by 6,000 jurors, and of the boulē. Athens’ naval empire required an increasing number of officials and military personnel to reside in the cities as magistrates and garrison soldiers, and to patrol the Aegean region. A factor in the increase of Athenians abroad will have been disaffection among Athens’ subjects, requiring even more oversight and punitive measures.22 I would add a final factor, the Peloponnesian War, which entailed mass periodic confinement within the city walls and may have increased participation in public institutions.23 Pay, initially an incentive, became a necessity, and, ultimately, the defining characteristic of Athens’ democracy, which critics like Plato found abhorrent. Pay would have come in the form of fractional coinage, that is, small change. This has important implications. Once one factors in pay for thousands of Athenians in direct conjunction with the form of government, small change circulating among the citizenry at large will have cemented and reinforced the

21

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23

When offices began to be paid is unclear. There is an assumption, noted by P.J. Rhodes, The Athenian Boule (Oxford: Clarendon Press, 1972) 13 n. 14, that jury pay is shorthand for the wider application of paid participation at the same time; cf. [Arist.] Ath. Pol. 27.3–4 with P.J. Rhodes, A Commentary on the Aristotelian Athenaion Politeia (Oxford: Clarendon Press, 1981) ad loc; Arist. Pol. 1274a8–9; Plut. Per. 9.2–3. On public payments more generally, [Arist.] Ath. Pol. 24.3 with Rhodes, Commentary ad loc.; see also V. Rosivach, ‘State Pay as War Relief in Peloponnesian-War Athens’, G&R, 58 (2011), 176–183; M.H. Hansen, ‘Misthos for Magistrates in Classical Athens’, SymbOslo, 54 (1979), 5–22. A standard, or minimum, wage is uncertain; as an estimate, 2–3 obols p.d. would supplement a citizen’s income, whereas 1 drachma would be a living wage and as such a payment for special skills or obligations, though there may well have been a hierarchy of pay rates, e.g. for the boulē, see Rhodes, Boule, 13. The building accounts of the Erechtheion, with a few exceptions, list a one-drachma wage for all work, but should not necessarily be regarded as typical. W.T. Loomis, Wages, Welfare Costs and Inflation in Classical Athens (Ann Arbor: University of Michigan Press, 1998) is indispensable on the subject; see 105–108 and 257–340 for a comprehensive table. By 440 many important poleis and regions had revolted, unsuccessfully (e.g. Naxos, Thasos, Euboea, Samos, see Thuc. 1.98, 100–101, 114) or were forced to join the alliance (Karystos and Aegina, 1.98, 105.2, 108.4). The inhabitants of Athens and Attica evacuated their property and local shrines as part of their defensive strategy, in which the Athenians would leave the land open for the annual Spartan invasions (Thuc. 1.143.4–5; 2.13.2, 14–16). Henceforth, all formerly domestic goods and commodities had to be imported by sea via a set of Long Walls linking the Peiraieus and the urban centre.

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linkage between numeracy and democracy.24 I shall return to this point below when we consider the evidence of Old Comedy. 2.2 Exposure to Numbers in Public Debate The courts (dikastēria) and the assembly (ekklēsia) involved thousands of citizens in deliberations that required decisions of a financial nature, whether directly or indirectly relevant to the main point of discussion, and such decisions required a financially informed citizenry.25 Unlike the 40 meetings of the assembly, the agendas of which were known in advance, in the courts the jurors could not predict whether a cavalcade of numbers might feature in a case (concerned with, for example, embezzlement, commercial loans, tax farming, property and inheritance disputes, sales of confiscated property, tribute issues, the assessment of fines or, frequently, cases arising from contested euthynai).26 We should not assume that all attendees controlled every financial detail and could apply their knowledge to an assessment of the pros and cons, or guilt and innocence; numeric skill will have varied among the citizenry and what was demanded was basic arithmetical competence, the ability to count, add, subtract, and to evaluate small and large sums in their context. Proper assessment also entailed the ability to appreciate the rhetorical function of numbers in their deliberative or forensic context in the assembly and courts.27 Lysias’ speech (21) for a defendant accused of taking bribes is a prime example. The speaker evidently failed to pass his audit (euthynē) after completing his term of office. (An unsuccessful defence would have meant a fine and potential exile.) This speech, then, though incomplete, is exceptionally valuable as an example of a case that would have come before a jury with frequency, given the number of citizens who had to render their accounts annually. The speech concludes by listing 14 liturgies undertaken on behalf of the city and their costs. The strategy is typical but the monetary scale, over ten talents, is astonishing. A juror could be counted on to know the average cost of each liturgy, whether dramatic or military, and so to be able to judge whether a defendant was generous

24

25 26 27

My focus on democracy and numeracy is not to deny that there were plenty of other opportunities to acquire numerate skills: money circulated widely in Athens, and as noted above, n. 9, the need for counting and calculating in the market economy, in businesses and trades, meant in some cases a high degree of numerate facility and, in others, a basic level. See Netz, ‘Counter Culture’, 334–335 on the centrality of numbers in the political sphere. Cf. Ar. Vesp. 104 with D.M. MacDowell, Aristophanes Wasps (Oxford: Clarendon Press, 1971), 145. On which, see further Sing in this volume.

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or miserly in the performance of the service and, accordingly, his investment in the democracy. Thus, the expenditure is a vital part of the rhetorical strategy aimed at proving that the defendant is a citizen who uses his private wealth unstintingly for the good of the city (at a time when the treasuries were near exhausted at the end of the Peloponnesian War). The point to take away is that the expenditure itself is a vital part of the rhetorical strategy aimed at proving that he is an admirable, upstanding citizen. 2.3 Service on Boards Participation in most if not all of the major and minor administrative offices necessitated numerate skill. While evidence of the extent and nature of the numeric work is lacking in most cases, apart from the major magistracies,28 we can nonetheless assume that the receipt and allocation of funds within a budget will have been a function of all boards responsible for maintaining the physical infrastructure of the city.29 Two complementary effects follow. First, repeated exposure to numerate information acquired through sitting on one of the administrative boards would result in collective financial knowledge. Given the principle of rotation for all but a few offices, over time, many thousands of citizens will have acquired numerate skills.30 Moreover, though the principle of non-iteration will have prevented a citizen from serving on the same board twice, if he were a civic-minded sort, he might put himself forward for any of the other boards. Second, while these many boards presumed no special expertise or formal training, a consequence of the acquisition of skills was that boards would have included members who had acquired knowledge and had joined the ranks of the numerate, and who will therefore have been instrumental in sharing that 28

29

30

Details about major financial boards show up more in the extant epigraphic record, for the obvious reason that the Athenians tended to publish accounts of monetary transactions on stone, especially those that concerned the gods. For example, one of the many responsibilities of the logistai was to receive and certify as received the portion of tribute (one-sixtieth) from the Hellēnotamiai to be dedicated to Athena, beginning in 454/3 (IG i3 259 = OR 119, with discussion of the series); they oversaw the borrowings from the sacred treasuries, recording them, including the interest (IG i3 369 = OR 160) as well as the annual end-of-term euthynai of magistrates. The poletai were responsible for all public contracts ([Arist.] Ath. Pol. 47.2–3) including confiscated property, mine leases, tax farming, etc. See A. Schärlig, Compter avec des cailloux: le calcul élémentaire sur l’abaque chez les anciennes Grecs, (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001) for an estimate of 30 such boards. These will have included the officials in charge of the maintenance of the walls, roads, fountains, and the like, who would have drawn a salary and have had funds to allocate for works projects. Netz, ‘Counter Culture’, 339, on the degree of numeracy in boards.

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knowledge with colleagues who might be ‘first-timers’ on a board, though such individuals would at least have attended assemblies and garnered financial experience on that basis. Accordingly, in the absence of formal education in mathematics, the on-the-job education acquired was sufficient.31 Let us consider two boards of different kinds, the boulē and the teichopoioi (the board responsible for maintaining the city’s walls). The boulē, ‘regarded as generally responsible for the financial well-being of Athens’, stands out.32 It had a far reach: all boards with a financial remit of any kind, from tribute collection and the stewardship of sacred moneys to the sale of houses, would have presented their accounts, contracts, and evidence of tax farming bids, leases and loans, interest, repayments, sales and rentals to the boulē. Receipts of moneys, counted out by hand, needed to agree with the recorded totals.33 The ‘instruction’ in revenue in Aristophanes’ Wasps gives a good idea of the diversity of foreign and domestic revenues. The individual boards responsible for the collection of ‘tribute, taxes and the many one percents, court dues, mines, markets, harbours, rents, and proceeds from confiscations’ (657–659) would have needed to bring their accounts, and the money, to the boulē for checking.34

31

32 33 34

On shared knowledge in boards, see Ober, Democracy and Knowledge, esp. 118–167 with good discussion, though his application of a business model which reimagines Athenian boards as ‘teams’ is removed from the ancient setting of boards requiring specific kinds of knowledge. On the other end of the spectrum, M.H. Hansen, The Athenian Democracy in the Age of Demosthenes (Oxford: Blackwell, 1991), 244 (see also 256–257), finds it ‘baffling’ to understand how the democracy functioned with any efficiency when the bureaucracy was staffed by amateurs, whose terms of office were short, could not be repeated and did not overlap with more experienced office-holders. He finds an answer in the clerical staff attached to the important boards, such as secretaries (grammateis), and various assistants (e.g. hypogrammateis, paredroi) who, if not magistrates themselves, might be citizen, metic or slave and who provided some administrative continuity. Attention to these facilitators is salutary but it should be noted that these subordinate staffers had fixed terms as well. See also P. Ismard, La démocratie contre les experts. Les esclaves publics en Grèce ancienne (Paris: Les Éditions du Seuil, 2015) and Rhodes, Boule, 134–143 for the boulē; on the secretaries and assistants to the overseers (epistatai) of the Acropolis building projects, see G. Marginesu, Gli epietati dell’ Acropoli: Edilizia sacra nella città di Pericle 447/6–433/2 a.C. (Athens: Scuola archeologica italiana di Atene / Pandemos, 2010) 64–65, 124. Cuomo, ‘Accounts’, 259, rejects (from an argument ex silentio) the notion that public slaves were essential, mathematical experts in the fifth century (see also above, p. 28). Rhodes, Boule, 88–113 at 89, citing varied literary and epigraphic sources, cf. [Xen.] Ath. pol. 3.2; [Arist.] Ath. Pol. 45.2, 47–48, 49.4, with Rhodes, Commentary, ad loc. Major discrepancies could, and did, occur, requiring new measures to check corruption; regarding tribute collection, see IG i3 68 = OR 152 and IG i3 34 = OR 154. The role of the boulē in the financial realm immediately qualifies any implication that boards that dealt with moneys on any level were autonomous until, that is, their end-of-

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The bouleutai collectively, then, had a prodigious number of duties requiring numerate proficiency.35 In addition, since the boulē was effectively a board— albeit a very large one—that might be subdivided into committees, shared knowledge was essential. Bouleutai will have known the signal importance of their duties to the welfare of the polis: the Old Oligarch ([Xen.] Ath. pol. 3.2), lists ‘revenue’ immediately after ‘war’ among the major categories of responsibility. Significantly, he also speaks of the overload on major boards like the boulē, rather than incompetence—or rampant dishonesty.36 A consequence of the size of the boulē is that, over the course of a decade, its cumulative exmembers would have numbered 5,000, over two decades, 10,000 Athenians, and so on. Bouleutai would have attended the assembly, and it is attractive to think that they would have put their expertise to use on other boards. In contrast with a position like membership of the boulē, the teichopoioi were charged with maintaining the city’s walls. They were allocated a sum of money to be spent on materials, equipment, and wages, of which they had to make an account at the end of the year, as was the case for all other officials. Perhaps they also started the year with moneys remaining from the previous year, or they themselves may have had a surplus. The latter is suggested by the appearance of the teichopoioi on an account recording the construction of the Parthenon, which lists a contribution (partially missing) from them.37 We cannot know whether they decided to allocate their surplus to the building of this magnificent temple, for which they will have received honour, or whether the public treasurers (the kōlakretai) requested contributions from all boards that had a surplus for the particular year. In any case, it tracks nicely an aspect of one board’s finances. In sum, Athenians on administrative boards trafficked in number. They will have come to their duties already equipped with basic numerical skills,

35 36

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term audits: the boulē was continuously and directly involved in the scrutiny of magistrates, and will have sent the message that magistrates’ behaviour and actions had better be above board. See [Arist.] Ath. Pol. 45–49. [Xen.] Ath. pol. 3.1–3. For an exceptional incident regarding members of another key board, the Hellēnotamiai, who lost the tribute quota and were executed (Antiph. 5.69– 71), see S.V. Tracy, Athenian Lettering of the Fifth Century bc: The Rise of the Professional Letter Cutter (Berlin: De Gruyter, 2016) 46–50 and 207–215 (Appendix 2) with discussion of the crisis, its likely date, and, especially important, its implications for the history of the mid-century empire. IG i3 440 col. ii.126, other minor boards contributed supplementary funds as well: the xenodikai (col. ii.125, partially restored), possibly the triēropoioi (IG i3 439 col. ii.76, partially restored) and the hephaistikoi at Laureion (IG i3 440 col. v. 249 (‘at Laureion’ is extant), 445 col. v. 294 (both references partially restored) ).

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whether acquired in their household, market, business, or military service. Civic-minded individuals will have attended annual meetings of the assembly (normally four each prytany by the late fourth century, [Arist.] Ath. Pol. 48.3). In other words, numeracy was not contained in any one sphere but diffused throughout the polis, more so, of course, in or near the urban centre. In their posts, citizens will have worked mostly as part of a group, counting on each other and teaching each other on the basics. Their tasks will have regularly included producing a budget, allocating funds, recording income and expenditures, and preparing and submitting an account (one per board). 2.4 Published Records Another form of exposure to number were the visual testimonies of Athens’ monetary wealth in the form of the hundreds of inscribed stelae, some of monumental proportions, that dotted the urban centre and the demes of Attica; most spectacular were those on the Acropolis and in the agora.38 Many, if not a majority, contained financial records of sacred wealth, designed for publicity, accountability, and transparency, as required by the democracy, but also meant to attest to the wealth and power of the polis, represented and expressed through number. These documents included records of expenditures, inventories, accounts of loans to be repaid with interest, and building accounts detailing donors and amounts contributed to the construction of temples, such as the Parthenon and the ostentatious chryselephantine statue of Athena housed within.39 Other kinds of inscribed stelae containing lists of items of a financial 38

39

T. Crump, The Anthropology of Numbers (Cambridge: Cambridge University Press, 1990), 41–46 discusses the development of visual, i.e. written, representation of number. Against the view that epigraphic literacy figured in the rural demes, cf. N.F. Jones, Rural Athens under the Democracy (Philadelphia: University of Philadelphia Press, 2004), 177–181. This is a difficult position to maintain given the epigraphic presence in the demes, in which decrees of the deme assemblies (e.g. OR 107, from Skambonidai) and sacred matters such as sacrificial calendars (e.g. OR 146, from Thorikos) will have been published on stone. Of course, as was the case in Athens’ assembly, not all documents were inscribed, but it is important not to draw conclusions from the relative paucity of finds; see D. Whitehead, The Demes of Attica 508/7–ca. 250 b.c.: A Political and Social Study (Princeton: Princeton University Press, 1986), 39–46 and Appendix 3 (374–393). IG i3 449 (OR 145). The accounts associated with monuments such as the Parthenon, built over the period 448/7–434/3, and the Erechtheion, built during the Peloponnesian War, and displayed prominently on the Acropolis, were far from mundane records. The inscription pertaining to the construction of the Erechtheion (IG i3 474, 476 = OR 181A–B), is particularly informative, since it includes details about the particular occupations of the workmen, their status (citizen, metic, slave) and pay; see the helpful summary and table in M.M. Austin and P. Vidal-Naquet, Economic and Social History of Ancient Greece: An Introduction (Berkeley: University of California Press, 1977) no. 73, 276–282.

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figure 1.1 IG i3 260–262: A portion of the three tribute quota lists for 453/2– 451/0 on the Lapis Primus. Epigraphic Museum, Athens © hellenic ministry of culture and sports/ hellenic organization of cultural resources development

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nature, such as public auctions, proliferated as well. They attest to the ‘significant public presence of mathematics’.40 Acrophonic numerals and the layout of many of these inscriptions encouraged accessible viewing and reading: one could recognise a financial document, or the category of document, from both the list form and the presence of numerals; individuals could read them simply by knowing the alphabet and putting together names.41 Even monumental stelae, like the Lapis Primus, on which are inscribed the one-sixtieth of each city’s tribute payment (the aparchē or ‘quota’ as it is usually translated) that was dedicated to Athena, could be easily navigated and read (at least at eye level) since the quota lists took the form of columns of numerals and of names.42 On the other hand, some financial documents might have actually discouraged reading or even spending much time viewing them, by their use of continuous text in which numerals were interspersed.43 Someone wandering around the sacred and civic spaces of the polis, on the Acropolis, in the agora, other sanctuaries and deme centres, would see a veritable forest of inscriptions of a financial nature. Regarding them merely as physical demonstrations of accountability and transparency, a hallmark of this democracy, misses the larger meaning of these documents as manifestations of the culture of number—visual cues or prompts reinforcing the identity of Athenians as a counting people. Similarly, we can regard performative rituals like the parading of tribute on the festival stage, and indeed the counting of tribute and other monetary revenue in the presence of the boulē, as perpetually reinforcing lessons in how to think about power, and ultimately, value, in relation to number. This discussion of the many physical, political spaces around Athens in which numeracy figured leads us beyond the conclusion that numeracy was the necessary bureaucratic skill that it was, to posit an Athenian predisposition as a ‘counting people’ who think in terms of number in the context of democracy and empire, specifically the benefits those brought to individuals as well as to the collective. 40 41 42

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S. Cuomo, Ancient Mathematics (London: Routledge, 2001), 15. Cuomo, ‘Accounts’, 267–268. IG i3 259–272, see fig. 1.1. After the Lapis Primus, the series (IG i3 273–280) continues with a smaller but still very large stele (Lapis Secundus) for the second set of years down to the Peloponnesian War; afterwards, single stelae were used for each year’s list (IG i3 281–291). A good example is the almost-impenetrable inscription recording loans from the sacred treasuries, with interest calculated (IG i3 369 = OR 160). See further Osborne, this volume, on the visual presentation of numbers in inscriptions and why ease of comprehension, in many cases, appears not to have been a priority.

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This is observable, for example, in the tribute paraded in the theatre at the Great Dionysia, which is a kind of visual monetary list, and in catalogues that crop up in Old Comedy, like the spectacular list of assorted imports transported by the shipowner Dionysos and consisting of an assortment of delicacies, strategic goods, and political ‘commodities’ like the Macedonian king Perdiccas’ lies.44 Athens was an economic powerhouse, and Athenian identity stemmed therefrom: they were a ‘counting people’; they measured, quantified and characterised the good life by what mattered to them, namely, monetary wealth in the form of coined money.45 On the larger scale, they thought about democracy and power in terms of number. These ways of conceptualising what matters are peculiarly Athenian; they would be out of place in a polis like Sparta.46

3

Old Comedy

If these ways of looking at Athenian numeracy are valid, then we might expect to find indications and resonances in Athenian culture. I would like to test the notion of a ‘counting people’ by considering the genre most likely to reflect it, namely, Old Comedy. Because of the genre’s performative nature, plays like these help to understand the extent to which numeracy was familiarised and even embedded in popular culture. Moreover, while the genre is topical and political, its interests shift from the polis to the personal, often in relation to the private economy. While money in its different economic contexts— market, debt, pay, and revenues, and its broader associations with corruption and power—appear in Aristophanes’ plays generally, Acharnians, Clouds, and Wasps are especially useful in that they have a prominent thematic coherence (and together, as rich, cultural artefacts of the Archidamian War, they help us 44

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Hermippos, fr. 63 KA apud Ath. i.27e–28a. Lists are a staple in Greek (oral) culture from its earliest stage and in diverse genres, e.g. Hom. Il. 2.494–759 (catalogue of ships); Hes. Theog. (passim, e.g., origins, gods, nature); Hdt. 3.89–95 (tribute to Darius), 7.61–99 (troops and clothing); Pl. Hp. mai. 285d (genealogies recited at Sparta), 285e (the list of archons). The good life included what money could buy: one index is the ability to import anything desired or needed, including luxury goods from all corners of the world, ‘democratised’ by making them (theoretically or rhetorically) accessible to all. See P. van Alfen, ‘AegeanLevantine Trade, 600–300 bce: Commodities, Consumers, and the Problem of Autarkeia’ on the democratisation of commodities, in E. Harris, D. Lewis and M. Woolmer (eds), The Ancient Greek Economy: Markets, Households and City-States (Cambridge: Cambridge University Press, 2015), 277–298; cf. also L. Kallet, ‘The Athenian Economy’, in L.J. Samons ii (ed.), The Cambridge Companion to the Age of Pericles (Cambridge: Cambridge University Press, 2007), 70–95, at 70–71, 81–83, where I speak of an ‘economic mentality.’ See pp. 51–54 below.

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think about the material concerns of Athenians in those years).47 That coherence should allow us to think about attitudes, assumptions, and the prevalence of number in Athenian life. Calculations of benefit and dissatisfaction, and the question of who gets what out of the democracy and empire, offer revealing indicators of a numerate people who think in numerical quantities. 3.1 Acharnians Produced in 425 at the Lenaia, the initial setting is an assembly meeting. Waiting for it to start is a contrarian Athenian villager, Dicaeopolis. The war with Sparta (now in its seventh year) has meant confinement within the city walls; he yearns for the simple, country life.48 When the assembly refuses to consider the question of peace, he resolves to make a private peace with Sparta so that he can return home. The crux of his dissatisfaction is two-fold: the cash economy that rules his daily life in the city, and the disparity between the material benefits from the democracy and the empire enjoyed by some better-off Athenians and those received by others, like himself—the everyman citizen. Having arrived early for the meeting, Dicaeopolis occupies himself with a variety of bodily activities (a stock-in-trade of Old Comedy): ‘in my solitude, I sigh, I yawn, I stretch myself, I fart, I fiddle, scribble, pluck my beard, do sums’.49 If his corporeal distractions amuse, what about his accounting? The juxtaposition of his self-grooming with calculating may have had a comic effect, but the calculating also feeds the plot: it is not simply the war that drives him to make his private peace with Sparta, but more so the inescapable ‘buy-this, buy-that’ mentality of city life.50 Once Dicaeopolis returns home with his peace treaty (purchased for eight drachmae with the aid of the divine Amphitheos, 129– 132), he promptly opens a market, with a mixture of monetary transactions and payments in kind.51 47

48

49

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While much would be gained by compiling a list of all the monetary references in both extant and fragmentary plays, and in so doing one would come away with an excellent appreciation of the extent to which numbers were the lingua franca of daily life (the first 150 lines or so of Acharnians makes the point well), my goal here is different. The sentiment is paralleled in Aristophanes’ lost play, Islands (fr. 402 KA) in which a character pines for peace back home, away from the city and its retail market, grumbling about the crooked fishmonger with his thumb pressed on the scale. Ach. 29–31. Dicaeopolis ‘does sums’, ‘calculates’, (λογίζομαι) either in his head or by writing down the figures, since he is portrayed as literate (γράφω), though Henderson translates the latter verb as ‘draw’. Ach. 32–36. Though that mentality, and Dicaeopolis’ exposure to it, is also blamed on the war (as it likely was in Islands and other lost plays); criticism of Pericles for starting it comes later (530–534). Ach. 719–970. Some scholars regard Dicaeopolis’ market, based in kind, as reflecting the

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Money continues to be a source of humour and concern in Dicaeopolis’ further musing on his pains and pleasures, especially pertaining to the unequal distribution of pay for work done, and the benefits reaped by politicians. Examples are the massive five-talent bribe accepted by Cleon,52 and the two drachmae p.d. pay drawn by the ambassadors to the Great King for 11 years (which is recognised as a sinecure).53 The issue of benefit disparity for the jobs being done is picked up later on in the exchange between Dicaeopolis and the general Lamachus (μισθαρχίδης ‘Mr High Pay’, 597) in which Dicaeopolis points to ‘young men like you’ who draw three drachmae in Thrace and Sicily (599– 606) while the Acharnians of the chorus get none. These allusions are hardly esoteric, but they still depend on an audience predisposed to think in terms of the cash economy and the monetary world of Athens. Audience familiarity with large or inflated sums is presumed, and tested in the examples of Cleon’s five-talent bribe and pay of two-to-three drachmae a day attributed to generals and envoys.54 That economy, moreover, drives purchases involving credit that lead to debt, and, hence, the likelihood of interest. 3.2 Clouds Clouds, produced in 423, has a two-part comic strategy. Its primary theme is the ‘new sophistic education’, in which the lampooning of Socrates, head of

52

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reality of a non-monetised rural life (e.g. R. Osborne, Classical Landscape with Figures: The Ancient Greek City and its Countryside (Cambridge: George Philip, 1987) 180; S.D. Olson, ‘Dicaiopolis’ Motivations in Aristophanes’ Acharnians’, JHS, 111 (1991), 200–203; R.L. Tordoff, ‘Coins, Money, and Exchange in Aristophanes’ Wealth’, TAPA, 142 (2012), 257–293). But references to profit do imply monetary gain, 898–899, 947; and 961–962 is explicit about a monetary transaction. Dicaeopolis’ rural market is, on the one hand, recognisable to the audience (described as ‘historically situated’ by C. Pelling, Literary Texts and the Greek Historian (London: Routledge, 2000) 126), as is typical of Old Comedy, but the audience would also have expected an exaggerated, fantasised version, the better to serve the plot, with its contrast between a town and country market; see A. Moreno and S. Lape, ‘Comedy and the Social Historian’, in M. Revermann (ed.), The Cambridge Companion to Greek Comedy (Cambridge: Cambridge University Press, 2014), 336–369 at 344–345. Ach. 6: ‘Those five talents Cleon had to disgorge’. On whether the allusion is invented or real, see Pelling, Literary Texts, 126–128; on what it could refer to, with a bit of heavy weather, A.S. Sommerstein, Acharnians (Warminster: Aris & Phillips, 1980), ad loc.; S.D. Olson, Aristophanes Acharnians (Oxford: Oxford University Press, 2002) ad loc. Ach. 65–90. The ‘work’ justifying the high pay over this duration consists of living in the lap of luxury in Persia; meanwhile Dicaeopolis and his lot had to guard the border forts of Attica (71–72), see further Pelling, Literary Texts, 129–130. The pay is twice as much as an envoy and other such officials might receive; Loomis, Wages, 205–206 discusses the passage; see also Olson, Aristophanes Acharnians, 65–67.

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the phrontistērion (‘Thinkery’) is key; but the driver of the plot is debt, and that will lead the protagonist Strepsiades to Socrates’ Thinkery for lessons in debt evasion.55 The play features a quintessentially dysfunctional comic family. Strepsiades, a simple old-fashioned sort, is married to an upscale wife, who has passed on her expensive tastes to their son, Pheidippides. Strepsiades has purchased a racehorse for him for 12 minae—a substantial sum—and this has saddled Strepsiades with debt:56 Strepsiades: … I can’t get to sleep, poor soul; I am being eaten alive by my bills and stable fees and debts, on account of this son of mine. He wears his hair long and rides horses and races chariots, and even dreams about horses, while I go to pieces as I watch the moon in her twenties, because my interest payment looms just ahead.57 Boy! Light a lamp, and bring me my ledger book, so I can count my creditors and reckon the interest (λογίσωμαι τοὺς τόκους).58 Let’s see, what do I owe? 12 minae to Pasias. What were the 12 minae to Pasias for? What did I use it for? When I bought that branded hack (κοππατίαν). Oh me oh my! I wish I’d had my eye knocked out with a stone first ar. Nub. 13–24

Strepsiades is in straightened circumstances: on top of the cost of the horse, a month’s interest is overdue, he must calculate the interest himself (λογίσωμαι τοὺς τόκους), his creditors are suing him, and he risks the loss of property (34). 55

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The prominence of the motif of debt and its linkage with sophistic education suggest to me that the original Clouds, of which this is the partially revised version, had similar emphases. On the revision and the original, see K.J. Dover, Aristophanes: Clouds (1968; Oxford: Clarendon Press, 1989), lxxx–xcv. 12 minae (repeated at 1224) equals 1,200 drachmae, the maximum cost of a fine horse (in the Athenian cavalry) in the third century and probably in the fourth on the basis of the annually recorded valuations (J.H. Kroll, ‘An Archive of the Athenian Cavalry’, Hesperia, 46 (1977), 83–146 at 88–89). A speech attributed to Lysias (8.10) gives a figure for a horse of 1,200 dr. as surety; Xen. Anab. 7.8.6 has Xenophon’s horse being sold at Lampsacus for 50 darics (= 1,200 dr). A racehorse, such as Strepsiades bought for his son (koppatias hippos), could have cost more than 1,200 dr. but we should perhaps take Aristophanes’ figure as at the lower end of what a fine racehorse would have cost: Pheidippides wants to race the horse but rides as well (there is something illogical here: Strepsiades borrowed money for one horse, but the verb xunōrikeuomai (15) refers to a two-horse chariot that Pheidippides races). Interest payments were calculated by the month (i.e. by the moon). Calculation is the logical inference here from the verb logizomai, as with Dicaeopolis in Acharnians (31).

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The scene is a tale of private debt on a large scale; 12 minae borrowed for the horse (and an additional three minae loan for a small stool and wheels, 30– 31), with lawsuits by the creditors to recover their loans. Strepsiades, however, is most anxious about the interest. He is determined to evade the debt through a clever, unjust argument; this leads him to Socrates’ school. Thereupon Strepsiades is elated: Socrates assures him no amount of witnesses to his loans can obstruct his defeat of his creditors: ‘Hah, mourn you money-lenders, you and your principal and the interest on your interest’ (1155–1156).59 The humour in this scenario is undeniable: sophistic education is deployed for the sole goal of averting lawsuits and evading debt. Strepsiades fails, however, addled by old age, and is sent home by Socrates. Pheidippides must take his place and ends up mastering the Unjust Argument. The test comes when the creditors arrive at Strepsiades’ house along with witnesses, but Strepsiades (Pheidippides does not appear in the scene) uses what he has learnt at the Thinkery by feigning ignorance: ‘this interest, what sort of beast is it?’ (1286). The second creditor supplies a definition, it is ‘none other than the tendency of a given sum of money to grow ever bigger and bigger, day by day and month by month, as time flows by’ (1287–1289). He is run off by Strepsiades. The extended premise of Clouds, namely, the interest-laden debt that leads Strepsiades to Socrates, the victory of the Unjust Argument over the Just Argument, and Strepsiades’ success in refusing to repay the debt, or even just the interest (1285), is summed up by the Chorus (1304–1305).60 The prevalence of this motif of debt presupposes numeracy, and for the play to work, it should resonate with the spectators (who are called upon several times for their tacit views). They are assumed to understand how credit works, and the ease with which one can go into debt, and to be familiar with the stereotype of the chiselling money-lender. The specific focus on the structure of interest presumes that audience members were not learning anything new. The world that informs Clouds is a private, numerate one and the thematic coherence of debt points to the good life, measured through quantification: while Pheidippides’ horse, valued at 1,200 drachmae stands in for its achievement of satisfaction and pleasure, debt, compounded by interest, serves as its negation. 3.3 Wasps Money, pay, and the distribution of monetary wealth are prominent themes in the final play I want to examine, Aristophanes’ Wasps of 422. The play is set 59 60

The term for money-lender here is obolostatēs—a small-time, chiselling money-lender and debt-collector. At that point, generational conflict between father and son, brought on by the overthrow

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in a house, its plot revolving around another elderly father, who is addicted to jury service, and his son, who is determined to curb the old man’s obsession by preventing him from going to the courts. The father, Philocleon (‘CleonLover’), protests his confinement by telling his son Bdelycleon (‘Cleon-Hater’) the many benefits of being a juror, culminating in the clincher, namely, the pay he brings home, which confirms his power over the rich, in fact, he is the ‘ruler of everyone’ (518). What follows is a mock-lecture by his son, here in the role of a fiscal economist à la Pericles, to disprove Philocleon’s illusion of power. Philocleon’s power is put in terms of number—his three-obol pay (and the guilty verdicts he pronounces); Bdelycleon’s strategy is to meet like with like. He rattles off a dizzying list of the sources of domestic and imperial revenue, presenting a kind of balance sheet, juxtaposing, and distorting for the sake of the lesson, the gigantic annual revenue of Athens, and the pittance expended on the all-important institution of the jury courts (dikastēria). While the individual revenue streams are not enumerated, the annual total is quantified and contrasted with the annual expenditure on jury pay for the 6,000 dicasts: Bdelycleon: Then listen, pop, and relax your frown a bit. First of all, calculate roughly, not with counters but on your fingers, how much tribute we receive altogether from the allied cities. Then make a separate count of the taxes and the many one percents, court dues, mines, markets, harbours, rents, proceeds from confiscations. Our total income from all this is nearly 2,000 talents. Now set aside the annual payment to the jurors, all 6,000 of them, “for never yet have more dwelt in this land”. We get, I reckon, a sum of 150 talents. Philocleon: So the pay we’ve been getting doesn’t even amount to a tenth of the revenue!61

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of convention in Socrates’ school, gives way to Strepsiades’ repentance at the folly of his ways in trying to cheat the creditors. ἀκρόασαί νυν ὦ παππίδιον χαλάσας ὀλίγον τὸ μέτωπον· |καὶ πρῶτον μὲν λόγισαι φαύλως, μὴ ψήφοις ἀλλ’ ἀπὸ χειρός, |τὸν φόρον ἡμῖν ἀπὸ τῶν πόλεων συλλήβδην τὸν προσιόντα·|κἄξω τούτου τὰ τέλη χωρὶς καὶ τὰς πολλὰς ἑκατοστάς,|πρυτανεῖα μέταλλ’ ἀγορὰς λιμένας μεσθοὺς καὶ δημιόπρατα.| τούτων πλήρωμα τάλαντ’ ἐγγὺς δισχίλια γίγνεται ἡμῖν. |ἀπὸ τούτου νυν κατάθες μισθὸν τοῖσι δικασταῖς ἐνιαυτοῦ |—“ἓξ χιλιάσιν, κοὔπω πλείους ἐν τῇ χώρᾳ κατένασθεν”,| γίγνεται ἡμῖν ἑκατὸν δήπου καὶ πεντήκοντα τάλαντα | οὐδ’ ἡ δεκάτη τῶν προσιόντων ἡμῖν ἄρ’ ἐγίγνεθ’ ὁ μισθός. 655–664. The list is not comprehensive; on the particular items, see MacDowell, Aristophanes Wasps, 220–222.

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Such a list of revenues in a modern annual report would be dry, humourless, imprecise and incomplete, but in its ancient Greek context, as noted earlier, lists themselves were a source of satisfaction, even pleasure, to the listeners. Beyond that, in Aristophanes’ hands, Bdelycleon’s list is hilarious, partly because of the stage direction to Philocleon: it consists of a frantic, escalating catalogue of revenues that Philocleon is directed to ‘calculate roughly, not with counters, but on your fingers’; we should imagine that doubtless some spectators will have tried their hands at counting, in vain.62 That the sums brought in by the individual revenues are not supplied creates comic tension, or anticipation—how much will the total be? The figure of 2,000 talents, a whopping exaggeration,63 does not disappoint, both on its own and compared to the expenditure of 150 talents on the juries,64 a contrast that is patently (and comically) ridiculous.65 At the same time, the humour should not divert our attention from the strategy of representing power as number: Bdelycleon’s figures are of rhetorical, not historical, significance, and as such, remind us of the assessment of tribute in 425, as much a rhetorical document as it is taken to be a key wartime fiscal strategy. Here, the implicit linkage between tribute and power is not so surprising, but the inclusion of diverse domestic revenues—‘taxes and the

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MacDowell, Wasps, ad loc. notes that φαύλως (‘roughly’) indicates that precision is not required, indeed, it would be impossible. P. Meineck, Aristophanes i: Clouds, Wasps, Birds (Indianapolis: Hackett Publishing Co, 1998), 174–175 rightly supposes that the finger count is part of the humour, as it implicitly draws attention to the impossibility of following his suggested stage directions, which draw attention to Philocleon’s ‘feverish’ attempt to keep up, his confusion, his further attempts to calculate, and, finally, his astonishment when the total spent on jury pay is a comparative pittance. See, especially, Sing’s analysis of the cognitive difficulties involved in the passage (pp. 199–200). See also below. Estimated total revenue from all sources comes closer to 1,000 talents per annum; and by 423, the Athenians, some 7,000 talents in debt to Athena’s Treasury by the following year (though one should keep in mind that such loans were the normal method of financing war), had come close to exhausting the treasury; see Samons, Empire, 193– 215; L. Kallet, ‘Epigraphic Geography: The Tribute Quota Fragments Assigned to 421/0 to 415/4’, Hesperia, 73 (2004), 465–496, at 492–494. On this exaggeration, MacDowell, Wasps, ad loc., and A.S. Sommerstein, Aristophanes Wasps (rev. repr., Oxford: Oxford University Press, 2004) on 663, both attempt to make sense of the figure, the former (‘a maximum’) and the latter (‘considerable exaggeration’) but we need not suppose that Aristophanes has got all his figures to hand, on the basis of which he arrives at his total of 150 talents! See also Hansen, ‘Misthos’. The balance-sheet approach implies that pay in the popular courts, without any context, was the only significant expense of the city, but its risible comparison in my view only adds to the humour. Also humorous is Philocleon’s sudden, if fleeting, bout of numerate skill, as he correctly notes the differential of jury pay against revenue as 1:10.

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many one percents, court dues, mines, markets, harbours, rents, proceeds from confiscations’—is quite remarkable, even peculiar: many of these sources were routine, typical revenue streams in Greek cities;66 here they are marshalled in a negative argument about the power of the collective, and, specifically, individuals’ power within it. Following his list of revenues and its comparison with jury pay Bdelycleon amplifies the message. He continues the instruction supporting his argument with a potpourri of the material benefits of empire enjoyed by the ‘haves’, who misappropriate the fruits of empire and withhold them from the ‘have-nots’, partly through deception (667–724), which underscores the inequity. The demagogic, populist leaders reap ‘50-talent bribes at a time’ (669), and are offered delicacies and luxurious accoutrements (676–677) through intimidation of the allies (671). On the other side is the demos, which undertakes the hard work of maintaining Athenian rule over a vast number of tributary cities ‘from the Black Sea to Sardo’ (700) numbered at ‘1,000’ (707). Yet, ‘content to gnaw the rinds of empire’ (672), ordinary Athenians get nothing, not even a head of garlic (679), apart from a miserable three obols for their jury service (unless they are late), while the prosecutor gets six in any case (690–691). Politicians drip-feed pay ‘like droplets of oil from a tuft of wool’ (701–702) and their promise, when under pressure, of ‘50-bushel’ rations is an empty one: the demos gets ‘five-bushel’ handouts consisting of ‘barley in one-quart instalments’ (716– 717).67 Altogether this extended section of the play constitutes a cost-benefit analysis in which financial advantage and disadvantage are quantified and contrasted: the demagogues are continually enriched at no cost to them—their advantage is repeatedly quantified (the lion’s share of 2,000 talents, 50-talent bribes, the list of valuable delicacies, the prosecutors’ pay rate of six obols)— and the masses realise no commensurate benefit to themselves; their side of the ledger is scarcely filled in, but where it is, it is likewise put as number.68 66

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N. Purcell, ‘The Ancient Mediterranean: The View from the Customs House’, in W. Harris (ed.), Rethinking the Mediterranean (Oxford: Oxford University Press 2005), 200–228; L. Migeotte, Les finances des cites grecques (Paris: Les Belles Lettres 2014), 248–277; A. Bresson, The Making of the Ancient Greek Economy: Institutions, Markets, and Growth in the City-States, trans. S. Rendall (Princeton: Princeton University Press 2016), esp. 102– 104, 286–299. MacDowell, Wasps, ad loc. rejects a connection to the attested gift of grain to the Athenians in 445 (Philochorus FGrH 328 F119), instead taking the reference to refer to an otherwise unknown distribution of grain in 423. Of course, in the Old Oligarch’s view, the demos does rule, and the rich put up with it, so

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Yet, the issue is not simply one of material advantage in a cycle of pragmatic quid pro quo. By casting the power relationship between demagogue and demos as that of master and slave (so too, differently, in Aristophanes’ Knights performed a few years before), number is also arguably engaged in a moral imbalance: the demos rows and soldiers (685) and therefore is unjustly enslaved to the demagogues.69 This is the negative argument; the Old Oligarch inverts the relationship (i.2), stating that it is ‘right’ (δικαίως) that the ‘poor and the demos rule’ and the ‘rich and noble’ submit, because the poor row in the fleet and bring the city its power (δύναμις). It is, thus, not just monetary profit and self-interest at issue in this quantified realm; it is also pragmatism with a moral tinge that shapes reciprocity in relation to empire—at least, to a point: this is, after all, comedy. Let us return to the question of broad-strokes exaggeration, a typical element of Old Comedy but one that has direct bearing on the numeracy of the citizenry. Bdelycleon’s inflated numbers masquerade as objective data and achieve their aim: Philocleon is duped; is the audience? The simple answer is that all the figures that bombard Philocleon and the audience are inflated, some wildly so. The most conspicuous exaggerations are the figures of 2,000 talents for Athens’ annual revenue, 1,000 cities for the extent of its tributary empire (along with its geographical extent, reaching all the way to Sardinia)70

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the implicit argument goes, because they like its benefits. Closer to the relationship is the analogy of Athens’ relationship with its allies: Athens’ power comes at the literal expense of its tributary subjects (1.99). Sommerstein reminds us (Aristophanes Wasps at 678) that ‘Philocleon knows quite well that he is poor and the politicians are rich but does not see how that in itself makes him a slave’; Sommerstein points out that Philocleon, through menial work, has lost his autonomy. Bdelycleon makes this point starkly at 705 with an analogy of a well-trained attack dog: the demagogues want you to be poor, ‘so you’ll recognize your trainer, and whenever he whistles at you, you’ll leap on that man like a savage’ (cf. also 684–685, 711, 1075–1121). The metaphorical context of slavery is cast in moral terms, a good example of which is Thucydides’ phrasing of the quashed revolt of Naxos in the 460s: the Naxians were ‘enslaved’ (the first example of many) by the Athenians as a punishment (1.98). The possession of empire itself could be thought of in moral terms, for example, in the last speech Thucydides composes for Pericles, in which slavery and freedom, justice vs expedience are a rhetorical stance, to convey that any moral grounds for objecting to the empire are almost irrelevant because of the danger to, and implied precariousness of, the Athenians’ position as a harsh imperialistic power (2.63.1–2). See also Bdelycleon’s calculation of what the Athenians’ rule of 1000 tributary cities could do for the demos if the demagogues so chose: ‘if someone ordered each one to support 20 men, then 20,000 loyal proles (τῶν δημοτικῶν),’ the ones who fought at Marathon, could be living it up (706–711).

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as well as the 50-talent bribes, and the 50 bushels of grain. On the other end of the statistical spectrum, the seemingly understated figure of 150 talents for juror pay each year is likewise a significantly inflated sum. Exaggeration commonly serves the comic strategy; here it widens the gulf between leaders and demos. Aristophanes’ construction of Bdelycleon is both knowledgeable and deceptive when it comes to Athens’ fiscal portfolio. For the exaggerations to work the spectators must recognise the deception and in effect be complicit in his strategy of persuasion.71 They will have gone along with the accuracy of the (partial) list of revenues—including their knowledge of tribute and a variety of domestic taxes, especially those levied on maritime commerce; but that takes no specialist education, or, to put it the other way, Athenians generally will have been fiscally au courant and therefore it is simply basic information, readily understood through democratic participation. By the internal logic of the play, as Philocleon accepts his son’s knowledge, the spectators will have as well, but also, in recognising the twin roles of expertise and exaggeration, will have regarded Bdelycleon as both expert and charlatan. More than any other piece of literary evidence I can think of, Wasps highlights the role, even the potency, of numeracy in citizens’ lives in relation to power and the quality of life. The pervasiveness of quantification in description, analysis, and persuasion affirms that number is deeply embedded in Athenian culture. 3.4 The Numerate Audience Recognition of the theatre audience’s role in a comic production, in this case, one that features money in the construction of character, plot, theme, setting, and jokes, expands our appreciation of the quantitative mentality. Comedy thrives on exaggeration, but it banks on the spectators’ familiarity with the world from which its topicality draws; it is a mirror, however exaggerated or distorted. The topicality with which I have been concerned is from the diverse spheres in which money features—buying and selling in the private economy, pay and accounting in democratic institutions, credit, debt and its hazards, and the monetary rewards of empire, individually and collectively. They have in common arithmetical facility: this is what the theatre audience is presumed to have. Moreover, as we have seen, wealth disparities and other monetary inequalities, depending on whether one is fortunate or unfortunate, are meas-

71

MacDowell, Wasps, on l. 707 takes the passage as evidence of the general ignorance of Aristophanes and likely most of the spectators as well, citing also the earlier figure of 2,000

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urable by means of quantification and would not be a surprising facet in scene setting, the construction of plot, theme, jokes, characters, and situations—any and all situations in which counting and calculating, and the uses to which they are put, are present. In short, the plays, in different ways, and taking different forms, are a guide to the Athenians’ numerate knowledge. The thematic interlocking of numeracy (and implied education, however obtained), power, the individual citizen, democracy and empire in Wasps is especially illuminating: it too speaks directly to the audience’s predisposition. From gripes about money, to its cultivation in relation to Athens’ power, spectators can identify. Two general points are important to keep in mind about the audience. One is the awareness that no audience is monolithic in viewpoint and knowledge, and, two, specifically with respect to the finances of the city and its citizens, information, ranging from the city’s revenues, the minutiae of imperial and public finance, to the financial worth of citizens, was not hidden away in some bureaucrat’s or politician’s office. The demos formally controlled the purse strings of both city and rich citizen. Of course, citizens expected politicians, as mentioned at the start of this paper, to show their knowledge in this area. But members of the dramatic audience, and in their capacity as participants in a democracy in control of an empire, were conversant and educated in the ways reviewed above.

4

Numeracy and Value

‘Literacy appears prima facie to have been socially more valued than numeracy. This asymmetry is far from being self-explanatory—there were ancient societies (the Assyrian empire, for instance) where numeracy was very highly valued indeed’.72 This comment, referring to Greek culture generally, deserves attention in light of the above examination. Some brief observations and snapshots by way of conclusion follow. Numbers were ubiquitous in fifth-century Athens and conspicuous in democratic institutions. They were seen, read, heard, and judged. Numeracy and democracy were symbiotically linked; the democracy would have foundered with an innumerate or barely numerate citizenry. Omnipresence, of course, does not substantiate value; but as we have seen, numbers were not just back-

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talents for the total annual revenue (though he does think the audience would know that the empire did not stretch to Sardinia). This misses entirely the point of the exaggeration. Cuomo, ‘Accounts’, 257.

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ground noise, mundane and functional, irrelevant to the calculus of worth, whether of persons or things. If one counts only what is deemed worth counting then the path forward would seem to be straight, if it did not risk circularity and raising the question, worth counting to whom? Authority, power, and prosperity might individually or collectively be useful ways of evaluating the significance of number, on both public and private levels. What is seen is revealing. For example, the Lapis Primus, mentioned above, lists 15 years of tribute payments by individual cities in terms of the onesixtieth portions thereof that the Athenians dedicated to Athena. Technically it is a dry financial document certifying that the public accountants have received from the Hellēnotamiai moneys destined for Athena’s treasury. In some societies, an account like this, the receipt of funds from one board to another, might be stored in an archive, on a wooden board or the like. It was clearly important for Athenians, judging from the extant record, to inscribe documents pertaining to sacred moneys. It was a matter of transparency and a form of proper behaviour toward the property of the city’s gods. Moreover, we might say that the Athenians count in the first place because record-keeping is a necessary hallmark of their democracy (and a bulwark against dishonesty). Yet, the appearance of the Lapis Primus is telling: the layout of this towering marble stele was standardised: numerals were positioned before names, a single inscriber tended to be used, and the names and numerals were rendered in a fine, neat hand, in a checkerboard (stoichedon) pattern,73 so that its overall appearance was as uniform and elegant as possible. That this account was designed to impress is beyond obvious. It projected power and authority on a grand scale, and it was not simply for domestic consumption. Unusually, the dating formula, the eponymous archon of the year, included ‘at Athens’. This was a statement of Athens’ power for the benefit of its subjects in the empire and other foreigners who might view it.74 Arguably, the placement of the numerals before the cities’ names gave the sums primacy, expressing that power in numerical terms, down to the last obol.75 The extraordinary wartime assessment of tribute in 425 (IG i3 71 = OR 153), was also inscribed on a monumental marble stele, and it too quantifies Athen-

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Tracy, Athenian Lettering, 44–45. See also above, p. 40. IG i3 259 col. i.3: ἐ]πὶ Ἀρίσ̣[τονος] ἄρχοντος Ἀ[θεν]αίοις. See Kallet-Marx, ‘Money Talks’ on the explicit reference to tribute as the source of Athens’ power; the epigraphic evidence is a fine corroboration.

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ian power. After a lengthy decree outlining purpose, procedures and punishments, it lists cities (including some claimed by Athens which were not in the tributary empire, such as Melos), with figures that represent the doubling or trebling of cities’ previous assessments. The grand total, at the bottom of the stele, is wrought in large figures so as not to be missed. We need to recognise that this inscribed document was a rhetorical statement, intended to project enormous power and authority in the Greek world, but its provisions were largely unsuccessful. Its subtext was weakness.76 Athenians collectively quantified their power and authority explicitly through lists. Conveying an impression of success entailed enumerating its criteria, so that when proposers, first in the boulē and then in the assembly, advocated a course of action, numeracy was an essential instrument of persuasion. We can see this in the 425 reassessment, and in Pericles’ list of the ingredients of military preparedness and success when, alongside intelligent leadership, he quantifies by saying that Athens has some 600 talents of revenue from the empire and 6,000 talents of reserve in ‘our own coinage’ (2.13.3). We also saw above (p. 34) an example of a client of Lysias using statistics as proof in court that he was an impeccable citizen. The egalitarian principle that the rich need to give back their worth makes the amount important. It was up to auditors in the courtroom to calculate the total if they wished. Lysias will have known that a list of particular expenditures attached to each liturgy was likely to be more rhetorically effective. The example elides both collective and individual identities: the city prospers because of quantified contributions and the individual prospers in the collective environment because he is held in esteem as a model citizen; he is valued. Aristophanes features characters and plots revolving around numbers that speak to the collective and private good as well, but in a more complicated way. In Wasps, being a juror might be thought to benefit both the collective and the individual; collective social order is maintained through the courts, and individuals get paid to allow them to join in achieving that equilibrium. Philocleon, however, reverses the justification of pay at its outset. He serves as a juror to make the rich suffer (for self-serving reasons: it makes him feel happy and empowered), but most of all his service is a means to an end, the triobolon.77

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The war encouraged defections to Sparta, and Athens had been losing control over its subjects by this point. With an emphasis on the epigraphic evidence, see Kallet, ‘Epigraphic Geography’. ‘The sweetest part of all, which slipped my mind, is when I come home with my pay’ (605), his family welcomes him ‘because of the money’ (argurion, 607), his daughter tries to pry

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Philocleon fetishises the triobolon. His son accepts the premise of his father’s jury service, but he sets out to demonstrate to his father that he is evaluating the sum incorrectly, and so devalues the three obols through a lesson in quantification in which the total revenue of the city is contrasted with his father’s pay. In that case, a total sum is more instructive than its (non-quantified) parts. Dicaeopolis, in turn, does not quantify his own monetary distress in the cash economy, but his gripes against those who get more out of the democracy than is right are quantified, in necessarily exaggerated terms. There would therefore seem to be a good argument against quantifying worth explicitly or implicitly, because doing so exposes inequity. Yet in the enumeration of who gets what and why, the subject—broadly, numeracy in the service of value by and in society—is centre stage. So too, but differently, Strepsiades needs to calculate his debts on a horse; in his case, quantifying leads to potential ruin, while his son is happy, oblivious to its cost. In all cases the good life is still enumerated: the balance sheet needs realignment, so that those who do not deserve their wealth are, or should be, deprived of it, as in the case of Cleon’s bribe of five talents in Acharnians and the lion’s share of the demagogues in Wasps. In this respect, Athens was a society of numbers, its collective identity forged through quantification, specifically of monetary wealth and what it could buy. The quantitative mentality values what is counted—the plethora of coin, subjects, tribute, imports—and regards it as the measure of power (both collective and individual), the good life, and as the key to economic betterment.78

Bibliography Austin, M.M. and P. Vidal-Naquet, Economic and Social History of Ancient Greece: An Introduction (Berkeley: University of California Press, 1977). Bresson, B., The Making of the Ancient Greek Economy: Institutions, Markets, and Growth in the City-States, trans. S. Rendall (Princeton: Princeton University Press 2016). Cohen, P.C., A Calculating People: The Spread of Numeracy in Early America (New York: Routledge, 1999).

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the triobolon from his mouth (609); and his wife generally pampers him (610–612). It is the pay which ‘shields me from troubles’ (615) taking τάδε, with Henderson, to refer to pay, though it could refer to the general reception the father gets at home (so Sommerstein). See Cohen, A Calculating People, 205–206, quoted above. It is a pleasure to thank Rob Sing and Tazuko van Berkel, organisers of the Leiden conference; I also thank the referees for their comments on an early draft, and, especially, Rob Sing, for his patience and assistance during the preparation of the paper.

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Crump, T., The Anthropology of Numbers (Cambridge: Cambridge University Press, 1990). Cuomo, S., Ancient Mathematics (London: Routledge, 2001). Cuomo, S., ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper (ed.), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278 Davies, J.K., ‘Accounts and Accountability in Classical Athens’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 201–212. Davies, J.K., ‘Corridors, Cleruchies, Commodities, and Coins: the Pre-history of the Athenian Empire’, in A. Slawisch (ed.), Handels- und Finanzgebaren in der Ägäis im 5. Jh.V.Chr./ Trade and Finance in the 5th c. bc Aegean World (BYZAS, 18; Istanbul: Ege Yayinlari, 2013), 43–66. Dover, K.J., Aristophanes: Clouds (1968; Oxford: Clarendon Press, 1989). Hansen, M.H., ‘Misthos for Magistrates in Classical Athens’, SymbOslo, 54 (1979), 5–22. Hansen, M.H., The Athenian Democracy in the Age of Demosthenes (Oxford: Blackwell, 1991). Harris, E.M., ‘Workshop, Marketplace and Household: the Nature of Technical Specialisation in Classical Athens and its Influence on Economy and Society’, in P. Cartledge, E.E. Cohen and L. Foxhall (eds), Money, Labour and Land: Approaches to the Economies of Ancient Greece (London: 2002), 67–99. Ismard, P., La démocratie contre les experts. Les esclaves publics en Grèce ancienne (Paris: Les Éditions du Seuil, 2015). Jones, N.F., Rural Athens under the Democracy (Philadelphia: University of Philadelphia Press, 2004). Kallet-Marx, L., Money, Expense and Naval Power in Thucydides’ History, 1–5.24 (Berkeley: University of California Press, 1993). Kallet-Marx, L., ‘Money Talks: Rhetor, Demos and the Resources of the Athenian Empire’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics (Oxford: Clarendon Press, 1994), 227–251. Kallet, L., ‘Epigraphic Geography: The Tribute Quota Fragments Assigned to 421/0 to 415/4’, Hesperia, 73 (2004), 465–496. Kallet, L., ‘The Athenian Economy’, in L.J. Samons ii (ed.), The Cambridge Companion to the Age of Pericles (Cambridge: Cambridge University Press, 2007), 70–95. Kallet, L., ‘The Origins of the Athenian Economic Arche’, JHS, 133 (2013), 34–60. Kallet, L. and J.H. Kroll, The Athenian Empire: Using Coins as Sources (Cambridge: Cambridge University Press, 2020). Kim, H.S., ‘Small Change and the Moneyed Economy’, in P. Cartledge, E.E. Cohen and L. Foxhall (eds), Money, Labour and Land: Approaches to the Economies of Ancient Greece (London: Routledge, 2002), 44–51.

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Kim, H.S. and J.H. Kroll, ‘A Hoard of Archaic Coins of Colophon and Unminted Silver (CH i.3)’, AJN, 20 (2008), 53–104. Kroll, J.H., ‘An Archive of the Athenian Cavalry’, Hesperia, 46 (1977), 83–146. Kroll, J.H., ‘What about Coinage?’, in J. Ma, N. Papazarkadas and R. Parker (eds), Interpreting the Athenian Empire (London: Duckworth, 2009), 195–209. Lerner, R., ‘Commerce and Character: The Anglo-American as a New-Model Man’, William and Mary Quarterly, 34 (1979), 3–26. Loomis, W.T., Wages, Welfare Costs and Inflation in Classical Athens (Ann Arbor: University of Michigan Press, 1998). MacDowell, D.M., Aristophanes Wasps (Oxford: Clarendon Press, 1971). Marginesu, G., Gli epietati dell’ Acropoli: Edilizia sacra nella città di Pericle 447/6–433/2 a.C. (Athens: Scuola archeologica italiana di Atene / Pandemos, 2010). Meineck, P., Aristophanes i: Clouds, Wasps, Birds (Indianapolis: Hackett Publishing Co, 1998). Migeotte, L., Les finances des cites grecques (Paris: Les Belles Lettres, 2014). Moreno, A. and S. Lape, ‘Comedy and the Social Historian’, in M. Revermann (ed.), The Cambridge Companion to Greek Comedy (Cambridge: Cambridge University Press, 2014), 336–369. Mueller, I., ‘Mathematics and Education: Some Notes on the Platonic Program’, Apeiron, 24 (1991), 85–104. Netz, R., ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321– 352. Ober, J., Democracy and Knowledge: Innovation and Learning in Classical Athens (Princeton: Princeton University Press, 2008). Olson, S.D., ‘Dicaiopolis’ Motivations in Aristophanes’ Acharnians’, JHS, 111 (1991), 200– 203. Olson, S.D., Aristophanes Acharnians (Oxford: Oxford University Press, 2002). Osborne, R., Classical Landscape with Figures: the Ancient Greek City and its Countryside (Cambridge: George Philip, 1987). Pelling, C., Literary Texts and the Greek Historian (London: Routledge, 2000). Purcell, N., ‘The Ancient Mediterranean: the View from the Customs House’, in W. Harris (ed.), Rethinking the Mediterranean (Oxford: Oxford University Press 2005), 200– 228. Raubitschek, A., ‘Two Notes on Isocrates’, TAPA, 72 (1941), 356–362. Rhodes, P.J., The Athenian Boule (Oxford: Clarendon Press, 1972). Rhodes, P.J., A Commentary on the Aristotelian Athenaion Politeia (Oxford: Clarendon Press, 1981). Robinson, E.W., Democracy Beyond Athens: Popular Government in the Greek Classical Age (Cambridge: Cambridge University Press, 2011). Rosivach, V., ‘State Pay as War Relief in Peloponnesian-War Athens’, G&R, 58 (2011), 176– 183.

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Samons, L.J., ii, Empire of the Owl: Athenian Imperial Finance (Historia Einzelshriften, 142; Stuttgart: Franz Steiner, 2000). Schärlig, A., Compter avec des cailloux: le calcul élémentaire sur l’abaque chez les anciennes Grecs (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001). Sommerstein, A.S., Acharnians (Warminster: Aris & Phillips, 1980). Sommerstein, A.S., Aristophanes Wasps (rev. repr., Oxford: Oxford University Press, 2004). Tocqueville, A. de, Democracy in America, J.P. Mayer and M. Lerner (eds), trans. G. Lawrence (New York: Harper & Row, 1966). Tordoff, R.L., ‘Coins, Money, and Exchange in Aristophanes’ Wealth’, TAPA, 142 (2012), 257–293. Tracy, S.V., Athenian Lettering of the Fifth Century bc: the Rise of the Professional Letter Cutter (Berlin: De Gruyter, 2016). Van Alfen, P.G., ‘Aegean-Levantine Trade, 600–300 bce: Commodities, Consumers, and the Problem of Autarkeia’, in E. Harris, D. Lewis and M. Woolmer (eds), The Ancient Greek Economy: Markets, Households and City-States (Cambridge: Cambridge University Press, 2015), 277–298. Wees, H. van, Ships and Silver, Taxes and Tribute: A Fiscal History of Archaic Athens (London: I.B. Tauris, 2013). Whitehead, D., The Demes of Attica 508/7– ca. 250b.c.: A Political and Social Study (Princeton: Princeton University Press, 1986). Yunis, H., ‘How do the People Decide? Thucydides on Periclean Rhetoric and Civic Instruction’, AJP, 112 (1991), 179–200.

chapter 2

The Appearance of Numbers Robin Osborne

Modern scholars are convinced that the single most important message that the gravestone of Dexileos is trying to convey is that he was just 19 when he died.1 This matters, Colin Edmonson suggested (and Ober and others have followed him), because his youthful death enabled sympathy to be harvested for the cavalry who had fallen under a shadow because of their collaboration with the Thirty.2 We might expect the inscription to say ‘He was only 19’. A modern inscription might line up the dates thus: Born Died

10 Anthesterion 8 Hekatombaion

413 394

Yet the text offers no numbers at all. Or at least the only number it offers is ‘five’—the mysterious ‘five cavalrymen’, with ‘five’ spelt out in words, of whom Dexileos was apparently one. All it does give—uniquely, hence the speculation as to its political significance—is the names of the archons in office when he was born and when he died. The number 19 does not appear here at all, in any shape or form, neither stated nor deducible by a mathematical calculation. The effect that we might achieve with numbers is here achieved by the line-up of ‘was born’ (ἐγένετο) at the beginning of line 2, and died (ἀπέθανε) at the beginning of line 3. The desire to make a political point about how mistaken it would be to assume that the cavalry is opposed to democracy seems to compete with another politics, the prejudice against use of numerals outside accounts.

1 IG ii2 6217 = RO 7B. 2 Δεξίλεως Λυσανίο Θορίκιος Dexileos son of Lysanias of Thorikos ἐγένετο ἐπὶ Τεισάνδρο ἄρχοντος, Born in the archonship of Teisandros [414/13]; ἀπέθανε ἐπ’ Εὐβολίδο died in that of Euboulides [394/3], ἐγ Κορίνθωι τῶν πέντε ἱππέων. at Corinth as one of the five cavalrymen. In addition to the commentary in RO, which cites Edmonson’s unpublished views, see also J. Ober, Athenian Legacies: Essays on the Politics of Going On Together (Princeton: Princeton University Press, 2005), 241–243; R. Osborne, ‘Democratic Ideology, the Events of War and the Iconography of Attic Funerary Sculpture’, in D. Pritchard (ed.), War and Democracy in Classical Athens (Cambridge: Cambridge University Press, 2010), 245–265.

© Robin Osborne, 2022 | doi:10.1163/9789004467224_004

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It is with the nature of the prejudices about how quantities are expressed in Athenian inscriptions that this paper is concerned. I ask when numbers first appeared in Athenian inscriptions and what they look like when they do appear.3 I begin with the back history of epigraphic numbers in Greece.4

1

The First Epigraphic Appearance of Numbers in Archaic Greece

Quantities appear all over Greek inscriptions from an early date—to record how many things or occasions are in question, how far things are from each other, how much things cost. Constitutional bodies from the beginning are defined by their size, the length of office is spelled out and the interval between offices may also be prescribed; constitutional and other laws express penalties for infringement of the rules quantitatively. The Dreros law, conventionally regarded as having a good chance of being the earliest law extant, provides an example. Here we have first the interval, ten years, between being kosmos and being kosmos again; anyone who infringes the law is to pay double the amount of the fines that they impose in their judgements, and those who swear to the law include the Twenty of the city. All of these numbers are spelt out in words in continuous text.5 Equally, numbers appear in early private inscriptions. So we find a sixth-century dedication of 580–570 from the Samian Heraion spelling out the total cost of the dedications some Perinthians have made in fulfilling 3 Much of the material discussed here is also discussed in S. Cuomo, ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper and A.-M. Kanthak (eds), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278. But Cuomo’s interest is in who did the mathematics involved when numbers appear and with who read the inscriptions, and although noting that numbers may be indicated by numerals or be written out, she does not systematically note the difference. My interest, by contrast, is with the appearance of the numbers. I leave aside entirely here the issue of why inscriptions including numbers were inscribed in the first place. 4 The classic discussion of the epigraphic expression of numbers is M.N. Tod, Ancient Greek Numerical Systems: Six Studies (Chicago: Ares, 1979), a convenient republication of a number of separate papers published much earlier. 5 ML 2, Gagarin and Perlman Dr1: ἇδ’ ἔϝαδε | πόλι· | ἐπεί κα κ̣οσμήσει | δέκα ϝετίον τὸν ἀϝτὸν | μὴ κόσμεν, | αἰ δὲ κοσμησιε, | ὀ(π)ε δικακσιε, | ἀϝτὸν ὀπῆλεν | διπλεῖ | κἀϝτὸν ἄκρηστον | ἦμεν, | ἆς δόοι, | κὄτι κοσμησίε | μηδὲν ἤμην. vac. X ὀμόται δὲ | κόσμος | κοἰ δάμιοι | κοἰ | ἴκατι | οἰ τᾶς πόλ̣[ιο]ς.̣ vac. The city decided. Whenever a man serves as kosmos, the same man is not to serve as kosmos again for ten years. If he does serve as kosmos, whatever he decides he shall himself incur double and be useless as long as he lives, and whatever he does as kosmos shall be as nothing. Swearers: the kosmos, and the Damioi and the Twenty of the city.

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a tithe (IG xii 6 577). This is a stone whose short lines result in almost every line starting in the middle of a word, and the numbers disappear for us into the jumble of letters.6 Or we find a dedication at Nemea from the middle of the sixth century in which Aristis celebrates having won the pankration four times (ML 9). This is a metrical inscription (at least as far as ἐν Νεμέαι), but neither metrically nor visually, in its position in the inscription, is the crucial boast of winning four times emphasised.7 No surviving inscription suggests that any Greek state was using numerals, as opposed to words, to indicate numbers during the seventh century. Such indications as we have suggest that the beginning of representation of numbers by some symbolic shorthand, most frequently involving the re-use of letters, either in an acrophonic or some alphabetic system, came only in the sixth century. Some non-acrophonic systems made use of letters no longer employed in writing words as numerical symbols, and were presumably invented while those letters were still remembered and included in their alphabet.8 Johnston 6 [..]νίσκος Ξ[εν][..]niskos, son of Xen[ο]δόκο, Δῆμι[ς] odokos, Demis [Π]υθοκλέος οson of Pythokles, [ἰ]κήϊ{ηι}οι Περ[ί] Perinthian kinsνθιοι τῆι Ἥρmen to Heηι ἀνέθεσαν ra dedicated δεκάτην ἔρa tithe, offδοντες γορerring a goldγύρην χρυσῆen jar, ν, σερῆνα ἀργa silver siύρεον, φιαληren, a silver ν ἀργυρῆν, λυoffering bowl, a χνίην χαλκῆbronze lamp, ν, ὀνονημένα bought σύνπαντα δall together for t[ι]ηκοσίων δυwo hundred and twωδέκων στατelve Samήρων Σαμίωian staters, ν σὺν τῶι λίθω[ι]. with the stone. For a photograph see A.J. Graham, ‘ΟΙΚΗΙΟΙ ΠΕΡΙΝΘΙΟΙ’, JHS, 84 (1964), pl. ii. 7 Ἀριστις με ἀνέθAristis dedicated me εκε Δὶ ϙρονίονι ϝάto lord Zeus son of Kronos νακτι πανκράτιοafter winning in the panν νιϙο͂ν τετράκις kration four times ἐν Νεμέαι· Φείδοat Nemea. The son νος ϝhιὸς το͂ Κλεο of Pheidon of Kleναίο. onai. For an illustration, see LSAG pl. 24.5. 8 For an example see LSAG 327.

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suggested that the first Ionic (sometimes called Milesian), alphabetic, numeral appears in a dipinto of around 575 on a Middle Corinthian crater, interpreting the letters as Ionic sigma, upsilon, mu and (perhaps) zeta and the whole thing as συμμικτα ζ ‘mixed batch of 7’.9 These scrawled marks are necessarily fraught as to their interpretation, but by the middle of the sixth century there are several more that might plausibly be thought to represent numerals in an alphabetic system.10 By the end of the sixth century examples are plentiful, but in the early fifth century they diminish, disappearing c. 475. The acrophonic system, or at least the practice of representing 10 by the letter delta, and 50 by pi modified with a stroke or a delta, appears in the late sixth century on graffiti on pots and then occasionally through the first half of the fifth century. Its first manifestation outside ceramics is on lead loan tablets from Corcyra dating perhaps to 500–450.11 Perhaps the clearest of these reads ‘Nikoteles, pemptas of the Akoroi, owes 138 to the sons of Gnathios, witnesses Thedoros Brnon’ (Calligas no. 5).12 On these loan tablets the sums owed are generally written in numerals, but in one or probably two cases they are given in words (ϝεξεϙον|τα καὶ ϝεξακατια̣ ̣[ς] (i.e. 660), Calligas no. 3). Even on these pieces of lead, the advantage of numerals in standing out from the script is clear: no one could doubt the size of the debt in no. 5, whereas it takes rather longer to notice and absorb the number involved in no. 3.13

2

The Appearance of Numbers in Fifth-Century Athens

More or less exactly contemporary with these Corcyra tablets is the earliest account from Rhamnous, also on lead.14 It records ‘The money has been spent, 9 10 11 12

13 14

A.W. Johnston, ‘Two-and-a-half Corinthian Dipinti’, ABSA, 68 (1973), 185–186. A.W. Johnston, Trademarks on Greek Vases (Warminster: Aris & Phillips, 1979), 27. P.G. Calligas, ‘An Inscribed Lead Plaque from Korkyra’, ABSA, 66 (1971), 79–93. Calligas no. 5: Γναθιου παισι πεμπτας Αϝορον Νικοτελης [ὀφειλ]ει Η ΔΔΔΙΙΙΙΙΙΙΙ ἐπακο Θεδορος Βρνον vac. Cuomo, ‘Accounts’, 271 for number recognition being easier when figures are used. IG i3 247B (p. 957), I.Rhamnous 181: τὸ χρε͂μα The money ἀνέλοται has been spent τὀς hιεροποιὸς that given to the hieropoioi τὸ ἐν το͂ι μολυβδίοι and recorded

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the money given to the hieropoioi, the money written on the lead’ and then records to whom the money has been loaned. This is followed by a heading ‘public’ and a further record of sums received from three individuals, two of whom seem to have the same name as two of the four debtors. Striking here is the clarity of the layout: a new debtor or creditor gets a new line, the sums of money appear after the names, separated by two or three dots. For clarity of presentation this is in a new league. Rhamnous maintained a comparable clarity on its famous mid-fifth-century accounts of Nemesis.15 These record not particular debtors and creditors but annual sums loaned. Each year starts a new line, and proceeds to give various totals. Although the desire to present a uniform stoichedon appearance on the stone means that not every entry starts a new line, there is an obvious attempt to achieve clarity.16 This is similarly the case with the slightly later accounts from the deme Icaria, where, as at Rhamnous, we seem to have a document compiled over time with different hands adding new entries. Here too sums

15

16

hιγραμμένο on the lead: Νεοκλέει: Η𐅄Δ𐅂𐅂 to Neokles: 162 Πυθοδόροι: Η𐅄Δ𐅂̣ to Pythodoros: 161 Τεισαμενο͂ι: Η to Teisamenos: 100 Στράτον⟨ι⟩: Η𐅄𐅂𐅂 to Straton: 152 — — Public: They have [δε]μόσιον: hέχ[οσι] [παρ]ὰ Δίονος: Η — — from Dion: 100+ [παρ]ὰ Στράτονο[ς — —] from Straton: — [πα]ρ̣ὰ Τεισαμεν̣[ο͂ — —] from Teisamenos: — IG i3 248.1–14 = OR 134 reads: ἐπ’ ΑὐτοκλείδUnder Autokleides ο δεμαρχο͂ντοserving as demarch ς: το͂ τε͂ς Νεμέσof the money εος ἀργυρίο: κof Nemesis εφάλαιον: το͂ πthe total of αρὰ τοῖσι τὰς the money from those διακοσίας δρowing the αχμὰς ὀφέλοσι two hundred drachmae: ΜΜΜ𐅆:ΧΧ: το͂ δὲ ἄ37,000; of the λλο ἀργυρίο: τrest of the money ο͂ τε͂ς Νεμέσεοof Nemesis ς· κεφάλαι{:}ον:Μ the total: 1 ΧΧ𐅅ΗΗΔΔ𐅃𐅂𐅂𐅂 2,729 dr. 𐅂ΙΙΙ. 3 ob. This attempt was not entirely successful: some modern scholars have missed the symbol for 10,000 at the end of line 12. See R. Osborne and P.J. Rhodes (eds), Greek Historical Inscriptions 478–404 bc (Oxford: Oxford University Press, 2017), 201 n. 1.

