sdi: Oil painting of the Heliconian Muse whispering inspiration to Hesiod. (Default)
sdi ([personal profile] sdi) wrote 2023-11-13 05:42 pm (UTC)

What's the old saying?

Yup, that's Gödel's Incompleteness Theorems!


I was wondering if there's something to be made of the "steps" between the various three number combinations[...]

Good question. That reminds me of Euclid's formula for generating Pythagorean triples. In any case, yes, the gaps will always be even, since the numbers straddling the gaps are always odd—to go from one odd number to the next, you always add 2, so if you have to go a bunch of odd numbers up, it'll always be a multiple of 2.


[...] which I think shades into the pejorative.

I agree, it should be stressed that we're speaking in relative terms, here. 2 isn't inherently "weak," rather only in comparison to 1 or 3, etc.

Regarding Proclus, I'm not actually sure what henads are yet, so let me get back to you on that one once I'm further in the Elements. In Plotinus' schema (which is quite different), though, the One is the entire number line, while the Intellect is 1, and the World Soul (e.g. the greatest soul of all) is 2. Numbers beyond that are not really described in any depth except to say that they are forms. What I'm proposing here, though, is that the primes are "gods," while all other souls are composites—hence the gods are infinite in number, but any given soul only participates in a fixed number of gods (depending on their "prime factorization").

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