Chaos vs Order

You can have your "pi" and eat it too

© Bryan Zepp Jamieson

7/2/05

http://www.mytown.ca/zepp

http://zeppscommentaries.com/S&E/chaos.htm

Last night, I watched a DVD movie called "π" (for those staring in frustration at a tiny black rectangle in quotes, that’s supposed to be the symbol for "pi"). It wasn’t a very good movie. Aside from the density of the subject matter (advanced math) it featured a poor soundtrack that made it nearly impossible to tell what the characters were saying. Then, too, there’s a suspicion that the math the premise of the movie rested upon wasn’t just abstruse, but was actually incoherent.

In the movie, a brilliant mathematician with no visible source of income has outfitted his apartment with several tons of 1970s computer equipment, and is searching for a way to predict the stock market. Or something. Like all good mathematicians, he suffers from migraines, fainting spells, epileptic seizures, and paranoid schizophrenia. It’s a wonder these guys can count to eleven without having to pull off a sock, let alone solve the mysteries of the universe.

In any event, he discovers a 216 digit number that does – well, something. Like Douglas Adams’ "42" it’s the answer to Life, the Universe, and Everything. Or something. You wouldn’t think in a place like New York City, a paranoid schizophrenic with an apartment full of antique computers would draw much attention, but he is quickly chased by government agents or something, who think he really has come up with a way to predict the stock market. Or something. Apparently this is a bad thing. And a group of Qabbala cultists are also on his ass, because the magic number is supposed to be the True Name of G-d. Or something. Apparently this is even worse than tips on how to play the market.

As I said, it wasn’t a very good movie. If you’re tempted, rent "The Incredibles" instead. It makes sense, and it’s interesting. If π shows up on my TV, I expect to see Joel and the ‘bots sitting down in the front row.

But it did make me think about the relationship of math to the universe. Math is order, the universe seems to be largely chaos, and yet the two are intertwined. Chaos from order (entropy) is a reasonably easy one to grasp. Weather is nothing more than the interaction of several constants: the amount of energy coming from the sun, the volume and composition of air, and the ratio of land surface to water surface. But as any meteorologist can tell you, weather patterns appear to be chaotic in nature.

Order from chaos is the one that gives people trouble and causes them to do silly things like run out and get religion. Even Einstein, rejecting the chaos that underlay the order he was trying to wrest from the universe, snapped "God does not play dice with the universe." I once showed a friend who rejected the notion of order from chaos how it worked. I had him leave my office for a few minutes, and when he came back, I had an image on my computer screen. It was zoomed in to about 100:1, so the screen was filled with a pattern of square pixels of varying shades of grey, about 12 wide and 8 high. I asked my friend to tell me what he saw. He said he saw a random collection of rectangles. I pulled out to 24 by 16. Still random. 48 by 32. He peered. There WAS something. He just wasn’t sure what...96 by 64. It was a nose. A human nose. I pulled out to 192 by 128, and my friend recognized his own face, from a greyscale image of him I had. "Ok," he agreed with some asperity, "you made your point. But it wasn’t true chaos, was it?"

And that’s the thing. True chaos, outside of Los Angeles Dodgers hitting, is an immensely rare phenomenon. Computer experts are still trying to devise a algorithm that generates truly random numbers.

What we see as chaos is usually nothing more than our own ability to discern a pattern.

This isn’t exactly a new idea. The ancient Greeks wrestled with it.

We took a big step forward in deciphering randomness about twenty years ago, when we discovered fractals. These equations can describe the apparently random development of branches on a tree or a snowflake, so that no two trees or snowflakes are exactly alike. But it isn’t truly random, of course: you can still recognize each as a tree or a snowflake. You can easily recognize different types of trees, even though each is unique, just as you can recognize breeds of dogs. We’re geared to recognize patterns through a certain amount of "noise." Fractals helped explain how we did that. Even people who don’t know what "pi" is can tell an oak from a cedar.

The relationship of math and humanity is even more intriguing. All that we are apparently stems from the interaction of just four chemicals: cytosine, adenine, guanine, and thymine. Three billion molecules of these four substances form the human genome. The pattern of the genome is largely random noise, we believe. The remaining one fifth determines our size, our height, our health, our intelligence, and all the other things that make up being a person. Out of noise, an individual, unique from every other individual, but indisputably human.

Not just us, of course. All plants and animals have DNA, all result from the dance of A, C, T, and G. Right down to behavior and temperament. Take cats: cats indisputably have individual personalities. And those personalities are indisputably feline. Each different, each part of a pattern. Order from chaos.

Even plants. Ever wondered why two adjacent roses, same background (same clone parent, even), same soil, same light and water, same tending, are differeent, with one more robust than the other. Is it possible that one rose is simply more AGGRESSIVE than the other?

Recently, they discovered a "gay gene" in mice. They implanted the gene into ordinary mice, and watched in disbelief as they turned gay. In humans, they have evidence that SCENT is a big part of gay behavior. Gays smell different from other people, apparently. (Yes, I know this sounds like a particularly unpleasant racial stereotype, but lB il est.)

The notion that four chemicals can do all that is disturbing. It calls into question the whole notion of "free will" which is the religious term for "randomness." "Predetermined," religiousity for "order," is even pricklier, because the nature of DNA, amazing as it is, doesn’t say, "Copyright, 4004, BCE, God" on it.

It is disturbing. I find myself wondering as I finish this essay, what particular combination of A, C, T, and G might have caused me to write it? Or does human volition reside outside of those myriad chemical interactions? I find that to be a more reassuring answer.