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come at the end of entries and seem to be restricted to a single line.17 The early appearance of acrophonic numerals, with no sign at all that they are unfamiliar or not fully understood, in documents from demes is notable. We cannot be dealing here with a ‘learned code’, developed by a formal bureaucracy. Rather, as the use of the system on pots suggests, this number system is a bottom-up development, which the state eventually adopts, rather than a system that is imposed from above. It is apt that it also appears in Athenian documents in a ‘bottom up’ fashion, manifesting itself in deme documents before it manifests itself in state documents. Numerals appear in Athenian state documents only in the middle of the fifth century with the tribute quota lists. The first list follows the practice we have already seen, and gives a name followed by the amount that applies to the name.18 But from the second list on the order is reversed: the number comes first, then the name. In fact, the number and the name are in separate columns (see fig. 1.1 for the arrangement).19

17

18

19

IG i3 253. The accounts of the first two demarchs recorded (ll. 1–7) read: [....8....] δημαρχο͂ν παρέδωκεν serving as demarch, handed over [κεφάλαιον] ἀργυρίο Διονύσο Χ̣[ΧΧ..] the total of the silver of Dionysos: 3,000+ dr. [..5.. Ἰκαρ]⟨ί⟩ο: ΧΧΗ𐅃𐅂𐅂𐅁 —of Ikarios: 2,107 ½ dr. [ὁσίο ΤΤΤΤ]ΧΧ𐅅ΗΗΗΗΔΔΔ𐅂𐅂𐅂ΙΙΙΙ of the sacred money: 4 tal., 2,933 dr., 4 ob. [..c. 7.. δημαρχῶν] παρέδωκε κεφάλαιον serving as demarch, handed over the total of ἀργυρίο silver [το͂ Διονύσο ΧΧΧ]𐅅Η, Ἰκαρίο κεφάλαιον of Dionysos 3,600 dr., of Ikarios total 2,200 dr. ΧΧΗΗ of sacred money 4 tal., 3 dr., 4 ob. [ὁσίο κεφάλαιον ΤΤ]Τ̣ Τ𐅂̣𐅂̣𐅂̣Ι ΙΙΙ IG i3 259.5–10 of column 3 read: Πεδασε͂ς: ΗΗ Pedaseis: 200 dr. Ἀστυρενο[ί:𐅃𐅂𐅂𐅂ΙΙ] Astyrenoi: 8 dr., 2 ob. Βυζάντιο[ι:Χ𐅅] Byzantinoi: 1,500 dr. [Κ]αμιρε͂ς:𐅅[ΗΗΗΗ] Kamireis 900 dr. Θερμαῖοι Thermaioi [ἐν] Ἰκάρο[ι:𐅄] on Ikaros 500 dr. IG i3 260.11–19 of column 7 read: Η Στρεφσαῖ[οι] 100 dr. Strephsaioi 𐅅Η̣ Η̣ Η̣ Χ̣α̣λχ̣εδ̣[όνιοι] 800 dr. Chalchedonioi ———— —————— ———— —————— Δ𐅃𐅂̣[ΙΙΙΙ] —————— 16 dr., 4 ob. —————— 𐅃𐅂𐅂⟨𐅂⟩ιι Ἀ[στυρενοί] 8 dr., 2 ob. Astyrenoi Δ𐅃𐅂ΙΙΙΙ Γρυν̣[ειε͂ς] 16 dr., 4 ob. Grynieis Δ𐅃𐅂ΙΙΙΙ Πιτανα̣[ῖοι] 16 dr., 4 ob. Pitanaioi Η𐅄 Ἀστακεν[οί] 150 dr. Astakenoi ΗΗ Σπαρτόλιο[ι] 200 dr. Spartolioi

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Shortly afterwards, numerals appear in the accounts of money spent on public building programmes. There are two accounts relating to unknown projects that seem to date to c. 450. The former gives eight years’ accounts of a project involving expenses in excess of 30,000 drachmae, written up in various hands. The sums, expressed in acrophonic numerals, are embedded in the text.20 An account traditionally related to the statue of Athena Promachos, but now shown by Stroud and Foley to relate to some other monument, and to date after 440, has expenses in a separate column.21 This is the pattern then followed by the accounts of the Parthenon, of which various fragments survive from 447/6 on.22 Separate accounts were kept in similar two-column format for the gold and ivory statue of Athena Parthenos;23 but in this case, as well as the annual accounts, the Athenians included a summary figure of very different appearance where the numbers practically shout out:24 what IG i3 calls ‘litt. Att. Magnificae’ are 1.6cm high, but the numerals are twice that or more (3.2–4.3cm), and occupy the horizontal space of two letters. What is more, advantage is taken of the space that this size offers to write the largest numerals differently, with the symbols for talents and for hundreds stacked, Russian-doll style, within the symbol for the operative numeral (see fig. 2.1). The accounts for the statues of Athena and Hephaestus produced in 421/0 seem to learn from this. They follow the two-column format, but at the end give a total figure, and this is marked off by a space before it, by being written across the whole width of the stele (across the column of numbers as well as across the text), and by distinctly larger, though not tremendously elegant, letters.25 By contrast the accounts from 430/29, 426/5 and some years after 410 for golden victories

20 21 22 23 24 25

I prefer ‘embedded’ to Cuomo’s term ‘interspersed’ (‘Accounts’, 268–271). The accounts are IG i3 433, 434. IG i3 435, E. Foley and R.S. Stroud, ‘A Reappraisal of the Athena Promachos Accounts from the Acropolis (IG i3 435)’, Hesperia, 88 (2019), 87–153. IG i3 436–451 = OR 145. IG i3 453–460 = OR 135A. See volume cover image. IG i3 460 = OR 135B. IG i3 472. For a photograph see W.E. Thompson, ‘The Inscriptions in the Hephaisteion’, Hesperia, 38/1 (1969) pl. 34b. I reproduce the effect of the final lines (155–161): χσύλα ἐονέθε τὸ κλίμακε ποιε͂σαι, ἐν hοῖν τὸ wood was bought to make the two ladders on which ἀγάλματε ἐσεγέσθεν [κ]αὶ ἐφ’ ὁν͂ hοι λίθοι ἐσ- the two statues were brought in and one which the εκομίζοντο hοι ἐς τὸ βάθρον, καὶ φάρχσαι stones were transported for the base and to fence the τὸ βάθρον τοῖν ἀγαλμ̣ά̣τοιν base of the two statues and the doors and to ̣ καὶ τὰς ̣ θ̣ύρας, build

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embed their numerals.26 Similarly, although the earliest account that we have for the Erechtheion, when building recommences in 409/8, records quantities of blocks etc. in a separate column (actually making comprehension quite hard!), subsequent accounts that detail wages embed these figures, using words for numbers and for dimensions of items, and only use numerals for sums in drachmae.27 For the campaigns against Samos and, probably, Byzantium in 441/0 and 440/39, the Athenians specially recorded the money they had borrowed from Athena, as they did for the 433/2 Corcyra campaign.28 The Samos accounts seem to start new lines with figures, making the large totals easy to pick out. The Corcyra campaign embeds the figures in an account that enumerates the officials involved in detail, burying the figures in the middle of the lines. From 432/1 the Athenians annually recorded expenditure from the treasury of Athena;29 and these accounts from the start embed the figures, and give such a level of detail that only an expert would be able to pick up the important figures— though an experienced eye would know to look to the end, where a total seems

καὶ ἰκριο͂σαι περὶ τὸ ἀγάλματε καὶ κλίμακε

26 27

28 29

scaffolding around the two statues and ladders against the scaffolding.

πρὸς τὰ ἴκρια. 5 vv. vacant [ἀναλόματ]ος κεφάλαιον 𐅈ΧΧΧΗΗΗΔ Total expense 5 tal., 3,310 dr. IG i3 467–471. IG i3 474–479 (extracts in OR 181). For a visual illustration of the latter practice, see figure 2.2. Here I reproduce IG i3 475.272–285 with numbers of men in words and their wages, at a drachma a day, in numerals: On the second day of the prytany [— — — — — δ]ε[υ]τέρα[ι τε͂ς πρυτα][νείας ἀν]δράσιν ⋮ hενὸ[ς δέοσιν] to nineteen men [εἴκοσιν ⋮Δ]𐅃𐅂𐅂𐅂𐅂⋮ τρίτει τ[ε͂ς πρυτ]19 dr. On the third day of the prytany to thirty-one 275 [ανείας ⋮ ἀ]νδράσιν τριάκο[ντα καὶ] [hενὶ ⋮ΔΔ]Δ𐅂⋮ τετάρτει τε͂[ς πρυτα]men 31 dr. On the fourth day of the [νείας ἀ]νδράσιν τρισὶ καὶ τρ[ι]ά[κον]prytany to thirty-three [τα ⋮ΔΔ]Δ⟨𐅂𐅂𐅂⟩⋮ πέμπτει τε͂ς π[ρυτανε]men 33 dr. On the fifth day of the [ίας] ἀνδράσιν τρισὶ καὶ τρ[ιάκοντ]prytany to thirty-three men 280 [α ⋮Δ]ΔΔ⟨𐅂𐅂𐅂⟩⋮ hέ[κ]τει τε͂ς πρυταν[είας] 33 dr. On the sixth day of the prytany [ἀ]νδράσιν ἑνὸς δέοσι τριά[κοντα] to twenty-nine men [Δ]Δ𐅃𐅂𐅂𐅂𐅂⋮ hεβδόμει τε͂ς π[ρυτανε]29 dr. On the seventh day of the prytany ίας ἀνδράσιν τρισὶ καὶ εἴκο[σιν ⋮ΔΔ] to twenty-three men 2 𐅂𐅂𐅂⋮ hογδόηι τε͂ς πρυταν[είας ἀν]3 dr. On the eighth day of the prytany 285 δράσιν ἑνὶ καὶ εἴκοσιν ⋮ΔΔ𐅂 — — — — — to twenty-one men, 21 dr. IG i3 363, 364 = OR 148. IG i3 365, 366, 371–374.

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figure 2.1 IG i3 460 (EM 6769): Fragment of the summary accounts of Pheidias’ statue of Athena Parthenos (438/7bce)

the appearance of numbers

figure 2.2 IG i3 476 (EM 6667). Part of the accounts of the Erechtheion for 408/7 bce

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to have been given. One example, but only one example, does lay out quite clearly the moneys borrowed from each of the gods, with a new line for each entry and the sum following the identification of the god:30 it is as if the Athenians knew how to make things clear if they wanted to, but sometimes did not want to. We do not know who made the decision: was it left to the stonemasons responsible for the writing up to decide whether to make things clear or not, or was some member of the relevant board detailed to oversee the exercise and take responsibility for the layout? We have one account of the content of the treasury of the Other Gods, dated to 429/8 and curiously this takes a different form from either the inventories or the accounts of the treasury of Athena, with one column for the sum involved and a second column recording which god is involved and what the sum consists of (Aeginetan staters, Chian silver drachmae, Corinthian staters, Acanthian silver, and so on)—and that despite the fact that the form of the numerals is itself modified to show when it is staters that are at issue, just as it is modified to show when talents are at issue.31 When the Athenians began enumerating the treasures to be found on the Acropolis, in 434/3, the numbers and weights of those too were recorded in 30

31

IG i3 369.112–117 = OR 160: [Ἀθεναίας Νίκες ἀρχαῖον ὀφέλοσιν ἐν] ἕνδεκα ἔτεσιν ⋮⟨𐅉𐅉⟩𐅈ΤΤΤΧΧΧ𐅅ΔΔΔΔ𐅃𐅂𐅂𐅂ΙΙ vacat [Ἀθεναίας Νίκες τόκος ἐγένετο ⋮ 𐅈 — —]ΔΔΔ𐅂ΙΙ𐅁 vacat [Ἀθεναίας Πολιάδος ἐν ἕνδεκα ἔτεσιν] τὸ ἀρχαῖον [ὀ]φέλοσιν ⋮ 𐅍𐅍𐅍𐅍𐅌𐅋𐅋𐅉𐅉𐅉𐅉𐅈ΤΤΤ𐅆̣𐅅Η [Η𐅄ΔΔ𐅃]· [Ἀθεναίας Πολιάδος τόκος ἐγένετο ἐν] ἕνδεκα ἔτεσ[ιν ⋮] 𐅍𐅋𐅋𐅉 𐅉𐅉𐅉ΤΤΤΧΧΧ𐅅ΗΗΗ̣𐅂̣𐅂𐅂𐅂 vacat [ἐν ἕνδεκα ἔτεσιν Ἀθεναίας Νίκες καὶ] Πολιάδος ⋮[𐅍𐅍𐅍𐅍]𐅌𐅋𐅋𐅊⟨𐅉⟩𐅉𐅈ΤΤΧΧΧΗΗ[ΗΔΔ𐅂 𐅂𐅂ΙΙ]· [ἐν ἕνδεκα ἔτεσιν κεφάλαιον το͂ Πολιά]δος καὶ Νίκ[ες τόκ]ο ⋮𐅍𐅋𐅋𐅉𐅉𐅉𐅉𐅈ΤΤΤ — — — Of Athena Nike, original sum due in eleven years: 28 tal., 3,548 dr., 2 ob.; of Athena Nike, the interest was 5 tal. (+), 31 dr. (+), 2½ ob. Of Athena Polias, in eleven years, the original sum due: 4,748 tal., 5,775 dr. of Athena Polias, the interest in eleven years was: 1,243 tal., 3,804 dr. In eleven years of Athena Nike and Polias: 4,748 tal., 3,323 dr., 2 ob; in eleven years the total interest of Polias and Nike: 1,248 tal. (+) IG i3 383. I reproduce lines 26–33: 𐅐𐅐𐅐𐅐 στα[τε͂ρες] 40 st. Staters ΗΗΗΗ𐅄 Χῖα[ι δραχμαὶ] 489 Chian drachmae ΔΔΔ𐅃ΙΙΙΙ ἀργυρ̣[αῖ] of silver 𐅐𐅐𐅏Σ Κορίνθιο[ι] 16 st. Corinthian στατε͂ρες staters ΗΗΗ𐅄 Ἀκάνθιον 386 Acanthian ἀργύριον silver [Δ]ΔΔ𐅃𐅂 [Δ]ΔΙΙ Σάμια ἑμίεκτα 22 Samian half hekteis

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numerals, and in the run of the account.32 So too at Eleusis, from which we have various relevant small fragments, one perhaps as early as 450, and then systematic accounts of the epistatai from 408/7 and 407/6.33 The appearance of numbers in other forms of public documents did not change practice in decrees, however. Although decrees frequently had occasion to refer to sums of money, they continued always to do so in words. So in a proxeny decree from the middle of the century someone prosecuting on behalf of Acheloion is let off prytaneia except for five drachmae, and any community in which he or his children are killed is mulcted for five talents—both these sums are written out.34 Only when decrees concern tribute reassessment or building projects do numerals sometimes appear.35

3

The Appearance of Numbers in Fourth-Century Athens

In the fourth century the use of numerals spreads. Early fourth-century decrees, like those of the fifth century, spell out all the sums of money, including the costs of crowns and the costs of inscribing a stele. But in the 370s and 360s practice changes and it becomes regular to indicate these with numerals. In 378/7 we find the cost of a stele, 20 drachmae, being spelled out in words in IG ii2 76 but the numeral 20 is plausibly restored in a contemporary text, IG ii2 82, and

32 33 34

35

IG i3 292–362. IG i3 384–401, I.Eleusis 23–25, 32–38, 42, 45–48, 50, 52. IG i3 19: ͂ [.... ἐναι] δ α[ὐτὸν πρόχσενον Ἀθενα]… he is to be proxenos of the Athen[ίον καὶ ε]ὐεργέτε̣ [ν· ians and benefactor. If Acheloïon is wronged by ̣ ἐὰν δὲ ὑπό τινον] any individuals, he is to obtain court [ἀδικε͂τ]αι Ἀχελοΐο[ν, τὰς δίκας λαγχ][άνεν κ]ατὰ τούτον Ἀ[θένεσιν πρὸς τὸ]hearings against these at Athens before [μ πολ]έμαρχον, πρυτ[ανεῖα δὲ μὲ τελε͂]- the polemarch, and the person who has [ν πλ]ὲν πέντε δραχμ[ο͂ν τὸν γραφσάμε]- brought the charge is not to pay court fees except for five [νον]· ἐὰν δέ τις ἀπο[κτένει Ἀχελοΐον]drachmae. And if someone kills Acheloïon [α ἒ τ]ο͂ν παίδον τιν[ὰ ἔν τινι το͂ν πόλε]or one of his children in any of the cities [ον ὅ]σον Ἀθεναῖο[ι κρατο͂σιν, τὲν πόλ]over which the Athenians have power, that [ιν π]έντε τάλαντ[α ὀφέλεν ὁς ἐὰν Ἀθε]- city is to pay a fine of five talents, as if someone [ναί]ον τις ἀποθά[νει· γραφὲν δὲ Ἀθέν]killed an Athenian; and the prosecution is to be ͂ [εσι ἐ]ναι κατὰ τ[ὸ αὐτὸ ὅσπερ Ἀθεναί]- conducted at Athens in the same way as if an [ο ἀπο]θανόν̣[τος — — — — — — —] Athenian was killed. So the famous 425/4 decree of Thoudippos, IG i3 71 = OR 153; cf. also IG i3 77, or IG i3 64, apparently to do with Athena Nike.

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the numeral 20 appears for travel expenses in IG ii2 102 of c. 370. Subsequently, using the numeral seems to become standard, though not universal.36 A decree about the Chalkotheke on the Acropolis and its contents from the 350s, as well as specifying in numerals the payment of 30 drachmae for the inscription of the stone, lists what was found in an examination of the Chalkotheke using numerals, which are simply included in the continuous prose rather than set out as a list.37 A decree honouring members of the Council of 343/2 uses a numeral to state the value of a crown (500 drachmae) but words continue to be used in a comparable inscription of 340/39.38 Nevertheless, numerals become more normal in decrees of the 330s.39 More extensive use of numerals seems to creep into other types of inscription also. Of the two laws from the 370s, the Grain Tax law of 374/3 (RO 26) spells out all its numbers, but the law on silver coinage of the previous year (RO 25) mixes words and numerals in spelling out sums of money: the fines and additional penalties for non-compliance by thesmothetai or archons are given in numerals, as is the number of lashes of the whip to be given to a slave offender, but the limit to the jurisdiction of the archons (ten drachmae) is written out in words. Although the law on the little Panathenaea of c. 335, with one exception (the 50 drachmae to cover expenses), uses words to express numbers,40 in 333/2 the number of medimnoi of Sicilian grain handed over to the demos is given as a numeral despite being a round number (4,000);41 in 330/29 the amount Eudemos of Plataia gave, although probably the same round number, is again expressed as a numeral while the 1,000 yoked beasts he supplied are written out in full.42 In the honours for Heracleides of Salamis, the amount of grain he gave, the price at which he gave it, and the value

36

37 38 39 40 41 42

For use of numerals: IG ii2 106.18 [368/7], 107.24 [368/7], 109B.28 [363/2], 116.45 [361/0]; for continued use of words, IG ii3 1 312.24 (340/39) spells out εἴκοσι, IG ii3 1 316.37 (338/7) τριάκοντα. IG ii2 120. IG ii3 1 306.46, 313.36. IG ii3 1 327.62 [336/5], 338.21 [333/2], 348.27 [332/1] for Phanodemos, 349.17, 20 [332/1] for Amphiaraos. IG ii3 1 447 = RO 81. IG ii3 1 339.12. IG ii3 1 352.12–18 = RO 94: [Εὔδημ]ος πρότερόν τε ἐπηγγ[εί]Since Eudemos previously offered [λατο τ]ῶι δήμωι ἐπιδώσειν [εἰ]ς to the people to make a voluntary gift towards the war if there were any need, of 4000 (?) [τὸν π]όλεμον, εἴ τ[ι] δέ[οι]το, [ΧΧΧ]Χ [δ]ραχμὰς καὶ νῦν [ἐπ]ι[δέδ]ωκ̣[εν] drachmae, and now has made a voluntary gift εἰς τὴν ποίησιν τοῦ σταδ[ί]ου towards the making of the stadium καὶ τοῦ θεάτρου τοῦ Παναθην[αϊ]and the Panathenaic theatre κοῦ χίλια ζεύγη … of a thousand yoke of oxen …

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of his donation in money are all given in numerals.43 As Hallof’s indices to IG ii3 nicely show, all dates and days of month and prytany continue to be written out in ordinal form; an ordinal number that might be shown as a numeral was never developed. Deme decrees show a somewhat similar pattern. So the Peiraieus lease of c. 360 uses numerals for the sums paid by those who take the lease of the theatre, but spells out in words that Theaios had caused the deme to increase its income by 300 drachmae.44 The decree perhaps from Hagnous expresses the deme quorum in numerals in the third quarter of the century.45 But in the middle of the century the decree from Cholargos about the Thesmophoria has a mix of words and numerals, with weights expressed as staters set out in words and sums of money in drachmae in numerals (but a monetary value in obols is set out in words).46 The decree from Eleusis from c. 300 honouring Euthy43

44

45 46

IG ii3 1 367.9–13 = RO 95: ⟨κ⟩αὶ πρότερόν τε ἐπέδωκεν ἐν τῆι σand previously he made a voluntary gift in the πανοσιτίαι: ΧΧΧ:μεδίμνους πυρῶν:𐅃: corn shortage of 3,000 medimnoi of wheat at a δράχμουprice of 5 ς πρῶτος τῶν καταπλευσάντων ἐνπόρων, drachmae, as the first of the merchants to sail καὶ πάλιν, in; and again ὅτε αἱ ἐπιδόσεις ἦσαν, ἐπέδωκε: ΧΧΧ: when there were voluntary gifts, he made a gift δραχμὰς εἰof 3,000 ς σιτωνίαν … drachmae for corn-buying … IG ii2 1176.21–28: … ὠνηταὶ Ἀριστοφάνης Σμικύθο:𐅅Η: Μελησίας Ἀριστοκράτο:ΧΗ Ἀρεθούσιος Ἀριστόλεω Πήληξ:𐅅: Οἰνοφῶν Εὐφιλήτου Πειραιεύς:ΧΗ Καλλιάδης εἶπεν· ἐψηφίσθαι Πειραεῦσι· ἐπειδὴ Θεαῖος φιλοτιμεῖται πρὸς τοὺς δημότας καὶ νῦν καὶ ἐν τῶι ἔμπροσθε χρόνωι καὶ πεπόηκεν τριακοσίαις δραχμαῖς πλέον εὑρεῖν τὸ θέατρον … purchasers Aristophanes son of Smikythos, 600; Melesias son of Aristokrates, 1,100; Arethousios son of Aristoleos of Pelex, 500; Oinophon son of Euphiletos of Peiraieus, 1,100. Kalliades said: the people of Peiraieus decree: since Theaios shows love of honour towards the demesmen, both now and in earlier times, and has made the theatre bring in three hundred drachmae more … On this inscription see R.S. Stroud, ‘Three Attic Decrees’, California Studies in Classical Antiquity, 7 (1974), 290–298. IG ii2 1183.22 = RO 63. IG ii2 1184.3–18: τὰς δὲ ἀρχούσας κοινεῖ ἀμφοτthe presiding officials both together

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demos uses a numeral for the fine to be imposed on the demarch if he does not do his duty, and makes that figure stand out by leaving spaces on either side of the ‘H’.47 The fifth-century Thorikos sacred calendar had used words for the only prices it refers to,48 and so too the sums of money in the regulations from Oropos (RO 27) are spelt out, but the decree of the Salaminioi of 363/2 (RO 37) uses numerals for all its sums of money, and numerals dominate the calendars from the Tetrapolis and Erchia and a deme of unknown identity.49 In all those cases the numbers are embedded in the text, except in as far as at Erchia they tend to conclude sentences and lines. The calendar from Teithras not only uses numerals but puts them in a separate column, as does the fragment of a calendar from Eleusis.50 Since the very purpose of these inscriptions, more or less explicitly, is to regulate who spent what, it is notable that the format does not assist this purpose.

47 48 49 50

έρας διδόναι τῆς ἱερείας εἰς are to give, in the name of the priestess, for τὴν ἑορτὴν καὶ τὴν ἐπιμέλειαthe festival and to provide for ν τῶν Θεσμοφορίων ἡμιεκτεῖον the Thesmophoria, a half-hekteus κριθῶν, ἡμιεκτεῖον πυρῶν, ἡμιof barley, a half-hekteus of wheat, a εκτέον ἀλφίτων, ἡμιεκτέον ἀλhalf-hekteus of groats, a half-hekteus [ε]ύρων, ἰσχάδων ἡμιεκτέον, χοᾶ̣ of flour, a half-hekteus of figs, a chous οἴνου, ἡμίχουν ἐλαίου, δύο κοτof wine, a half-chous of oil, two kotylai ύλας μέλιτος, σησάμων λευκῶν χοίof honey, a choinix of white sesame, νικα, μελάνων χοίνικα, [μ]ήκωνος a choinix of black, a choinix χοίνικα, τυροῦ δύο τροφαλίδας μὴ of poppyseed, two rounds of cheese each ἔλαττον ἢ στατηρια[ί]αν ἑκατέραν not less than a stater in weight καὶ σκόρδων δύο στατῆρας καὶ δᾶιδand two staters of garlic, and a torch [α] μὴ ἐλάττονος ἢ δυεῖν ὀβολοῖν καὶ of not less than two obols and ἀργυρίου 𐅂𐅂𐅂𐅂 δραχμάς·ρταῦτα δὲ δι4 drachmae of silver coins. These δόναι τὰς ἀρχούσας· the officials are to give. IG ii2 1194.16; see J.C. Threpsiades, ‘Decree in Honor of Euthydemos of Eleusis’, Hesperia, 8/2 (1939), 177–180 for full text. IG i3 256B = OR 146. Tetrapolis: S.D. Lambert, ‘The Sacrificial Calendar of the Marathonian Tetrapolis: a Revised Text’, ZPE, 130 (2000), 43–70; Erchia: SEG xxi 541; unknown deme: IG ii2 1356. Teithras, SEG xxi 542.2–8: Βοηδ[ρομιῶνος] During Boedromion τετρ̣[άδι — — — — — on the fourth — — Διί: ἐντ̣ — — — — — to Zeus: — — Δ𐅃𐅂𐅂 οἶν: ἄρρεν — — — — 17 dr. a sheep: male — — 𐅂ΙΙ ἱερειώσυνα 1 dr., 2 ob reward for the priest τετράδι φθ[ίνοντος] on the fourth from the end of the month 𐅂𐅂𐅂𐅂 Ἀθηνᾶι οἶν — — — — 4 dr. To Athena, a sheep Eleusis, IG ii2 1363.

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Fourth-century accounts, including the accounts of the treasurers of Athena and of the Other Gods, the Amphictyons on Delos and the accounts from Eleusis, are full of figures, but those figures are all embedded in the text. This is true too of fourth-century poletai accounts.51 By contrast to fifth-century practice, listing numbers in separate columns is not found in any of these documents. The only clear case of this is the list of prizes at the Panathenaea where the number of amphorae of oil is given in a separate column.52 When mortgage horoi appear in the 360s, the sums of money that they record are almost always in numerals, but regularly incorporated into the text. However, some of the figures that come at the end of a text and on a separate line and may be distinctly set apart.53 The one case where numerals are not used is a problematic text.54 Two documents are particularly interesting for their abundant numbers and their lack of numerals. These are the inscriptions laying out the specifications for the portico of the Telesterion at Eleusis, and the later contracts for the foundations and for column drums for it, on the one hand, and for Philo’s arsenal, on the other.55 Lengths and quantities of stone etc. are at issue here, rather than sums of money (except that the contract allows itself numerals for the sum of money paid), but the avoidance of numerals seems studied. The contrast with the accounts of the epistatai at Eleusis, which use numerals for quantities of things and of money alike, is marked.56 But even at Eleusis

51

52 53 54

55

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Langdon in G.V. Lalonde, M.K. Langdon and M.B. Walbank, Inscriptions. Horoi, Poletai Records, Leases of Public Lands (Athenian Agora 19; Princeton: American School of Classical Studies at Athens, 1991), 53–144. IG ii2 2311. IG ii2 2760, 2711 (M.I. Finley, Studies in Land and Credit in Ancient Athens, 500–200bc. The Horos-Inscriptions (New Brunswick, N.J.: Rutgers University Press, 1951), nos 7, 52). See J.V.A. Fine, Horoi. Studies in Mortgage, Real Security, and Tenure in Ancient Athens (Princeton: American School of Classical Studies at Athens, 1951) no 28; Finley, Studies, no. 114A; Lalonde, Langdon and Walbank, Inscriptions, H124. Telesterion: IG ii2 1667 (I.Eleusis 146), 356/5 to 353/2 for specifications; 1671 (I.Eleusis 151), c. 342, contract for foundations; 1675 (I.Eleusis 157) of 337/6 for column drums; Arsenal: IG ii2 1668, 347/6. Especially I.Eleusis 177 (IG ii2 1672) of 329/8, of which lines 1–10 give a flavour: [λόγος ἐπιστατῶν Ἐλευσινόθεν καὶ] ταμιῶν τοῖν θεοῖν· ἐπὶ Κηφισοφῶντος ἄρχοντος ἐπὶ τῆς Ἀντιοχίδο[ς πρώτης πρυτανείας· τὸ περ]ιὸν [π]αρὰ ταμίαιν τοῖν θεοῖν Χ𐅅𐅄Δ𐅃ΙΙTΧ, καὶ παρὰ ταμίαι τοῖν θεοῖν Νικο[φίλωι Ἀλωπε: 𐅃ΙΙΙΙΧ: καὶ π]α[ρὰ] τ[αμί]αι[ν] τοῖν [θ]εοῖ[ν] Νικοφίλωι Ἀλ Τ𐅅ΗΗ: καὶ παρ ἐπιστάταις Ἐλευσινόθεν [ΔΔ𐅃· ἀπὸ τούτου τάδε ἀνή]λωτ[αι· σ]πο[ν]δοφόροις ἐπὶ νή[σ]ων εἰς μυστήρια τὰ μεγάλα ΗΗ𐅄· δημοσίοις τροφήν, [ἀνδρ]άσιν δεκα[επτὰ καὶ] τῶι [ἐπιστάτηι] τῆς ἡμέρας τῶι ἀνδρὶ:ΙΙΙ: κεφάλαιο[ν]:ΗΗΗΔΔ𐅂

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many numbers, e.g. lengths, numbers of days, sometimes numbers of things, are spelled out, with no pattern or consistency that I can detect. Finally a puzzle: a stone found on the Acropolis, is divided up by vertical lines into columns and in each column are rows of paired letters.57 The letter forms suggest a date in the middle of the fifth century, but the letters are Ionic, not Attic, and seem to represent numbers according to the alphabetical numbering system, something otherwise unknown in classical Athens. What exactly this was counting, or how anyone knew, is quite obscure.

Conclusion Is there a story to be told here? It is clear that from the first use of numerals rather than words to express numbers, the decision over which to use was not random. Numerals were, and remained, workaday, belonging primarily to the realm of the efficient, not the dignified. The decision to use numerals rather than number words was more important for enabling sums to be picked out

57

𐅂𐅂𐅂: ἐπιστάτηι δημοσίων μισθὸς τῆς προτανεί[ας:Δ: τοῖς τὰ] γράμματα ἐπικολάψασιν ἐπὶ τὸ ἀνάθημα ἐν τῶι Ἐλευσινίωι σιτία:𐅃𐅂𐅂𐅂: καὶ ἐπὶ τῆς Λειωντ[ίδ]ος τῆς ἡμέρας:𐅂Ι: ἡμερῶν:Δ𐅃ΙΙ: κεφάλαι:Δ𐅃𐅂𐅂𐅂𐅂ΙΙΙΙΙ: καὶ ἐπὶ τῆς Οἰνηΐδος δεκάτης προτανείας σιτία [ΔΔΔΔ𐅂𐅂]𐅂𐅂ΙΙ: μισθωτεῖ τοῦ τείχους τῆς ὑπολογῆς Εὐθυμίδει ἐν Κολλυτῶι οἰκοῦντι, λίθους αὑτῶι παρ[εχ]ο[μέν]ωι πρὸς τῶι ἔργωι, τῆς ὀργυᾶς:𐅃𐅂𐅂𐅂:ΗΗ𐅄 [:] ξύλα ἐλάϊνα εἰσφῆνας παρὰ Ἡρακλείδου ἐκ τοῦ Θησέου, εἰ[σ]φῆνα[ς τ]άλαντα:Δ: τὸ τάλαντον:𐅂ΙΙ: κεφά:Δ𐅂𐅂𐅂Ι[Ι]· … Account of the epistatai from Eleusis and of the Treasurers of the Two Goddesses: In the archonship of Kephisophon, in the first prytany of Antiochis: the surplus from the two Treasurers of the Two Goddesses: 1,565 dr., 2 ob., 3 ch., and from the Treasurer of the Two Goddesses Nikophilos of Alopeke 5 dr., 4 ob., 1 ch.; and from the two Treasurers of the Two Goddesses to Nikophilos of Alopeke 1 tal., 700 dr. and from the epistatai from Eleusis 25 dr. From this sum, these expenditures were made: to the sphondophoroi from the islands for the Great Mysteries 250 dr.; to the public slaves for maintenance, for seventeen men and their overseer at 3 ob. per person per day, total 324 dr. To the foreman of the public slaves, salary for the prytany, 10 dr.; to those inscribing the letters on the dedication in the Eleusinion, food: 8 dr.; and for the prytany of Leontis, per day 1 dr., 1 ob., 17 days, total 19 dr., 5 ob.; and for the prytany of Oineis, the tenth prytany, food 44 dr., 2 ob.; to the hired labourer for the foundation of the wall, to Euthymides living in Kollytos, providing stone himself for the work, 8 dr. per fathom: 250 dr.; olive wood wedges from Herakleides from the Theseium, 10 talents of wedges, 1 dr., 2 ob. per talent, total 13 dr., 2 ob. IG i3 1387 (H.R. Immerwahr, Attic Script: a Survey (Oxford: Clarendon Press, 1990) no. 958,

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and for calculations to be done than the decision of whether to leave the numbers embedded in the text or to separate them in a column. Almost certainly taken over from traders and others who needed clear and succinct records of numbers, numerals were used for sums of money in accounts from the start of inscribing accounts, but the use of numerals outside accounts was limited, and when it occurred it was primarily for sums of money. How far was this practice adopted out of concerns for clarity—keeping sums of money distinct from quantities of other things—and how far was it a matter of aesthetics? We might note here that putting figures into a separate column does not always aid counting: it is useful when all the figures in a column refer to the same thing (sums of money in drachmae, for instance), but can actually be confusing when the numbers in the column refer to different things (as in the account of the treasury of the Other Gods and parts of the Erechtheion accounts). But putting figures into a separate column makes for a more handsome document because it keeps different sorts of signs apart—as does not using numerals at all. A document written for display purposes—like the specifications for an architecturally ambitious building such as Philo’s Arsenal, did not use numerals. There may be an element of discrimination here with regard to readership. The advertisement of how much the Athenians had spent on the Parthenon used numerals boldly and prominently—but this was clearly meant for mass consumption. Most Athenian decrees, and documents like Philo’s Arsenal specifications, were not expecting to attract more than limited attention, and primarily from readers who were themselves interested parties. Was it that some Athenians were more literate in numerals than in continuous prose? It is perhaps worth noting that, given what we find in later papyrus and manuscript traditions, it seems that literary sources never adopted acrophonic numerals, and limited alphabetic numerals to very particular contexts. In the fifth century there are clear signs that the power of numerals to communicate with an immediacy that written-out numbers could not match was realised, both in terms of the impression that a single physically large figure could make and in terms of the way an accumulation of figures would be more impressive if the figures were grouped. The final accounts for the gold and ivory statue of Athena Parthenos provide our best example of the former, the deme accounts at Rhamnous perhaps the epigraphically most striking example of the latter. But in the fourth century, just as the increase in writing on stone fig. 170), discussed by A. Schärlig, Compter avec des cailloux: Le calcul élémentaire sur l’ abaque chez les anciens Grecs (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001), 95–96.

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is accompanied by a decrease in the size of letters and the general legibility of the product, so it is hard to see that the expressive possibilities of numerals are much regarded. Setting numerals clearly apart becomes the exception, and more often they are so embedded in continuous writing that they can be hard to pick out. In fourth-century inscriptions numerals do a job; it is a bit lazy, perhaps, to use them, but easier. Clarity has ceased to be a concern. Scholars have long been concerned to describe the differences between the Athenian democracy of the fifth century and the Athenian democracy of the fourth. The focus of the discussion has been on the formal rules according to which democracy and its various institutions operated. But just as it is apparent that essentially the same rules in the assembly nevertheless allowed quite distinct political behaviour,58 we would do well to look across Athenian behaviour more generally if we are to understand just how far apart fifth- and fourthcentury Athenian democracy were. The humble numeral has its part to play in this bigger story. Numeracy is not the only thing that numbers illuminate.

Acknowledgements I am grateful to Rob Sing and Tazuko van Berkel for the provocation to write this paper, and to them and to Stephen Lambert, Peter Rhodes, and the two anonymous readers for improving it.

Bibliography Calligas, P.G., ‘An Inscribed Lead Plaque from Korkyra’, ABSA, 66 (1971), 79–93. Cuomo, S., ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper and A.-M. Kanthak (eds), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278. Fine, J.V.A., Horoi. Studies in Mortgage, Real Security, and Tenure in Ancient Athens (Princeton: American School of Classical Studies at Athens, 1951). Finley, M.I., Studies in Land and Credit in Ancient Athens, 500–200bc. The Horos-Inscriptions (New Brunswick, N.J.: Rutgers University Press, 1951).

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For one particular example of this see my forthcoming, ‘The Politics of the Amendment and the Transformation of Athenian Democracy in the Fourth Century’, in A. Makres and P.J. Rhodes (eds), στήλη Ἀττική: Athenian Papers in Memory of David M. Lewis (Athens: Greek Epigraphic Society).

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Foley, E. and R.S. Stroud, ‘A Reappraisal of the Athena Promachos Accounts from the Acropolis (IG i3 435)’, Hesperia, 88 (2019), 87–153. Graham, A.J., ‘ΟΙΚΗΙΟΙ ΠΕΡΙΝΘΙΟΙ’, JHS, 84 (1964), 73–75. Immerwahr, H.R., Attic Script: a Survey (Oxford: Clarendon Press, 1990). Johnston, A.W., ‘Two-and-a-half Corinthian Dipinti’, ABSA, 68 (1973), 185–186. Johnston, A.W., Trademarks on Greek Vases (Warminster: Aris & Phillips, 1979). Lalonde, G.V., M.K. Langdon and M.B. Walbank, Inscriptions. Horoi, Poletai Records, Leases of Public Lands (Athenian Agora 19; Princeton: American School of Classical Studies at Athens, 1991). Lambert, S.D., ‘The Sacrificial Calendar of the Marathonian Tetrapolis: a Revised Text’, ZPE, 130 (2000), 43–70. Ober, J., Athenian Legacies: Essays on the Politics of Going On Together (Princeton: Princeton University Press, 2005). Osborne, R., ‘Democratic Ideology, the Events of War and the Iconography of Attic Funerary Sculpture’, in D. Pritchard (ed.), War and Democracy in Classical Athens (Cambridge: Cambridge University Press, 2010), 245–265. Osborne, R. (forthcoming), ‘The Politics of the Amendment and the Transformation of Athenian Democracy in the Fourth Century’, in A. Makres and P.J. Rhodes (eds), στήλη Ἀττική: Athenian Papers in Memory of David M. Lewis (Athens: Greek Epigraphic Society). Schärlig, A., Compter avec des cailloux: Le calcul élémentaire sur l’abaque chez les anciens Grecs (Lausanne: Presses Polytechniques et Universitaires Romanes, 2001). Stroud, R.S., ‘Three Attic Decrees’, California Studies in Classical Antiquity, 7 (1974), 279– 298. Thompson, W.E., ‘The Inscriptions in the Hephaisteion’, Hesperia, 38/1 (1969), 114–118. Threpsiades, J.C., ‘Decree in Honor of Euthydemos of Eleusis’, Hesperia, 8/2 (1939), 177– 180. Tod, M.N., Ancient Greek Numerical Systems: Six Studies (Chicago: Ares, 1979).

chapter 3

Punishing and Valuing Steven Johnstone

In the ancient Greek polis, citizens’ relationships with the city often required them to become valuers, to assess honour and infamy in precisely quantified, monetary terms. I documented some of the ways Greek citizens settled money values in political relationships in my History of Trust in Ancient Greece, especially the processes by which Greek citizens determined their membership in wealth classes and their tax obligations to the polis. I emphasised that these practices had no direct relationship to what we would call ‘market values’— which you could find in the bilateral and contingent process of haggling in the agora—but that they usually derived from declarations by one party that could be challenged by another party and settled rhetorically, that is, by the decision of a third party. In this paper, I would like to extend this analysis of Greek citizens as valuers. I will argue that the ways that Greeks used numbers in prescribing punishments shows the central importance of quantification in constructing relationships among citizens—not so much because these numbers represented values (though they may have) but because they had meanings. For Greek citizens, numeracy required an ability not just to calculate with numbers but to interpret them. This suggestion is not completely eccentric. In examining numbers in Roman literary works (including histories), Walter Scheidel concludes that the highly skewed patterns of distribution indicate that the monetary figures in the texts do not reflect a knowledge of real underlying values (even in rounded form), but are mostly ‘symbolic’—which is to say that these numbers do not have values, but only meanings.1 Similarly, here I will argue that Greek monetary penalties should not be linked primarily to market values; rather, they constituted a system through which Greeks attributed meanings to punishments. Sometimes they did this by establishing a series of quantified penalties that allowed for the comparison of the statuses of victims or perpetrators, or the circumstances of the crimes. At other times, Greeks used numbers to mark radical dissimilarities, qualitative and even incomparable differences.

1 W. Scheidel, ‘Finances, Figures and Fiction’, CQ, 46 (1996), 222–238. He concludes that modern

© Steven Johnstone, 2022 | doi:10.1163/9789004467224_005

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A history of numeracy should start with a basic rule: follow the numbers. In tracking the ways Greeks used numbers in their political activities, I will reject a circumscribed definition of numeracy. One scholar, for example, has defined numeracy as ‘the ability to count, keep records of these counts, and make rational calculations’.2 While these might be the skills we would want children to learn in school nowadays, I prefer a more open-ended definition of the phenomenon I would like to study: whatever Greeks did with numbers. Athenian legal speeches suggest that many Athenians could count, record, and make mathematical calculations, but Athenians were not (or not primarily) doing these activities when they valued punishments. I want, finally, to lodge a sharp objection to the idea that only ‘rational’ calculations count as numeracy; as a historian I will insist that whatever people did with numbers, seemingly rational or not, is of interest and matters. The nature of the evidence imposes a number of conditions on what can be inferred from it. Dependent largely on inscriptions, this study ranges broadly, from the Archaic period to the Hellenistic and across the Greek speaking world. Even with this vast ambit, there is not enough evidence to ground many internal distinctions securely (e.g., changes over time or regional variations) since most cities that provide any evidence at all give only one or two instances. Josine Blok’s argument in this volume that in the late fifth century the Athenians changed the amounts of quantified fines for delinquent officials represents an exception made possible by the relative abundance of inscriptions from Athens from the middle of the fifth to the middle of the fourth century. But Athens is unparalleled, both because of its habit of inscribing official acts and also because of the unique evidence from the hundred or so preserved speeches from its courts. Athens must have been typical in some ways and exceptional in others, though it is sometimes hard to know which. Because Athens provides a quantity of evidence on these questions that is an order of magnitude greater than any other city, one is tempted to reach for broader conclusions, about, for example, the relationships between numeracy and democracy, the Athenians’ specific political system. It is worth remembering, however, that there were many democratic poleis and it is not possible to know whether they conformed to the patterns found in Athens. This paper develops its arguments through four major sections and a conclusion. I begin by surveying the repertoire of non-quantified penalties Greek

historians’ attempts to calculate with these figures, to use them to compute prices of Roman commodities or values of things, are fundamentally faulty. 2 R.J. Emigh, ‘Numeracy or Enumeration?’, Social Science History, 24 (2002), 653–698, at 653.

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laws contained. Because quantifying practices often exist in close relationship to, or are even part of, practices which are essentially qualitative, when investigating punishments that use numbers it is also important to understand punishments which do not. In ancient Greece, non-quantified punishments tended to be those which applied to the person, understood as a body or a legal entity, and might be generalised as death or metaphoric forms of death. Such punishments, involving a change of incomparable statuses (e.g. from living to dead, from citizen to nonperson), contrast to quantified, usually monetised, penalties, but also, it turns out, provide an important parallel for how many monetised fines actually operated. I then turn to the common quantified penalties in Greek laws. By setting a tariff or schedule of monetary fines for particular wrongs—for example, a precise fine for assault—laws encouraged a sometimes complex commensuration of crimes, criminals, and victims. However, I next attend to the widely attested practice of applying very large fines to officials of the polis who failed to do their duties. In contrast to other schedules of fines, these penalties established a hierarchy of incommensurables because the impossibility of paying them entailed a change in status: disenfranchisement, loss of legal personhood. A 10,000 drachmae fine had a stupefying economic value to most men, but it carried a formidable meaning. Finally, at Athens and perhaps elsewhere, some laws prescribed no specific penalty at all, neither monetary nor of the person, instead instituting a procedure of valuation (timēsis) by which the jury that convicted determined the penalty. So far as we can tell from the Athenian legal speeches, this process of timēsis was less about precisely calibrating the value of the harm as about choosing between incommensurable statuses. I conclude that legal penalties show Greeks assigning money values in more than one way, and that some prices—that is, monetised legal penalties—could have non-quantified meanings in addition to their numerical values.

1

Non-quantified Penalties

To analyse how Greek laws used numbers, I begin with those that did not. Greek laws contained a repertoire of non-quantified penalties. Athenians commonly divided punishments into two categories, suffering or paying a fine (παθεῖν ἢ ἀποτεῖσαι).3 The range of penalties a person might suffer in the first category

3 Dem. 20.155, 24.118, 146. Documents from Delos c. 200 (IG xi 4 1299) and Paros in the first half of the second century (SEG xxxiii 679) make the same distinction. All ancient dates are bce.

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included death and a set of punishments which might be understood as juridical or metaphoric death: exile, confiscation of property, and full or partial loss of citizen rights (atimia). ‘Suffering’, then, was not fundamentally a corporal punishment, and it is commonly said that a citizen’s freedom entailed the inviolability of his body. Physical force applied to a citizen by the state as a form of punishment seems to have been unusual. Thus torture and imprisonment are not frequently attested punishments, and there is little evidence that Greek cities mutilated citizens’ bodies as punishment.4 Inversely, to the degree that laws recognised the possibility of punishing slaves, they suffered with their bodies (through torture, like being beaten) often with punishments that were precisely quantified (e.g., 50 lashes).5 Nevertheless, the sanctity of the free person’s body was not absolute since free people were sometimes tortured (for example, in the form of execution known as apotumpanismos), confined and humiliated (publicly in the stocks), and some laws sanctioned violent private punishments. Thus, one might from a different perspective note that what distinguished the free from the servile was that, except for the period of confinement in the stocks, free people’s bodies did not suffer quantified punishments. It is as if the notion of ‘suffering’ applied not to the citizen’s body, but described an unquantifiable and incomparable state change from honour to disgrace. Slaves, without honour (timē) to begin with, could not suffer the transformation to absolute infamy; instead, their bodies were subject to quantified pains.

2

Quantified Penalties

Greek laws often used numbers to establish precise penalties for infractions. Sometimes these numbers operated somewhat like prices, establishing relationships among offenders, offences, or circumstances, but at other times

4 Later stories are told about Archaic laws that punished with blinding (Dem. 24.140–141; Diod. Sic. 12.17.4–5; and Diog. Laert. 1.57). The point of these stories seems to be the unfairness of knocking out only a single eye from an assailant who knocked out the only eye of a one-eyed man—that is, they critique the fairness of a literal application of a lex talionis. Aelian (VH 13.25) reports that Zaleukos supposedly commanded that an adulterer taken in the act have his eyes knocked out. J.Q. Whitman, ‘At the Origins of Law and the State: Supervision of Violence, Mutilation of Bodies, or Setting of Prices?’, Chicago-Kent Law Review, 71 (1995), 41–84, discusses the concern for and relationship of mutilation and prices in early Near Eastern law codes. 5 e.g. Athens 375/4 (RO 25.30–32); Athens, second half of the fourth century (IG ii2 1362.9–10); Athens late second century (IG ii2 1013.5). A second-century law from the Delphic Amphicty-

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Greek laws used monetary penalties in ways that seem to have asserted the incommensurability of the offence. Greek laws used numbers to establish proportional relationships among different offences, offenders, victims, or circumstances—to commensurate. In a few instances, they did this by presenting a tariff or schedule of penalties. Of the many (usually fragmentary) laws from Crete from the Archaic and Classical periods, at least three listed several, related offences and their fines.6 The ‘Great Code’ from Gortyn contains five sections with tariffs of monetary penalties, the longest of which establishes a series of ratios through monetised penalties: If someone rapes a free man or woman, he will pay 100 staters.7 If (someone rapes) an apetairos, (he will pay) 10. If a slave (rapes) a free man or women, he will pay double. If a free man (rapes) a male or female slave, (he will pay) five drachmas. And if a serf (rapes) a male or female slave, five staters. vac. If someone should subdue by force a household slave woman, he will pay two staters; but if she has already had intercourse, (he will pay) one obol during the day, but if at night, two obols. And the slave woman is to be the one who swears. vac. If someone attempts to have intercourse with a free woman while a relative is watching over her, he will pay ten staters if a witness testifies. vac. If someone is caught committing adultery with a free woman in her father’s or brother’s or husband’s house, he will pay 100 staters. And if in someone else’s house, 50. And if (he is caught committing adultery) with the woman of an apetairos, (he will pay) ten. And if a slave with a free woman, (he will pay) double. vac. And if a slave with a slave’s (woman), five (staters).8 This law’s juxtaposition of precisely quantified fines establishes relationships between kinds of perpetrators, kinds of victims, kinds of offences, and circumstances of offences. The fact that the law maintains the same ratios (in fact, the same amounts) for the same set of classes (free, apetairos, slave) across two different offences, rape and adultery, encourages reading this section as a system of penalties calibrated to circumstances through money values. In this law

ony (Syll.3 729.5–6) prescribes fining free people and beating slaves without quantifying the number of blows. 6 In the reference system of M. Gagarin and P. Perlman, The Laws of Ancient Crete c. 650–400bce (Oxford: Oxford University Press, 2016): Elt2 (Eltynia, c. 500), G47 (Gortyn, 500–450?) and G72 (Gortyn, 450?). IPArk 17 (Stymphalos, 303–300) also contains a schedule. 7 A stater equalled two drachmae, a drachma equalled six obols. 8 G72.2.2–27 (trans. Gagarin and Perlman, The Laws of Ancient Crete, 345–346 modified).

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money commensurates, so that you might say that the law treats rape and adultery with equal seriousness, or that the worth of a free man was more than an order of magnitude more than that of a slave. There are, however, few extensive schedules of fines like this, and the laws which have been preserved are more likely to use numbers to establish ratios by using multiples, as the previous law did when it stated (in the penultimate sentence) that a slave committing adultery with a free woman will pay ‘double’. It is not (or not only) the use of money in these laws that allows for commensuration of circumstances. The text enables, even encourages, a particular mode of reading—which also entails a particular kind of numerical calculation—by so closely juxtaposing these items. Physical continuity of texts encourages commensuration with numbers. By contrast, establishing relationships among chronologically, topically, and physically disparate laws was a much more complex task for Athenians, even after they had put in place mechanisms to coordinate them. As I have argued in an earlier book, litigants did this through the fiction of a single ‘lawgiver’ whose intention pervaded all the laws.9 Thus, while physically proximate schedules of monetary fines induce commensuration, it required more interpretative labour to commensurate other penalties, quantified or not, with each other.10

3

Punishments of Officials

Quantified monetary penalties did not always establish a common metric among crimes, perpetrators, or circumstances; sometimes they designated incomparable statuses. Here I turn to one of the most conspicuous ways that laws used numbers to specify fines: for polis officials who failed to act according to a law. Many laws required officials to act in some way (to spend money, hold a hearing, or carry out some duty specific to the office), but in some instances, particular laws added a clause explicitly penalising an official who failed to do what was required; most laws, however, did not. In 418/17, for example, the 9

10

S. Johnstone, Disputes and Democracy: The Consequences of Litigation in Ancient Athens (Austin: University of Texas Press, 1999), 25–33. One might understand ‘the lawgiver’ as the metaphor for, or personification of, the Athenian lawmaking process. Scholars have vigorously debated whether the laws of particular Greek cities can be considered ‘law codes’, see R. Osborne ‘Law and Laws: How Do We Join Up the Dots?’, in L. Mitchell and P.J. Rhodes (eds), The Development of the Polis in Archaic Greece (London: Routledge, 1997), 74–82. I would note only that this is not just an objective question about the texts of the laws or the procedures for making laws, but also how Greeks read them. The Athenian fiction of ‘the lawgiver’ enabled codification through interpretation.

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Athenians passed a decree on the fencing of the sanctuary and leasing of the precinct of Kodros, Neleos, and Basile. The proposal forwarded to the assembly by the boulē directed the king archon, the pōlētai, and the horistai (boundary markers) to take certain actions, then concluded: ‘Let the current boulē get these things done before leaving office or each (member) will be fined 1,000 drachmae according to the proposal’.11 A longer amendment (made by the original proposer but in the assembly) elaborated the details of the lease, including this: ‘If the king archon or anyone else to whom orders have been given about this in the prytany of Aigeis does not do what has been decreed, he will be fined 10,000 drachmae.’12 In each of these clauses there is an excessiveness regarding their use of numbers. The second clause serves no purpose other than to set the amount of the penalty—officials were, after all, already accountable for doing their jobs—an enormous penalty which exceeded the size of most people’s total property. The first clause, it is true, does more than this; it sets a deadline, the end of the term of the current boulē, and apportions joint liability among all members.13 But it is even more excessive, because while its stated fine is less, 1,000 drachmae (still probably beyond the means of most citizens to pay), it offers the astonishing idea that the polis might collect (multiplying 1,000 drachmae by 500 members of the boulē) half a million drachmae in penalties. This excessiveness points to a problem: the value of a fine (as determined by what else a person could have bought with the money, or by the estimated cost of the harm done by the wrongdoer) is not the same as—and may be secondary to—its meaning. The excess in these numbered penalties is the degree to which the fines have a meaning which cannot be reduced to their value. These laws assert an incomparable penalty precisely by using an enormous number. Numeracy requires hermeneutics. While in any particular instance you might profitably look to the local, specific context to determine the meaning of a fine (as Blok does in this volume), beginning more broadly is revealing in a different way. Clauses penalising officials who failed to act can be found throughout the Greek world in the Archaic, Classical, and Hellenistic periods; a few dozen instances have been preserved. Several patterns emerge in this body of evidence. Cumulatively they suggest that monetary penalties for polis officials operated not (or not merely) to assign

11 12 13

IG i3 84.9–11 = OR 167. OR 167.18–20. S. Johnstone, A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011), 127–147, discusses how Greeks treated liability in groups.

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economic values to punishments, but in a hierarchical system of honour and infamy that depended on their meanings. First, while laws sometimes punished officials with non-monetary penalties—loss of office, confiscation of property, disenfranchisement, even death—many more proposed money fines as penalties. Death or disenfranchisement might be extreme penalties for an official who failed to execute his duties, but by quantifying an enormous number, a fine became excessive. Second, with some exceptions, the fines proposed for officials were so onerous as to mark a qualitative threshold. One defendant in the Athenian courts referred to a 1,000 drachmae fine as ‘hard on those who have little property’ (though, in truth, this defendant had more than just a little).14 We occasionally find a small fine that seems reasonably correlated to the cost of the harm. In a decree from Thasos at the end of the fourth century, for example, the officials charged with making sure that the person who leased a garden kept it free from dung were each fined one-twelfth of a stater per day if it was filthy, and the apologoi were liable to this fine if they did not prosecute them.15 Similarly, sub-polis institutions typically fined their own officers smaller amounts, like the phratry at Delphi in the Classical period that fined its officials 10 drachmae for receiving sacrifices on the wrong day, or one obol for any official who missed a meeting.16 Still, considering the scale of these institutions, the fines could sometimes be relatively large. An Athenian phratry in the early fourth century fined the phratriarch 50 drachmae for failing to perform a sacrifice and 500 drachmae for not putting to a vote the yearly review of membership.17 But among laws pertaining to officials of the polis, clauses enumerating fines of 1,000 drachmae or more exceed those with fines in the hundreds or less by a ratio of more than 3 to 1 (see Figure 3.1).18 14 15 16 17 18

Dem. 55.35. IG xii 8 265. RO 1. As the editors note, this group, while certainly like an Athenian phratry, may not have called itself by that term. IG ii2 1237 = RO 5. This graph includes fines of polis officials, but not of officials of sub-polis groups or organisations. In some cases, the fines were directed at both officials and others. In this graph, I have converted all values to drachmae. To build the inventory of fines on which this graph is based, I first read through some of the widely available collections of selected Greek inscriptions, observing that the most common verbs for penalising officials were ὀφείλω, εὐθύνομαι, ἀποτίνω, and εἰσπράσσομαι (listed here in descending order of frequency). I then searched the Packard Humanities Institute website of Greek inscriptions for instances of these words (taking account of dialectical and verbal variants) down through the second century bce. Although this may have missed some instances, it yielded a reasonable number to work from. I omitted from my final pool any

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figure 3.1 Fines of officials in Greek cities valued in drachmae

Third, despite the immensity of these fines, laws almost always enumerate them in drachmae or staters, basic coinage denominations, not in larger units of accounting like talents or minae (the one exception is an early fifthcentury law from Elis that fines officials ‘ten minae’19—which would be 1,000 drachmae). Using the smaller units of physical coinage not only amplified the numbers, it also used units that were immediate and tangible, part of almost everyone’s routine lives, not abstract and notional. Finally, in Figure 3.1 I converted all fines to a standard denomination, drachmae. But not all laws stated their fines in this unit. As noted earlier, some used staters, usually treated as equal to two drachmae. If we leave these fines in their native units and catalogue the numbers they use—that is, if we do not treat the units as values but the numbers as meanings—the graph looks somewhat different. For example, the three fines registered in Figure 3.1 as valued at 4,000 drachmae are each stated as fines of 1,000 (staters) due twice, once to the city, once to Apollo (that is, they do not say ‘2,000 staters’).20 Similarly, the number used to describe most of the fines valued at 200 drachmae is 100 (staters). Charting not the value but the number used reveals more clearly the basic ratios underneath most of these penalties (Figure 3.2). As Figure 3.2 shows, these laws did not just use round numbers; they progressed in a nonlinear way, largely by orders of magnitude. But even describing

19 20

inscriptions in which the amount of the penalty was completely missing from the inscription and had been restored by the editors. I.Olympia 2. These all come from Thasos in the third century: IG xii 8 267, IG xii Suppl. 358, and IG xii Suppl. 362.

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figure 3.2 Numbers used in fines of Greek officials

it that way converts it back to (our) mathematical language. Perhaps it would be better to say that the laws operated in a system that did not simply establish ratios (mathematical relationships) but progressed by qualitative ranks: 100, 1,000, and 10,000. The monetary penalties for officials’ misconduct had meanings that transcended their values. I have noted that 10,000 or even 1,000 drachmae was probably beyond the means of most men to pay. At Athens, at least, failure to pay a fine due to the state would ultimately result in the loss of citizen rights. A litigant in an Athenian case elaborated the problem: … I am a defendant in a case for five talents. And although the accusation refers to money, I’m contending about whether I continue to be a member of the polis. For although the same penalties are set down, the risk is not the same for everyone even with the same penalties; rather, the wealthy are contending about a fine, but the poor like myself about the loss of their citizenship ….21

21

Isoc. 16.46–47. This speaker, Alcibiades the younger, son of the famous Alcibiades who had been in his time one of the richest men in Greece, may have been posturing as an ordinary man here, but the problem he described could have pertained to anyone, depending on the amount of the fine.

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Citizenship could not be legally purchased, though the city might grant it as a gift in return for exceptional service to the state,22 so these laws essentially created an asymmetric mode of valuing: 10,000 drachmae was (for most citizens) equivalent to atimia, but citizen rights could not be acquired at any price. I might say then that a 1,000 drachmae fine for an official had a meaning of great dishonour. Indeed, such fines operated in a system of honour and infamy that designated hierarchical ranks with numbers. As I have argued elsewhere, Greeks used numerical ratios to establish ranks that were, despite their quantification, meant to be incomparable.23 While Greeks frequently used round numbers like 1,000 and 10,000, they would have had a special resonance as the measure of dishonour because they were also used as descriptors of honour. One of the honours bestowed by the city was a crown, often with its value quantified. The Athenian archons wore crowns in the course of their duties, a mark of their authority and honour.24 Athenians granted golden crowns both to foreign benefactors25 and to Athenians for their service in office.26 At the very end of the fourth century, Athenian honorary decrees stopped including a quantified value for the crown, instead afterwards specifying that it be made ‘according to the law’,27 but before this Athenians awarded crowns in specified values of hundreds of drachmae up to a thousand. Though these inscriptions sometimes put monetary values on crowns, they did not constitute prices in any mean22

23 24 25

26 27

There is some evidence for a black market in citizenship—aliens bribing their way in— but it seems to have been limited. This was, in any case, a high-risk transaction since the punishment for falsely claiming citizenship was enslavement. Johnstone, History of Trust, 107–109. D. MacDowell, Demosthenes: Against Meidias (Oration 21) (Oxford: Oxford University Press, 1990), 241. e.g., for the people of Sicyon, Athens’ new allies, a 1,000 drachma golden crown (IG ii3 1 378.25 [323/2]); for the people of Tenedos, for their assistance, a 1,000 drachma golden crown (IG ii3 1 313.35–36 = RO 72 [340/39]); for Spartokos and Pairisades, rulers of the Bosporos, for expediting the shipping of wheat to Athens, a 1,000 drachma crown each (IG ii3 1 298.24 = RO 64 [346]). P.J. Rhodes, The Athenian Boule (Oxford: Clarendon Press, 1985), 14–16. T.L. Shear, Jr., Kallias of Sphettos and the Revolt of Athens in 286 b.c. (Princeton: American School of Classical Studies at Athens, 1978), 55. J.K. Davies, ‘Temples, Credit, and the Circulation of Money’, in A. Meadows and K. Shipton (eds), Money and Its Uses in the Ancient Greek World (Oxford: Oxford University Press, 2001), 126, has suggested that an Athenian desire for convenience of accounting for temple wealth explains the precise specification of the crowns (by value or in a law), resulting in a standardisation. While this is possible, it does not explain why other cities also specified crowns of 1,000 drachmae, nor will the theory work if the quantification concerns the price of the crown since this would not always translate to the same weight (value).

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ingful sense, both because a person could not buy the acclaim that came with a crown (they were usually bestowed at a public occasion like a festival) and because they often had no exchange value for the recipient since they were usually dedicated in a temple where they stood perpetually as a memorial of honour. The ways in which crowns and fines operated in a hierarchy of honour and infamy is well illustrated by an Athenian decree of 325/4 initiating a colonial settlement in the Adriatic.28 To spur the trierarchs assigned to the enterprise, the first to get his ship ready was awarded a gold crown of 500 drachmae, the second a crown of 300, and the third of 200, all to be proclaimed at a public festival.29 Any official or private individual who failed to obey the decree would be fined 10,000 drachmae (and officials who refused to pronounce judgment against them would themselves owe the fine)30 and if the boulē oversaw everything competently, it was eligible for a gold crown of 1,000 drachmae.31 I do not want to deny that these fines and honours might have had economic (exchange) values, particularly for the people who had to pay for them, but for the people on whom they operated—immediately, agents of the polis, but more distantly the general public—they had a meaning that could not be reduced to their price.32 These values did not commensurate—as though finishing second and third would be equivalent to finishing first, or that failing to obey the decree was ten times worse than carrying it out was good; instead, they ranked things. The crown of the boulē was a greater honour than the crown won by the most prompt trierarch.

4

Timēsis

Many laws which did not use numbers nevertheless compelled the litigants and jurors to become valuers if the defendant was convicted. Rather than specifying a penalty, or tying the penalty to the value of harm, these laws left it to the jury to choose between a proposal by the prosecutor and one by the defendant, no compromise. The litigants might propose monetary fines or personal penalties, but not both.33 We know of this process, timēsis, from Athens, 28 29 30 31 32 33

IG ii3 1 370 = RO 100. This decree is preserved with the inscribed yearly accounts of the epimeletai of the dockyards. ll. 190–204. ll. 233–242. ll. 258–263. E.A. Meyer, ‘Inscriptions as Honors and the Athenian Epigraphic Habit’, Historia, 62 (2013), 453–505, discusses the particularly Athenian system of honour through inscriptions. Dem. 20.155.

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especially from the forensic speeches that mention it, though there is some evidence that other cities had similar procedures.34 In Athenian cases that might end in timēsis, prosecutors proposed a penalty in their charge.35 Aristophanes offered a comic (and streamlined) version of such a charge in his Wasps: ‘Demadogue, the watchdog of Cydathenaeum indicts Grabes of Aexone of malefaction in that he devoured a Sicilian cheese all by himself. Proposed penalty: a collar of impeach wood’.36 If the jury voted to convict, the defendant immediately proposed a counter-penalty. Each side spoke briefly in favour of their proposal,37 and the jurors voted for one or the other. Some have argued that procedures like this promote reasonableness, reconciliation, and social harmony. The modern procedure of final offer arbitration, which tracks the Athenian procedure of timēsis closely (and is used, prominently, in some sports like American baseball to resolve salary disputes), is said to do just this: each side will propose an offer toward the middle thinking that the arbitrator will choose the less extreme proposal. Danielle Allen has suggested that something like this happened at Athens: after disputants had expressed their hostility in the main proceedings, in timēsis ‘the anger that had inspired punishment would at last be channeled into a more restrained outcome oriented toward securing public peace and satisfying all parties, prosecutor, defendant, and community’.38 This is a model of calm, convergent valuing. The evidence, however, does not suggest that the process worked this way. Allen’s example is the case of Socrates, which she actually has to make into a hypothetical (‘If Socrates had been willing to play by the rules ….’), though even this counterfactual ignores the fact that his prosecutors did not moderate their proposed penalty, demanding the most extreme penalty possible,

34

35 36 37 38

The most detailed is from Delphi in 285–280 (F.Delphes iii, 1 486), but also Lesbos in the latter half of the fifth century (IG xii 2 1), Delos around 200 (IG xi 4 1299), and Paros around 175–150 (SEG xxxiii 679). G. Thür, ‘The Principle of Fairness in Athenian Legal Procedure: Thoughts on the Echinos and Enklema’, Dike, 11 (2008), 51–73, discusses the charge. ll. 894–897 trans. J. Henderson, Aristophanes: Clouds, Wasps, Peace (Cambridge: Cambridge University Press, 1998), 337. D. MacDowell, ‘The Length of the Speeches on the Assessment of the Penalty in Athenian Courts’, CQ, 35 (1985), 525–526, discusses the time allotted to each side. D.S. Allen, ‘Punishment in Ancient Athens’, in Adriaan Lanni (ed.), ‘Athenian Law in its Democratic Context’, Center for Hellenic Studies On-line Discussion Series, republished in C.W. Blackwell (ed.), Dēmos: Classical Athenian Democracy (The Stoa: a Consortium for Electronic Publication in the Humanities), 23 Mar 2003, http://www.stoa.org/demos/, accessed 29 April 2017.

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death. The evidence from actual Athenian court speeches suggests that litigants often remained far apart in their assessments of penalties. One prosecutor expressed concern that jurors were accustomed to convicting the guilty but then letting them off without punishment (azēmious).39 His suggestion that those convicted were routinely given no punishment at all seems like it just might be hyperbole (so he may mean, punishments too slight for his tastes), and, in any event, this is part of his argument that in the case at hand the jurors must both convict and vote for execution.40 Episodes from the Athenian courts show that timēsis did not always (or maybe even usually) lead to convergent valuing. Here is how Epichares described Theocrines’ treatment of his father: Theocrines ‘deceived the jurors [that is, won a conviction against Epichares’ father] and then refused to assess a measured penalty against my father even though I begged him very much and grasped his knees in supplication. Instead, as if my father had betrayed the city, he penalised him ten talents’.41 The jurors endorsed this enormous penalty and, unable to pay, Epichares’ father lost his citizen rights. Theomnestos described a similar scene when Stephanos convicted Apollodoros: ‘When the jurors were taking their ballots for the penalty assessment, he refused to compromise although we begged him. Instead, he assessed a penalty of 15 talents, so that Apollodoros and his children should lose their citizen rights …’.42 In this case the jurors voted for the defendant’s lesser proposal, a fine of one talent. These two instances were related by friends or family of the convicted men, who were claiming in subsequent lawsuits that the unreasonable enormity of the proposed penalties moved them to sue the prosecutors in turn, so we might expect them to represent the timēsis as leading to extremes. But here is how a prosecutor who had been successful in the timēsis described it: in the trial of Aphobos ‘after the verdict had been reached, (Onetor) got up in front of the court and did supplication on Aphobos’ behalf, entreating and weeping tears, and begged that the penalty be assessed at a talent …’.43 Defending his demand that the jury assess damages at ten talents, Demosthenes represented Onetor’s supplication as yet another of his slippery attempts to cheat him out of his money. The jurors, by the way, voted for the larger assessment.

39 40

41 42 43

Lys. 27.16. He says this not in the timēsis but in the primary adjudication. No speeches from the timēsis portion of a trial have been preserved; what we have are litigants talking about it during the main trial. Dem. 58.70. [Dem.] 59.6. Dem. 30.32.

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The evidence that might suggest that the timēsis procedure did lead to convergent valuing is less persuasive. There is one litigant who says he compromised: Apollodoros (the same man referred to just above) described a case where he indicted and convicted Arethusios for falsely attesting the serving of a summons. Later he reported that in the timēsis the jurors wanted to kill Arethusios, but Apollodoros did not want to be responsible for the death of a citizen, so he agreed to a fine of one talent which the defendant’s friends proposed and he begged the jurors to accept it.44 It is possible that here at last we have an instance of a happy accommodation over a penalty. However, Apollodoros’ exaggerated representation (the jurors—and not just some of them— wanted to kill Arethusios) and the rhetorical force of this incident in his speech, capping as it does a long narrative of the wrongs that Arethusios and his brother Nikostratos had perpetrated on Apollodoros, make Apollodoros seem like a victim entitled to more revenge than he has received up to now. All this raises doubts about the truthfulness of Apollodoros’ story. Whether Apollodoros knew the minds of the jurors, however accurately he reported these earlier events, indeed whether he acceded to the defendant’s proposal or had transformed his defeat into a concession, the one secure fact in this story is that the jurors voted for the defendant’s proposed penalty. Relative circumstances in part determined the meaning of these penalties. If a 15-talent fine represented disenfranchisement for a rich citizen, 1,000 drachmae might well carry the same threat for an ordinary one. There is a risk, of course, that the disputes of the super-rich—and the four cases just discussed fall into that category—may not represent the society as a whole. This is a problem anyone working with the Athenian legal speeches as evidence faces, since those who could hire a speechwriter were significantly wealthier than most.45 These men had the resources to more easily perpetuate their disputes through multiple legal cases, and all four stories cited here come from subsequent litigation between the parties. This may introduce a selection bias, and, indeed, the rich may have been less likely to seek a compromise in a timēsis. But although the valuations in these instances were exceptionally large, the people doing the valuing, the jurors, were ordinary Athenians. The process of timēsis in the Athenian courts may look like a mode of valuing analogous to an economic one, a sort of bargaining. It was, however, an emotional decision by hundreds of citizens about another citizen’s status. Not 44 45

[Dem.] 53.18, 26. Johnstone, Disputes and Democracy, 19–20, 93–99. Half of all defendants talked about their liturgies. Though fewer prosecutors did, as I argued there were structural reasons prosecutors were less likely to mention their public services.

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all final or proposed penalties would have taken the form of a fine—litigants might have proposed personal punishments instead, forms of ‘suffering’—but most probably did since in the four cases only one of the proposals might have taken a personal form (the jurors may have clamoured for Arethusios’ death because Apollodoros’ charge asked for it, though we do not know). This process of assigning a value was, as the stories make clear, emotionally charged. Defendants and their supporters might beg the prosecutor, engaging in the ritual of supplication and weeping. Prosecutors might remain implacably wrathful or succumb to their defeated opponent’s abasement. Jurors might shout their preferences. The situation does not seem amenable either to the economists’ model of the rational actor (each side aiming to find the mutually agreeable ‘contract zone’) or to Allen’s model of the prosecutor cured of his anger by talking about it. Indeed, Allen’s model ignores the rhetorical context, focusing on just the prosecutor and his speech.46 One might wonder how much anger would be curtailed when both parties not only got to talk out their grievances but had to listen to their opponent say the most terrible things about them. Moreover, the jurors, forced to choose between two alternatives, neither of which may be close to their own, might have found themselves feeling ambivalent about either result.47 The fines established through this emotional procedure had qualitative meanings in addition to quantitative values. Among the convicted defendants, the three whose offers we know all proposed one talent; although the circumstances of the cases differ, perhaps this was seen as the acceptable minimum fine for a wealthy man convicted by a jury. More securely, I would note that a large fine—large meaning more than a man and his friends could hope to pay—was equivalent to atimia. That is, at a certain threshold (which would differ for each defendant) the quantitative increase in the fine effected a qualitative transformation from a monetary into a personal penalty.

