Numbers, counting, and calculation in Attic oratory

Peter O'Connell

  O'Connell, Peter. "Numbers, counting, and calculation in Attic oratory." CHS Research Bulletin 8 (2020).



Abstract

My project studies the role of numbers, counting, and calculation in Attic oratory. At the CHS, I focused on two issues. The first is the relationship between numbers and prose style. In oratory, numbers tend to appear near the end of sentences, as they also do in inscriptions. This recurring organizational pattern encourages the audience to focus on the numbers and perhaps facilitates calculation. Numbers also lend themselves to stylistic figures, especially rhyme, which would have had both a practical and aesthetic effect on the audience. The second is the effect of numbers on an audience’s imaginations. The physical, tactile connotations of numbers would have encouraged audiences to imagine movements and physical sensations associated with handling counters whenever they heard individual numbers or calculations. Such imagined experiences would have helped make them participants in speakers’ reasoning rather than mere listeners.

Introduction to the project

Aeschines compares the judges in Ctesiphon’s trial to auditors reviewing accounts. Just as auditors have to put aside their preconceptions and follow only the numbers, jurors have to follow the facts even if they lead to surprising conclusions (3.59-61). In reply, Demosthenes borrows Aeschines’ metaphor, but he mocks the idea that jurors resemble the kind of accountants who move pebbles on an abacus. These accountants strike numbers from their records when the accounts balance. Facts aren’t like numbers, however. They don’t cancel each other out and then disappear. The jurors, as accountants making an audit of facts, must consider how the facts will be remembered for all time (18.227-231).

The distinction between what jurors do and what accountants do is not as clear as Demosthenes claims it is in On the Crown. In other surviving forensic speeches, including many by Demosthenes himself, the jurors are asked to consider numbers and calculations of all sorts. They judge cases that involve assets, interest, and returns on investments. Sometimes they have to take into account how many days, weeks, months, or years have passed, how large or small something is, or how many degrees of kinship separate relatives. Numbers also factor into almost every surviving speech from the assembly. The assemblymen hear about amounts of money, amounts of ships, and amounts of Athenians, as well as how these amounts are related to each other. Aristotle (Rhetoric 1.4.7-8 1359b) and Xenophon (Memorabilia 3.6.4-13) both insist that numerical, and especially financial, expertise is a prerequisite for speaking in the assembly. Speakers in the assembly and the courts are never neutral sources of information, however, even when they seem to be providing impartial data such as numbers. They choose the numbers to present and how to present them, influencing the way audiences react. Numbers are a fundamental aspect of Athenian persuasion, but one that ancient rhetorical theorists rarely address.

I began my fellowship at the CHS with three foundational questions about the role of numbers in persuasion besides as factual evidence. What is the relationship between numbers and the character of the speaker? What is the connection between numbers and prose style? How did the tactile, material aspect of counting affect how Athenian audiences heard and internalized numbers and calculations? My research during the past year focused primarily on the second and third questions. In the rest of this report I will present some of my preliminary results.

Numbers and Prose Style: Aesthetics and Practicality

(1.) Parallels with visual media

In Attic documentary inscriptions, numbers tend to appear in either “tabular” or “interspersed” format, in the terminology of Serafina Cuomo. Numbers in “tabular” format are arranged in columns rather than in complete sentences (abcde 12345). This characterizes such inscriptions as the Attic stelai or the tribute lists. Numbers in “interspersed” format appear in sentences rather than in columns (abcde12345defgh67890), for instance in the accounts of the Temple of Nemesis at Rhamnous. In the latter format, numbers tend to appear at the end of cola, after the items that are being counted. The same thing is true of Attic oratory. Numbers tend to appear at or near the end of cola (e.g., Lys. 19.42-43; Dem. 27.4) rather than at the beginning or the middle. Although this is not a hard and fast rule, it is the general pattern in Greek prose (e.g., Hdt. 1.50-51, Lys. 21.1-5). The position of numbers in sentences in poetry is more variable, although they tend to appear at either the beginning or end of cola rather than the middle. This may reflect a desire to place numbers in marked positions, although there continues to be controversy about emphasis in Greek word order.

I suggest that the parallel between inscriptions and oratory reflects an overlap between oral and visual media. This is not necessarily a case of speakers imitating stones or inscriptions imitating spoken models, although imitation may play a role. Rather, it may be a convention of intelligibility. Placing numbers in columns or at the end of cola in inscriptions would have made them easier for viewers to identify and, perhaps, to total up. Similarly, placing them at the end of cola in speeches may have created a kind of aural column, so to speak, especially if pauses contributed to the parallelism across sentences. This could have drawn listeners’ attention to the numbers and made it easier to follow a speaker’s calculations.

