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November 20, 2006


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That really is astonishing. Sadly, I don't really know enough to say any more.


I think today the problem would be a mid-level Olympiad question, but that's only because partitions and recursion are now everyday concepts in math.

In ancient Greek mathematics, there's very little evidence of either the idea of a partition -- the number of ways a whole number can be put together additively, like 3 = 2 + 1 = 1 + 1 + 1 -- or the idea of recursion, the way a Fibonacci number is the sum of the previous two Fibonacci numbers.

What would be truly freaky is if there were an ancient manuscript of Hipparchus which posited something like, "the number of partitions of four objects, nine objects, and every fifth collection of objects further, is divisible by five; and the number of partitions of five objects, twelve objevts, and every seventh collections of objects further, is divisible by seven." (Ramanujan's congruences, restated in verbal form.) This is probably not going to happen.

Incidentally, one can guess what method Chrysippus used to calculate the number of ten element statements in Stoic logic: he probably estimated it as 2^10 * 2^10 = 1024 * 1024 = 1048576, which is slightly over a million. But as Plutarch remarks, it's not a careful investigation of the problem.

(Also, look at those names: Chrysippus, "Golden Horse"; Hipparchus, "Horse Master". Sometimes, while parsing Greek, you want to break out the war bonnets.)

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