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Monday, September 30, 2002 By Byron Spice, PostGazette Science Editor
A few years ago, Lenore Blum was looking for a new way to challenge her then5yearold grandson, Alex, so she sat him down with a piece of graph paper.
Color one of the squares at the top of the page, she told him. Then, on each successive line, color in the squares based on some simple rule, such as "color a square if only one of the three neighboring squares in the line above is colored."
"Alex adored it," reported Lenore Blum, who is a mathematician and theoretical computer scientist at Carnegie Mellon University as well as a doting grandmother. The boy found that these simple rules, if repeated enough, could generate interesting, even intricate patterns. Most such rules proved monotonous, but sometimes just a slight rule tweak would cause wild, unexpected results. What Alex Blum was creating are what scientists call "cellular automata." But however great his fascination might have been, it no doubt paled compared with that of Stephen Wolfram. The Londonborn Wolfram, who earned his doctorate in theoretical physics at Caltech at age 20 and, a year later in 1981, became the youngest recipient of the MacArthur Foundation "genius" award, began dabbling in cellular automata in the 1980s and publishing research papers on them as he worked to develop a theory of complexity. By 1991, however, Wolfram had become convinced that these simple computer programs were the key to some fundamental truth. By then a rich man, thanks to a software package he developed called Mathematica, he retreated to his office for the next decade, staying up night after night as his computers churned out cellular automata that he analyzed and categorized. When he emerged earlier this year, Wolfram proclaimed that he had discovered nothing less than "A New Kind of Science," the concepts of which he laid out in a 1,200page, selfpublished book of the same name.
Simple rules can result in great complexity, he said, and nature can best be described as a set of simple computer programs, rather than the mathematical equations prized by most scientists. In fact, Wolfram maintains that all processes, whether occurring in nature or generated by humans, can be considered computations. This "new law of nature," which he calls the Principle of Computational Equivalence, holds that all computations, aside from those of the very simplest systems, are of equivalent complexity. Wolfram looks at the shape of a leaf, the branching patterns of a tree, the intricate patterns of a mollusk shell, the behavior of elementary particles, the pull of gravity and the way a rock cracks and sees similarities to some of his cellular automata, leading him to conclude that all are the consequence of simple stepbystep programs, even if he can't be sure what those programs are. The book was heralded by stories in The New York Times, Newsweek and Time, among others, and became a bestseller despite its $44.95 pricetag. There are now 200,000 copies in print. But the reaction from the scientific community, Wolfram acknowledged last week, "was sort of a shock." Most new scientific ideas emerge as a series of papers in research journals and talks at scientific conferences; here Wolfram was proposing a new structure for interpreting the universe that he had developed in isolation, without any of the giveandtake from colleagues that traditionally occurs in science. Some were impressed, others nonplussed. Only this month has "Rip Van Wolfram" begun to reconnect with scientific audiences, beginning a lecture tour that will take him to at least 20 universities and government labs by early next year. "I used to know a lot of scientists a long time ago," Wolfram said. "I haven't seen some of them for 17 years." Pittsburgh this week will be the first city to get a double dose of Wolfram, as he presents public lectures Thursday at Carnegie Mellon University and Friday at the University of Pittsburgh. "This is a big, important mathematical event for Pittsburgh," said Thomas Hales, a Pitt mathematician who invited Wolfram to campus. He also helped persuade CMU computer scientist Manuel Blum to extend an invitation as well. Though a lot of the ideas discussed in the book have been in the air for years, he said, Wolfram has tied them together in a coherent way that addresses some fundamental questions, at least in regards to mathematics. "The book cannot be dismissed," maintained Hales, who says he bought his own copy the day it was released. Manuel Blum admits he hasn't read the whole book as yet. As is his habit with new books, he opened Wolfram's in the middle and began reading. "I've been quite impressed," he said. "It's wellknown that very short [computer] programs can do very interesting things," said Manuel Blum, a leading figure in theoretical computer science. Though he long has thought it would be interesting to catalog and analyze all simple programs, "I've had trouble doing this, as have others." No one has even been sure what sort of programming language should be used for the task. "Wolfram solved that," he said, "and I consider that, by itself, a major contribution." But Manuel Blum also acknowledged some discomfort that Wolfram relies mostly on his cellular automata