POETRY AND NUMBER IN GRAECO-ROMAN

ANTIQUITY

Poetry and mathematics might seem to be worlds apart. Nevertheless, a number

of Greek and Roman poets incorporated counting and calculation within their

verses. Setting the work of authors such as Callimachus, Catullus and

Archimedes in dialogue with the less well-known isopsephic epigrams of

Leonides of Alexandria and the anonymous arithmetical poems preserved in

the Palatine Anthology, this book reveals the various roles that number played

in ancient poetry. Focusing especially on counting and arithmetic, Max Leventhal

demonstrates how the discussion, rejection or enacting of these two operations

was bound up with wider conceptions of the nature of poetry. Practices of

composing, reading, interpreting and critiquing poetry emerge in these texts as

having a numerical component. The result is an illuminating new way of

approaching Greek and Latin poetry – and one that reaches across modern

disciplinary divisions.

max leventhal is Bye-Fellow and College Lecturer in Classics at Downing

College, Cambridge. He was previously the Thole Research Fellow at Trinity

Hall, Cambridge and a British Academy Postdoctoral Fellow in the Faculty of

Classics.

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cambridge classical studies

General editors

j. p. t. clackson, w. m. beard, g. betegh, r. l. hunter,

m. j. millett,

s. p. oakley, r. g. osborne, c. vout, t. j. g. whitmarsh

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POETRY AND NUMBER IN GRAECO-ROMAN

ANTIQUITY

MAX LEVENTHAL

Downing College, Cambridge

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4 my family and friends, with love;

2 Alex, the 1 that counts the most.

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CONTENTS

Acknowledgements page viii

List of Abbreviations and Editions xi

Introduction: Numbers Up 1

1.1 Poetic Figures 1

1.2 Poetry by Numbers 7

1.3 ‘Poetic Numeracy’ and Greek Mathematics 17

Part I Counting and Criticism 21

1 Callimachus and His Legacy 23

1.1 Counting in Callimachus’ Reply to the Telchines 25

1.2 Erinna and the Epigrammatists 41

1.3 Roman Reckonings 52

2 Leonides of Alexandria’s Isopsephic Epigrams 73

2.1 Callimachus Compressed 79

2.2 Cups and Sources 96

2.3 Pebbles in the Stream 102

Part II Arithmetic and Aesthetics 113

3 Archimedes’ Cattle Problem 121

3.1 Archimedes’ Art 127

3.2 Cattle and Catalogues 139

3.3 Calculating Cattle and Cultural Competition 151

4 The Arithmetical Poems in AP 14 162

4.1 An Archaeology of Arithmetical Poetry 165

4.2 The Cultural Capital of Calculation 178

4.3 Arithmetic Anthologised 189

4.4 Arithmetical Poetry beyond Late Antiquity 197

Conclusion: Summing Up Poetry 209

Bibliography 213

Index 227

vii

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ACKNOWLEDGEMENTS

This book has had a considerably long gestation and several

origins. I ﬁrst began thinking about the intersection of poetry

and number as a Master’s student. The result was a dissertation

on Archimedes’ Cattle Problem, and it would eventually become

an article in Ramus (2015), which is substantially reworked and

expanded here as Chapter 3. I then pursued a doctorate on

a different topic. Still, Leonides of Alexandria and his isopsephic

epigrams constituted one distraction from the main task of my

thesis; in fact, some of the material of Chapter 2 had originally

been submitted to the Cambridge Classical Journal as an article.

I thank the anonymous reviewers of that piece for their challenging

but supportive feedback. A failed Oxford interview in 2008 bears

special mention, too, since it was there that I ﬁrst encountered

Catullus cc. 5 and 7 – and I have been ruminating on those poems

ever since. The beginnings of a postdoctoral position afforded me

the time to write up these ideas while, once again, I should have

been working on other things. Thus, this book is quite a different

beast to one’s typical ﬁrst book in academia. It is the product of

a lengthy obsession and not the direct result of my doctoral studies.

Yet I hope and believe that the passage of so much time has

imbued it with a certain intellectual maturity – of the kind which

I did not yet possess as a fresh postgraduate – and has streamlined

its arguments so as to avoid the bloatedness that is a residual

characteristic of many a thesis turned monograph.

