GRAND CLAIMS OF A NEW KIND OF SCIENCE

Saturday, June 29, 2002

Stephen Wolfram wrote a 1200-page book on cellular automata, and it's selling like popcorn at the movies.

Before you say "What?" and turn the page, I must tell you that A New Kind of Science is breathtakingly audacious and strikingly beautiful. Audacious, because it's nothing less than a grand theory of everything from free will to relativity theory. And beautiful -- well, that you will have to see for yourself. If you can, check out the sample pages at wolframscience.com on the Web.

Wolfram is a mathematician and scientist. He developed a program called Mathematica for the handling and display of all kinds of symbolic systems, and built it into a very successful company, Wolfram Research. Since about 1991, he writes, he has spent most of his time using Mathematica to explore the phenomena described in his book -- and the sort of person who gets a Ph.D. from Caltech at age 20 can do a lot of exploring in a decade.

A cellular automaton is a row of little boxes -- think checkerboard -- and a rule for deciding how to color the next row down. For a checkerboard, the rule is simple; change the color of the box. The results are entirely predictable and boring.

But make the rule just a little more complicated, allowing the color of a square to depend on the square immediately above it and that square's two nearest neighbors. There are 256 such rules, because there are eight possible ways to color three squares, and for each of the eight there are two choices for the result (that is, 2 to the 8th power).

Many of the rules produce either simple patterns or intricate but predictable designs. But a few display behavior that is both complex and unpredictable. And at least one of them, named Rule 110 for its patterns of 1s and 0s in binary notation, is complicated enough that it can be used to simulate the behavior of a universal computer.

If that seems a trifle swift, it's because I am summarizing several hundred pages of text and pictures designed to lead the reader's developing intuition along the path Wolfram has traveled. One reason is so that the reader can follow the proof of universality.

But more fundamentally it is so that the reader will be primed to agree with Wolfram's claim that everything that is complicated at all (at least as complicated as Rule 110) is exactly as complicated as everything else.

Life, the universe and everything else.

He could be right. I certainly don't have the tools to disprove him. But it could be that he's wrong and no one will ever have the tools to disprove him.

Going from simple rules to complex behavior is easy; you program the computer and let it run for billions of steps. The universe could be the computer, running a program generated by simple rules.

But going the opposite way is unimaginably difficult. Given complex behavior, does it arise from a simple rule? In general that question cannot be answered. If I were to take a picture of Wolfram's Rule 110, and change one specific pixel from black to white, is it now generated by a simple rule? Yes, in one sense, because I just told you how to do it in a few words. But can it be generated by a cellular automaton? There's no way to tell.

Perhaps complexity will turn out to resemble the mathematics of infinite sets, which are not all the same size. Developing one's intuition so that statements like that make sense is a big part of learning mathematics, and it takes time for a whole field to settle on how students' intuition should develop. It's not automatic.

I'm intrigued by the role Mathematica itself has in this process. Without it, neither the research nor the book would have been possible, since it generates the pictures of automatons' behavior over millions of steps.

Suppose Johann Sebastian Bach had been born in 1685 in an isolated rural village in China, where he would never hear anything more complicated than a gong, a drum and a two-string violin. How far could his genius have taken him? Instead, he was born in Eisenach, Germany. As a composer he had at his disposal pipe organ, orchestra and polyphonic choir, and he used them to build monuments.

Whether Wolfram's grand claim proves true or not, he's built a tool worthy of monuments.