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The World According to Wolfram

Brian Hayes

What to Make of It

Wolfram warns that developing an intuition for his new kind of science will take months, "even for the most talented and open-minded people." For me I suppose it may take years. But even if I am premature in passing judgment, I want to give a preliminary assessment of a few major themes.

The core notion—that simple rules or programs can yield complex behavior—is surely both true and important. Whether it constitutes "a new kind of science" remains to be seen.

A closely related point is Wolfram's insistence that programs or algorithms are the best way of expressing ideas in the sciences. In particular, explicit rules of evolution are preferable to equations, which merely state the constraints that a system must satisfy without necessarily showing how to satisfy them. Perhaps he's right; my own experience is that I understand best what I can program. But Wolfram would expand this observation into a broad indictment of "the mathematical framework traditionally used in the exact sciences," which is reckless overkill. Wolfram obviously needs that framework (and uses it expertly) in his own work.

The concepts of randomness and complexity are central to the argument of this book, and yet Wolfram is curiously lax about defining them. He doesn't address the issue directly until 550 pages into his narrative, after many references to "intrinsic generation of randomness" in cellular automata and other simple systems. If you are accustomed to thinking of randomness as an inherent property of a pattern—something that can be traced back to the way it was created—"intrinsic generation" makes no sense in this context, because the mechanism that created the pattern is totally deterministic. It turns out that Wolfram defines randomness and complexity in terms of how patterns are perceived rather than how they are created. Roughly speaking, if it looks random, it is random. Fair enough, but it remains unclear just what is being generated intrinsically.

With the exception of the cosmic causal net, the examples that illustrate applications of Wolfram's ideas are strangely bland. Snowflakes, fluid turbulence, branching in plants, pigment patterns in animals—these are all rather shopworn specimens, which have long been explained by models of the same general type. (Alan Turing gave a computational account of leopard spots and zebra stripes 50 years ago.) If the new kind of science is to have much generality, it will need to show its worth in other areas. In developmental biology, for example, can we write a simple program that explains the complex structure of Caenorhabditis elegans? Anatomists have traced the paths of all 959 somatic cells in this worm, but expressing the underlying algorithm in terms of a few simple rules looks like a challenge.

Wolfram's comments on evolutionary biology are perhaps the lamest passages of the entire book. Noting that some traits of some organisms seem to explore the entire space of available variations, he concludes that Darwinian selection can't be acting on those traits. "It is my suspicion," he writes, "that at least many of the visually most striking differences—associated for example with texture and pigmentation patterns—in the end have almost nothing to do with natural selection. And instead what I believe is that such differences are in essence just reflections of completely random changes in underlying genetic programs." He writes as if he were unaware that a debate between neutralists and selectionists had ever entered biology.

All of the programmable systems explored in A New Kind of Science have a distinctive trait in common: They have a densely occupied space of programs. In a cellular automaton, for example, any rule relating a neighborhood configuration to a next state is a valid program. Other programmable systems—such as desktop computers and the DNA-reading apparatus of the living cell—are much choosier about what they will recognize as a valid program. If you try feeding them random strings of bits or random sequences of nucleotides, you're in for a frustrating experience. It's not obvious to me how the paradigm of complex behavior from simple rules can be extended to such systems.

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