Conclusion As the makers of laws in the assembly and as jurors in the courts, Greek citizens assigned numbers to punishments, a mode of valuing which was not fundamentally economic. In an essay in The Construction of Value in the Ancient

46 47

I have critiqued this model (Johnstone, A History of Trust, 149–153). I have analysed the dynamics of the jurors’ dichotomised choice (Johnstone, A History of Trust, 148–170).

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World, Colin Renfrew objects to using the idea of ‘value’ to understand nonmonetary realms in the ancient world.48 He insists that in antiquity, unlike our world, only market exchanges created values so that extending this category beyond the economic is anachronistic. While I am sympathetic to the desire for analytic precision and for not unwittingly imposing our own ideas onto the past, it is not true that Greeks valued only in market relationships. Greek laws and courts assigned monetary values to things—to honour and infamy— outside voluntary exchange relationships. Such values might underwrite comparisons or, on the contrary, assert an incomparability, but in neither case were Greeks performing mathematical or economic calculations with them.

Bibliography Allen, D.S., ‘Punishment in Ancient Athens’, in Adriaan Lanni (ed.), ‘Athenian Law in its Democratic Context’, Center for Hellenic Studies On-line Discussion Series, republished in C.W. Blackwell (ed.), Dēmos: Classical Athenian Democracy (The Stoa: a Consortium for Electronic Publication in the Humanities, 23 Mar 2003, http://www​ .stoa.org/demos/, accessed 29 April 2017. Davies, J.K., ‘Temples, Credit, and the Circulation of Money’, in A. Meadows and K. Shipton (eds), Money and Its Uses in the Ancient Greek World (Oxford: Oxford University Press, 2001), 117–128. Emigh, R.J., ‘Numeracy or Enumeration?’, Social Science History, 24 (2002), 653–698. Gagarin, M. and P. Perlman, The Laws of Ancient Crete c. 650–400bce (Oxford: Oxford University Press, 2016). Henderson, J., Aristophanes: Clouds, Wasps, Peace (Cambridge, MA: Harvard University Press, 1998). Johnstone, S., Disputes and Democracy: The Consequences of Litigation in Ancient Athens (Austin: University of Texas Press, 1999). Johnstone, S., A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011). MacDowell, D., ‘The Length of the Speeches on the Assessment of the Penalty in Athenian Courts’, CQ, 35 (1985), 525–526. MacDowell, D., Demosthenes: Against Meidias (Oration 21) (Oxford: Oxford University Press, 1990).

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C. Renfrew, ‘Systems of Value Among Material Things: The Nexus of Fungibility and Measure’, in J. Papadopoulos and G. Urton (eds), The Construction of Value in the Ancient World (Los Angeles: Cotsen Institute of Archaeology Press, 2012), 249–260.

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Meyer, E.A., ‘Inscriptions as Honors and the Athenian Epigraphic Habit’, Historia, 62 (2013), 453–505. Osborne, R., ‘Law and Laws: How Do We Join Up the Dots?’, in L. Mitchell and P.J. Rhodes (eds), The Development of the Polis in Archaic Greece (London: Routledge, 1997), 74– 82. Renfrew, C., ‘Systems of Value Among Material Things: The Nexus of Fungibility and Measure’, in J. Papadopoulos and G. Urton (eds), The Construction of Value in the Ancient World (Los Angeles: Cotsen Institute of Archaeology Press, 2012), 249–260. Rhodes, P.J., The Athenian Boule (Oxford: Clarendon Press, 1985). Scheidel, W., ‘Finances, Figures and Fiction’, CQ, 46 (1996), 222–238. Shear, T.L., Jr., Kallias of Sphettos and the Revolt of Athens in 286b.c. (Princeton: American School of Classical Studies at Athens, 1978). Thür, G., ‘The Principle of Fairness in Athenian Legal Procedure: Thoughts on the Echinos and Enklema’, Dike, 11 (2008), 51–73. Whitman, J.Q., ‘At the Origins of Law and the State: Supervision of Violence, Mutilation of Bodies, or Setting of Prices?’, Chicago-Kent Law Review, 71 (1995), 41–84.

chapter 4

Ten Thousand: Fines, Numbers and Institutional Change in Fifth-Century Athens Josine Blok

The ‘ten thousand’ that will be the focus of this article are the number of drachmae set as a fine in some Athenian decrees of the Classical period. Unlike the Greek mercenaries whose retreat through Asia Minor Xenophon famously described, this ‘ten thousand’ is unlikely to spark wide recognition as a fact of historical interest. Yet I will argue that the 10,000 drachmae fine in these decrees marks a much-discussed shift in the institutions of Athens of the later fifth century bc. Most Athenians and others targeted with this fine were just ordinary citizens, to whom 10,000 drachmae must have seemed a zillion. Indeed, myrioi, beside the number 10,000, means ‘countless’. Did the Athenians who imposed this incredible fine on their fellow-citizens have numbers, but no math? In other words, is this amount real? It is definitely not an error, as in the case of the 10,000 or 11,000 virgins who, on the misreading of a medieval text, became the set group accompanying Saint Ursula to be martyred at Cologne.1 In Athenian accounts, amounts of drachmae were written in acrophonic numerals, in which errors of single digits might occur, but in decrees the amounts were normally written in full, so this inconceivable amount really was what the Athenians meant to impose.2 Let me explicate, to avoid misunderstanding, the difference between fines set in decrees and fines imposed by a court after a trial for some misdemeanour, for instance embezzlement (klopē) or a proposal against the law (graphē paranomōn). In the latter group, fines could be any sum the court thought appropriate and usually they were very high—often many talents. Such fines

1 C.M. Cusack, ‘Hagiography and History: the Legend of Saint Ursula’, in C.M. Cusack and P. Oldmeadow (eds), This Immense Panorama: Studies in Honour of Eric J. Sharpe (Sydney: University of Sydney, 1999), 89–104. 2 On the use of letters versus digits for numbers in inscribed documents, see Osborne in this volume; on the use and efficiency of acrophonic numerals, see J.H. Blok (forthcoming), ‘Greek numerals and numeracy’, in Y. Suto (ed.), Transmission and Organisation of Knowledge in the Ancient World. Proceedings of the Fourth Euro-Japanese Colloquium on the Ancient Mediterranean World, University of Nagoya, Japan. 3–7 Sept. 2018 (Vienna: Phoibos Verlag).

© Josine Blok, 2022 | doi:10.1163/9789004467224_006

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tend to appear in our literary sources when they hit prominent, wealthy Athenians.3 The fines in inscribed decrees, by contrast, were fixed sums, set in advance to anyone who would act contrary to the decree. Many of them target officials who fail in some specific way, and most of these officials were average citizens taking their turn in the running of the polis. We shall compare the two types of fines further below, keeping in mind the differences between them. When we situate the decrees imposing these fines in their historical context, we need to take the effects of the epigraphic habit into account, such as the increase in the number of inscribed decrees in Athens from the 450s onwards. The corpus of decrees with fines is collected in the appendix, with exposition of technical details, and is discussed further below. It shows, I think, enough consistency to allow us to sketch the tendencies in Athenian fining practices from the late sixth to the fourth century. I will first briefly review the main features of the decrees with 10,000 drachmae fines, then compare them to other fines, and finally address the political context that may explain this mind-boggling penalty.

1

The 10,000 Drachmae Fine: The Evidence

The 10,000 drachmae fine appears in the later fifth century in a group of seven inscribed decrees.4 We cannot be sure that there were not more of these decrees, the stelae of which got lost or were not inscribed at all, but I will advance some reasons why our current collection may be considered roughly representative of the period in which they were issued. For three of them, we have definite dates based on the archon year. For the rest, no archon date is known, and their estimated dates have been revised recently following the abandoning of the three-bar sigma criterion. No firm consensus has yet emerged on these new dates, and some are more contested than others. While the main arguments concerning each decree are collected in the appendix, I review the most important aspects here. Three decrees are securely dated: No. 16 (IG i3 61(2)) of 426/5, regarding the grain trade of Methone on the Macedonian coast; the fine will be meted out to any guardian of the

3 For this procedure and the resulting fines, see Johnstone in this volume (pp. 89–93). An exception to high fines as the outcome of a court case is the fine imposed on seven Delians (IG ii2 1635 = RO 28) which appear in an inscribed account; see below p. 103. 4 See the appendix. In no. 5, no. 7, no. 20, and no. 25, the amounts are restored in IG but illegible on the stone; they are included in the appendix for the sake of completeness.

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Hellespont who somehow hampers the export of grain. No. 18 (IG i3 71) of 425/4 consists of Thoudippos’ decrees on the tribute to be paid by the allies; the fine appears in two different clauses, targeting any official who fails to handle the assessments in time. No. 23 (IG i3 84) of 418/7, the decree on leasing the temenos of Kodros, Neleus and Basile; any official will be fined who is slow in handling the necessary affairs. Less securely dated, but not deeply controversial (anymore), are: No. 15 (IG i3 133) probably dates to between 430 and 426; it is a decree on a 2% tax on trade in the Peiraieus to fund the cult of the Anakes; the fine is imposed on any hieropoios who fails to handle the tax in the prescribed manner. No. 17 (IG i3 63) probably dates to c. 426; it deals with the trade, especially of grain, of Aphytis, on the western headland of Chalcidice: anyone who prevents the Aphytaeans from sailing to Athens will be punished with this fine. No. 24 (IG i3 1453), the Coinage or Standards decree imposing Athenian coins and measures on the allied cities, is now commonly dated between the mid-420s and 414—perhaps shortly before 414 is the most plausible date. The fine threatens officials who fail to send the heralds in time. The date of no. 19 (IG i3 10), a decree adding new judicial agreements to a previous alliance with Phaselis, on the southern coast of Asia Minor, seems the most controversial and therefore needs more comment. Osborne and Rhodes (OR) in their recent edition prefer the ‘old’ date of before 450, but they do not advance strong arguments in favour of it, rejecting or ignoring arguments brought forward by others for c. 425/4.5 Jameson, Papazarkadas and Beretta

5 OR 120; on p. 112 they claim that ‘most recent commentators have dated this text between Phaselis’ entry into the League and c. 450’ (emphasis added), but that is not exactly true. Their most recent is M.H. Jameson, ‘Athens and Phaselis, IG i3 10 (EM 6918)’, Horos, 14–16 (2000–2003), 23–29 who argued for a date c. 425, and so do N. Papazarkadas, ‘Epigraphy and the Athenian Empire: Reshuffling the Chronological Cards’, in J. Ma, N. Papazarkadas and R. Parker (eds), Interpreting the Athenian Empire (Oxford: Duckworth, 2009), 70–71, and M. Beretta Liverani, ‘I decreto ateniese per i Faseliti (IG i3 10) e le multe di 10.000 dracme nel v. sec.’ Historiká, 3 (2013), 131–158, who revisits points raised by Mattingly in several publications, and by Jameson. On the latter, OR contend that Jameson defended the later date ‘half-heartedly’, but his tone seems to me careful rather than reluctant, and realistic about the difficulties in identifying the epistatēs Neokleides.

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Liverani have demonstrated how the decree fits the series of alliances Athens created or renewed between 427 and 423 on both sides of the Aegean, almost all of them previously dated to before 450 due to their three-bar sigma and now more convincingly situated in the Archidamian War.6 OR mention Phaselis’ importance to Athens’ trade with the Levant, but recently historians have pointed out its crucial role in connections with Egypt, being one of the founding cities of the Hellenion,7 and here again the grain trade may have been a factor. The name of the proposer, Leon, occurs in various texts, but it is notable that a Leon proposed the treaty with Hermione and took part in the oath of the truce of 422 (Thuc. 5.19.2, 24.1); he might well be the one proposing the treaty with Phaselis. The cutter of the decree has not been identified, but Meritt and McGregor in IG held him to be the same man who cut IG i3 9, the alliance with the Delphic Amphiktyons, conventionally dated to c. 458, a further reason why the treaty with Phaselis got associated with the early 450s. However, as Stephen Tracy shows, this identification is untenable, creating further doubts about the conventional date of IG i3 10.8 If, as I believe, all these considerations point to a date c. 425 rather than before 450, a final reason for choosing the former date is the comparison of the fine with others in the fifth century. The fine of 10,000 drachmae is an anomaly before 450, but fits the picture without any ado in c. 425.9 This date, then, seems to me to be the most plausible for IG i3 10. Beside these seven decrees that may now be taken to date from c. 430 at the earliest to c. 414 at the latest, there is one outlier: no. 26 (IG ii3 1 370), dealing with the founding of a colony in the Adriatic, c. 325/4. The decree targets anyone, private citizen or official, who fails in the aims of the decree with a fine of 10,000 drachmae. Dating roughly a century later than the others, it will be discussed separately. After this one, no Athenian decree set the 10,000 drachmae fine again.

6 Papazarkadas, ‘Epigraphy’, 70–71; the treaties are with Hermione (IG i3 31), Halieis (IG i3 75), Colophon (IG i3 37), Mytilene (IG i3 66), and Miletus (IG i3 21). 7 A. Bresson, The Making of the Ancient Greek Economy: Institutions, Markets, and Growth in the City-States, trans. Steven Rendall (Princeton: Princeton University Press, 2016), 319–320; C. Pébarthe, ‘Contrats et justice dans l’ empire Athénien: les symbola dans le décret d’Athènes relatif à Phasélis (IG, i3, 10)’, in P. Brun (ed.) Scripta Anatolica: Hommages à Pierre Debord (Bordeaux: Ausonius, 2007), 237–238 with further references. Pébarthe does not decide between the earlier and later date, but for practical reasons chooses the middle (c. 440) because a more precise date is not essential for his legal and administrative analysis. 8 S.V. Tracy, Athenian Lettering of the Fifth Century b.c.: the Rise of the Professional Letter Cutter (Berlin: De Gruyter, 2016), 24–25, refering to observations by A.P. Matthaiou; cf. Jameson, ‘Athens’, 25–26. 9 See for the same argument Beretta Liverani, ‘I decreto ateniese’.

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The targets of these penalties may be specified as, first, anyone who does not act in accordance with the decree or who raises his voice against it, and second, any official who fails in the duty the decree assigned to him. The first group is targeted in the decrees for Phaselis and Aphytis; the money is to be sacred to Athena, as underlined by the verb opheilō, indicating the debt to the deity under whose authority the provision is made. The second group targeted in these decrees are officials convicted at their euthynai, whose fines normally went into the dēmosion.10 These officials are hieropoioi in the Anakes decree, guardians of the Hellespont in the Methone decree, officials in charge of the assessment procedures and the prytaneis in Thoudippos’ decrees, the basileus and all other officials involved in the lease in the decree on the temenos of Kodros, Neleus and Basile, and officials, possibly the stratēgoi, in the Coinage Decree.

2

Fines in Athens: Mounting Amounts

Athenians had always set their fines high, and those penalising officials for falling short of their duty were even higher. The latter practice is also found elsewhere in the Greek world: decrees ruled that magistrates and other officials who failed to act appropriately were to be fined double the amount of ordinary citizens.11 In his contribution to this volume, Steve Johnstone shows the range in the amounts and the frequency of the fines attested throughout Archaic and Classical Greece. Yet at Athens, at least, the amounts of fines in extant inscribed decrees do not appear at random or evenly spread, but seem to display a historical pattern. No. 1, the Salamis-decree (IG i3 1, c. 500), made the archon accountable at his euthynai if he failed to penalise cleruchs involved in illegal leases of land on Salamis; the amount of his fine is not stated. 10

11

For both procedures, A. Scafuro, ‘Patterns of Penalty in Fifth Century Attic Decrees’, in A.P. Matthaiou and R.K. Pitt (eds), ΑΘΗΝΑΙΩΝ ΕΠΙΣΚΟΠΟΣ: Studies in Honour of Harold B. Mattingly (Athens: Hellēnikē Epigraphikē Hetaireia, 2014), 299–326; she notes (314–315) the difference between ὀφείλω typical of penalties owed to the gods, notably Athena, and the absence of such penalties owed to Athena in the εὐθύνεσθαι formulae. We should note, however, that ὀφείλω is not used only for fines owed to hieros treasuries, but can also be used for money owed (here: fines) to non-sacred treasuries; see e.g. no. 4 (IG i3 245.8–11) (Sypalettos) and no. 9 (IG i3 59.47): τὸς το͂ι δε]μοσίοι ὀφέλ[οντας. In the Archaic law of Dreros (ML 2 = Gagarin and Perlman Dr1, c. 650) the man who holds the position of kosmos unlawfully for a second time owes twice the amount of any fine

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No. 2, the Hekatompedon decree (IG i3 4), probably inscribed in 485, perhaps after an earlier one, threatened with penalties (θωή) of 3 obols to 2 drachmae anyone misbehaving on the Acropolis;12 this fine can be compared to the fines that, according to the tradition, Solon had set as a penalty for the slander of living people, namely 3 drachmae to be paid to the offended person and 2 drachmae to the public treasury.13 The decree set a fine of 100 drachmae for the priestesses and zakoroi who did something not allowed there and 100 drachmae for the tamiai who let them do so, all at their euthynai. The 100 drachmae fine was twice the maximum fine of 50 drachmae that lower officials such as demarchs, priests and hieropoioi could impose on people disobeying decrees.14 No. 6 (IG i3 256), a deme decree dated between 440 and 420, set the fines for private persons using the waters of the Halykon without properly paying for them at 5 and 50 drachmae. Let us label these fines of a maximum of 50 drachmae for private persons and 100 drachmae for failing officials as the ‘traditional penalty’. At some point, decrees begin setting a 1,000 drachmae fine, a tenfold increase of what we just dubbed the traditional fine. Since the boulē could impose fines up to 500 drachmae and had to assign cases concerning higher amounts to a jury court,15 it seems that these decrees set a standard of twice the maximum penalty the boulē could impose, probably to underline the grav-

12

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he imposed in that capacity. In Thasos (OR 104.101–103, 460s), officials who fail to fine trespassers messing up the streets are fined double the amount. If he did so knowingly: IG i3 4B.6–7, 9–10; cf. E.M. Harris, ‘How Strictly Did the Athenian Courts Apply the Law? The Role of Epieikeia’, in The Rule of Law in Action in Democratic Athens (Oxford: Oxford University Press, 2013), 296. The fine in the Hekatompedon decree can be compared to a fine on a horos-stone at Corinth, of about the same date, of eight obols for those who ignore the boundaries of the sacred space, Corinth viii 1 22, cf. Tod (1926/27) 142; (1936/37) 238: 2A. Plut. Sol. 21.1; LR fr. 32a: κακῶς λέγειν. Solon, according to this account, also forbade anyone to speak ill of the dead. Elon Heymans (in personal communication) has pointed out that the money paid to the offended person can be considered a form of Wergeld. For this fine of 50 drachmae, see, for example, in the fifth century e.g. IG i3 82.26: ‘… and if anyone behaves at all disorderly, they [i.e. the hieropoioi in charge of the procession for Hephaistos and Athena] shall have the authority to impose fines of up to fifty drachmas and communicate it in writing to the --;’ (trans. AIO); and in the fourth century IG ii2 1237.54–58; IG ii2 1362.15. For the fifth century, see IG i3 105 = OR 183B; see also the AIO commentary on the same, n. 4; for the fourth century, see Dem. 43.43; [Arist.] Ath. Pol. 45.1; RO 25.35–36 with commentary. For the capacity of the boulē to fine and punish, see Ath. Pol. 8.4.

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ity of the issue. Due to the patchy evidence, however, it is difficult to say when the 1,000 drachmae fines exactly began. At first sight, two decrees would seem to be our first cases: No. 3 (IG i3 6), a decree on the administration of the Eleusinian Mysteries, usually dated to the 460s, imposes a 1,000 drachmae fine on members of the genē Kerykes and Eumolpidai if they initiate more than one person at a time; this is explicitly a case of ‘failing officials’, to be fined at their euthynai. No. 4 (IG i3 245) is a decree from the deme Sypalettos, dated in IG to 470–460, which imposes a fine of 1,000 drachmae on anyone who tries to upset the agreements of the deme on the common budget. However, in the forms presented in IG, both decrees pose problems. In no. 3, the amount is restored; the χιλιάσι (1,000) in IG (retained in OR) is not necessarily correct, as hεκατὸν (100) is equally possible; hence I leave this decree out from the 1,000 drachmae fine group. In no. 4, the amount is unmistakable, but the date proposed by David Lewis in IG of c. 470–460, is not convincing. On the arguments set out in the appendix, a date between c. 450 and 430 or even the 420s is more likely. We have, therefore, no secure cases of the 1,000 drachmae fine before 450. Of six other cases in which the 1,000 drachmae fine is certain, unfortunately none are secured by an archon date. Yet, of three such decrees the approximate dates are largely accepted: No. 9 (IG i3 59) of c. 430, a decree about the navy in which the amount of the fine is plausibly restored. No. 12 (IG i3 78a), the First-Fruits decree, commonly dated to c. 435, which penalises hieropoioi who fail to take action within five days. No. 13 (IG i3 55), a decree for Aristonous, of c. 431, which threatens a fine of 1,000 drachmae to the polemarchos and to the prytaneis (?) if they fail to take adequate steps for the legal protection of Aristonous. Of three further decrees the time span of their dates is still quite wide: No. 8 (IG i3 157), a decree concerning the allies dated to c. 440–410, which penalises anyone with the 1,000 dr. fine who acts contrary to the decree. No. 10 (IG i3 153), a decree about the navy dating to c. 440–425. No. 14 (IG i3 149), on relations with Eretria, dated between c. 430 and 412.

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No. 22 (IG i3 165), finally, is a proxeny decree in which the fine is clearly legible, and the date estimated before 420; the prytaneis are to be fined if they fail in (illegible) obligations to the proxenos. On this evidence, the ‘traditional fine’ of a few to 50 drachmae is still applied in no. 6, of c. 440–420, but fines leap to 1,000 drachmae, with no. 4, the Sypalettos decree of c. 450–420, no. 8 on the allies of 440–410, and no. 10 about the navy of 440–425 potentially being the earliest cases. All these dates have a wide margin. If we take the more precisely dated no. 12, the First-Fruits decree, and no. 13, for Aristonous, as a lead, the change would appear to begin in the 430s; this date would also account for nos. 14 (Eretria) and 22 (proxeny). These private fines are owed to Athena. Officials who fail in their duties are to pay the fine at their euthynai into the dēmosion. For them, the ‘traditional fine’ of up to 100 drachmae is still used in some regulations of no. 18 (Thoudippos’ decrees of 425/4), but the leap to a 1,000 drachmae fine appears in no. 9, on the navy (c. 430), no. 12, the First-Fruits decree (c. 435), no. 13 for Aristonous (c. 431), no. 14, on Eretria (c. 430–412), no. 22, a proxeny decree estimated to be before 420, and no. 23, on the temenos of Kodros et al. (418/17). We can now sketch the pattern of fines in the fifth century. The same kinds of offences, namely acting in defiance of the decree in the case of private citizens and failing in the duties specified in the decree for officials, are penalised with steeply rising fines. The ‘traditional’ fines of a maximum of 50 and 100 drachmae respectively do not disappear after 450, but fines leap to 1,000 drachmae for both groups after the mid-century, more specifically from the 430s. The 10,000 drachmae fines, as we saw earlier, date from c. 430 at the earliest to c. 414 at the latest; five decrees (no. 15, 16, 18, 23, 24) target officials, two decrees (nos. 17 and 19) private citizens. In sum, there is a tenfold leap to 1,000 drachmae clearly visible from the 430s onward and yet another tenfold leap, to 10,000 drachmae clearly visible from c. 430 to c. 415. How does this group of fines compare to other cases? In the 370s, the Athenians imposed a 10,000 drachmae penalty—and perpetual exile—on each of seven Delians convicted of asebeia because they had attacked the Athenian Amphiktyons on Delos.16 It is a hefty fine, but mild compared to no. 11 (IG i3 1454) of c. 435, a decree for the Eteokarpathians, in which anyone who acts con-

16

IG ii2 1635 = RO 28 = AIUK vol. 3, no. 3, accounts of the Athenian Amphiktyons of 377– 373. The fine of 10,000 drachmae imposed on each Delian appears in B (a) ll. 24–30. The seven Delians were penalised after a trial; they had ‘dragged the Amphiktyons from the temple and struck them’ (26–27). The fine was hieros, owed to Apollo.

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trary to the decree has to pay 50 talents to (probably) the Athenians, of which a tithe is for Athena (see also below, p. 109); and no. 21 (IG i3 19), a proxeny-decree for Acheloion, of the late 420s, which sets a fine of 5 talents for the polis of anyone who kills Acheloion or his children. One would expect that an actual attack on high Athenian sacred officials would be penalised more severely than any misdemeanour against allied poleis and individuals. And one might expect that Delians who attacked high Athenian sacred officials would be penalised more heavily than fellow Athenians in office who were late in carrying out what the demos had decided. But the opposite is the case. It seems, again, that in the last decades of the fifth century the Athenians were inclined to fine higher and more severely than before and after, and for similar or perhaps even less damaging offences.17 Why these high fines? Fines this size were paradoxical: they might seem to generate income for the polis, but unpayable fines generated citizens who were indebted to the polis and hence atimos instead. The archon of Salamis (no. 1) in c. 500 was probably a wealthy citizen, and the tamiai (no. 2) were certainly so; they could easily pay 100 drachmae fines. But in the last three decades of the fifth century, the hieropoioi, bouleutai, prytaneis, polemarchoi, basileis and other officials who were the potential victims of the 1,000 and 10,000 drachmae fines were average citizens who happened to be in office, selected by lot. Would the threat of unpayable fines pressurise them into haste? In her excellent article of 2014 on this evidence, Scafuro argues that the issues to which these penalties apply ‘brook no delay’ and that the clustering of such decrees with high fines in the 420s suggests an empire in crisis. The 10,000 drachmae fine was meant to put on extra pressure, rather than as a ‘real’ fine; surely no one wanted to make, for instance, all 50 prytaneis into atimoi at their euthynai (as in no. 18). By 425/4, the 10,000 drachmae fine was so

17

Fines of 10,000 drachmae occur elsewhere, too. A decree of Telos concerning Kos (IG xii 4 132) of c. 300, ll. 123–124 has a fine of 10,000 drachmae payable to Zeus Polieus and Athena Polias by anyone who acts against the agreements. In Arsinoë (Cilicia: SEG xxxix 1426.43) after 238 bce, a fine of 10,000 drachmae is set for an archon who put to the vote a proposal against the decree, with a fine of 1,000 drachmae for the proposer; the proposal will be invalid and the money will be for the sanctuary of Arsinoë (for these lines, G. Petzl, ‘Das Inschriftendossier zur Neugründung von Arsinoë in Kilikien: Textkorrekturen’, ZPE, 139 (2002), 87–88). On Keos, c. 200, officials (tamiai, hieropoioi, thesmophylakes) are to pay this fine if they fail to carry out the decree (IG xii 5 595). An agreement between Troezen and Arsinoë (Methana) of 163–146 (IG iv2 1 76), sets a fine of 10,000 drachmae for a polis and 1,000 for an individual who acts against the agreement. All of these appear incidental cases, unlike the cluster of high fines in Athens during the 420s.

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clearly a fiction that in no. 18, Thoudippos’ decrees, real fines of 100 drachmae were tacked on, according to Scafuro.18 In sum, her answer to the question ‘is this amount of 10,000 drachmae real?’ is clearly: no. Although I agree with Scafuro that these high fines were meant as a deterrent and that the war aggravated the situation, I think the evidence also allows a different reading. Certainly, some of these decrees set a fine to put pressure on officials to make haste: in no. 12, the hieropoioi are to act within five days; in no. 13, the polemarch is fined 1,000 drachmae for every day of delay after five days; in no. 18, the assessors are facing a fine of an unknown amount for each day of delay in assessing the tribute. It also seems that it often took the polis administration a while to get things done, and the high fine would signify a matter of importance, to be dealt with at once.19 But not all issues of these decrees were so urgent as to explain these high fines satisfactorily: in the decree (no. 23) on the temenos of Kodros et al., for instance, the haste seems to be artificial and is not actually necessary. This decree and the Coinage Decree (no. 24), furthermore, belong to what was officially peace time. We may also note that some of the decrees had to do with issues of the highest importance to the demos: the grain supply (nos. 16, 17), the collection of taxes, tribute and other income of the polis and the polis’ gods (nos. 15, 18, 23, 24) the handling of which was liable to corruption. The international standing of Athens was at stake in proxeny relations and dealings with the allies (nos. 19, 21), for which the pressure of high fines might seem justified. But why are some delays in the assessment of tribute in Thoudippos’ decrees (no. 18) penalised with only 100 drachmae, and others with 10,000? Why was the tiny community of the Eteokarpathians worth imposing a fine of 50 talents on anyone who did something undesirable to it, after it presented a great gift to Athens? An even more telling comparison, perhaps, is the absence of fines, either for delays or any other failure of officials, in the so-called Grain-Tax Law of 374/3 (RO 26). And why would the huge fine work as a threat if everybody knew it was not real, as Scafuro suggests? Finally, as we shall see, by 405 there were indeed large numbers of atimoi due to their euthynai. So, I propose to look once again at these numbers.

18 19

Scafuro, ‘Patterns of penalty’, 318, 322. [Xen.] Ath. pol. 3.1–8 observes that many complain that things take so long to get done by the boulē and assembly in Athens, and next explains why this is the case: a combination of the sheer mass of matters to be settled and the numerous festivals in Athens, stopping the administration from actually operating on many days.

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Crippling Fines

Who could pay such fines? Of course, the answer must be different for the wealthy and for citizens at the lower end of the economic scale. For the fourth century, far more evidence is available on these issues than for the fifth. In her comparative analysis of various approaches to the questions of income and wealth, Claire Taylor finds that around half the Athenian citizen population lived below the median income of 450 drachmae a year, and around 20 % at or below half the median income of 3 obols a day; 77% of the citizens owned less than the median wealth of 2,650 drachmae.20 In the later fifth century, the average daily wage of a skilled labourer was one drachma, i.e. c. 300 drachmae a year.21 Many Athenians owned a tiny piece of land and/or a modest house they could sell, lease or mortgage, but its value does not seem to have been very high; Socrates’ property, for instance, was estimated at 500 drachmae (Xen. Oec. 2.3) and, as van Wees argues, even many citizens serving as hoplites probably owned property valued at less than 1,000 drachmae.22 Many citizens owned no property at all, earning their living by other means. For an average Athenian, then, a fine of 1,000 drachmae was a burden, for which family and friends had to be called upon to help collect the money; a 10,000 drachmae fine was a disaster. At the top end of society, the liturgical class comprised c. 4–5% of Athenian citizens.23 For those in its lower ranks, who owned 3–4 talents, paying 10,000 drachmae meant losing around half their 20

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23

C. Taylor, Poverty, Wealth, & Well-Being: Experiencing Penia in Democratic Athens (Oxford: Oxford University Press, 2017), 77–84; she draws mainly on J. Ober, ‘Wealthy Hellas’, TAPA, 140 (2010), 241–289, and G. Kron, ‘The distribution of wealth in Athens in comparative perspective’, ZPE, 179 (2011), 129–138. In the Netherlands (in 2021), the minimum wage for adults of 21 years is €77 per day. Although comparison with present-day earnings cannot carry real weight because the economic and social circumstances are fundamentally different, just for clarification’s sake we note that the 10,000 drachmae fine would be €770,000 in the Netherlands today. H. van Wees, ‘Demetrius and Draco: Athens’ property classes and population in and before 317 bc’, JHS, 131 (2011), 98; for the hoplite census in 411, see ‘The Myth of the Middle-Class Army: Military and Social Status in Ancient Athens’, in T. Bekker Nielsen and L. Hannesta (eds), War as a Cultural and Social Force: Essays on Warfare in Antiquity (Copenhagen: Kongelige Danske Videnskabernes Selskab, 2001), 45–71; Wees, H. van, ‘Mass and Elite in Solon’s Athens: the Property Classes Revisited’, in J.H. Blok and A.P.H.M. Lardinois (eds), Solon of Athens: New Historical and Philological Approaches (Leiden: Brill, 2006), 351–389, at 371–375. For the wealth of buyers of public property at 1,000 and 100 drachmae in the later fourth century, see S.D. Lambert, Rationes Centesimarum: Sales of Public Lands in Lykourgan Athens (Amsterdam: Gieben, 1997), 243–250. For criteria defining the wealthy and the estimated size of this group, Taylor, Poverty, 70– 76, with further refs.

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property: painful, but not fatal.24 Only for the exceptionally wealthy few, c. 1 % of the citizens, owning 5 talents and more, did this fine pose no serious problems. This group of the wealthy, however, was targeted with crippling fines of many talents in a different way, namely imposed by the jury courts through a procedure of eisangelia or a graphē paranomōn, trials instigated more often than not by political opponents of the defendants. In the later fifth and fourth centuries, this practice was well-established.25 But when did it begin? Of the three earliest cases of such trials with crippling fines mentioned in our sources, which concern Miltiades, Cimon and Callias, the historicity is at least partly doubtful. Herodotus (6.132–136) recounts that Miltiades (the Younger), when he failed to capture Paros in 489, was convicted for deceiving the demos (τῆς Ἀθηναίων ἀπάτης εἵνεκεν) and had to pay a fine of 50 talents, i.e. 300,000 drachmae. Miltiades died the same year from wounds incurred in the adventure and the fine was paid by his son Cimon. The background to this story seems plausible enough: the Parian expedition is a typical case of an alliance between the Athenian demos and a prominent Athenian, to serve the economic interests of both parties in the northern Aegean.26 For the demos, securing access to grain-producing areas was probably the decisive motive. And since Miltiades the Elder had created a colony in the Chersonese in the midsixth century, the Philaidai had laid a claim to gold mines in the area, which Miltiades further secured by marrying Hegesipyle, the daughter of the Thracian king Oloros. But regarding the fine imposed on Miltiades, this account has odd features.27 Cimon inherited enormous wealth, largely consisting of the properties 24

25

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Athenians owning 4 talents or more fell into the liturgical class in the fourth century, J.K. Davies, Athenian Propertied Families (Oxford: Oxford University Press, 1971), xxiv; this group comprised approximately 1–2 % of the citizens, J.K. Davies, Wealth and the Power of Wealth in Classical Athens (Salem, N.H.: Ayer, 1984), 27–28; Taylor, Poverty, 70–76. M.H. Hansen, The Athenian Ecclesia ii: A Collection of Articles 1983–1989 (Copenhagen: Museum Tusculanum Press, 1989) 271–281; for the pre-Ephialtic practices, see in particular E.M. Carawan, ‘Eisangelia and Euthyna: the Trials of Miltiades, Themistocles, and Cimon’, GRBS, 28 (1987), 167–208. For such alliances in these profitable enterprises, L. Kallet, ‘The Origins of the Athenian Economic Arche’, JHS, 133 (2013), esp. 53–54. For the significance of the northern region for the Athenian grain supply and the intricate connections between the Athenian elite and their counterparts in the wide northern area, A. Moreno, Feeding the Democracy: the Athenian Grain Supply in the Fifth and Fourth Centuries b.c. (Oxford: Oxford University Press, 2007), 144–169; for the importance of the cleruchies on Lemnos for the grain supply, 102–115. Details of the failed attempt of Miltiades to capture Paros—a seeming betrayal of the polis by a priestess, which the Parians claim was later vindicated by Delphi as a ruse because

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in Thrace, from his father (and mother). Why could Miltiades not pay the fine himself? And where does the stupendous amount of 50 talents suddenly come from? In the procedure of eisangelia, as was the case here, penalties of any kind or size could be proposed—including the death penalty, depending on the charge.28 But in 489, a fine of this size was without any precedent or plausible motive. Later sources name two men who allegedly paid Miltiades’ fine for him: either his son Cimon or Callias, cast as the wealthy ‘Lakkoploutos’ member of the genos Kerykes who became Miltiades’ son-in-law. A second version features another Callias, namely Cimon’s son, who paid a fine of 50 talents for his father.29 The accuracy of these accounts, preserved by Diodorus and Plutarch and providing a mishmash of private entanglements, does not inspire trust. They all seem to embroider a tradition that Cimon and Callias each paid a 50 talent fine. While for Diodorus and Plutarch these fines had to do either with Miltiades’ fine or with Cimon’s incestuous relationship with his sister, Demosthenes contended that both men were required to pay the 50 talent fine because they were convicted of eisangelia, barely escaping the death penalty.30 In his speeches against Aristocrates (Dem. 23) and Aeschines (Dem. 19) respectively, Demosthenes holds up both cases for emulation. Although both Cimon and Callias were wealthy men, highly respected and important to the polis,

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she had been instrumental in bringing about Miltiades’ death (Hdt. 6.134–135)—and the highly mythological coverage of Miltiades’ capture of Lemnos (Hdt. 6.137–140) do not inspire much faith in the historical accuracy of the accounts Herodotus heard about the Philaid family; cf. R. Thomas, Oral Tradition and Written Record in Classical Athens (Cambridge: Cambridge University Press, 1989), esp. 161–173. See also Johnstone, this volume, pp. 89–93, on timēsis; Carawan, ‘Eisangelia’, esp. 192–194. Given the nature of Athenian politics in these years, alternatively we might expect that his opponents would have tried to get the general of Marathon ostracised. See S. Forsdyke, Exile, Ostracism, and Democracy: the Politics of Expulsion in Ancient Greece (Princeton: Princeton University Press, 2005), 281–284 for the debate on the introduction of ostracism and arguments for a Cleisthenic date, observing that the institution was perhaps applied unsuccessfully until 488/7, when the first known case, that of Hipparchos, took place. Diodorus (perhaps after Ephorus, see FGrH 70 F64) 10.30–31 says that, when Miltiades died in prison unable to pay off the fine, Cimon retrieved his father’s body for burial and assumed the debt himself, delivering himself for imprisonment. With Isodike, an Alcmeonid, Cimon had a son, Callias, but he had also lived with his own sister, Elpinike; Callias paid a fine of 50 talents to prevent his father being punished for this disgraceful relationship. 10.32 holds that Cimon owed his wealth to his wife. According to Plutarch (Cim. 4), Miltiades died in prison because he had not yet found the money to pay the fine, but Callias (here the son of Hipponikos, of the Kerykes and exceptionally wealthy) wishing to marry Elpinike, Cimon’s sister, offered to pay the fine imposed on Miltiades, now his father-in-law. Cimon: Dem. 23.205; Callias: Dem. 19.273–275.

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Demosthenes says that the ancestors of his present audience did not hesitate to punish them heavily for the same type of misconduct they were trying right now: undermining the constitution (Cimon and Aristocrates) in the one case (Dem. 23.205), and bribery (Callias and Aeschines) in the other (Dem. 19.273). According to Plutarch, however, Cimon was charged twice by the demos. In 463, when he did not push to conquer Macedonia, he was charged with bribery but acquitted (Cim. 14), and in 461, after the Spartans had first asked and next refused the help of Athens against the Messenians and helots, he was ostracised as friend of the Spartans but very soon recalled (Cim. 17). No fine was imposed on Cimon, if we believe Plutarch, who gives a highly virtuous portrait of Miltiades’ son. On this rather shaky evidence, I think we should hesitate to accept the historicity of the 50 talent fines of Miltiades, Cimon or Callias. Yet, by the 430s, plausible cases of a 50 talent fine do appear. Thucydides recounts that in 430, when the demos blamed Pericles for the Spartan invasions of Attica (2.59), he was charged, probably by eisangelia, convicted, fined and removed from office (2.65.3).31 Thucydides only mentions the fine, Diodorus (12.45.4) holds that the fine was 80 talents, while Plutarch (Per. 35.4) says that the lowest fine mentioned in his sources was 15 talents, the highest 50. That the demos was prepared to hand out fines of 50 talents in these years is confirmed by the decree for the Eteokarpathians (no. 11, IG i3 1454) of c. 435, briefly mentioned above; the beneficiaries had supplied a cypress for the temple of Athena, probably of Athena Polias on the Acropolis. In the damaged text, the 50 talents are legible (l. 24), as is the obligation to pay one tenth of the fine to the goddess (Athena); the latter clause plausibly suggests that the fine was to be paid to the Athenians, who then were to receive 45 talents in case someone was convicted. But who was threatened with this exorbitant fine? In ll. 20–23, we can only read that ‘if someone’ (ἐὰν δέ τις) does something in connection to the Eteokarpathians—anyone who acts contrary to the decree—they are liable to this penalty. Would the Athenians hold a single man accountable to pay this fine, or rather his entire city? The latter is how the relevant clause in the proxeny decree for Acheloion (no. 21, IG i3 19) of the late 420s has been restored, setting a fine of 5 talents (30,000 drachmae) to be paid by the city of the man who kills Acheloion or one of his children. Yet, in the Eteokarpathians decree, there is hardly room for a clause that shifts the burden of this bizarre fine to a city; rather, it seems to target an individual. How the demos imagined it would actually realise a fine of this size from someone who was not an Athenian citizen is obscure, but on the evidence just discussed we must conclude that in

31

Plato (Grg. 516a) reports that the charge was embezzlement (klopē).

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the 430s the Athenians did not hesitate to hold out fines of 50 talents to individuals who somehow thwarted their wishes, and that they probably imposed this fine on Pericles soon after the beginning of the war. It seems plausible that his fate played a role in stories of the same fine imposed on Miltiades, Cimon and Callias, projected back in time.32 Before turning to the political context in which we may situate these exorbitant fines, one more case is relevant. The Athenian general Phormion was reputedly crippled by a debt, and various accounts of its details circulated. Androtion (FGrH 324 F8) reports that Phormion could not pay 100 minae at his euthynai (no additional reason given), hence he became atimos. When the Akarnanians asked him to help them in the war, he answered that, being atimos, he was unable to do so; hence, the demos lifted his atimia by paying his debt for him.33 Pausanias (1.23.10) heard the story that when Phormion was in debt (again, no reason given), the Athenians asked him to be their stratēgos; he refused, and only consented when the Athenians paid his debts for him. They gave him a state burial and a statue that was still visible in Pausanias’ time. Thucydides (2.80–92, 103) does not mention any debt; he recounts Phormion’s military successes, his aid to the Akarnanians and his return to Athens, where he dealt with the war captives, in 429/8. Phormion was elected stratēgos in 440, 439, 436, 432, 431, 430 and 429. Androtion’s version of the story implies that Phormion’s euthynai and his debt took place at some point (shortly) before the campaign of 429/8, perhaps after his service as stratēgos in 431/0; the version of Pausanias is even more difficult to pin down in time.34 Thucydides’ silence on the debt does not necessarily mean that this element of the story is fictitious: for his account of the war at this point Phormion’s euthynai was simply not relevant. As we shall see below, Thucydides aptly describes the political atmosphere in Athens during the Archidamian war without going into the details of 32

33 34

Likewise, the fine of 1,000 drachmae that according to Herodotus (6.21.2) the demos imposed on the poet Phrynichus in 492 because his play about the fall of Miletus upset them too much, may have been a sum fitting the fining conventions of the 430s rather than the 490s, and the charge probably had more to do with a breach of the rules of the Dionysia, as Carawan, ‘Eisangelia’, 195 plausibly argues. FGrH 324 F8 = schol. Ar. Pax 347: ἀτιμωθεὶς δὲ τῶι μὴ δύνασθαι τὰς ρ̅ μνᾶς τῆς εὐθύνης ἀποδοῦναι. Cf. P.E. Harding, Androtion and the Atthis (Oxford: Oxford University Press, 1994), 99–104 c. 430. R. Develin, Athenian Officials 684–321 bc (Cambridge: Cambridge University Press, 1989), 121 suggests Phormion was fined after the campaign of 428, but that date cannot be reconciled with the tenet of the story that requires Phormion to be fined before his (last) campaign. See also Thuc. 2.68.7–8, with S. Hornblower, A Commentary on Thucydides, i: Books i–iii (Oxford: Clarendon Press, 1997), 353–354 on an earlier campaign of Phormion involving the Akarnanians, probably in the early 430s.

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the fines meted out to officials. Although we see only the contours of this episode, its core is a sum of 100 minae that Phormion had to pay but could not, a debt of which the demos relieved him. I am inclined to recognise in this sum, which, according to Androtion, Phormion had to pay at his euthynai and which made him atimos, the 10,000 drachmae fine which was imposed on officials at their euthynai as attested in decrees from c. 430 onward. Taken together, the accounts about Pericles and Phormion indicate that from c. 430 the demos not only held up devastating fines as a threat, but actually imposed them.

4

Athenian Political Institutions

Losing one’s property crippled a citizen’s position in the polis and unpayable fines made citizens atimos. In the fourth century, politicians used litigation with unpayable fines to remove their opponents from the political arena, a strategy that gradually had come to replace ostracism as a political weapon amongst the elite.35 For the average citizen, as we just saw, the 10,000 drachmae fines of the last decades of the fifth century were as disastrous as were the multi-talent fines for the wealthy elite. Why and how could such fines ever have seemed to make sense to the polis? The amounts of these fines are not just monetary values, but penalties with a forceful social meaning.36 Rewards and punishments operated in a conception of the relationship between citizens and polis based on reciprocity, in which the material or immaterial contribution to the polis, or, adversely, any damage done to the polis affected the valuation of the individual by the community.37 The Greek word for ‘fine’ was the same as for ‘honour’, namely timē, which I prefer to translate as ‘value’.38 In fines, numbers indicated amounts representing a negative valuation of citizens, which were mirrored in amounts for gold crowns awarded as positive valuation: for both fines and crowns, 500 and 1,000 drachmae became the standard values in the fourth century.39 While on a

35 36 37

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For this effect, see esp. M. Zimm, ‘Constraints on Speech in Democratic Athens: 480– 270 b.c.e.’, MA thesis (Yale University, 2016). See also Johnstone, this volume. See further J.H. Blok, Citizenship in Classical Athens (Cambridge: Cambridge University Press, 2017), 198–248 for reciprocity structuring the relationships between citizens and polis. Blok, Citizenship, 198–200 for timē as ‘value’ and 187–248 for its function as a measure of citizens’ value to the polis, with concomitant honours and penalties. Until the mid-fourth century, epigraphic evidence on crowns is extremely scarce; for the

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structural level these sums were monetary expressions of social valuation, the precise amounts came to be set in particular historical circumstances. As we just saw, after the first leap to 1,000 drachmae fines just after 450, perhaps in the 430s, the 10,000 drachmae fine was meant to devastate the offending citizen’s civic and social life. What circumstances may account for this extravagantly harmful application of the demos’ legislative power? Our sources indicate two features of Athenian institutions that are relevant to answer this question. Both were institutionally embedded in the democratic polis, but could take a problematic turn under particular conditions. The first occurred when the demos’ notion of its sovereignty turned into a view of sheer unlimited entitlement. Empowered by the democracy, the demos felt that it could justly claim a maximum return for its political excellence, both within its own polis from its own citizens and beyond, notably from the empire in the fifth century. As Danielle Allen aptly observes, anyone who thwarted this expectation by losing a battle, refusing to obey or missing a deadline was to be punished heavily, raising the anger of the demos for failing to reciprocate its favours.40 The other feature was the financing of a court system on which the politeia ultimately relied. The Athenaion Politeia (27.4), in a passage (27– 28) overtly critical of the democracy, puts the blame for Athens’ decay on the misthos introduced by Pericles, possibly in the 440s or 430s, because it laid the power of the courts in the hands of the mob.41 This critical statement oversimplifies an institutional set-up better illuminated by Scafuro. She shows how the Athenian judicial system operated on an economy of risk: court procedures potentially ending in fines or confiscations would, if the case was lost, backfire in a fine on the plaintiff, but if the case was won, it meant a substantial profit for the plaintiff and/or the demos. Balancing the costs of the courts by meting out punishments and rewards was not inherently the aim of the system,

40

41

fifth century, the only inscribed case concerns the crown of (1,000?) drachmae for Thrasyboulos of Kalydon (IG i3 102.1–14, 410/9). For a summary of the evidence and the costs involved, D.M. Pritchard, Public Spending and Democracy in Classical Athens (Austin: University of Texas Press, 2015), 87–90. D.S. Allen, The World of Prometheus: the Politics of Punishing in Democratic Athens (Princeton: Princeton University Press, 2000), reciprocity 62–65; anger: 128–133; conflict between the rule of judgment and the rule of law: 179–183. Ath. Pol. does not mention the date of the introduction of misthos for the dikasteria; although many scholars assume this happened shortly after Ephialtes’ changes in the 450s (M.H. Hansen, The Athenian Democracy in the Age of Demosthenes: Structure, Principles, and Ideology (Oxford: Oxford University Press, 1991; Norman: University of Oklahoma Press, 1999), 38, 188; Pritchard, Public Spending, 52–53. See J.H. Blok, ‘Perikles’ Citizenship Law: a New Perspective’, Historia, 58 (2009), 148 n. 23 on why the 440s or 430s are more likely.

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but nonetheless speakers in court tried to influence the dikastai, admonishing them that they were to reimburse themselves through fines.42 At the beginning of the Peloponnesian War the conditions were indeed conducive to a problematic turn, when the Athenians decided to ‘run their politeia themselves’, as the Ath. Pol. (27.2) puts it.43 Thucydides, Aristophanes and Xenophon, each in their own way, describe how in the final decades of the fifth century political leaders fanned the flames of expectation and wrath in the courts and assembly. Generals were penalised at their euthynai for any failure the demos could be persuaded to hold them responsible for with huge fines, like Phormion, or with exile, like Thucydides, or even with death, such as the generals after the battle of the Arginusai, with a conviction in absentia if they avoided trial by not returning to Athens. This extreme vindictiveness against anyone who was found guilty of any shortcoming was not against the law— and it could not be, for the demos was the sovereign of the laws of its own making. Harris, examining how the laws at Athens were applied, concludes that not only ‘the Athenians were obsessed with preventing the abuse of power by officials’, but also that in political contests about such alleged abuse political spokesmen and leaders used legal means and arguments grounded in law.44 Revisiting the ways in which Cleon made litigation against rivals and the prosecution of generals the new strategy for political success, Harris convincingly 42

43

44

A. Scafuro, ‘The Economics of the Athenian Court System’, in A.P. Matthaiou and N. Papazarkadas (eds), ΑΞΩΝ: Studies in Honour of Ronald S. Stroud (Athens: Hellēnikē Epigraphikē Hetaireia, 2015), 363–392. Ath. Pol. 27.2: τὴν πολιτείαν διοικεῖν αυτός. Arist. Pol. 1274a5–8 seems to refer to this tendency when he states: ‘For as the law-court grew strong, men courted favour with the people as with a tyrant, and so brought the constitution to the present democracy’ (trans. H. Rackham, Loeb edition). The context is whether Solon was ultimately to blame for this process, because he founded the Athenian public court system, cf. 1313b38: the demos wants to be monarchos. For the financial side of the demos tyrannos, L. Kallet, ‘Dêmos Tyrannos: Wealth, Power, and Economic Patronage’, in K.A. Morgan (ed.), Popular Tyranny: Sovereignty and its Discontents in Ancient Greece (Austin: University of Texas Press, 2003), 117– 154. E.M. Harris, ‘Cleon and the Defeat of Athens’, in The Rule of Law in Action in Democratic Athens (Oxford: Oxford University Press, 2013), quoted 346; cf. Zimm, ‘Constraints’ who argues that imposing unpayable fines was the legal instrument par excellence against political opponents, being, in effect, ‘lawfully applied constraints of free speech’. M.H. Hansen (per. ep.) observes the surprisingly scarce evidence of euthynai as a type of public action heard by the court, see Hansen, Athenian Ecclesia ii, 10 n. 32; Hansen, Athenian Democracy, 224. In some cases, a source uses the term euthynai for what other sources describe as an eisangelia, cf. the eisangeliai against Iphikrates (Hansen, Athenian Ecclesia ii no. 100) and Timotheos (no. 101), both called euthynai at Isoc. 15.129.

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argues that it was not the allegedly different social background of Cleon that earned him the disgust of his peers. Rather, it was the different policy he represented, using the institutions of Athens to raise his own profile without considering adverse consequences or the common good in the long run. Cleon applied this strategy not only in the courts, but also in the assembly: in the Mytilene debate as rendered by Thucydides, he insisted that killing the population of the city was in accordance with the law and that it befitted Athens’ power to enforce the law (Thuc. 3.37–40). After Cleon’s death in 422, political leaders continued this policy, first Hyperbolus and then others up to the Arginusai trial of 406.45 The 10,000 drachmae fines fit this climate. They hit persons even of modest wealth with a vindictiveness for which Zimm rightly uses the notion of ‘punitive force’: the demos used fines not as a means of enacting justice but as punitive legal instruments.46 Imposing such penalties demonstrated the demos’ power, inflamed by orators to an emotional intensity that probably also enforced a strong sense of collectivity and discouraged voicing disagreement.47 The decrees on Aphytis and Phaselis (nos. 17 and 19) penalise anyone, Athenian and non-Athenian, acting contrary to the statutes of the decree or speaking against it with a fine of 10,000 drachmae owed to Athena (opheilein). With these crippling fines the decrees threaten offending citizens in effect with being rendered atimos. The decrees about the colony to Brea (IG i3 46), for Miletus (IG i3 21) and for Chalcis (IG i3 40) do explicitly punish a citizen and his children with becoming atimos, together with the loss of his property of which a tenth is to be dedicated to the deity, for acting contrary to the statutes of the decree or speaking against it, i.e. the same offences as in the decrees on Aphytis and Phaselis.48 Officials convicted at their euthynai paid their fines to the polis 45 46

47

48

Harris, ‘Cleon’. M. Zimm, ‘The Punitive Force of Fines in Athenian Law’, paper given at the 111th Meeting of the Classical Association of the Middle West and South, Boulder, CO, 25–28 Mar. 2015: ‘punitive force is force that is used to punish rather than to accomplish lawful results’; cf. R.V. del Carmen and C. Hemmens, Criminal Procedure: Law and Practice (10th edn., Boston: Cengage Learning, 2017), 180–181. Cf. D. Moon, ‘Powerful Emotions: Symbolic Power and the (Productive and Punitive) Force of Collective Feeling’, Theory and Society, 42 (2013), 261–294 for strong collective feeling creating a heightened sense of power, as well as disciplinary force against dissent. In IG i3 46, the Brea decree, ll. 24–30, anyone proposing to bring to the vote an action against the decree is liable to this penalty, and if this fails, the colonists themselves owe (what the penalty should have been?); the dekatē is to be paid to Athena. The latter provision probably also applies in IG i3 21.26–28. In IG i3 40.32–36, all adult Chalcidians are to swear the oath of allegiance to Athens; anyone who does not swear is to be punished with atimia and loss of property with one tenth for Olympian Zeus.

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treasury, if they could do so; no tithe for the gods is mentioned here. No. 18, Thoudippos’ decrees, and no. 24, the Coinage Decree, have it all: the traditional fine, the high fine of 10,000 drachmae and atimia with property confiscated.49 With these penalties the demos was convinced that it was punishing offenders as they deserved; the atimia that might result was not just collateral damage, but intentional. That the fines also funded the newly empowered court system was an additional benefit; if the Athenians really believed the annual costs of the dikasteria to be 150 talents, as is claimed in Aristophanes’ Wasps (663) of 422, they needed huge income from fines to keep the system going.50 That this policy was carried out on a large scale may be inferred from attempts to terminate it. Abolishing eisangelia and graphē paranomōn, the legal instruments hitting primarily the political elite, was among the first measures of the changed constitution of 412/11; everyone was now to feel free to speak about the situation, with threats, this time, to those trying to prosecute a citizen for doing so (Ath. Pol. 29.4). However, after the fall of the oligarchs both procedures were clearly reinstated,51 and in the fourth century they became the legal weapons par excellence in the competition between political leaders. The fines at euthynai, however, fared somewhat differently. Andocides in On the Mysteries recounts how in 405, on a proposal of Patrocleides, the Athenians decided to restore many categories of atimoi to their former status to strengthen the active citizen population. The first group of atimoi consisted of citizens indebted to the dēmosion, notably those who, following their euthynai, had lost a civil suit (dikē exoulēs) and those fined by a graphē or by a magistrate.52 Clearly, the numbers of such atimoi were by now considerable and at this low point in the war the Athenians wanted to undo the results of their 49

50

51

52

No. 24, IG i3 1453: copy B 7–8 sets for each thesmothetēs an (illegible) fine if they fail to bring (?) to the heliaia, and ll. 8–14 punishes with atimia and the loss of property, with a tenth to the goddess, the officials in the allied cities who do not act at once in accordance with the decree. If there are no Athenian officials in a city, those of the city itself are responsible in the same manner. Copy C 18–21 lays down the death penalty for anyone who acts against the decree or puts a proposal against it to a vote. For the 10,000 drachmae fine for stratēgoi (?) in copy D and E, see the appendix. On the estimation of Pritchard, Public Spending, 56–57, the real costs of the dikastēria were 53 talents 2,800 drachmae annually in the 420s, but what mattered here is what the Athenians believed them to be. These procedures were central in the Arginusai-trial of 406 (cf. Carawan, ‘Eisangelia’, 173– 175). The prosecution of Erasinides by Archidamos (Xen. Hell. 1.7.2) for withholding public money and badly handling his stratēgia, could be either a euthynai or eisangelia. Andoc.1. 73–76: οἱ μὲν ἀργύριον ὀφείλοντες τῶι δημοσίωι, ὁπόσοι εὐθυνας ὦφλον ἄρξαντες ἀρχάς, ἢ ἐξούλας ἢ γραφὰς ἢ ἐπιβολὰς ὦφλον (etc.).

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policy of fining their (ex-)magistrates. But some evidence suggest that they came to realise there was something wrong with the system itself, too. That in a constitution where all (male) citizens together made the law and where the rule of law applied to all equally, the laws could nevertheless be unjust, posed a paradox that few apparently were aware of.53 But what the Athenians did notice was that the system was counterproductive. Such may be inferred from a change visible in subsequent extant decrees. In the fourth century, after the revision of the Athenian laws, only two decrees threaten officials at their euthynai with a fine, the amount of which is unfortunately not legible, compared to the fourteen such decrees in the fifth century.54 As to high amounts, in the fourth century there are four decrees setting a 1,000 drachmae fine, one of which fines magistrates for failing in a specific duty set by the decree, the other three fine private persons acting contrary to the decree.55 In all these cases the 1,000 drachmae are to be paid to a deity; there is no stimulus to benefit the dēmosion directly. In the fifth century, there are twelve certain or plausible cases of a 1,000 drachmae fine in decrees, of which three are to be paid to a deity (opheilein) and nine to the dēmosion, usually following euthynai. To this number, we should add the seven 10,000 drachmae fines. In one, unique, fourth-century decree, a fine of 3,000 drachmae is to be paid to the dēmosion by each magistrate failing in a specific duty set by the decree.56 Given that overall there are more than twice as many extant polis decrees of the fourth century than of the fifth,57

53

54

55 56

57

[Xen.] Ath. pol. 3.12–13, responding to a (rhetorical) claim that at Athens no one was unjustly deprived of citizen rights, observes that in fact some atimoi lost their rights in Athens unjustly, but that it is difficult to maintain that many citizens lose their rights unjustly because the citizens themselves are the people filling the offices. Beside the matter of legal principle discussed here, the text (probably dating to the late 420s–early 410s) suggests that the number of atimoi and the justice of their situation were topics of contemporary debate. Euthynesthai: Scafuro nos. 15 and 16. No 15: SEG xxx 61 fr A+B; Agora xvi 56 [1] A, c. 380– 350, a law on the city Eleusinion concerning the Mysteries; ll. 36–37: the basileus and the epimeletai each owe [?] drachmae to the Two Goddesses. No. 16: SEG xxvi 72.26–28; Agora xvi 106 C (375/4): a law regulating silver coinage. No. 15 is also included in Scafuro’s opheilein-list (as no. 23) because in ll. 11–14 a board of magistrates owes (opheilein) a sum to the goddesses if they fail to do something. Not included is the very lacunose ii2 1240. Officials: IG ii3 1 452 (334 bce). Private persons acting against statutes: ii2 17; IG ii3 1 433.31; ii2 1237.22–26 = RO 5 (Demotionidai; 396 bce). IG ii2 1631 about Sopolis, ll.392–393: ‘the magistrates of the dockyards and the secretary of the Eleven, if they do not wipe out from the debt of Sopolis the money […] each owes (opheileto) to the demosion 3,000 drachmae’. From c. 500 to 403, c. 225 polis decrees are known, and from 403 to 322/1, 572 polis decrees.

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this picture suggests that the Athenians revised their previous policy of threatening citizen office holders with devastating fines at their euthynai. There is no certain case of the 10,000 drachmae fine after 415, except the outlier no. 26 (IG ii3 1 370) of c. 325/4. After promising crowns to the first who succeed in its aims, the decree sets a fine of 10,000 drachmae owed to Athena (opheilein) for anyone acting against it and for the euthynos and his paredroi if they fail to impose the fine.58 The decree concerns founding a colony in the Adriatic, led by Miltiades, a descendant of the famous general of Marathon and coloniser of the Thracian shores, to secure, once again, the grain trade to Athens.59 Stephen Lambert points to the historicising features of this decree, fitting the atmosphere of Lycurgan Athens looking back to the glories of the fifth century.60 It would seem, then, that the fine set in the decree was also copied from the fifth century. Had the Athenians forgotten that this fine of the past was far from glorious, or was the amount of 10,000 drachmae no more than a hollow threat—in other words, was 10,000 by now indeed unreal?

Conclusion The 10,000 drachmae fine set in decrees from c. 430 to c. 414 was a punitive force hitting anyone who did not comply with the wishes of the Athenian demos, especially officials found wanting at their euthynai. The first steps towards this exorbitant fine were fines of 1,000 drachmae appearing shortly before or in the 430s. Yet the 10,000 drachmae fine reflects a particular political climate, exemplified by a fine of 50 talents imposed on Pericles and other cases of heavy

58 59

60

On this decree, see also Johnstone in this volume, p.89. Lines 48–62. J.M. Camp ii, ‘Drought and famine in the 4th century b.c.’, Studies in Athenian Architecture, Sculpture and Topography, Presented to Homer A. Thompson (Hesperia Supplements, 20; Princeton: American School of Classical Studies at Athens, 1982), 15 n. 19 remarks: ‘Colonization was a standard response to famine, and it is interesting to note this late revival of the institution’. S.D. Lambert, ‘Connecting with the Past in Lykourgan Athens: an Epigraphical Perspective’, in L. Foxhall, H.-J. Gehrke, and N. Luraghi (eds), Intentional History: Spinning Time in Ancient Greece (Stuttgart: Franz Steiner, 2010), 225–238. J. Ober, ‘Comparing Democracies: A Spatial Method with Application to Ancient Athens’, in V. Azoulay and P. Ismard (eds), Clisthène et Lycurgue d’Athènes: Autour du Politique dans la Cité Classique (Paris: Publications de la Sorbonne, 2011), 307–322, in a thought experiment features a fifth-century citizen, Poseidippos, checking how the fourth-century democracy compares to his own. On reading the decree no. 26 discussed here with the 10,000 drachmae fine, ‘Poseidippos would note that the decree provided for very severe sanctions for disobedience’ (318)— indeed, old-fashioned severity!

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penalties, in which the demos acted as a violent, impatient and unforgiving master of its own citizens and others. Thucydides, Aristophanes, Xenophon and the Ath. Pol. sharply portray the political climate of this era from c. 430 to c. 405 (the oligarchic episode excepted) as marked by political leaders intent on pursuing their own agenda by fuelling the demos’ sense of entitlement and concomitant desires, as well as its anger and vindictiveness. This portrayal, not above some suspicion of anti-democratic bias, is now found to be fairly true to reality thanks to the evidence of the decrees. The legislative power of the demos to act on these feelings was reinforced by their judicial powers, exacerbated by their concern to fund the jury courts by fines and confiscations. This wave of punitive extravagance fitted the wider system of Athenian institutions for dispensing rewards and punishments, honour and dishonour to its citizens, embedded in the underlying reciprocity between citizens and polis. Within this system, however, the 10,000 drachmae fine was an excess, for which, tellingly, no equivalent in honours existed; the most prominent honours for citizens (such as sitēsis or a statue) were not expressed in monetary values. Expressing citizens’ valuation for the polis in amounts of money may be considered one of the most significant effects of numeracy on the polis since the Archaic age.

Acknowledgements Many thanks to the members of the European Network for the Study of Ancient Greek History, meeting at Copenhagen 25–27 Aug. 2016, for commenting on the first draft of this paper, especially to Thomas Heine Nielsen for hosting us and to Mogens H. Hansen for valuable comments; to Stephen Lambert, John Ma and Elon Heymans for comments on the draft; to the participants of the conference on ‘Numbers and Numeracy in Ancient Greece’ in Leiden on 2–3 Sept. 2016 for their responses, and last but not least to Tazuko van Berkel and Rob Sing for organising it all.

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Appendix table 4.1

1.

Fines in Attic Decrees of the Fifth Century bce

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

IG i3 1 (1) Salamis decree

c. 510–500 ll. 4–7 The tenant and landlord who lease property on Salamis ll. 5–8 The archon who fails to exact the fine in the above case

Fine

Conditions/ terms

unknown

ἀποτίν[εν] to the dēmosion;

unknown

εὐθ]ύ[νεσθαι

Moreno (2007) 102–106, esp. n. 121 with further ref. and n. 139, suggests that the obligations of the cleruchs (tax, army service) were laid down in Solon’s time, when Salamis became part of Athens, and that the decree was inscribed in the late sixth century. The verb euthynesthai is almost entirely restored, but quite plausible. In l. 10, a sum of 30 dr. is mentioned, which cannot be made out to be a fine. 2.

IG i3 4 (2) Hekatompedondecree

485/4?

A l. 5: unclear (to do with a guard)

A l. 5: 50 dr.

unclear

A l. 26: unclear

A ll. 26–27: 2 dr.

to the dēmosion

B ll. 7–8: anyone performing rituals in the wrong place/ manner (?)

B ll. 7–8: up to 3 ob.

θοᾶν to the tamiai

B ll. 12–13 anyone doing something wrong near the sanctuaries

B ll. 12–13: up to 3 ob.

θοᾶν to the tamiai

B. ll. 13–16 priestesses and zakoroi roasting barley (?) on the Acropolis

B. ll. 15–16: 100 dr. each

εὐθύνε[σθαι]

B ll. 16–17: the tamiai who let them do this

B. ll. 16–17: 100 dr. each

[εὐθύνεσθαι]

B ll. 21–23: tamiai who fail to be present

B. l. 22: 2 dr. each time; the prytanis is to fine them

[ἀποτίνε]ν

120 table 4.1

blok Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

B. ll. 23–24: the prytanis who fails to fine them

B. l. 23: 2 dr.

εὐθ/[ύνεσ]θ̣αι

IG i3 4A.14–15 and B.27–28 assign the decree to archon (restored) Philocrates, 485/4; for an earlier date of the decree with possible reinscription: Jordan (1979); contra Stroud (2004); cf. Butz (2010) ix for further refs. 3.

IG i3 6 (3) = I.Eleusis 19 = OR 106 Eleusis decree

c. 460

The Kerykes and Eumolpidai; if they (initiate) more than one person at a time

C ll. 29–30; [...] dr. each

εὐθύνεσθα[ι...6.../ .1] δρα[χ]με͂σι]

The date is approximate, based on letterforms. The amount of the fine was restored by Meritt (1945) 71: εὐθύνεσθα[ι χιλιάσι] δρα[χ]με͂σι and retained in subsequent editions; see e.g. OR who keep square brackets in the text but not in the translation; AIO: [a thousand]. However, hεκατὸν is equally possible. 4.

IG i3 245 Deme decree of Sypalettos

c. 450–420 Anyone who brings to a vote a proposal about the distribution or the donation of the money

ll. 5–12: 1,000 dr. (χιλίας δ̣ρ̣[αχμὰς]) to the koinon of the Sypalettioi

ὀφειλέτο

The stone is roughly worked (Lewis’ supposition in IG of a crown on the top is unwarranted) and inscribed in an unsophisticated manner. IG i suppl. p. 134 estimated the date mid-fifth century or a bit later. The date in IG i3, 470–460, is probably strongly influenced by the three-bar sigma criterion, which is now abandoned. Some elements point to before 450: the short, paratactic phrases; Φ as a circle with a vertical line through it (cf. Tracy (2016) 217) and N bending slightly to the right. Others point to a later date: E with horizontals that are not very angled; Attic script with some Ionic elements intruding, occasionally wrongly: l. 6: λέχσεως but l. 7 δόσεος and l. 10 [τ]ο͂ι κωινο͂ι. Other deme documents with Ionic script are dated approximately to c. 450–415; Matthaiou (2009a) 208. Missiou (2011) 139 points to the ‘unfamiliarity of Athenians with the proper use of the omega’ in this deme decree and in IG i3 7, the Praxiergidai decree issued by the polis. The latter is dated in IG i3 to 460– 450, but see now AIO and OR 108 for c. 460–420 or perhaps 440–420, due amongst other factors to a dative plural in -αις, common after 420. For λέχσις (distribution, from λαγχάνω) among demesmen, cf. IG i3 244C.5 = OR 107. I thank S. Lambert and A.P. Matthaiou for their comments on the date on autopsy.

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5.

Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

IG i3 41 (6) Decrees on Hestiaia

c. 446/5? after 428/7?

The nautodikai who fail to provide a [fully manned] court

ll. 91–92: amount unknown (1,000 dr.?)

εὐ]θυνέσθο

It is very difficult to connect this heavily damaged decree securely either to the aftermath of the revolt of Euboea in 447/6 (Thuc. 1.114–115; Diod. Sic. 12.22) or after 428/7: Mattingly (1996) 246–248; cf. Lambert (AIO-paper 8, 2017). The amount of the fine is entirely restored. 6.

IG i3 256 440–420? Decree on the waters of the nymphs on authority of a Pythian oracle

Who, without paying the annual hieros obol, drinks from the well of the Halykon; who takes away an amphora of water

l. 10: 5 dr. (πέντε) ἀποτίνειν

1. 12–13: 50 dr. (𐅄)

ὀφειλέτω

Deme decree, probably from Lamptrai, in Ionic script, dated in IG i3 to 440–430; cf. Matthaiou (2009a) 205, 208. However, in l. 13 τα[ῖς] Νύμφαις may point to a later date, after 420. 7.

IG i3 14 Erythrai decree OR 121

435/4

The boulē of E. if they fail to sacrifice properly (?)

l. 18 [1,000 dr.] (restored in IG: [χι]λ[ία]σ[ι]ν)

ζεμιο͂σαι ̣

Dated in IG to c. 453/2? and in AIO to 454–450?, but see Papazarkadas (2009) 78 for doubts, and Moroo (2014), who makes a strong case for 435/4. OR, following Malouchou (2014) leave out the amount of the fine (illegible), neither is the amount restored in AIO. 8.

c. 440–410 Anyone who acts contrary to IG i3 157 Decree about jurisdecree diction concerning allies (very damaged)

l. 13: 1,000 [to Athen]a χιλία[ς] δραχμὰς ̣ [hιερὰς τε͂ι Ἀθεν]/[αία]ι.

[ὀφειλέτο]

Dated in IG to c. 440–410. 9.

IG i3 59 Decree about the navy

c. 430

each (official)

l. 45 1,000[? dr.] l. 50 […] dr. to Athena

The text is heavily damaged; plausibly dated to c. 430 in IG. In a section clearly dealing with fines, l. 45 [δραχμε͂σι χιλί]ασι hέκ̣α̣[στος] is a plausible restoration; in ll. 49–50 the fine payable to Athena cannot be restored.

122 table 4.1

10.

blok Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

IG i3 153 (20) Decree about the navy

c. 440–425 Every trierarch, steersman or anyone who acts against the rules of this decree on how the ships are to be manned

Fine

Conditions/ terms

ll. 16–18: 1,000 dr. to Athena

ὀφελέτο χιλία[ς] [δραχμὰς hιερὰς τε͂ι] Ἀθεναίαι

ll. 24–26: 50 talents to the Athenians (?), of which 1/10 to Athena (?)

ὀ[φέλεν πεντ]ήκοντα τάλαντα/ [Ἀθηναίοις κ]αὶ τὀπιδέκα[το][ν τῆς θεο͂ εἶνα]ι·

Text is heavily damaged; dated in IG to c. 440–425. 11.

IG i3 1454; OR 136 Decree for the Eteokarpathians

c. 435

Anyone who acts contrary to the decree

The decree grants a special status to the ‘Eteokarpathians’ because the beneficiaries supplied a huge cypress for the temple of Athena Polias; see OR 136; Ma (2009). In l. 25, Ἀθηναίοις is restored, as is the tithe for the goddess, but the context, which explicitly refers to the thesmothetai in Athens (ll. 27–28) makes this restoration plausible. 12.

IG i3 78a (10) = I.Eleusis 28 = OR 141, First-Fruits decree

c. 435

The hieropoioi who fail to take action within five days after it has been announced, when grain from cities comes in

l. 20: 1,000 dr. each

εὐθυνόσθον hοι hιεροποιοὶ χιλίαισιν v δραχμε͂σι

This much-discussed decree is dated in IG i3 to c. 422, but to c. 435 by Cavanaugh (1996) 73–95, to c. 440–435 by I. Eleusis and c. 435 or earlier by OR. Tracy (2016) 115–116 assigned it to the cutter of IG i3 50. The only datable inscription associated with that cutter is IG i3 302 of 424/3; he also inscribed IG i3 131 (Prytaneion decree), dated by Blok and van ’t Wout (2018) on historical grounds to the early 420s (see also below no. 15, IG i3 133). Other decrees cut by the cutter of IG i3 50 date from c. 435 (IG i3 50) to c. 409 (IG i3 105). 13.

