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...

One summer, when I was a child, I went to visit my grandparents. We were sitting around the dinner table, which looked out over their forested backyard, and I saw a bird feeder standing in the middle of it, with a squirrel sitting on it and eating the birdseed as if it was all for him.

"Grandpa, it looks like a squirrel is stealing the birdseed."

He didn't even look. "That he is."

"I wonder if there's anything you can do about it."

"Well, originally, I had a normal bird feeder—the kind that hangs from a tree branch, with a little tray in the bottom that the feed falls into and that the birds can eat from. But the squirrels would just climb down the cord, sit on the perch, and gobble up all the birdseed as if it was theirs.

"So I went to the hardware store and asked the clerk about it. He recommended getting a 'squirrel-proof' bird feeder: the perch is like a scale, and if weight is placed on it, it closes the bird feeder shut. This way, the birds—who are too light to trip the scale—can eat what they want, while the squirrels—who are too heavy—can't get anything. So I went and bought it and installed it. The squirrels couldn't get at the birdseed at first, but it didn't take them long to figure out that if they climbed up under the middle of the bird feeder, clinging there like a bat, and reached their little arms up and over the perch, they could still grab the seed and eat it without tripping the scale.

"So I went back to the hardware store and asked the clerk about it again. This time he recommended putting the bird feeder on a pole, with a wide disc like a frisbee beneath it. The squirrels would be able to climb up the pole, but they wouldn't be able to climb around the frisbee, and so the birdseed would be safe. So I bought it and installed it, and sure enough, the squirrels couldn't get around the frisbee. They just sorta sat and watched the birds eating the seed. The next day, though, I noticed the birdseed was all gone, and the birds wouldn't have eaten it so fast. So I refilled it and watched. The squirrels had learned to take a running leap from the branches way, way above—if they did it just right, they'd land on the birdfeeder, and then be able to eat as much as they liked, just as before.

"So I went back to the hardware store a third time and asked the clerk about it again. He thought about it for a minute and said, 'I'm sorry, mister, but I don't think we can help you. You see, we may be smarter than the squirrels, but we're only trying to spend a few minutes to keep them out; meanwhile, they're spending their entire lives trying to get in!'"

Then thus replied the prophetess divine:
"O goddess-born of great Anchises' line,
The gates of hell are open night and day;
Smooth the descent, and easy is the way:
But to return, and view the cheerful skies,
In this the task and mighty labour lies.
To few great Jupiter imparts this grace,
And those of shining worth and heav'nly race.
Betwixt those regions and our upper light,
Deep forests and impenetrable night
Possess the middle space: th' infernal bounds
Cocytus, with his sable waves, surrounds."

(Virgil, Æneid VI, as translated by John Dryden)

Rich indeed is he who can keep his gates open day and night! (But riches of what kind?)

Critobulus once asked Socrates, "Socrates, you are wise; do you know any magic spells for attracting love?"

Socrates answered, "Well, Themistocles made Athens fall in love with him by adorning her with amulets..."

(Adapted from Xenophon, Memorabilia II 6.)

...

(Okay, okay, I'll explain the joke. Themistocles was an Athenian general and politician who, after Athens and Sparta managed to (barely) repel Persia at the Battle of Marathon, managed to drain the treasury to build Athens a massive navy and fortifications (the "amulets" Socrates is jokingly referring to). When Persia returned for revenge a decade later, this navy was instrumental in defeating the Persians at Salamis, thus ensuring Athenian dominance of Greece until the Peloponnesian War.)