Concerning Twelve

[sdi]

Why are there twelve gods? I suppose the traditional explanation would be that there are twelve signs to the zodiac, though I haven't seen any explanation of how or why the Babylonians came to this number. (There are twelve months in a year? Except a third of the time, when there aren't?) The philosophers, for their part, say it's because there are four functions with three phases each, making twelve total.

You may recall that I've been toying with the pseudo-neo-Pythagorean conception of unity being representative of the Intellect while numbers are representative of souls, with prime numbers being representative of indivisible natures (e.g. gods). Well, I woke up with an odd math problem in my head: what is the point at which there are more composites than primes? After all, the first number (two) is prime, so initially there are more primes than composites; but since every even number and some odd numbers are composite, there are eventually more composites than primes; so what is the point at which it crosses over?

It turns out that it's very easy to find by hand, and as you've probably guessed from my first paragraph, it's the twelfth number: at this point, there are six primes (2, 3, 5, 7, 11, 13) and six composites (4, 6, 8, 9, 10, 12). After that, the composites dominate and the primes never catch up.

What's curious about this, to me, is that if you consider the Olympians, six of them are first-generation (Hestia, Demeter, Hera, Poseidon, and Zeus are Cronus's children, while Aphrodite was created from Uranus by Cronus' actions) and six of them are second-generation (Artemis, Apollo, Athena, Ares, Hephaestus, and Hermes are all Zeus's children). This is just like how of the first twelve numbers, six of them are prime, while the other six are generated from the first six.

This is not to say that looking at the prime numbers is where the Greeks (or, for that matter, the Babylonians) got their cosmogony; it seems quite likely to me that the number theory antedates the theology, and anyway the particular genealogy of the composites doesn't match Hesiod. (All of the second-generation Olympians are sired by Zeus, but there is no prime shared among all six composites.) So I don't have my answer for "why twelve?" But it is nonetheless interesting that my odd little number speculation has a parallel to the theology.