(A book review of Stephen Wolfram’s A New Kind of Science.)

In 1952, Alan Turing, the so-called father of computer science, published a paper describing how patterns in nature, such as the stripes and spots of animal pelts, can arise naturally from simple, local rules. These Turing patterns have been shown to occur on windswept sand, seashell surface spirals, the distribution of stars in galaxies, and the patterns of hair follicle placement on our heads. Or perhaps I should be calling them Wolfram patterns, since Stephen Wolfram discovered in 1981 that simple rules can give rise to great complexity. Never mind that 1981 is 29 years after 1952. Stephen Wolfram (also the creator of WolframAlpha) is an impressive mind, and the work he describes in his magnum opus A New Kind of Science is so revolutionary that it actually revolutionized science decades before its own publication!

The first four chapters of A New Kind of Science (I didn’t make it past that) have nothing interesting to say except for the solitary idea that “simple rules can give rise to great complexity”, an idea Wolfram refers to as his own “surprising discovery”. In the first chapters of the book, he mischaracterizes or ignores past science to make his own work seem more impressive. Conway’s famous Game of Life, an experiment showing how complex states can arise from a simple set of rules on a grid, was created by John Horton Conway in 1970, over a decade before Wolfram’s own work. But Stephen Wolfram claims nevertheless to have been the one to discover that simple programs can give rise to great complexity.

I was shocked when reading this. I thought it would be a good book! I thought it would give me some insight into the thoughts I’ve had lately about computational irreducibility and board games. But no, it seems like it’s just intellectual fraud stretched out to 800+ pages.

Chaos theory, a field stretching back into the 1800s, concerns itself with how some systems with simple initial conditions can lead to very chaotic, apparently random behaviour. Stephen Wolfram says of chaos theory:

Indeed, all that it shows is that if there is complexity in the details of the initial conditions, then this complexity will eventually appear in the large-scale behaviour of the system. But if the initial conditions are simple, then there is no reason for the behaviour not to be correspondingly simple. What I show in this book, however, is that even when their initial conditions are very simple, there are many systems that still produce highly complex behaviour.

He tries desperately to convince the reader that all past work related to his work has only ever claimed that complex starting conditions lead to complex behaviour, never that simple initial conditions lead to complex behaviour. This is a lie. Conway’s Game of Life shows how extremely complex behaviour can arise from simple rules and simple initial conditions. Chaos theory shows incredibly complex behaviour can arise from something as simple as a double-rod pendulum. That’s kind of the point of chaos theory. He is simply lying.

He says of the complex cellular automaton he discovered in 1981, “But how could something as fundamental as this never have been noticed before?” Yet this was 11 years after Conway. And he admits to knowing about the existing work, too. “I searched the scientific literature, talked to many people, and found out that systems similar to the ones I was studying had been named “cellular automata” some thirty years earlier.” But instead of saying, “oh, well, I guess I didn’t discover it” (as I did when I “discovered” artificial neural networks in high school), he wouldn’t let the dream of revolutionizing science go. “Nothing even close to the phenomenon as a whole seemed to have ever been studied before,” he lies.

But until my work in the 1980s the actual investigations of cellular automata that were done consisted mainly in constructions of rather complicated sets of rules that could be shown to lead to specific kinds of fairly simple behaviour.

Liar! Conway’s Game of Life existed 10 years prior! So did Turing patterns, for that matter, and Turing machines!

Wolfram wished dearly that his idea had been original, and now he has written a mammoth of a book to try to manipulate you into believing it was. And God, is it an obnoxious read. His writting style is incredibly repetitive and embarrassingly autoerotic. Here is a made-up example of what reading A New Kind of Science feels like:

“In my experience, one might have thought that one might enjoy being punched in the face. And yet, observation can be made from the experiments I have performed that this is not the case. For when you are punched repeatedly in the face, pain often occurs. And it is this remarkable discovery that we have made that will form the basis of a new kind of science. For it implies that when one is punched in the face over and over again, suffering emerges. Indeed, without this surprising discovery, traditional science would never progress beyond a certain point…”

The whole book feels like that.

There’s really little in the book — at least, the parts I’ve read — besides him planting a flag on the entire concept of “computation is a general concept that applies in a lot of domains and can describe complex systems with simple rules.” Presumably, he hopes anyone using computation to study any domain of science will be seen as being downstream of “his” ideas, and he will get indirect credit. Nevermind the fact that people were using computers before the ’80s to model the weather, nuclear reactions, orbits of planets, artificial neural networks, animal population dynamics, fluid flow, and many other things. Nobody was surprised when Wolfram’s book came out decades later and stated the obvious fact that computation maps onto nature pretty well sometimes.

I don’t see any actual testable hypotheses in this book (besides the idea that a specific cellular automaton, rule 110, was Turing-complete, which was later proved by someone else, to Wolfram’s chagrin). He says it’s a new kind of science, but I don’t see any science here at all. Science requires testable hypotheses and experiments, not plausible-sounding guesses. He claims computation could be the basis for a fundamental theory of physics, but he hasn’t actually provided such a theory, so… Good hunch, I guess?

Stephen Wolfram wants to claim credit for guesses and for the real work of people who came before him. You get credit for neither, Wolfram. Anyway, I gave up on Chapter 4. Maybe in Chapter 5 — 169 pages into the book — he says: sike! Actually I give Conway and Turing and the rest full credit for their ideas, and actually here are some genuinely new ideas and testable hypotheses. But I think that’s unlikely enough that I won’t subject myself to the rest of it.

Secret Rich Text Copyer for Substack