Thursday, February 28, 2008

Fractal flames




Images from Fractal World Gallery.


In my dream last night, Euclid had been a kind of sorcerer, and his Elements was not just a book of geometry but of wizardry. The forms he had constructed were pentagrams and hexes. I remember that it was important to have exactly the right instruments, and that people were searching for Euclid's own compass and straightedge, which had been made of some incorruptible gold alloy and placed in a green velvet lined box in a hidden drawer. In the dream, Newton was also a mage and his Principia was not just about forces and planets, but how to wield forces and take advantage of astrology.

It's easy to guess where it all came from: my dad's own drafting tools, the Golden Compass, a conversation I had a couple days ago about geometric arguments in Newton's work, the Baroque Trilogy, the whole Hermetic tradition. It also matches my intuition that magic couldn't work the way it does in most books, where a couple of words suffice for every spell. More complicated effects would require a more complicated description. It would be more like programming the universe than saying the right password.

Friday, February 22, 2008

Thursday, February 14, 2008

The Opposite of the Pride Cycle

The "Pride Cycle" is pretty clearly understood, and I'm sure it's very applicable at the level of civilizations. But at the level of individuals, I see another cycle happening more often. It could be called "The Shame Cycle."
Take overeating, for example. Someone gets a little overweight, and starts to feel ashamed of his weight. It's hard to sleep; he starts to feel worthless, and just wants to make it stop. He feels bad, and just wants to feel good, now. So what does he do? He does the thing he knows will bring him instant pleasure, namely, eating. He feels like he's already worthless, so he might as well pile it on. The shame has turned into self-hatred which is self-destructive.
Of course that's just one example, but it works with any addiction. But what sin isn't, in the end, turned into an addiction? No one would do wrong if it didn't bring immediate pleasure. But the delayed consequence of doing wrong will eventually make them feel even worse, meaning the urge for that pleasure is all the stronger.
This is the sentiment, I think, behind "Amazing Grace." It's only with outside help, being saved, that the cycle can be broken.

Tuesday, February 12, 2008

The Republic of Codes

Here is another article about the development from Kircher's Ars Magna Scienta to Leibniz's Universal Character. The whole project of a philosophical language was to allow general thought to be calculated automatically in a way similar to how mathematical thought is calculated automatically. By studying cryptography and languages, they hoped to discover the key to artificial intelligence. By the way, the book by John Wilkins on this subject, An Essay towards a Real Character and a Philosophical Language, proposed the ideas that would eventually become the metric system.

Monday, February 4, 2008

Political Balance

The election in 2000 was statistically exactly balanced. 2004 was pretty close, too. At the time, I guessed that some trend must be driving the elections to be so close. Here is an article from Slate that supports that idea. There are a few links at the bottom to others with the same thought, including a more interesting one from David Levy. Turns out it was first formulated in 1929.
It's an example of experimental mathematics.