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The World According to Wolfram

Brian Hayes

Clarity and Modesty

So much for the content of A New Kind of Science. The book also has a personal and historical context that requires comment.

In a note titled "clarity and modesty," Wolfram explains that he had to sacrifice the latter to attain the former. But immodesty is only half the issue here. The problem is not just the rosy spotlight that Wolfram shines upon himself at center stage; it's also the utter darkness that enshrouds all the other actors in this drama. The main text of A New Kind of Science (850 pages) names no names at all; the only work attributed to a specific individual is Wolfram's. The notes at the end of the book (another 350 pages in smaller type) do mention names of people, but briefly, grudgingly and often dismissively. (It's remarkable how many discoverers failed to appreciate the significance of their own work.) And many of the historical notes manage to present an anonymized history, written in the passive voice: "By the end of the 1950s it had been noted that...." "Over the course of the 1960s constructions were found...."

The book has no bibliography; the only references listed are Wolfram's own publications.

Here is a precis of Wolfram's history of cellular automata. He discovered them in 1981 (although he had made important precursor experiments earlier, as a teenager). Some time later he learned that John von Neumann had had the idea 30 years earlier. But von Neumann missed making the crucial discovery that simple rules could produce complex behavior, and so did others who toyed with the systems in the intervening years. By the late 1970s, "research on systems equivalent to cellular automata had largely petered out." But then the publication of Wolfram's papers redefined and reinvigorated the field, drawing in many followers—although most of them went off on the wrong tangent or wasted their time on trivial details.

It didn't happen that way. To begin with, interest in cellular automata did not peter out in the 1970s; it was thriving. The field continued to grow in the 1980s, when Wolfram's participation doubtless helped, but more important was work on the physics of computation and reversible cellular automata. Wolfram took no part in that. The main actors were Edward Fredkin, Charles Bennett, Tommaso Toffoli and Norman Margolus—who were also, as it happens, the ones who explained to Wolfram in 1981 the nature and historical context of his own work.

Wolfram's telling of the mollusk-shell story is another notable example of delusional history. The shells have been known since antiquity, he says, "but almost no efforts to understand the origins of such patterns seem ever to have been made." He then mentions one such effort, by C. H. Waddington and Russell Cowe, but says it was too narrow. He ignores entirely a cellular automaton devised in 1973 by G. T. Herman and W. H. Liu to model one of the shell patterns. According to Wolfram, only his 1982 discovery brought the matter to wide attention and led others to take it up. Among those others was Hans Meinhardt, but Wolfram disparages his models as being too elaborate. In fact, Meinhardt came to the problem independently of Wolfram; what brought the shell to his attention was seeing it on his dinner plate in an Italian restaurant. And his models are elaborate because they account for the specific features observed on actual shells, rather than simply declaring that all shells look like one cellular automaton or another.

At the end of a long lunch with Wolfram, our conversation turned to these matters of history and attribution, then drifted on to a related topic. I asked why he had not given his new kind of science a name. In the book, he refers constantly to "the new kind of science I describe in this book," which gets cumbersome after the first 50 repetitions. He said he'd struggled to come up with a suitable name, but nothing quite fit the bill. At Wolfram Research, people spoke of "NKS," he said, or sometimes "Wolfram science."

"Are there any sciences named for people?" I wondered aloud.

"Well, there's Newtonian physics," he replied.

It was not the first time the names Wolfram and Newton have been mentioned in the same breath, and I suppose it might be taken as further evidence of an ego bursting all bounds. But I see it in another light: He is simply too modest to name the field Wolframian science. That part is left to us.

© Brian Hayes

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