IG i3 55 (7) c. 431 Decree for Aristonous

The polemarch for every day of delay after five days of having filed a charge, if an Athenian or an ally wrongs A. or a child of his; the [prytaneis] (?) for every day after 10 days that they fail to implement legal protection measures for A.

A, ll. 8–9: 1,000 dr.

εὐθυνέσθω

B, l. 20: 1,000 dr.

[εὐθύνεσθαι]

123

ten thousand table 4.1

Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

Dated in IG on prosopographical grounds to 431 or slightly later; the honorand is probably Aristonous of Larissa, a leader of the Thessalian cavalry fighting for Athens in 431 (Thuc. 2.22.2–3); cf. Matthaiou (2009a) 202. 14.

IG i3 149 (13) Decree on relations with Eretria; concerning court cases

c. 430–412

The polemarch? if he fails to file a charge within twenty days (?);

ll. 9–10: [1,000 dr.(?)]

[εὐθυνέσθο χιλία][ις δρα]χμαῖς

(official)

ll. 17–18: 1,000 dr.

[εὐθυν]έσθο χι[λί]α[ις δραχμαῖς

The decree is heavily damaged, but in ll. 9–10 the stoichedon and legible dative fem. plur. of the drachmae give some support to the restoration of the fine and context (euthynai), an amount and condition recurring in better shape in ll. 17–18. The kōlakretai in l. 3 provide a date ante quem. 15.

IG i3 133 (12) Decree on a tax for the cult of the Anakes

430–428 or two years later

The hieropoioi if they fail to account for (?) the money received for the Anakes

l. 18: 10,000 dr.

εὐθυνόσ[θον] μ[υρίαις δραχμαῖς

The heavily damaged decree seems to impose a tax of 2 % (l. 25) on sea captains and merchants, to be collected by hieropoioi and overseen by the tamiai (restored) of the Other Gods. The latter officials provide a post quem based on IG i3 52A, conventionally dated to 434/3 (IG; OR 144; AIO) but see Kallet (1989) and Samons (2000) 113–138 for 433/2. Mattingly (1999) 121 argues for 430–428 or two years later for IG i3 133, as do Blok and van ’t Wout (2018), due to its connection to IG i3 131 and to no. 12, IG i3 78. 16.

IG i3 61 = OR 150 (2) (8) Decrees about Methone

426/5

17.

IG i3 63 (18) c. 426 Decree about trade, especially of grain, from Aphytis to Athens

the guardians of the Hellespont if they somehow prevent Methonians from exporting grain

ll. 38–39: 10,000 dr. each

εὐθυνέσθον μυρίαισι δρ[αχ][με͂ισ]ιν ἕκαστος·

Anyone who proposes a vote against this decree;

ll. 4–5: (10,000? 1,000?) dr. sacred to Athena

(a) ὀφελέτο

Anyone who prevents the Aphytaeans from sailing to Athens

ll. 18–19: 10,000 dr.

(b) [ὀφελέτ]ο μυρ[ίας δραχμὰς]

Non-stoichedon. In ll. 4–5, IG restores μυρίας δραχμὰς, but χιλίας is also possible.

124 table 4.1

18.

blok Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

IG i3 71 = ML 69 = OR 153 (9; 19) Thoudippos’ decrees on tribute

425/4

– Each assessor for each day of delay of assessment – Oath administrators who fail to … – The polemarch (?) … who fails to take the assessments (?)

l. 10 (100 dr.? AIO); [1,000 dr. IG]; […] OR l. 11: ‘same penalty’

[ἀποτεισάτο] [ἒ ὀφελέτο hέκαστος τὲ]ν αὐτὲν ζεμ[ίαν·

l. 15: 10,000 dr.

εὐθυ]νέσθο μ[υ]ρίασι δραχ̣[με͂σι

ll. 28–30: 100 dr. to Athena and 100 dr. to the dēmosion, and l.30: 1,000 dr.? 10,000? each

ὀφ[έλεν

– The prytaneis (at Gr. Panathenaea) who (in the future) fail to put the assessment on the agenda within their term of office

[εὐθύνεσθαι] [χιλί]ασι? [μυρί]ασι?

– Anyone preventing the ll. 32–33 assessments being made at ἄτ/[ι]μος ἔσ[το], Gr. Panathenaea property to be dēmosion, and a tithe to the goddess – Each of the prytaneis if they fail to finish the assessments within their term of office

ll. 37–38: 10,000 dr.

εὐθυν]έσθο μυ̣ρίασι δρ[αχμε͂]si

IG i3 71, ‘Thoudippos’ decrees’, is inscribed in stoichedon 70; the text is heavily damaged and overly restored; for text and comm. see Matthaiou (2009b) 18–68; Lambert, AIO-paper 8 (2017) and OR 153. In l. 10, AIO follows Matthaiou in reading ἑκατὸν, but although Attic h is occasionally omitted (l. 10 ἑμέρας, l. 15 ἑλιαίαι, ἑ]λιαστῶν) it is used almost throughout and notably with h[εκατὸν] (l. 30), so the restoration in IG χιλίας is also plausible; OR leave the passage open. 19.

IG i3 10 (17); OR 120 Phaselis decree

c. 425/4

Anyone violating the contents of the decree

10,000 dr. sacred ὀφελέτο to Athena

125

ten thousand table 4.1

Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

The date in IG of c. 460 is defended by OR; they concur with the view that the dat. plur. fem. ending in -αις is not a criterion for a date after c. 420 in this case because the text is entirely in Ionic script. This view is contested by Jameson (2000–2003) 26, pointing out that the dialect of the decree is entirely Attic and that script and dialect should not be confused. Papazarkadas (2009: 70–71) and Beretta Liverani (2013), revisiting Mattingly (1964; 1996: 215–258) and Jameson (2000–2003) situate the decree in the context of the alliances Athens made between 427 and 423 (OR’s option that the treaty with Hermione might date to c. 450, rather than to c. 425, for no clear reason refuses to accept Mattingly’s and Jameson’s strong arguments for the later date). The proposer Leon may be the same man who proposed the treaty with Hermione (IG i3 31) and took part in the oath of the truce of 422 (Thuc. 5.19.2; 24.1). For the cutter, Tracy (2016) 24–26, cf. Scafuro (2014) 316–317 for other connections with nos. 17 and 18. 20.

IG i3 34 (5) 425/4 or Kleinias’ decree on slightly tribute later

The prytanis who fails to bring a complaint filed by an Athenian or ally into the boulē

l. 37: 1,000? 10,000? dr. on a charge of bribery

εὐθ]υνέσθο δόρο[ν

The date in IG (448/7) is now revised to 425/4 or a little later, as the decree presupposes IG i3 68 and 71 (cf. comm. in AIO). In l. 37, the amount of the fine is illegible; given the stoichedon (23) and, where legible, the consistent use of Attic h, there is space for either μυρίαισι (as in IG: εὐθ]/υνέσθο δόρο[ν μυρίαισι δραχμ]ε͂σ[ι ̣ h]έκαστος·) or χιλίαισι, but hεκατόν would not fit. AIO leave the amount open. 21.

IG i3 19 Proxeny decree for Acheloion

Late 420s.

[the polis of] anyone who kills Acheloion or one of his children, as if he were an Athenian

l. 10: 5 T. (= 30,000 dr.)

ὀφέλεν (restored)

Dated in IG to c. 450/49; Mattingly (1996) 363–366: 422/1; Rhodes (2008): late 420s. 22.

IG i3 165 Decree about honours and proxeny

Before 420?

The prytaneis who fail to bring ll. 2–5: 1,000 dr. forward … to Athena and each … dr. [at their euthynai]

[ὀφελεν χι]λίας δ[ραχμὰς] … [δρ]αχμαῖσι [εὐθύνεσθαι ἕκαστον αὐτο͂ν]

IG dates this inscription before 420(?). The [δρ]αχμαῖσι in ll. 4–5 could also point to a later date. The amount in l. 3 is secure, but in l. 4 it cannot be restored.

126 table 4.1

23.

blok Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

IG i3 84 = OR 167, (11) Decree on the sanctuary of Kodros, Neleus and Basile (enacted in the prytany of Pandionis)

418/7

Every bouleutēs if the decree l. 10: 1,000 dr. has not been implemented by the end of their term; for the basileus and all others instructed about these matters, if they fail to carry out what is decreed by the prytany of Aegeis l. 20: 10,000 dr.

Conditions/ terms

εὐθύνεσθαι

εὐθυνέσθω μυρίεσι δραχμε͂σιν

The officials targeted with the huge fine of l. 20 were, beside the basileus, probably the poletai responsible for contracts (ll. 5–6), the horistai who were to demarcate the territory of the temenos to be leased (l. 7) and perhaps others. The deadline with the fine is set in the following prytany. 24.

IG i3 1453 = OR 155, (14) Standards or Coinage Decree

Between mid420s and shortly before 414

Officials (stratēgoi?) who fail to send heralds announcing the measure

E, l. 1: 10,000 dr.

εὐθυ]νόσθω μυρίαισι δραχμῆσι

There is now consensus that this decree, dated in IG to c. 449, must be down-dated; see Papazarkadas (2009) 72, and for a plausible date shortly before 414 see Kroll (2009) 201–203, AIO and OR 155. Multiple fragments of non-verbatim copies, sent to the cities of the Athenian empire, have come to light; the clauses of the decree include various penalties to be meted out to those officials and cities who somehow fail to comply with the decree. Here, the fragment found on Siphnos (E) is relevant, where in l. 1 an Athenian official (in the singular) is threatened with a 10,000 dr. fine; in the copy from Syme (D), l. 6 IG restore οἱ στρατηγοὶ, who are to despatch heralds to every region of the empire, so who exactly is targeted with this fine, is unclear. In AIO, this clause is rendered as clause 7. 25.

IG i3 117 (21) = OR 188 Provisions for the construction of ships in Macedon and honours for Archelaos, King of Macedon

407/6

Anyone who fails to do what is stated in order to get the ships as quickly as possible to Athens

ll. 20–22: 1,000? 10,000?

ὀφελ[εν μυρίας δραχμὰς αὐτὸ]ν hιερὰς τε͂ι Ἀθ[εναίαι·

The decree is heavily restored; the restoration in IG μυρίας could also be χιλίας; OR leave the amount open. The date is uncontested; the decree was cut by the prolific cutter of IG ii2 17, Tracy (2016) 151.

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ten thousand table 4.1

26.

Fines in Attic Decrees of the Fifth Century bce (cont.)

Corpus number; Scafuro (2014) number (bold) and topic

Date

Who and why?

Fine

Conditions/ terms

IG ii3 1 370 = RO 100, Decree on founding a colony in the Adriatic

c. 325/4

Anyone, private or official, who does not act according to the decree and the same fine for the euthynos and paredroi if they fail to impose that fine.

ll. 65–72: 10,000 dr.

ὀφειλέτω to Athena

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chapter 5

Numeric Communication in the Greek Historians: Quantification and Qualification Catherine Rubincam

What kinds of numeric communication are found in works of ancient Greek historiography? What kinds of things were regularly quantified in these works, and how was the quantification expressed? To answer these questions it is necessary to look systematically at all the numbers in the relatively complete parts of the corpus of Greek historiography. Ideally, a means must be found to compile statistics on a standard set of aspects of every number in the texts of the Greek historians so as to create a numeric profile for each author and each work. This makes it possible to quantify the numeric practice of these historians, so as to get a clear picture of what kinds of things each quantifies and how. The coding system set out here1 captures three aspects of each number: (i) the type of number (i.e., a cardinal—a number in the series one, two, three, etc.; an ordinal—a number in the series first, second, third, etc.; a numeric compound—a compound containing a numeric element (e.g., ‘of-30-years’) or some other kind of numeric word (e.g., ‘single’, ‘both’, ‘thrice’); a fraction—‘onetenth’, ‘half’, ‘one-twentieth’; a non-explicit but precisely ascertainable number (e.g., ‘a year’, ‘a ship’, ‘the same number of ships [as just mentioned]’)), (ii) the subject category to which it refers (TIME, DISTANCE-SIZE, MILITARY, POPULATION, MONEY, MISCELLANEOUS), and (iii) whether and how it is qualified (by an approximating expression (e.g., ‘about’), a comparative expression (e.g., ‘more than’), an alternative form of words (e.g., ‘two or three’), or an emphatic expression (e.g., ‘only’)).2 I have applied this coding system in an ana1 For a full explanation, see ‘Coding System for Numbers’ in the Appendix. 2 The system outlined here was developed by the author through the 45-year duration of the Numbers Project. A full account of this project, which compiled all the numbers in the six bibliographic works named here, parsed according to the system outlined in the Appendix, is provided in my monograph, Quantifying Mentalities: the Use of Numbers by Ancient Greek Historians, forthcoming from the University of Michigan Press. A large selection of the coded data can be accessed at the following site: https://dataverse.scholarsportal.info/dataverse/​ rubincam. From 1999 until 2019 a series of four research grants from the Social Sciences and Humanities Research Council of Canada helped to fund teams of research assistants (mostly graduate students in the Graduate Department of Classics at the University of Toronto and

© Catherine Rubincam, 2022 | doi:10.1163/9789004467224_007

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lysis of the six earliest substantially preserved works of Greek historiography: Herodotus, Thucydides, Xenophon (Anabasis and Hellenica), Polybius (Books 1–5), and Diodorus (Books 1–5, 11–20).3 The database compiled by this means makes it possible to view any particular number in these texts in the context of the numeric practice of its author or work, or of a group of works of similar date or purpose. Thus one can simulate the situation of the original author or reader of that text. This paper will highlight some examples of the major insights that emerge from this work. The immediate benefit of such an analysis is that it heightens one’s awareness of both the similarities and the differences between ancient Greek numeric practice and modern, Western practice. This is extremely important if we are to avoid applying anachronistic assumptions to the understanding of the numbers in these ancient texts. Let me give an example. Some years ago I set a new undergraduate research assistant the task of highlighting all the numbers in a modern narrative of Xerxes’ invasion of Greece.4 I explained that Sealey’s narrative was based on a section of Herodotus’ Histories, and that I wanted to compare the use of numbers by the ancient historian with that of his modern adapter. The student came back a week later and asked, ‘How many of the dates in Sealey’s text come from Herodotus?’ Like many modern historians retelling events first narrated by an ancient historian, Sealey introduces standard Julio-Gregoriancalendar dates—numbered days and years with named months—to make the chronology more comprehensible to modern readers. When I replied that none of these dates were in Herodotus, my student expressed astonishment, and a long discussion ensued of the difference between ancient and modern calendar systems and time measurement. I meant, of course, not that Herodotus’ narrative contained no chronological information, but rather that he did not assign numbers to specific days, months, or years; his TIME numbers all describe the duration of some state of affairs or the interval between two events. This significant restriction on the nature and extent of TIME quantification applies also to other ancient Greek historians: the texts in my database contain only undergraduate students at the University of Toronto Mississauga), whose collaboration was essential to the success of the project. No less essential was the digital Greek text of the historical works being analysed, to which access became available in the late 1990s thanks to the Thesaurus Linguae Graecae Project. My thanks are due to all these individuals and organisations for their indispensable assistance. 3 Only works of which at least a substantial portion has survived in the manuscript tradition can be subjected to this treatment, because we cannot be sure who was responsible for the choice of words in fragmentary works. 4 R. Sealey, A History of the Greek City States ca. 700–338 b.c. (Berkeley: University of California Press, 1976), Chapter 8.

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eight indications of time, out of a total of over 1,200, that could be in any sense counted as dates.5 Five of these are located in quoted or paraphrased official documents; the other three involve major religious festivals. All use the official civic calendar of the state concerned, and each numbers only the day within the month, identifying both the month and the year by name rather than number. Why are calendar dates so rare in Greek historiography? Because there was no single, generally agreed, calendar to which Greeks from every polis could refer. Consequently, a historian might have difficulty establishing a precise date for any event in terms understandable by readers from more than one polis.6 Full consciousness of the problems of quantifying time in the world of not-easily-synchronised Greek civic calendars heightens one’s respect for Thucydides’ creation of his own chronological framework for his narrative of the Peloponnesian War, using the sequence of war-years, counted in ordinals and anchored at its start to the official calendars of three major Greek states.7 Feeney, whose book on Caesar’s reform of the Roman calendar lucidly explains its revolutionary significance, recommends that modern students of ancient history ‘regularly defamiliariz[e]’ the convenience of what he terms ‘our universalizing cross-cultural and supranational numerical dating’ so as to appreciate fully the difficulties an ancient historian had in quantifying intervals and periods of time.8 My numeric database promotes precisely this kind of ‘defamiliarization’ as can be seen in the case of a much-discussed passage from Thucydides (8.68.4) on the oligarchic revolution of the 400, provided here with the coding system shorthand:

5 Greek historians’ statements containing calendar dates: Thuc. 2.15.4, 4.118.12, 4.119.1, 5.19.1 (2 dates), 5.54.3; Diod. Sic. 12.36.2, 18.56.6. 6 Only histories of a single state (e.g., Atthides) were to some extent exempt from this problem. 7 See Appendix, ‘Thucydides’ synchronisation of Greek civic calendars (Thuc. 2.2.1)’ for his dating of the start of the war. 8 D. Feeney, Caesar’s Calendar: Ancient Time and the Beginnings of History (Berkeley: University of California Press, 2007), 12: ‘The ease and apparent naturalness of our dating system conspire to beguile us into overlooking the fact that all of the dates it generates are themselves ultimately synchronisms. The centuries-long work on constructing a coherent historical chronology on an axis of b.c.e./c.e. time has been absorbed and naturalized so thoroughly by all of us that we can take it completely for granted, and forget just how much synchronistic work our predecessors going back to the Renaissance had to do in order for us to be able to say something like “Xerxes invaded Greece in 480 b.c.e.” ’. Compare also P.-J. Shaw, Discrepancies in Olympiad Dating and Chronological Problems of Archaic Peloponnesian History (Historia Einzelschriften, 166; Stuttgart: Franz Steiner, 2003), 25: ‘Classical authors possessed no cog-

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it was difficult to put an end to freedom for the Athenian demos in the 100th year approximately [μάλιστα] {Ord, TIME, Q1} after the tyrants had been deposed, when it [sc., the demos] had not only not been subservient, but for over [ὑπέρ] half of that time {Frac, TIME, Q2} had been accustomed to rule over others.9 This reference to the interval between the expulsion of the Peisistratid tyrants and the institution of the oligarchy of the 400 is one of a very few cases where an ordinal statement of a year interval (‘100th’) is qualified. Commentators have difficulty explaining why the historian used an ordinal rather than a cardinal number (‘100’), for two reasons: (i) the best modern calculation concerning the two events mentioned puts the (temporary) end of the democracy in 412/11 bce, i.e. exactly ‘in the 100th year’ after the expulsion of the tyrants in 511/10 bce; and (ii) the use of a qualifier like μάλιστα to modify the precision inherent in the ordinal number involves a logical contradiction. In fact, it turns out that this is the only such statement in Thucydides, and one of only eleven cases (4.5 %), out of 245 ordinal year specifications found in 16 historical works, to which such a qualification is attached.10 The most likely explanation for this rare anomaly, I believe, is that the ordinal statement originated with someone else, in this case probably one of the 411bce oligarchic leaders, who fled Athens after the reinstitution of democracy and thus became accessible to the exiled Thucydides as sources of information on these events. It must surely have been someone with both education and strong motivation—the impulse to inspire his fellow oligarchs with the desirable coincidence of terminating the democracy in its 100th year?—who consulted the list of archons recently erected in the Athenian agora11 and counted the names on it from Harpactides (511/10 bce) to Callias (412/11 bce). This would have been the only way to compute the time

9 10

11

nitive awareness of absolute chronology, nor had they a means of identifying each day by a universally acknowledged date. What is more important, they did not expect to do so, or to be able to do so, nor did they think it necessary’. The Greek text for each of the case study passages is provided in the Appendix. All translations of ancient authors are my own, except where otherwise attributed. The full version of this argument can be found in C. Rubincam, ‘“In the 100th Year Approximately…” (Thuc. 8.68.4): Qualified Ordinal Statements of Time in Greek Historical Narrative’, Mouseion, 8 (2008), 319–332, and ‘Thucydides 8.68.4: A Highly Unusual Numeric Statement’, AHB, 22 (2008), 83–87. B.D. Meritt, ‘Greek Inscriptions (14–27)’, Hesperia, 8/1 (1939), 48–82 at 59–65 identifies the fragmentary inscription #21, described as ‘An Early Archon List’, as part of ‘the public copy inscribed on stone in the Agora’ (65), and estimates its date as ‘ca. 425b.c.’ on the basis of ‘[t]he beautifully even and carefully cut letters’ (59).

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interval between years lacking numeric designations. The historian then added a cautious μάλιστα to the figure, to indicate that he could not vouch for its correctness. Case #1 thus highlights the crucial importance of the distinction between cardinal and ordinal numbers in TIME statements made by Greek historians— a distinction by no means always faithfully rendered by modern translators.12 It also enables us to appreciate properly the extraordinary originality of Thucydides in designing his own chronological framework of ordinal years of the war for his historical narrative, as well as clarifying his specific criticism of Hellanicus for chronological inaccuracy, and his general comments on the importance and the difficulty of making precise chronological statements.13 Case #2 is a passage from Xenophon Anabasis (5.6.9) that illustrates a particular problem concerning DISTANCE, one of the subject categories where measurements are expressed in systems of units whose size and relationship to one another are unfamiliar to most modern readers. This passage reports the problems encountered by the remnant of the 10,000 in finding a means of getting back from the shores of the Black Sea to their homes in Greece. Here a local informant, Hecatonymus of Sinope (one of the Greek cities eager to get this potentially troublesome body of seasoned mercenary troops out of their territories as soon as possible), tries to deter them from making an overland march. He says that, in the unlikely event that they can seize a strongly-held mountain pass and then fight their way past a formidable cavalry force plus more than 120,000 infantry, they will undoubtedly have trouble crossing the rivers that intersect their route: first of all {Ord, MISC}, the Thermodon, of three plethra {Card, DIST} in width, which I think will be difficult to cross, especially with many enemies in front of you, and many following behind, second {Ord, MISC} the Iris, similarly a-three-plethra-distance {Comp, DIST} in width, and

12

13

Here are four modern translations of this passage, all of which substitute a cardinal for Thucydides’ ordinal number: ‘almost a hundred years’ (R. Crawley); ‘almost one hundred years’ (C.F. Smith); ‘about a hundred years’ (R. Warner); ‘ziemlich genau 100 Jahre’ (G.P. Landmann). For Thucydides’ criticism of Hellanicus, see 1.97.2; for his comments on the difficulty of precision in chronology, see 5.20.1 and 26. See also J.D. Smart, ‘Thucydides and Hellanicus’, in I.S. Moxon, J.D. Smart, and A.J. Woodman (eds), Past Perspectives: Studies in Greek and Roman Historical Writing (Cambridge: Cambridge University Press, 1986), 19–35 for elucidation of Thucydides’ views on chronology and C. Rubincam, ‘The Numeric Practice of the Hellenica Oxyrhynchia’, Mouseion, 9 (2009), 313–315 for the possibility that the author of the Hellenica Oxyrhynchia created a similar chronological framework for his narrative.

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third {Ord, MISC} the Halys, of no less than two stades {Card, DIST, Q2} [in width], which you will not be able to cross without boats. But who will be there to supply you with boats? And the Parthenius [river] is similarly uncrossable, to which you would come if you were to cross the Halys. English translations produced since World War ii have striven above all to remove impediments to the reading of the ancient Greek historians for a readership with little knowledge of the ancient world. To this end they routinely convert unfamiliar units of measurement into modern equivalents. This requires changing the numbers, which has consequences for the qualifiers. Thus in Warner’s Penguin translation (1972) Xenophon’s climactic ‘no less than two stades’ for the width of the third and widest river (the Halys) becomes ‘a quarter of a mile’, which weakens the rhetoric of the escalating difficulties. Case #3, a more complex comparison between a passage of Herodotus and its treatment by a series of translators and adapters, involves MONEY, another category in which unfamiliar ancient quantifying units appear. This is the memorable story of bribery of and by Themistocles during the Greek withdrawal from Thermopylae and Artemisium (Hdt. 8.4.2–5.3).14 Herodotus gives four numbers: the Euboeans gave Themistocles 30 talents {Card, MON}; he passed on five {Card, MON} to Eurybiades and three {Card, MON} to Adeimantus, keeping the rest of the money {Ø, MON}. Rawlinson keeps unchanged Herodotus’ three cardinals plus one non-explicit number, but adds a second mention of the original sum {4 Cards + 1 Ø}. Another translator, de Sélincourt,15 converts the original bribe from 30 talents {Card, MON} into ‘some £ 7,000’ {Card, MON, Q1}. The five-talent bribe to Eurybiades becomes ‘a sixth part {Frac, MON} of the sum … received from the Euboeans {Ø, MON}’, while the third bribe, to Adeimantus, is rendered as ‘three talents of silver {Card, MON}—some £700 {Card, MON, Q1}’. Thus Herodotus’ three cardinals plus one non-explicit number have become, in the shorthand of the coding system, 3 Cards (2x Q1) + 1 Frac + 2 Ø. As for the modern adapters, Grote reproduces Herodotus’ three cardinals, with no embellishments.16 Green, however, gives for the original bribe both Herodotus’ 30 talents and a conversion into ‘over £ 7,000’, reports Eurybiades’ five talents and Adeimantus’ three talents as in Herodotus, but inserts a story from Plutarch of a one-talent bribe given to a

14 15 16

For a fuller discussion of this passage, see C. Rubincam, ‘Herodotus and his Descendants’, HSPh, 104 (2008) 93–138, at 105–107. The qualifier inserted by de Sélincourt presumably marks the conversion as only approximate. G. Grote, A History of Greece, v (1846, London: J.M. Dent & Co, 1918), 209.

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different commander, before summing up: ‘There remained a net surplus of 21 talents’ which Themistocles ‘now blandly pocketed’.17 This gives a total count of 6 Cards (1x Q2) for Green’s narrative. Note particularly the change in the qualifier attached to the original bribe’s conversion into pounds sterling: where de Sélincourt had ‘some £7,000’, Green wrote ‘over £ 7,000’; this change, from approximating to comparative qualifier, makes the £ 7,000 a minimum rather than an approximate estimate.18 These variations in how two translators and two adapters treat the sums of money reported in Herodotus’ narrative took me by surprise. In each case the more recent writer, concerned to make the amounts of money intelligible to modern readers, inserts qualifiers for his own purpose where Herodotus had none. Surely, in an era when ever more students are encountering the narratives of ancient historians in translation, the issue of how modern translators should treat ancient measurements and their qualifications deserves some serious discussion. Case #4 concerns the comparison of two different reports on the casualties from the Athenian plague. Thucydides’ famous description of the initial outbreak in 430bce (2.47–54) includes no casualty numbers at all. When describing the second outbreak, in 427bce, he expresses the judgement that ‘nothing depressed and damaged the power of Athens more than this [the plague]’, continuing: ‘For not less than [οὐκ ἐλάσσους] 4,400 hoplites died {Card, MIL1, Q2} from the military ranks, and [not less than] 400 cavalry {Card, MIL1, Q2},19 and of the remaining masses an undiscoverable number’ (Thuc. 3.87.3). Thus he gives definite numbers, both emphasised by comparative qualifiers, for the men whose status would have been listed in the deme registers (lexiarchika grammateia) as liable for cavalry or hoplite service, while lumping everyone else into the ‘undiscoverable number of the remaining masses (τοῦ δὲ ἄλλου ὄχλου ἀνεξεύρετος ἀριθμός)’. How are we to interpret ho allos ochlos? Does it mean, as Gomme takes it, ‘all the rest of the whole population {POP1}’,20 or, 17 18

19 20

P. Green, Xerxes at Salamis (New York: Praeger, 1970), 130. When I discussed this in a 2002 conference paper, I asked, rhetorically, ‘Did Green work out a fresh conversion, using a different formula, or did he simply adopt de Sélincourt’s figure, changing the qualifier in recognition that the pound’s value had depreciated in the 16 years since the publication of de Sélincourt’s translation?’ I was able to put this question to Peter Green in person a few years later at a meeting of the American Philological Association (now the Society for Classical Studies). He smiled and whispered, ‘I wouldn’t do it now!’ The syntax of Thucydides’ sentence requires that the qualifier ‘not less than’ be understood as modifying the numbers of both cavalry and infantry. A.W. Gomme, A. Andrewes, and K.J. Dover, A Historical Commentary on Thucydides, ii (Oxford: Clarendon Press, 1945), ad loc.: ‘metics, foreigners, women and children, slaves (both men and women)’.

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as Hornblower implies, only citizen fighters from the lowest Solonian class (thētes), excluding non-combatants {MIL1}?21 I would argue, with Hornblower, that Thucydides is distinguishing between groups of fighting men of whom the city kept some sort of count (cavalry and hoplites) and fighting men not organised or trained for a particular function, of whom this was not true.22 It is surely relevant that among the 21 other cases where Thucydides applies the term ochlos to people (as opposed to ships) it nowhere refers unambiguously to those not normally liable for military service, such as women, children, and slaves.23 This argument is strengthened by the contrast with Diodorus’ report (12.58.2) on the same subject: ‘They [the Athenians] were so much affected by the disease that they lost of the fighting forces over 4,000 infantry {Card, MIL1, Q2}, and 400 cavalry {Card, MIL1},24 and of others, both free men and slaves, over 10,000 {Card, POP1, Q2}’. Here the structure of the sentence, contrasting the numbers of infantry and cavalry who died, under the general term of ‘soldiers’ (τῶν στρατιωτῶν), with those of ‘[all] the others, both free and slaves’, avoids the ambiguity of Thucydides’ report.25 The statistics provided by the database on the number and nature of civilian casualty reports provide a context that illuminates this difference between these two narratives: threequarters (26) of the 34 civilian casualty numbers ≥1,000 come from Diodorus, whereas the numbers in the other five works are all in the low single digits.26 Diodorus thus seems to show a particular interest in reporting numbers of civilian casualties, which he must have found in sources now lost to us.27 21

22 23

24

25 26 27

S. Hornblower, A Commentary on Thucydides, i (Oxford: Clarendon Press, 1991), ad loc.: ‘Th[ucydides]’ precise information reaches down only as far as the first three of the four Solonian classes: or rather (a cynical narratologist might wish to say) the confession of ignorance about the “other ranks” is designed to increase confidence in the precise information, just given, about the cavalry and zeugite casualties’. Compare Thuc. 4.94.1 and 101.2 on the psiloi who took part in the Delium campaign. Other Thucydidean uses of ochlos to refer to people: 1.80.3, 3.109.2, 4.28.3, 4.56, 4.126.6, 6.17.2, 6.20.2, 6.57.4, 6.63.2, 6.64, 6.89.5, 7.8.2, 7.62.2, 7.75.5, 7.78.2, 7.82.4, 8.25.4, 8.48.3, 8.72.2, 8.86.5, 8.92.11. Note that because Diodorus chose to qualify his figure for the hoplite casualties with a preposition governing the accusative case (ὑπέρ), instead of Thucydides’ οὐκ ἐλάσσους, which governs the genitive, it is impossible to tell whether Diodorus’ qualifier, like that of Thucydides, was intended to carry over from the infantry to the cavalry casualties. Diodorus has also changed the numbers slightly: ‘over 4,000 infantry’ for Thucydides’ ‘not less than 4,400 hoplites’, and ‘400 cavalry’ for Thucydides’ ‘[no less than] 400 cavalry’. Three in Herodotus, two in Thucydides, one in Xenophon Anab. none in Hell., and two in Polybius. Diodorus’ major source for this period of Greek history is usually assumed to be the fourthcentury historian Ephorus (see E. Schwartz, ‘Diodorus 38’, in G. Wissowa (ed.), RE, v. 1: Demogenes–Donatianus (Munich: J.B. Metzler, 1903), col. 669).

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Case #5 is an account in Diodorus of a victory won by Cimon over the Persian navy near Cyprus (11.60.6), which, by an amazing stroke of luck, can be matched with a papyrus fragment (POxy 1610) of the main source that Diodorus was using at this point (probably the fourth-century historian Ephorus).28 The first editors of the papyrus, Grenfell and Hunt, looked with particular care for discrepancies of fact between the two texts, which they thought might require them to reject the identification of Ephorus as the author of the papyrus text.29 They found only one possible discrepancy: the addition of the qualifier πλείους to the number of ships destroyed in this battle (MIL1). The crucial question, which they could not answer, was whether this addition should be counted as a change of fact (for which Diodorus, on their assumptions, would have needed another source) or of style (for which he himself might be responsible). The database can now be used to answer this question. It shows a significant difference between Diodorus and all the other works surveyed in the ratio of approximating to comparative qualifiers: in the other five texts the number of approximating qualifiers greatly exceeds that of comparative qualifiers, whereas in Diodorus this ratio is reversed: 63% comparative to 32 % approximating. Since none of the texts of the major sources used by Diodorus have survived intact, this indirect argument provides the best justification for reconstructing an important aspect of his working method. Qualification is an element that blurs the distinction made by Schwartz (above, n. 27) between the ‘facts’ and the ‘style’ of a narrative, partly, no doubt, because most writers and readers rarely focus consciously on it. In my discussion of Diodorus’ two descriptions of the Dead Sea (2.48 and 19.96–99),30 I argued that the minor differences between them in both numbers and qualifiers are easier to explain if one assumes for Diodorus a more flexible method of composition than the standard reconstruction, which imagines him sitting, like a modern graduate 28

29

30

The comparable sections of the two texts (Diod. Sic. 11.60.6 and POxy 1610, frags. 9+10+53) are set out in the Appendix. C. Rubincam, ‘A Note on Oxyrhynchus Papyrus 1610’, Phoenix, 30 (1976), 357–366 presents a full examination of the correspondence between POxy 1610 and the relevant sections of Diodorus, criticising and emending the text proposed by B.P. Grenfell and A.S. Hunt, The Oxyrhynchus Papyri, xiii (London: Egypt Exploration Fund, 1919) 98–127, while accepting their identification of the author as Ephorus (an interpretation challenged by T.W. Africa, ‘Ephorus and Oxyrhynchus Papyrus 1610’, AJPh, 83 (1962), 86–89). E. Schwartz, in his authoritative Pauly-Wissowa article on Diodorus (see n. 27 above) had stated firmly that Diodorus had taken over all the facts of his narrative of fifth- and fourthcentury Greek history from Ephorus’ lost history, making small changes only in the style. C. Rubincam, ‘New and Old Approaches to Diodoros: Can they be Reconciled?’, in L.I. Hau, A. Meeus and B. Sheridan (eds), Diodoros of Sicily: Historiographical Theory and Practice in the Bibliotheke (Leuven: Peeters, 2018), 13–44, at 26–29.

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student, in a library equipped with all the books he needs, to which he can refer whenever he wishes. I think it much more probable that he worked more in the manner described by Cassius Dio (72.23.5), namely by compiling notes on various sources, which had then to be worked up into his own continuous narrative without direct reference to the books. This reconstruction leaves much more space for reliance on memory, so that it is easier to understand how such minor differences could have arisen between two Dead Sea descriptions based on the same sources. The comparison of these two passages certainly provides a warning against the assumption that any historian will necessarily reproduce qualifiers as well as numbers from his source. Case #6 is a passage of Thucydides frequently criticised by modern scholars for apparent inaccuracies in the measurements of DISTANCE: his description of the island of Sphacteria (Thuc. 4.8.6). A literal translation would read as follows: For the island called Sphacteria, stretching out parallel and lying close to the harbour, makes it safe and its entrances narrow—on the one side, near the fortification of the Athenians and Pylos [i.e., at the north end] a passage for two ships {Card, MIL2}, and on the other, towards the rest of the mainland [i.e., at the south end], [a passage] for eight {Card, MIL2, Qalt} or nine [ships] {Card, MIL2, Qalt}; it is entirely wooded and without paths because of being uninhabited, and in length about 15 stades approximately [περὶ πέντε καὶ δέκα σταδίους μάλιστα] {Card, DIST, Q1[x2]}. Scholars have pointed out that the measurements in the text for both the width of the south channel and the length of the island are significantly too small— an observation that would tarnish Thucydides’ reputation as an exceptionally careful and accurate historian.31 Solutions that save Thucydides’ credit have generally involved emending the text.32 Coding the numbers (as in the literal translation above) draws attention to two elements that had previously attracted insufficient attention: two of the three measurements are qualified (the width of the south channel by an alternative number [Qalt], the length of the island by two approximating expressions [Q1 x2]); in addition, the channel

31

32

See C. Rubincam, ‘The Topography of Pylos and Sphakteria and Thucydides’ Measurements of Distance’, JHS, 121 (2001), 77–90 for the full details of the topographical problem, as well as the solution summarised here. Proposed emendations of the text are discussed and criticised in Rubincam, ‘The Topography’, 78–79.

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widths are given in highly unconventional units (ship-space; i.e., the amount of sea-room required for a trireme’s passage). The statistics provided by the database show how unusual all these elements are: this is the only occurrence among Thucydides’ 46 DISTANCE measurements of double approximating qualification (περὶ…μάλιστα), as well as the qualifying use of περί itself; and there is only one partial parallel for the unconventional unit used for the channel measurements.33 The most likely explanation for these unusual features is that these were visual estimates made for practical purposes by someone serving with the Athenian naval force,34 whom the historian interrogated when the expedition returned to Athens. Thus, there is no need to emend the text or castigate Thucydides for the inaccuracy. These case studies highlight some of the most striking new insights obtainable from the systematic coding of every numeric expression in the texts of these six Greek historiographic works. The more holistic approach to the interpretation of numbers facilitated by both the coding process and the resulting database not only sheds new light on some old issues (the originality of Thucydides’ chronological system; discrepancies of detail between Thucydides and Diodorus; some questionable topographic measurements in Thucydides; and the compositional methods of Diodorus) but also focusses much needed attention on how translators deal with numbers—an issue that should be of significant concern to all students of ancient history. Both the process of applying the coding system to the numbers and the database generated by this means bring modern readers closer to the thinking of the ancient author and the experience of his original readers, thus helping us to avoid the unthinking assumption that a numeric statement that strikes us as odd is most likely due to incompetence on the part of the historian or carelessness by a copyist. 33

34

The nearest parallel for this unconventional measurement is Thucydides’ description of the thickness of the Themistoclean wall around Athens and Peiraieus (1.93.5) as wide enough to accommodate ‘two wagons bringing up stones from opposite directions’. Since the Athenians kept the Peloponnesian garrison imprisoned on the island for a considerable time by deploying triremes to row around it, what mattered to them was how much sea room was available at each end of it. The argument made here (set out in full in the article cited above, n. 31) assumed that Thucydides’ topographical description was based only on Athenian sources. L.J. Samons ii has argued more recently (‘Thucydides’ Sources and the Spartan Plan at Pylos’, Hesperia, 75/4 (2006), 525–540) that the historian might have been further misled by a conversation with some deliberately misleading Spartan informants, whom he interrogated during his exile from Athens (after Brasidas’ capture of Amphipolis in 424 bce). That is certainly an interesting possibility. While we are agreed, however, that Thucydides did not visit Pylos, I would argue that Samons’ description of that ‘failure’ as ‘disturbing’ suggests the application to the ancient historian of a somewhat anachronistic standard of research methodology.

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Appendix 1 table 5.1

Coding System for Numbers in Historical Narrative Types of number

Name

Description

Examples

Card[inals]

Members of series ‘one, two, three etc.’ Members of series ‘first, second, third etc.’ Compound words whose formation includes a numeric element or numeric expression other than cardinals or ordinals Words denoting fractional parts Indications of specific quantity without an explicit number word

10, ten, 55, fifty-five, 520, five hundred and twenty 10th, tenth, 25th, twenty-fifth, 100th, one hundredth ‘of-three-stories’, ‘of-thirty-years’, three-times, four-sided, ‘a-groupof-ten-ships’

Ord[inals] [Numeric] Comp[ounds]

Frac[tions] Non-explicit numbers = Ø

table 5.2

one-tenth, half, 1/20 a-year, a-ship, ‘the same number of ships [sc., as just mentioned]’

Subject categories to which numbers may refer

Name

Description

Examples

TIME DIST[ance]

Numbers used to count units of time Numbers used to count units of linear measurement Numbers used to count other units of measurement Numbers of fighting forces or pieces of military equipment: Individuals or groups killed, wounded, or captured in war; items of military equipment destroyed or captured Individuals mentioned as part of a fighting force (other than those in MIL1 and MIL3)

years, months, days, hours feet, plethra, stades; miles, kilometers, meters medimnoi; pounds, kilos

SIZE MIL[itary]: MIL1

MIL2

hoplites, cavalry, elephants, ships, siege engines

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numeric communication in the greek historians table 5.2

Subject categories to which numbers may refer (cont.)

Name

Description

MIL3

POP[ulation] POP1 POP2

POP3

MON[ey] MISC[ellaneous]

table 5.3

(a)

Military units

(b)

Military formations

(c) Holders of military office Numbers of non-military individuals & groups: Non-military individuals or groups killed, wounded, or captured Individuals mentioned as part of the non-military population (other than those in POP1 and POP3) (a) Divisions of civilian population (b) Individuals holding elected, appointed, or hereditary office in government or administration Amounts of money or valuations in terms of money Any other number

Examples brigades, regiments, fleets, ship squadrons, armies a hoplite force drawn up ‘toa-depth-of eight’ generals, captains, trierarchs individuals in non-military roles

households, tribes, villages, cities, peoples, nations members of a city board, committee, or embassy kings, priests, gods, angels

obols, drachmae, talents

Qualification of numbers

Type

Description

Examples

Approximating = Q1

Expressions attached to a number indicating that the number specified is in the neighbourhood of the precise number Expressions attached to a number implicitly comparing the number mentioned with another number either lower or higher Two numbers mentioned as alternatives

about, around, approximately, up to, more or less, on average

two or three, twenty and thirty

Expressions that emphasise size of number

only, even

Comparative = Q2 Alternative = Qalt Emphatic = Qemph

more than, less than, not less than, at least, above, under

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Τέσσαρα μὲν γὰρ καὶ δέκα ἔτη {Card, TIME} ἐνέμειναν αἱ τριακοντούτεις σπονδαὶ {Comp, TIME} αἳ ἐγένοντο μετ’ Εὐβοίας ἅλωσιν· τῷ δὲ πέμπτῳ καὶ δεκάτῳ ἔτει {Ord, TIME}, ἐπὶ Χρυσίδος ἐν Ἄργει τότε πεντήκοντα δυοῖν δέοντα ἔτη ἱερωμένης {Card, TIME} καὶ Αἰνησίου ἐφόρου ἐν Σπάρτῃ καὶ Πυθοδώρου ἔτι δύο μῆνας ἄρχοντος Ἀθηναίοις {Card, TIME}, μετὰ τὴν ἐν Ποτειδαίᾳ μάχην μηνὶ ἕκτῳ {Ord, TIME} καὶ ἅμα ἦρι ἀρχομένῳ Θηβαίων ἄνδρες ὀλίγῳ πλείους τριακοσίων {Card, MIL2, Q2} (ἡγοῦντο δὲ αὐτῶν βοιωταρχοῦντες Πυθάγγελός τε ὁ Φυλείδου καὶ Διέμπορος ὁ Ὀνητορίδου) ἐσῆλθον περὶ πρῶτον ὕπνον {Ord, TIME, Q1} ξὺν ὅπλοις ἐς Πλάταιαν τῆς Βοιωτίας οὖσαν Ἀθηναίων ξυμμαχίδα. The thirty-years peace that was made after the capture of Euboea lasted fourteen years. In the fifteenth year, when Chrysis had served forty-eight years as priestess at Argos and Ainesias was ephor at Sparta and Pythodorus was archon for the Athenians with two months still to go, in the sixth month after the battle at Potidaea, just as spring was beginning, a few more than 300 men of Thebes, led by the Boeotarchs Pythangelus son of Phylides and Diemporus son of Onetorides, entered around first sleep with weapons into Plataea, a city of Boeotia, which was an ally of the Athenians. 3

Case Studies

Case #1. Thuc. 8.68.4. An unusual TIME statement elucidated by means of the database: χαλεπὸν γὰρ ἦν τὸν Ἀθηναίων δῆμον ἐπ’ ἔτει ἑκατοστῷ μάλιστα {Ord, TIME, Q1} ἐπειδὴ οἱ τύραννοι κατελύθησαν ἐλευθερίας παῦσαι, καὶ οὐ μόνον μὴ ὑπήκοον ὄντα, ἀλλὰ καὶ ὑπὲρ ἥμισυ τοῦ χρόνου τούτου αὐτὸν ἄλλων ἄρχειν εἰωθότα. [interval between institution of Athenian democracy (512/1bce) and its (temporary) abolition (411/0bce)] Cases ##2 and 3. Problems involving conversion of measurement units and qualification: Case #2. Xen. Anab. 5.6.9: ‘ἥξετε ἐπὶ τοὺς ποταμούς, πρῶτον {Ord, MISC} μὲν τὸν Θερμώδοντα, εὖρος τριῶν πλέθρων {Card, DIST}, ὃν χαλεπὸν οἶμαι διαβαίνειν ἄλλως τε καὶ πολεμίων πολλῶν ἔμπροσθεν ὄντων, πολλῶν δὲ ὄπισθεν ἑπομένων· δεύτερον {Ord, MISC} δὲ Ἶριν, τρίπλεθρον {Comp, DIST} ὡσαύτως· τρίτον {Ord, MISC} δὲ Ἅλυν, οὐ μεῖον δυοῖν σταδίοιν {Card, DIST, Q2}, ὃν οὐκ ἂν δύναισθε ἄνευ πλοίων διαβῆναι· πλοῖα δὲ τίς ἔσται ὁ παρέχων ὡς δ’ αὔτως καὶ ὁ Παρθένιος ἄβατος· ἐφ’ ὃν ἔλθοιτε ἄν, εἰ τὸν Ἅλυν διαβαίητε’.

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Case #3. Hdt. 8.4.2–5.3: Γνόντες δέ σφεας οἱ Εὐβοέες ταῦτα βουλευομένους ἐδέοντο Εὐρυβιάδεω προσμεῖναι χρόνον ὀλίγον, ἔστ’ ἂν αὐτοὶ τέκνα τε καὶ τοὺς οἰκέτας ὑπεκθέωνται. Ὡς δ’ οὐκ ἔπειθον, μεταβάντες τὸν Ἀθηναίων στρατηγὸν πείθουσι Θεμιστοκλέα ἐπὶ μισθῷ τριήκοντα ταλάντοισι {Card, MON}, ἐπ’ ᾧ τε καταμείναντες πρὸ τῆς Εὐβοίης ποιήσονται τὴν ναυμαχίην. [5.1] Ὁ δὲ Θεμιστοκλέης τοὺς Ἕλληνας ἐπισχεῖν ὧδε ποιέει. Εὐρυβιάδῃ τούτων τῶν χρημάτων μεταδιδοῖ πέντε τάλαντα {Card, MON} ὡς παρ’ ἑωυτοῦ δῆθεν διδούς. Ὡς δέ οἱ οὗτος ἀνεπέπειστο (Ἀδείμαντος γὰρ ὁ Ὠκύτου ὁ Κορίνθιος στρατηγὸς τῶν λοιπῶν ἤσπαιρε μοῦνος, φάμενος ἀποπλεύσεσθαί τε ἀπὸ τοῦ Ἀρτεμισίου καὶ οὐ παραμενέειν), πρὸς δὴ τοῦτον εἶπε ὁ Θεμιστοκλέης ἐπομόσας· [2] ‘Οὐ σύ γε ἡμέας ἀπολείψεις, ἐπεί τοι ἐγὼ μέζω δῶρα δώσω ἢ βασιλεὺς ἄν τοι ὁ Μήδων πέμψειε ἀπολιπόντι τοὺς συμμάχους.’ Ταῦτά τε ἅμα ἠγόρευε καὶ πέμπει ἐπὶ τὴν νέα τὴν Ἀδειμάντου τάλαντα ἀργυρίου τρία {Card, MON}. [3] Οὗτοί τε δὴ πληγέντες δώροισι ἀναπεπεισμένοι ἦσαν καὶ τοῖσι Εὐβοεῦσι ἐκεχάριστο, αὐτός τε ὁ Θεμιστοκλέης ἐκέρδηνε. Ἐλάνθανε δὲ τὰ λοιπὰ {Ø, MON} ἔχων, ἀλλ’ ἠπιστέατο οἱ μεταλαβόντες τούτων τῶν χρημάτων ἐκ τῶν Ἀθηνέων ἐλθεῖν ἐπὶ τῷ λόγῳ τούτῳ [τὰ χρήματα]. Count of MONEY numbers: 3x Card, 1x Ø Rawlinson 1942: … [the Euboeans] gave [to Themistocles] a bribe of thirty talents {Card, MON} …. He [Themistocles] made over to Eurybiades five talents {Card, MON} out of the thirty paid him {Card, MON} … he sent on board the ship of Adeimantus a present of three talents of silver {Card, MON} … . He likewise made his own gain on the occasion; for he kept the rest of the money {Ø, MON}, and no one knew of it. Count of MONEY numbers: 4x Card; 1x Ø de Sélincourt 1952: … [the Euboeans] went to Themistocles … and by a bribe of some £7,000 {Card, MON, Q1} induced him so to arrange matters that the Greek fleet should stay and fight on the coast of Euboea. … Themistocles … pass[ed] on to Eurybiades … a sixth part {Frac, MON} of the sum he had received {Ø, MON} from the Euboeans … . He sent aboard Ademantus’ ship three talents of silver {Card, MON}—some £700 {Card, MON, Q1} … . Themistocles, too, made something out of the transaction, for he kept the rest of the money {Ø, MON} himself. Count of MONEY numbers: 3x Card (2x Q1); 1x Frac; 2x Ø Grote 1918: … the Euboeans sent their envoy Pelagon to Themistoklês with the offer of thirty talents {Card, MON} … Themistoklês employed the money adroitly and successfully, giving five talents {Card, MON} to Eurybiadês, with large presents besides to

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the other leading chiefs. … [Adeimantus’] alarm was silenced, if not tranquillised, by a present of three talents {Card, MON}. Count of MONEY numbers: 3x Card Green 1970: One of their [the Euboeans’] number, Pelagon, was entrusted with a massive sum of money—thirty talents {Card, MON}, or over £7,000 {Card, MON, Q2}—and privately offered it all to the Athenian commander if he would, somehow keep the Greek fleet in situ, and stave off the threat of a Persian invasion. … Five talents {Card, MON} … sufficed to bring Eurybiades round; and most of the other commanders then fell into line as well. … Three talents {Card, MON}, delivered aboard Adeimantus’s flagship, duly secured his cooperation … [There follows an anecdote from Plut. Them. 7.5 of how Themistocles bribed another Athenian captain, Architeles, with one talent {Card, MON}.] … There remained a net surplus of twenty-one talents {Card, MON}, … [which] he now blandly pocketed … himself. Count of MONEY numbers: 6x Card (1x Q2) Case #4. Two versions of the casualties from the Athenian plague illuminated by POPULATION statistics from the database. (a) Thuc. 3.87.1–3. Τοῦ δ’ ἐπιγιγνομένου χειμῶνος ἡ νόσος τὸ δεύτερον ἐπέπεσε τοῖς Ἀθηναίοις, ἐκλιποῦσα μὲν οὐδένα χρόνον τὸ παντάπασιν, ἐγένετο δέ τις ὅμως διοκωχή. [2] παρέμεινε δὲ τὸ μὲν ὕστερον οὐκ ἔλασσον ἐνιαυτοῦ {Ø, TIME, Q2}, τὸ δὲ πρότερον καὶ δύο ἔτη {Card, TIME, Qemph}, ὥστε Ἀθηναίους γε μὴ εἶναι ὅτι μᾶλλον τούτου ἐπίεσε καὶ ἐκάκωσε τὴν δύναμιν· [3] τετρακοσίων γὰρ ὁπλιτῶν καὶ τετρακισχιλίων οὐκ ἐλάσσους ἀπέθανον ἐκ τῶν τάξεων {Card, MIL1, Q2} καὶ τριακοσίων ἱππέων… {Card, MIL1, Q2}, τοῦ δὲ ἄλλου ὄχλου ἀνεξεύρετος ἀριθμός (b) Diod. Sic. 12.58.2. οὕτω γὰρ ὑπὸ τῆς νόσου διετέθησαν, ὥστε τῶν στρατιωτῶν ἀποβαλεῖν πεζοὺς μὲν ὑπὲρ τοὺς τετρακισχιλίους {Card, MIL1, Q2}, ἱππεῖς δὲ τετρακοσίους {Card, MIL1}, τῶν δ’ ἄλλων ἐλευθέρων τε καὶ δούλων ὑπὲρ τοὺς μυρίους {Card, MIL1, Q2}. Case #5. New light on Diodorus’ methods. (a) Diod. Sic. 11.60.6. Κίμων δὲ πυνθανόμενος τὸν στόλον τῶν Περσῶν διατρίβειν περὶ τὴν Κύπρον, καὶ πλεύσας ἐπὶ τοὺς βαρβάρους, ἐναυμάχησε διακοσίαις καὶ πεντήκοντα ναυσὶ {Card, MIL2} πρὸς τριακοσίας καὶ τετταράκοντα {Card, MIL2}. γενομένου δ’ ἀγῶνος ἰσχυροῦ καὶ τῶν στόλων ἀμφοτέρων {Comp, MIL3} λαμπρῶς ἀγωνιζομένων, τὸ τελευταῖον

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ἐνίκων οἱ Ἀθηναῖοι, καὶ πολλὰς μὲν τῶν ἐναντίων ναῦς διέφθειραν, πλείους δὲ τῶν ἑκατὸν {Card, MIL1, Q2} σὺν αὐτοῖς τοῖς ἀνδράσιν εἷλον. (b) POxy 1610, fragments 9+10+53 (from Ephorus’ History (?)): [Text as restored in Grenfell and Hunt 1919; with minor emendation proposed in Rubincam 1976] [… Κιμων πυνθανομενος το]ν τ[ων Περσων στολο]ν περι [την Κυπρον συ]ντετα[χθαι διακοσια]αις πεν[τηκοντα π]ρ[ος]τρια[κοσιας κ]αι τετταρ[ακοντα] ναυμαχη[σ]ας δε πολυν χρονο[ν πολλας μεν των κ[ινδυνευουσων βαρβα[ρικων νεων διεφθε[ιρ]εν; εκατον {Card, MIL2} δαυτοις [α]νδρασιν [ε]ιλε ζωγρησας τ]ον π[ Case #6. Statistics on Thucydides’ use of qualifiers suggest a new solution to an old problem regarding his DISTANCE measurements. Thuc. 4.8.6. ἡ γὰρ νῆσος ἡ Σφακτηρία καλουμένη τόν τε λιμένα παρατείνουσα καὶ ἐγγὺς ἐπικειμένη ἐχυρὸν ποιεῖ καὶ τοὺς ἔσπλους στενούς, τῇ μὲν δυοῖν νεοῖν διάπλουν {Card, MIL2} κατὰ τὸ τείχισμα τῶν Ἀθηναίων καὶ τὴν Πύλον, τῇ δὲ πρὸς τὴν ἄλλην ἤπειρον ὀκτὼ {Card, MIL2, Qalt} ἢ ἐννέα {Card, MIL2, Qalt}· ὑλώδης τε καὶ ἀτριβὴς πᾶσα ὑπ’ ἐρημίας ἦν καὶ μέγεθος περὶ πέντε καὶ δέκα σταδίους μάλιστα {Card, DIST, Q1[x2]}.

Bibliography Secondary Sources Africa, T.W., ‘Ephorus and Oxyrhynchus Papyrus 1610’, AJPh, 83 (1962), 86–89. Feeney, D., Caesar’s Calendar: Ancient Time and the Beginnings of History (Berkeley: University of California Press, 2007). Gomme, A.W., A. Andrewes, and K.J. Dover, A Historical Commentary on Thucydides, 5 vols. (Oxford: Clarendon Press, 1945–1981). Green, P., Xerxes at Salamis (New York: Praeger, 1970). Grenfell, B. P and A.S. Hunt, The Oxyrhynchus Papyri, xiii (London: Egypt Exploration Fund, 1919). Grote, G., A History of Greece, v (1846, London: J.M. Dent & Co, 1918). Hornblower, S., A Commentary on Thucydides, 3 vols. (Oxford: Oxford University Press, 1991–2008). Meritt, B.D., ‘Greek Inscriptions (14–27)’, Hesperia, 8/1 (1939), 48–82. Rubincam, C., ‘A Note on Oxyrhynchus Papyrus 1610’, Phoenix, 30 (1976), 357–366. Rubincam, C., ‘The Topography of Pylos and Sphakteria and Thucydides’ Measurements of Distance’, JHS, 121 (2001), 77–90.

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Rubincam, C., ‘Herodotus and His Descendants’, HSPh, 104 (2008), 93–138. Rubincam, C., ‘“In the 100th Year Approximately …” (Thuc. 8.68.4): Qualified Ordinal Statements of Time in Greek Historical Narrative’, Mouseion, 8 (2008), 319–332. Rubincam, C., ‘Thucydides 8.68.4: A Highly Unusual Numeric Statement’, AHB, 22 (2008), 83–87. Rubincam, C., ‘The Numeric Practice of the Hellenica Oxyrhynchia’, Mouseion, 9 (2009), 303–329. Rubincam, C., ‘New and Old Approaches to Diodoros: Can They be Reconciled?’, in L.I. Hau, A. Meeus, and B. Sheridan (eds), Diodoros of Sicily: Historiographical Theory and Practice in the Bibliotheke (Leuven: Peeters, 2018), 13–44. Rubincam, C., (forthcoming), Quantifying Mentalities: The Use of Numbers by Ancient Greek Historians (Ann Arbor: University of Michigan Press, 2021). Samons, L.J., ii, ‘Thucydides’ Sources and the Spartan Plan at Pylos’, Hesperia, 75/4 (2006), 525–540. Schwartz, E., ‘Diodorus 38’, in G. Wissowa (ed.), RE, v. 1: Demogenes–Donatianus (Munich: J.B. Metzler, 1903). Sealey, R., A History of the Greek City States ca. 700–338 b.c. (Berkeley: University of California Press, 1976). Shaw, P.-J., Discrepancies in Olympiad Dating and Chronological Problems of Archaic Peloponnesian History (Historia Einzelschriften, 166; Stuttgart: Franz Steiner, 2003). Smart, J.D., ‘Thucydides and Hellanicus’, in I.S. Moxon, J.D. Smart, and A.J. Woodman (eds), Past Perspectives: Studies in Greek and Roman Historical Writing (Cambridge: Cambridge University Press, 1986), 19–35.

Translations Crawley, R., The Complete Writings of Thucydides: The Peloponnesian War (New York: Random House, 1951). Landmann, G.P., Thukydides, Geschichte des Peloponnesischen Krieges (Munich: Artemis Verlag, 1991). Rawlinson, G., Herodotus, The Persian Wars (New York: Random House, 1942). Sélincourt, A. de, Herodotus, The Histories (Harmondsworth: Penguin Books, 1961). Smith, C.F., Thucydides, 4 vols. (Loeb Classical Library; London: William Heinemann, 1965–1969). Warner, R., Thucydides, History of the Peloponnesian War (Harmondsworth: Penguin Books, 1959). Warner, R., Xenophon, The Persian Expedition (rev. repr., Harmondsworth: Penguin Books, 1972).

part 2 Communicating with Numbers

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chapter 6

Creative Accounting? Strategies of Enumeration in Epinician Texts Daniel Mahendra Jan Sicka

The 2016 Rio Olympics captured the attention of a diverse array of people, thrilling devotees of elite sport but also not disappointing those with a professional interest in biochemical enhancement or political corruption. There is perhaps one group, however, that the Olympics gratify beyond all others, namely the lovers of records and statistics. When Wayde van Niekerk won gold in the men’s 400m, both the glory of his achievement, and the spectators’ pleasure in viewing it, were heightened by the knowledge that he had cut 15 one-hundredths of a second off the world record set by Michael Johnson 17 years before. Michael Phelps’ nickname of ‘The GOAT’ (i.e. ‘The Greatest Of All Time’) is justified by his tally of 23 gold, 3 silver, and 2 bronze Olympic medals, almost twice as many victories as the ancient record of 12 individual victories accumulated by the runner Leonidas of Rhodes between 164 and 152 bce.1 The meticulous cataloguing of sporting data in the present day by a range of official organisations and public media, all instantly accessible online, endows that data with an impression of objectivity, permanence, and public ownership. However, that impression can be misleading—just as today the perennial caveat remains that one cannot believe everything one reads on the internet, so too in antiquity the ostensibly-neutral commemoration of athletic triumphs was liable to diverge to some degree from a purely objective presentation of fact. This chapter examines and categorises instances of the various techniques of departure from neutrality that occur across the twin media of epinician odes and inscriptions, especially as they relate to the numerical accounting of victories. An assessment is also made of the factors that may explain the appearance of these phenomena, whether in a particular text or across the genre as a whole.

1 Paus. 6.13.3–4.

© Daniel Mahendra Jan Sicka, 2022 | doi:10.1163/9789004467224_008

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The inception of a genre of epinician songs dedicated to a specific honorand may be dated to the period 550–520 bce; its practitioners included Simonides and Ibycus.2 In the epigraphic medium, the earliest known athletic victory inscriptions are dated c. 600–550bce, and it appears that inscriptions of that type are unlikely to have predated the sixth century.3 These victory commemorations in song and stone (or bronze) co-existed in a dynamic relationship of competition, appropriation, and interdependence.4 That inscribed texts appeared first is significant in granting them a degree of independence from poetic memorialisation, although the two are interconnected from an early date. On the one hand, commemorative inscriptions are not only chronologically but conceptually prior to victory-song, since they established the essential criteria by which an athletic record was assessed and thus formed the basis upon which a poet might begin to elaborate; in particular, the naming conventions, the prestigious sites and events, and above all the tally of victories. The simplest form of inscription is the list, and IG i3 893.1–7 provides a concise example:5 Καλλίας Δ[ιδυμίο]. νῖκαι·̣ Ὀλυ[μ]πίασι Πύθια ⋮ δίς Ἴσθμια ⋮ πεντάκις Νέμεια ⋮ τετράκις Παναθέναια με⟨γά⟩λ[α] 2 See further R. Thomas, ‘Fame, Memorial, and Choral Poetry: the Origins of Epinician Poetry— An Historical Study’, in S. Hornblower and C. Morgan (eds), Pindar’s Poetry, Patrons and Festivals (Oxford: Oxford University Press, 2007), 141–166; R. Rawles, ‘Early Epinician: Ibycus and Simonides’, in P. Agócs, C. Carey, and R. Rawles (eds), Reading the Victory Ode (Cambridge: Cambridge University Press, 2012), 3–27. For our purposes, generic brief victory-chants such as those attested at Hom. Od.9.1–4 are excluded from consideration. 3 P. Christesen, Olympic Victor Lists and Ancient Greek History (Cambridge: Cambridge University Press, 2007), 143–144. 4 Cf. J. Day, Archaic Greek Epigram and Dedication: Representation and Reperformance (Cambridge: Cambridge University Press, 2010); ‘Epigraphic Literacy in Fifth-Century Epinician and its Audiences’, in P. Liddel and P. Low (eds), Inscriptions and their Uses in Greek and Latin Literature (Oxford: Oxford University Press, 2013), 217–230; D. Fearn, ‘Kleos v Stone? Lyric Poetry and Contexts for Memorialization’, in P. Liddel and P. Low (eds), Inscriptions and their Uses in Greek and Latin Literature (Oxford: Oxford University Press, 2013), 231–253. 5 Athenian Acropolis, fifth century.

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Callias, son of Didymias. Victories: Olympia. Pythia: twice. Isthmia: five times. Nemea: four times. Great Panathenaea. Its elegant brevity communicates the data in a pellucid manner that needs no artistry to be impressive. As here, epigraphic texts regularly list the four major Games (plus the Panathenaea, if relevant) in decreasing order of prestige,6 a convention followed by the epinician poets except where there is a special reason to deviate.7 Examples such as the above account for a large proportion of the epigraphic corpus. In both written and oral commemoration, however, an imperative was often felt to elevate the victory data by means of various devices ranging from the refined to the unsubtle.

2

Numerical Ambiguity

A starting-point for the analysis of this phenomenon is provided by Thomas Cole’s 1987 article on Pindar’s arithmetic.8 His contribution concerns Pindar’s treatment of the victory-catalogue, a key feature of the epinician genre that enumerates the agonistic achievements of the victor and his family at the Panhellenic and local level. Cole observed that Pindar frequently encodes a degree of linguistic ambiguity in his catalogues of multiple victories, thereby creating the impression of a greater tally of wins than was in fact the case, while ‘always [being] careful not to commit himself … to any statement which is untrue’ (566). The ambiguities he identifies primarily involve the use of numbers in such a way as to potentially confuse totals and subtotals, cardinals and distributives. Let us examine a few illustrative examples. The first, Isthm. 6.58–61, is a passage cataloguing the pancratium victories of the Aeginetan brothers Phylacidas and Pytheas, as well as of their uncle Euthymenes:

6 Christesen, Olympic Victor Lists, 139–140. 7 See below on Bacchyl. 12 and Isthm. 2. 8 T. Cole, ‘1 + 1 = 3: Studies in Pindar’s Arithmetic’, AJPh, 108/4 (1987), 553–568.

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τὸν Ἀργείων τρόπον εἰρήσεταί που κἀν βραχίστοις. ἄραντο γὰρ νίκας ἀπὸ παγκρατίου τρεῖς ἀπ’ Ἰσθμοῦ, τὰς δ’ ἀπ’ εὐφύλλου Νεμέας. In the Argive manner it will be stated, I think, in the briefest terms. For in the pancratium they carried off three victories from the Isthmus, and others from leafy Nemea. The translation given here is that of the Loeb edition of William Race,9 which reflects the implication of the word-order that there were ‘three from the Isthmus, and the rest from leafy Nemea’, i.e. at least five victories. However, punctuating after τρεῖς allows the rendering ‘three in total, namely one from the Isthmus, and the rest from Nemea’. This is in keeping with the evidence of Pindar’s earlier Nem. 5 and Bacchyl. 13, which attest to one Nemean victory for Pytheas (Nem. 5.4–5; Bacchyl. 13.67–68, 190–191), and one Nemean for Euthymenes (Nem. 5.44), while Isthm. 6 specifies a single Isthmian for Phylacidas (vv. 5–7). In this case, Pindar constructs the catalogue in a manner that does not deny the informed and diligent listener a more minimalist interpretation of the figures, but which certainly provides a slanted perspective to anyone else. The laudator’s insistence on the need for proverbial Argive brevity10 itself insinuates the higher total by implying that there are too many victories to list individually, elegantly echoing the phrase with which the preceding myth had been broken off a few lines earlier: ἐμοὶ δὲ μακρὸν πάσας ἀναγήσασθ’ ἀρετάς (v. 56: ‘But it would take me too long to recount all their deeds’). At the same time, however, we cannot say that Pindar does not give us a sort of knowing wink—brevity, after all, is not the same as accuracy. This is not to deny, of course, that Pindar could be crystal-clear when he wished, as the contrast between the following two passages demonstrates. First, Nem. 10.25–28: ἐκράτησε δὲ καί ποθ’ Ἕλλανα στρατὸν Πυθῶνι, τύχᾳ τε μολὼν καὶ τὸν Ἰσθμοῖ καὶ Νεμέᾳ στέφανον, Μοίσαισί τ’ ἔδωκ’ ἀρόσαι, 9

10

W.H. Race, Pindar: Olympian Odes, Pythian Odes (Cambridge, MA: Harvard University Press, 1997); Pindar: Nemean Odes, Isthmian Odes, Fragments (Cambridge, MA: Harvard University Press, 1997). Cf. Soph. fr. 462.2 (Radt).

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τρὶς μὲν ἐν πόντοιο πύλαισι λαχών, τρὶς δὲ καὶ σεμνοῖς δαπέδοις ἐν Ἀδραστείῳ νόμῳ. Before that, he also defeated the Hellenic host at Pytho, and coming with fortune won the Isthmian and Nemean crown, and gave the Muses work for their plough, thrice winning crowns at the gates to the sea, and thrice on the hallowed grounds at Adrastus’ institution. Here, the victory-sites are clearly distinguished from one another by both name and by periphrasis, and the number of wins at each is clearly stated. By contrast, at Pyth. 9.90–91 we find a single numeral adverb indicating the number of wins at multiple victory-sites which are connected by τε … τε: Αἰγίνᾳ τε γὰρ | φαμὶ Νίσου τ’ ἐν λόφῳ τρὶς δὴ πόλιν τάνδ’ εὐκλέιξας (‘For both at Aegina and at the hill of Nisus a full three times, I avow, you glorified this city’). It is worth noting that the ambiguous formulation is once again accompanied by an explicit avowal reliant on the laudator’s authority (as at Isthm. 6.59, εἰρήσεταί), an important point to which we shall return later. Having surveyed some of Pindar’s polysemous approaches to epinician counting, we can begin to expand the discussion further. Cole had examined the odes of Bacchylides, as well as the agonistic epigrams collected by Ebert, and concluded that there was ‘nothing comparable’ to be found in them, i.e. that the phenomenon of arithmetic ambiguity was essentially a Pindaric idiosyncrasy.11 Although I agree that Pindar is its most frequent practitioner, it will be shown that other epinician media can play with numbers in a manner similar to that which we have seen so far. Bacchyl. 12.36–42, for the Nemean wrestling victory of Teisias of Aegina, assigns a total of 30 victories to either the victor’s polis or his family (the text is too fragmentary to determine which), and distributes them amongst the four Panhellenic Games with a studied lack of specificity: σὺν τρι[άκο]ντ’ ἀγλααῖσιν νίκαις [ἐκ]ωμάσθησαν οἱ μὲν [Πυθόϊ, οἱ δ’ ἐν Πέλοπος ζαθέας | νάσου π[ι]τυώδεϊ δείραι, οἱ δὲ φοινικοστερόπα τεμένει

11

Cole, ‘1 + 1 = 3’, 565 n. 16; J. Ebert, Griechische Epigramme auf Sieger an gymnischen und hippischen Agonen (Berlin: Akademie-Verlag, 1972).

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Ζηνὸς Νεμεαίου· …] ταύτας καὶ ἐπ’ ἀργυροδίνα for thirty glorious victories were they celebrated, some as winners in Pytho, others at the pine-rich neck of Pelops’ holy island, others in the precinct of Nemean Zeus of the red lightning … also on the banks of the silver-eddying [Alpheus] … The order in which the Games are listed also deviates from epigraphic convention, as noted above. Whereas the Pythian, Isthmian, and Nemean victories are listed in the standard order, the Olympics produce a surprising climax: this combination of ostentatious vagueness and unusual catalogue-order obscures the reality that the vast majority of the victories were won at lesser Games, with only one or a few at Olympia.12 Bacchyl. 4.4–6 at first sight appears straightforward in characterising Hieron of Syracuse’s 470 chariot-victory as his third Pythian victory of that type: τρίτον γὰρ παρ’ ὀμφα]λὸν ὑψιδείρου χθονὸς Πυθιόνικ[ος ἀείδε]ται ὠκυπόδ[ων ἀρετᾶι] σὺν ἵππων. For it is for the third time that by the navel of the high-ridged land he is hymned as a Pythian victor, thanks to the excellence of his swift-footed horses. However, the plural ἵππων occludes the fact that Hieron’s earlier Pythian wins in 482 and 478 had been merely single-horse (kelēs) victories. His touchiness on the subject can be inferred from the fact that in Pindar’s Olympian 1, celebrating Hieron’s Olympic kelēs-victory of 476 (the Games at which Theron of Acragas had taken the superior chariot-victory), every equestrian reference in

12

Nemean and Isthmian wins predominate amongst Aeginetans’ recorded victories and concomitant odes (cf. C. Morgan, ‘Debating Patronage: the Cases of Argos and Corinth’, in S. Hornblower and C. Morgan (eds), Pindar’s Poetry, Patrons, and Festivals From Archaic Greece to the Roman Empire (Oxford: Oxford University Press, 2007), 225–226). Their Olympic wins were sparse: the celebration of the laudandus’ grandfather as Aegina’s first Olympic victor at Nem. 6.15–22 camouflages both how long it took since the Games’ founding to achieve that first win in 544 and how rarely it had been successfully imitated since.

