A useful word

Written by David Mimno

I was reading a paper the other day and came across the word aleatory. This turns out to be an excellent word. It comes from the Latin alea for “dice”, as in alea jacta est, which is what you say when you’re Julius Caesar and you cross the Rubicon. It means random, or subject to chance. It seems to come up mainly in legal contexts: an aleatory contract is one whose terms depend on future events, like an insurance policy. This got me thinking about other words for the property of randomness.

Random, of course, is the most frequent and familiar word, so by default it should be a good choice. But many people tend to think of random as unstructured or messy. So what’s a good word for having an element of chance, but in specific, quantifiable, and non-uniform ways?

The first thing that came to mind was stochastic. Since I had my Shorter Oxford English Dictionary (2nd ed., 1936) out, I looked that up too. It’s derived from στόχος, an aim or a shot, usually with a javelin or something similar. I was interested to see that, where aleatory is from the gambling world, stochastic is more military. But what really caught my eye was that the SOED listed stochastic as archaic and extremely rare. Huh? How could such a fun and important word have been almost lost, and how did it come to be found again?

I checked the Google n-gram viewer, and found that indeed, stochastic is now common, but almost never occurs until — you guessed it — 1936. Aleatory, in comparison, was well attested throughout the 20th century, but at about the same frequency over the whole period. Even more surprisingly, probabilistic, which I thought would dominate both terms, is less frequent than stochastic and didn’t really take off until 1950.

Here’s the zoomed-in chart for pre-1940 books, showing the dawn of the stochastic era:

What caused this increase? Again, relying on Google Books, there are some indications. The works that use stochastic between 1935 and 1938 include, from 1938, Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems by Paul Richard Halmos and a paper that may or may not be by Alonzo Church from the Journal of Symbolic Logic (it’s hard to tell from the Books interface whether the author metadata is at the journal or article level), and, from 1935, Prices in the Trade Cycle by Gerhard Tintner, who puts “Stochastic” in scare quotes. I’d love to know if anyone can fill in the details.

So what about aleatory? It never declined, and has actually gained popularity along with its more frequent cousins, but never took off in the same way. Could it be stuck in a legal context, as an ossified part of a fixed phrase? I checked the frequency of aleatory contract along with the base adjective, and it doesn’t seem to account for even a significant fraction of uses. Again, just from isolated frequencies it’s hard to tell what rock this word has been living under, but I’ll bet a little scholarship could turn up some interesting usages.

So, two points. First, aleatory is a great word, and we should use it when discussing stochastic, probabilistic modeling. And second, the next time you see one of those lists of “great archaic words we should bring back”, don’t laugh. Sometimes words do have a rebirth, but the process is (ahem) aleatory.