Some Guesswork

This week, we'll look at the Russian word догадок (transliteration dogadok), which, in the context we're interested in, means conjectures or guesswork. Our focus is really on the declension of догадок (genitive plural) rather than its meaning: any Russian noun would do, but I chose that one because this post is based on a guess or conjecture — or possibly just an inkling. Here is the (not very precise) conjecture: the declension of Russian nouns after numbers is related to the fact that the variance scales with the mean in count distributions.

Count Distributions

Richard McElreath brings up the relationship between the variance and the mean of a count distribution when introducing count models in his Winter 2015 Statistical Rethinking lectures. He also describes how this relationship is reflected in human languages. The discussion relevant to this post begins here and continues for just over a minute:

"This is a very important thing about count variables. All count distributions are like this: the variance inflates with the mean. And that's true in nature as well: the bigger the magnitude of a count the more uncertainty there is around the mean and that's a normal thing about counts. This is actually kind of embedded intuitively in the inate human counting system which is logarithmic [...] it's present in all human languages: one, few, many. Right, that's logarithmic because it's magnitudes and people intuitively — even if they're not numerate beyond one, few, many — understand that many is vaguer than few and few is vaguer than one, so the precision goes down as [the mean] goes up as well."

Numbers and Declension

This remark about one, few, and many got me thinking about declension of nouns after numbers in Russian. The rules can get somewhat complex so I want to focus on the simplest example: counting objects.

The Basic Rule

We'll start with the following rule which is not quite correct and refine it later: When there is exactly one of an object, use the nominative singular. When there are two, three, or four of an object, use the genitive singular. When there are five or more, use the genitive plural. (Note that we have different cases for one, few, and many.) For example, we have

одна догадка (one guess, nominative singular)
две догадки (two guesses, genitive singular)
пять догадок (five guesses, genitive plural)

"One guess, two guesses, five guesses" is a faithful translation, but if we were to try and force the grammar upon the English translation, it might take the form of "one guess, two [instances] of guess, five [instances] of guesses." It may help to see how the nominative and genitive cases are used in another context:

Эта догадка такая же хорошая, как и любая другая. (This guess is as good as any other.)
Причина этой догадки неизвестна. (The reason for this conjecture is unknown.)
Случайность этих догадок поражает. (The randomness of these guesses is astounding.)

Both the form of the number preceding the noun and the noun-ending itself depend on the gender of the noun, but the pattern of nominative singular, genitive singular, genitive plural is followed across all genders:

один суп (one soup)
два супа (two soups)
пять супов (five soups)

одна ворона (one crow)
две вороны (two crows)
пять ворон (five crows)

одно слово (one word)
два слова (two words)
пять слов (five words)

The Catch

So far so good, we seem to have different rules for one, few (two, three, four), and many (five or more). However, rule described above only works as long as the objects number twenty or fewer. As soon as we hit twenty-one, we start over. Numbers ending in one (but not in eleven) take us back to the nominative singular:

одна догадка (one guess)
двадцать одна догадка (twenty-one guesses)
сто девяносто одна догадка (one hundred ninety-one guesses)

Similarly, numbers ending in two, three, or four (but not in twelve, thirteen, or fourteen) are followed by nouns in the genitive singular. For all others, we're back at the genitive plural.

So, now that we know the full rule, is the conjecture still valid? Your guess is as good as mine.