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that ode’s myth is to plural horses or chariots (Ol. 1.41, 77, 87), and it ends with an explicit wish that Hieron win an ‘even-sweeter’ chariot-victory (vv. 108–111). As discussed above in relation to epigraphy, the list may to some extent be considered the Ur-type of victory commemoration. However, even amongst our earliest athletic inscriptions are found examples composed in hexameters and elegiacs, presumably by versifiers competent in those traditional forms, if not in the greater complexities of lyric.13 Extant sixth- and fifth-century inscriptions of that type appear not to avail themselves of arithmetic ambiguity, but examples do appear in the fourth century, continuing the poetic artifices of lyric epinician after it had expired as a living form. One such case is F.Delphes iii.1, 507 p. 332 1–6:14 [πλ]είστοις δὴ Σικυῶνα πάτραν, [Σω]σιστράτου υἱέ, Σώστρατε, καλλίστοις τ’ ἠγλάισας στεφάνοις· [ν]ικῶ[ν] πανκράτιον τρὶς Ὀλύμπια, δὶς δ’ ἐνὶ Πυθοῖ, δώδεκα δ’ ἐξ Ἰσθμοῦ [καὶ Νεμ]έας στεφάνους· [τ]οὺς δ’ ἄλλους ἄπο[ρον στεφά]νους [ἐπι]δεῖξαι ἀριθμόν, [πα]ύσας δ’ ἀντι[πάλους πάν]τα [ἐ]κρατεις ἀμαχεί. With the greatest number of crowns, Sostratus, son of Sosistratus, and with the fairest, did you glorify your homeland of Sicyon, winning pancratium crowns thrice at Olympia, twice at Pytho, and twelve of them from the Isthmus and Nemea. It is impossible to set out the number of the others, and in stopping your opponents you conquered every man without a fight. Sostratus, nicknamed ‘Acrochersites’ for his technique of bending his rivals’ fingers, possessed a superb number of wins, and the epigram is intended to maximise their effect from its opening words: the programmatic [πλ]είστοις δὴ. V. 4 demonstrates a classic Pindaric ambiguity of the sort we have seen earlier; δώδεκα δ’ ἐξ Ἰσθμοῦ [καὶ Νεμ]έας στεφάνους can just as easily mean ‘12 13

14

e.g. SEG xviii 140 (600–550); SEG xi 290 (c. 550). That is not to say that the lyric poets could not profit from reading inscriptions. Pindar’s spectacular τρισολυμπιονίκαν (‘tripleOlympic-victor’), which occupies the entire first verse of his Ol. 13 for Xenophon of Corinth (464 bce), is isometric with the final two-and-a-half feet of a hexameter, such as the feet concluding the first line of the 472 bce dedication under the statue of the triple Olympic victor Euthymus of Locri (i.Olympia 144): τρὶς Ὀλύμπι ἐνίκων—a remarkable coincidence, if Pindar did not in fact harvest it for his neologism. Delphi, c. 356 bce.

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from the Isthmus and 12 from Nemea’ as it can ‘a total of 12 from both’.15 The paradigm of countlessness in v. 5 recalls the motif’s characteristic appearance in Pindaric epinician.16 In part, the device performs a structural function similar to that found at Nem. 2.23, where it brings to a conclusion both the victorycatalogue (by avoiding a long account of minor wins) and the entire poem. As in epinician, this metatextual break enacts the medium’s inability to process the immensity of its message, conveying the sublimity of both the victor’s achievement and the laudator’s efforts in expressing it.17 Here, a further effect is achieved: its juxtaposition with the arithmetic ambiguity in v. 4 subconsciously directs the reader’s mind towards preferring the higher total.

3

Qualitative Enhancement

The tally of victories alone was not necessarily all that mattered in victory celebration. In seeking to persuade others that one record of victories was greater than another, commemorative texts could also emphasise the special qualities that distinguished it. These qualitative evaluations occur across epinician media, and frequently centre on the uniqueness of the overall accomplishment, such as the competitor being the first or only one to achieve a feat,18 or on the flawless execution of a particular event, as in the case of those wrestlers who triumphed without falling, suffering a waistlock, or sitting out a round,19 or athletes whose effortless superiority led them to win ἀκονιτί.20 For our purposes, we are most interested in examples in which evaluations of this sort appear to conceal a numerical deficiency. Bacchylides 5.42–45, composed for the same victory as Pindar’s Olympian 1, concludes a list of Hieron’s Olympic and Pythian wins (vv. 38–41) by stressing a unique aspect of the manner in which the present victory was won:

15 16 17 18

19 20

Paus. 6.4.2 explicitly clarifies that it records a combined total. Cf. Ol. 13.43–46, 112–115, Nem. 2.23, 10.45–46, Isthm. 1.60–63; Anth. Pal. 13.14.5 ([Simon.]). Cf. J.I. Porter, The Sublime in Antiquity (Cambridge: Cambridge University Press, 2016), 350–360. Cf. M.N. Tod, ‘Greek Record-Keeping and Record-Breaking’, CQ, 43 (1949), 105–112; D.C. Young, ‘First with the Most: Greek Athletic Records and “Specialization”’, Nikephoros, 9 (1996), 175–197. S. Brunet, ‘Winning the Olympics without Taking a Fall, Getting Caught in a Waistlock, or Sitting out a Round’, ZPE, 172 (2010), 115–124. ‘Dustless’, i.e. ‘unopposed’, cf. H. Wankel, Demosthenes: Rede für Ktesiphon über den Kranz, ii (Heidelberg: Carl Winter, 1976), 934–935; N.B. Crowther, ‘Victories Without Competition in the Greek Games’, Nikephoros, 14 (2001), 29–44.

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γᾶι δ’ ἐπισκήπτων πιφαύσκω· οὔπω νιν ὑπὸ προτέ[ρω]ν ἵππων ἐν ἀγῶνι κατέχρανεν κόνις πρὸς τέλος ὀρνύμενον· And resting my hand on the earth do I proclaim: never yet in the contest was Pherenicus befouled by the dust of the horses ahead of him as he raced to the finish. The laudator interposes his authority for a special quality of the way the victory was achieved, precisely in order to compensate for the fact that the victory itself had not raised Hieron’s count in the race he had most desired to win that year, namely the tethrippon. Bacchyl. 8.17–25 has the laudator deliver an identical oath as he avoids giving the specific number of the victor’s Pythian, Nemean, and Isthmian wins, but instead attests the uniquely brief period in which they were won: Πυθῶνά τε μηλοθύταν ὑμνέων Νεμέαν τε καὶ Ἰσθ[μ]όν· γᾶι δ’ ἐπισκήπτων χέρα κομπάσομαι· σὺν ἀλαθείαι δὲ πᾶν λάμπει χρέος· οὔτις ἀνθρώπων κ[αθ’ Ἕλλανας σὺν ἅλικι χρόνω[ι παῖς ἐὼν ἀνήρ τε π[λεῦνας ἐδέξατο νίκας. … as I sing in praise of Pytho where sheep are sacrificed and of Nemea and of the Isthmus. And resting my hand on the earth I shall make my vaunt—for with the help of the truth any matter shines forth: no one among the Greeks, has in equal time,21 as boy or as man, won more victories.

21

Alternatively, ‘amongst the same age-class’.

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One may speculate that in this case it is the (relative) inadequacy of the tally that inclines Bacchylides to lay extraordinary focus on its concentration. This time the oath is followed by a gnome that underscores the point by expressly laying claim to the force of truth. The proviso in v. 23 thus does a great deal of work—without it, the vaunt would have sought to insert its subject amongst the greatest champions of all time.

4

Counterfactuals

An unusual tactic, the epinician examples of which are restricted to lyric,22 insinuates that a higher tally of wins would have been won had some circumstance beyond the victor’s control not deprived him of his due. Returning to Bacchylides 4, the verses previously cited were not the end of the need to soothe Hieron’s sense of having suffered a competitive injustice. Verses 11–13 employ a counterfactual to indicate that Hieron had in some way been cheated of a fourth victory: ἔτι δὲ τέ]τρατον, εἴ τις ὀρθὰ θεὸς] εἷλκε Δίκας τάλαν[τα, Δεινομένεός κ’ ἐγερα[ίρ]ομεν υἱόν. And for yet a fourth time, if some god had held level the balance of Justice, would we be honouring Deinomenes’ son. This striking technique for claiming a ‘missing’ victory, found everywhere from the school playground to the courts of tyrants, enjoyed a notable epinician vogue: Bacchylides employs it again at 11.24–29: φάσω δὲ καὶ ἐν ζαθέοις ἁγνοῦ Πέλοπος δαπέδοις Ἀλφεὸν πάρα καλλιρόαν, δίκας κέλευθον εἰ μή τις ἀπέτραπεν ὀρθᾶς, παγξένωι χαίταν ἐλαίαι γλαυκᾶι στεφανωσάμενον. I shall assert that also in the sacred grounds of holy Pelops, 22

But cf. Hom. Il. 23.382–397 for its epic archetype.

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by the fair-flowing Alpheus, if someone had not twisted the course of upright justice, he would have garlanded his hair with the grey olive open for all comers. Thus a failure of justice is once again avowed, and imputed (in vv. 34–36) to either a god or to mortals’ warped judgement: these concepts are elegantly united in the ode’s myth, which tells how Hera’s mental derangement of the daughters of Proetus was cured through Artemis’ intervention, just as the victory granted to the honorand by Artemis qua patron goddess of Metapontum soothes his loss at Olympia, which was caused by either divine intervention or human irrationality. Pindar likewise embraces the counterfactual. At Nem. 11.22–28, the laudator swears—in a manner that is surely only inadvertently humorous—that it was only Aristagoras’ overprotective parents that prevented him from becoming an Olympic champion instead of a minor local politician: ἐλπίδες δ’ ὀκνηρότεραι γονέων παιδὸς βίαν ἔσχον ἐν Πυθῶνι πειρᾶσθαι καὶ Ὀλυμπίᾳ ἀέθλων. ναὶ μὰ γὰρ ὅρκον, ἐμὰν δόξαν παρὰ Κασταλίᾳ καὶ παρ’ εὐδένδρῳ μολὼν ὄχθῳ Κρόνου κάλλιον ἂν δηριώντων ἐνόστησ’ ἀντιπάλων, πενταετηρίδ’ ἑορτὰν Ἡρακλέος τέθμιον κωμάσαις. But his parents’ overly-cautious expectations kept their mighty son from competing in the games at Pytho and Olympia. For I swear that, in my judgement, had he gone, then at Castalia and at the well-wooded hill of Cronus, he would have won a nobler homecoming than his wrestling opponents, having celebrated the quadrennial festival ordained by Heracles with a victory-revel. Our final counterfactual example, Nem. 6.57b–63, follows the laudator’s proclamation that Alcimidas of Aegina has won his family’s twenty-fifth victory with the commiseration that an unlucky draw alone denied him (at least) one Olympic triumph: ἄγγελος ἔβαν, πέμπτον ἐπὶ εἴκοσι τοῦτο γαρύων

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εὖχος ἀγώνων ἄπο, τοὺς ἐνέποισιν ἱερούς, Ἀλκιμίδα, σέ γ’ ἐπαρκέσαι κλειτᾷ γενεᾷ: δύο μὲν Κρονίου πὰρ τεμένει, παῖ, σέ τ’ ἐνόσφισε καὶ Πουλυτιμίδαν κλᾶρος προπετὴς ἄνθε’ Ὀλυμπιάδος. I have come as a messenger, proclaiming that this is the twenty-fifth vaunt won from the games that men call sacred, which you, Alcimidas, have provided for your glorious family—but two Olympic crowns by the Cronian’s precinct were stolen both from you, my boy, and from Polytimidas, by a random lot. It is amusing to note that even as the laudator makes confident assertions about these hypothetical Olympic victories, he carefully inserts an ambiguity concerning their distribution—were the kinsmen deprived of two victories in total, or of two each? The emphatic position of δύο first in its sentence, combined with the intimate personal address to Alcimidas (παῖ), creates the impression that the two were associated with him, even before we then take Polytimidas into account. The potential multiplication of a non-existent entity is a bold amplificatory gambit indeed. At the same time, by enfolding Alcimidas’ win into those of his family, the laudator does not imply that he had personally provided all 25 of the wins, but he does create the space for future listeners to assume that Alcimidas had been responsible for more than one of them.

5

Attribution

In a manner similar to that encountered in the previous example, Bacchyl. 2.6– 10 for Argeius of Ceos contextualises his single Isthmian victory within the 70 claimed for his home island: καλῶν δ’ ἀνέμνασεν, ὅσ’ ἐν κλε[εν]νῶι αὐχένι Ἰσθμοῦ ζαθέαν λιπόντες Εὐξαντίδα νᾶσον ἐπεδείξαμεν ἑβδομήκοντα[σὺ]ν στεφάνοισιν.

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And he reminded us of all the fine achievements we had displayed at the famous neck of the Isthmus when we left the sacred island of Euxantius and won seventy crowns. Whilst it is unlikely that any listener would have misattributed the full tally to Argeius, the communalising ‘we’ (which carries particular force given the poet and victor’s shared Cean origin) simultaneously piles Argeius’ recent win onto his island’s running grand total and makes that total his own. Argeius also appears in the fourth-century inscription IG xii 5 608 which records the achievements of a selection of Cean victors, ranging from the sixth to the fourth centuries, who may have been included on the basis of their shared membership of a particular deme or phratry.23 Its existence both attests to a longestablished Cean interest in record-keeping, and provides a counterpoint to Bacchylides’ approach in his ode: whereas the poet draws in the achievements of the entire polis to augment and be augmented by the victor, the inscription creates a tightly-circumscribed circle of glory confined to a select membership. F.Delphes iii 1, 510 is especially ambitious in its manipulation of attribution.24 The text has been substantially reinterpreted on the basis of a new fragment published in 1992 in an article by Jean Bousquet:25 εἰκόνες αἵδ’ ἵππ[ων] αἳ Πύθια [καὶ Νεμ]έαι δίς, Ἰσθμοῖ τε στεφ[άνους] Καλλία[ι] ἀμφέθεσαν. ͂ Σκηπτροφόρ[ō δ’ ἄθλον π]ατρὸς πατρώϊον ἐχο[ν]. These are the images of the horses which twice at the Pythia and Nemea, and at the Isthmus, garlanded Callias with crowns. But the sceptre-bearing father’s prize26 I already possessed from my fathers.

23 24 25 26

D. Schmidt, ‘An Unusual Victory List from Keos: IG xii, 5, 608 and the Dating of Bakchylides’, JHS, 119 (1999), 81–82. Delphi, mid-fourth century bce. ‘Deux épigrammes grecques’, BCH, 116 (1992), 585–606. We may note in passing the numerical ambiguity caused by the position of δίς. i.e. an Olympic victory.

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This Callias has been identified as Callias iii (c. 450–367 bce), son of Hipponicus, who led the embassy to Sparta in 371bce. Xenophon (Xen. Hell. 6.3.3– 4) introduces him as οἷος μηδὲν ἧττον ἥδεσθαι ὑφ’ αὑτοῦ ἢ ὑπ’ ἄλλων ἐπαινούμενος (‘a man who took no less delight in being praised by himself than by others’), and gives us the first sentence of his speech in a form strikingly similar to that of our inscription, at Xen. Hell. 6.3.4: ὦ ἄνδρες Λακεδαιμόνιοι, τὴν μὲν προξενίαν ὑμῶν οὐκ ἐγὼ ἔχω μόνος, ἀλλὰ καὶ πατρὸς πατὴρ πατρῴαν ἔχων παρεδίδου τῷ γένει. O men of Sparta, I am not the only one of my family to possess the status of proxenos with you, but my father’s father took possession of it from his father and passed it on to his descendants. Both of these details from the Hellenica make him an excellent fit with the inscription, and his grandfather Callias is elsewhere reported to have been an Olympic chariot-victor. This remarkable use of a relative’s victory to round out a set of Panhellenic wins finds an echo in Pindar’s Isthmian 2 for the Emmenid Xenocrates of Acragas. A victory-catalogue forms the core of the ode (vv. 12–32), and its treatment implies an ingenious solution to an unusual obstacle to the victor’s praise. The dilemma here was that Xenocrates’ three victories were in Games inferior to his brother Theron’s Olympic win: to omit that Olympic victory would be to unacceptably diminish the family’s glory, but to follow Pindar’s almostinvariable practice of organising Panhellenic victories in descending order of prestige (i.e. Olympic, Pythian, Isthmian, Nemean, Panathenaic)27 would be to render Xenocrates’ wins anticlimactic. Pindar’s solution is to abandon his typical ordering by listing Xenocrates’ three victories first: his Isthmian (his most recent); his Pythian (his first); then his Panathenaic. The Panathenaic’s position is explained by the fact that the same charioteer, Nicomachus, drove both in it and in Theron’s Olympic victory, to which Nicomachus forms a segue and in respect of which he is characterised as almost a surrogate-victor himself, subtly displacing Theron. Finally, the Olympic victory is attributed explicitly to both brothers: ἵν’ ἀθανάτοις Αἰνησιδάμου | παῖδες ἐν τιμαῖς ἔμιχθεν (vv. 28–29: ‘There with immortal honours were Aenesidamus’ | sons commingled’). Xenocrates’ catalogue is thus completed by appropriating an Olympic victory that was not his own.

27

See p. 153 on IG i3 893.1–7.

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The foregoing discussion of F.Delphes iii 1, 510 and Isthmian 2 demonstrates the importance, in oral and epigraphic media alike, of the victory’s attribution: in these cases, the skilful manipulation of attribution produces as it were a quantum effect, allowing a single win to exist in two places at once and thus be counted twice over.

6

Misrepresentation

As noted above, victory commemoration appears to have eschewed the direct falsification of records, preferring the subtler techniques of augmentation already adumbrated. There are, however, instances in which we are able to detect the former. In the Olympics of 416, Alcibiades entered seven teams in the four-horse chariot race, a spectacular display of wealth and status. This feat prompted several sources to record superlative evaluations of the sort encountered in several passages of epinician lyric, both for the number of teams entered, and for the quality of the victory: (1) Eur. fr. 755 PMG σὲ δ’ ἄγαμαι, ὦ Κλεινίου παῖ· καλὸν ἁ νίκα, κάλλιστον δ’, ὃ μήτις ἄλλος Ἑλλάνων, ἅρματι πρῶτα δραμεῖν καὶ δεύτερα καὶ τρίτα⟨τα⟩, βῆναί τ’ ἀπονητὶ Διὸς στεφθέντ’ ἐλαίαι κάρυκι βοὰν παραδοῦναι. I wonder at you, o son of Cleinias. Fair is victory, but fairest of all is what no other Greek has achieved, to run first and second and third with the chariot, to arrive without toil, and, wreathed with the olive of Zeus, to provide a theme for the herald’s proclamation. (2) Thuc. 6.16.2 ἅρματα μὲν ἑπτὰ καθῆκα, ὅσα οὐδείς πω ἰδιώτης πρότερον, ἐνίκησα δὲ καὶ δεύτερος καὶ τέταρτος ἐγενόμην. I entered seven chariots, more than any private citizen ever had before, and I won the victory and came second and fourth.

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(3) Isoc. 16.34 οὐ μόνον τοὺς ἀνταγωνιστὰς ἀλλὰ καὶ τοὺς πώποτε νικήσαντας ὑπερεβάλετο. ζεύγη γὰρ καθῆκε τοσαῦτα μὲν τὸν ἀριθμὸν ὅσοις οὐδ’ αἱ μέγισται τῶν πόλεων ἠγωνίσαντο, τοιαῦτα δὲ τὴν ἀρετὴν ὥστε καὶ πρῶτος καὶ δεύτερος γενέσθαι καὶ τρίτος. He excelled not only his fellow competitors, but also all those who had ever been victors in the event. For he entered so large a number of chariots that not even the greatest cities had ever competed with so many, and they were of such quality that he not only came first, but second and third as well. There is a clear discrepancy between the version of the places won by Alcibiades’ teams presented by Euripides’ epinician fragment and Isocrates (first, second, third), and that placed in the speech of Alcibiades by Thucydides (first, second, fourth). How might this have arisen? The most logical answer is that the Euripidean version is a fabrication intended to raise the almost flawless result recorded by Thucydides to perfection.28 Isocrates’ speech, which was written for Alcibiades’ son and is directly concerned with his actions in the 416 Olympics, would hardly have chosen to diverge from the more exalted version—he even dispenses with Thucydides’ qualification that Alcibiades entered more chariots than any other private citizen, and includes states in the comparison as well. This apparent willingness to directly alter the numerical facts of a victory in spite of contemporary knowledge of the actual result marks a contrast with Pindaric and Bacchylidean practice as discussed above (at least insofar as their figures can be verified). The phenomenon invites explanation: was it the poet or the patron who determined that the praise-song should twist the truth? If Euripides himself was its originator, we might assume that he acted out of a deliberate shattering of epinician convention rather than from unfamiliarity with the non-dramatic genres. On the other hand, if Alcibiades had personally insisted that the poet not allow historical reality to stand in the way of his glory (a view that we might be prepared to accept on the basis of his character), it is notable that Thucydides places the correct result in Alcibiades’ mouth—an elegant method of correcting the record, if that was his intention.

28

Cf. S. Hornblower, A Commentary on Thucydides, iii: Books 5.25–8.109 (Oxford: Oxford University Press, 2008), 343–345.

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The Daochus Monument at Delphi illustrates an even more explicit rectification. The inscription, when first dedicated in the 330s, claimed five Pythian victories for Agias, a fifth-century ancestor of Daochus. It was soon recut, however, to denote three victories instead, reflecting the public inscription of the catalogue of Pythian victors by Aristotle and Callisthenes upon stelae in Delphi.29 The implications for the ease with which inaccurate tallies could be publicly displayed in the absence of an authoritative contradiction are significant, although they are diminished by the fact that the exaggeration concerned a victor from the previous century, rather than a contemporary.

7

Interpretation

What conclusions can be drawn from this survey of epinician accountancy? In respect to the distribution of the techniques discussed above, the earliest elaborations of the unvarnished tally across all media appear to be the qualitative enhancements.30 Lyric seems to have led the way in numerical ambiguity and the manipulation of attribution, which later found epigraphic successors; counterfactuals were apparently a lyric idiosyncrasy. Cases of outright misrepresentation are difficult to detect due to the nature of our sources, but a late fifth-century case for lyric and a fourth-century instance for epigraphy are clear, with the potential for significantly earlier examples.31 The question of motivation is in one sense the simplest to construe—if an honorand’s glory is proportional to his achievements, there is a natural imperative for partisan commemorative media to magnify them as far as possible. We should, however, distinguish the private inscriptions that form the majority of the survivals from those institutional inscriptions set up by magistrates to list all the victors in a particular year of a particular Games; the latter’s interests lay in neutrality.32 Whilst it would be unwise to assume that the numerical tally was the only factor that mattered, the sustained and varied methods employed to massage it imply that for many Greeks it was in fact the pre-eminent datum.

29 30 31

32

Cf. Christesen, Olympic Victor Lists, 124. A sixth-century halter at Olympia (SEG. xi 1227, c. 550–525bce) displays the form ἀσσκονικτεί (for ἀκονιτί). P. Christesen, ‘Kings Playing Politics: the Heroization of Chionis of Sparta’, Historia, 59/1 (2010), 32–37, argues that when the Spartans inscribed a stele at Olympia for their seventhcentury compatriot Chionis c. 470 bce, they upgraded his tally of victories from 6 to 7 in order to match those of Astylus of Croton. See Christesen, Olympic Victor Lists, 126–128.

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Next comes the issue of the opportunities and contexts for the use of these techniques across the media. Those concerning inscriptions at Panhellenic sites cut both ways. On the one hand, perpetual display before an endless parade of knowledgeable and partisan viewers drawn from across the Hellenic world should have provided a check on excessive embellishment. Although few visitors would have had the voracious and critical eye of Pausanias,33 he must have had some predecessors. On the other, most of their detailed knowledge would have been subject to the restrictions of oral tradition (hence the greater ease of fabricating inscriptions concerning figures from previous centuries), and the lack of centralised records was a serious impediment to verification; comprehensive lists of Nemean and Isthmian victors were never compiled.34 This might explain why victories in those Games appear particularly susceptible to numerically-ambiguous treatment in the collected examples across all media. The texts of lyric epinician were almost never put on public display: the inscription of Ol. 7 in letters of gold upon the temple of Athene Lindos, recorded by a scholion to the ode, is the exception that proves the rule. Given that lack of exposure, why does lyric epinician (save the rogue contribution of Euripides) appear not to tolerate outright misrepresentation, but still permits the use of more subtle techniques? We may construct a hypothesis that the odes were composed in such a way as to capitalise on the expectation that the communicative situations in which their message was received would vary with time: if odes were regularly reperformed orally and disseminated through the circulation of written texts,35 these texts would ultimately find themselves received in times and places increasingly removed from the original performance context, and therefore also removed from those with direct knowledge of the raw data. Andrew Morrison usefully classifies these levels of performance as ‘primary’ (i.e. the premiere), ‘secondary’ (reperformance close in space, time, and / or milieu to the premiere), and ‘tertiary’ (more distant reperformances or

33 34 35

Cf. I.Z. Tzifopoulos, ‘Pausanias as a Steloskopas: An Epigraphical Commentary of Pausanias’ Eliakon A and B’, Ph.D thesis (Ohio State University, 1991), 1–23, 406–414. Christesen, Olympic Victor Lists, 108–109. See J. Irigoin, Histoire du texte de Pindare (Paris: C. Klincksieck, 1952), 1–28; B. Currie, ‘Reperformance Scenarios for Pindar’s Odes’, in C. Mackie (ed.), Oral Performance and Its Context (Mnemosyne Supplements, 248; Leiden: Brill, 2004), 49–69; T.K. Hubbard, ‘The Dissemination of Epinician Lyric: Pan-Hellenism, Reperformance, Written Texts’, in C. Mackie (ed.), Oral Performance, 71–93; H. Spelman, Pindar and the Poetics of Permanence (Oxford: Oxford University Press, 2018), 39–43.

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textual receptions).36 The lyric poets played a long game—wary of being seen to deceive the present, they carefully moulded their language in a manner that might beguile the future. Can we say more about how these techniques reflected contemporary attitudes? From our modern perspective, presenting the numerical facts of sporting data in an ambiguous or slanted way is quite an alien concept, and would be seen in professional and amateur contexts alike as an unacceptable form of tampering.37 Why might some Greeks of the Archaic and Classical periods have felt differently? I would suggest that part of the answer lies in their conception of what exactly they were doing when they lent their voices to support claims about others’ achievements. In his recent book, Boris Maslov revives a useful distinction made by Robert Stoddart between different types of witnessing in his discussion of veridiction in epinician.38 The first group, which is the only type known to Homer and Hesiod, are the gezogene Zeugen (‘summoned witnesses’). These attend a ritual or legal procedure and can later attest that it took place. The second, the Tatzeugen (‘witnesses of the deed’), represents the modern concept of an eyewitness,39 although it was not the sole mode of witnessing in Attic law, which retained traces of a third category. This final group, the Eideshelfer (‘oath helpers’ or ‘co-swearers’), are fundamentally distinct from the other two. They are partisan witnesses whose testimony is constituted not on a basis of fact, but on making ‘an affirmation of solidarity that is validated in justice by the religious force that the oath confers upon it’,40 in their capacity as a group of committed supporters of the person concerned. The Gortyn law code expresses the point succinctly: νικε͂ν δ’ ὄτερά κ’ οἰ π̣[λί]- | [ες ὀ]μόσοντι (‘The side that swears more oaths, wins’).41 Maslov observes that the epinician laudator often expresses a 36

37

38

39 40 41

A.D. Morrison, Performances and Audiences in Pindar’s Sicilian Victory Odes (BICS Supplement, 95; London: Institute of Classical Studies, 2007). For an overview of Pindaric performance contexts, see A. Neumann-Hartmann, Epinikien und ihr Aufführungsrahmen (Nikephoros Beihefte, 17; Hildesheim: Weidmann, 2009). For instance, when Manchester City won the 2017–2018 Premier League with 100 points, and their rivals Manchester United came second on 81, it would have been odd to have hailed the performance of the latter with the observation that Mancunians had achieved a spectacular total of 181. B. Maslov, Pindar and the Emergence of Literature (Cambridge: Cambridge University Press, 2015), 212–245; R. Stoddart, Pindar and Greek Family Law (New York: Garland, 1990), 29–49. Cf. [Dem.] 46.6. L. Gernet, The Anthropology of Ancient Greece (Baltimore: Johns Hopkins University Press, 1981), 224. I.Cret. iv 81, 15–16.

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close bond of solidarity between himself and the laudandus that may also affect the character of his oaths: ‘Viewed as an oath helper, the Pindaric martus is the one who confirms the victor’s achievement by an authoritative speech act, rather than one who testifies to the mere fact of the victory having taken place. As an affirmation of a social tie, the rhetoric of marturia is thus akin to the rhetoric of xenia or philia, ‘(guest-)friendship’, a familiar stance of the Pindaric speaker’.42 At the same time, if epinician was chorally-performed, that medium was ideally suited to the multivocal expression of a unanimous solidarity. I would argue that it is not coincidental that some version of this protojuridical modality of veridiction recurs in many cases where a form of creative accountancy is to be found. Amongst the passages discussed above, some of the most suggestive are the oaths supporting the unique qualities of the victory in Bacchyl. 5 and 8, and the oath and asseverations guaranteeing the counterfactuals at Nem. 11.22–28, Bacchyl. 11.24–29, and Nem. 6.57b–63, since in the latter group the laudator gives his word to underwrite something that by definition did not happen. Veridiction and oath combine to guarantee the most formidable victory-total in Pindar at Ol. 13.98–100: Ἰσθμοῖ τά τ’ ἐν Νεμέᾳ παύρῳ ἔπει θήσω φανέρ’ ἀθρό’, ἀλαθής τέ μοι ἔξορκος ἐπέσσεται ἑξηκοντάκι δὴ ἀμφοτέρωθεν ἁδύγλωσσος βοὰ κάρυκος ἐσλοῦ. Their Isthmian and Nemean victories I shall sum up in a brief word, and my true witness under oath shall be the noble herald’s sweet-tongued shout heard full sixty times from both those places. ἀμφοτέρωθεν looks emphatic, but pace W.S. Barrett,43 it need not mean anything more than that both the Isthmus and Nemea contributed to a total of 60. We may conclude with a truth-claim that opens a fifth-century victory inscription from Olympia, I.Olympia 170:44 [αὕτα πευθο]μένοις ἐτύμα φάτις, ἱππ̣ά̣δ̣α [νίκαν] [κείνᾳ καλλίστ]α̣ν̣ εἶναι Ὀλυμπιάδι, [ᾇ] Κ̣ώιων ὅ[σ]ι[ον δρομι]κοῦ Πισαῖον ἄεθλον πρῶτος ἑλὼν Μ̣έροπος νᾶ̣σ̣ον ἐσαγ̣άγ̣[ετο] 42 43 44

Maslov, Emergence of Literature, 216. W.S. Barrett, ‘The Oligaithidai and their Victories (Pindar, Olympian 13; SLG 339, 340)’, in R.D. Dawe et al. (eds), Dionysiaca (Cambridge: Gerald Duckworth & Co, 1978), 1–20. Olympia, c. 420 bce.

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τοῖο̣[ς], ὁποῖον̣ ὁ[ρ]ᾶις, Ξεινόμβροτο[ς· ἁ δέ νιν] Ἑλλὰς ἄφθιτον ἀείδε[ι] ̣ μνωμένα ἱπποσύνας. For those who seek to learn, this is the true report, that this was the finest equestrian victory in that Olympiad, in which Xeinobrotos, just as you see him, was the first of the Coans to win the sacred prize of Pisa’s racecourse and bring it to Merops’ island. And of him does Hellas sing deathlessly, remembering his horsemanship. It is striking to observe how seamlessly the inscription appropriates the lyric poets’ characteristic technique of veridiction to achieve one of their characteristic goals: stressing the unique qualities of a victory to make a solitary win seem like more than it is.

Conclusion To sum up, this audit of epinician accountancy has uncovered a range of irregularities and anomalies across the various authors and media, most of which produce the effect of exaggerating, fudging, or excusing the figures. Although the pervasiveness of this tendency outside lyric should not be overstated, it is there to be found in a number of cases. For the authors of these texts, when it came to ensuring the fate of their honorands’ reputations, the future was sometimes regarded less as the ultimate receptacle of a meticulous transcript of their deeds than as an opportunity to embellish them with ever-lessening fear of contradiction. The resources of poetic authority appealed to a truth orientated around the interests of the victor, not the fastidious beliefs in arithmetic exactitude that are curiously popular in the modern day.

Bibliography Barrett, W.S., ‘The Oligaithidai and their Victories (Pindar, Olympian 13; SLG 339, 340)’, in R.D. Dawe et al. (eds), Dionysiaca (Cambridge: Gerald Duckworth & Co, 1978), 1– 20. Bousquet, J., ‘Deux épigrammes grecques’, BCH, 116 (1992), 585–606. Brunet, S., ‘Winning the Olympics without Taking a Fall, Getting Caught in a Waistlock, or Sitting out a Round’, ZPE, 172 (2010), 115–124.

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Christesen, P., Olympic Victor Lists and Ancient Greek History (Cambridge: Cambridge University Press, 2007). Christesen, P., ‘Kings Playing Politics: the Heroization of Chionis of Sparta’, Historia, 59/1 (2010), 26–73. Cole, T., ‘1+1 = 3: Studies in Pindar’s Arithmetic’, AJPh, 108/4 (1987), 553–568. Crowther, N.B., ‘Victories Without Competition in the Greek Games’, Nikephoros, 14 (2001), 29–44. Currie, B., ‘Reperformance Scenarios for Pindar’s Odes’, in C. Mackie (ed.), Oral Performance and Its Context (Mnemosyne Supplements, 248; Leiden: Brill, 2004), 49–69. Day, J., Archaic Greek Epigram and Dedication: Representation and Reperformance (Cambridge: Cambridge University Press, 2010). Day, J., ‘Epigraphic Literacy in Fifth-Century Epinician and its Audiences’, in P. Liddel and P. Low (eds), Inscriptions and their Uses in Greek and Latin Literature (Oxford: Oxford University Press, 2013), 217–230. Ebert, J., Griechische Epigramme auf Sieger an gymnischen und hippischen Agonen (Berlin: Akademie-Verlag, 1972). Fearn, D., ‘Kleos v Stone? Lyric Poetry and Contexts for Memorialization’, in P. Liddel and P. Low (eds), Inscriptions and their Uses in Greek and Latin Literature (Oxford: Oxford University Press, 2013), 231–253. Gernet, L., The Anthropology of Ancient Greece (Baltimore: Johns Hopkins University Press, 1981). Hornblower, S., A Commentary on Thucydides, iii: Books 5.25–8.109 (Oxford: Oxford University Press, 2008). Hubbard, T.K., ‘The Dissemination of Epinician Lyric: Pan-Hellenism, Reperformance, Written Texts’, in C. Mackie (ed.), Oral Performance and Its Context (Mnemosyne Supplements, 248; Leiden: Brill, 2004), 71–93. Irigoin, J., Histoire du texte de Pindare (Paris: C. Klincksieck, 1952). Maslov, B., Pindar and the Emergence of Literature (Cambridge: Cambridge University Press, 2015). Morgan, C., ‘Debating Patronage: the Cases of Argos and Corinth’, in S. Hornblower and C. Morgan (eds), Pindar’s Poetry, Patrons, and Festivals From Archaic Greece to the Roman Empire (Oxford: Oxford University Press, 2007), 213–264. Morrison, A.D., Performances and Audiences in Pindar’s Sicilian Victory Odes (BICS Supplement, 95; London: Institute of Classical Studies, 2007). Neumann-Hartmann, A., Epinikien und ihr Aufführungsrahmen (Nikephoros Beihefte, 17; Hildesheim: Weidmann, 2009). Porter, J.I., The Sublime in Antiquity (Cambridge: Cambridge University Press, 2016). Race, W.H., Pindar: Olympian Odes, Pythian Odes (Cambridge, MA: Harvard University Press, 1997). Race, W.H., Pindar: Nemean Odes, Isthmian Odes, Fragments (Cambridge, MA: Harvard University Press, 1997).

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Rawles, R., ‘Early Epinician: Ibycus and Simonides’, in P. Agócs, C. Carey, and R. Rawles (eds), Reading the Victory Ode (Cambridge: Cambridge University Press, 2012), 3–27. Schmidt, D., ‘An Unusual Victory List from Keos: IG xii, 5, 608 and the Dating of Bakchylides’, JHS, 119 (1999), 67–85. Spelman, H., Pindar and the Poetics of Permanence (Oxford: Oxford University Press, 2018). Stoddart, R., Pindar and Greek Family Law (New York: Garland, 1990). Thomas, R., ‘Fame, Memorial, and Choral Poetry: the Origins of Epinician Poetry—An Historical Study’, in S. Hornblower and C. Morgan (eds), Pindar’s Poetry, Patrons and Festivals (Oxford: Oxford University Press, 2007), 141–166. Tod, M.N., ‘Greek Record-Keeping and Record-Breaking,’ CQ, 43 (1949), 105–112. Tzifopoulos, I.Z., ‘Pausanias as a Steloskopas: An Epigraphical Commentary of Pausanias’ Eliakon A and B’, Ph.D thesis (Ohio State University, 1991). Wankel, H., Demosthenes: Rede für Ktesiphon über den Kranz, ii (Heidelberg: Carl Winter, 1976). Young, D.C., ‘First with the Most: Greek Athletic Records and “Specialization”’, Nikephoros, 9 (1996), 175–197.

chapter 7

Hidden Judgments and Failing Figures: Nicias’ Number Rhetoric Tazuko Angela van Berkel

Not less than 100 triremes from Athens itself, and more from allies; a hoplite force embarked, Athenian and allied, in total not less than 5,000, and more if possible; a proportionate enlistment of the other units: archers from home and from Crete, and slingers; and other provisions … (Paraphrase of Thuc. 6.25.2)

∵ These are deterrent numbers. That is, they are intended as deterrent numbers, by the Athenian general Nicias: using steering qualifiers, exaggerated numbers and suggestive quantity markers, Nicias hopes to dampen the Athenians’ enthusiasm for what he thinks is a disastrous idea, an expedition to Sicily. But in the notorious dynamics of the Sicilian Debate, Nicias’ strategy backfires and the Athenian assembly ends up understanding Nicias’ inventory as a wish list. The assembly approves. This is one of only two ‘number speeches’ in Thucydides where we see a mass audience react to numbers produced by a politician. The other instance is Pericles’ inventory of Athenian resources in 2.13, where the sheer list of impressive numbers inspires courage and resolve (θάρσος) in the populace—exactly as Pericles had envisioned.1 In 6.25, by contrast, we see the assembly respond to Nicias’ numbers with the mad enthusiasm he had intended to curb—fatal

1 On this speech, see: L. Kallet-Marx, ‘Money Talks: Rhetor, Demos, and the Resources of the Athenian Empire’, in R. Osborne and Simon Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 227–251, esp. 233–239; E. Foster, Thucydides, Pericles, and Periclean Imperialism (Cambridge: Cambridge University Press, 2010), 151–182; T.A. van Berkel, ‘Pericles’ Rhetoric of Numbers’, in S. Papaioannou, A. Serafim and K. Demetriou (eds), The Ancient Art of Persuasion Across Genres and Topics (Leiden: Brill, 2019), 339–355.

© Tazuko Angela van Berkel, 2022 | doi:10.1163/9789004467224_009

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ἔρως for an impossible project. Intention and interpretation do not always align. Historiographical texts not only give us representations of political speeches, but also a glimpse of the ways in which speeches were received, interpreted and responded to. This also goes for ‘number speeches’, publicly performed pieces of quantitative reasoning, where the audience is expected to process quantitative information and integrate such information in their decision-making process. This must have been ubiquitous practice in Classical Athens: Attic oratory abounds in numbers.2 Yet ancient rhetorical theory is silent on the topic of numbers. Although the relevance and use of numbers may be implied in the questions of policy that symbouloi are expected to master,3 the fact that rhetorical theory does not identify quantitative reasoning as a rhetorical tool in its own right suggests an instrumentalist view of numbers according to which numbers are either plainly informative, neutral and rhetorically ‘inert’, or, alternatively, simply untrue and deceptive. Historiographic representations of number rhetoric reveal a more sophisticated view on the communicative effects of numbers and quantitative reasoning: Herodotus, Thucydides and Xenophon not only give us the ‘number speeches’, but often supply us with the intentions attributed to the speaker by the narrator, the immediate effect of the speech, the ways in which the speech is understood by its audience, its veracity and prognostic quality. Speaker and audience may attribute different meanings to the same number, as for instance Xerxes and Demaratus have different understandings of the staggering result of Xerxes’ census.4 Furthermore, narrator and character may differ in their interpretations, as has been argued by Matthew Christ: Herodotus pits the monumentalising aspirations behind his own surveying activities against the distorted versions of this activity by ‘inquisitive kings’, who also count and measure, but do so for purposes of self-aggrandisement.5 Does Thucydides create a similar dynamic between the descriptive uses of numbers in his authorial voice and quantitative reasoning on character level? In this chapter, I will argue that Nicias’ number speech is not an isolated rhetorical fluke, but part of what Thucydides sees as the problem of democratic uses of quantitative reasoning; such ‘democratic numeracy’ is, I argue, contrasted with Thucydides’ own critical numeracy.

2 See Sing in this volume. 3 e.g. Aristotle (Rhet. 1359b19–60b3) specifies ways and means, war and peace, defence of the country, imports and exports, and legislation. 4 Hdt. 7.102–103. 5 M.R. Christ, ‘Herodotean Kings and Historical Inquiry’, CA, 13/2 (1994), 167–202.

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In addition, I will argue that a proper understanding of number rhetoric in Thucydides (and elsewhere) also requires analysis of contexts where concrete numbers are lacking, but where discussion instead revolves around quantitative judgments (‘large’, ‘enough’, ‘less’, ‘too much’)—i.e. of a broader category of quantitative discourse. It is within this broader context that it becomes clear that in the Thucydidean universe, problems with quantitative reasoning occur not so much because people get the math wrong, but because they fail to weigh and include information about the meaning, reliability and certainty of quantitative information.6

1

Figured Figures

Nicias’ fatal numbers come in the coda to his second speech in the Sicilian Debate. Four days earlier, in a previous assembly meeting, the Athenians had agreed to honour the request of their Egestan allies and send off 60 ships to Sicily.7 Although the second assembly was convened to consider logistical issues, Nicias seizes the opportunity to question the very objective of the meeting, trying to persuade the Athenians not to send a military expedition to Sicily at all. The Sicilian Debate has an unusual structure:8 after the classical format of Nicias arguing against, and Alcibiades arguing in favour of the expedition, Thucydides has Nicias deliver a second speech. This presentation, pitting two speeches of Nicias against one, effective, speech by Alcibiades, underscores the part that Nicias, inadvertently, plays in the escalation of the expedition plans. It also dramatises Nicias’ change of strategy. Whereas his first speech is openly aimed at having the Athenians vote down the expedition, in his second speech the same Nicias, who earlier proudly claimed to have never said anything against his convictions (παρὰ γνήμην),9 engages in double speak: while 6 Cf. D. Kahneman, Thinking, Fast and Slow (New York: Farrar, Straus and Giroux, 2011), 118: ‘[W]e pay more attention to the content of messages than to information about their reliability’. 7 Thuc. 6.8.2. 8 On the debate, see in particular the analyses of L. Kallet, Money and the Corrosion of Power in Thucydides (Berkeley: University of California Press, 2001), 31–48; J. Ober, Political Dissent in Democratic Athens: Intellectual Critics of Popular Rule (Princeton: Princeton University Press, 1998), 104–118; H. Yunis, Taming Democracy: Models of Political Rhetoric in Classical Athens (Ithaca, NY: Cornell University Press, 1996); R. Vattuone, Logoi e storia in Tucidide: Contributo allo studio della spedizione ateniese in Sicilia del 415 a.C. (Bologna: Cooperativa libraria universitaria editrice Bologna, 1978); W. Kohl, Die Redetrias vor der sizilischen Expedition (Thukydides 6, 9–23) (Meisenheim am Glan: Anton Hain, 1977). 9 Thuc. 6.9.2.

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overtly conceding to the will of the Athenians, claiming to inform them of what is needed, Nicias exaggerates the costs of the expedition to such an extent that he, covertly, expects the Athenians to vote it down after all.10 In ancient rhetorical theory, this would be a ‘figured speech’, a speech with a covert purpose in addition to (or even contradicting) its overt intent—a mode of speaking with direct consequences for the way Nicias’ stipulative numbers are understood by the assembly.11 The speech achieved the opposite effect (καὶ τοὐναντίον περιέστη αὐτῷ): the majority of the Athenians, young and old alike, had fallen in love with the enterprise (ἔρως ἐνέπεσε τοῖς πᾶσιν ὁμοίως ἐκπλεῦσαι).12 It is in this context that an anonymous speaker comes forward: Finally one of the Athenians came forward, called on Nicias, and said that there must be no more excuses or delays: he should now declare in front of them all what forces he wanted the Athenians to vote him. [2] Nicias was reluctant to reply, saying (ὁ δὲ ἄκων μὲν εἶπεν ὅτι) that he would prefer to have time to discuss the matter with his fellow commanders: but as far as he could see at present, they would need to sail with at least a hundred triremes (τριήρεσι μὲν οὐκ ἔλασσον ἢ ἑκατὸν πλευστέα εἶναι) from Athens itself (of which an agreed number would be troop-transports), and send for others from their allies; the hoplite force embarked, Athenian and allied, should be a total of at least five thousand, and more if possible (ὁπλίταις δὲ τοῖς ξύμπασιν Ἀθηναίων καὶ τῶν ξυμμάχων πεντακισχιλίων μὲν οὐκ ἐλάσσοσιν, ἢν δέ τι δύνωνται, καὶ πλέοσιν); the generals would see to proportionate enlistment of the other units they would take with them—archers from home and from Crete, and slingers—and any other provisions they thought appropriate.13 thuc. 6.25.1–2

There are multiple qualifications that couch Nicias’ reaction: there is the narrator’s attribution of the speaker’s motives, that marks the reluctance behind the answer (ἄκων);14 there are Nicias’ own reservations, reported by the narrator

10 11 12 13 14

Thuc. 6.19.2. The double agenda is flagged again by the narrator in the capping phrase in 6.24.1. e.g. Demetr. Eloc. 287–298; Quint. Inst. 9.2.74; [Dion. Hal.] Rhet. c. 8–9. Thuc. 6.24.2–4. All translations are taken from M. Hammond, Thucydides. The Peloponnesian War (Oxford: Oxford University Press, 2009). Cf. ἀκούσιος in the preamble of his first speech (6.8.4).

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in indirect discourse, that mark his response as provisional and conjectural (he began by saying that he would rather discuss the subject matter with his fellow commanders, and so spoke just ‘as it now seemed to him’); and, last but not least, there are the expressions that qualify the numbers that Nicias proposes: ‘not less than’ (οὐκ ἔλασσον ἤ) one hundred triremes and ‘not less than—and if possible more than—5,000’ (πεντακισχιλίων μὲν οὐκ ἐλάσσοσιν, ἢν δέ τι δύνωνται, καὶ πλέοσιν) hoplites in total. The rub is in the number qualifiers, the ‘not less than’ locutions. Whose are they really? Number qualification presupposes agency, someone who is doing the qualifying. In the case of indirect discourse, as we have here, it is not immediately self-evident who is qualifying.15 Are the qualifiers part of Thucydides’ self-presentation or part of his characterisation of Nicias, and whose communicative intentions do they reflect? Indirect discourse does not necessarily imply that the numerical qualifier is authorial: indirect discourse plays a range of different roles in Thucydides’ work, depending on narrative mode and focalisation, and on the level of syntactic intrusion by the narrator and his narrative or argumentative presence.16 As for Nicias’ indirect speech in 6.25.2, the phrasing of his reported qualifications (‘he said that he would prefer … but as far as he could see at present …’) seem to faithfully reflect his style of speaking in his two previous speeches,17 and the use of ἤδη (implying the temporal orientation of the character) and of verbal adjectives (πλευστέα, μεταπεμπτέας) suggest embedded focalisation.18 15

16

17

18

A similar question can be raised about the qualifier οὐκ ἐλάσσονος ἤ in Thuc. 2.13.4 where Pericles’ number speech is reported in indirect discourse too. On the issue of perspective in this speech, see Foster, Thucydides, 167–173. The only other instance in the History (together with 2.13.4 and 6.25) of οὐκ ἐλάσσων as a number qualifier that might imply the perspective or stance of a character is 2.98.3, where λέγεται signals reported discourse. The other 14 instances occur in narrative discourse. On the hybrid nature of indirect speech, C. Scardino, ‘Indirect Discourse in Herodotus and Thucydides’, in E. Foster and D. Lateiner (eds), Thucydides and Herodotus (Oxford: Oxford University Press, 2007), 67–96, at 69, cf. S. Hornblower, A Commentary on Thucydides, iii: Books 5.25–28.109 (Oxford: Oxford University Press, 2008), 32–35 on the range of functions; P. Debnar, ‘Blurring the Boundaries of Speech: Thucydides and Indirect Discourse’, in A. Tsakmakis and M. Tamiolaki (eds), Thucydides Between History and Literature (Berlin: De Gruyter, 2013), 271–285. On Nicias’ speaking style, characterised by hypotaxis, concessives, abstractions and the potential optative, see D. Tompkins, ‘Stylistic Characterization in Thucydides’, YClS, 22 (1972), 181–214. On the colloquial origin and nature of verbal adjectives, see A. Willi, The Languages of Aristophanes: Aspects of Linguistic Variation in Classical Attic Greek (Oxford: Oxford University Press, 2003), 121. I have checked the 31 instances of the verbal adjective in Thucydides counted by P. Stork, Index of Verb Forms in Thucydides (Leiden: Brill, 2008), 227, and found

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The most natural reading is therefore to take the comparative qualifiers ‘not less than’ (οὐκ ἔλασσον/οὐκ ἐλάσσους ἤ) to reflect qualifications that Nicias made, expressing his perspective. The qualifiers are in line with his double language technique. On one level, they indicate a minimum limit (made even more explicit by the phrase ἢν δέ τι δύνωνται, καὶ πλέοσιν)—something that is, as Catherine Rubincam points out, precisely what one would expect from an expert when asked for advice,19 and in line with the caution for which Nicias was known. On an ulterior level, the comparative qualifiers serve to emphasise the sheer magnitude of the numbers: they ‘magnify by implication the size of the figures’20—consistent with Nicias’ covert purpose of dissuading the assembly from pursuing the expedition. The comparative qualifiers turn Nicias’ numbers into ‘figured figures’. Moreover, the litotic phrasing of the qualifier (‘not less than 100’ instead of its logical equivalent ‘100 or more’) marks a deviation from the audience’s preconceived estimate:21 the phrase explicitly evokes the rejected estimate (‘less than 100’, i.e. the 60 ships of the moderately sized expedition that the Athenians had originally agreed on), only to dramatically abandon it.22 All qualifications get lost in the reaction of the assembly. The Athenians buy Nicias’ figures without qualms:23 they ‘immediately decide by vote’ (ἐψηφίσαντο εὐθύς) to grant the generals absolute discretionary power to take whatever decisions on the size (περὶ πλήθους) and preparation of the force they judge best—an instantaneous response that stands in marked contrast with Nicias’ careful and qualified formulation. Later retellings of the Sicilian Debate omit mention of Nicias’ figured figures.24 Thucydides’ choice to include this incident tells us something about his interest in pitting intention against interpretation. In the following section, I will argue that Nicias’ qualified numbers and figured figures are woven into

19 20 21 22 23 24

that only one occurs in a ‘pure’ context of narration (6.50.5: πολεμητέα); eight instances occur in direct discourse, five in indirect discourse with verba dicendi, four in indirect discourse as content of a λόγος, γνώμη or ψήφισμα and 13 in attributions with propositional content (with verbs like νομίζειν or δοκεῖν). C. Rubincam, ‘Qualification of Numerals in Thucydides’, AJAH, 4 (1979), 77–95, esp. 83–84. Rubincam, ‘Qualification of Numerals’, 85. This effect is presumably stronger in litotic expressions than in simple comparative expressions. P. Pontier, ‘The Litotes of Thucydides’, in A. Tsakmakis and M. Tamiolaki (eds), Thucydides Between History and Literature (Berlin: De Gruyter, 2013), 353–370, at 355–356. Thuc. 6.8.1–2. See below pp. 181–182. Thuc 6.26. Neither Plutarch in Alc. 18 and Nic. 12, nor Diodorus Siculus (12.84) draws attention to Nicias’ role in raising the stakes of the expedition, his rhetorical ploy or his numerical estimates.

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the fabric of Thucydides’ larger thematic concerns about the rhetorical use of numbers and quantitative reasoning in the Sicilian Debate.

2

Democratic Numeracy

Thucydides’ account of the Sicilian Debate calls attention to the fraught relation between information and democratic decision-making. Owing to the authorial description of Sicily that precedes the presentation of the Sicilian Debate (the Sikelika),25 the reader is placed in an epistemologically privileged position compared to the members of the Athenian assembly who decided on the expedition: Most Athenians were ignorant (ἄπειροι) of the extent of the island (τοῦ μεγέθους τῆς νήσου) and the size of its population (τῶν ἐνοικούντων τοῦ πλήθους), both Greek and barbarian, and had no idea that they were undertaking a war almost as formidable as (οὐ πολλῷ τινὶ ὑποδεέστερον) their war against the Peloponnesians. To circumnavigate Sicily would take a merchant ship nearly eight days (οὐ πολλῷ τινὶ ἔλασσον ἢ ὀκτὼ ἡμερῶν), and yet this large island is separated from the mainland by ⟨about⟩ 20 stades (ἐν εἰκοσισταδίῳ μάλιστα μέτρῳ) of sea thuc. 6.1.1–2

The Athenians’ ignorance is of two kinds: they lack first-hand knowledge of the territory they are about to invade; and they do not have access to the historical hindsight that reveals that the Sicilian expedition is of a scale ‘not much short of’ (οὐ πολλῷ τινὶ ὑποδέεστερον) their war against the Peloponnesians. To demonstrate this lack of knowledge, Thucydides informs his reader of the real size of Sicily: ‘not much less than eight days’ (οὐ πολλῷ τινὶ ἔλασσον ἢ ὀκτὼ ἡμερῶν) of circumnavigation, separated from the mainland by ‘about 20 stades of the sea’ (ἐν εἰκοσισταδίῳ μάλιστα μέτρῳ τῆς θαλάσσης).26 This introductory chapter gives the reader a taste of the kind of information that is relevant for a military expedition. This information is markedly quantitative in nature: it is about size (μέγεθος), numerosity (πλῆθος) and the scale of their undertaking. The first issue, size, is addressed in numerical terms (with the rare comparative qualifier, οὐ πολλῷ τινι ἔλασσον ἤ),27 and a fur25 26 27

Thuc. 6.1.2–6.5. Hornblower, Commentary, iii, 261, on the implications of the units of measurement used. Only occurring once in combination with a numeral in Thucydides, see Rubincam, ‘Qualification of numerals’, 93.

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ther piece of tangentially relevant information, distance, expressed in numerical terms (with the approximating qualifier μάλιστα). Here too, as in Nicias’ speech, the comparative qualifier serves a magnifying function while at the same time producing the litotic effect of eliminating a preconception projected onto the Athenian assembly (‘they thought Sicily was only a tiny island, but it requires almost eight days of circumnavigation!’).28 But we see an additional effect in this authorial passage: numbers and qualifiers together create a ‘rhetoric of accuracy’,29 where the historian can perform his expertise by being self-conscious about accuracy and uncertainty. Thucydides uses numbers as a shorthand for proper expert knowledge. Thucydides’ emphatic use of numbers anticipates a contrast with the Sicilian Debate where numbers are conspicuously absent. This interpretation is in line with the analysis of the Sicilian Debate by Josiah Ober, who reads the debate as a sharpening of ‘the contrast (…) between the historical way of knowing the world and democratic knowledge’.30 Because of the agonistic nature of assembly debate, democratic modes of knowledge tend to be based on misinformation; historiographic knowledge is held against a higher standard of critical testing. This contrast, I argue, is also reflected in different modes of dealing with numbers and quantitative information. In the following sections we will see three epistemologically problematic cases of quantitative reasoning in democratic contexts of decision-making: a deceptively clear number (the Egestan sixty talents), the pseudo-scientific rejection of numerical information (Alcibiades) and the conspicuous absence of numbers in a military expert’s speech (Nicias). These episodes display a contrast with Thucydides’ authorial ‘critical numeracy’. 2.1 A Misinforming Number The first policy number comes up in the narration of the first assembly meeting,31 where the Egestans substantiate their earlier claim that they have ‘sufficient money’ (ἱκανὰ χρήματα) to fund the expedition:32 ‘60 talents of uncoined silver, for 60 ships a month’s pay’ (ἑξήκοντα τάλαντα ἀσήμου ἀργυρίου ὡς ἐς ἑξήκοντα ναῦς μηνὸς μισθόν).33 The elliptical narrative suggests that the Athenians 28 29 30 31 32

33

οὐ πολλῷ τινὶ ὑποδεέστερον, although without a numeral, has a similar effect. E. Greenwood, Thucydides and the Shaping of History (London: Duckworth, 2006), 121. Ober, Political Dissent, 106. Thuc. 6.8.1–3. Thuc. 6.6.2. The Athenian envoys were sent to Egesta to investigate if the promised money in the public treasuries and the temples existed (εἰ ὑπάρχει). On this passage, see Kallet, Money and the Corrosion of Power, 27–31. Thuc. 6.8.1.

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understand the 60 talents as a token of much more to come.34 This inference will turn out to be false, as the narrator flags with the phrase ‘attractive falsehoods’ (τά τε ἄλλα ἐπαγωγὰ καὶ οὐκ ἀληθῆ)—an authorial comment to be vindicated when the Athenian fleet lands in Rhegion and finds out that the sums of money, so visible and real, were not what they seemed to be: there is no funding beyond a mere 30 talents.35 The decision of the Athenians is presented as an unreflective response— an automatic conversion of 60 talents into 60 ships, of a visual presentation into a performative speech act (ἐψηφίσαντο). This effect is amplified by the neat numeric correspondence between the ἑξήκοντα τάλαντα ἀσήμου ἀργυρίου (sixty talents of uncoined silver) and ἐς ἑξήκοντα ναῦς μηνὸς μισθόν (for sixty ships a month’s pay)36 that effectively eclipses the modifiers ‘of uncoined silver’ and ‘a month’s pay’: the pressing question of what sort of funds there will be after the one month’s worth of funds dries up is not asked.37 With the high-pace presentation of events, Thucydides brings out the unreflective nature of the assembly’s reaction and its tendency to make decisions on the basis of false and incomplete information disguised as clean numbers. 2.2 Populistic Number Scepticism The deceptive potential of numbers is more explicit in Alcibiades’ speech. Although Alcibiades never provides numbers,38 he is the one who brings up the topic of size and quantity, when he tells the Athenians not to change their minds in the belief that their fleet will come up against some great power (ἐπὶ μεγάλην δύναμιν); Sicilian cities may be densely populated (πολυανδροῦσιν), but their populations are mixed rabbles liable to changes and new influxes.39 Thucydides’ reader, having read the Sikelika, knows that none of the claims that Alcibiades makes about Sicily are true and that the degree of confidence attached to such loose conjectures is unwarranted. Moreover, Thucydides’ reader may recognise battle speech tropes here: throughout the History, army commanders facing adverse odds in battle urge their forces to reinterpret the numerical superiority of their opponents, with tropes such as ‘numerical 34 35 36

37 38 39

Kallet, Money and the Corrosion of Power, 28. 6.46.1, cf. Kallet, Money and the Corrosion of Power, 28–31. In this locution ἐς is not a numeral qualifier but a preposition with μισθόν to disambiguate its syntactic relation to μηνός. See C. Rubincam, ‘Thucydides 1.71.1 and the Use of ἘΣ with Numerals’, CPh, 74/4 (1979), 327–337. The specific relevance of the ‘uncoined’ silver is persuasively discussed in Kallet, Money and the Corrosion of Power, 28–29. B. Jordan, ‘The Sicilian Expedition was a Potemkin Fleet’, CQ, 50 (2000), 63–79, at 72. Thuc. 6.17.2.

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advantage is a sign of weakness and self-doubt’,40 or ‘now is the time to forgo calculation, for the enemy’s numerosity will not bring them advantage on this terrain’.41 Good Thucydidean leaders exert control over the way in which quantitative information is interpreted by their audience. Alcibiades engages in a similar pre-emptive invalidation of any kind of quantitative information: Sicilian cities may be populous, but that is not the same as being ‘a great power’; it is the quality of the people that counts.42 The discrediting of information takes even more serious forms when he explicitly raises suspicion against the quality of self-reported military data: Moreover, their hoplite numbers are nothing like what they claim (ὅσοιπερ κομποῦνται), just as we have seen in the other Greek states too, whose own estimates of their numbers (ὅσους ἕκαστοι σφᾶς αὐτοὺς ἠρίθμουν) proved a gross exaggeration (μέγιστον δὴ … ἐψευσμένη), when in fact they could barely muster an adequate force for this war. thuc. 6.17.5–6

The Sicilians and the Peloponnesians are mere paper tigers. Harvey Yunis comments on this passage rather dismissively: ‘Even the number of their hoplites, a crucial point of fact, is deemed irrelevant, since, Alcibiades absurdly argues, all Greeks always exaggerate the number of their hoplites’.43 The argument is, however, less absurd than it may seem. For one thing, Alcibiades’ distrust in Sicilian troop numbers seems vindicated by a remark that Hermogenes makes in his speech at Syracuse that he is ‘quite sure that the reports would exaggerate our strength’.44 Moreover, by using the verb ἀριθμέω, Alcibiades draws attention to the implied agency behind counting, activating the trope of ‘self-serving counting’, the activity of the selfaggrandising Herodotean king. Alcibiades is, it seems, engaged in a form of

40 41 42

43 44

Thuc. 2.89.2 (Phormio before the battle at Naupactus). See van Berkel, ‘Pericles’ Rhetoric of Numbers’. Thuc. 4.10.1–4 (Demosthenes on the battlefield of Pylos). This analysis of power, as consisting of something other than manpower, resembles Pericles’ instruction of the Athenian people in 2.13, L. Kallet-Marx, Money, Expense, and Naval Power in Thucydides’ History 1–5.24 (Berkeley: University of California Press, 1993), 96–107; Kallet, Money and the Corrosion of Power, 45–47. There is also some similarity to the cautious reaction of the Herodotean Demaratus to Xerxes’ number fetishism: Spartans will fight with Xerxes ‘whether they have an army of a thousand men, or more than that, or less’ (Hdt. 7.103). Yunis, Taming Democracy, 106. Thuc. 6.34.7.

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critical numeracy that comes close to two earlier moments in the History where numbers are treated with critical suspicion. The first occurs in the methodological chapters, where Thucydides argues that the Peloponnesian War was the greatest war of all time—even greater than the Trojan War: It is reasonable to think that that Trojan expedition was greater than all in previous history, but still short of the modern scale. If once more we can trust Homer’s poems in this respect—and it is likely that, being a poet, he would exaggerate (ἣν εἰκὸς ἐπὶ τὸ μεῖζον μὲν ποιητὴν ὄντα κοσμῆσαι)—even so Agamemnon’s forces seem less than those of the present day. thuc. 1.10.3

In this authorial prelude to an ‘epideictic calculation’ of the size of Agamemnon’s fleet Thucydides corrects for the cosmetic exaggeration (ἐπὶ τὸ μεῖζον κοσμῆσαι) that poets are prone to:45 numbers in poetry tend to be larger than life. In a somewhat similar authorial remark, again preceding a calculation, Thucydides thematises the historiographical difficulty of acquiring accurate numerical information about enemy forces: This, then, was the make-up and disposition of the forces on either side. The Spartan army appeared the larger (μεῖζον ἐφάνη), but I could not have given an accurate account of the numbers in each contingent or the total numbers on either side (ἀριθμὸν δὲ γράψαι ἢ καθ’ ἑκάστους ἑκατέρων ἢ ξύμπαντας οὐκ ἂν ἐδυνάμην ἀκριβῶς). The secrecy of their system prevented knowledge of the Spartan strength, and estimates on the other side were suspect, given the natural tendency of men to exaggerate (διὰ τὸ ἀνθρώπειον κομπῶδες) the numbers of their own city. The following calculation, though, affords a view (ἐκ μέντοι τοιοῦδε λογισμοῦ ἔξεστί τῳ σκοπεῖν) of the Spartan numbers on this occasion. thuc. 5.68.1–2

Contrasting visual appearance (ἐφάνη) and an accurately curated number (ἀριθμὸν δὲ γράψαι … ἀκριβῶς), Thucydides explains how both the particular secrecy of the Spartan political system and the general human tendency to boast and exaggerate one’s own numerosity (διὰ τὸ ἀνθρώπειον κομπῶδες ἐς τὰ οἰκεῖα

45

Elsewhere (Thuc. 1.21.1), people in general are said to have a tendency towards cosmetic exaggeration (not necessarily in numbers).

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πλήθη) are obstacles for knowledge that meets historiographical standards. What follows is a conjectural computation that affords a ‘critical view’ (σκοπεῖν) of Spartans’ military numbers. It is this historiographical trope about the unreliability of (self-)reported numbers, originating in Thucydides’ own sceptical and polemical treatment of numbers, that Alcibiades recycles in the context of the Sicilian Debate. Hence, Alcibiades’ ‘absurd’ argument seems as salutary as critical historiography can get. The character Alcibiades here engages in a populist reuse of scientific scepticism. The difference between the two modes of knowledge is plain: the historiographer flags the problem of reliable numbers but still gives his audience a means of estimating numerosity; Alcibiades only invalidates military intelligence without offering better data. What Alcibiades offers instead is the perverse calculus of empire,46 where ‘there is no bookkeeping (ταμιεύεσθαι) that can establish the extent of the rule we desire’47 and where ‘on the basis of the calculation (λογισάμενοι) that we shall increase further our power here’ Alcibiades exhorts the Athenians to set sail.48 To Alcibiades, this expansionist calculus trumps the numerical expertise of experience and military intelligence. 2.3 Hidden Figures Does Nicias meet Thucydides’ standards of critical numeracy? In his second speech, aimed at changing the Athenians’ mind by insisting on the massive scale (πλῆθος) of the expedition,49 Nicias embarks on a piece of quantitative rhetoric, detailing the tactical difficulties of the expedition. However, nowhere in the entire speech is any quantity made concrete; moreover, there is hardly any argumentation or order in the jumble of items that make up his speech. Kallet persuasively argues that the ‘messiness of the presentation of information’ is deliberate: it is with this disorderly heap of vague information that Nicias hopes to convey the complicated and cumbersome nature of the project.50 Part of this conspicuous vagueness is Nicias’ use of words that indicate magnitude and quantity: the Sicilian cities are ‘great’ (μεγάλας),51 and ‘numer-

46 47 48 49 50 51

Kallet, Money and the Corrosion of Power, 40, see also 41–42 for a succinct comparison between Alcibiades’ version of the expansionist doctrine and that of Pericles in 2.65. Thuc. 6.18.3. Thuc. 6.18.4. Thuc. 6.19.2. Kallet, Money and the Corrosion of Power, 42. Thuc. 6.20.1.

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ous (πολλὰς) in number (τὸ πλῆθος) for one island’;52 there are ‘many’ (πολλοί) hoplites and ‘many’ (πολλαί) triremes,53 ‘many’ (πολλούς) horses.54 Against such a power, the Athenians not only need a naval and ‘otherwise inadequate’ (οὐ … φαύλου) force, but also a ‘large’ (πολύν) infantry, ‘many’ (πολλῶν) horses,55 and ‘adequate’ (ἀξιόχρεῳ) supplies, because the expedition will take them to places ‘far away’ (πολύ ἀπὸ τῆς ἡμετέρας).56 What will be required will be ‘many’ (πολλούς) hoplites, and ‘many’ (πολλούς) archers and slingers, ships for ‘great’ (πολύ) naval superiority; supplies are needed to cater for a ‘large’ (πολλή) army. All personnel will need to be equipped ‘as completely as possible’ (ὅσον δυνατόν) and therefore ‘a very big’ (ὡς πλεῖστα) sum of money will be needed.57 From Nicias’ point of view, the lack of precise numbers in his speech can thus be explained as part of his rhetoric of vagueness. From an authorial point of view, the lack of concrete numbers conveys something about the type of expertise that Nicias displays. While adversaries may be prone to exaggerate their own numbers, Nicias is intentionally exaggerating the costs of an expedition, not merely reinterpreting quantitative information, as a good commander should, but distorting information. Moreover, while Alcibiades’ number scepticism may be a perversion of Thucydides’ guidelines for critical numeracy, Nicias is incapacitating his audience by deliberately withholding from them the means of evaluating the quantitative assessments he makes. He intentionally creates a situation in which nobody seems to know what figures they are actually talking about—until he is called out to produce concrete numbers.

3

Critical Numeracy

So, what is Thucydides’ take on numerical expertise? As for the performance of numeracy, Paul Keyser has pointed out that in contrast to Herodotus, Thucy-

52 53 54 55 56 57

Thuc. 6.20.2. Thuc. 6.20.3. Thuc. 6.20.4. Thuc. 6.21.1. Thuc. 6.21.2. Thuc. 6.22.1. There are only three ‘real’ numbers in this speech: the ‘one island’ that Sicily is (6.20.2), the ‘four months’ that communication home takes in the winter (6.21.2), and the ‘seven other cities’ (ἄλλαι εἰσὶν ἑπτά, 6.20.3) that, apart from Naxos and Catana, are fully equipped with the sort of forces comparable to those of Athens. S. Berger, ‘Seven Cities in Sicily: Thuc. 6.20.2–3’, Hermes, 120/1 (1992), 421–424, argues that this can only refer to three cities (Selinus, Syracuse and Leontinoi). Seven is, Berger points out, a formulaic number, sometimes almost as vague as ‘much’.

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dides does not display facility with contemporary methods of arithmetical computation (the use of the abacus, making divisions and multiplications) and rarely engages in calculations; when he does, calculations tend to be ‘incomplete’, omitting figures required for analysis or totals, or plainly wrong.58 In response, Catherine Rubincam has argued that this may not so much be a lack of arithmetical competence as a matter of ‘authorial persona’: Thucydides may have refrained from displaying calculations because he preferred to present the result of his historiographical judgment and sifting of evidence.59 Moreover, Rubincam argues, Thucydides’ judicious use of number qualifiers points to alternative ways of flagging issues of reliability, accuracy and certainty about numbers.60 The two passages of Thucydides cited earlier (1.10 and 5.68) shed some additional light on Thucydides’ views on numerical information: they showcase the critical numeracy that is to be conducted in the face of insufficient or unreliable information. I treat the first passage in detail. Although Thucydides flags the problem of the reliability of numeric data from poetic sources, this does not stop him from using these very numbers to conduct a calculation: Homer gives a total of 1,200 ships, with the Boeotian ships carrying 120 men and Philoctetes’ ships 50, thereby indicating, it seems to me, the largest and the smallest (δηλῶν, ὡς ἑμοὶ δοκεῖ, τὰς μεγίστας καὶ ἐλαχίστας): at any rate there is no other mention (οὐκ ἐμνήσθη) of complement in the Catalogue of Ships. That all were fighting men as well as rowers is clear from this description of Philoctetes’ ships, where he has all those at the oars [as] archers too. It is unlikely (οὐκ εἰκός) that there were many non-rowing passengers apart from the kings and the highest other commanders, especially since they had to cross the open sea with all their military equipment and in ships without fenced decking, built in the old piratical style. [5] So ⟨when one takes⟩ the mean of the largest and the smallest ships (πρὸς τὰς μεγίστας δ’οὖν καὶ ἐλαχίστας ναῦς τὸ μέσον σκοποῦντι) the numbers embarked do not seem very great (οὐ πολλοί) for a combined expedition from the whole of Greece. thuc. 1.10.4–5 58 59

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P.T. Keyser, ‘(Un)natural Accounts in Herodotus and Thucydides’, Mouseion, 3/6 (2006), 323–351. C. Rubincam, ‘The ‘Rationality’ of Herodotus and Thucydides as Evidenced by their Respective Use of Numbers’, in E. Foster and D. Lateiner (eds), Thucydides and Herodotus (Oxford: Oxford University Press, 2012), 97–122. Rubincam, ‘The ‘Rationality’ ’, 103. C. Rubincam, ‘The Numeric Practice of the Hellenica Oxyrhynchia’, Mouseion, 3/9 (2009), 303–329, at 327, table 3, shows that 15.4% of Thucydides’ numbers have qualifiers, against 10.5 % in Herodotus.

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It is not unusual to have mixed feelings about this ‘computation’. On the one hand, this passage abounds in analysis of numerical information. In addition to (i) a critical disclaimer about the reliability of the information used as input for this computation, we find: (ii) a methodological decision to accept Homer’s figures as an upper limit;61 (iii) a specification of information found in Homer (there are 1,200 ships in total, 120 men in Boeotian ships, 50 men in Philoctetes’ ships); (iv) separately, an interpretation of Homer’s use of these numbers (i.e. 120 must be a maximum and 50 a minimum number of men on a ship); (v) transparency about what information is and is not available (οὐκ ἐμνήσθη) in the Catalogue of Ships; (vi) a plausibility argument (οὐκ εἰκός) about who were counted among these 50 or 120 men; (vii) a computation method: to strike an average of the largest and smallest ships; (viii) a hypothetical inference that ‘not many’ (οὐ πολλοί) seem to have embarked on the Trojan Expedition. On the other hand, what is conspicuously lacking in this ‘over-rational argument’62 is the computation itself and its result: what is the average between 50 and 120? And what is the result of multiplying this average with the total number of ships, 1,200? Keyser, who cites this passage as an example of Thucydides’ ‘incomplete calculations’, suspects that Thucydides omitted these results ‘because he had no reliable way to finding the average complement.’63 Moreover, could we really say that the Greeks before Troy were οὐ πολλοί, when on Thucydides’ computation (if τὸ μέσον refers to an arithmetical mean), there would have been 102,000 of them?64 Nor does Thucydides give his audience the means to evaluate the Homeric numbers. An arithmetically competent reader could perhaps arrive at the number of 102,000, but how does one get from there to the quantitative judgment οὐ πολλοί? There are no totals given for the Athenian and allied forces involved in the Peloponnesian War, so how does one make the comparison? However, it is important to account for the fact that the computation cited here is markedly conditional (if Homer’s numbers are reliable …) and hypothetical ( for someone who ‘critically views the average’ (τὸ μέσον σκοποῦντι)).

