Idle Speculation on Number Theology

[sdi]

(As a disclaimer, before I begin, I should note that I am not a magician and everything I say here is entirely speculative. Don't rely on it for anything other than ideas!)

I have an idiosyncratic theory (per Plotinus and the other Neopythagoreans that I have read) that various types of numbers fall into three different categories based on their essential potency:

• The weakest numbers are the even numbers. This is because they may be divided into two equal groups and set against each other, tying their energies up and preventing action. (It is for this reason, I think, that the Pythagoreans considered even numbers passive.)

• The middle class of numbers are the odd composite numbers. These may not be set against themselves—there's always a "tie breaker," a majority, and so there is always direction and the possibility of action—but they may still be divided is some way or other, and thereby weakened.

• The strongest numbers are the odd prime numbers. These may not be divided at all, and thus always possess their essential unity. (And, as Proclus tells us, unity is power.)

(We may as well classify 1 with the prime numbers, even though it is not technically prime, since obviously it is as indivisible as it gets; further, within a class, smaller numbers have greater potency than larger numbers.)

One thing that is common in folk magical practice is the combining of harmonious elements into a whole (e.g. in an amulet, etc.). I wondered to myself whether it were possible to combine elements that were each individually strong (e.g. odd, prime) and strong in combination (e.g. odd, prime). For any two elements it is not, and the proof is trivial: two odd numbers, when summed, form an even number. Therefore, one must add an even number to an odd number to get another odd number, thereby introducing a weakness. However, it is possible with three elements: a couple trivial examples are 1+3+7=11 and 3+5+11=19.

I might suppose a prime number of ingredients, combined in prime terms into a prime total, might be more potent than other combinations. But an esoteric number theory of this sort does not seem to be well-developed: all systems I've seen only assign meanings to 1-10 (and higher numbers are considered in light of those). I'd be curious to see a theory treating the primes as conveyors of essential meaning, but there is an infinity of those...

Comments

[boccaderlupo]

This is fascinating. The maths ain't my strong suit, but this seems worth exploring.

Axé

[sdi]

The difficulty I've been having with going much further is that every systematic attempt to apprehend divinity that I've seen is complete: that is, it divides divinity into a finite number of "chunks" and then makes sure that everything is accounted for. (See also the Babylonian treatment of the zodiac, or how Pythagoras treated the numbers 1-10, or how Sallustius discusses the Olympians, etc.)

But the system I'm sketching out, above, has an infinite number of prime numbers! I mean, it seems reasonable to me to assume divinity is infinite, but how does one begin to try and make sense of the infinite!? So for the moment, I am waiting for illumination. (Story of my life!)

[boccaderlupo]

What's the old saying? You can only ever have a model that is complete but insufficient, or one that is incomplete and sufficient...? Something to that effect...paraphrasing.

I was wondering if there's something to be made of the "steps" between the various three number combinations (i.e. 1 + 3 + 7 = 11 is 2 "steps" + 4 steps = 6, 3 + 5 + 11 = 19, 2 steps + 6 steps = 8, etc.) I tried a few of these and they all seemed to turn up even, but of course not a very in-depth survey...

The only quibble I might offer is the idea of "weakness," which I think shades into the pejorative. You're better acquainted with Proclus et al. than I, but would prime numbers then effectively be the henads, while the even would be things participating in the henads...? With "1" as the sort-of stand-in for the utterly transcendent One of the philosophers...?

[sdi]

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").