(2.) Sound effects

Numbers lend themselves to sound effects associated with Gorgianic style. To take one simple but representative example, after Demosthenes reckons up the property he says was stolen by his guardians, he calculates the assessment: πεντεκαίδεκα ταλάντων γὰρ τρία τάλαντα τίμημα (“Out of fifteen talents, the assessment was three talents,” trans. MacDowell, 27.9). There is alliteration with the repeated tau’s and homoeoteleuton with the final alphas. There are also exactly eight syllables on each side of the gar. These effects can be heightened when numbers are used with rhyming words such as mnas and drachmas. They would have had an aesthetic effect, but they also would have had the practical consequences of remaining in the judges’ minds, especially when they are complemented by still more sound effects, as in On the Symmories, where numbers ending with -ious surround a set of infinitives ending in ­-sai and -nai (14.16).  

The Tactile, Material Aspect of Counting

Reviel Netz influentially wrote that, “We imagine numbers as an entity seen on the page; the Greeks imagined them as an entity grasped between the thumb and the finger.” An Athenian audience who heard numbers and calculations in a speech would have associated them with counters being manipulated on an abacus. In Against Aphobus, Demosthenes draws attention to the parallel between the numbers the judges hear him say and the money they could have seen being counted out in the agora (27.58-59).

The parallel between seeing and hearing suggests that numbers in speeches contributed to enargeia, that is, the effect of language on the imagination. Enargeia is traditionally associated with a sense of imaginary sight, but recent work by scholars such as Ruth Webb, Jonas Grethlein, and Luuk Huitink has stressed its multisensory nature. Numbers would have appealed to what Webb calls the “kinaesthetic imagination” of listeners because they were above all associated with touch and movement. When listeners heard a number, say twenty-one or three-hundred-forty-seven, they would have remembered and re-experienced the feel of counters between their fingers being moved around an abacus. This would have created the sense that they were not simply hearing numbers and calculations but participating in them at first hand, helping, as enargeia always should, to turn the audience into supporters of the speaker. It may also have enabled the audience to confirm the calculations of the speaker, or, just as importantly, to give them the impression they were confirming them. In other contexts, measurements may similarly have activated the kinaesthetic imagination through an association with physicality and movement. Metrological reliefs that use images of body parts to illustrate standard units of length reflect the close link between physicality and numbers.

Conclusion

As my research continues away from the CHS, I plan to investigate these topics further and eventually to turn to some broader issues, including the power of rhetoric to coopt the expertise of tekhnai such as arithmetic and use them for the ends of persuasion.

While I was a fellow of the CHS, I also had the opportunity to explore the use of numbers in Greek authors from a range of genres and periods, including Hesiod, Aristophanes, Callimachus, and Callixenus of Rhodes. I anticipate that this research will contribute to this project on the Attic orators and form the basis for future work.


Select Bibliography

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———. 2013. “Accounts, Numeracy and Democracy in Classical Athens.” In Writing Science, ed. M. Asper, 255-278. Berlin.

Doxiadis, A., and M. Sialaros. 2013. “Sing, Muse, of the Hypotenuse: Influences of Poetry and Rhetoric on the Formation of Greek Mathematics.” In Writing Science, ed. M. Asper, 367-409. Berlin.

Grethlein, J., and L. Huitink. 2017. “Homer’s Vividness: An Enactive Approach.” Journal of Hellenic Studies 137:67–91.

Kallet-Marx, L. 2008. “Money Talks: Rhetor, Demos, and the Resources of the Athenian Empire.” In The Athenian Empire, ed. P. Low, 185-210. Edinburgh.

Netz, R. 2002. “Counter Culture: Towards a History of Greek Numeracy.” History of Science 40:321-352.

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———. 2020. “Pericles’ Rhetoric of Numbers.” In The Ancient Art of Persuasion across Genres and Topics, ed. S. Papaioannou, et al., 339-355. Leiden.

von Reden, S. 2002. “Demosthenes’ Phialê and the Rhetoric of Money in Fourth-century Athens.” In Money, Labour, and Land, ed. P. Cartledge, et al., 52-66. London.

Webb, R. 2020. “As If You Were There: Enargeia and Spatiality in Lysias 1.” In Forensic Narratives in Athenian Courts, ed. M. Edwards and D. Spatharas, 157-170. Abingdon, Oxon.




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