Saturday, 2/3/01

Finally finished that Chaos book. That was the most painful reading I've done in a long time. Unfortunately, I'm really interested in the subject and that book is considered to be the best comprehensive introduction, so I suffered through it. But I passionately hate James Gleick's writing style. First of all, it's irritatingly anecdotal, as Donna put it. "Comfortable in his Atlanta office, the winter sun setting outside, Ford sipped soda from an oversized mug with the word CHAOS painted in bright colors." 300 pages of that. I want to know about the scientist's research, dammit, not the size of his mug. "Mitchell Feigenbaum stands at streamside. He is sweating slightly in sports coat and corduroys and puffing on a cigarette." What the hell is this crap? It wouldn't be so bad if he actually gave a reasonably technical description of the the subject, but evidently in his desire to make the text accessible to the layman (or simply due to his own incomprehension?) he glosses over the interesting details. For example, using Barnsley's "Collage Theorem", you can produce "a few simple rules" whereby the entire structure of a fern or other complex shape can be generated. Do we get to see these few simple rules, or have any idea what they might look like? Of course not. Instead, we get a full page describing the picturesque scenery at UC Santa Cruz. Some of the mathematics is simplified to the point of being incorrect, but I can forgive that. Although it's annoying to read through one of the few technical passages, saying, "Um... that's simply wrong," every couple pages. What I really don't like is Gleick's attitude toward "traditional" science and mathematics. Scientists usually try to find linear models for phenomena, and linearize the non-linear stuff. They do this so they can solve the problem in the first place, not because, as Gleick would have you believe, they are stupid or naive. The author represents his heroes as missionaries, bringing the light of Truth to the uncivilized scientific backwater. In other words, he manages to insult everyone not working on chaos. That's annoying. Enough ranting. I actually did work today! If that in itself isn't amazing enough, I figured out the proof that was my biggest loose end (maximality of the class 0 clique). For EE 244, I had proved it for a special case using a couple pages of ugly grungy math, and punted on the general case. Today I tried out various different ways of thinking about the problem, and transformed it from one form to another to another, drew some pictures, and sitting in the car on the way to dinner, it all fell into place. The problem was equivalent to this: You have two numbers, a and b, and they both start out as 1. At each step, choose one of the numbers and add it to the other. In other words, at each step, choose either a=a+b or b=a+b. The goal is to make, after so many steps, a+b as big as possible. Well, it's pretty easy to see that you do that by alternating your choices, first by adding b to a, then adding a to b, and so on. And that's all I needed to prove the theorem. Take that back up the chain of abstractions and transformations, and that proves the maximality of the class 0 clique. No messy math, no coshs or sinhs or Fibonnaci exponentials. Damn, it's beautiful. It's all about thinking about the problem in the right way.