61

62 63 64

G. Crane, The Blinded Eye: Thucydides and the New Written Word (Lanham, MD: Rowman & Littlefield Publishers, 1996), 130: ‘Again, Thucydides gives Homer the benefit of the doubt and, like a careful statistician, conservatively chooses a high figure.’ S. Hornblower, A Commentary on Thucydides, i: Books i–iii (Oxford: Clarendon Press, 1991), 35. Keyser, ‘(Un)natural Accounts’, 338. See Crane, Blinded Eye, 132, for an argument that the total numbers of Athenian cum allied forces for the entire duration of the war would indeed exceed the magnificent force of 102,000 Greeks that went to Troy.

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The conditionality points to an awareness of the principle of ‘garbage in garbage out’, but it also suggests a way of working with numbers that are not completely, or unconditionally, certain and reliable. In contrast to Alcibiades, for whom the potential unreliability of enemy force numbers is a reason to ostentatiously renounce the use of numerical data in toto, Thucydides here demonstrates how to work with uncertainty by applying the methodological principles listed above. One could even imagine good reasons for refraining from producing a total: once a number is on the table, qualifications of its epistemic qualities (How certain is it? How accurate is it? Is it a precise value or a limit?) easily get lost. Instead, the reader is invited to σκοπεῖν for himself the resulting number:65 to develop a view on a number by conducting his own calculation that may produce a qualified estimate that provides ways of working around the inherent unreliability of military numbers.66

4

Minding the Gap

When we compare Thucydides’ incomplete arithmetic to Nicias’ non-arithmetic, we again see a contrast: Thucydides adduces concrete numbers to leap to a quantitative judgment (οὐ πολλοί), because he refuses to produce an extrapolated number that is based on uncertain input; Nicias throws his quantitative judgments (πολλοί, πολλαί, πολύ etc.) around and arrives at ‘no less than 100 triremes and no less than 5,000 hoplites’. Both numbers and quantitative judgments only give partial information. A concrete number is explicit and precise, but depends on contextual cues for its ‘meaning’. ‘14’ is unambiguously and explicitly ‘14’, but without further cues, we have no idea if ‘14’ is much or not. ‘Many’, on the other hand, is a quantitative judgment with an implicit reference point that is inferable either from

65

66

For σκοπεῖν in the authorial invitations to critically assess the text as monument, see 1.22.1 with E.J. Bakker, ‘Contract and Design: Thucydides’ Writing’, in A. Rengakos and A. Tsakmakis (eds), Brill’s Companion to Thucydides (Leiden: Brill, 2006), 109–129; on the epigraphic phrase τῷ βουλομένῳ σκοπεῖν as subtext for this authorial invitation, see J. Moles, ‘ΑΝΑΘΗΜΑ ΚΑΙ ΚΤΗΜΑ: the Inscriptional Inheritance of Ancient Historiography’, Histos, 3 (1999), 7–69. The issue of the size of the Spartan army before Mantinea (Thuc. 6.68.2–3) is treated in a very similar way. Here too, there is an incomplete and, according to many commentators, incorrect calculation. However, the calculation is merely an alternative to a quantitative impression (μεῖζον ἐφάνη), allowing one to ‘develop a view’ (σκοπεῖν) on the numbers, but against Thucydides’ own standards, this remains second best, cf. Rubincam, ‘The ‘Rationality’ ’, 108.

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the conversational context or from presupposed common knowledge. Cities are ‘big’ and hoplites are ‘many’, compared to a norm that sometimes is contextually accessible to all conversation participants, but sometimes intentionally obfuscated (we then ask: ‘What do you mean with ‘big’? Name a number!’). Nicias seems to be deliberately obscuring his reference points. He works from judgment to numbers, making a leap from vague quantitative judgments to specific numbers that seem to exude expertise but are in fact fabricated on the spot to match a pre-established judgment. Nicias fails: the Athenians may see that 100 triremes and 5,000 hoplites are much, but they do not arrive at the judgment that it is too much. Nicias thinks his numbers are hyperbolic, the Athenians do not. Why not? Part of the answer must be that Nicias misjudges the Athenians’ implicit reference point—or, perhaps, rather that he overestimates his hold on their reference point. The problem is Nicias’ own double agenda that sends mixed signals about the reference point implied in all the vague quantifiers in his second speech: (1) no expedition (covert aim): quantitative judgments about risks and required resources, such as ‘many’ and ‘large’, are to be understood as ‘too many’ and ‘too large’—relative to the status quo (no expedition). Relative to this reference point οὐκ ἔλασσων acquires a magnifying and deterrent force. (2) an expedition with minimised risks and maximum security (overt aim): quantitative judgments about risks and required resources, such as ‘high’, ‘many’ and ‘large’, are to be understood in relation to what the assembly takes to be the status quo: the already agreed upon expedition (the new status quo and the new reference point).67 ‘Many’ and ‘large’ mean ‘more’ and ‘larger’ relative to the reference point of the original plan: the moderately sized expedition of 60 ships. Relative to this reference point litotic οὐκ ἔλασσων serves to redefine the scale of the project by providing a new minimum requirement. It is the price of insurance for an expedition already bought.68 67

68

Cf. the paragraph preceding Nicias’ number speech (Thuc. 6.24.3): everybody has fallen in love with the enterprise, and is committed to the expedition, imagining conquest and safety (the older men), foreign travel and the sights abroad and a safe return (the young men), immediate pay and the prospect of further resources (the general mass). They all mentally treat the expedition as a given. Cf. Nicias’ own use of words that suggest safety and security at the end of his speech (Thuc. 6.23.3): ἀσφαλής, βεβαιότατα. It is this part of the speech that resonates with the audience, who now consider the safety (ἀσφάλεια) of the expedition as a given (6.24.2), anticipating ‘no possible failure for such a large armament’ (οὐδὲν ἂν σφαλεῖσαν μεγάλην δύναμιν, 6.24.3), and being ‘confident about a safe return’ (εὐέλπιδες ὄντες σωθήσεσθαι, 6.24.3).

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The discrepancy between the covert intention of Nicias and the actual interpretation of the assembly results in two different quantitative judgments for the same numbers.69 Nevertheless, Thucydides’ presentation of the debate suggests that there is more to Nicias’ failure than a tragic misjudgment of his audience’s reference point. Nicias’ expert estimate stands in marked contrast to Thucydides’ authorial quantitative judgments (however imperfect these may be): there are no critical disclaimers about reliability, no statement of method, no transparency about what information is and is not available. One could object that such a scientific approach is not feasible in the domain of political decision-making. To Thucydides, this is exactly the problem: the agonistic nature of political debate favours unqualified, misleading and incomplete information. Within the historiographic build-up of the themes of quantitative ignorance, numerical misinformation and information scepticism, Nicias’ figured figures expand the list of infelicitous symptoms of democratic numeracy.

Conclusion After the debate, the problem of democratic numeracy is brought to a dramatic climax when Thucydides describes the exodus of the spectacular Athenian armada, ‘the costliest and most magnificent ever to sail from a single city’.70 However, ‘numerically speaking (ἀριθμῷ)’, the fleets taken to Epidaurus and Potidaea in 430 were ‘not less’ (οὐκ ἐλάσσων)71—which takes up the earlier authorial remark in 6.1.1 that the Sicilian Expedition was οὐ πολλῷ τινὶ ὑποδεέστερον than the war against the Peloponnesians. The numerical details then offered by Thucydides pertain to the force in 430, not the present forces. The omission of numerical details for the present

69

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My use of the term ‘reference point’ for the standard against which quantities are judged is not to be confused with the notion of reference point in prospect theory, that is, a point relative to which gains and losses are defined, cf. J. Ober and T.J. Perry, ‘Thucydides as a Prospect Theorist’, Polis, 31 (2014), 206–232, for an argument that Thucydides had an intuitive grasp of the principles of prospect theory as developed by Kahneman and Tversky (see Kahneman, Thinking, Fast and Slow, 278–288, 293–294). While I concur with the overall gist of their analysis, my analysis focuses not directly on the Athenians’ decision but on their assessment of Nicias’ numbers; I therefore use the term ‘reference point’ in a nontechnical sense. Thuc. 6.31.1. Thuc. 6.31.2.

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armada underscores the point that Thucydides makes in this chapter:72 the Athenians were so impressed by the visual spectacle of their fleet and the optical allure of size and numerosity,73 the display of power and capability, and the emotional response that this spectacle elicited,74 that nobody bothered to actually count.75 Thucydides drives the point home with a counterfactual calculation: ‘If anyone had calculated (εἰ γάρ τις ἐλογίσατο) the combined public and private expenditure on this expedition …. he would have found that in total a vast sum of money was leaving the city (πολλὰ ἂν τάλαντα ηὑρέθη ἐκ τῆς πόλεως τὰ πάντα ἐξαγόμενα).’76 The counterfactual calculation pits the real response of the Athenian citizens in 415 against that of an ideal citizen or reader who would have performed this calculation to scrutinise critically, σκοπεῖν, the real costs of an inauspicious expedition. The Sicilian Debate forms a prelude to this climactic revelation of the failings of democratic numeracy. The debate can be read as a reflection on the genesis of numbers that are fraught with conflicting intentions and interpretations, and that inadvertently lose qualifications of conditionality and certainty. What the demos is left with are deceptively clear numbers, pseudo-scientific numbers and the conspicuous absence of numbers where they were needed most.

Acknowledgements This chapter is part of my research program Counting and Accountability, financed by the Netherlands Organisation for Scientific Research (NWO). I would like to express my gratitude to the participants at the conference for their comments and thought-provoking discussion, and especially to the two anonymous referees for suggestions and comments on content and style.

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74 75 76

The Catalogue of Troops in Thuc. 6.43–44.1 shows that Thucydides at least had access to the numeric data of the forces (not the resources). Kallet, Money and the Corrosion of Power, 60: ‘The vagueness of the exposition (…) fits Thucydides’ historiographical purpose.’ ὄψοιντο (Thuc. 6.30.2), ἑώρων (6.31.1), τῇ ὄψει (6.31.1), κατὰ θέαν (6.31.1), ὄψεως λαμπρότετι (6.31.6). See also Jordan, ‘The Sicilian Expedition’, 65–70, 76–79, and Kallet, Money and the Corrosion of Power, 48–66. ἀνεθάρσουν (Thuc. 6.31.1), ὡρμήθησαν (6.31.3), τόλμης (6.31.6), θάμβει (6.31.6). Kallet, Money and the Corrosion of Power, 60. Thuc. 6.31.4–6.

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Bibliography Bakker, E.J., ‘Contract and Design: Thucydides’ Writing’, in A. Rengakos and A. Tsakmakis (eds), Brill’s Companion to Thucydides (Leiden: Brill, 2006), 109–129. Berger, S., ‘Seven Cities in Sicily: Thuc. 6.20.2–3’, Hermes, 120/1 (1992), 421–424. Christ, M.R., ‘Herodotean Kings and Historical Inquiry’, CA, 13/2 (1994), 167–202. Crane, G., The Blinded Eye: Thucydides and the New Written Word (Lanham, MD: Rowman & Littlefield Publishers, 1996). Debnar, P., ‘Blurring the Boundaries of Speech: Thucydides and Indirect Discourse’, in A. Tsakmakis and M. Tamiolaki (eds), Thucydides Between History and Literature (Berlin: De Gruyter, 2013), 271–285. Foster, E., Thucydides, Pericles, and Periclean Imperialism (Cambridge: Cambridge University Press, 2010). Greenwood, E., Thucydides and the Shaping of History (London: Duckworth, 2006). Hornblower, S., A Commentary on Thucydides, 3 vols. (Oxford: Clarendon Press, 1991– 2008). Jordan, B., ‘The Sicilian Expedition was a Potemkin Fleet’, CQ, 50 (2000), 63–79. Kahneman, D., Thinking, Fast and Slow (New York: Farrar, Straus and Giroux, 2011). Kallet-Marx, L., Money, Expense, and Naval Power in Thucydides’ History 1–5.24 (Berkeley: University of California Press, 1993). Kallet-Marx, L., ‘Money Talks: Rhetor, Demos, and the Resources of the Athenian Empire’, in R. Osborne and Simon Hornblower (eds), Ritual, Finance, Politics: Athenian Democratic Accounts Presented to David Lewis (Oxford: Clarendon Press, 1994), 227–251. Kallet, L., Money and the Corrosion of Power in Thucydides (Berkeley: University of California Press, 2001). Keyser, P.T., ‘(Un)natural Accounts in Herodotus and Thucydides’, Mouseion, 3/6 (2006), 323–351. Kohl, W., Die Redetrias vor der sizilischen Expedition (Thukydides 6, 9–23) (Meisenheim am Glan: Anton Hain, 1977). Moles, J., ‘ΑΝΑΘΗΜΑ ΚΑΙ ΚΤΗΜΑ: the Inscriptional Inheritance of Ancient Historiography’, Histos, 3 (1999), 7–69. Ober, J., Political Dissent in Democratic Athens: Intellectual Critics of Popular Rule (Princeton: Princeton University Press, 1998). Ober, J. and T.J. Perry, ‘Thucydides as a Prospect Theorist’, Polis, 31 (2014), 206–232. Pontier, P., ‘The Litotes of Thucydides’, in A. Tsakmakis and M. Tamiolaki (eds), Thucydides Between History and Literature (Berlin: De Gruyter, 2013), 353–370. Rubincam, C., ‘Thucydides 1.71.1 and the Use of ἘΣ with Numerals’, CPh, 74/4 (1979), 327–337. Rubincam, C., ‘Qualification of Numerals in Thucydides’, AJAH, 4 (1979), 77–95.

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Rubincam, C., ‘The Numeric Practice of the Hellenica Oxyrhynchia’, Mouseion, 3/9 (2009), 303–329. Rubincam, C., ‘The ‘Rationality’ of Herodotus and Thucydides as Evidenced by their Respective Use of Numbers’, in E. Foster and D. Lateiner (eds), Thucydides and Herodotus (Oxford: Oxford University Press, 2012), 97–122. Scardino, C., ‘Indirect Discourse in Herodotus and Thucydides’, in E. Foster and D. Lateiner (eds), Thucydides and Herodotus (Oxford: Oxford University Press, 2007), 67– 96. Stork, P., Index of Verb Forms in Thucydides (Leiden: Brill, 2008). Tompkins, D., ‘Stylistic Characterization in Thucydides’, YClS, 22 (1972), 181–214. Van Berkel, T.A., ‘Pericles’ Rhetoric of Numbers’, in S. Papaioannou, A. Serafim and K. Demetriou (eds), The Ancient Art of Persuasion Across Genres and Topics (Leiden: Brill, 2019), 339–355. Vattuone, R., Logoi e storia in Tucidide: Contributo allo studio della spedizione ateniese in Sicilia del 415 a.C. (Bologna: Cooperativa libraria universitaria editrice Bologna, 1978). Willi, A., The Languages of Aristophanes: Aspects of Linguistic Variation in Classical Attic Greek (Oxford: Oxford University Press, 2003). Yunis, H., Taming Democracy: Models of Political Rhetoric in Classical Athens (Ithaca, NY: Cornell University Press, 1996).

Translations Hammond, M., Thucydides, The Peloponnesian War (Oxford: Oxford University Press, 2009).

chapter 8

Performing Numbers in the Attic Orators Robert Sing

The way the Athenian polis generated and verified numbers helped to safeguard the power of the demos. The counting of votes, the maintenance of accounts and inventories, and the managing of state debts and property, were handled collegially and visibly—typically by groups of non-expert officials who were responsible for the accuracy of their counting.1 Aeschines observes the consensus that numbers could inspire when generated and verified in this way: Yet whenever the accounts have been balanced (ὁ λογισμὸς συγκεφαλαιωθῇ), no one is so stubborn that he does not leave without agreeing that whatever the accounts have established is true.2 aeschin. 3.59

Rhetorical speech was equally fundamental to the democracy, and the frequency of numbers in fourth-century oratory makes it clear that quantification and calculation mattered to the decision-making process.3 Yet the Athenian relationship with numbers in the assembly and the courts was ambivalent and complex. Spoken calculations are difficult to follow and recall.4 More problem1 e.g. the pōlētai and apodektai processed payments ‘in the presence of the boulē ([Arist.] Ath. Pol. 47.2, 48.1), and four allotted jurors counted ballots in front of the litigants (69.1). Similarly, private individuals might perform counts publicly for the purpose of witnessing (cf. Dem. 27.58). On numbers in the functioning of the democracy, see R. Netz, The Shaping of Deduction in Greek Mathematics (Cambridge: Cambridge University Press, 2002), 334–340. 2 All translations modified from those of the Loeb Classical Library. 3 Ancient commentators stress that speakers must know their facts (Xen. Mem. 3.6; Arist. Rhet. 1359b19–1360b3, cf. 1396a4–12). The presence of numerical manipulations and mathematical errors (see n. 21 below) suggests that surviving speeches were not heavily revised with a readership in mind. Even if some post-delivery revision took place, as texts purporting to be real rhetorical artefacts they are unlikely to contain anything that could not actually have been said. The corpus itself is large enough to give us a reasonable idea of how numbers were deployed to persuade ordinary Athenians. 4 On the cognitive difficulty of mental arithmetic, and the challenge of using Greek numeric notation for written calculation, see T.A. van Berkel, ‘Voiced Mathematics: Orality and Numeracy’, in N.W. Slater (ed.), Voice and Voices in Antiquity: Orality and Literacy in the Ancient World, Vol.11 (Leiden: Brill, 2017), 321–350, at 321–324.

© Robert Sing, 2022 | doi:10.1163/9789004467224_010

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atically, the presence of numbers amplified the Athenian distrust of rhetoric as potentially deceptive.5 A citizen suffered particular vulnerability when it came to numbers. Unlike the experience of handling numbers when part of an official board, a citizen had little time to fact-check a spoken numeric claim before having to make a decision. Beyond the speeches, the only sources of information available were an individual’s own knowledge and whatever others sitting nearby might share.6 Fourth-century orators consequently performed numeric claims for audiences in ways that tried to foster the kind of confidence that Athenians felt in the numbers that they understood and controlled.7 Certain presentational strategies could help, but Athenians ultimately judged the credibility of numbers with reference to the calculator’s character (ēthos). Contentious numbers could acquire verisimilitude by being integrated into a compelling portrayal of character. On the other hand, numbers were not just a rhetorical risk to be managed. Since the way a citizen was seen to handle numbers was freighted with cultural meaning, every performance of numbers made some contribution to the construction of character. Numbers must therefore be understood as a rhetorical resource, handled according to cultural anxieties around advice-giving and the expectation that good democrats will be reliable, transparent calculators.

5 Aristophanes observes the power of spoken numbers to mislead (cf. Ar. Vesp. 655–663, Ecc. 812–829). On deception and rhetoric see J. Ober, Mass and Elite in Democratic Athens (Princeton: Princeton University Press, 1989), 165–170, 187–191; J. Hesk, Deception and Democracy in Classical Athens (Cambridge: Cambridge University Press, 2000), 202–241; S. Johnstone, A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011), 163–170. 6 Some numeric knowledge (e.g. prices) would have been widespread, but few politicallyrelevant and up-to-date numbers would have been common knowledge. Many key figures, like the total number of citizens, were probably never calculated to begin with. A report on polis revenues was made to the assembly every prytany, but this stopped sometime after 350 (Aeschin. 3.25). Some Athenians would have knowledge picked up through current or recent office-holding, but such experience always had its limits (see L. Kallet-Marx, ‘Money Talks: Rhetor, Demos and the Resources of the Athenian Empire’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics (Oxford: Oxford University Press, 1994), 227–251 at 228–232). Moreover, even if a knowledgeable citizen spoke up, he still had to convince many strangers that he was right, pace J. Ober, Democracy and Knowledge (Princeton: Princeton University Press, 2008), 160–165. 7 This is not to consider the question of whether the most successful performance of numbers tended to be the most truthful. One aim of Thucydides’ account of the debate on Sicily (Thuc. 6.8–26), with its completely ignorant audience and self-interested and deceptive speakers, seems to have been to depict the very worst deliberative malpractice involving numbers. As such, it is not particularly reliable. See further van Berkel, this volume.

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Configuring Figures

Before all else, speakers tailored their numeric arguments to their rhetorical setting. The jury courts offered the greatest scope for numeric rhetoric. The value of estates, dowries, expenditures and debts were at the heart of the ‘private’ suits (dikai) over property and business transactions that dominate the forensic corpus. Litigants also had time to collect and prepare numbers, and the opportunity to deliver them at length. The much greater time spent explaining and analysing numbers in the courts compared to the assembly must have been one of the distinctive features of forensic rhetoric. Private trial speeches may even have become more numerically dense over the course of the fourth century, as the greater liquidity in the fortunes of elites sparked more intricate disputes.8 Far less rhetoric from the assembly survives, most of it from Demosthenes and most of that from the first decade of his career, but it suggests that the assembly saw less argument with, and about, numbers. There are several reasons for this. On many subjects relevant numeric data were quite simply not available, and numerical exactness was not always possible when so many discussions focused on the necessarily speculative future. The frequency of those debates for which plausible numbers were available, like the financial management of the polis, must have declined once the budgetary organisation of the merismos, governed by nomos, was introduced after 403/2. This change, however, would have been partially offset in the second half of the century by a greater expectation that leading orators be financially competent.9 Numbers certainly lost none of their importance for decisions that remained with the assembly—not least the expensive business of waging war (e.g. Dem. 14.18–19). There were, however, more practical hurdles to using numbers in the assembly. The unpredictable course of debates meant that the preparation required to deploy numeric arguments was not always time well spent. The greater size of the assembly, the exposed situation of the Pnyx, and interventions from other speakers all made it harder to secure the level of attention required for arguments involving numbers. As we shall see, these differences in subject matter and setting between the assembly and the courts

8 For the financial pressures on fourth-century elites and their corresponding economic strategies see R. Osborne, ‘Pride and Prejudice, Sense and Subsistence: Exchange and Society in the Greek City’, in J. Rich and A. Wallace-Hadrill (eds), City and Country in the Ancient World (London: Routledge, 1991), 119–145. 9 See below n. 11.

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meant that comparable rhetorical strategies concerning numbers played out in slightly different ways. The simplest technique to encourage trust in a numeric claim was to explain it: to break it down and back it up using contextual details. A client of Isaeus in the fragmentary Against Hagnotheus insists that the only credible way for someone to make their case against a former guardian is to engage in an exhaustive scrutiny of his accounts: If he had any thought for justice and were not seeking to mislead your judgement, he ought not, by Zeus, to do these things but should proceed to an exact reckoning (λογισμός) supported by witnesses and examine every item in the accounts, interrogating me in the following manner: ‘How much do you calculate you contributed in eisphorai?’ ‘So much’. ‘On what basis was the money paid?’ ‘On such and such a basis’. ‘In accordance with what decrees?’ ‘These’. ‘Who received the money?’ ‘These men’. And he ought to scrutinise my evidence on these points—the decrees, the number of contributions, the sums paid, and the receivers of them—and if everything were exact and in order, he ought to trust my reckoning; and if not, he should then produce witnesses regarding any falsehood in the accounts that I submitted to them. dion. hal. On Isaeus 12

Demosthenes, a supposed student of Isaeus,10 seems to follow this sort of prescription in Against Aphobus (Dem. 27). He explains that his painstaking level of detail will enable the jury to know all the facts accurately (akribōs) (1–3, 7, cf. 29.30; Is. 11.38) and to see through his opponents’ obfuscations. Yet Demosthenes’ approach in Aphobus is exceptional. Isaeus’ strictures are meant to cast suspicion on an opponent who had decided it would be unwise to deliver such a scripted audit. In truth, speakers tend to make judicious use of supporting detail. Too much could easily become counter-productive, especially in the assembly, and a mass release of information might have been beyond the knowledge or skill of some litigants in court. Exposition could be reinforced with corroborating evidence. Court cases could involve the citation of wills (Lys. 19.39–41), annotated bank records (e.g. [Dem.] 49.5, 43–44), private account books (e.g. Dem. 27.49, 50.10, 30, 65), the testimony of witnesses (e.g. Aeschin. 1.99–100), and, in public matters, the records and acts of the polis.11 Demosthenes, no doubt mindful of the special 10 11

Dion. Hal. On Isaeus 1; Lib. Hyp. Dem. 31. e.g. the registers of the grain commissioners (Dem. 20.32) and decrees (Dem. 20.115;

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need for brevity and clarity in the assembly, manages to combine the support of documents and witnesses for his proposal to send two military forces against Philip ii in the First Philippic (Dem. 4). When he comes to explain the sources that will provide the required 92 talents, the words πόρου ἀπόδειξις ‘outline of funding’ (29) appear in the manuscript—a lemma almost certainly designating a lost document. It must have been a fundraising plan, rather than a mere list, and Demosthenes provides a clue as to why it was nevertheless sectioned off when he concludes his reading of it by saying ‘these are the things, Athenians, that we have been able to find’ (30). The ‘we’ may refer to allied orators, bouleutai, or colleagues on a board. Demosthenes, still an up-and-coming orator, understood the need to inspire confidence in the feasibility of his scheme at a time of financial stress (cf. 4.23) by having several other people vouch for it. By brandishing the apodeixis as a separate document, Demosthenes achieves an effect comparable to the extra-textual persuasion of a witness statement, underscoring that other Athenians, with more time and knowledge than most, already believed that his numbers added up. Written records could not, however, be circulated among an audience for indepth scrutiny, just as witnesses could not be cross-examined. As such, orators’ desire to reinforce their claims sees them perform, literally, the calculations behind their figures. This substantiation of numbers through real-time calculation could be an effective device, comparable to Aristotle’s ‘artless’ (ἄτεχνος) category of proof (Rhet. 1355b35–39), where a speaker introduces an external source (like a law) that appears to be independent from the potentially misleading rhetoric of the speech.12 Setting out calculations also had the benefit of implicitly flattering the jurors as fully engaged co-calculators. Demosthenes’ mode of address in Against Aphobus makes this explicit: e.g. ‘you will find on examination …’ (27.11), ‘if one were to add together …’ (17), ‘if one were to …’ (23), ‘if you add … you will find’ (35), ‘if you take …’ (37, cf. 20.19). Sometimes speakers will also add caveats, as if anticipating a careful scrutiny (e.g. Lys. 19.44). Yet the performance of calculation could present a major oratorical challenge. Reviel Netz has argued that Athenians tended to conceive of numbers

12

Aeschin. 3.101–102). Individuals like Eubulus could make decisive interventions with authoritative advice about what was financially feasible (Dem. 19.291; Lycurg. fr. 1.5 (Conomis); [Plut.] Mor. 818e), but such arguments were only possible because of their unusual personal authority, see G.L. Cawkwell, ‘Eubulus’, JHS, 83 (1963), 47–67 on Eubulus, and M. Faraguna, Atene nell’età di Alessandro: Problemi Politici, Economici, Finanziari (Rome: Accademia Nazionale dei Lincei, 1992), 196–205 on Lycurgus. See C. Carey, ‘ ‘Artless’ Proofs in Aristotle and the Orators’, BICS, 39 (1994), 95–106 on the two types of proof.

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as tactile objects that could be manipulated in space, rather than abstract entities.13 When Bdelycleon assures Philocleon in Wasps that his verbalised calculation is simple, he says the latter will not need pebbles but can use his fingers—he does not say he can do it in his head.14 Jurors might have brought their own counters; they might have done sums during a speech, not just before it like Dicaeopolis (λογίζομαι, Ar. Ach.31), and perhaps Philocleon was not alone in wanting a tablet on which to make notes (Ar. Vesp. 529, 537). Apart from these isolated references, we have no evidence of audience members making use of aids. Nor is there any evidence that visual aids were employed by speakers.15 There are calculations, however, that do seem to have been straightforward for Athenians because speakers make no effort to break them down or repeat them even when they are critical to the argument.16 Other examples suggest that when numbers were larger or more numerous, or the arithmetic was more complex, audiences might struggle.17 In Against Leptines (20.32) Demosthenes wishes to show that the Bosporan dynast Leucon effectively donates 13,000 medimnoi of grain to Athens each year by waiving the one-thirtieth export duty on Athens-bound ships. Demosthenes breaks up the sum to make it more manageable, dividing the 400,000 medimnoi Athens imports each year into the easier figures of 300,000 and 100,000, calculating one-thirtieth of each and then adding them together.

13 14 15 16 17

R. Netz, ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321–352, at 324–329. Ar. Vesp. 656, cf. πεμπάζω ‘to count’ is literally ‘to count on five fingers’. On this passage, see further Kallet in this volume (pp. 45–50). One litigant decided against displaying a family tree because not all the jurors would have an equally good view ([Dem.] 43.18). Lys. 10.4 (31 minus 19); Is. 6.14 (52 minus 20); Dem. 19.251 (240 minus 50), 38.2 (3,000 multiplied by 4). On Athenians’ underlying numeric skill, as opposed to their ability to comprehend verbalised calculations, see Kallet in this volume; Netz, ‘Counter Culture’, 299–300 on ‘basic’ Greek numeracy. Mass, functional literacy appears to have existed in Athens (see C. Pébarthe, Cité, Démocratie et Écriture (Paris: De Boccard, 2006), 33–67; A. Missiou, Literacy and Democracy in Fifth-Century Athens (Cambridge: Cambridge University Press, 2011), 109–142) and what we might call rudimentary numeracy (the ability to add and subtract) must have been at least as common. For many Athenians, daily life would have been conducive to acquiring more developed numeric skills thanks to an economy that was, even by Greek standards, highly monetised, and widespread office-holding with its attendant account-keeping, see S. Cuomo, ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper and A.-M. Kanthak (eds), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278, at 259–265. Some Athenians who lived farther away from the asty or large demes may have used numbers less intensely, see Johnstone, Trust, 63–65, 71–77.

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When it was necessary to sustain complicated calculation like this over an extended portion of a speech, speakers could take further steps to make their working intelligible and important numbers memorable. In Against Aphobus Demosthenes crafts a rhetorical infrastructure to manage an exceptional proliferation of numbers that would otherwise overwhelm the listener.18 The numbers are used to refute the claim of his former guardians that his father’s estate was only ever worth 5 talents (27.62) and that they owe him no more than he had already been given. Demosthenes provides four key numbers: how much his father left him (4–11), what Aphobus took (12–23), how much Aphobus took in league with the other guardians (24–33), and what all of them owe at a bare minimum (34–40). He eases the cognitive burden on his listeners by indicating that not all the numbers he mentions require the same degree of attention as these four. Each of the key numbers is calculated by working out its constituent amounts (for example, the figure for the estate comprises the value of ‘productive’ (ἐνεργά) assets, household goods, deposits and eranos loans, 9–11). The repetition of these subtotals at both the beginning and end of the calculations, and sometimes in between, signals their importance.19 Demosthenes then pauses to show how the subtotals combine to make the four key totals and to flag the next stage in his demonstration, for example: These 30 minae, then, he received from the workshop, along with the interest for eight years; and if one calculates the interest at only a drachma per month [12%], he will find there are 30 minae more. This is the money that Aphobus has embezzled on his own, and once it is added to the dowry, the combined total of the principal and interest is about 4 talents. I will now show you what money he embezzled in cooperation with the other guardians … dem. 27.23

The jury is made to feel that they have checked all the workings, when they have actually been given no choice but to accept the multiplicity of small 18

19

We know that Demosthenes won the case (Dem. 29.8) and his preoccupation with how his numbers would be heard, together with their centrality to his argument, makes it unlikely that the numbers were not actually delivered in court. The same is probably not true, for example, of all the lengthy calculations of Cicero (Verr. 3.116), see S. Pittia, ‘Données chiffrées dans le de Frumento de Cicerón’, in J.R.W. Prag (ed.), Sicilia Nutrix Plebis Romanae (London: Institute of Classical Studies, 2007), 49–80, at 70–72. e.g. the 80 minae dowry (12, 13, 16), 30 minae in knife workshop profit (18, 21, 23), and 40 minae from the bed workshop (24, 29), cf. Isaeus 3 where the key figure of 3 talents is repeated frequently (2, 8, 18, 25, 29, 49, 80).

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numbers on which Demosthenes ultimately relies. Using this method, Demosthenes carefully demonstrates that his father’s estate was 14 talents and that Aphobus owes him 4 talents.20 He then suddenly sets all this aside at 35 and works out the minimum that Aphobus owes him based only on the lump sum that Aphobus had allegedly admitted to taking, 108 minae, which with 10 years’ interest amounts to 3 talents 1,000 drachmae (34, 39).21 By claiming—if only temporarily, as it turns out22—a sum smaller than the one to which he had emphatically proved his entitlement, Demosthenes makes an impressive show of his reasonableness and his guardians’ guilt. This caps off a series of devices intended to put his claims beyond doubt: assumptions of low interest rates (e.g. 17), rounding that favours the guardians, deductions, and wide margins of error (e.g. 36–37, cf. Lys. 19.44, 32.28).23 It is, as a result, virtually impossible for Aphobus to quibble and for the jury to refuse.

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3 talents 5,480 drachmae (17, 23) to be precise. Once the sums given later are added (24– 33), the total is more than 5 talents: one-third of 2 talents 40 minae (5,333 drachmae) from the bed workshop (29) + one-third of at least 1 talent of unaccounted ivory (33) = 5 talents 813 drachmae. Demosthenes’ numbers are not always as precise as they appear. 12% interest on 108 minae (a figure presumably explained in Aphobus’ speech (34)) over 10 years is 3 talents 5,760 drachmae, and in total Demosthenes should be owed 8 talents 4,000 drachmae (not 1,000) (35). The occasional rounding up of figures and questionable assumptions (e.g. that income from both workshops should have been consistent), may be intended to inflate Demosthenes’ claims. Elsewhere, imprecision may serve to conceal his own lack of precise information or avoid unnecessary complication, see L. Pearson, The Art of Demosthenes (Meisenheim am Glan: Anton Hain, 1974), 44–47; D.M. MacDowell, Demosthenes, Speeches 27–34 (Austin: University of Texas Press, 2004), 41–42; D.-A. Daix and M. Fernandez, Démosthène Contre Aphobus i & ii, Contre Midias (Paris: Les Belles Lettres, 2017), 57–61, 90–93. In his second speech, Aphobus ii (Dem. 28), Demosthenes does not claim 3 talents 1,000 drachmae. After recapitulating some of the calculations in Aphobus i of the specific amounts he is owed (27.17, 23, 29, 33), albeit without making any deductions (cf. 27.36– 37), Demosthenes instead demands 10 talents (28.13). Confusingly, the first portion of these 10 talents—3 talents 1,000 drachmae (28.13)—is not the sum claimed in Aphobus i (27.34, 39). The latter should be 3 talents 5,760 drachmae to begin with (see previous note), and the figure in Aphobus ii does not include interest. The origins of the other 5 talents of capital that make up the 10 talents is never explained. Demosthenes appears so confident in the rhetoric of Aphobus i (and sufficiently pressed for time), that in his second speech he felt the jury no longer needed to follow his numbers in order to believe them. Demosthenes’ willingness to qualify numbers about which he does not have precise knowledge also adds to his credibility, see van Berkel, ‘Voiced Mathematics’, 341–343.

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It is also difficult to spot outright fabrication in Against Aphobus, but its many unsubstantiated numbers suggest how calculation can be an effective vehicle for smuggling through precisely the sort of deception that audiences feared.24 In the dynamic debates of the assembly, with less scrutiny from opponents than in court, a speaker could risk manipulations that can be detected fairly quickly in a text.25 Demosthenes in the First Philippic minimises his estimate of how much his proposed expeditions against Philip will cost by simply failing to cost the first force (4.16–17) and leaving out pay for the crew of the cavalry transports in the second (4.21, 28–29). In court, speakers typically faced opponents who were well-versed in the relevant numbers, and so used more subtle manipulations that can only be detected through careful rereading. Isaeus proves himself particularly wily when writing for a guardian accused of mismanagement in On the Estate of Hagnias (Is. 11). The speaker, Theopompus, refutes the impassioned claim that he lives in luxury while his nephew, who was also his ward, lives in poverty, by comparing his estate with that of his late brother Stratocles. There is a suspicious imbalance of detail in the two inventories. The wealth of Stratocles is carefully itemised (42–43) but Theopompus only mentions his own real estate (44) and says nothing of the sort of assets that he lists for his brother (loans, ready cash). The sleight of hand comes with the overall reckoning, when Theopompus says his ward was left 5.5 talents (42), that is, 11,000 drachmae more than he has (44). The inventory of Stratocles’ assets, however, amounts to 4 talents 5,300 drachmae—7,300 drachmae more than his own stated wealth. Theopompus has evidently included the 2,000 drachmae dowry of Stratocles’ wife (40)—also the value of his own wife’s dowry but which he later fails to factor in—and the estate’s income, or other unspecified property, contrary to his word (43). The proof that his nephew is almost 2 talents better off is, as such, apparent rather than real.26 Given our reliance on internal evidence when assessing calculations, the frequency of such deception must have been greater than we can know.27

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26

27

Cf. Pl. Hp mi. 366c–367c, where Socrates points out that, despite the verifiability of arithmetic, the more skilled someone is at calculating the easier they find it to deceive using numbers. This, in turn, suggests that the texts were circulated so long after the fact that these manipulations were inconsequential, and/or that readers were not expected to scrutinise this aspect of the speeches. W.E. Thompson, De Hagniae Hereditate (Leiden: Brill, 1976), 53 suggests that this unspecified wealth was described in the lost later part of the speech, but 11.40 suggests that we have all that Theopompus had to say about the composition of the respective estates. Lysias provides two other examples. The prosecutor in Lysias 30 claims that Nicomachus caused an additional 12 talents to be spent over the past two years because he had intro-

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With examples like this, it is unsurprising that calculation was not enough, on its own, to put a law court or the assembly at ease. Aeschines, attacking Demosthenes in Against Ctesiphon (Aeschin. 3), points us toward the most important and rhetorically difficult element of any numeric performance. He describes how, back in 342, Demosthenes orchestrated the appearance of Callias of Chalchis in front of the assembly. Callias enumerated the pledges of money that he had secured from various Greek states for a future war against Philip, totalling 100 talents (95–96). Demosthenes, on Callias’ (pre-arranged) invitation, then confirmed this information and added that: the contribution of money was sufficient for 100 fast ships, 10,000 foot soldiers and 1,000 cavalry, and that in addition to these forces citizen troops would be ready, from the Peloponnese more than 10,000 hoplites, and just as many from the Acarnanians … aeschin. 3.97–98

All this support did not ultimately materialise, and this allows Aeschines to dismiss the whole thing as a ruse; Callias’ testimony had been written by Demosthenes (95), who had in turn been bribed to support Callias’ plan for an independent Euboean league (91–93). Aeschines claims that providing detailed information, like numbers, is in fact Demosthenes’ ‘personal and peculiar way’ (ἴδιον καὶ οὐ κοινόν) (98) of lying: Other charlatans, when they are lying, try to talk about indefinite and ambiguous things, since they are afraid of being caught out; but whenever Demosthenes deceives you, first he lies with an oath … and then he dares to say when things will take place which he knows perfectly well will not happen, and he gives the names of those whom he has not seen, making you distrust what you hear (κλέπτων τὴν ἀκρόασιν) and imitating those who speak the truth. For this reason he is entirely worthy of your hatred, for he is not only a scoundrel but he destroys your trust in the signs of honesty (τὰ τῶν χρηστῶν σημεῖα) aeschin. 3.99, cf. dem. 29.30 duced new sacrifices that cost 6 talents a year (20). In reality, these new sacrifices represented a total increase in spending of 6 talents over the period because, as the speaker actually says, they left the polis without the money it would have otherwise spent on sacrifices costing 3 talents each year. In Lysias 17 the speaker omits key numbers and information in order to pass off his claim for part of an estate as admirably modest. The fact he was making the claim against the polis, rather than well-informed family members, presumably emboldened him to take this risk, see G. Bolonyai, ‘A Numbers Game: An Interpretation of Lysias 17’, CQ, 58/2 (2008), 491–499.

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Aeschines constructs Demosthenes’ alleged behaviour as dangerous to the entire decision-making process through a disingenuous reframing of the way audiences normally evaluated factual claims. Just like Isaeus’ self-interested sermonising in Against Hagnotheus on how numbers should be tackled, Aeschines distorts reality. In his world, one that no doubt held some attraction for the wary audience, the persuasive power of detail is massively inflated. Insincere speakers out themselves by having no exact information to offer, and Athenians are consequently able to use details, such as numbers, as their primary diagnostic tool of truth. Aeschines, in other words, denies the very ‘rhetoricality’ of numbers in rhetoric (except those of Demosthenes), implicitly assimilating his own numbers with the most trustworthy figures of the public record. Earlier in Against Ctesiphon Aeschines in fact denies the rhetoricality of his entire speech by likening it to one big calculation. It will be a ‘logismos of truth’ that jurors ought to judge without recourse to any other information, just as if they were logistai auditing a set of accounts (3.59–60, 168).28 Demosthenes, in response, makes the untenable result of this conflation clear: jurors would be reduced to passive checkers of pre-packaged information (18.227–229). Yet even if the jury could be brought to believe that numbers in rhetoric were as straightforward as Aeschines claims, why should they believe that the numbers of Demosthenes were the exception?

2

Corroboration through Character

Though Aeschines implicitly denies its relevance to the evaluative process, the credibility of his extraordinary allegation at 3.99 comes from the way it fits into his wider, long-term characterisation of Demosthenes as being, among other things, a crafty and over-elaborate dissembler (e.g. Aeschin. 2.153, 3.137).29 Since detail, corroboration and calculation were always potentially counterfeit, numeric arguments were at their most persuasive for Athenians when they were integrated into a compelling portrayal of character.30 While well-

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On the logistai as the financial auditors of accounts in euthynai trials, see [Arist.] Ath. Pol. 48.3–5. See N. Worman, Abusive Mouths in Classical Athens (Cambridge: Cambridge University Press, 2010), 255–266. Aristotle (Rhet. 1356a4–13, 1377b20–1378a19) identifies ēthos as the most important means of persuasion: audiences will trust a speaker who seems to be intelligent, moral, and public-spirited, especially when facts are uncertain.

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known speakers had reputations that preceded them, private litigants and novice orators, as we shall see, had to work to construct their ēthos through their speeches. Numeric claims that appear to be consistent with a given ēthos were endorsed on the basis of probability (eikos); something is or is not likely to be true because the individual (whether the speaker or someone else) appears to be a certain sort of person. It is the deftly-drawn characters in Against Diogeiton (Lys. 32), for example, that allow Lysias to deliver his numeric arguments with such economy and emotive force. Diogeiton is accused of plundering the estate of his wards, who are also his grandsons, and most of the surviving part of the speech is devoted to narrating the death of the children’s father and the reaction to Diogeiton’s announcement seven years later that virtually none of the estate is left. The description of the distraught children (9–12) is followed by the sustained quotation of the attack that their outraged mother made on their grandfather in the presence of relatives and acquaintances (12–19). Her pleas sit alongside a series of numeric assertions with which she ‘convicted’ (ἐξήλεγχεν, 14) Diogeiton, ‘demonstrated’ (ἀπέφηνε, 15) his deceit, and moved those assembled to mournful silence. The account is essentially a restaging of what Lysias presents as an earlier, successful prosecution, one in which the mother’s compelling ēthos is critical. Calculation is mingled with high pathos, and while she breaks norms of gendered behaviour by skilfully using numbers to assert herself against her own father, she does so within the home and in defence of her children—it is Lysias who has moved her alleged words into the public, political space of the court. The behaviour is extraordinary without being straightforwardly transgressive. Among the sources, the episode is in fact unique as our only Athenian example of formal, persuasive female speech using numbers. It is an exception to the near-invisibility of the non-citizens who performed the majority of daily domestic and commercial calculations in the polis.31 The account induces the jury to agree that Diogeiton’s conduct must been outrageous to have provoked such a performance, while reinforcing the credibility of the numeric claims that get repeated by the speaker. Lysias builds on this impression of Diogeiton as a heartless, shameless embezzler by selecting a few key expenditures to show that he had tried to disguise his crimes behind ridiculously inflated expense claims (9, 20). He is said to have charged his grandsons the full 2,500 drachmae cost of their father’s tomb on the pretence that it cost 5,000 drachmae and that he paid the other half (21). The

31

Another rare example are the women traders of the agora in Aristophanes who, in their brief appearances, are shown calculating monetary costs (Vesp. 496–499, 1388–1412).

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same trick was even used to charge the boys for the cost of contributing to a syntrierarchy—something that also happened to be illegal (26–27). The syntrierarchy is the only expense that can be proved via external records, and by separating the eyewitness corroboration of this allegation (27) from the allegation itself (24) and placing the former at the end of the speech, Lysias appears to prove all the preceding allegations.32 Even if a listener does not fall for this ploy, Lysias offers the eikos-argument that if Diogeiton was prepared to hazard the risk of behaving as he did over a syntrierarchy, then he must have habitually done much worse (27). A simple calculation finally shows what the jury has already inferred: maintenance costs for the wards were nowhere near what Diogeiton claims (28–29). In contrast to the meticulous, measured approach taken by Demosthenes against Aphobus, the vividness of Lysias’ characters allow a handful of expenses and a final calculation to act as a plausible indictment of Diogeiton’s seven-year guardianship, and to discount the possibility of any extenuating circumstances.33 Such was the power of ēthos that it could win over a jury that had resolved to ignore numbers altogether. Lysias penned On the Property of Aristophanes (Lys. 19) for a defendant who was being prosecuted because the polis refused to believe that the confiscated estate of the man’s late brother-in-law, Aristophanes, was really as small as it was found to be. Numbers generated in private, like numbers in rhetoric, were neither controlled nor trusted by the demos, and so Athenians were accustomed to compare the property declarations of rich men with popular belief (doxa) about the size of their fortunes. Aeschines’ declaration, encountered earlier, that jurors should be prepared to accept his logismos and abandon their pre-existing doxa in making judgements (3.59– 60) is, accordingly, denounced by Demosthenes as sophistic and undemocratic (18.227).34 In Lysias 19, the pre-existing doxa was that Aristophanes had been 32

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C. Carey, Lysias: Selected Speeches (Cambridge: Cambridge University Press, 1989), 223. A point-by-point proof of all the allegations is actually dismissed on the grounds that it would take too long (Lys. 32.26, cf. Dem. 22.60). This use of numbers in one area to overshadow their absence in another is not unique. The catalogue of Apollodorus’ wealth (Dem. 36.36–38) diverts attention from the fact that no evidence is offered for the claim that Apollodorus spent just 200 drachmae over 10 years on liturgies (39–41, cf. 50.7–13). Similarly, Demosthenes uses calculation to pass off correlation as causation in On the False Embassy, carefully showing that the Phocians surrendered after (and therefore, according to Demosthenes, because) they heard that the Athenians were not going to assist them (19.57–60, cf. Aeschin. 2.130–135). M. Gagarin, ‘Methods of Argument in Lysias and Demosthenes: a Comparison’, in L.C. Montefusco and M.S. Celentano (eds), Papers on Rhetoric, xii (Perugia: Editrice Pliniana, 2014), 87–97 also compares the two speeches along similar lines. Orators also speak of the authority of phēmē ‘popular report’ as another, closely related,

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far richer than the (private) numbers showed (11, 34, 45). It followed that the rest of his property must be in the hands of his family and that the speaker is a specimen of the dissembling, selfish rich man. Lysias’ strategy to overcome the contradiction between real and imagined numbers is not just to attribute this doxa to slander (diabolē) but to articulate an alternative ēthos for Aristophanes: ‘You will perceive that I speak the truth from this man’s own conduct’ (19).35 His Aristophanes is a spendthrift, very different in his phusis to the selfeffacing speaker and his family (12–18, 55– 64). Aristophanes spent most of the liquid assets, which the polis now accuses the speaker of hiding, on seeking glory for himself and the polis (18). We are given an account of his enthusiastic expenditures and frenzied borrowing in preparation for his expedition to help Athens’ ally, Evagoras of Cyprus, against Persia (21–27), after which the speaker asks: What man do you think, jurors, who loved glory and had heard from his father that he would lack for nothing in Cyprus, and who had been elected as ambassador and was preparing to sail, would have left behind anything that he possessed rather than provide everything he could in order to please Evagoras and secure no less in return? lys. 19.23

The account concludes with the ‘greatest evidence’ that Aristophanes had no movable wealth left: the memorable vignette of his refusal of the almost irresistible offer of a golden cup from the Great King as security for a short-term loan at 25% (24–26). If the audience happens to wonder why Aristophanes left so little of his own plate, it is told that his fortune only ever really consisted of cash, and that this cash was quickly spent on his estate and liturgies (29). It is only after these preparations, which establish the basis for a new eikos-

35

type of trustworthy democratic knowledge (Aeschin. 2.145, 3.127–130; Dem. 19.244, cf. Hyp. 1.14, 4.40), see Ober, Mass and Elite, 148–151; Hesk, Deception, 227–231. See Johnstone, Trust, 81–98 on the ‘socialisation’ of valuing. Against Phaenippus (Dem. 42), from an antidosis trial, is the most blatant and well-known example of numbers relying on typecasting. Measurements of length, without any relationship to area, are used to give the impression that Phaenippus’ estate is vast (5–6), and no evidence is provided for allegations of massive agricultural production and profit (7, 20, 24, 31). In the end, the numbers are actually beside the point: Phaenippus, as the archetypal rich, arrogant man, deserves to perform the trierarchy (25). See G.E.M. de Ste. Croix, ‘The Estate of Phaenippus (Ps.-Dem., xlii)’, in E. Badian (ed), Ancient Society and Institutions: Studies Presented to Victor Ehrenberg on his 75th Birthday (Oxford: Blackwell, 1966), 109–114; Osborne, ‘Pride and Prejudice’, 123–129.

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argument, that we come to the numbers. Curiously, Lysias does not provide a final inventory of Aristophanes’ wealth but a rather heterogeneous list consisting of real estate, liturgical expenses and even borrowed sums (cf. 22), but apparently no investments, totalling just under 15 talents (43–44). The comparison Lysias makes with estates that also proved disappointingly small, like that of Conon, consequently counts for little (38–41, 44–52). The nature of Aristophanes’ wealth was evidently opaque. We are not told its origin, or how much he made in Cyprus (it was at least enough to repay his creditors) (24).36 Lysias, determined to exclude the possibility of still extant concealed wealth, implausibly suggests that Aristophanes had acquired and then spent a finite sum. Characterisation distracts from this dubious accounting and creates the impression that the case has indeed been made with ‘a great deal of weighty evidence’ (45).

3

Characterisation through Numbers

Athenian cultural judgements about different numeric behaviours meant that numeric usages—the way numbers and calculations are delivered in a speech, as distinct from the numeric claims themselves—always, at some level, construct character. The falsification of expenses by Diogeiton and the suppression of numbers by Demosthenes’ guardians (27.40–41) are, for instance, further evidence of their shameless greed.37 The skill of arranging numbers to help build an ēthos can most easily be seen in cases of self-characterisation where the quantity of quantification, or indeed its very presence, is incidental to the argument. Litigants often style themselves as public-spirited citizens by mentioning their liturgical spending, but two clients of Lysias, speaking at a time of financial hardship for the polis, underscore their zealous service by carefully listing and costing the individual liturgies that they or their families undertook. Our speaker in On the Property of Aristophanes shows that his dead father was not the sort to hide Aristophanes’ property from the polis by setting out his father’s liturgical record in such detail that he had to rely on a written text (Lys. 19.56– 59, 61–63).38 The young liturgist of Lysias 21 bases part of his defence on his

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It is denied that his wealth comes from his father in Cyprus (35–37). The fact that all his spending took place over just four to five years (29) makes it unlikely that Aristophanes’ farm, as large as it was (42), was his only income-generating asset. On this aspect of Lys. 32, see van Berkel, ‘Voiced Mathematics’, 328–332. Cf. Lys. 19.42–43, 25.12 for other liturgy lists. Benefactions of grain and money are listed, liturgy-like, in Dem. 34.38–39. The dense recitation of numbers is used elsewhere to cre-

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liturgical record, launching into a catalogue of his liturgies ‘so that you may understand what kind of person I am’ (1). The record is perhaps no greater than the records of those with comparable wealth, but by quantifying his expenditure in such detail the speaker creates a spectacle of enormous expenditure, in effect reassembling several years of benefaction and exhibiting it all at once. The decision not to convert the many sums cited into a single denomination adds to a sense of bewildering scale. Since the accumulation of detail is the point, the speaker does not provide a total at the end but instead makes the unprovable claim that ‘if I wished to spend only what the letter of the law requires, I would not have spent a quarter’ (5).39 The sharing of precise numeric records by both of these clients of Lysias, moreover, reinforces their secondary argument that because they are such careful stewards of their estates the polis will profit far more by leaving their property in their care than by seizing it (19.61–64, 21.13–16).40 Self-characterisation, rather than incompetence or obfuscation, can again be the explanation when a speaker makes little or no effort to help an audience follow a calculation, as Demosthenes does in Against Phormio (Dem. 34): Now interest on real (ἔγγειος) property was one-sixth,41 and there [Byzantium] the Cyzicene stater was worth 28 Attic drachmae. It is necessary for you to understand how much money he says he paid. 120 staters is 3,360 drachmae, and 16 2/3 percent interest on 33 minae and 60 drachmae is 560 drachmae, and the sum total comes to … 3,920 drachmae dem. 34.23–25

Despite the declared necessity of the audience understanding all of this, for such numbers to be comprehended and remembered (instead of merely heard)

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ate an impression of magnitude (Dem. 20.77; Aeschin. 2.70–71; Isoc. 8.86–87). The pointed absence of number, due to the alleged impossibility of quantification, makes the same point with even greater force (Lys. 2.27; Isoc. 4.93). The list of Lysias 21, which not only contains no total but lists liturgies by archon year instead of grouping them by type, may be another illustration of Greek norms of inventorying as described by A. Kirk, ‘The List as Treasury in the Greek World’, Ph.D. thesis (University of California Berkeley, 2011), 76–109. Kirk argues that Athens’ inscribed treasury inventories recreate the experience of a visual inspection by allowing the reader to pick out specific objects (or, in Lysias 21, liturgies) and appreciate overall abundance, but not to quantify the total value. Though one may wonder if some jurors felt that such a long list projected arrogance rather than conscientiousness (cf. Dem. 21.153). i.e. 16 2/3 %.

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the speaker would have to slow to a crawl. This might well have happened, but in light of the calculation in Against Leptines (see p. 200 above) we might suspect that ordinary Athenians would need not just time but hand-holding from the speaker to follow a kind of calculation many of them probably had little experience performing.42 Rather than persuading audiences with ‘open’ calculations that can be verified in real-time, passages like this persuade by demonstrating the speaker’s commitment to, and capacity for, transparency in the face of his opponent. While the numbers of Aphobus are carefully curated to allow the jury to follow the higher-level calculation, the thickets of figures within the rhetorical structure belong to this same category of ‘closed’ calculation. Sometimes in Aphobus, this detail is not just comprehensive, but excessive: Apart from these things, he left ivory and iron, for use in the workshop, and wood for the couches worth 80 minae, gall and copper bought for 70 minae, a house worth 3,000 drachmae, furniture and plate, and my mother’s jewellery, clothing and ornaments, altogether worth 10,000 drachmae, along with 80 minae of silver in the house. While all this money was left at home, there was a maritime loan of 70 minae to Xuthus, 2,400 drachmae in the bank of Pasion, 600 drachmae in the bank of Pylades, 1,600 drachmae with Demomeles son of Demon, and about 1 talent loaned without interest in sums of 200 and 300 drachmae. The total of all these sums comes to more than 8 talents 50 minae. dem. 27.10–11

None of these individual loans are mentioned again. This numeric tour de force not only parades Demosthenes’ desire to be entirely open with the jury, but makes it clear that he is not the sort to be bamboozled by his more experienced opponents even though they have refused to show him his father’s will. His confidence and exactitude in handling numbers provides a counterweight to his obvious youth and builds an impression of an intelligent and confident citizen acting in the defence of his oikos (66–67, cf. 28.19–22). Ten years later, at the start of his political career in the 350s, we still see Demosthenes building a reputation through numerical ability. This was the time Eubulus achieved political pre-eminence through financial knowledge and skill, and the adroit handling of numbers would, in truth, be a long-term part of the construction of Demosthenes’ political ēthos. On the Symmories

42

L. Pearson, Art, 45 n. 11 notes that speakers sometimes think it necessary to explain basic banking procedures to juries (e.g. [Dem.] 49.5, 52.4).

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(Dem. 14), Demosthenes’ earliest surviving assembly speech, demonstrates that while self-characterisation through impressive numeric display was harder to manage in front of the assembly, it could still occur. He begins with a plea not to over-react to rumours of a Persian attack, before calling on Athens to increase its preparedness for war. To assist in this, he offers a sweeping plan (syntaxis) for reforming the organisation and financing of the fleet (14.16–23), part of which he outlines as follows: I urge you to fix the total number of ships to 300, to divide them into 20 groups of 15 ships each, assigning to each group 5 of the 100 first-rate ships, 5 of the 100 second-rate ships, and 5 of the 100 third-rate ships, and then to allot a group of 15 to each symmory, and each symmory is to assign 3 of its ships to each of the 5 sections within it. When these things are done, I urge that your finances be re-organised as follows. Since the assessable value of your land is 6,000 talents, I urge you to divide this into 100 portions of 60 talents, and then to assign 5 of these 60-talent portions to each of the 20 symmories, and each symmory should then give a 60-talent portion to each of its sections. dem. 14.18–19

Though the sums themselves are relatively straightforward, number is heaped upon number, and Demosthenes does not show how the proposed reorganisation will be superior to the status quo or less radical alternatives. In light of these perceived rhetorical weaknesses, the proposal has been branded as a failure, or one made insincerely.43 The overall skill seen in Against Aphobus, however, should give us pause before writing off this numeric performance as the work of a poor speaker.44 In its scale and detail, the plan also looks like a serious effort from a confident calculator at a time of severe financial strain for the polis. The way Demosthenes sets out his plans is not inconsistent with what an orator might choose to do in order to debut a complicated set of reforms. The goal is not to provide an in-depth knowledge of all aspects of the scheme in

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See W.W. Jaeger, Demosthenes: the Origin and Growth of his Policy (New York: Octogon, 1963), 78–79; C. Karvounis, Demosthenes: Studien zu den Demegorien orr. xiv, xvi, xv, iv, i, ii, iii (Tübingen: Gunter Narr, 2002), 92–94. Like Aphobus, of course, the speech is not perfect. The use of μέρος in 18–19 to refer both to squadrons of ships and sections within a symmory can cause confusion, and Demosthenes over-uses the emphatic κελεύω. More generally, see L. Pearson, ‘The Development of Demosthenes as a Political Actor’, Phoenix, 18/2 (1964), 95–109.

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a single speech. Rather, prior to beginning the protracted legislative process of nomothesia, the aim is to leave the assembly with a positive first impression of the scheme as intrinsically intelligible and logical, and of its author as trustworthy and talented.45 The approach Demosthenes takes provides a particularly vivid, final illustration of the cultural embeddedness of numeric practice in rhetoric. Beyond the comprehension and presentation of so much information, the organising logic of successive layers of equal division reflects the arithmetic equality associated with democracy, and celebrates Athenian faith in transparent processes of numeric production and verification to protect democratic government. Indeed, the scheme is nothing but number, to the point that the key questions that naturally arise with such a proposal (and to which Demosthenes refers in passing)—its fairness, practicality and efficiency46—seem to be self-evidently guaranteed through the proper arrangement and abundance of numbers. The same confidence in the power of numbers can be seen in the heights of overcomplication attained by the juror-selecting process by the 320s, involving several redundant rounds of sortition ([Arist.] Ath. Pol. 63–67). In its very elaboration, the selection process constituted a public ritual that not only ensured but proclaimed the incorruptibility of the judicial system. Similarly, Demosthenes’ scheme is a personal creation that exhibits his own commitment to the ideological underpinnings of democratic numeric practice.47 It is on this deepest level of ethical construction that Aeschines makes what appears to have been his sustained counter-characterisation of Demosthenes in On the Embassy (2.153) and later, as we saw, in Against Ctesiphon (3.99): Demosthenes does not just deceive his audience, he undermines its fundamental belief in the trustworthiness of numbers. By contrast, the young Demosthenes’ brand-new piece of democratic numeric architecture shows his fellow Athenians that he shares their ideological investment in numbers, freed from the compromising taint of rhetoric, as a key democratic resource, while simultaneously making a powerful rhetorical bid for the value of his advice.

45 46

47

For R. Sealey, Demosthenes and His Time (New York: Oxford University Press, 1993), 129, this is actually the sole point of the entire proposal. The proposals constitute the ‘fastest’ (τάχιστα, 14) method of mobilisation, and will be ‘clear and easy’ (σαφὴς ἔσται καὶ ῥᾳδία, 22) as well as ‘practical’ (δυνάτα, 28). We are left to infer that the navy will function more efficiently thanks to the equal and consistent distribution of responsibilities. In Aristotelian terms, Demosthenes uses numbers to persuade not only by demonstrating his intelligence, but the right values for a democratic citizen: ‘the ēthos most likely to persuade must be that which is characteristic of [the politeia]’ (Rhet. 1366a12–14).

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Acknowledgements It is my pleasure to thank my fellow editors and all the contributors for their hard work and patience. I am likewise indebted to the anonymous reviewers and subsequent readers for greatly improving this paper.

Bibliography Bolonyai, G., ‘A Numbers Game: An Interpretation of Lysias 17’, CQ, 58/2 (2008), 491– 499. Carey, C., Lysias: Selected Speeches (Cambridge: Cambridge University Press, 1989). Carey, C., ‘‘Artless’ Proofs in Aristotle and the Orators’, BICS, 39 (1994), 95–106. Cawkwell, G.L., ‘Eubulus’, JHS, 83 (1963), 47–67. Cuomo, S., ‘Accounts, Numeracy and Democracy in Classical Athens’, in M. Asper and A.-M. Kanthak (eds), Writing Science: Medical and Mathematical Authorship in Ancient Greece (Berlin: De Gruyter, 2013), 255–278. Daix, D.-A. and M. Fernandez, Démosthène Contre Aphobus i & ii, Contre Midias (Paris: Les Belles Lettres, 2017). Faraguna, M., Atene nell’età di Alessandro: Problemi Politici, Economici, Finanziari (Rome: Accademia Nazionale dei Lincei, 1992). Gagarin, M., ‘Methods of Argument in Lysias and Demosthenes: a Comparison’, in L.C. Montefusco and M.S. Celentano (eds), Papers on Rhetoric, xii (Perugia: Editrice Pliniana, 2014), 87–97. Hesk, J., Deception and Democracy in Classical Athens (Cambridge: Cambridge University Press, 2000). Jaeger, W.W., Demosthenes: the Origin and Growth of his Policy (New York: Octagon, 1963). Johnstone, S., A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011). Kallet-Marx, L., ‘Money Talks: Rhetor, Demos and the Resources of the Athenian Empire’, in R. Osborne and S. Hornblower (eds), Ritual, Finance, Politics (Oxford: Oxford University Press, 1994), 227–251. Karvounis, C., Demosthenes: Studien zu den Demegorien orr. xiv, xvi, xv, iv, i, ii, iii (Tübingen: Gunter Narr, 2002). Kirk, A., ‘The List as Treasury in the Greek World’, Ph.D. thesis (University of California Berkeley, 2011). MacDowell, D.M., Demosthenes, Speeches 27–34 (Austin: University of Texas Press, 2004). Missiou, A., Literacy and Democracy in Fifth-Century Athens (Cambridge: Cambridge University Press, 2011).

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Netz, R., The Shaping of Deduction in Greek Mathematics (Cambridge: Cambridge University Press, 1999). Netz, R., ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321– 352. Ober, J., Mass and Elite in Democratic Athens (Princeton: Princeton University Press, 1989). Ober, J., Democracy and Knowledge (Princeton: Princeton University Press, 2008). Osborne, R., ‘Pride and Prejudice, Sense and Subsistence: Exchange and Society in the Greek City’, in J. Rich and A. Wallace-Hadrill (eds), City and Country in the Ancient World (London: Routledge, 1991), 119–145. Pearson, L., ‘The Development of Demosthenes as a Political Actor’, Phoenix, 18/2 (1964), 95–109. Pearson, L., The Art of Demosthenes (Meisenheim am Glan: Anton Hain, 1974). Pébarthe, C., Cité, Démocratie et Écriture (Paris: De Boccard, 2006). Pittia, S., ‘Données chiffrées dans le de Frumento de Cicerón’, in J.R.W. Prag (ed.), Sicilia Nutrix Plebis Romanae (London: Institute of Classical Studies, 2007), 49–80. Sealey, R., Demosthenes and His Time (New York: Oxford University Press, 1993). Ste. Croix, G.E.M. de, ‘The Estate of Phaenippus (Ps.-Dem., xlii)’, in E. Badian (ed.), Ancient Society and Institutions: Studies Presented to Victor Ehrenberg on his 75th Birthday (Oxford: Blackwell, 1966), 109–114. Thompson, W.E., De Hagniae Hereditate (Leiden: Brill, 1976). Van Berkel, T.A., ‘Voiced Mathematics: Orality and Numeracy’, in N.W. Slater (ed.), Voice and Voices in Antiquity: Orality and Literacy in the Ancient World, Vol. 11 (Leiden: Brill, 2017), 321–350. Worman, N., Abusive Mouths in Classical Athens (Cambridge: Cambridge University Press, 2010).

part 3 Conceptualising Number

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chapter 9

Numbers, Ontologically Speaking: Plato on Numerosity Florin George Calian

The conceptualisation of numbers is culturally bound. This may seem like a counterintuitive claim, but one illustration thereof is the limitations of the resemblance of the ancient Greek concept of number to that in modern mathematics.1 We may take Greek mathematics as familiar and transferable, and are accustomed to perceive Euclid’s Elements as universal and transcultural. Natural numbers, the most common numbers, are currently conceived in a Euclidean key as quantitative units taken together, distributed into sequences initiated by a unit.2 As Aristotle (Metaph. 1080a22–23) put it, each unit of a number has the same value. This would imply an understanding of ἀριθμός and its units as devoid of any qualitative features relative to each other. But this apparent continuity of understanding with the Greeks is a projection of our own mathematical understanding. Even if Thomas Kuhn did not explicitly discuss a mathematical paradigm shift, his theory leads us to question the equivalences drawn between modern and ancient mathematics. As Bruce Pourciau highlighted, ‘Kuhnian revolutions in mathematics are logically possible, in the sense of not being inconsistent with the nature of

1 Most strikingly, some peoples do not count higher than three or six, or do not count at all, since they do not have words in their natural language to designate these discrete quantitative concepts. This contradicts the idea that every culture has developed a concept of number which is translatable and understandable by any human being, and could confirm the classical Whorfian thesis that language can determine thought, and, in this case, arithmetical skills. An example is given by the Pirahã tribe, from Amazon, who use a ‘one, two, many’ system of counting, for which see P. Gordon, ‘Numerical Cognition Without Words’, Science 15 (2004), 496–499. For a critique of Gordon see S. Laurence and E. Margolis, ‘Linguistic Determinism and the Innate Basis of Number’, in P. Carruthers, P. Laurence and S. Stich (eds), The Innate Mind (Oxford: Oxford University Press, 2008), 139–169. Further, C. Everett, Numbers and the Making of Us: Counting and the Course of Human Cultures (Cambridge, MA: Harvard University Press, 2017), 60–100. 2 Euclid (vii, Def. 2) defines it thus: ‘a number is a multitude composed of units’. See T. Heath, A History of Greek Mathematics, ii: From Aristarchus to Diophantus ([Oxford: Clarendon Press, 1921] New York: Dover, 1981), 69.

© Florin George Calian, 2022 | doi:10.1163/9789004467224_011

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mathematics’.3 And more pointedly: ‘the one science where Kuhn apparently believed his ideas on incommensurability did not apply [mathematics], is the science that reveals the deepest incommensurability of all’.4 Ancient Greek mathematicians and philosophers understood numbers as integers, and beyond the integer there was nothing that could be called number. However, the fifth-century discovery of incommensurable magnitudes,5 a real achievement of Greek mathematics, could be taken as a case of paradigm shift because it challenged the reflex assumption of number as integer. This conceptual shift, which took place within the world of mathematics itself, is instructional for modern mathematics in its partial inheritance of ancient mathematical impasses.6 The difference between the modern and the ancient understanding of numbers is not only marked by the initial ancient Greek inability to work with irrational numbers, or by post-Renaissance algebraisation of mathematics,7 but by the iconoclastic modern understanding of numbers as devoid of ontolo-

3 B. Pourciau, ‘Intuitionism as a (Failed) Kuhnian Revolution in Mathematics’, SHPS, 31 (2000), 297–329, at 297. 4 Pourciau, ‘Intuitionism’, 328. For an up-to-date discussion see M. Sialaros (ed.) Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), especially the introduction by Sialaros, ‘Introduction: Revolutions in Greek Mathematics’, 1–15. 5 For example, there is no unit that makes it possible for a square to be commensurable with both its side and its diagonal. Plato (Resp. 5.546c4–5) calls the diagonal of the square ἄρρητον (irrational). Euclid calls it ἀσύμμετρος (incommensurable). For a detailed discussion, see Heath, Greek Mathematics, ii, 90–91. For a contextualisation of the testimony, see L. Zhmud, Pythagoras and the Early Pythagoreans, trans. K. Windle and R. Ireland (Oxford: Oxford University Press, 2012), 263–265. 6 As seen, for example, in the question allegedly posed by Leopold Kronecker to Ferdinand von Lindemann: ‘Why study such problems [the proof that Pi is transcendental], when irrational numbers do not exist?’ See R.S. Wolf, A Tour Through Mathematical Logic (Washington DC: Mathematical Association of America, 2005), 323. 7 J. Klein, Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (New York: Dover, 1992 [1968]) stresses that our concept of number should be traced to the Renaissance, when algebra found its place within mathematics. This revolutionary idea is taken further by several scholars, including P. Pritchard, who underscores the Greek understanding of unity and number (ἀριθμός) as distinct from ‘post-Renaissance number notions’, and Gottlob Frege’s ‘Platonic’ understanding of numbers, see P. Pritchard, Plato’s Philosophy of Mathematics (Sankt Augustin: Academia Verlag, 1995), esp. chapter 4. Pritchard’s thesis of discontinuity between Greek and post-Renaissance mathematics is followed by M. Burnyeat, ‘Plato on Why Mathematics is Good for the Soul’, in T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy (Oxford: Oxford University Press, 2000), 1–81, and ‘Platonism and Mathematics: A Prelude to Discussion’, in A. Graeser (ed.), Mathematics and Metaphysics in Aristotle (Bern: Paul Hapt, 1987), 213–240. For a critical review of Pritchard’s analysis of Plato see V. Harte’s review in JHS, 118 (1998), 227.

