Some Terrifying Numbers

So a lot of us have spent the past month or two staring at some scary numbers and working out their implications. These numbers are based on counts, even if the authors had to make some assumptions and do some arithmetic to turn something they can count into what they want to know. I spend a lot of time staring at Greek numbers for barbarian armies, and if they were based on counts they are hard to understand:

• If we have multiple sources, they give numbers which vary widely, even if they all drew on the same earlier writers
• The smallest Greek number for a barbarian army, 100,000, is as big as the largest army we can document in western Eurasia before the Napoleonic Wars, even if we are very generous about what counts as ‘documentation’ (hard-hearted historians would say we need archives so no army strength can be known until about a thousand years ago)
• The smallest Greek number for a barbarian army is about as many as the biggest army which any Near Eastern ruler claims to have commanded.
• Either there are no numbers for individual units, or the numbers given add up to a much smaller number than the grand total
• Usually, no source for the numbers is given: we are not told whether they are an estimate by scouts or by the enemy’s clerks.
• Such vast armies could not march, camp, and fight in the usual fashion or on the described battlefield.

If we assume that these numbers are based on counts, we have to chose one of the figures in our different sources, then ‘correct’ it by adding, subtracting, multiplying or dividing until it fits our expectations. As a fellow named Whatley said in 1920, these theories often sound convincing until you read the next article with another ingenious theory that contradicts the first one. So assuming that these numbers are based on counts has not lead to new knowledge that people with different perspectives can agree on, it has just lead to endless arguments and speculation.

So a few years ago, I asked myself what would we expect to see if these numbers are drawn from something other than counting. And instead of looking at different writers’ figures for the same army, I looked for the same number in stories about different armies. Have a look at the fifteen nineteen lines on this table and decide if you see what I see.

These texts span a thousand years, three languages, and even more cultures and religions, but the figure of 120,000 (2 × 60 × the largest named number in most Semitic languages) or 1,200,000 (2 × 60 × the largest named number in ancient Greek) shows up again and again. Most of these sources are not ones which ancient historians find trustworthy for numbers, they are stories about long ago and far away. And I think stories is the key word. This number does not appear in documents about the actual strength of specific units on specific days, just in stories that someone might ask to hear for the sheer joy of hearing them.

It is comforting to think that Greek and Roman numbers for barbarian armies are based on counts, because that makes them sound rational and empirical and lets us use those numbers to say something about the ancient world. But that assumption creates a lot of problems. If we assume that the numbers in one story are often based on numbers in another story, then suddenly we can explain some of the things that were hard to understand. And this would not make the ancients any more or less irrational than the moderns who give their own numbers for the Persian wars, multiplying or dividing ancient numbers until they have something they can believe in and that fits numbers they have read in stories about the Siege of Vienna or Napoleon’s invasion of Russia. Basing numbers for big frightening things on counts is not natural, it is one of the hardest things in the world to do.

After I wrote this post, I learned that my old sparring partner Patrick Waterson, who was a firm believer in the big armies in the Old Testament and Herodotus and an active member of the Society of Ancients, UK, died in the UK on 14 January 2020. SIT·TERRA·TIBI·LEVIS·COMILES

Further Reading:

• Whatley, N. (1964) “On the Possibility of Reconstructing Marathon and Other Ancient Battles,” The Journal of Hellenic Studies 84 pp. 119-139
• Skepdic ‘Anchoring Effect’
• John Gagné, “Counting the Dead: Traditions of Enumeration and the Italian Wars,” Renaissance Quarterly 67 (2014) pp. 791–840 (added 2024-01-25)

This is based on chapter 6.6.1 of my first book which is forthcoming from Franz Steiner Verlag in winter 2020/2021.

Edit 2023-02-14: added Cassius Dio

Edit 2023-02-21: added the royal army in Xen. Anab. 3.5.16

Edit 2023-03-08: addded Xen. Cyr. 6.2.10

Edit 2023-05-04: over on his blog, Andrew Gelman points to an article in The Atlantic with the phrase “These numbers are what we might call “decorative statistics.” Their purpose is not to convey an actual amount of money but to sound big and impressive. That doesn’t keep them from being added, subtracted, divided, or multiplied to yield other decorative statistics”

Edit 2023-05-29: see also Lock, F. P. (2012) The rhetoric of numbers in Gibbon’s History (Newark : University of Delaware Press)

Edit 2023-10-01: someone almost got it!

I’m sometimes embarrassed by where I have been forced to find my statistics … Often, the only place to find numbers is in a newspaper article, almanac, chronicle or encyclopedia which needs to summarize major events into a few short sentences or into one scary number, and occasionally I get the feeling that some writers use numbers as pure rhetorical flourishes. To them, “over a million” does not mean “>10⁶“; it’s just synonymous with “a lot”.

Matthew ‘Atrocitology’ White http://necrometrics.com/warstats.htm#Recurring

Edit 2023-10-24: added Arrian, Indica 19.5

Edit 2023-12-21: add Historia Augusta, Life of Severus Alexander, 56.5 (Lacus Curtius)