Although this is not the ‘book of the thesis’, I nevertheless owe

a debt of gratitude to several supervisors and mentors, for the

profound inﬂuence they have had on me as a scholar and as

a person. Liba Taub supervised my Master’s thesis and has been

a continual source of support. She frequently saw the value of my

thinking before I did and encouraged me to pursue many lines of

enquiry that are now to be found in this book. In that sense, it could

viii

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not have been written without her. Renaud Gagné supervised my

doctoral thesis, and I am indebted to his inexhaustible generosity,

which has been truly formative. Richard Hunter, my second super-

visor, has read over more drafts of my various musings than I can

recall; he has vastly improved them all with his knack for asking

just the right question to make one reﬂect on both matters of detail

and the larger picture. Tim Whitmarsh served as the internal

examiner of my thesis along with Annette Harder, who served as

the external examiner: their feedback was as constructive as it was

honest. I have been fortunate also to have Tim as my postdoctoral

mentor; his kindness, support and advice on all manner of subjects

have been a real inspiration.

It gives me great pleasure also to acknowledge those colleagues

and friends whose efforts have improved this ﬁnal product. As

well as Richard Hunter and the anonymous reviewer at CCS, drafts

of this entire book were read by Jan Kwapisz, Arthur Harris and

Sam Oliver, who all brought their own expertise to bear in enhan-

cing its clarity and avoiding any infelicities. Likewise, individual

chapters were read over and sharpened by Simon Goldhill, Talitha

Kearey, Thomas Nelson, Floris Overduin and Ivana Petrovic. The

Introduction in particular beneﬁted from being exposed to the

exacting eyes of the Postdoctoral Work in Progress Seminar

(PWiPS) in Cambridge. I would also like to thank Francesco

Grillo, Richard Hunter and Jan Kwapisz, who all shared their

unpublished work with me.

I was lucky enough to receive funding as a postgraduate student

from Corpus Christi College, Cambridge, the Faculty of Classics,

University of Cambridge and the Jebb Fund. I was even more

fortunate subsequently to be awarded a Research Fellowship at

Trinity Hall, Cambridge and a British Academy Postdoctoral

Fellowship at the Faculty of Classics. These institutions have

provided me with the time, space and (relative) job security with

which to pursue several projects, including this present book.

Cambridge has been a truly wonderful place to grow intellec-

tually, and this is down to its enriching and lively community. If

sometimes I have felt the weight of academia as a solitary endeav-

our pulling me under, it has been the friendship of Talitha Kearey,

Thomas Nelson and, above all, of Hannah Price that has buoyed

Acknowledgements

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me up. I owe them so much. Of course, there is more to life than

books (but not much more), and I want also to thank those friends

outside academia who have kept me sane and have brought me

great joy beyond the job: Sam Isaacs, Dan Keane, Raj Mistry, Joe

Smallman, Sam Oliver and Hannah Price (again!).

The most personal debts, though, I cannot ever hope to repay.

For their love, I am forever grateful to my parents, Sue, Michael,

Ross and Kirsteen, to my siblings Rebecca, William and Robbie,

and to my grandparents, Peter, Mary and Pam. But the deepest

thanks go to my partner, Alex, whose incalculable love, support

and immeasurable patience – when it comes to academic tribula-

tions and more besides – have kept me going now for a full decade

(but who’s counting?).

Acknowledgements

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ABBREVIATIONS AND EDITIONS

Below is a list of abbreviation conventions and editions that I

employ in this book. For all else I follow the abbreviations of

names and works of Greek and Latin authors as given in the

Oxford Classical Dictionary.

AB Austin, C. and Bastianini, G. (2002) Posidippi

Pellaei quae supersunt omnia. Milan.

AP Anthologia Palatina (Palatine Anthology).

Broggiato Broggiato, M. (2001) Cratete di Mallo. I

Frammenti: edizione, introduzione e nota.La

Spezia.

Cougny Cougny, E. (1890) Epigrammatum anthologia

Palatina cum Planudeis et appendice nova epi-

grammatum veterum ex libris et marmoribus

ductorum, 3 vols. Paris.

FGE Page, D. L. (1981) Further Greek Epigrams .

Cambridge.

GP Gow, A. S. F. and Page, D. L. (1968) The Greek

Anthology: The Garland of Philip and Some

Contemporary Epigrams, 2 vols. Cambridge.

Harder Harder, M. A. (2012) Callimachus: Aetia, 2 vols.

Oxford.