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gical or symbolical value.8 For Greek philosophers, mathematical questions are ontological questions, and ontological questions have their corresponding mathematical expressions. Some Greek philosopher-mathematicians, especially the Pythagoreans and the early Platonists, understood numbers as ‘generated’ (Arist. Metaph. 1081a14, 1098b7). For the Pythagoreans and early Academics, the world is likewise ‘generated’ and numbers have a pivotal role in the generation process: fundamental ingredients (unity, unity and duality, odd and even, etc.) generate and inform numbers which, in their turn, generate geometrical entities, which then generate physical bodies.9 Plato himself dealt dialectically with the problem of the generation of the world, of the soul, and, as I argue, of numbers. Several scholars and mathematicians take for granted that Plato’s philosophy of mathematics was devoted only to the elaboration of the famous number-form theory, in which number is eternal, unchanged, and ungenerated.10 Nevertheless, an argument from the Parmenides (142b1–144a4), which is seldom mentioned in Plato’s philosophy of numbers, explains numbers in terms of generation. Talking about numbers in terms of generation, and not in terms of forms, implies a scaling down of numbers to basic principal ingredients, instead of the assertion of numbers as simple and uncomposed abstract and eternal entities.11 8

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The Greek concept of number of course had a pragmatic function (number calculations), but the Pythagoreans also endowed it with religious and ontological importance. Modern number theory leaves little room for this more speculative aspect; though some, such us Kepler and Newton, had a ‘superstitious’ understanding of numbers that complemented their scientific endeavours: see J. Henry, Religion, Magic, and the Origins of Science in Early Modern England (London: Routledge, 2018). Some pieces of evidence in this regard are provided by Aristotle (Metaph. 1084a10, 25, 1090b20–24, De an. 404b20–24, Ph. 206b33). Even if these testimonies come to us filtered through the Aristotelian lens, they nevertheless provide a substantial starting point for understanding at least the controversies around number theories and the concept of generation. See, for example, Phaedo (101c5): ‘no other reason for their coming to be two, save participation in twoness: things that are going to be two must participate in that, and whatever is going to be one must participate in oneness’. The place of these number-forms at the level of forms or as intermediary objects (between intelligible forms and participated things) is an ongoing debate which has meaning only if one accepts that Plato conceived for each number a correspondent number-form. Even if this number-form theory is the source for modern ‘Platonism’ in mathematics, it is far from clear whether Plato’s conception on number was ‘Platonist’ all throughout his dialogues. The ‘Platonism’ of Plato is only one facet of his explorations into mathematical philosophy: Aristotle attributed at least seven partly contradictory views to Plato, see F.G. Calian, ‘One, Two, Three … A Discussion on the Generation of Numbers in Plato’s Parmenides’, New Europe College, (2015), 50–51. The subject has received little attention from scholarship, but the now classic treatments are those of R.E. Allen, ‘The Generation of Numbers in Plato’s Parmenides’, CPh, 65, (1970),

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Being generated does not automatically, however, imply that numbers are less abstract and eternal entities, but that they are composed (i.e. not simple) and reducible to more basic entities, and therefore they cannot be plain forms.12 Even if isolated, the argument from the Parmenides draws on a type of onto-mathematics which resembles Pythagorean mathematical philosophy, foreshadows elements from later Platonic dialogues, such as the Sophist (254b– 264b) and the Timaeus (34c–35b), and anticipates some of the ideas of the early Academy.13 The exegesis of this argument for the generation of numbers provides us with another facet of Plato’s ontology and philosophy of numbers. If one takes the argument ad litteram, Plato has here an understanding of numbers that displays Pythagorean elements (as I show below), and, since the argument contains ideas present in later dialogues, this trait should not be ignored as a peculiarity of the second part of the Parmenides alone. Moreover, the hidden premises of the argument are also relevant for the historiography of Ancient Greek numerical thinking.

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The Generation of Numbers

The Parmenides is conventionally divided into two parts: the first part (126a– 137c) stands as an outstanding critique of the theory of forms, while the second part (137c–166c) is an elaborate debate on the concept of ἓν – ‘one’.14 The

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30–34, followed by ‘Unity and Infinity: Parmenides 142b–145a’, RMeta, 27 (1974), 697–725. For a recent revision of the argument in the context of an alternative understanding of Platonic philosophy and mathematics, see S. Negrepontis, ‘The Anthyphairetic Revolutions of the Platonic Ideas’, in M. Sialaros (ed.), Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 335–381. For a detailed analytic presentation of the argument see F.G. Calian, ‘One, Two, Three’, 52–53. One of the reasons for attempting to articulate a formula for the generation of numbers could be that it is difficult to conceive an infinite number of forms, corresponding to the infinite string of numbers. According to Aristotle (Metaphysics, Books M and N), early Academics, such as Speusippus and Xenocrates, considered not only numbers, but also forms and beings, as generated from two principles (‘One’ and its opposite principle, sometimes called ‘the indefinite dyad’). Alternately, ‘the one’, ‘the Parmenidean one’, ‘unity’, ‘number one’. G. Ryle, ‘Plato’s Parmenides’, Mind, 48/190 (1939), 129–151, translates as ‘unity’, as does R.E. Allen, Plato’s Parmenides (rev. New Haven: Yale University Press, 1997). G.E.L. Owen, ‘Notes On Ryle’s Plato’, in Logic, Science and Dialectic (London: Duckworth, 1986), 85–103 prefers to translate as ‘one’ and ‘the one’ and uses them interchangeably. S. Scolnicov, Plato’s Parmenides (Berkeley: University of California Press, 2003) translates as ‘one’, and I do the same since there is a numerical context in which ἓν is conceived in its numerical value.

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two parts seem to have been written at different moments and for different purposes, and later brought together to form one text. The dialogue’s second part consists of a series of eight inferences, which are usually referred to as ‘arguments’ (Scolnicov), ‘deductions’ (Kahn, Ryle, Owen, Allen, Rickless), or ‘hypotheses’ (Cornford).15 I focus on the beginning of the second argument, specifically the first (ontological) argument (142b1–143a2) therein, and, correspondingly, the second (mathematical) argument (143a4–144a4). For reasons that are apparent below, I refer to the first argument as the ontological argument, and to the second argument as the mathematical argument. I refer to both these arguments, when considered together, as the general argument for the generation of numbers. The general argument is exceptional in several ways. I quote Kahn for a good illustration of its richness: ‘Although all the deductions make some positive contribution, Deduction 2 presents philosophical thought on an entirely different scale, as an outline theory of the conceptual properties required for spatial-temporal being and becoming.’16 The main lines of the general argument, along which Plato differentiates ‘one’ and ‘being’ and institutes numbers, are as follows: – The first argument (the ontological argument) Although ‘one’ participates in ‘being’, ‘one’ is not ‘being’, since ‘is’ signifies something other than ‘one’; ‘one’ is a whole, ‘being’ and ‘one’ are its parts (μόρια), each of the two parts possesses oneness and being, and by necessity, it always comes to be ‘two’, it is never ‘one’ (ἀνάγκη δύ’ ἀεὶ γιγνόμενον μηδέποτε ἓν εἶναι) (142e7–143a1).17 The ‘one’ is infinitely many (πολλά), unlimited (ἄπειρον) and multitude (πλῆθος) (143a1). – The second argument (the mathematical argument) ‘One’ is not different from ‘being’ because of its oneness, and ‘being’ is not different from ‘one’ by virtue of being itself but because of ‘difference’; therefore, there is ‘difference’ and it is distinct from ‘one’ and ‘being’. Since there are three distinct entities the argument (143c3) goes further by picking out τινε (pairs).18 The pairs (143c4) are called ἀμφοτέρω (both/couple),19

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For a rejection of the term ‘hypothesis’ see Scolnicov, Plato’s Parmenides, 3. C. Kahn, Plato and the Post-Socratic Dialogue: The Return to the Philosophy of Nature (Cambridge: Cambridge University Press, 2013), 21. All translations from the Parmenides are my own. It is not clear if there is an exact correspondent in Greek for ‘pair’. The Greek dual τινε means literally ‘two somethings’. A more neutral conceptualisation of τινε should be understood in this argument as, for example, (a,b), (b,c), (a,c). ἀμφοτέρω is understood as: ‘x’, ‘y’ = ‘both (x, y)’.

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and what is called both is δύο (two).20 From here, the argument switches back to ‘one’: each of the ‘two’ is ‘one’ (δύο ἦτον > ἓν εἶναι) (143d2–3, 4–5), and, further, one added to any sort of pair is three (τρία γίγνεται) (143d7).21 And from here, if there is two and three, then there are all the numbers.22 The transition from ontology towards numbers may be represented graphically as follows: The argument for the generation of numbers: if one is The first argument (the ontological argument, 142b1–143a2) the first demonstration (142b–c): one partakes in being. i. ii. the second demonstration (142d–143a1): one is many. The second argument (the mathematical argument, 143a–144a4): if one is, there is number. Both Plato’s condensed arguments are not easily intelligible, and, as I have already emphasised, they contradict Plato’s view on numbers in terms of the theory of forms in other dialogues (e.g. Phaedo) and are unique among philosophies of mathematics. Plato’s intention—namely to show that ‘one’ is not only ‘one’, but that ‘one’ is also ‘many’—appears to be logically incongruent. There is an ambiguity in how ‘being’ is understood, but also how ‘part’ is used.23 Deciphering the texture of the arguments is important for getting to grips with Plato’s understanding of the ontology of numbers, for Plato builds upon the conclusions of these arguments (especially the ontological one) in later dialogues where there is no recourse to a theory of forms.24 The ontological argument states that, if ‘one’ is, then ‘one’ has ‘being’, and thus ‘one’ and ‘being’ are separate and distinct entities (142b5–143a2), and thus 20 21 22 23

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δύο is identified as a set with two members corresponding to the cardinal number two. A set of three members corresponding to the cardinal number three. See also Calian, ‘One, Two, Three’, 52–54. Thus, Bertrand Russell, Introduction to Mathematical Philosophy (London: Allen & Unwin, 1919; rev. repr. London: Routledge, 1993) believed that ‘This argument is fallacious, partly because ‘being’ is not a term having any definite meaning, and still more because, if a definite meaning were invented for it, it would be found that numbers do not have being—they are, in fact, what are called logical fictions’ (138). The same idea is reinforced by F.M. Cornford, Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides (London: Kegan Paul, 1939), 139; M. Schofield, ‘A Neglected Regress Argument in the Parmenides’, CQ, 23 (1973), 44; W. Kelsey, Troubling Play: Meaning and Entity in Plato’s Parmenides (New York: SUNY Press, 2012), 94. For example, two of the very basic elements for generating numbers, such as ‘difference’ and ‘being’, are found among the greatest kinds of the Sophist (254b–264b), and in the generation of the soul in the Timaeus (35a1–b3).

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the ‘is’-ness of ‘one’ could be conceived independently from ‘one’. It is not clear here whether ‘one’ gets multiplied or divided by two.25 The text might favour the second option, rather than multiplication as repeated addition.26 It is relevant that the Greek word used by Plato for ‘part’ is τὸ μόριον (also ‘piece’ or ‘member’), but it can also mean, in arithmetic, ‘fraction’. Diophantus (Arith. 1.23, 3.19, 5.20) later uses τὸ μόριον as ‘fraction with one for numerator’, ‘fraction in general’ or ‘denominator of a fraction’. Another usage that would incline the balance towards division rather than multiplication are the expressions μορίου or ἐν μορίῳ ‘divided by’. As a sub-unitary process of building pairs from ‘one’ and ‘being’, the line between division and multiplication is actually blurred,27 as each item of the ‘one-being’ pair (the ‘one’ or ‘being’) becomes even more divided. It must be acknowledged that, ultimately, the question over multiplication versus division must yield to the overarching ontological conception of one as many. This ontological argument (142b5–143a2) would thus be enough to justify the generation of ‘two’ by division or multiplication, since ‘one’ turning into ‘one’ and ‘being’ creates only ‘twos’ (142e7–143a1). Yet the obtained duos from the ontological argument are not yet the placeholders of numerical twos, but an attempt to conceptualise how ‘one’ implies multiplicity in its being. The second, mathematical, argument (143a4–144a4) reaffirms the division of ‘one’, announcing, in conjunction with ‘one’ and ‘being’, the logical operator of ‘difference’ that makes possible the identification of ‘one’ and ‘being’. We get the feeling as we read through the argument that the emphasis on ‘difference’ as an equal player in the argument—just like ‘one’ and ‘being’—makes it not only a logical operator, but an ontological entity as well. ‘One’ is not different from ‘being’ by virtue of its oneness (of being ‘one’), nor is ‘being’ different from ‘one’ because of its ‘is-ness’ (of being ‘being’), but because of ‘difference’ or otherness.

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In the Phaedo (101b8–10), Plato keeps this ambiguity regarding the origin of two, that is, whether it comes about by the operation of addition or division: ‘Then would you not avoid saying that when one is added to one it is the addition and when it is divided it is the division that is the cause of two?’ (trans. G.M.A. Grube). Even if the verb γίγνεσθαι is commonly used for mathematical products (cf. Pl. Tht. 148a; Euc. vii, Def. 18). Cornford reads the argument as using division. Later, where numbers are brought into discussion, he interprets addition and multiplication as an alternative to division, i.e. ‘The sort of division here intended can only be the mental act of distinguishing the two elements in ‘One Entity’ ’ (Plato and Parmenides, 138–140, at 139). Examining the natural cause of things (Pl. Phd. 96e6–97b3), Socrates shows his perplexity by giving the example of the becoming (generation) of two, asserting that two is formed by the addition of one to another one or by the division of one thing, and thus getting to two things. Socrates’

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It is this triadic differentiation—‘one’, ‘being’, and ‘difference’—that imperceptibly brings about numerical generation, but its presence in the discussion does not draw our attention to numbers in themselves. Nevertheless, this shift does happen. With no explanation, the argument strangely continues by picking up pairs. Plato asserts that since there are three discrete entities, we can form three sorts of pairs (τινε) (143c3): ‘being’ and ‘difference’, or ‘being’ and ‘one’, or ‘one’ and ‘difference’. The name of such pairs is ‘both’ (ἀμφοτέρω) (143c4); and both, subsequently, is ‘two’ (δύο) (143d2). Thus, we witness the derivation of cardinality δύο, which refers to groups of two elements and to number two, from the collective dual ἄμφω.28 Drawing on the numerical value of the pairs created, Plato moves from an ontological discussion towards a mathematical one, thereby opening the argument on the generation of numbers.29 Additionally, focusing on the semantic layers of these assemblages, the mathematical argument reviews dualities in their collective, cardinal, and ordinal meanings. The collective (linguistic) duality of ἄμφω seems independent from the ordinality or the cardinality of number two, and stays as a precondition for them: duality stays as an ontological and linguistic token that is prior to any counting operation. The cardinality of δύο, adds Plato, is subsequent and a natural consequence of the pair condition of ἀμφοτέρω. Here Plato seems to be ‘deceived’ by the nature of the Greek language which uses dual as a distinct grammatical number to refer to objects that come in pairs. The argument suggests that this ‘linguistic priority’ is also ontological, prior to effective cardinality as two. The reverse might be expected: to stipulate cardinality first, and then to advance the possibility of building pairs.30 On the contrary, Plato’s argument does not endorse the idea that duality is deduced from the cardinality and counting of two instances. Should the argument advance cardinality first, its

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perplexity arises from the fact that one cannot have two opposite causes—addition and division—for reaching the same result, which is two. See also Calian, ‘One, Two, Three’, 58. D. Blyth, ‘Platonic Number in the Parmenides and Metaphysics xiii’, IJPS, 8 (2000), 23– 45, bases all numerical argumentation on the ability to count. He distinguishes between form-numbers, originally ordinal and so differentiated by position, and cardinals as mathematical numbers. But Blyth’s interpretation falls short in justifying why Plato uses ‘one’, ‘being’ and ‘difference’ as the primordia of counting. Aristotle criticises Plato for not pointing to cardinality first, but the dyad: ‘for it follows that not the dyad but number is first, i.e., that the relative is prior to the absolute’ (Metaph. 990b18–20). Aristotle probably has this specific argument in mind, see Calian, ‘One, Two, Three’, 58.

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whole structure would be meaningless. To summarise, first there is ‘pair’ (τινε) (143c3), and since the pair is called ‘both’ (ἀμφοτέρω) (143c4), we then get to ‘two’ (δύο) (143d2), with each of the ‘two’ (δύο) as ‘one’ (ἓν εἶναι) (143d4–5). Since Plato’s argument does not start from ‘one’ in order to build the number series but determines the number series starting with number two, the argument assumes number two as the first actual number.31 This method of obtaining number δύο—positing a set with two elements, from a pair relation (ἀμφοτέρω)—is indeed unusual but it is not inconsistent with Greek mathematics, which understood the first number of the number series as being number two. For Greek mathematicians, the unit lacks a proper definition, since it is not a number but the condition of numbers, while for Plato the unit is not the condition, but the ‘numerical’ derivation from two (δύο). Thus ‘one’ is not the fundamental unit for ‘two’, but rather on the contrary, ‘two’ is the condition for ‘one’—the ‘unit’ for calculation. Both Plato and Greek mathematicians, by different logical routes, seem to agree that the number series starts with ‘two’. Although one would expect to proceed from δύο to number three, we go instead back (or forth) to number one. Plato does not consider ἕν, from which the ontological and mathematical argument starts, as having any numerical value since he does not consider it countable. The ontological argument stated the foundation of the ontological multiplicity and stressed that the initial ἕν must be understood not as a unitary being, but as a part of the ‘one-being’ pair—‘since [one] always proves to be two, it must never be one’ (142e7). The subsequent mathematical argument mirrors the division of ‘one’ into ‘twos’, concluding that ‘each of the two is one’. The direction is from ἕν towards δύο, and from δύο towards another type of ἕν. In Plato’s words, from ἂν δύο ἦτον (if there are two), to ἑκάτερον αὐτοῖν ἓν εἶναι (each of the two to be one) (143d3), the argument enforces the idea that by way of duality we are given an account of ‘one’. Thus, the initial ἕν is the ontological basis for the numerical ἕν. Having generated the numerical one, Plato goes further towards obtaining number three (143d7). The new ἕν, in its role as numerical unit, would have populated, for the modern mind, the whole of the numeric axis by mere successive addition, and should have easily led to number three from plain self-addition (i.e. 1+1+1). Moreover, if the pairs ‘one-being’, ‘being-difference’,

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See also A. Wedberg, Plato’s Philosophy of Mathematics (Stockholm: Almqvist & Wiksel, 1955), 23; D. Ross (ed.), Aristotle’s Physics (Oxford: Clarendon Press, 1936), 604.

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and ‘difference-one’ lead to the revelation of duality and thereof, to numerical two, would not ‘one’, ‘being’, and ‘difference’ suggests an analogous trinity, and thereof, a numerical three? If we do not follow Plato’s line of argumentation thoroughly, we can definitely be misled, as David Ross was when he took ‘one’, ‘being’ and ‘difference’ as the three first countable entities.32 However, the argument is again surprising and offers solutions for the generation of numbers that go against what the reader would expect. Any initial structure of three concepts (or any other instantiations) would not be enough, since the general argument seems to develop arbitrarily from ‘any two’ towards ‘one’, and from ‘any two’ and ‘one’ towards three. A question that one could ask is whether one could reach number two and number three from any two or three given concepts. One could perhaps think that any triadic structure could be the starting point for further insights into the generation of numbers. Could this initial triad be any triad or is it bound to be a conceptual triad, made up out of specific ontological concepts? Should the constituents of such a triad be necessarily and precisely the three concepts of ‘one’, ‘being’ and ‘difference’, or any other three? The construction of the whole argument, namely from an ontological argument towards a mathematical argument, and the interplay between one-multiple (ontologically speaking) and one-multiple (numerically understood) might testify that numbers could not have been articulated unless we proceed from an ontological one to a numerical one.33 The initial three entities which are different from each other—‘difference is not the same as oneness or being’ (143b6–7)—are not straightforwardly counted to obtain number three, but, on the contrary, the stress is on ‘one’ added to a pair. I venture to say that a possible reason for getting to three through such an elaborate and unexpected operation might be the need to highlight oddness—that one is what is added to any pair. Reaching number three just from plain counting of ‘one’, ‘being’ and ‘difference’ would not stress the oddness of number three, a matter in which Plato is very interested. After reaching three (143d9–e2) from 2+1, the next step is to emphasise that three is

32 33

D. Ross, Plato’s Theory of Ideas (Oxford: Clarendon Press, 1951), 187: ‘The difference […] is different, so that we already have three things. And three is odd’. G.E.M. Anscombe, From Parmenides to Wittgenstein, i: Collected Philosophical Papers (Oxford: Basil Blackwell, 1991) commenting on this argument, notices that ‘one itself is infinitely divided, each of the numbers being one’ (25). If numbers are unitary because of ‘one’, then it follows that their ‘existence’ is given by ‘being’ and their identity is made possible by ‘difference’.

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figure 9.1 Knorr’s depiction of the formula for 2k + 1

odd (τρία … περιττά), and, of course, that two is even (δύο ἄρτια). Through the operation of 2+1 the argument brings into focus the idea of oddness, rather than the actual numerical value of three. This becomes more evident if we consider that in the Phaedo (105c) Plato states that oneness makes an odd number odd: ‘if asked the presence of what in a number makes it odd (περιττός), I will not say oddness (περιττότης) but oneness (μονάς)’.34 Knorr’s visual representation of even numbers (Figure 9.1) highlights how one is essential to the definition of odd numbers.35 Plato’s understanding of odd numbers, at least according to this argument, would be to identify odd numbers as being of type 2k+1, while the 2k expression defines even numbers. After the classification of oddness and evenness is established, the next step is to use another arithmetical operation.36 After addition, used to obtain three, multiplication is introduced (143e5–e7): there will be even times even (ἄρτια ἀρτιάκις), odd times odd (περιττὰ περιττάκις), odd times even (ἄρτια περιττάκις), and even times odd (περιττὰ ἀρτιάκις). Since multiplication is immediately added, and since one (the condition for three and odd) is derived from two (which is even), we need only number two, and the generation of the rest of the numbers is assured. Hence the argument seems to stress that if there is one, there are numbers one, two, three, but not in standard ‘chronological’ order. If one is, numbers are subsequently 2, 1, and 2 + 1 (3), and by multiplication,

34

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The Greek περιττός has the basic meaning of something that is beyond the average, something in excess, more in quantity, and it could have also referred to the additional one. W.R. Knorr, The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Dordrecht: D. Reidel, 1975), 140. The very use of a mathematical operation here actually goes against the frame of Plato’s mathematical discussions elsewhere in his dialogues. As J.M. Moravcsik, ‘Forms and Dialectic in the Second Half of the Parmenides’, in M. Schofield and M.C. Nussbaum (eds), Language and Logos: Studies in Ancient Greek Philosophy Presented to G.E.L. Owen (Cambridge: Cambridge University Press, 1982) puts it: ‘There is nothing in Plato’s ontology that corresponds to mathematical operations; the ontology reflects only mathematical truths’ (144).

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the rest of the numbers.37 Two, one, and three—in this order of generation— stand thus as the basic numbers for Plato’s generation of numbers.38 This could be understood as an innovation from the ‘one’ and the model of the ‘first four numbers’ (1, 2, 3, 4—the tetractys) that were the elementary ingredients for the generation of numbers for the Pythagoreans.39 In addition to having all the numbers generated through two and three by multiplying them, and by bringing into discussion evenness and oddness, the argument traces the operations that lead to the identification of some kind of primordia, or generating conditions, for numbers.

2

Odd, Even and Prime Numbers

It may seem unnecessary for the argument to jump to the discussion of evenness and oddness, since two and three would do the multiplication process without the necessity of classification. However, by avoiding the direct resol-

37 38

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J.M. Moravcsik, ‘Forms and Dialectic’, 144 draws attention to this feature of number three: ‘Plato might add the number 3 as basic if 1 is not acknowledged as a number’. This reminds us of intuitionism in mathematics. For example, for L.E.J. Brouwer, number generation starts from the intuition of pure twoness: ‘This intuition of two-oneness, the basal intuition of mathematics, creates not only the numbers one and two, but also all finite ordinal numbers, inasmuch as one of the elements of the two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely’ (‘Intuitionism and Formalism’ [1912], in P. Benacerraf and H. Putnam (eds), Philosophy of Mathematics: Selected Readings (Cambridge: Cambridge University Press, 1984), 77–89, at 80). See also M. Panza and A. Sereni, Plato’s Problem: An Introduction to Mathematical Platonism (New York: Palgrave Macmillan, 2013), 88. However, Brouwer’s intuitionism with regards to duality is not based on Plato’s argument, but on Kant’s. J. Annas, Aristotle’s Metaphysics: Books M and N (Oxford: Clarendon Press, 1976), 43, also draws a parallel with Brouwer, when referring to the Aristotelian critique of Plato, namely that according to the so-called ‘unwritten doctrine’ numbers are generated from one and ‘indefinite two’. In Pythagorean philosophy there is an intermingling between cosmology and generation of numbers. I agree on this point with Cornford’s classical study, which argued that Pythagoras ‘could not yet distinguish between a purely logical ‘process’ such as the ‘generation’ of the series of numbers, and an actual process in time such as the generation of the visible Heaven […]. The cosmological process was thus confused with the generation of numbers from One’, see F.M. Cornford, ‘Mystery Religions and Pre-Socratic Philosophy’, in J.B. Bury, S.A. Cook and F.E. Adcock (eds), The Cambridge Ancient History, iv: The Persian Empire and the West (Cambridge: Cambridge University Press, 1926), 522–678, at 550–551. Aristotle mentions more than once that Plato followed the Pythagoreans (e.g. Metaph. 987a29). For a reassessment of the Pythagoreanism of Plato, see P.S. Horky, Plato and Pythagoreanism (Oxford: Oxford University Press, 2013).

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ution of the generation process that could be achieved by multiplying only two and three, and by instead insisting on multiplying oddness and evenness, Plato makes a leap into the field of number properties. This is not only a dialogic device, but a logical development of the whole argument. The abrupt emphasis on evenness and oddness is a progression from a particular—there must be ‘twice two’ (δύο δίς, 143e3), and there must be ‘thrice three’ (τρία τρίς, 143e3), thus there must be twice three (τρία δίς) and thrice two (δύο τρίς, 143e5)—to a universal rule (143e7): there will be even times even (ἄρτια ἀρτιάκις), odd times odd (περιττὰ περιττάκις), odd times even (ἄρτια περιττάκις), and even times odd (περιττὰ ἀρτιάκις). It appears that one of the most important aims within the argument is to obtain the first odd and the first even; these are not features of numbers; rather numbers are features and derivations of odd and even.40 Plato is thus consistent with his views in other dialogues, at least at the epistemological level, where the knowledge of numbers is the knowledge of the odd and even.41 The specific classification of numbers as odd and even shows also the use of a specific differentia of numbers in order to classify them. Hence, what the mathematical argument offers us is not a linear progression of numbers, but a generation and classification of numbers according to odd an even. If we emphasise this distribution, odd and even work for the classification of numbers from two elementary categories (odd and even) towards four composite categories (odd-even, even-odd, even-even, and odd-odd).42 It is probable that the ancient Greeks understood even, odd, and odd-even as species.43 Similar ways of classifying numbers, by odd and even, are described by Philolaus: ‘Number, indeed, has two proper kinds, odd and even, and a third mixed together from both, the even-odd (αρτιοπέριττον)’.44 Whether there is a link between

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As it is pointed out in Euthyphro (12d–e): ‘Shame is a part of fear just as odd is a part of number, with the result that it is not true that where there is number there is also oddness, but that where there is oddness there is also number’ (emphasis added). Resp. 7.524d, Tht. 198a, Grg. 453e, Chrm. 166a. See further, for example, L. Zhmud, The Origin of the History of Science in Classical Antiquity, trans. Alexander Chernoglazov (Berlin: De Gruyter, 2006), 223. From the four composite categories only three are distinct, because odd-even and evenodd share the same multitude of elements. The mixture of odd and even is thus a derivate of the two main species. See in this regard J. Klein, ‘The Concept of Number in Greek Mathematics and Philosophy’, in R.B. Williamson and E. Zuckerman (eds), Lectures and Essays (Annapolis, MD: St John’s College Press, 1985), 43–52, at 47. Philolaus fr. 5 DK, see C.A. Huffman, Philolaus of Croton: Pythagorean and Presocratic (Cambridge: Cambridge University Press, 1993), 178.

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Philolaus here and Plato’s understanding of numbers in terms of odd and even, is still an issue to be clarified,45 but it is significant that Euclid continues the same classification.46 As stated earlier, we would expect to derive numbers with the help of addition rather than multiplication. Apart from setting out oddness and evenness, another possible motivation for the use of multiplication may be that it offers a simpler and more schematic pattern for numbers. They are to be factorially generated from the fundamentals two and three, rather than through an increase of one (e.g., operations with units: 6 = 1+1+1+1 + 1 + 1 versus, planius, 6 = 3 × 2 or 2×3).47 Factorial deduction of numbers would contradict Aristotle’s view, according to which ‘each number is said to be many because it consists of ones and because each number is measurable by one’ (Metaph. 1056b23). Even if the argument ends with the conclusion that there is no number left that does not necessarily exist (144a3), we cannot get the entire number series by reducing numbers to odd and even and their multiplication. The argument fails to include prime numbers—Aristotle notes Plato’s failure to address the subject (Metaph. 987b29–988a1)—since these numbers have no divisors other than themselves and one; after two and three the rest of the prime numbers cannot be generated. Conceivable solutions to the generation of primes would eventually be limited to the subsequent operations. We could combine addition and multiplication, and therefore get to a prime number like 5 as the result of 2×2+1. Primes could also be the result of odd times odd, and numbers like 5 or 7 would be 5×1 or 7×1, which would be possible if 1 is considered odd, or 45

46 47

C. Meinwald, ‘Plato’s Pythagoreanism’, AncPhil, 22 (2002), 87–101, at 87, rightly points out that ‘Pythagorean scholarship is too diverse and contentious to be a starting-point for reading Plato’; still, she identifies Philolaic remnants in Plato. Another resemblance with Philolaus could be found in fr. 8, where ‘one’ is understood as the ‘principle of all things’. But, as Huffman suggests (Philolaus, 346), this last fragment may be spurious. Hence, according to both Plato and Philolaus, numbers gravitate around one (or the ‘one that is’, in the case of Plato), which gives every number its unitary identity (see also footnote 33 in this article). When Plato pictures numbers as originating in one (that is) he could be reiterating a Philolaic idea, but by bringing ‘being’ and ‘difference’ into discussion he nevertheless develops the idea further. Plato’s incursion into the problem of the generation of numbers may thus echo a Pythagorean discussion on the generation of the world and of numbers. As T. Heath, Greek Mathematics, ii, 72, noticed: ‘Euclid’s classification does not go much beyond this [Plato’s classification]’. There are similarities here with the series of numbers used by some cultures: some Indigenous Australians limited their number systems to one and two (i.e., a binary system), and out of them composed numbers up to six, e.g. three is made by two and one, while six is made by two and two and two. See T. Dantzig, Number: The Language of Science (1930; 4th edn., New York: Macmillan, 1954), 14.

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primes could be a subcategory of odd numbers. The question of how exactly one gets to primes remains, however, unanswered. Given that any solution would eventually be controversial, for the moment I propose that Plato tries to achieve a governing law of the number series encompassing their primordia and their related operations: oddness, evenness, and multiplication. In stressing a general law for the generation of numbers, Plato might have oversimplified the whole discussion and, as a result, failed to give a satisfying and explicit account of primes. Primes could have been intentionally left out since there is no law for their generation (only ways to validate them), and ancient mathematicians knew that.48 But beyond these geometrical attempts to ‘work’ with primes, no arithmetic operation clarified how non-composite (i.e. prime) numbers came to be.49 For Plato, one could go as far as speculating that each prime number would have a corresponding prime number-form, while the rest— reachable through factorial operations—would have corresponding combinations of one or two forms (e.g., seven would participate in the prime number form, while six would participate in even-odd).

Conclusion The line on which Plato develops his thoughts seems to move imperceptibly from ontology towards arithmetic, as if there is a continuum from the ontological differentiation between ‘one’ and ‘being’ towards number differentiation and thus their generation and classification. Once the ontological differentiation is made (by the atypical instrumentalisation of ‘difference’ that introduces differentia—perceived as an ontological-logical device), arithmetical inferences follow. The arguments are consequential: there are numbers (the second argument) only because ‘one’ is ‘one’ and ‘being’ (the first argu-

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Greek mathematicians were aware that each integer number could undergo prime factorisation, and they were the first to study prime numbers in themselves (πρώτοι ἀριθμοί). According to Iamblichus, the Pythagorean mathematician Thymaridas of Paros (400– 350 bce) called prime numbers ‘rectilinear’ since they can be represented only as onedimensional segments, while non-prime numbers can be represented in two-dimensional planes. Euclid, in Books vii and ix of the Elements, which deals with number theory, discusses thoroughly the problem of prime numbers. One of the biggest achievements of Euclid, in number theory, was to show that any number is either a prime, or divisible by a prime number (vii, 32), and that there are infinitely many prime numbers (ix, 20). Only recent research into the question of primes advances algorithms as key for identifying prime numbers, e.g., R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective (New York: Springer, 2006).

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ment). The ‘one’ and its related concepts of ‘being’ and ‘difference’ are distinguished as separate entities for an account of the question of generation. These distinct concepts do not lead us to discover twoness or threeness: their very distinctiveness endorses the idea of multiplicity. The first duality observed (i.e., ‘one’ and ‘being’) is the pair ‘one-multiple’. In itself, it has no mathematical meaning, but it does establish a basis for understanding ontological multiplicity, and thus the numeric value of multiplicity. Without recognising this shift from ontology to mathematics as purposeful, and not fallacious, one can only agree with Sabetai Unguru, that ‘it is impossible for a modern man to think like an ancient Greek.’50 Plato did not just understand the role of mathematics differently, he also explored the ontology of numbers differently. Though there may be little value for modern mathematics in Plato’s argument, what the Parmenides brings forth is a philosophical discourse on the ontological fundamentals of mathematics.

Bibliography Allen, R.E., ‘The Generation of Numbers in Plato’s Parmenides’, CPh, 65 (1970), 30–34. Allen, R.E., ‘Unity and Infinity: Parmenides 142b–145a’, RMeta, 27 (1974), 697–725. Allen, R.E., Plato’s Parmenides (rev. New Haven: Yale University Press, 1997). Annas, J., Aristotle’s Metaphysics: Books M and N (Oxford: Clarendon Press, 1976). Anscombe, G.E.M., From Parmenides to Wittgenstein, i: Collected Philosophical Papers (Oxford: Basil Blackwell, 1991). Blyth, D., ‘Platonic Number in the Parmenides and Metaphysics xiii’, IJPS, 8 (2000), 23– 45. Brouwer, L.E.J., ‘Intuitionism and Formalism’ [1912], in P. Benacerraf and H. Putnam (eds), Philosophy of Mathematics: Selected Readings (Cambridge: Cambridge University Press, 1983), 77–89. Burnyeat, M.F., ‘Platonism and Mathematics: A Prelude to Discussion’, in A. Graeser (ed.), Mathematics and Metaphysics in Aristotle (Bern: Paul Hapt, 1987), 213–240. Burnyeat, M.F., ‘Plato on Why Mathematics is Good for the Soul’, in T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy (Oxford: Oxford University Press, 2000), 1–81. Calian, F.G., ‘One, Two, Three… A Discussion on the Generation of Numbers in Plato’s Parmenides’, New Europe College, (2015), 49–78.

50

S. Unguru, ‘Counter-Revolutions in Mathematics’, in Michalis Sialaros (ed.), Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 19–34, at 29.

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Cornford, F.M., ‘Mystery Religions and Pre-Socratic Philosophy’, in J.B. Bury, S.A. Cook and F.E. Adcock (eds), The Cambridge Ancient History, iv: The Persian Empire and the West (Cambridge: Cambridge University Press, 1926), 522–678. Cornford, F.M., Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides (London: Kegan Paul, 1939). Crandall, R. and C. Pomerance, Prime Numbers: A Computational Perspective (New York: Springer, 2006). Dantzig, T., Number: The Language of Science (1930; 4th edn., New York: Macmillan, 1954). Everett, C., Numbers and the Making of Us: Counting and the Course of Human Cultures (Cambridge, MA: Harvard University Press, 2017). Gordon, P., ‘Numerical Cognition Without Words’, Science, 15 (2004), 496–499. Harte, V., review of P. Pritchard, Plato’s Philosophy of Mathematics (Sankt Augustin: Academia Verlag, 1995), in JHS, 118 (1998), 227. Heath, T., A History of Greek Mathematics, ii: From Aristarchus to Diophantus ([Oxford: Clarendon, 1921] New York: Dover, 1981). Henry, J., Religion, Magic, and the Origins of Science in Early Modern England (London: Routledge, 2018). Horky, P.S., Plato and Pythagoreanism (Oxford: Oxford University Press, 2013). Huffman, C.A., Philolaus of Croton: Pythagorean and Presocratic (Cambridge: Cambridge University Press, 1993). Kahn, C., Plato and the Post-Socratic Dialogue: The Return to the Philosophy of Nature (Cambridge: Cambridge University Press, 2013). Kelsey, W., Troubling Play: Meaning and Entity in Plato’s Parmenides (New York: SUNY Press, 2012). Klein, J., ‘The Concept of Number in Greek Mathematics and Philosophy’, in R.B. Williamson and E. Zuckerman (eds), Lectures and Essays (Annapolis, MD: St John’s College Press, 1985), 43–52. Klein, J., Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (Cambridge, MA: MIT Press, 1968; repr. New York: Dover, 1992). Knorr, W.R., The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Dordrecht: D. Reidel, 1975). Laurence, S. and E. Margolis, ‘Linguistic Determinism and the Innate Basis of Number’, in P. Carruthers, P. Laurence and S. Stich (eds), The Innate Mind (Oxford: Oxford University Press, 2008), 139–169. Meinwald, C., ‘Plato’s Pythagoreanism’, AncPhil, 22 (2002), 87–101. Moravcsik, J.M., ‘Forms and Dialectic in the Second Half of the Parmenides’, in M. Schofield and M.C. Nussbaum (eds), Language and Logos: Studies in Ancient Greek Philosophy Presented to G.E.L. Owen (Cambridge: Cambridge University Press, 1982), 135–154.

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Negrepontis, S., ‘The Anthyphairetic Revolutions of the Platonic Ideas’, in M. Sialaros (ed.), Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 335–381. Owen, G.E.L., ‘Notes On Ryle’s Plato’, in Logic, Science and Dialectic (London: Duckworth, 1986), 85–103. Panza, M. and A. Sereni, Plato’s Problem: An Introduction to Mathematical Platonism (New York: Palgrave Macmillan, 2013). Pourciau, B., ‘Intuitionism as a (Failed) Kuhnian Revolution in Mathematics’, SHPS, 31 (2000), 297–329. Pritchard, P., Plato’s Philosophy of Mathematics (Sankt Augustin: Academia Verlag, 1995). Rickless, S.C., Plato’s Forms in Transition: A Reading of the Parmenides (Cambridge: Cambridge University Press, 2006). Ross, D., (ed.), Aristotle’s Physics (Oxford: Clarendon Press, 1936). Ross, D., Plato’s Theory of Ideas (Oxford: Clarendon Press, 1951). Russell, B., Introduction to Mathematical Philosophy (London: Allen & Unwin, 1919; rev. repr. London: Routledge, 1993). Ryle, G., ‘Plato’s Parmenides’, Mind, 48/190 (1939), 129–151. Schofield, M., ‘A Neglected Regress Argument in the Parmenides’, CQ, 23/1 (1973), 29–44. Scolnicov, S., Plato’s Parmenides (Berkeley: University of California Press, 2003). Sialaros, M., ‘Introduction: Revolutions in Greek Mathematics’, in M. Sialaros (ed.), Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 1–15. Unguru, S., ‘Counter-Revolutions in Mathematics’, in M. Sialaros (ed.), Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 19–34. Wedberg, A., Plato’s Philosophy of Mathematics (Stockholm: Almqvist & Wiksel, 1955). Wolf, R.S., A Tour Through Mathematical Logic (Washington DC: Mathematical Association of America, 2005). Zhmud, L., The Origin of the History of Science in Classical Antiquity, trans. Alexander Chernoglazov (Berlin: De Gruyter, 2006). Zhmud, L., Pythagoras and the Early Pythagoreans, trans. K. Windle and R. Ireland (Oxford: Oxford University Press, 2012).

chapter 10

Doing Geometry without Numbers: Re-reading Euclid’s Elements Eunsoo Lee

To modern students, geometry is reduced to calculations using the arithmetic operations of addition, subtraction, multiplication, division, and exponentiation. With the development of analytical geometry, elements of geometry have been digitised or quantified; points are positioned by coordinates, lines are measured by length, and areas and volumes are represented by numbers found through arithmetic operations. This synchronisation of geometric elements with numbers has established an arithmetic framework for geometric inquiries. As the eighteenth-century mathematician Joseph-Louis Lagrange articulated, geometry is a lingua mortua.1 The reader of Euclid’s Elements today would naturally expect to see a formula for the area of a triangle or the volume of a cone, as these are included in geometry textbooks. The reader will soon find, however, that the ancient Greek geometer did not provide such formulas. It was not a primary concern of his geometry to teach a formalised way of finding the area or volume of a figure.2 The Elements does not seem, at least, to be our geometry. What, then, is his geometry?3 The contrast can be epitomised by the absence of numbers in the Elements. For example, David Fowler describes the phenomenon as follows:

1 F. Peyrard, Les oeuvres d’Euclide, traduites en latin et en français, d’après un manuscrit trèsancien qui était inconnu jusqu’à nos jours, i (Paris: Patris, 1814), 9–10: ‘D. Lagrange quem extinctum luget et diu lugebit Europa, mihi dictitabat Geometriam esse linguam mortuam; et qui in Euclidis Elementis Geometriae non studebat, eum perinde facere ac si quis graecam latinamve linguam in recentioribus operibus graece et latine scriptis discere velit.’ 2 When referring to Greek geometry, I target the golden age of the third century bce. The works of Heron (first century ce) would be the definite terminus ante quem of the appearance of geometric/measurement formulas. We have to approach the geometry of the Classical period through extant materials in the Elements and other surviving mathematical works. 3 As is well known, Euclid did not name his work geometria. See section 2.4 for discussion of the title.

© Eunsoo Lee, 2022 | doi:10.1163/9789004467224_012

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Almost the only notation for numbers (i.e. numerals) found in the earliest and best manuscripts of Euclid’s works (apart from the Sectio Canonis) is used to label the propositions; with the exception of three numerals in Elements xiii.11, those few numbers that are used in the text are written out as words. This is an extreme case; most mathematical texts, and all manner of financial, administrative, and legal documents, employ a notation [for numerals].4 Shapes appear on the stage, but numbers are absent.5 In this framework, geometric inquiries are resolved only with diagrammatic elements such as lines, angles, and areas—numbers are not conferred on them. This absence of numbers in the Elements is especially significant given that numbers were ubiquitous in many aspects of daily life in Classical Greece.6 Here, two questions arise: (1) Why were numbers, which enabled Greeks to secure objectivity in many spheres of activity, set aside in the exploration of the geometric relationship between figures? (2) Did the absence of numbers have desirable effects for geometers and readers? In attempting to find an answer to these questions, this paper focuses on a specific, numberless strand of Greek geometry (the Elements and some Archimedean works) and analyses the exclusion of numbers: numbers were powerful in Classical Greece, as discussed in other articles in this volume, but they were not the mathematician’s ἀριθμός yet. The paper starts with the classification of geometry with numbers. Then, I define geometry without numbers as the denial of the permeation of num-

4 D.H. Fowler, The Mathematics of Plato’s Academy: A New Reconstruction (Oxford: Clarendon Press, 1999), 222. This absence of numbers contrasts with the diagrams of later manuscript traditions for the Elements. For example, in some manuscripts (such as the Vatican Codex (Vat. Gr.190) and the Bodleian Codex (D’ Orville 301)) of the Elements, some readers wrote numbers on diagrams. Based on palaeographic evidence, most of these numbers were written by later hands. Given that arithmetisation became popular after the end of the first millennium as a result of Arabic influence, the number-added diagrams make sense because they enable readers to check easily that the proposition is true. See E. Lee, ‘Visual Agency in Euclid’s Elements: A Study of the Transmission of Visual Knowledge’, Ph.D. thesis (Stanford University, 2020). 5 The absence of numbers means more specifically the absence of numerals. 6 For the contrast between theoretical and practical mathematics in ancient Greece, see M. Asper, ‘The Two Cultures of Mathematics in Ancient Greece’, in E. Robson and J.A. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2009), 107–132.

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bers into geometry at various levels (section 1.1). The contextualisation of the absence of numbers in the Elements in terms of contemporary strategies of everyday measurement leads to the conclusion that its exceptional geometry reflects the decision of the geometer to measure figures with figures (section 1.2). In Part 2, I explain how measurement is reformed and introduced in this more elaborated way in the Elements. Numerals were not the main tool of the geometer’s geometrical explanations. Instead, he introduced the way to measure a figure with figures. I define ancient measurement—a measuring system that relies on natural and discrete units—as ‘magnitude counting’. By this I refer to the number of units required to match up to the object being measured (section 2.1). I trace the process of how the Elements develops this new type of measuring in three phases: 1) comparative measuring in ratio (section 2.2); 2) extended measuring in proportion (section 2.3); and 3) numerical measuring by the synthesis of magnitude and number (section 2.4). Finally, in Part 3, I focus on the continuation of geometry without numbers by the geometer’s successors. The factors behind the success of this geometry, notwithstanding or due to the absence of numbers, need to be found. A plausible explanation must consider whether there was a tacit agreement, at least among Greek mathematicians, that resulted in the fixed style of Greek mathematics. If not, what other benefits were realised by doing geometry without numbers?

1

Part 1

1.1 Geometry With or Without Numbers Let me start by first explaining geometry with numbers. Whenever a geometrical object is given, we tend to measure its sides, angles, surface areas and volumes with numerical values. Our geometrical practices are obsessed with measuring and thus expressing magnitude with numerals. In this sense, geometry with numbers simply conveys the gist of our school geometry. If we look at this synchronisation more deeply, however, we find various layers of the permeation of numbers into figures: 1. Giving numerical values to basic geometric objects like lines and angles (Numerical Quantification) 2. Manipulating numbers based on geometric relations (Numerical Calculation) 3. Interpreting geometric results with algebraic expressions (Algebraisation)

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figure 10.1 Geometry with numbers (Quantification)

figure 10.2 Geometry with numbers (Calculation)

Geometry with numbers starts with the work of assigning numbers to each of the geometric elements. Numbers are given as a result of the quantification of geometric components. For example, in figure 10.1, the magnitude of an angle or the length of a line segment are given in numerical values. Second, geometry with numbers develops when quantification is combined with calculation. The calculation is performed based on a convenient set of abbreviations, i.e. using letters or simple signs for quantities and operations. For example, in figure 10.2, readers are supposed to find the angles by making and solving an equation: 9x + 16 = (6x + 4) + (4x − 2).7 This is the geometry with which we should already be familiar. Third, geometry may use algebra as a communicative device to convey the pertinent theory efficiently. For example, the greatest obstacle to understanding the Pythagorean theorem for the mathematical novice (see figure 10.3) is the cognitive strain of visualising complex relational language; however, a simple equation, a2 = b2 + c2 , can provide an effective way to capture this theorem quickly. Modern interpretations of ancient geometry tend to convert geometrical results into algebraic formulas. Based on this classification, we can imagine a geometry without numbers by denying the permeation of numbers at each of these levels, and this is what we

7 i.e. one exterior angle of a triangle is equal to the sum of two non-adjacent interior angles.

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figure 10.3

241

Geometry with numbers (Algebraisation) Proposition i.47: ‘In right-angled triangles the square on the side opposite the right angle equals the sum of the squares containing the right angle’. All translations of the Elements in this paper follow T.L. Heath, The Thirteen Books of Euclid’s Elements (Cambridge: University Press, 1908). Diagrams for the Elements and Archimedean works in this paper are based on manuscript diagrams. For the difference between manuscript diagrams and their reproductions in modern printed editions, see K. Saito and N. Sidoli, ‘Diagrams and Arguments in Ancient Greek Mathematics: Lessons Drawn from Comparisons of the Manuscript Diagrams with Those in Modern Critical Editions’, in K. Chemla (ed.), The History of Mathematical Proof in Ancient Traditions (Cambridge: Cambridge University Press, 2012), 135–162.

see in the geometry of the Elements. First, diagrams mostly lack measures and thus numbers, thereby denying numerical quantification. Second, figures are compared and equated directly with other figures, and so deny numerical calculation.8 This interesting feature is highlighted in the so-called application of areas which will be discussed below. It is said that an area is given, but there is no mention about the width of the area. Similarly, when it is said that an angle 8 Figures in Greek geometry are understood as objects that, through abstraction (aphaeresis), have lost their numerical values just as they have lost their physical features, such as colour and texture. Thus, calculation, which is available only after numerical values are given, is not the core issue in Greek geometry.

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figure 10.4

Geometry with numbers (Geometrisation) Proposition ii.4. If a straight line is cut at random, the square on the whole equals the squares on the segments plus twice the rectangle contained by the segments. Let ΑΒ = x, ΑΓ = y, ΒΓ = z. Then, x2 = (y + z)2 = y2 + z2 + 2yz.

is given, there seems to be no interest in the degree of the angle.9 So, in geometry without numbers, measurement is silenced, and numbers, it appears, are regarded as an insufficient means of conducting geometry. Finally, algebraic results are understood and interpreted with geometric expressions in the Elements, denying algebraisation. Algebra can provide an epistemological basis for a theory. For example, if we interpret Proposition ii.4 (figure 10.4) as having an algebraic root in its conception, even though it is geometric in its content, then we may say that algebra directs geometry at the theoretical level.10 What lies behind this geometry without numbers? How can we interpret this endeavour without numbers? Does the absence of numbers imply the absence of measurement? My answer is no. I do not think the geometer in the Elements was unconcerned about measurement. On the contrary, he denied numbers in order to measure a figure with figures. As shall be discussed in the following sections, this geometry was rooted in the Greek mentalité of measurement. 1.2 Euclid as a Metronomos in Greek Geometry Let us situate the Elements in its context. In Classical Greece, there were a number of practitioners who measured and calculated areas and volumes. For

9 10

The idea of application of areas seems, to some extent, known beyond geometry. In a famous mathematical passage in Plato’s Meno (86e–87a), similar ideas are found. The so-called ‘geometrical algebra’ was widely believed to be the basis of Book ii of the Elements until Sebatai Unguru criticised the concept in his famous 1975 article ‘On the Need to Rewrite the History of Greek Mathematics’, AHES, 15 (1975), 67–114.

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example, David Fowler explains the methods used in surveying and measuring in detail,11 and Markus Asper establishes strong philological evidence for measuring oi harpēdonaptai (‘rope-stretchers’).12 Therefore, theoretical mathematicians had methods of measurement available and the geometry without numbers in the Elements looks exceptional. Therefore, we need to emphasise the agency in the question with which I began: why did the geometer disregard number in solving or proving the geometric relationship of figures? Critical evidence, ironically, comes from the practice of the Greeks who clung to measurements. Officials known as metronomoi are attested from the second half of the fourth century bce in Athens, where they were responsible for supervising measures and weights.13 They had to impose penalties on sellers in the agora who sold goods using containers that were smaller than the prescribed standard, and then break these non-standard measures. An inscription of the second century bce, IG ii2 1013, gives a glimpse of Athenian efforts to maintain and manage the standardisation of measures and weights: [7] The magistracies, as they are required to do by laws, shall make metrological instruments (σηκώματα) in accordance with the established standards (σύμβολα) that have been made for the liquid measures (ὑγρά), the dry measures (ξηρά), and the weights (σταθμά), and shall require any seller, in the agora or in the workshops or in the retail stores or in the taverns or in the warehouses, to use these measures (μέτρα) and weights (σταθμά), and to measure (μετρέω) all the liquids (ὑγρά) with the same measure (μέτρον), and no magistracy shall no more be allowed to make measures (μέτρα) or weights (στάθμια) [larger] or smaller than these … [17] So that no one among the sellers or the buyers uses a measure (μέτρον) or a weight (σταθμόν) discordant with the standard (ἀσύμβλητον), but only correct ones14 For this system of supervision, Athenians had to keep the standards (σύμβολα) of liquid measures, dry measures, and weights somewhere. In order to know whether the containers being used in the agora conformed or not, the 11 12 13 14

Fowler, Mathematics, 270–276. Asper, ‘The Two Cultures’, 113. Metronomoi appear for instance in [Arist.] Ath. Pol. 51.2, and Dinarchus (fr. 19.8 Conomis, with Poll. 4.167). Translation modified from that of C. Doyen. For an analysis of the structure of the inscription, see Doyen’s ‘An Athenian Decree Revisited’, CHS Research Bulletin, 4/1 (2015), http://​ nrs.harvard.edu/urn3:hlnc.essay:DoyenC.An_Athenian_Decree_Revisited.2016, accessed 1 Mar. 2021.

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metronomoi had to compare them with the standardised metrological instruments (σηκώματα) based on the σύμβολα: [37] [So that] the measures (μέτρα) and the weights (σταθμά) are preserved in the future: [38] The appointee to establish the measures (μέτρα) and the weights (σταθμά), Diodoros, (son) of Theophilos, (from the deme) of Halai, shall transmit the standards (σύμβολα) to the public slave appointed in the Skias, to the one at Peiraieus assigned to the [epimelet]es?, and to the one at Eleusis. [40] Those shall conserve them and give metrological instruments (σηκώματα) of the measures (μέτρα) and the weights (σταθμά) to the magistracies and to anyone else who needs them, without being allowed to modify [the standards (σύμβολα)] or to remove them outside of the appointed designated premises, except for the metrological instruments (σηκώματα) created in lead, and sealed [- - -]. What can be seen here is an emphasis on standardised norms rather than the pursuit of absolute accuracy. We are strangers to this ancient concept of measurement. It is mainly because of our use of instruments that instantly show the result of measurement using numbers. Absolute measurement is quite a modern concept, in that it requires standardisation and calibration among measuring instruments.15 Our measurement is more concerned with continuous quantities rather than discrete quantities. Rulers, protractors, and scales are all devised to make a one-to-one correspondence between the magnitude and the number. Admittedly, ancient measurement also gives a number as a result of measuring, but the result was normally expressed as a natural number. While counting had an absolute meaning thanks to natural numbers, measuring remained, critically, a relative activity until numerical measuring instruments were used; the measuring units such as pous and daktylos were practical but each instance of their use might be different from one another.16

15

16

For example, H. Chang has excellently described the history of attempts to numericise temperature in his book Inventing Temperature: Measurement and Scientific Progress (Oxford: Oxford University Press, 2004). As Steven Johnstone points out, we should not assume that ‘the actual vessels they [sc. ordinary Greeks] had were gauged to standard sizes’. The standard measures, as he argues, ‘usually spread when authorities compel others to use them’. See S. Johnstone, A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011), 63–74.

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Why did the standard matter? Ancients used a specific unit that would fit with their practice, and basic measurement could be reduced to counting the number of the units, such as daktylos for length, pous for area, and kochliarion for volume. Using standards of these units as metrological instruments, they quantified in two ways: comparing and counting. This comparison centred on the question of whether the comparanda were equal to or less than the standard. The standard was also used as a counting unit for quantification. For measures and weights, quantity was measured as a multiple of the proper counting unit such as two standard olpes, three standard olpes, etc. Only the question of posology, of ‘how many multiples of the unit are there?’ steered the activity of measuring; counting was the main activity, and the natural number (also termed the counting number) was used as the basic tool for measurement. For this kind of reasoning, finding a unit that enabled natural number counting would be the most critical task in measuring. Can we find a similar approach in geometry without numbers? The geometry in the Elements was born from a counting and comparing mentalité. Then what is the standard (σύμβολον) in geometry by which one can quantify a geometrical figure? We can find a clue from the instructive definition of the line. In the Elements the line is defined as ‘a length with no breadth’ (γραμμὴ δὲ μῆκος ἀπλατές). From the ancient period, scholarly attention has been given to the dimension of the line, i.e. not its breadth.17 I focus on the way in which magnitude came to define the line itself. This may seem odd to our eyes, since we normally distinguish the length of a line from the line itself; line means a geometrical object, and length is a magnitude that is conferred upon the object. Euclid’s definition of the line as ‘a length’ is worth noting in that two entities, the geometrical object and its magnitude, are conflated together; thus the line visually conveys the information about the length. This idea is distinct from the tradition of writing a number on top of the line to indicate its length.18 The definition of the line as a length foreshadows what will follow in the Elements. Once defined as a length, the line becomes a measuring tool to measure other lines. This is where we get insights about figure counting. The core question in the Elements is not much different from what we see in the agora with the metronomoi. The geometer starts from how many multiples of a line would be required to match another line. Then the geometer applies the same question of posology to more various figures. The main obstacle in this plan is that some figures are more challenging to count. This is why the geometer does

17 18

Heath, The Thirteen Books, 158–165. See, for example, the Rhind Papyrus and the Babylonian clay tablet YBC 7289.

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the preliminary work for figure counting in the first four books of the Elements before the introduction of the ratio in Book v. Therefore, the re-reading of the Elements in terms of figure counting is justified by the internal evidence as well as its external and contextual evidence. This observation leads to my thesis that the figure in the Elements is not an object of measurement, but a tool of measurement. I term Euclid’s method of measurement ‘visual magnitude counting’ and discuss it in detail in the next section.

2

Part 2

What are the implications of saying that figures measure figures? Throughout Part 2, I will show that the definition of the line as a magnitude can be interpreted as a visual turn in the history of measurement in the sense that the figure becomes a tool for measurement instead of being a mere object to be passively measured. 2.1 Counting Figures As we move through the propositions in the Elements, we can see the geometer building a more sophisticated type of measurement by arranging figures, defining equalness, and explaining how to transform the shape of figures. First, some terms in the Elements imply that the geometer assumed that the figures are arranged in rows. Such an arrangement was a key preliminary task to the counting of figures. In fact, the geometer introduces how to line up the lines (Proposition i.2) and how to arrange parallelograms in a row (Proposition i.45). Thus, from Book ii, he enjoys the licentia of assuming figures ‘laid down together (συγκείμενον)’. After the figures are laid down in a row, the ‘carnival of comparison’ starts.19 The geometer first deals with a figure that is said to be equal in its form to another figure—congruence in our sense. For this purpose, as is well known, he moves or superposes a figure on top of another figure. This motion of figures, ‘to fit exactly (ἐφαρμόζειν)’, can be regarded as a reasonable description if the reader keeps in mind that the figure measures a figure. In fact, the idea ‘to be equal (ἴσα)’ introduced in the common notions foreshadows the figure counting and, in particular, the obsession with equalness and unequalness:20 19 20

See R. Netz, Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic (Cambridge: Cambridge University Press, 2009), chapter 1. The common notions are a set of axioms presented following definitions and postulates, and are principles about equality and mereology. For the first appraisal of the number of

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figure 10.5 Diagram of Proposition i.35

αʹ. 1. βʹ. 2. γʹ. 3. δʹ. 4. εʹ. 5.

τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα. Things which equal the same thing also equal one another. καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα. If equals are added to equals, then the wholes are equal. καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα. If equals are subtracted from equals, then the remainders are equal. καὶ τὰ ἐφαρμόζοντα ἐπ’ ἀλλήλα ἴσα ἀλλήλοις ἐστίν. Things which coincide with one another equal one another. καὶ τὸ ὅλον τοῦ μέρους μεῖζόν [ἐστιν]. The whole is greater than the part. euc. 1.CN.1–5

The understanding of equalness in the common notions seems obvious. At least, it seems much more elementary than the postulates preceding these common notions. However, if we read the Elements in terms of the measurement of figures with a figure, the common notions form the core foundation of the geometer’s design. Proposition i.35, (figure 10.5), with its explanation of the equalness of two parallelograms, is an example of how the concept of ‘equal’ is different from ours: τὰ παραλληλόγραμμα τὰ ἐπὶ τῆς αὐτῆς βάσεως ὄντα καὶ ἐν ταῖς αὐταῖς παραλλήλοις ἴσα ἀλλήλοις ἐστίν. Parallelograms which are on the same base and in the same parallels equal one another. common notions in manuscripts and printed editions of the Elements, see V. De Risi, ‘The Development of Euclidean Axiomatics. The Systems of Principles and the Foundations of Mathematics in Editions of the Elements from Antiquity to the Eighteenth Century’, AHES, 70 (2016), 591–676. De Risi also investigates their authenticity and their actual role in the demonstrations, see ‘Euclid’s Common Notions and the Theory of Equivalence’, Foundations of Science, 26/2 (2021), 301–324.

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figure 10.6 Diagram of Proposition i.42

Before this proposition, equality was introduced in the sense of congruence only. Now, as Heath noted, ‘without any explicit reference to any change in the meaning of the term, figures are inferred to be equal which are equal in area or in content but need not be of the same form.’21 In the Elements, there is no mediator—such as number to indicate size—between two figures that can be used to demonstrate equalness or greaterness. Without relying upon numbers, the geometer directly says that one figure is equal to another or one figure is greater than the other. After explaining the equality, the geometer measures a figure by counting how many unit figures should be laid down to match the measured figure.22 Therefore, he expresses the measurement with counting terms, such as twofold (διπλάσια), tri-fold (τριπλάσια), and multiplied (πολλαπλάσια). However, there is a problem with figure counting. If the unit figure has a different shape from the figure to be measured, it is not easy to count how many unit figures it would take to match the measured figure exactly. To solve this problem, the geometer introduces the idea of transforming the measured figure through the application of areas. For example, Proposition i.42 (figure 10.6) says the following regarding equality between a triangle and a rectangle: τῷ δοθέντι τριγώνῳ ἴσον παραλληλόγραμμον συστήσασθαι ἐν τῇ δοθείσῃ γωνίᾳ εὐθυγράμμῳ. To construct a parallelogram equal to a given triangle in a given rectilinear angle. 21 22

Heath, The Thirteen Books, 327–328. When measuring a figure with a figure, the key requirement is that the figures should not be incommensurable. About how the geometer distinguished incommensurable magnitudes from commensurable magnitudes, see section 2.4 below.

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figure 10.7 Diagram of Proposition i.45

He does not specifically say ‘to construct a parallelogram with an area equal to the area of a given triangle’. Nevertheless, in this problem, the triangle ΑΒΓ and the parallelogram ΖΕΓΗ are said to be equal because their areas are the same, not because of any congruence between them. Proposition i.45 (figure 10.7) then explains how to construct a parallelogram equal to a given rectilinear figure using a given rectilinear angle. First, the parallelogram ΖΚΘΗ is constructed as equal to the triangle ΑΒΔ in the angle ΖΚΘ, which is equal to the given rectilinear angle E. Then, the parallelogram ΗΘΜΛ is constructed, which is equal to the triangle ΔΒΓ. The ultimate meaning of the application of areas is that one figure transforms into another figure with the same area. Using the application of areas, the geometer can transform the figure to be measured into the same shape as the measuring unit. For example, if the measuring unit is a parallelogram while the figure to be measured is a triangle, the triangle is to be converted into a parallelogram that is the same shape as the measuring unit. Once this is done, measurement can take place by arranging measuring units until they fill the figure to be measured (see table 10.1). 2.2 Comparative Measuring in Ratio When there was no absolute measuring unit, the basic activity was to compare two magnitudes. So ancient measurement first focused on comparison. The concern here was to decide whether two comparanda were equal and if not, which was bigger and which was lesser. This basic comparison, however, does

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table 10.1 Figure counting after transforming figures

Measuring unit

Figure to be measured

How many units fill in

Before application of areas

After application of areas

not yield an answer to the question of how big is the bigger and how small is the smaller. Thus, the next development in measuring was to quantify the comparison. To this end, the Elements contains an elaborate plan which I set out below (table 10.2). Once a line becomes a tool for magnitude counting itself, it opens the possibility of measuring through counting i.e., to count how many multiples of the line will exceed, be equal to, or be less than a certain line to be measured (see table 10.3). In order to compare/quantify the comparison between two magnitudes the second step is to conceptualise the comparison in terms of ratio.23 In Definition v.3, ratio (logos) is not defined as a ratio of numbers as we expect. It is suggested to be a relation (schesis), i.e. a more abstract expression of comparison, between two magnitudes of the same kind according to a magnitude/size: ‘A ratio is a certain type of condition with respect to the size of two magnitudes of the same kind’ (Λόγος ἐστὶ δύο μεγεθῶν ὁμογενῶν ἡ κατὰ πηλικότητά ποια σχέσις).24 After giving the brief definition above, the geometer spotlights 23

24

For the significance of ratio and proportion outside of the confines of the Elements, see Fowler, Mathematics, chapters 2 and 10. For the synopsis of the ratio and proportion discussions in the Elements, see also I. Grattan-Guinness, ‘Numbers, Magnitudes, Ratios, and Proportions in Euclid’s Elements: How Did He Handle Them?’, HM, 23 (1996), 355– 375. Cf. Heath’s translation: ‘A ratio is a sort of relation in respect of size between two magnitudes of the same kind’, (p. 114). Scholars have wondered why a more elaborate definition of the ratio was not provided in the Elements. But the definition is sufficient if understood

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doing geometry without numbers table 10.2 Comparison of magnitudes

Less than

Equal to

Greater than

table 10.3 Visual magnitude counting

3 times (less than)

4 times (equal to)

5 times (greater than)

ratio as a new object of discussion. First, he begins by explaining the condition of the existence of ratio: ‘(those) magnitudes are said to have a ratio with respect to one another which, being multiplied are capable of exceeding one another’ (λόγον ἔχειν πρὸς ἄλληλα μεγέθη λέγεται, ἃ δύναται πολλαπλασιαζόμενα ἀλλήλων ὑπερέχειν) (Def.v.4). This can be interpreted as a prerequisite for discussing a ratio. As Heath mentions, this specification excludes the comparison between finite magnitude and infinite magnitude.25 In the end, it becomes possible to quantify the comparison of two magnitudes by expressing the equality and inequality of two ratios. Essential questions such as when two ratios are said to be equal, or when one ratio is greater or less than the other are discussed: ἐν τῷ αὐτῷ λόγῳ μεγέθη λέγεται εἶναι πρῶτον πρὸς δεύτερον καὶ τρίτον πρὸς τέταρτον, ὅταν τὰ τοῦ πρώτου καί τρίτου ἰσάκις πολλαπλάσια τῶν τοῦ δευτέρου

25

as a quantification of comparison. It is not necessary to redefine counting here because counting had naturally been given and practiced. Heath, The Thirteen Books, 120.

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καὶ τετάρτου ἰσάκις πολλαπλασίων καθ’ ὁποιονοῦν πολλαπλασιασμὸν ἑκάτερον ἑκατέρου ἢ ἅμα ὑπερέχῃ ἢ ἅμα ἴσα ᾖ ἢ ἅμα ἐλλείπῇ ληφθέντα κατάλληλα. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever are taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order. Def.v.5

ὅταν δὲ τῶν ἰσάκις πολλαπλασίων τὸ μὲν τοῦ πρώτου πολλαπλάσιον ὑπερέχῃ τοῦ τοῦ δευτέρου πολλαπλασίου, τὸ δὲ τοῦ τρίτου πολλαπλάσιον μὴ ὑπερέχῃ τοῦ τοῦ τετάρτου πολλαπλασίου, τότε τὸ πρῶτον πρὸς τὸ δεύτερον μείζονα λόγον ἔχειν λέγεται, ἤπερ τὸ τρίτον πρὸς τὸ τέταρτον. When, of the equimultiples, the multiple of the first magnitude exceeds the multiple of the second, but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth. Def.v.7

These definitions on the equality and inequality of two ratios enabled measurers to quantify the comparison. For example, let us suppose that two ratios are given as seen in table 10.4. Both ratios express the common situation that the antecedent is less than the consequent. But the antecedent is much lesser than the consequent in the second ratio than the first ratio. Using our presentday approach to the numerical ratio, the first ratio can be expressed as 2:3 and the second ratio is 3:7. If we make the antecedents a common number, each ratio is converted into 6:9 and 6:14 respectively. So, we easily conclude that the first has a greater ratio than the second one. According to Euclid’s design, the two ratios are compared by counting. While two multiples of the magnitude A exceed magnitude B, the equal two multiples of magnitude C do not exceed the magnitude D. Thus, by the definition in v.7, we may conclude that the magnitude A has a greater ratio to magnitude B than the magnitude C has to the magnitude D.26

26

At this stage, Euclid had not fully developed the concept of ratio. The concept remained at the level of magnitude relation without using numbers. The concern about whether

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table 10.4 Inequality of two ratios

A ×2 B

(2)

C

(3)

(3)

D

(7)

2.3 Extended Measuring in Proportion In Book vi, measurement as magnitude counting develops into an ambitious plan to measure universally. In Book v ratio was suggested as a relation of two magnitudes of the same kind. It is easy to count how many multiples of the line will exceed, be equal to, or be less than a certain other line. But the counting of other magnitudes, such as areas or volumes, is more complicated. For example, how can we count how many times a circle will exceed, be equal to, or less than another circle? Proportion reduces the difficulty of the magnitude counting problem through line counting. It allows measurers to find an analogia between different kinds of magnitudes. Roughly, five types of magnitudes are provided in the Elements: angles, lines, regions, surfaces, and solids. By proportion, heterogeneous kinds of ratio are compared to each other. Figure 10.8 is a reproduction of manuscript diagrams for Proposition vi.1, and it effectively shows how the use of proportion increases the power of measurement. The proposition teaches us that the area of the triangle ΑΘΗ has the same ratio (proportional) to the triangle ΑΗΒ as the base ΘΗ has to the base ΗΒ. So the ratio between areas becomes equivalent with the ratio of lines: ‘triangles and parallelograms which are of the same height are to one another as their bases’ (τὰ τρίγωνα καὶ τὰ παραλληλόγραμμα τὰ ὑπὸ τὸ αὐτὸ ὕψος ὄντα πρὸς ἄλληλά ἐστιν ὡς αἱ βάσεις). This definition of proportion increased the compatibility and versatility of magnitude counting. In addition, the transformational equivalences achieved through the application of areas give more discretion to the geometer in magnitude counting. By using the application of areas, it is possible to change a figure with a difficult shape into an easier one for magnitude counting. The entire conversion process for magnitude counting would then be what is shown in figure 10.9. Furthermore, proportion provided geometers with the idea of a common magnitude to determine the equality and inequality of two magnitudes (Prop.v.9–10). While basic comparison is concerned with two magnitudes, proportion juggles three magnitudes. magnitude ratio could be converted into numerical ratio was postponed until Book x (see section 2.4 below).

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figure 10.8 Reproduced diagram for Proposition vi.1

figure 10.9

Conversion map of the magnitude counting

τὰ πρὸς τὸ αὐτὸ τὸν αὐτὸν ἔχοντα λὸγον ἴσα ἀλλήλοις ἐστίν· καὶ πρὸς ἃ τὸ αὐτὸ τὸν αὐτὸν ἕχει λόγον, ἐκεῖνα ἴσα ἐστίν. Magnitudes which have the same ratio to the same equal one another; and magnitudes to which the same has the same ratio are equal. Prop.v.9

As Proposition v.9 shows (figure 10.10), if the magnitudes A and B each have the same ratio to magnitude C, it is said that magnitudes A and B are equal (If A : C :: B : C, then A = B). When saying that two magnitudes are equal, the measurer introduced a third magnitude as a common basis to confirm the equality: τῶν πρὸς τὸ αὐτὸ λόγον ἐχόντων τὸ μείζονα λόγον ἔχον ἐκεῖνο μεῖζόν ἐστιν· πρὸς ὃ δὲ τὸ αὐτὸ μείζονα λόγον ἔχει, ἐκεῖνο ἔλαττόν ἐστιν. Of magnitudes which have a ratio to the same, that which has a greater ratio is greater; and that to which the same has a greater ratio is less. Prop.v.10

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figure 10.10 Diagram of Proposition v.9 figure 10.11 Diagram of Proposition v.10

A similar approach is established for the inequality of two magnitudes (figure 10.11). If the magnitude A has a greater ratio to the magnitude C than the magnitude B (has) to the magnitude C, it is said that the magnitude A is greater than the magnitude B (If A : C > B : C then A > B). The use of the common magnitude (magnitude C in our examples) for the comparison of magnitudes predicts the use of the common measure. In the end, the ultimate form of the magnitude comparison is to count the multiplitude of the common measure. However, it should be noted that any discussion of the unit (for number) or common measure (for magnitude) was yet to come in the Elements. In this situation, the only way to figure out the equality and inequality of magnitudes was to rely upon proportionality. 2.4 Numerical Measuring Finally, numerical counting for measurement emerges. The idea is hinted at in the term multiplitude (πολλαπλάσιον). But another prerequisite precedes the discussion of how to find the common measure. Common measure (κοινὸν μέτρον) is mentioned seven times in the Elements (Prop.vii.2, vii.3, vii.33, Def.x.1, x.2, x.3, x.4). Since it is not always possible to find a common measure between two or more magnitudes, Propositions vii.1 and x.2 explain when two numbers or two magnitudes, respectively, are prime to one another or incommensurable: δύο ἀριθμῶν ἀνίσων ἐκκειμένων, ἀνθυφαιρουμένου δὲ εὶ τοῦ ἐλάσσονος ἀπὸ τοῦ μείζονος, ἐὰν ὁ λειπόμενος μηδέποτε καταμετρῇ τὸν πρὸ ἑαυτοῦ, ἕως οὗ λειφθῇ μονάς, οἱ ἐξ ἀρχῆς ἀριθμοὶ πρῶτοι πρὸς ἀλλὴλους ἔσονται. When two unequal numbers are set out, and the less is continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, then the original numbers are relatively prime. Prop.vii.1

ἐὰν δύο μεγεθῶν [ἐκκειμένων] ἀνίσων ἀνθυφαιρουμένου εὶ τοῦ ἐλάσσονος ἀπὸ τοῦ μείζονος τὸ καταλειπόμενον μηδέποτε καταμετρῇ τὸ πρὸ ἑαυτοῦ, ἀσύμμετρα ἔσται τὰ μεγέθη.

