The Bactra Review: Occasional and eclectic book reviews by Cosma Shalizi 132
Stephen Wolfram, A New Kind of Science
A New Kind of Science
by Stephen<br>Wolfram
Wolfram Media, 2002
A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity
Attention conservation notice: Once, I was one of the authors of a<br>paper on cellular automata.<br>Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our<br>employer, because one of our citations referred to a certain mathematical<br>proof, and they claimed the existence of this proof was a trade secret<br>of Wolfram Research. I am sorry to say that our employer knuckled under, and<br>so did we, and we replaced that version of the paper with another, without the<br>offending citation. I think my judgments on Wolfram and his works are<br>accurate, but they're not disinterested.
With that out of the way: it is my considered, professional opinion that<br>A New Kind of Science shows that Wolfram has become a crank in the<br>classic mold, which is a shame, since he's a really bright man, and once upon a<br>time did some good math, even if he has always been arrogant.
As is well-known (if only from his own publicity), Wolfram was a child<br>prodigy in mathematics, who got his Ph.D. in theoretical physics at a tender<br>age, and then, in the early and mid-1980s, was part of a wave of renewed<br>interest in the subject<br>of cellular automata. The<br>constant reader of these reviews will recall that these are mathematical<br>systems which are supposed to be toy models of physics. Space consists of<br>discrete cells arranged in a regular lattice (like a chess-board, or a<br>honeycomb), time advances in discrete ticks. At each time, each cell is in one<br>of a finite number of states, which it changes according to a preset rule,<br>after examining the states of its neighbors and its own state. A physicist<br>would call a CA a fully-discretized classical field theory; a computer<br>scientist would say each cell is a finite-state transducer, and the whole<br>system a parallel, distributed model of computation. They were introduced by<br>the great mathematician John von Neumann in the 1950s to settle the question of<br>whether a machine could reproduce itself (answer: yes), and have since found a<br>productive niche in modeling fluid mechanics, pattern formation, and many kinds<br>of self-organizing system.
After the foundational work of von Neumann and co., there was a long fallow<br>period in the study of CAs, when publications slowed to a trickle, and people<br>were more likely to think of themselves as studying the statistical mechanics<br>of spin systems, or the ergodic properties of interacting particle<br>systems, than cellular automata as such. The major exception was a popular CA<br>invented by John Conway, the Game of Life, or just Life, which spawned a<br>dedicated following, trying to fathom how such a ridiculously simple set of<br>rules could produce such monstrously complicated results. In the late 1970s,<br>mathematicians and physicists began to become increasingly interested in CAs as<br>such, largely owing to the advent of (comparatively) cheap and powerful desktop<br>computers, which let people simulate and visualize CAs. There was a school of<br>thought --- obscure, but surprisingly widely known --- which, following the<br>physicist Ed Fredkin, thought that the universe as<br>a whole might in some sense be a CA. Many people participated in this<br>revival, in many places --- prominent names include, alphabetically,<br>Crutchfield, Durrett, Farmer, Frisch, Goles, Grassberger, Liggett, Margolus,<br>Packard, Toffoli, Vichniac, etc.
Wolfram's first paper on CAs, published in 1983, was titled<br>"The<br>Statistical Mechanics of Cellular Automata". It focused its attention on<br>particular simple --- he said "elementary" --- CAs: one spatial dimension, two<br>possible states for each cell, and a neighborhood consisting of the sites to<br>the immediate right and left of a given cell. There are 8 possible<br>configurations for such neighborhoods, and so 256 possible elementary CA rules;<br>in the paper, Wolfram introduced a useful scheme for referring to those rules,<br>and others, by number, so that we speak of rule 18, rule 22, rule 90, rule 110<br>(of which much more below), etc. Beyond that, the paper largely consisted of<br>calculating the entropy of configurations generated by different rules, and<br>saying that, while the rules were simple, the patterns they could generate were<br>complicated and intriguing. Well, and so they were; and so said many other<br>people at the first major modern conference on CAs, organized by Farmer,<br>Toffoli and Wolfram at Los Alamos in 1983.
Wolfram went on to publish a bunch more papers on CAs over the next few<br>years: probably the most noteworthy are<br>"Computation<br>Theory of Cellular Automata" (1984), where he used a familiar device of<br>elementary computer science (regular languages and their equivalent finite<br>automata) to characterize the set of configurations it is possible for a CA to<br>produce, and<br>"Universality<br>and Complexity in Cellular Automata", where he...