HE Gow, A. S. F. and Page, D. L. (1965) The Greek

Anthology: Hellenistic Epigrams, 2 vols.

Cambridge.

IEG West, M. L. (1989–92) Iambi et elegi Graeci ante

Alexandrum cantati, 2nd ed., 2 vols. Oxford.

IMEGR Bernand, É. (1969) Inscriptions métriques de

l’Égypte gréco-romaine: Recherches sur la

poésie épigrammatique des Grecs en Égypte.

Paris.

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KA Kassel, R. and Austin, C. F. L. (1983–) Poetae

comici Graeci. Berlin and New York.

Kerkhecker Kerkhecker, A. (1999) Callimachus: Iambi.

Oxford.

Lightfoot Lightfoot, J. (2009) A Hellenistic Collection.

Cambridge, MA.

Mugler Mugler, C. (1972) Archimède, 4 vols. Paris.

Pf. Pfeiffer, R. (1949–53) Callimachus, 2 vols.

Oxford.

SH Lloyd-Jones, H. and Parsons, P. (1983)

Supplementum Hellenisticum. Berlin and New

York.

Sider Sider, D. (2020) Simonides: Epigrams and Elegies.

Oxford.

List of Abbreviations and Editions

xii

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introduction

NUMBERS UP

I.1 Poetic Figures

This book explores Graeco-Roman poetry’s engagement with and

use of numbers. What I mean by this can best be explained by

turning to Homer’s self-presentation in the Iliad, where the matter

of enumeration intersects with the question of poetic expression.

ἔσπετε νῦν μοι, Μοῦσαι Ὀλύμπια δώματ᾿ἔχουσαι –

ὑμεῖςγὰρ θεαίἐστε πάρεστέ τε ἴστέ τε πάντα,

ἡμεῖςδὲ κλέος οἶον ἀκούομεν οὐδέ τι ἴδμεν –

οἵ τινες ἡγεμόνες Δαναῶνκαὶ κοίρανοι ἦσαν.

πληθὺνδ᾿ οὐκ ἄν ἐγὼ μυθήσομαι οὐδ᾿ὀνομήνω,

οὐδ᾿ εἴ

μοι δέκα μὲνγλῶσσαι, δέκα δὲ στόματ᾿ εἶεν,

φωνὴ δ᾿ἄρρηκτος, χάλκεον δέ μοι ἦτορ ἐνείη,

εἰ μὴὈλυμπιάδες Μοῦσαι, Διὸςαἰγιόχοιο

θυγατέρες, μνησαίαθ᾿ὅσοι ὑπὸἼλιον ἦλθον·

ἀρχοὺςαὖ νηῶν ἐρέωνῆάς τε προπάσας.

(Homer Iliad 2.484–93)

Tell me now, you Muses who have dwellings on Olympus – for you are goddesses

and are present and know all things, but we hear only a rumour and know nothing –

who were the leaders and lords of the Danaans. But the multitude I could not tell or

name, not even if ten tongues were mine and ten mouths and a voice unwearying,

and the heart within me were of bronze, unless the Muses of Olympus, daughters of

Zeus who bears the aegis, were to call to my mind all those who came beneath Ilion.

Now I shall tell the leaders of the ships and all the ships.

The passage addresses the presence in poetry of numerical as well

as heroic ﬁgures. Faced with the prospect of describing the entirety

of the gathered Achaean troops in the ninth year of the war, Homer

turns to address the Muses again.

While it precedes the Catalogue

The Greek text of Homer follows Allen (1920), with translations adapted from Murray

and Wyatt (1999) for the Iliad and from Murray and Dimock (1995) for the Odyssey.

Scholarship on the Invocation and Catalogue is vast. One traditional concern has been the

historical period and geographical politics it encapsulates, see Allen (1921); Burr (1944);

Hope Simpson and Lazenby (1970); Visser (1997). In terms of the make-up of the Iliad,it

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of Ships and the detailed counting up of the troops, it also follows

on from Homer’s series of similes variously describing the gath-

ering. In the run of similes, the host’s armour shines like a ﬁre

ravaging a forest, the troops appear like ﬂocks of birds gathering in

a meadow, like all the leaves and ﬂowers in a meadow, and like

a swarm of ﬂies round a milk pail (Il. 2.445–73), and their organ-

isation is then likened to goatherds ordering their ﬂocks ( 474–7).

