New Science or Old Math?

Stephen Wolfram (PhD ’80), a 1981 MacArthur Foundation “genius” and the creator of the technical-computing software system Mathematica, spoke to a packed Beckman Auditorium on Saturday, February 1, about his book A New Kind of Science. He then engaged in an occasionally spirited discussion with a panel of cordial yet skeptical Caltech faculty members, after which he took questions from the floor.

According to Wolfram, his book represents 20 years of study and experiment, with about a decade of that going into the actual writing. Beginning with the discovery that computer programs carrying out simple rules over and over and over again—“cellular automata,” which have been known since the 1950s—could produce extremely complex behavior, he came to the conclusion that the iteration of simple rules can describe the workings of the natural world more successfully than can the often complex mathematical equations used by science up until now. He illustrated his thesis with numerous computer-generated images of complex patterns produced by simple rules, which he compared to similar patterns from nature: the forms of snowflakes, the markings on seashells,
the veining of leaves, and even the evolution of the universe. He averred that much of nature represents the same level of computational complexity as do human beings, though the human race remains unique through its own history of effort and development.

The panel comprised Christoph Adami, faculty associate in computation and neural systems and director of the Digital Life Laboratory at Caltech, as well as principal scientist in JPL’s quantum technologies group; John Preskill, the MacArthur Professor of Theoretical Physics and director of the Institute for Quantum Information; David Stevenson, the Van Osdol Professor of Planetary Science; and Steven Koonin (BS ’72), Caltech’s provost and a professor of theoretical physics, who moderated. Much of the discussion revolved around whether or not Wolfram’s work is genuinely science. Preskill, for instance, while granting that A New Kind of Science works well as science writing, was less sure of its usefulness for scientists, and Stevenson pointed out that one of the rules of “old” science is the production of testable predictions, of which he found in Wolfram’s book “not one.” Wolfram demurred, maintaining that his book is concerned with basic issues, not specific applications, and that his ideas are closer to those of mathematics and the biological sciences than
to physics. In response to a question by Koonin, he suggested that his concepts would no more be proved right in a laboratory than would those of calculus. Preskill, while accepting that one of the many models computers could generate might fit reality, wondered whether that offers anything in the way of genuine explanatory power. Wolfram felt that it does, and that his concepts’ potential to describe the natural world would allow one to generate testable predictions.

The most spirited exchange may have been with Adami, who stated that what biologists mean by complexity is very different from how Wolfram was using the term. Biologists deal with functional complexity: in cell division, metabolic processes, and other biological systems that have accumulated over billions of years of ensuring the survival of organisms in their environments. For such systems, he maintained, there is no single underlying rule that creates a pattern. Wolfram replied that it’s dangerous to quote “what biologists think,” since biology represents a wide spectrum of views.

Stevenson noted that, while Feynman diagrams—invented by the late Caltech professor of theoretical physics and Nobel laureate Richard Feynman as a way to visualize the interactions of atomic particles, and which a number of Wolfram’s patterns rather resembled—improved physics computations, they didn’t really change the underlying science, and wondered how Wolfram’s approach was any different. While conceding that his ideas could be construed as a computational method if one wished, Wolfram insisted that they are more useful than traditional methods. When Preskill questioned how far scientists could actually get with them, saying that there was little in the chapter on physics that he could, as he put it, “get my hands on,” Wolfram made the point that no one was going to know how his models would pan out until they
had panned out.

Koonin wrapped up the discussion with a spot-on imitation of John McLaughlin of TV’s McLaughlin Group, asking—“Yes or no!”—whether A New Kind of Science would be seen 20 years hence as a paradigm shift, that is, an event that transforms the way scientists view the world. None of the panelists thought so, and Koonin expressed the hope that they might be wrong, while Wolfram joked that he’d heard pretty much what he would expect to hear from scientists on the verge of such a shift. —MF