experiments in making arguments, rather than relying on theorems and proofs. "I don't think he solved the world by any means," he added. In fact, most scientists are inclined to dismiss the work as a bunch of hype, said Lenore Blum, who along with Manuel, her husband, is cited by Wolfram in his book preface for their help in his career. "It's not a new science," she said. "It's not a paradigm shift." Within the computer science community, for instance, the idea of explaining the world in terms of computer programs is nothing new. Ed Fredkin of the Massachusetts Institute of Technology, for instance, has long made the "universe as computer" argument, though without much acceptance to date. Unlike most computer scientists, however, Wolfram is not concerned with the input and outputs of a computation, but rather with the "trajectory" of the computation, Lenore Blum said. "He looks at what's happening as the computation proceeds," such as the patterns generated by cellular automata. It's a worthwhile observation, but one that can get lost among Wolfram's more sweeping claims of discovering a new science, she added. "If he wasn't making so many claims, I think people would take it more seriously." Bard Ermentrout, a Pitt mathematician who reviewed Wolfram's book for the Society for Industrial and Applied Mathematics, said he found little new in the book. He was troubled that Wolfram didn't provide direct citations to previous research and that he peppered the work with phrases such as "My guess is...," "I suspect that...," and "I believe that..." rather than providing evidence. "If he did discover a new kind of science, it's a science that doesn't require proof, that doesn't require citations. It's not the kind of science I want to pursue," Ermentrout said last week. Moreover, even if Wolfram is correct in his assertions, Ermentrout said he's not sure what it all means. "It's all rather vague to me." If the universe operates as a computer rather than by mathematical formula, "what do you do with that?" For his part, Wolfram said he's not surprised by any of the reaction. "In academia, there are typically two responses to a new idea  actually three responses," he said. "One, it's wrong. Two, it's been done before. Three, it's both of those." He said he feels vindicated thus far in abandoning the conventional scientific process in favor of extended study of a phenomenon and establishing a new, coherent structure for science that is then communicated in book form. "Not many scientists have the luxury to do this," said Pitt's Hales. But some problems require it. "I think there's not enough people like (Princeton University mathematician) Andrew Wiles, who essentially went up to his attic for seven years" and emerged in 1995 with the longsought proof to a famous mathematical problem called Fermat's Last Theorem. "I think it's working," Wolfram said of his strategy. Already, at least 20 college classes are being taught based on the book and "that's sort of ahead of where I expected it to be." He said he has received more response to the book than any work he's ever done and, despite early resistance to his claims, he has noticed that some scientists are slowly coming around as they digest the book. That's already been apparent in some of the questionandanswer sessions, he said, "and it's kind of nice for me to see that happening in real time." Rather than include citations of other people's work in the main text of the book, as is typically done in scientific papers, Wolfram opted for an extensive appendix that summarizes previous work and includes citations. Though many scientists have objected to that format, others have complimented him about it, he added. Thus far, biologists seem to have expressed the greatest interest in the book, Wolfram said. Biological research is booming right now and many biologists are trying to develop a better understanding of biological systems by designing model systems. Unlike physics, biological systems have been particularly difficult to describe by using mathematical formula, he explained, so many biologists hope his approach will lead to more success. But some problems, he warned, are "computationally irreducible." That is, it's impossible to make a prediction of what will happen, even if you understand the underlying program for the phenomenon. In these cases, the only way to know what will happen is to simply run the program and watch what happens over time. That also presumably will make it very difficult to discern that underlying program in the first place, or, once discovered, to prove that it's correct, Wolfram acknowledged. For the largest problems, such as the simple rules underlying the evolution of the universe, the only hope is that there will be "pockets of computational reducibility," that can be described successfully with mathematical formulas and that it will be possible to estimate behavior for other aspects of the system. That's why the notion that this New Kind of Science is "a magic modeling methodology" makes him nervous. "Modeling is hard. It takes judgment," he explained. His new science "may make some new modeling possible. It doesn't make it easy."
Byron Spice can be reached at bspice@postgazette.com or 4122631578.


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