The Invocation thus functions as a hinge, mediating between

poetic modes: the similes’ poetics of likeness and the

Catalogue’s poetics of enumeration. Yet it is not frequently

observed that the passage is an extended reﬂection on the tension

between poetic content (how many things you want to describe)

and the poetic resources required to recount it (how many verses it

will take). Prior to accounting for the ships at length in the

Catalogue, in other words, the poet is exploring and commenting

upon his enumerative abilities.

The role of the subsequent enumeration in the Catalogue

depends on the interpretation of this passage. On the one hand,

in contrast to the similes, which require no introduction or justiﬁ-

cation, the Catalogue’s poetics of enumeration need the support of

the Muses in order to be achieved. The ability to fully recall the

host lies solely with the Muses. On the other hand, the Muses’

support in recounting the entire host is in fact a condition (note the

optative mood of μνησαίαθ’), and the poet turns instead to recount-

ing only the leaders and the ships. The poet admits that the

problem is one of poetic capacity. The implication of his claim

that he ‘could not tell or name the multitude, not even if ten

tongues were his and ten mouths’ (Il. 2.488–90) is that a great

amount of content requires a concomitant extension of the poem,

which, in this case, even a division of labour by a multiplication of

mouths can do nothing to foreshorten. (Later Latin poets enact

their own numerical expansion from ten mouths to a hundred, but

has often been considered a later insertion, more appropriate to the gathering of the troops

at Aulis than to the troops on the Trojan plain in the ninth year of the war, see Allen

(1921) 169–70; Wade-Gery (1952) 53–7; Jachmann (1958); Kullmann (1960) 63. For

a more literary evaluation of the dislocation see Sammons (2010) 140–8. The following

is a necessarily brief account of the passage which glosses over certain interpretative

issues; see Chapter 3, Section 2 for more detail about the varying interpretations and for

my approach.

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equally to no avail.)

His solution to the expected increase in

extension is remarkable. The Catalogue accounts for the number

of men per ship, the number of ships per leader and the number of

leaders. So, in lieu of counting up the number of warriors who

went to Troy (ὅσοι ὑπὸἼλιον ἦλθον, 2.492), he allows for the

audience to reach a total instead based on the leaders and their

ships (ἀρχοὺςαὖ νηῶν ἐρέωνῆάς τε προπάσας, 2.493). Rather than

being an exhaustive count, the number of the host can be inferred

through what would now be called multiplication.

This strategy is used earlier in Iliad 2 by Agamemnon to calcu-

late the relative sizes of the Achaean and Trojan forces. He

imagines groups of ten Achaeans being served wine by one

Trojan and concludes that not all the Achaeans would be served

(Il. 2.119–28): the Achaeans outnumber Trojans by more than ten

to one. Equally, one of the similes preceding the Invocation dis-

plays a similar thinking. The leaders are described as organising

their troops like goatherds, and among them stands Agamemnon at

a higher level above those leaders (474–83). In both cases, indi-

vidual soldiers are organised into groups so as to make their

conceptualisation more manageable, and these groups are then

organised further: by Agamemnon when he compares the

Trojans with the Achaeans, and again by Agamemnon who rules

over the leaders who have already arranged their troops. The

organisation that enables the poet to encapsulate the host for the

audience is one which was understood both by ﬁgures within the

poem and by its audiences (to whom the simile is directed). Of

course, the use of multiplication is a traditional means of express-

ing quantity in Archaic epic.

What is so striking in Iliad 2 is that

the poet has harnessed these resources in order to explicitly reﬂect

on his capacity as a poet and how certain types of calculation shape

the catalogue as a poetic form.

Enn. Ann. 469–70 Skutsch; Hostius fr. 3 Courtney; Verg. G. 2.42–4 and Aen. 6.635–7.

Ovid gives up the count and settles for ‘many mouths’ (pluraque ... ora, Tr. 1.5.54).

Gowers (2005) 171–3.

For example at Il. 8.562–3 (1,000 ﬁres, 50 men by each); 9.85 (7 Greek leaders, each with

100 men); 9.383 (200 warriors coming out of each of the 100 gates of Thebes); and

16.168–71 (50 ships for Achilles, 50 men at hole pins in each and 5 leaders).

