Tuesday, May 31, 2005

a new kind of science?

I've just started an experiment that utilizes cellular automata to solve a problem, and looking through my books for some reference materials I found what is probably the most definitive treatment of the subject. Digging through the archives of this site, I find that I've never written about this before, so hey, math. W00t.

When Stephen Wolfram's book A New Kind Of Science came out, I dove right into its 1280 pages and fired up Mathematica to test the programs for myself. My impression then was the same as it is now: there are some interesting aspects of cellular automata (CA's) that defy conventional wisdom about complex systems, but there are only a few small domains to which these formulae can be applied. Once a real-world system gets above a certain level of complexity all of the sciences break down, new and old alike. But Wolfram makes a very long and protracted case for universal applicability of CA's, even going so far as to suggest that the universe itself functions according to simple CA-like rules:

Wolfram's theory that there is a single rule at the heart of everything - a single simple algorithm that, in effect, generates all the rules of physics and everything else - is bound to be one of his most controversial claims...

"I've got to ask you," I say. "How long do you envision this rule of the universe to be?"

"I'm guessing it's really very short."

"Like how long?"

"I don't know. In Mathematica, for example, perhaps three, four lines of code."

How many of you read that and immediately thought "bullshit"? And how many of you that did call bullshit on Wolfram believe that "In the beginning was the Word, and the Word was with God, and the Word was God"? How long do you think 'the Word' is?

Wolfram makes the following point repeatedly: "Whenever a phenomenon is encountered that seems complex it is taken almost for granted that the phenomenon must be the result of some underlying mechanism that is itself complex. But my discovery that simple programs can produce great complexity makes it clear that this is not in fact correct."

In the rarified air of extreme mathematics there are few that could hold their own against Wolfram, so when a couple of wunderkinder like Wolfram and Ray Kurzweil face off it's worth watching, if only to see how the sparks fly. That said, it is interesting to note that Kurzweil does not simply dismiss the book offhand... in fact he agrees with many of the ideas presented by Wolfram. He discusses the issues through to what he sees to be their logical end, then watches as Wolfram careens further outward; whether Wolfram is headed toward higher truths or will soon be chilling with Bobby Fischer remains to be seen.

Whatever the resolution, Wolfram, like Roger Penrose, makes a pretty good argument that our current understanding of how the universe works has limits that won't be surpassed by using our current tools faster or longer... to go forward from where we are, we may need to back up a bit and try a different path. If he's right, there could be some exciting new insights on the horizon. If he's wrong, I've got a 20 pound book for holding things down in a windstorm.