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table 10.5 Analogy between number and magnitude

Number

Magnitude

vii.1 When two unequal numbers are set out, and the less is continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, then the original numbers are relatively prime.

x.2 If, when the less of two unequal magnitudes is continually subtracted in turn from the greater that which is left never measures the one before it, then the two magnitudes are incommensurable.

vii.2 To find the greatest common measure of two given numbers not relatively prime.

x.3 To find the greatest common measure of two given commensurable magnitudes.

vii.3 To find the greatest common measure of three given numbers not relatively prime.

x.4 To find the greatest common measure of three given commensurable magnitudes

If, when the less of two unequal magnitudes is continually subtracted in turn from the greater that which is left never measures the one before it, then the two magnitudes are incommensurable. Prop.x.2

On the condition that two magnitudes are not incommensurable, it is possible to solve the problem of finding their measuring unit. The common measure between magnitudes is found by reciprocal subtraction, known as anthyphairesis.27 This measure, however, works as a temporary unit, not an absolute unit. So for each ratio, a different unit is given: the unit is flexible, not a fixed unit such as a natural number or absolute zero in chemistry. It can be changed according to the size of magnitude that one is comparing. Provided that two magnitudes are not incommensurable, the ratio between the two magnitudes

27

For convenience, I use numerical ratio to explain the method, though the Elements always starts from magnitude ratio. The method is thus: taking 18 and 24, I want to find a unit to count them. I will subtract the lesser from the greater continuously until I have zero. So from 18 and 24 I get remainder 6 and lesser number 18. Then I get 6 and 12 and finally 6 and 0. Thus, 6 is the unit that makes the ratio an integer ratio, provided that the two magnitudes are commensurable.

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is expressed as multiple of the common measure. This commensurability inevitably leads to a confluence of magnitude and numerical ratio, which marks the finale of Euclid’s master plan for measurement. The confluence is built up by introducing a series of analogies between magnitude and number (Prop.vii.1–3 and Prop.x.2–4) (see table 10.5 above). Without any hesitation, the commensurable magnitude ratio is then identified as numerical ratio: τὰ σύμμετρα μεγέθη πρὸς ἄλληλα λόγον ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν. Commensurable magnitudes have to one another the ratio which a number has to a number. Prop.x.5

ἐὰν δύο μεγέθη πρὸς ἄλληλα λόγον ἔχῃ, ὃν ἀριθμὸς πρὸς ἀριθμόν, σύμμετρα ἔσται τὰ μεγέθη. If two magnitudes have to one another the ratio which a number has to a number, then the magnitudes are commensurable. Prop.x.6

τὰ σύμμετρα μεγέθη πρὸς ἄλληλα λόγον οὐκ ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν. Incommensurable magnitudes do not have to one another the ratio which a number has to a number. Prop.x.7

ἐὰν δύο μεγέθη πρὸς ἄλληλα λόγον μὴ ἔχῃ, ὃν ἀριθμὸς πρὸς ἀριθμόν, σύμμετρα ἔσται τὰ μεγέθη. If two magnitudes do not have to one another the ratio which a number has to a number, then the magnitudes are incommensurable. Prop.x.8

This project of visual magnitude counting casts the original title of the work, stoicheion, in a new light. Since the word was used in the meaning of ‘principles, component, and element,’ the translation Elementa (or Elements) has been justified.28 Moreover, the title of geometrical works compiled by Hip28

For example, Plato (Plt. 278d, Tht. 201e, Ti. 48b) and Aristotle (Metaph. 998a26, 1014a36,

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pocrates of Chios, Leon, Theudios, and Euclid (Procl. in Euc. 66, 67, 68F) strengthened the meaning of the stoicheia as elements. However, the etymology of stoicheion implies that the word is closely related to the idea of length or measurement. According to LSJ, the word was used in the context of the sundial to mean ‘the shadow of the gnomon’ or ‘the length of which is indicated in the time of day’.29 In fact, the various meanings of the word resonate with our discussion of figure counting: ratio, and proportion in the Elements show that the title stoicheia is not totally isolated from the idea of lining, line-matching, and line-measuring.30

3

Part 3

The absence of numbers was not a hapax in the history of Greek mathematics. Netz reads it as a crucial feature of ancient Greek geometry, one that is in fact applicable to Greek science in general: A crucial feature of élite, literate Greek mathematics is its marginalization of the numerical. This is extremely remarkable for a field that, in all other cultures, is mostly organized around numbers. Numbers are only infrequently mentioned elsewhere in mainstream Greek mathematics, usually when simple ratios between geometrical objects are stated. Greek mathematics is centered on geometry and its qualitative features: Greek angles are not measured (inside Greek geometry proper) by degrees, and Greek lines do not have numerically determinate lengths. Relatively late in Greek science, and under the influence of Babylonian antecedents, Greek astronomy became more tied to actual measurable observations, i.e. numerical data. Even then, Greek astronomy remained essentially geometrical in its conception and goals. Thus Greek science as a whole was much less quantitative than any other comparable scientific culture.31

29 30

31

1014b1) use the word in the sense of ‘components into which matter is ultimately divisible,’ or ‘elements of proof’. Aristophanes (Eccl. 652) uses the word in the sense of ‘the length of the shadow’ i.e. ὅταν ᾖ δεκάπουν τὸ στοιχεῖον ‘when the shadow is ten feet long’. Derivatives of στείχω: στοιχάς ‘in a row one behind another’, στοιχιαῖος ‘equal to one row’, στοιχηδόν ‘line by line’, στοιχέω ‘to be drawn up in a line’. The original meanings (as line or line measures) of the word and its related words were gradually diluted, see R.S.P. Beekes, Etymological Dictionary of Greek (Leiden: Brill, 2009), 1395–1396. R. Netz, ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 346.

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Someone may then ask why we still see the similar style of geometry—i.e. the absence of numbers in geometry—in some subsequent Greek mathematical corpora. Did the canonical status of the Elements influence post-Euclidean Greek mathematics so that it followed the numberless style? The discovery of incommensurability could have been the reason.32 Incommensurability reveals, in a sense, that numbers were not omnipotent. At least two lines—such as the side and the diagonal of a square—were found which could not be expressed as a number at the same time. For curved figures, as well as incommensurable magnitudes, ancient Greek mathematicians did not have a method to express magnitude in numbers. No integration was known, even though they used some exhaustive methods. The liberation from the compulsion to use numerical expressions might have been welcomed, especially in the collection of various mathematical propositions such as the Elements. Since it was not possible to quantify every element of the figures, it was better not to confer numbers at all in order to maintain uniformity. Additionally, the absence of numbers could be connected with the pursuit of generality. Many examples from Mesopotamian mathematics show a procedure for the solution of practical problems.33 This procedure is normally presented with concrete numbers, so readers can confirm that the procedure is correct and valid by checking the numbers. However, the utility of the procedure would vary with the extent of the practitioners’ ability to apply the procedure to similar problems. In proof-centered geometry, the validity of the theorem comes from the logic contained in the theorem itself, not from its instantiation through numbers. These two suggestions assume ancient Greek geometers to be homogeneous, and they may appear so by using fewer numbers in their geometrical reasoning compared to ourselves. However, the following example of post-Euclidean numberless geometry shows a very specific aesthetic reason not to use num-

32

33

There have been several theories about the discovery of incommensurability, though the question does not affect my argument in this paper. See Fowler, Mathematics, in particular chapter 10; W.R. Knorr, The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Dordrecht, Holland: D. Reidel 1975). A particularly interesting question is whether the discovery was recognised by ordinary people and if so, how it affected the authority of numbers. In the case of counting, however, the discovery of incommensurability should not be exaggerated. Natural numbers are self-sufficient for counting. E. Robson, Mathematics in Ancient Iraq: A Social History (Princeton, NJ: Princeton University Press, 2008), presents an overview of mathematical practices in Mesopotamia and mathematical examples in chronological sequence.

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bers. This difference between Euclid and Archimedes implies that each mathematician may have also spared the use of numbers to achieve different goals. 3.1 Geometry without Numbers sui generis Archimedes illustrates the heterogeneous goals of geometry without numbers. Although he did not have the same degree of engagement that mathematicians centuries later enjoyed with fellow mathematicians in scientific journals, Archimedes tried to share his work with correspondents in and around Alexandria in the Hellenistic period. So, when Archimedes lamented Conon of Samos’ death, he grieved not merely for the man, but the loss of mathematical exuberance in their intellectual community:34 With many years now having passed since Conon’s death, we are not aware of even a single problem being set in motion, not by a single person archim. On Spirals Letter to Dositheus, trans. netz, 2004

The lull that Archimedes reports here is described as the disappearance of attractive and charming problems, in other words, as the loss of mathematical amazement. To Archimedes, Conon was remembered as a source of mathematical wonders: ἀκούσας Κόνωνα μὲν τετελευτηκέναι, ὃς ἦν οὐδὲν ἐπιλείπων ἁμῖν ἐν φιλίᾳ, τὶν δὲ Κόνωνος γνώριμονγεγενῆσθαι καὶ γεωμετρίας οἰκεῖον εἶμεν τοῦ μὲν τετελευτηκότος εἵνεκεν ἐλυπήθημες ὡς καὶ φίλου τοῦ ἀνδρὸς γεναμένου καὶ ἐν τοῖς μαθημάτεσσι θαυμαστοῦ τινος When I heard that Conon, who was my friend in his lifetime, was dead, but that you [Dositheus] were acquainted with Conon and withal versed in geometry, while I grieved for the loss not only of a friend but of an admirable mathematician… archim. Quadrature of the Parabola, Introduction: Letter to Dositheus, trans. heath, 1950.

Heath’s translation of ‘admirable’ for the word θαυμαστός is a fair choice, but ‘wonderful’ is even better, based on its etymology. Here, Archimedes deplores the loss of mathematical wonders and misses the ‘wonder-full’ mathematician. 34

Moreover, mathematicians in ancient Greece were relatively few in number compared to other philosophers, playwrights, or orators, see R. Netz, Scale, Space and Canon in Ancient Literary Culture (Cambridge: Cambridge University Press, 2020), 555– 7.

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Moreover, Aristotle’s view on wonders conveys a similar idea that wonder is at the heart of the pursuit of mathematical science. He explains wonder (τὸ θαυμάζειν) as the starting point of philosophy (φιλοσοφεῖν). Prior to philosophising, a man needs to be puzzled and amazed (ἀπορῶν καὶ θαυμάζων). In this Aristotelian scheme of epistemology, there could be no pursuit of science without wonder.35 As Netz argues, the pursuit of mathematical wonder resonates in Greece’s cultural context.36 In particular, intellectual debates and competitions created a favourable environment for investigating wonder and inventing proofs. The word paradoxa (παράδοξα) itself reveals the essence of surprise and wonder. People are amazed when a certain statement goes against one’s expectation (δόξα), and the pursuit of wonder was not marginal in the intellectual endeavours of ancient Greece.37 An intellectual who merely expounded what everyone already knew could expect to attract little attention. Paradoxical or unexpected argument was the most effective way to raise the volume of one’s own voice. Archimedean results concerning the area of parabolic segments or the volume of cone, sphere, and cylinder would have aroused curiosity and wonder, as found in the following report by Heron about Archimedean ideas (ἐπινοία): ὧν τὰς ἐπινοίας ὥσπερ παραδόξους οὔσας τινὲς εἰς Ἀρχιμήδην ἀναφέρουσιν κατὰ διαδοχὴν ἱστοροῦντες. Some historians, who work according to the order of events, carry the discovery of those methods [sc. finding the areas and the volume of rectilinear or curvilinear figures], as they are astonishing and unexpected, back to Archimedes. heron, ii Metrica i; trans. bruins 1964.

35 36

37

Metaph. 982b12–24. See R. Netz, The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations (Cambridge: Cambridge University Press, 2004), and Ludic Proof. In the latter (pp. 13–14), Netz’s case study of the spiral lines shows that ‘Archimedes made a deliberate choice to produce a mystifying, obscure, ‘jumpy’ treatise. And it is clear why he should have done so: so as to inspire a reader with the shocking delight of discovering, in Proposition 24, how things fit together; so as to have them stumble, with a gasp, into the final, very rich results of proposition 27–28’. Paradoxography, which collects the incredible and wonderful in the natural and human world, had its own position as a literary genre in the third century bce.

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figure 10.12 Parabolic segments

The power of mathematical thaumata comes from the fact that they sound implausible and unexpected (παράδοξα), but at the same time are not totally unlikely. The success of mathematical wonder rests on the extent to which they balance the likely and the unlikely. Therefore, a well-made mathematical wonder occupies an exceptional epistemological position, oscillating between the plausible and the implausible.38 Of course, the same statement may sound different to different listeners. Those who are more versed in mathematical or geometrical discourses will need a stronger stimulus than less experienced recipients. So the threshold of wonder will be determined by each audience member’s expectation. The charm of finding a mathematical wonder depends on fine-tuning the presentation according to the target audience. The desire to discover and share wonder is a key reason that Archimedes did not employ numbers. The suspension of explanation would have been crucial to maximising the thaumata. The longer the delay in explaining why the unlikely turns out to be the likely, the more effective the revelation will be. Numbers, however, disrupt the suspension. Numbers connote explanation because of their ingrained numerical operations, and so press readers to delve into the calculation and leave no room for amazement. For example, consider the beautiful thaumata found in the Archimedean spiral line.39 How would people have responded to the claim about the simple ratio between the area of the spiral line and the circle circumscribing it? Would it be possible for Archimedes to achieve the same thaumata with numbers?

38

39

In fact, the proof was sequential to the making of the wonder. The burden of proof is the obligation of the mathematician to produce evidence in exchange for exciting the audience’s expectations. The wonder remains incomplete until the proof balances the unlikely with the likely. In this vein, the proof is interpreted as alleviating the wonder or translating it into a more plausible one. ‘The area contained by both the spiral drawn in the first rotation, as well as the first line

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Conclusion In the public sphere, number, more precisely arithmetic skill, was an essential part of the Greek cognitive tool kit. To many Greeks, ἀριθμός would seem an impeccable means for counting and quantifying congeries of things. In the philosophical sphere, however, Plato, Speusippus, and Aristotle philosophised numbers, discussing how to classify them into ideal, sensible, and mathematical numbers.40 Put another way, the number as well as the figure, as a metaphysical object, needed to be abstracted by the removal of the particular. Similarly, in the mathematical sphere, the mathematician’s ἀριθμός eventually became geometrised. The geometrisation of the number is best exemplified in the Elements, where we see the geometer visualising and counting magnitudes. Through this approach, a number is redefined as a multitude composed of units (άριθμὸς δὲ τὸ ἐκ μονάδων συγκείμενον πλῆθος, Def.vii.2). Thus, I suggest a new reading of the key concepts of the Elements: ratio to quantify the comparison of magnitudes, proportion to extend ratio between magnitudes of different kinds, and anthyphairesis to find a flexible unit for magnitudes. The development of this kind of measurement saw the confluence of magnitude ratio and numerical ratio based on the condition that the magnitudes are not incommensurable. In this interpretation, therefore, numbers presuppose magnitudes. Through the synthesis of magnitude and numbers, Euclid explored how figures could be measured by figures, thus creating the opportunity for a markedly different geometry. Equally noteworthy for our purpose is that the Elements was not a hapax for this geometry without numbers. Other Greek mathematicians followed this model. Is Euclid the inventor of this unprecedented geometry? How was an agreement reached concerning this relatively fixed style of Greek mathematics? I do not know, and Greek mathematicians did not provide us with explanations about their mathematics. One possibility is that they used this geometry to achieve various goals such as the maximisation of mathematical paradoxes and wonders. Of course, this is only a reason ex post facto. At least one thing

40

among the ⟨lines⟩ at the start of the rotation, is a third part of the first circle’ (Archim. On Spirals, Proposition i.24, trans. Netz, 2017). L. Tarán, Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary (Leiden: Brill, 1981). For a critical review of Tarán’s book, see I. Mueller, ‘On Some Academic Theories of Mathematical Objects’, JHS 106 (1986), 111–120; Tarán’s response to Mueller’s critique: L. Tarán, ‘Ideas, Numbers, and Magnitudes: Remarks on Plato, Speusippus, and Aristotle’, RPhA, 9/2 (1991), 199–231.

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is certain: yes, number was lavishly used in the world of the Classical Greek polis, but paradoxically, it was used parsimoniously in its very own hometown, namely mathematics. Greek geometry without numbers eloquently conveys the aphorism that ‘nusquam est qui ubique est.’

Bibliography Asper, M., ‘The Two Cultures of Mathematics in Ancient Greece’, in E. Robson and J.A. Stedall (eds), The Oxford Handbook of the History of Mathematics (Oxford: Oxford University Press, 2009), 107–132. Beekes, R.S.P., Etymological Dictionary of Greek (Leiden: Brill, 2009). Bruins, E.M., Heronis Alexandrini Metrica (Leiden: Brill, 1964). Chang, H., Inventing Temperature: Measurement and Scientific Progress (Oxford: Oxford University Press, 2004). De Risi, V., ‘The Development of Euclidean Axiomatics. The Systems of Principles and the Foundations of Mathematics in Editions of the Elements from Antiquity to the Eighteenth Century’, AHES, 70 (2016), 591–676. De Risi, V., ‘Euclid’s Common Notions and the Theory of Equivalence’, Foundations of Science, 26/2 (2021), 301–324. Doyen, C., ‘An Athenian Decree Revisited’, CHS Research Bulletin, 4/1 (2015), https://​ research‑bulletin.chs.harvard.edu/2016/04/13/an‑athenian‑decree‑revisited/, accessed 1 Mar. 2021. Fowler, D.H., The Mathematics of Plato’s Academy: A New Reconstruction (Oxford: Clarendon Press, 1999). Grattan-Guinness, I., ‘Numbers, Magnitudes, Ratios, and Proportions in Euclid’s Elements: How Did He Handle Them?’, HM, 23 (1996), 355–375. Heath, T.L., The Thirteen Books of Euclid’s Elements (Cambridge: University Press, 1908). Heath, T.L., The Works of Archimedes (1897; New York: Dover Publications, 1950). Johnstone, S., A History of Trust in Ancient Greece (Chicago: University of Chicago Press, 2011). Knorr, W.R., The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Dordrecht, Holland: D. Reidel, 1975). Lee, E., ‘Visual Agency in Euclid’s Elements: A Study of the Transmission of Visual Knowledge’, Ph.D. thesis (Stanford University, 2020). Mueller, I., ‘On Some Academic Theories of Mathematical Objects’, JHS, 106 (1986), 111– 120. Netz, R., ‘Counter Culture: Towards a History of Greek Numeracy’, HS, 40 (2002), 321– 352.

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Netz, R., The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations (Cambridge: Cambridge University Press, 2004). Netz, R., Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic (Cambridge: Cambridge University Press, 2009). Netz, R., The Works of Archimedes, ii: On Spirals (Cambridge: Cambridge University Press, 2017). Netz, R., Scale, Space and Canon in Ancient Literary Culture (Cambridge: Cambridge University Press, 2020). Peyrard, F., Les oeuvres d’Euclide, traduites en latin et en français, d’après un manuscrit trèsancien qui était inconnu jusqu’à nos jours, i (Paris: Patris, 1814). Robson, E., Mathematics in Ancient Iraq: A Social History (Princeton, NJ: Princeton University Press, 2008). Saito, K. and N. Sidoli, ‘Diagrams and Arguments in Ancient Greek Mathematics: Lessons Drawn from Comparisons of the Manuscript Diagrams with Those in Modern Critical Editions’, in K. Chemla (ed.), The History of Mathematical Proof in Ancient Traditions (Cambridge: Cambridge University Press, 2012), 135–162. Tarán, L., Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary (Leiden: Brill, 1981). Tarán, L., ‘Ideas, Numbers, and Magnitudes: Remarks on Plato, Speusippus, and Aristotle’, RPhA, 9/2 (1991), 199–231. Unguru, S., ‘On the Need to Rewrite the History of Greek Mathematics’, AHES, 15 (1975), 67–114.

General Index Abacus 3n7, 28n4, 187, 200 Accounts 1n1, 4n9, 12, 28, 28n5, 33n21, 34, 35n28, 36–38, 51–53, 58, 61–69, 73–74, 74–76, 89n28, 96, 97n3, 195, 198–205, 205n28 See also Tribute, Athenian, quota lists of; Buildings, accounts related to Accounting 3, 3n7, 8–9, 8nn27–30, 28, 42–43, 51, 88, 151–173, 200n17, 209 Accountability 3, 4n9, 5, 12, 28n5, 38–40, 84, 100, 103n16, 109, 123 Accuracy 134, 135, 154, 181, 198 as a quality attributed to numbers 181 of numbers 50, 140, 141, 154, 167, 181–181, 182–185, 184, 186–189, 195, 198 Acheloion, proxeny decree for 69, 104, 105, 109, 125 Adriatic colony, decree on foundation of 89, 99, 117, 127 Aeschines 195, 198, 204–205, 207, 213 Aesthetic reasons for not using numbers 75, 259 Age, unique indication of on Athenian gravestones 58 Alcibiades, son of Cleinias 165–166, 176, 182–185 Alcidamas of Aegina, boys’ wrestling victor 161–162 Algebra, algebraisation 220, 220n7, 239, 240, 241, 242, 242n10 Allen, Danielle 90–93, 112 Amphiktyons, of Delos, accounts of 73 ἀμφοτέρω 223 Anakes, decree on a tax for the cult of 98, 103, 105, 122, 123 Androtion 110 Antiphon 37n36 Aphobus, son of Mnesiboulus, guardian of Demosthenes 198–199, 209 Aphytis, decree about grain trade to Athens 98, 103, 105, 114, 123, 125 Archimedes of Syracuse, mathematician 260–262 Archon, dating by 58 Archytas, of Tarentum 8n25

Argeius of Ceos, boys’ boxing victor 162– 163 Aristonous, decree for 102, 103, 105, 122 ἄρτια See Even Aristis, pancratiast four times victorious 60 Aristophanes, son of Philippus, playright 27, 34n26, 36, 42–50, 53, 54, 90, 113, 196n5, 200, 206n31 Aristophanes, son of Nicophemus, politician 207–208, 209 Aristotle 2n6, 8n25, 29n6, 35n28, 36n32, 37n35, 38, 112, 113, 167, 175, 175n3, 199, 205, 213n47, 219, 221nn9–10, 222, 222n13, 226n30, 230n39, 232, 257, 260, 263 ἀριθμέω 183–184, 191 Arithmetic See Calculation Arithmetic/mathematical operations addition 34, 46, 53, 54, 200, 225, 225n25, 225n27, 227, 229, 232, 237 calculation of a mean 187–189 division 187, 200, 212, 225, 225n25, 225n27, 227, 228n33, 237 multiplication 84, 187, 188, 200n16, 225, 225n27, 229–230, 230–233, 237, 248, 250–251, 252, 253, 255 subtraction 34, 200, 200n16, 237, 247, 255, 256 ἀριθμός 4n10, 17–18, 184, 191, 219–236 See also Number, concept of Asper, Markus 14n51, 238n6, 243 Assembly 17, 29, 34–35, 37, 38, 38n38, 42– 43, 53, 84, 105n19, 113, 174–175, 176, 177, 179, 180–181, 181, 190, 191, 195, 197, 198, 199, 203, 204, 212, 213 See also Numbers, context of use Athena Parthenos, statue of, accounts relating to 64, 75 Athena Promachos, statue of 64 Athenian exceptionalism 30–32, 79, 97 Athens 3, 10, 14, 27–57, 58–77, 96–130, 195– 215 Attic stelae 10, 10n36 ἀτιμία, ἄτιμος 80–81, 87, 88, 93, 104, 111, 114– 117 See also Honour; τιμή

268 Auditing 6, 28n5, 34–35, 36n34, 53, 195, 198, 205 See also Euthynē/euthynai Bacchylides 155–156, 158–160, 160–161, 162– 163, 170 Bdelycleon 46–50, 200 Being 222–230, 233–234 Best, Joel 2n3, 6n18, 6n20 Blok, Josine 15, 79, 84, 96–130 Boulē, Athenian 32–33, 33n21, 36, 36n31, 36n34, 37, 40, 53, 70, 84, 88–89, 101, 101n15, 104, 105n19, 121, 125–126, 195n1, 199 Boundlessness 13, 210n39 See also Countless Buildings, accounts related to 33n21, 38, 38n39, 64–65, 69 Bureaucracy 1n1, 28–29, 32 Byzantium, Athenian campaign against 65 Calculation/calculations 1, 2, 3, 5, 7, 11, 12, 13, 14, 17, 42, 44n58, 49n70, 75, 79, 83, 94, 183, 184, 185, 187–189, 192, 195–215, 227, 237, 239, 240, 241, 262 and empire 12, 14 as paradigm for decision-making 1, 195, 204–205 errors in 186–187, 195n3, 202 incomplete 187–189 mental 42n49, 195, 195n4 methods of 187, 188 open vs. closed 195–215 oral/live 195, 199 rhetorical exposition of 47–50, 199–203, 210–211, 212–213 vs. boldness 183 written/with the aid of writing 11–12, 42n49, 200 See also Quantitative reasoning Calendar/calendars 72, 132–133, 144 Calian, Florin George 17–18, 219–236 Callias ii, son of Cimon 107–110 Callias iii, son of Hipponicus 163–164 Callias of Chalcis 204 Callias, son of Didymias 152–153 Callias, tyrant of Chalchis 204 Cassius Dio 140 Catalogues 13, 41, 41n45

general index Cavalry, Athenian 58 Chalkotheke, decree concerning 70 Character (self-)characterisation through use of numbers 13, 17, 50–51, 53–54, 175, 178–179, 184–185, 185–186, 186–189, 209–213 using character (ēthos) to substantiate numbers 17, 205–209 Christ, Matthew 13, 13n46, 175 Cicero 201 Cimon 107–110, 139–140 Clarity 75, 76, 181 Cohen, Patricia 27–29, 54n78 Coinage 30n9, 30n11, 33–34 See also Money Coinage decree 98, 103, 105, 115, 126 Cole, Thomas 153–154 Colonisation/colonies 89, 99, 107, 114, 114n48, 117, 117n59 Commemoration 151–173 Commensuration 15, 80, 81–83, 89 See also Incommensurability Comparison 1, 7, 78 Conon, Athenian general 209 Conon of Samos, mathematician 260 Corcyra, Athenian campaign against 65 Corcyra, lead loan tablets from 61 Counter culture 11–12, 27–28 Counters/pebbles 11–12, 47, 200 Counting 2–3, 11–12, 16, 27–57, 75 See also ἀριθμέω; Magnitude Counting Countless/countlessness 13, 96, 157–158, 210n39 Crown(s) 70, 88–89, 111–112, 117 Crump, Thomas 5n16, 9n32, 38n38 Cuomo, Serafina 4n9, 9n32, 11, 12, 28, 28n5, 36n31, 40n40, 40n41, 51, 59n3, 61n13, 64n20, 200n17 Darius i 41n45 Dates, manner of recording dates at Athens 58, 71 Debt 41, 43–45, 47n63, 50, 54, 61–62, 100, 104, 108n29, 110–111, 116n56, 195, 197 See also Loans Decision-making 1, 6, 16–17, 28–29, 34–35, 78, 92–93, 174–194, 195–196, 197, 204– 205

general index Dehaene, Stanislas 5n14 Delians, fine imposed on 97n3, 103 Delphi, timēsis decree in 90n34 Demaratus 175, 183n42 Demes, decrees of, uses of numerals in 63, 71 Democracy, Athenian 3 and numeracy 4n9, 16–17, 28–29, 27–57, 75, 79, 174–194 changing nature of 76 participation in 29, 34–38 role and meaning of numbers in 3–4, 5, 12, 14, 195–196, 207, 213 Demosthenes 88, 91, 108–109, 197, 198, 200, 201–202, 203, 204–205, 207, 209, 210–213 Dexileos, epitaph of 58 Dicaeopolis 42–43, 54, 200 Difference/differentiation 223–224, 224n24, 225, 226, 226n29, 227–228, 231, 232n45, 233–234 Diodorus Siculus 81n4, 132, 108–109, 138, 139–140, 146–147 Diogeiton, guardian of Diodotus’ children 206–207, 209 Diophantus 225 Dreros, Archaic law from 59 Dishonour 80–81 See also τιμή; Dishonour; ἀτιμία δύο, duality 221, 223–230, 224n20, 230n38, 231, 232–234 Egestans 181–182 Eisangelia 106, 107, 108, 109, 110, 113, 115, 115n51 Eleusinian Mysteries, decree on the administration of 101, 120 Eleusis accounts from 73–74 inscription from 71–72 sacred calendar from 72 Elis, decree/law from 86 Empire, Athenian 12, 14, 28, 29–32 Emporion See Harbour Ephorus 139–140, 147 Epigraphic habit 9, 9n32, 79, 97 Epinician poetry 151–173 See also: odes, epinician/victory song Equality arithmetic/numerical 8, 213 geometric/proportional 8

269 Erchia, sacred calendar from 72 Erechtheion, accounts related to 65 Eretria, decree on Athenian relations with 102, 103, 123 Erythrai decree 97, 121 Estimates 2, 5, 84, 106, 141, 174–175, 179, 184– 185, 189, 191, 202, 203 Eteokarpathians, decree for the 103–104, 109, 122 ἦθος See Character Etynia, decree of 82 Eubulus, Athenian orator 211 Euclid 18, 219, 220n5, 232, 233n48, 237–260, 263–264 Eudemos of Plataia 70 Euripides 165–166 Phoenician Women 17n53 Euthymenes of Aegina, pancratium victor 153–154 Euthynē/euthynai 28n5, 34, 36n31, 36– 37n34, 53, 85n18, 100, 105, 110–111, 114–117, 119, 123, 205, 205n28 as paradigm for decision-making 195, 205 See also Auditing Evagoras I of Salamis 208 Even 18, 221–236 See also Odd Everett, Caleb 5n15, 5n16, 219n1 Expert/expertise 2, 5, 28–29, 179, 181 Feeney, Denis 133 Financial literacy 28–57, 195–215 collective 35–36, 37, 53 See also Knowledge Financial records 38–40, 198 Fines 15, 59, 70, 72, 78–95, 96–130 1,000 drachmae 15, 84, 85, 86, 87, 88, 92, 101–103, 106, 110n32, 116, 117–118, 120, 121, 122, 123, 124, 125, 126 10,000 drachmae 15–16, 80, 84, 87, 88, 89, 96–130, 103–105, 104n17, 106–111, 116–117, 123, 124, 125, 126, 127 100 minae 110–111 50 talents 104, 105, 107–110, 108n29, 115, 117–118, 122 See also Punishment(s) Finger counting 46, 47–48, 200

270 First-Fruits decree 102, 103, 105, 122 Fowler, David 2nn5–6, 237–238, 238n4, 243, 250n23, 259n32 Games, athletic 151–173 Generation of numbers 221–236 Geometrical figure/diagram 237–265 Geometrical operations abstraction (aphaeresis) 241n8 application of areas 241, 242n9, 248– 250, 253 reciprocal subtraction (anthyphairesis) 256, 263 See also Magnitude counting Geometry 236–265 Good life, the 29, 41, 45, 54 Gorgias 17n53 Gortyn, the Great Code of 82, 169–170 Grain, quantity and price of recorded in numerals 71 Grain supply 97–98, 99, 105, 107, 108n26, 117, 122, 123 Grain Tax law 70, 105 Graphē paranomōn 96, 107, 115 Green, Peter 137, 146 Greenwood, Emily 13 Grenfell, B.P. and A.S. Hunt 139 Gross Domestic Product 7, 8, 8n26 Grote, George 145–146 Hagnous, inscription from 71 Hansen, Mogens Herman 36n31 Harbour 30–32 Harpēdonaptai 243 Harris, Edward 113–114 Hart, Keith 7, 7n24 Heath, Thomas 2nn5–6, 219n2, 220n5, 232n46, 241, 245n17, 248, 250n24, 251, 260 Hekatompedon decree 101, 104, 119 Hellanicus 135 Hellēnotamiai 35n28, 37n36, 52 ἕν 221n10, 222, 223, 225, 228–229, 230nn38– 39, 232, 232n45, 232n47, 233–234 Hephaestus, status of 64 Herakleides of Salamis, honours for 70–71 Hermogenes 183–184 Herodotus 13, 41n45, 132–133, 136–137, 145, 175, 183–184, 186–187

general index Heron of Alexandria 237n2, 261–262 Hesiod 41n45 Hestiaia, decrees on 97, 121 Hieron of Syracuse, chariot and single-horse victor 156, 158–159, 160 Hippocrates of Chios, mathematician 257– 258 Historians/historiography 13, 16, 17, 131–148, 174–175 Historical contingency 5–13 Homer 41n45, 187–188 Honour 78, 80–81, 88 See also τιμή Horoi, recording mortgages 73 Huffman, Carl 2n6, 8n25, 231n44, 232n45 Iamblichus, Neoplatonist philosopher 233n48 Incommensurability 15, 80–82, 83–89, 220, 220n5, 248n22, 255–257, 259, 259n32, 263 Incomparability 15, 78, 80, 84 Inscriptions 12, 58–77, 78–95 Athenian 15, 38–40, 52, 58–77 commemorative 151–173 See also Epigraphic habit Interest 43–45 Intuitionism 220, 230n38 Inventories 13, 38, 68, 174–175, 195, 203, 208– 209, 210n39 Isaeus 198, 203, 205 Isocrates 87–88, 166 Johnston, A.W. 60–61 Johnstone, Steven 3n8, 12, 12n44, 15, 78– 95, 97n3, 100, 108n28, 111n36, 117n58, 196n5, 200n17, 208n34, 244n16 Jurisdiction concerning allies, decree 102, 103, 121 Jurors, selection of 213 Kahn, Charles 223, 223n16 Kahneman, Daniel 176n6, 191n69 Kallet, Lisa 27–57, 174n1, 176n6, 181n32, 182nn34-35, 182n37, 183n42, 185, 185n46, 185n50, 192n72, 192n75, 196n6 Keyser, Paul 186–187, 188n63 Kirk, Athena 9n32, 13, 210n39 Klein, Jacob 2n5, 17n52, 220n7, 231n43

general index Kleinias’ decree on tribute 36n33, 97, 125 Knorr, Wilbur 229, 259n32 Knowledge, collective/shared 35–36, 36n31, 37, 181 See also Financial literacy; Literacy; Numeracy Kodros, Neleus and Basile, decree on the lease of the temenos of 84, 98, 103, 105, 126 Kōlakretai 37 Kuhn, Thomas 219–220 Lagrange, Joseph-Louis 237 Laws, Athenian, use of numerals in 70 Lee, Eunsoo 18, 237–265 Leon, mathematician 258 Lists 9, 9n32, 10, 13, 34, 37, 38–40, 41, 41n45, 46–50, 52–53, 61–69, 70, 73, 82, 134, 134n11, 137, 152–153, 153–158, 167, 168, 174, 199, 203, 209, 209n38, 210nn39–40 Literacy 4n9, 9, 9n32, 28n6, 38n38, 42n49, 51–52, 75, 200n17, 258 Liturgies 14, 34–35, 207–210 Lloyd, G.E.R. 4n9 Loans 38, 62–63 loans, Athenian public, records of 65 loans, recorded on lead tablets 61–62 See also Debt λογισμός 184, 195, 198, 205, 207–208 Logistēs/logistai 35–38, 35n28, 205, 205n28 See also Magisterial boards λογίζομαι 27, 42n49, 44, 44n58, 185, 192, 200 Lysias 34, 53, 203n27, 206–207, 209–210 Magisterial boards 35–38, 52 Magistrates, named for their number 59 Magnitude counting 238n5, 239, 246, 250, 253, 254 visual magnitude counting 18, 246, 249– 253, 257 Maslov, Boris 169–170 Mathematical formulas 237–238 Mathematics, Greek 219–221, 237–265 Mathematics, Mesopotamian 258, 259, 259n33 Measure, measures 54, 88, 98 common measure 255–258 Measurement 12, 13, 29, 41, 45, 175, 237–265 absolute 244

271 comparative 249–250 geometric 239–264 numerical 255–258 of size or distance 135, 140–141, 142, 147, 208 of time 132–133, 134, 144 relative 244–246 Measurement units 135–137, 142, 144, 180n26 conversion of 135–137, 144, 210 Measuring 12, 18 Methone, decrees about 97, 103, 105, 123 Metronomoi 242–246 Miltiades, general at Marathon 107–110 Mines 30–31 μονάς 221n10, 223, 225, 228, 229, 255 Monetary sums, indicated with numerals 70 Monetisation 9, 9n32, 31n14 Money 9, 11–12, 14–15, 27–54 See also Coinage μόρια 223, 224, 225 Morrison, Andrew 168–169 Multiplication 230–233 Navy, decrees about 100, 102, 103, 121, 122 Nemea, dedication by athletic victor at 60 Netz, Reviel 3n7, 4n9, 9n33, 11–12, 11n41, 28, 34n25, 195n1, 199–200, 200n17, 246n19, 258–259, 260n34, 261, 261n36 Nicias, Athenian general 174–194 Number, concept of 4n10, 17, 219–236, 237– 239, 239–242, 263–264 See also ἀριθμός; Number theory Number-form 221, 221n10 Number line 5–6, 18 Number, qualified/qualification of 2, 3, 16, 17, 131–148, 174, 176–179, 187–189, 202n23 approximating 131, 134, 136–137, 139–140, 140–141, 143 malista/μάλιστα 134–135 peri/περί 140–141 double approximation 140–141 comparative 131, 134, 135–136, 136–137, 138, 139–140, 143, 176–179, 180–181, 191

272 hyper/ὑπέρ 134, 138 ‘more than’ 139–140 ‘no less than’ 135–136, 137–138, 177– 179, 190–191 ‘not much short of’ 180–181, 190–191 emphatic 131, 143 litotically 176–180, 180–181, 190 with an alternative 131, 140–141, 143 with a negative 187 Number, rounded 2, 32, 47, 70, 86–87, 88, 202, 202n21 Number sense 5–6, 5n14 Number, subject category it refers to 131– 148, 142 casualties 14, 137–138, 146 distance/size 131, 135–136, 140–141, 142, 147, 180–181 liturgies 14, 34–35, 207–210 military/manpower 3, 32, 41n45, 58, 131, 137–138, 140–141, 142, 146, 174, 177, 181, 183, 184–185, 187–189, 204, 212 money/financial items 3, 10, 12, 14, 29, 30, 31, 32–40, 41, 41n45, 43, 44– 45, 45–50, 65–68, 131, 143, 145–146, 174–175, 181, 195, 197–204, 205–209, 209–212 population 131, 143, 146, 180–181 time 131, 132–133, 134–135, 142, 144 victories 16, 60, 151–173 Number systems 5 Number theory 17–18, 219–236, 233n48 See also Number, concept of Number, type of 131–148, 142 cardinal 131, 134–135, 138, 140–141, 142 compound 131, 142 continuous vs. discrete 4n10, 5, 11, 219n1, 239, 244 distributive 153–158 formulaic 186 fraction 131, 142, 225 integer 4n10, 220, 233n48, 256n27 irrational 220–221 natural 5–6, 18, 219–236 non-explicit 131, 136–137, 142 ordinal 71, 131, 133, 134–135, 142 prime 230, 232–233, 233n48, 255, 256 totals/subtotals 36, 46–50, 53, 54, 59– 60, 62, 63, 64, 65, 68, 74, 153–158,

general index 162–163, 170, 174, 177, 178, 184, 187–189, 192, 200, 201–202, 203, 204, 209, 210, 211, 212 Numbers, ambiguous 16, 153–158, 162 Numbers, absence/avoidance of 18, 58, 80–81, 159–160, 174, 176, 182, 185–186, 191–192, 237–265 Numbers, as a social technology 3–4, 6–12, 14–16 Numbers, cognitive aspects of 4 Numbers, communicative functions of 1 (false) comfort/sense of security 13, 189–191 commemoration 5, 151–173 creating hierarchy 88 deterrent effect 174, 190–191 humour 40–51 impressing 174–175 inspiring courage and resolve 174–175 intimidation 5, 10, 52 keeping track 6–7 magnification 179, 181, 190–191 persuasion 1, 3–4, 13, 16–17, 46–50, 53 ranking 5, 7, 89 self-aggrandisement 13, 175, 183–184 Numbers, context of use assembly (ekklēsia) 17, 34–35, 174 commemorative 12, 151–173 commercial exchange and trade 3, 11, 15 daily life 11–13, 14, 17, 34–35, 174 debate 1, 7, 16–17, 18, 174–186, 189–191 forensic and deliberative settings 17, 34–35, 79, 175, 195–215 hierarchical 7, 10 imperial 12, 13, 14 Numbers, generation of 219–236 Numbers, in narrative 13, 178–179 Numbers, management by 1, 7 Numbers, meanings of 78, 80, 84, 93, 94, 78–95 ambiguous 10, 16 (demonstration of) power 7, 10, 13, 38– 40, 47–48, 52, 53, 111–117, 174 (demonstration of) wealth 38–40 symbolic 78 vs. value 80, 84–85, 93–94, 111–118 See also Accountability; Accuracy; Expert/Expertise; Transparency; Vindictiveness

general index Numbers, misinforming/misleading 2, 181– 182, 189–191 Numbers, ontology of 219–236 See also Number, concept of; Numbers, generation of; Number-form Numbers, presupposing judgment 7 Numbers, producing judgment 34–35 Numbers, qualities attributed to 1 deceptive 175, 181 democratic 5 kingly 5, 13 magical 5 objective 151, 175 permanent 151 reliable/unreliable 185–186, 187–189, 195–215 rhetorically inert 175 true/untrue 175 See also Accuracy; Transparency Numbers, responses to 179, 181–182 evaluation of 34–35, 181–183, 184, 188 interpretation of 10, 78, 174–194 popular suspicion of 196, 207–208 Numbers, rhetoric of 1–2, 16–17, 34–35, 53, 151–173, 174–194 accumulation of detail 204–205, 210 and leadership 183, 186 counterfactuals 160–162, 167 deceptive 203–209 deliberate ambiguity 153–158, 162, 167 disavowal of accuracy 184–185 exaggeration/amplification 47–48, 49– 50, 174, 177, 183–185, 187–189, 190–191 numbers, explanation of 197–205 in figured speech 176–177 manipulation of attribution 162–167 misrepresentation 165–167 non-numerical quantitative rhetoric 182–183, 185–186 omission of numbers 204n27 qualitative enhancement 158–160, 171 repetition 201–202, 206 selection of numbers 206–207 vagueness 185–186, 190–191 Numbers, social construction of 6–8, 11 Numbers, substantiation of 198–199 Numbers, trust/distrust in 2, 7, 17, 183–184, 196, 198, 204–205, 207, 213 Numbers, in modern translations 131–148

273 Numbers, uncertain 17, 181, 187–189 Numbers, verification/verifiability of 12, 168, 195–215 Numeracy 28–57, 75, 195–215 and education 14–15, 27–57 Athenian 14, 27–57, 75, 200, 210– 211 collective 35–36, 37, 53 critical 17, 175, 184, 185–186, 186–189 definition 79 democratic 17, 27–57, 79, 174–194 diffused 38 general knowledge 196n6 relational 9 vs. literacy 28n6, 50–51 See also Financial literacy Numerals 3, 3n7, 58–77 acrophonic 60, 61–76 alphabetic 60–61, 74, 75 avoidance of numerals 58, 73–74 choice of 58–75 definition of 4n9 highlighted by size 64 Hindu-Arabic 9 in juxtaposition 81–83 in tabular formatting/in separate columns 9, 9n32, 40, 52, 63, 64–69, 72, 73, 74, 75 interspersed/embedded 15, 40, 64–69, 70, 72, 73, 74–76 spelt out in words 59, 61, 69, 70, 71, 72, 73, 96 Numerosity 180–181, 181–185, 192, 219–236 See also πλῆθος Oath 169–171, 204 Ober, Josiah 36n31, 58, 176n8, 181, 191n69, 196nn5-6, 208n34 Obolostatēs 45n59 Odd 18, 221–236 See also Even Odes, epinician/victory song 16, 151–173 Old Comedy 14, 40–51 Old Oligarch 222–230 One, oneness See ἕν Orality/oral tradition 151–173 Osborne, Robin 15, 40n43, 43n51, 58–77, 83n10, 96n2, 98, 197n8

274 Panathenaea, prizes at 73 Pay/paid officials 32–35, 32n21, 43n53, 43n54, 45–50, 112 Peiraieus, lease from 71 πεμπάζω 200 Penalties See Fines; Punishment(s) Pericles 29, 32, 46, 49n69, 53, 109, 112, 174– 175 Perinthians, dedication by at Samos 59–60 περιττός See Odd Persia 208 Perdiccas ii of Macedon 41 Persian kings 13 Darius i 41n45 Xerxes i 175, 183n43 Phaselis decree 98–99, 103, 105, 114, 124 Philip ii of Macedon 199, 203–204 Philo, arsenal of 73, 75 Philocleon 46–47, 49–50, 53–54, 200 Philolaus of Croton 2n6, 231–232, 231n44, 232n45 Phormio, Athenian general 110–111, 113, 183n40 Phormio, Athenian politician 210–211 Phylacidas of Aegina, pancratium victor 153–154 Pindar 153–155, 156–157, 161–162, 164, 170 Plato 17–18, 32n19, 41n45, 203n24, 219–236, 257n28 Platonism, early Academy 221–222 πλῆθος 179, 180, 185–186 Plutarch 109 Pōlētēs/pōlētai 35n28, 73, 195n1 Political arithmetic 1n1 Polybius 132 Porter, Theodor 1n1, 6n21 Pourciau, Bruce 219, 220nn3–4 Price(s) 71, 72, 79n1, 80–81, 85–89, 196n6 Prime numbers See Number, type of Probability (εἰκός) 206–207, 208 Proof/demonstration 18 artless 199 Proportion/proportionality 8, 15, 18, 82, 239, 250n23, 253–255, 258, 263–264 Proxeny/proxenos 103–104, 105, 109, 125 Prytaneia, at Athens 69 Public finance, Athenian 195, 197, 199, 200, 203–204, 211–213

general index Punishment(s) (or penalties) 15–16, 59, 70, 72, 78–95 corporeal 70, 81 excessive 83–84, 85 non-quantified 80–81 of officials 83–89, 96–130 quantified 82–83, 85 Purves, Alex 13 Pytheas of Aegina, pancratium victor 153–154 Pythagorean theorem 240 Pythagoreans/Pythagoreanism 2n5, 221– 222, 221n8, 230, 230n39, 232n45, 233n48 Quantification 3–4, 11, 14–15, 16 glory 151–173 honour and infamy 78–95 power 29, 43–50, 52–53 time 133 value 70, 88–89 Quantifying/quantitative mentality 29n7, 40–51, 51–54 Quantitative judgments 176, 188, 189, 191 Quantitative reasoning 177, 183–185 and leadership 183 See also Calculation Quantity marker (non-numerical) 174, 182, 185–186, 187–189, 189–191 ‘much/many’ (πολύς) 180, 182, 186, 192 ‘not much’ 180, 181, 187, 188, 189, 191 Quorum, record of in numerals 71 Rank, ranking 1, 5, 7, 87, 89 Ratio(s) (λόγος) 18, 81–83, 85, 86–87, 88, 246, 249–253, 250n23–24, 252n26, 253– 255, 255–258, 263–264 Rawlinson, George 145 Reciprocity 111 Records, athletic 151–173 Reference point 189–191 Revenue 31, 36–37, 46–50 Rhamnous, accounts from 61–63, 75 Rotation of offices 35 Rubincam, Catherine 12–13, 12n45, 16, 131– 148, 179, 180n27, 182n36, 187 Sacred wealth 38–40 Salaminioi, Athenian genos, calendar of sacrifices by 72

general index Salamis decree 100, 104, 119 Samos, Athenian campaign against 65 Scafuro, Adele 104–105, 112–113 Schärlich, Alain 35n29 Scheidel, Walter 78 Sealey, Raphael 132 Secretaries 36n31 Sélincourt, Aubrey de 137, 145 Senses numbers, tactile vs. visual 11–12, 199– 200 numbers vs. visual spectacle (ὄψις) 184– 185, 191–192 Sergueenkova, Valeria 13 Sicilian Debate 17, 174–194, 196n7 Sicka, Daniel 16 Sigma, three bar 97, 99, 120 Sing, Robert 17, 34n27, 175n2 Slave, whipping of 70, 81 Social constructionism 6–13, 6n18 Socrates 32, 43–45, 90–91, 106, 203n24 Solon 101, 101n13 Sostratus, son of Sosistratus, pancratium victor 157–158 Speusippus, Academic philosopher 222n13, 263, 263n40 Sphacteria 140–141 Standardisation of metrics and measures 1n1, 7, 12, 88n27, 243–246, 244n16 Statistics 1–2, 2n2, 27, 151 Status 15, 78, 89–93 Stele, cost of 69–70 Stoicheion 257–258 Stymphalos, laws of 82 Sypalettos, deme decree of 100, 102, 103, 120 Teichopoioi 36, 37–38 Teisias of Aegina, wrestling victor 155–156 Teithras, sacred calendar from 72 Tetrapolis, sacred calendar from 72 Thasos, decree from 85, 86 Themistocles 136–137 Theopompus, second cousin of Hagnias 203 Thesmophoria, at Cholargos 71 Theudios 258 Thorikos, sacred calendar from 28n5, 72 Thoudippos’ decrees on tribute 52–53, 69n35, 98, 103, 105, 115, 124, 125

275 Threshold(s) 85, 87 See also Rank, ranking; Numbers, communicative functions of Thucydides 13, 16–17, 29, 31n17, 32, 33nn22– 23, 49n69, 53, 109, 196n7, 113, 132, 133–135, 137–138, 140–141, 144, 146, 147, 165–166, 174–194, 196n7 Thymaridas of Paros, Pythagorean mathematician 233n48 τιμή 80–81, 111–112 τίμησις 80, 89–93 See also Valuing Tod, Marcus N. 3n7, 59n4, 101n12, 158n18 Traders, influence of on inscribing practices 75 Transparency 38–40, 52, 210–213 as aim for the use of numbers 38–40 as meaning of numbers 5, 10, 12, 38–40 as quality attributed to numbers 16 of procedure/use of numbers 17, 188– 191, 196, 211, 213 Treasures, Athenian, records of 68–69, 73 τρία 224, 229, 231 Tribute 29–32, 33, 41 Tribute, Athenian, quota lists of 10, 10n37, 38–40, 52–53, 63, 69 Uncountability See Countless/countlessness Unity 220n7, 221–222 Valuing (or value) 3–4, 8, 12, 15, 40, 78–95, 111–118, 208 market values 12, 15, 45, 53, 78, 89, 197, 201, 212 monetary value 70, 71, 81–83, 83–89, 93– 94, 106, 118, 210n39 status 15, 78, 89–93 social value 111–112 See also τιμή Van Berkel, Tazuko 16–17, 174–194, 195n4, 196n7, 202n23, 209n37 Veridiction 169–171 Victories, athletic 151–173 See also Commemoration; Inscriptions/commemorative; Numbers, type of Vindictiveness 15–16, 112–113

276

general index

Waters of the Halykon, decree on 101, 103, 121 Witnesses 169–170, 198 Women, using numbers 206 Wonder (θαῦμα) 260–262, 263–264

Xenophon 29n7, 96, 113, 132, 135–136, 144, 164, 175, 183n43 Xerxes 175, 183n43

Xeinobrotos of Cos, equestrian victor 171 Xenocrates of Acragas, chariot victor 164 Xenocrates of Chalcedon, Academic philosopher 222n13

Zhmud, Leonid 220n5, 231n41

Yunis, Harvey 29n7, 176n8, 183

Index of Inscriptions Agora xvi 56 [1] A 106C

116n54 116n54

Corinth viii 1 22

101n12

EM 6667 6769

67 66

F.Delphes iii 1 486 507 510

90n34 157–158 163–164, 165

Gagarin and Perlman Dr1 Elt2 G47 G72

59 82n6 82n6 82

I.Eleusis 19 = IG i3 6 = OR 106 106 23–25 69n33 28 = IG i3 78a = OR 141 102, 103, 105, 122 32–38 69n33 42 69n33 45–48 69n33 50 69n33 52 69n33 146 73 151 73 157 73 177 73 IG i3 1 100, 104, 119 4 101, 104, 119 6 = I.Eleusis 19 = OR 106 102, 120 7 120 9 99 10 98–99, 103, 105, 114, 124

14 19

97, 121 69, 104, 105, 109, 125 21 99n6, 114 31 99n6, 125 34 = OR 154 36n33, 97, 125 40 114 41 97, 121 46 114 50 122 52A 123 55 102, 103, 105, 122 59 100, 102, 103, 121 61 = OR 150 97, 103, 105, 123 63 98, 103, 105, 114, 123, 125 64 69 66 99n6 68 = OR 152 36n33, 125 71 = OR 153 = ML 69 52–53, 69n35, 98, 103, 105, 115, 124, 125 75 99n6 77 69 78 123 78A = OR 141 = I.Eleusis 28 102, 103, 105, 122 82 101n14 84 = OR 167 84, 98, 103, 105, 126 102 112n39 105 = OR 183B 101n15, 122 117 = OR 188 97, 126 131 122, 123 133 98, 103, 105, 122, 123 149 102, 103, 123 153 102, 103, 122 157 102, 103, 121 165 103, 125 244 = OR 107 120 245 100, 102, 103, 120 247 61–62 248 = OR 134 62–63 253 62–63 256 = OR 146 70, 101, 103, 121 259 = OR 119 35n28, 52n74, 63 260 63 260–262 39

278 292–362 302 363 364 = OR 148 365 366 369 = OR 160 371–374 383 384–401 433 434 435 436–451 = OR 145 439 440 445 449 452 453–460 = OR 135A 460 = OR 135B 472 474 474–479 476 = OR 181A–B 476–471 893 1387 1453 = OR 155 1454 IG ii2 17 82 120 1013 1176 1183 = RO 63 1184 1194 1237 = RO 5 1356 1362 1363 1631 1635 = RO 28 1667 1668

index of inscriptions 69 122 65 65 65 65 35n28, 68 65 68 69 64 64 64 64 37n37 37n37 37n37 38n39 116n55 64 64, 66 64 38n39 65 38n39, 67 65 152, 164n27 74 98, 103, 105, 115, 115n49, 126 103–104, 109, 122

116n55, 126 70 70 81, 243–244 71 71 71 71–72 85, 101n14, 116n55 72n49 81n5, 101n14 72 116n56 97n3, 103n16 73 73

1671 1672 1675 2311 2711 2760 6217 = RO 7B

73 73 73 73 73 73 58

IG ii3 1 298 = RO 64 306 312 313 316 327 338 339 348 349 352 = RO 94 367 = RO 95 370 = RO 100 378 433 447 = RO 81 452

88n25 70 70n36 70, 88 70n36 70n39 70n39 70 70n39 70n39 70 71 89, 99, 117, 127 88n25 116n55 70 116n55

IG iv2 1 76

104n17

IG xi 4 1299

80, 90n34

IG xii 2 1

90n34

IG xii 4 132

104n17

IG xii 5 595 608

104n17 163

IG xii 6 577

59-60

IG xii 8 265 267

85n15 86n20

279

index of inscriptions I.Olympia 2 144 170

86 157n13 170–171

IPArk 17

82n6

ML 2 59, 100n11 9 60 69 = IG i3 71, OR 153 52–53, 69n35, 98, 103, 105, 115, 124, 125 OR 104 101 106 = IG i3 6, I.Eleusis 19 120 107 = IG i3 244 38n38, 120 108 120 119 = IG i3 256 35n28 120 98–99, 103, 105, 114, 124 121 121 134 = IG i3 248 62–63 135A = IG i3 453–460 64 135B = IG i3 460 64 136 103–104, 109, 122 141 = IG i3 78a = I.Eleusis 28 102, 103, 105, 122 144 123 145 = IG i3 436–451 38n39, 64 146 = IG i3 256 28n5, 38n38, 72 148 = IG i3 364 65 150 = IG i3 61 97, 103, 105, 123 152 = IG i3 68 36n33 153 = IG i3 71 = ML 69 52–53, 69n35, 98, 103, 105, 115, 124, 125 154 = IG i3 34 36n33

155 = IG i3 1453 160 = IG i3 369 167 = IG i3 84 181A–B = IG i3 476 181 183B = IG i3 105 188 = IG i3 117

98, 103, 105, 115, 126 35n28, 68n30 84, 98, 103, 105, 126 38n39 65 101n15 97, 126

RO 1 5 = IG ii2 1237 7B = IG ii2 6217 25 26 28 = IG ii2 1635 63 = IG ii2 1183 64 = IG ii3 1 298 72 81 = IG ii3 1 447 94 = IG ii3 1 352 95 = IG ii3 1 367 100 = IG ii3 1 370

85 85, 116n55 58 81n5, 101n15 105 97n3, 103n16 71 88 88 70 70 71 89, 99, 117, 127

SEG xi.290 xi.1227 xviii.140 xxi.541 xxi.542 xxvi.72 xxx.61 xxxiii.679 xxxix.1426

157n13 167n30 157n13 72n49 72n50 116n54 116n54 80, 90n34 104n17

Syll.3 729

81n5

Index Locorum Aelian Various Histories 13.25: 81n4 Aeschines Against Timarchus (Aeschin. 1) 99–100: 198 On the Embassy (Aeschin. 2) 213, 70–71: 210n38, 130–135: 207, 145: 208n34, 153: 205, 213 Against Ctesiphon (Aeschin. 3) 204– 205, 213, 25: 196n6, 59: 195, 207, 59–60: 205, 207, 95–96: 204, 205, 97–98: 204, 99: 204, 213, 101–102: 199n11, 127–130: 208n34, 137: 205, 168: 205 Aeschylus Prometheus Bound 343–378: 17n53 Androtion FGrH 324 F8 (= schol. Ar. Pax 347): 110 Anthologia Palatina 13.14.5: 158n16 Antiphon On the Murder of Herodes 69–71: 37n36 Archimedes of Syracuse 260–262 On Spirals Letter to Dositheus: 260 Quadrature of the Parabola Introduction: Letter to Dositheus: 260 Archytas, of Tarentum Fragments (Diels-Kranz) 47B3: 8n25 Aristophanes 42–50, 53, 113, 196n5, 200, 206n31 Acharnians 200, 1–150: 42n47, 6: 43n52, 29–31: 27, 42n49, 31: 200, 32–36: 42n50, 65–90: 43n53, 505: 32n18, 530–534: 42n50, 597: 43, 599–606: 43, 643: 32n18, 719–970: 42n51 Assemblywomen 652: 258, 812–829: 196n5 Clouds 43–45, 54, 13–24: 44, 15: 44n56, 34: 44, 1155–1156: 45 Islands (Fragments, Kassel-Austin) 402: 42n48 Knights 49 Wasps 104: 34n26, 496–499: 206n31, 518: 46, 529: 200, 537: 200, 655–663: 46, 196n5, 656: 200n14, 657–659: 36, 663: 115, 667–724: 48, 669: 48, 671: 48, 672: 48, 676–677: 48, 679: 48, 685: 49, 690–

691: 48, 701–702: 48, 700: 48, 706–711: 49n70, 707: 48, 716–717: 48, 894–897: 90, 1388–1412: 206n31 Aristotle [Ar.] Constitution of the Athenians 8.4: 101n15, 24.3: 32, 33n21, 27–28: 112, 27.2: 113n43, 27.3–4: 33n21, 27.4: 112, 29.4: 115, 45–49: 37n35, 45.1: 101n15, 45.2: 36n32, 47–48: 36n32, 47.2–3: 35n28, 47.2: 195n1, 48.1: 195n1, 48.3–5: 205n28, 48.3: 38, 49.4: 36n32, 51.2: 243n13, 63–67: 213, 69.1: 195n1 Metaphysics 982b12–24: 261, 987a29: 230n39, 987b29–988a1: 232, 990b18– 20: 226n30, 998a26: 257n28, 1014a36: 258n28, 1014b1: 258n28, 1056b23: 232, 1080a22–23: 219, 1081a14: 221, 1084a10: 221n9, 1090b20–24: 221n9, 1098b7: 221 Nicomachean Ethics 1131a20–32b24: 8n25 On the Soul 404b20–24: 221n9 Phenomena 206b33: 221n9 Politics 1274a5–8: 113n43, 1274a8–9: 33n21, 1301a19–1302a15: 8n25, 1313b38: 113n43, 1318a3–27: 8n25 Rhetoric 1355b35–39: 199, 1356a4–13: 205n30, 1359b8: 29n7, 1359b19–60b3: 175n3, 1377b20–1378a19: 205n30, 1396a4–12: 195n3 Bacchylides 2.6–10: 162–163, 4.11–13: 160, 5.42–45: 158–159, 8.17–25: 159– 160, 11.24–29: 160–161, 170, 12.36–42: 155–156, 13.67–68: 154, 13.190–191: 154 Cassius Dio 72.23.5: 140 Cicero Against Verres 3.116: 201 Demetrius On Style 287–298: 177n11 Demosthenes 91, 108–109, 197, 204–205, 211–212 First Philippic (Dem. 4) 198, 203, 16–17: 203, 23: 199, 28–29: 199, 203, 30: 199

281

index locorum On the Symmories (Dem. 14) 212–213, 14: 213n46, 16–23: 212, 18–19: 197, 22: 213n46, 28: 213n46 On the Crown (Dem. 18) 227–229: 205, 227: 207 On the False Embassy (Dem. 19) 108– 109, 244: 208n34, 251: 200n16, 273–275: 108n30, 273: 109, 291: 199n11 Against Leptines (Dem. 20) 200, 19: 199, 32: 198n11, 200, 77: 210n38, 155: 80n3, 89n33, 198n11 Against Meidias (Dem. 21) 88, 153: 210n40 Against Androtion (Dem. 22) 60: 207n32 Against Aristocrates (Dem. 23) 108–109, 140–141: 81n4, 205: 108n30, 109 Against Timocrates (Dem. 24) 118: 80n3, 140–141: 81n4, 146: 80n3 Against Aphobus i (Dem. 27) 201–202, 207, 209, 211, 1–3: 198, 2: 201n19, 4–11: 201, 7: 198, 8: 201n19, 9–11: 201, 10–11: 211, 11: 199, 12–23: 201, 12: 201n19, 13: 201n19, 16: 201n19, 17: 199, 202, 202n22, 18: 201n19, 21: 201n19, 23: 199, 201, 201n19, 202n22, 24–33: 201, 25: 201n19, 29: 201n19, 202n22, 33: 202n22, 34–40: 201, 34: 202n22, 202, 36–37: 202, 202n22, 37: 199, 39: 202n22, 202, 40–41: 209, 49: 198, 201n19, 62: 201, 66–67: 211, 80: 201n19 Against Aphobus ii (Dem. 28) 202n22, 13: 202n22, 19–22: 211 Against Aphobus iii (Dem. 29) 8: 201n18, 30: 198, 204 Against Onetor (Dem. 30) 32: 91n43 Against Phormio (Dem. 34) 210–211, 23– 25: 210, 38–39: 209n38 For Phormio (Dem. 36) 36–38: 207n32 Against Nausimachus and Xeinopeithes (Dem. 38) 2: 200n16 Against Phaenippus (Dem. 42) 208n35, 5–6: 208n35, 7: 208n35, 20: 208n35, 24: 208n35, 25: 208n35, 31: 208n35 Against Macartatus ([Dem.] 43) 18: 200n15 Against Stephanus ii ([Dem.] 46) 6: 169 Against Timotheus ([Dem.] 49) 5: 198, 211n42, 43–44: 198 Against Polycles (Dem. 50) 10: 198, 30: 198, 65: 198

Against Callipus ([Dem.] 52) 4: 211n42 Against Nicostratus ([Dem.] 53) 18: 92n44, 26: 92n44 Against Callicles (Dem. 55) 35: 85n14 Against Theocrines (Dem. 58) 70: 91n42 Against Neaera ([Dem.] 59) 6: 91n42 Dinarchus Fragments (Conomis) 19.8: 243n13 Diodorus Siculus 2.48: 139, 10.30–31: 108n29, 11.60.6: 139, 139n28, 146–147, 12.17.4–5: 81n4, 12.22: 121, 12.36.2: 133n5, 12.45.4: 109, 12.58.2: 138, 146, 12.84: 179, 18.56.6: 133n5, 19.96–99: 139 Diogenes Laertius 1.57: 81 Dionysius of Halicarnassus On Isaeus 1: 198n10, 12: 198 [Dion. Hal.] Art of Rhetoric 8–9: 177n11 Diophantus Arithmetics 1.23: 225, 3.19: 225, 5.20: 225 Ephorus FGrH 70 F64: 108n29 Euclid Elements Definitions: 5.3: 250–253, 5.4: 251, 5.5: 252, 5.7: 252, 7.2: 219n2, 7.18: 225n26, 10.1: 248, 255, 10.2: 255, 10.3: 255, 10.4: 255 Propositions: 1.2: 246, 1.35: 247, 1.42: 248, 1.45: 246, 249, 1.47: 241, 2.4: 242, 5.9: 253, 254, 255 5.10: 253, 254, 255, 6.1: 253, 7.1–3: 257, 7.1: 256, 7.2: 255, 256, 7.3: 255, 256, 7.32: 233, 9.20: 233, 10.2–4: 257, 10.2: 255–256, 10.3: 256, 10.4: 256, 10.5: 257, 10.6: 257, 10.7: 257, 10.8: 257, 13.11: 238 Euripides 165–166 Fragments (PMG) 755: 165–166 Phoenician Women 541: 17n53 Gorgias Palamedes (Fragments, Diels-Kranz) B11a30: 17n53

82

Hermippos Fragments (Kassel-Austin) 63: 41n45 Herodotus 3.89–95: 41n45, 6.21.1: 110n32, 6.132–136: 107, 6.134–135: 108n27, 6.137–140: 108n27, 7.61–99: 41n45, 7.102–103: 175, 7.103: 183, 8.4.2–5.3: 136, 145

282 Heron of Alexandria Metrica 2.1: 261 Homer Iliad 2.494–759: 41n45, 23.382–397: 160n22 Odyssey 9.1–4: 152n2 Hyperides 1.14: 208n34, 4.40: 208n34 Isaeus On the Estate of Pyrrhus (Is. 3) 2: 201n19, 8: 201n19, 25: 201n19, 29: 201n19, 49: 201n19, 80: 201n19 On the Estate of Philoctemon (Is. 6) 14: 200n16 On the Estate of Hagnias (Is. 11) 203, 38: 198, 42–43: 203, 44: 203 Against Hagnotheus See Dionysius of Halicarnassus, On Isaeus Isocrates 87–88, 166 Panegyricus (Isoc. 4) 93: 210n38 Areopagiticus (Isoc. 7) 21–22: 8n25 On the Peace (Isoc. 8) 82: 32n18, 86–87: 210n38 Antidosis (Isoc. 15) 129: 133n44 On the Team of Horses (Isoc. 16) 34: 166, 46–47: 87–88 Libanius Hypotheses to the Orations of Demosthenes 31: 198n10 Lycurgus (Fragments, Conomis) 1.5: 199n11 Lysias Funeral Oration (Lys. 2) 27: 210n38 Against the Members of a Sunousia (Lys. 8) 10: 44n56 Against Theomnestus i (Lys. 10) 4: 200n16 On the Property of Eraton (Lys. 17) 203n27 On the Property of Aristophanes (Lys. 19) 207–209, 11: 208, 12–18: 208, 18: 208, 19: 208, 21–27: 208, 22: 209, 23: 208, 24–26: 208, 29: 208, 209n36, 34: 208, 35–37: 209n36, 38–41: 209, 39–41: 198, 42–43: 209n38, 43–44: 209, 44–52: 209, 44: 199, 202, 45: 208, 209, 55– 64: 208, 56–59: 209, 61–64: 210, 61–63: 209

index locorum On a Charge of Taking Bribes (Lys. 21) 34, 53, 209–210, 1–5: 209, 1: 210, 5: 210, 13–16: 210 On the Charge of Overthrowing the Democracy (Lys. 25) 12: 209n38 Against Epicrates (Lys. 27) 16: 91n39 Against Nicomachus (Lys. 30) 203n27, 20: 204n27 Against Diogeiton (Lys. 32) 206–207, 209, 9–12: 206, 9: 206, 12–19: 206, 13: 206, 14: 206, 20: 206, 21: 206, 24: 207, 26–27: 207, 26: 207n32, 27: 207, 28–29: 207, 28: 202 Old Oligarch [Xen.] Constitution of the Athenians 222–230, 3.1–8: 105n19, 3.1–3: 37n36, 3.2: 36n32, 37, 3.12–13: 116 Philolaus of Croton Fragments (Diels-Kranz) 5: 231 Pindar 153–155 Isthmian Odes 164, 1.60–63: 158n16, 2.12– 32: 164, 2.28–29: 164, 6: 58–61, 6.5–7: 154, 6.56: 154, 6.59: 155 Nemean Odes 2.23: 158, 158n16, 5.4–5: 154, 5.44: 154, 6.15–22: 156n12, 6.57b–63: 161–162, 170, 10.25–28: 154–155, 10.45–46: 158n16, 11.22–28: 161, 170 Olympian Odes 156–157, 1.41: 157, 1.77: 157, 1.87: 157, 13: 157, 13.43–46: 158n16, 13.98– 100: 170, 13.112–115: 158n16 Pythian Odes 9.90–91: 155 Plato 17–18, 219–236, 257 Alcibiades i 126d2: 17n53 Charmides 166a: 231n41 Euthyphro 12d–e: 231n40 Gorgias 32n19, 453e: 231n41, 516a: 109n31 Hippias Maior 285d: 41n45, 285e: 41n45 Hippias Minor 366c–367c: 203n24 Parmenides 137c–166c: 222–223, 142b1– 144a4: 17–18, 221–234, 142b1–143a2: 223–230, 142b1–143a2: 224, 142b–c: 224, 142b5–143a2: 224, 225, 142d–143a1: 224, 142e7–143a1: 223, 225, 142e7: 227, 143a4– 144a4: 223–230, 224, 225, 143a1: 223, 143b6–7: 228, 143c3: 223, 226, 227, 143c4: 223, 226, 227, 143d2–3: 224, 143d2: 227, 143d3: 227, 143d4–5: 224, 227, 143d7: 224,

283

index locorum 227, 143d9–e2: 228, 143e3: 231, 143e5–e7: 229, 143e5: 231, 143e7: 231, 144a3: 232 Phaedo 96e6-97b3: 225n27, 101b8–10: 225n25, 101c5: 221n10, 105c: 229 Republic 7.524d: 231n41 Sophist 254b–264b: 222, 224n24 Theaetetus 148a: 225, 198a: 231n41 Timaeus 34c–35b: 222, 35a1–b3: 224n24, 257n28 Plutarch Life of Alcibiades 18: 179n24 Life of Cimon 4: 108n29, 14: 109, 17: 109 Life of Nicias 12: 179n24 Life of Pericles 9.2–3: 33n21, 35.4: 109 Life of Solon 21.1: 101 Life of Themistocles 7.5: 146 [Plutarch], Moralia 818e: 199n11 POxy 1610 139 Proclus Commentary on Euclid 66–67: 258, 68F: 258 68F: 258 Quintilian The Education of the Orator

9.2.74: 177n11

Thucydides 1.1: 191, 1.10: 187, 1.10.3: 184, 1.10.4– 5: 187–188, 1.21.1: 184n45, 1.22.1: 189n65, 1.91: 33n22, 141n33, 1.98: 33n22, 49n69, 1.100–101: 33n22, 1.105.2: 33n22, 1.108.4: 33n22, 1.114–115: 121, 1.114: 33n22, 1.143.4– 5: 33n23, 2.2.1: 133n6, 144, 2.13: 183n42, 2.13.2: 33n23, 2.13.3: 31n17, 32, 2.13.4:

178n15, 2.14–16: 33n23, 2.15.4: 133, 2.22.2– 3: 123, 2.41: 29, 2.59: 109, 2.63.1–2: 49n69, 2.65.3: 109, 2.68.7–8: 110n34, 2.80– 92: 110, 2.89.2: 183n40, 2.98.3: 178n15, 2.103: 110, 3.37–40: 114, 3.87.3: 137, 146, 4.8.6: 140, 147, 4.10.1–4: 183n41, 4.94.1: 138n22, 4.101.2: 138n22, 4.118.12: 133n5, 4.119.1: 133n5, 5.19.2: 99, 125, 5.24.1: 99, 125, 5.54.3: 133n5, 5.68: 187, 5.68.1–2: 184, 6.1.1–2: 180, 6.1.2–6.5: 180, 6.6.2: 181, 6.8.1–3: 181, 6.8.1–2: 179, 6.8.1: 181, 6.8.2: 176, 6.8.4: 177n14, 6.9.2: 176, 6.16.2: 165–166, 6.17.5–6: 183, 6.17.12: 182, 6.18.3: 185, 6.18.4: 185, 6.19.2: 177, 185, 6.20.1: 185, 6.20.2: 186, 186n57, 6.20.3: 186, 186n57, 6.20.4: 186, 6.21.1: 186, 186n57, 6.21.2: 186, 186n57, 6.23.3: 190n68, 6.24.1: 190n10, 6.24.2: 190n68, 6.24.2–4: 177n12, 6.24.3: 190nn67–68, 6.25: 174, 6.25.2: 174, 178, 6.26: 179, 6.30.2: 192n73, 6.31.1: 191, 192nn73-74, 6.31.2: 191, 6.31.3: 192n74, 6.31.4–6: 192n76, 6.31.6: 192nn73-74, 6.43–44.1: 192n72, 6.43.7: 183, 6.46.1: 182, 6.68.2–3: 189n66 Xenophon Anabasis 5.6.9: 144–145, 7.8.6: 44, 135– 136, 144 Constitution of the Athenians See Old Oligarch Hellenica 1.7.2: 115n51, 6.3.3–4: 164 Memorabilia 3.6: 195n3, 3.6.5–6: 29n7 Oeconomicus 2.3: 106 Ways and Means 2.7: 31n13