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Later readings of the passage, moreover, focus on and respond

to Homer’s counting. In arguing that the scale of the Trojan War

was not as great as often assumed, Thucydides makes his own

count based on Homer’s Catalogue (Thuc. 1.10.1–2). He ﬁrst

surmises there to be 1,200 ships, which is not far from the 1,186

ships that is reckoned in modern scholarship on the basis of the

Catalogue’s count. He then recognises that only the Boeotian

contingent and Philoctetes’ contingent are given explicit numbers

of men per ship, at 120 and 50 men respectively, and conjectures

that this is the upper and lower limit of the men per ship (Thuc.

1.10.4). From this he states – but does not calculate – that if one

were to take the mean number of men per ship (85) the force would

still be small at 102,000 men (Thuc. 1.10.5). Setting to one side

whether this is in fact a small contingent by ancient standards, he

brings to bear his own numerical abilities in reading Homer’s

Catalogue and so elevates the numerical aspect as a key point of

interest.

Other readers, though, could come to different totals. The

mythological handbook attributed to Apollodorus of Athens (a

historian and geographer) concludes in the relevant chapter that

‘the total number of ships was 1,013’ (νῆες μὲνοὖναἱ πᾶσαι ͵αιγʹ,

Apollod. Epit. 14). Similarly, in the Latin mythological handbook

attributed to Hyginus, the Fabulae, a count is made, although it is

marred by textual corruption. The chapter gives the reckoning of

the ships as 245 (summa naues CCXLV, Fab. 97.55) despite the

individual numbers given in Hyginus’ list adding up to 1,286

(which is a round 100 from the accepted 1,186). These counts of

ships and people also guided later readers approaching Homer’s

Catalogue. A scholium to the beginning of the Catalogue directly

invokes Thucydides’ language and his method of taking the mean

number of men per ship in explaining that Homer ‘further, does

have something to say about the multitude [of the host]’ (καίτοι

λέγει καὶ περὶ τοῦ πλήθους,bT-scholia on Homer Iliad 2.488) and

that the reader is readily able to compute the total. The lack of

a ﬁnal sum in the poem, which in an original oral context may have

contributed to a purposeful overload of information for the audi-

ence, became a prompt to engage numerically with epic for later

readers encountering Homeric poetry on the page.

Numbers Up

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These readings also fed into new poetic compositions and their

reformulations of the poet and his work. To keep with the

Catalogue of Ships, a more overt mathematicisation is found in

the Contest of Homer and Hesiod and its reimagining of Homer’s

Invocation. When asked by Hesiod how many men sailed to Troy,

he replies with a calculation much shorter in length than the Iliadic

catalogue.

πεντήκοντ’ ἦσαν πυρὸς ἐσχάραι, ἐνδὲἑκάστῃ

πεντήκοντ’ ὀβελοί, περὶ δὲ κρέα πεντήκοντα·

τρὶςδὲ τριηκόσιοι περὶἓν κρέας ἦσαν Ἀχαιοί.

(Contest of Homer and Hesiod 143–5 Bassino)

(50 × 50 × 900 = 2,250,000)

‘There were ﬁfty hearths of ﬁre, in each were ﬁfty spits, and around each were

ﬁfty pieces of meat: three times three hundred Achaeans were around one piece of

meat.’

The Homer of the Contest has progressed from the Catalogue that

counts to the more complex calculation that is multiplication. For

the audience(s) of the Iliad, it was necessary to estimate the

number of men in each ship and add together the troops under

each leader in order to reach a sum for the entire Achaean contin-

gent, in the manner that Thucydides had theorised. The Homer of

the Contest bypasses the need to display his counting, or indeed to

place his counting abilities under any scrutiny. He reaches

a number for the entire contingent in only a few lines where the

Iliadic Homer had professed his inability to account for the multi-

tude at all (πληθύν, Il. 2.488).

A further reworking of the Catalogue in Latin focuses on the

numerical abilities of the reader. The Ilias Latina, a Neronian-era

poem attributed to Baebius Italicus, compresses the key events of

the Iliad into 1,070 hexameter verses.

Its rewriting of the

Catalogue is prefaced by its own second invocation – Vos mihi

nunc, Musae ...referte (‘recount to me now, Muses’, 161–2) – and

it begins also with the Boeotian contingent: Boeoti decies quinas

egere carinas | et tumidos ualido pulsarunt remige ﬂuctus (‘the

I offer a more detailed analysis of this scene in the introduction to Part II.

For his name and date see Scaffai (1997) 15–29. The Latin text also follows Scaffai,

while the translations are my own.

I.1 Poetic Figures

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