'A New Kind of Science'
By Rich McManus
Photos by Ernie Branson
Sometimes, buzz alone can fill Masur Auditorium. Such was at least partially the case Sept. 17 when Dr. Stephen Wolfram famous for hatching, out of more than a decade of relative solitude, what he calls "A New Kind of Science" visited to explain his new book of that title, his new web site and his views on a mathematically contrived model system that appears to mimic, and perhaps underlie, forms found in nature.
"So, why did you come to this talk?" asked one guest, sitting in the fourth row, to his neighbor before the lecture began. "I don't know. Why did you come?"
"Because he's a famous guy."
So, in at least one neighborhood in the hall, folks had come simply to see what all the fuss was about. In a way, the rows of guests, some of whom communicated with neighbors to the side and rear, formed a kind of pattern of association, the sum of which could be represented by a series of black boxes and open boxes. Let black boxes indicate those who knew of Wolfram's work directly and open boxes represent those who knew him but barely, or only by reputation (Wolfram, a native of London, owes at least part of his fame to having been named a professor at Cal Tech at age 21, and for having won a MacArthur Foundation "genius" award early in his career; he is now CEO of Wolfram Research, Inc.). If you went row by row, all the way to the rear of the hall, applying the simple rules of "degree of familiarity with Wolfram," then the resulting matrix would either be interesting or not, depending on whether it was A) aesthetically pleasing in its own right, say, a nice sort of quilt pattern, or B) potentially meaningful to biology, because it resembles a form found in nature.
That's a simplified way of presenting Wolfram's thesis, which he illustrated with an elementary example: from a simple row of 7 boxes (meant to resemble a line of cells, though it could be of any length) the center one black and the three on either side open one can generate successive rows by applying easy rules governing the color of neighboring boxes. For example, one rule might be that if there's a black box in the line above, there must be a black box below it. Or, if the box above is open, but adjacent to a black box, the box below must be black. Wolfram has elucidated some 256 "rules" based on eight available options governing the color of boxes; the options themselves rely on simple if/then rules of coloration based on proximity. Each rule spawns so-called "cellular automata," or successive generations that obey the rule in each iteration (see box).
One rule that Wolfram demonstrated produces, quite reliably, a pyramid shape. But once you get up around Rule 30, fascinating forms result highly irregular and utterly random to the naive eye. Other rules create odd structures that proliferate awhile then die out, say after 3,000 steps or so. Fascinatingly, some of Wolfram's models are dead ringers for such natural forms as the variation seen in mollusk shell pigmentation patterns, and the forms taken by snowflakes and tree leaves. What so tantalizes Wolfram is that his models, which require such simple rules to generate, can result in such rich complexity; the math seems a good metaphor for rules embedded in nature. Or, in his words, "We've put so little in, but we've gotten so much out. It seems to violate our prejudices that incredibly simple rules can produce incredibly complex phenomena."
Wolfram said he spent most of the past decade working on a "big intellectual structure," that has resulted in his new 1,200-page book, only 59 of whose pages deal specifically with biology. "During the past 300 years, mathematics and equations have been used in a serious way in science," he said, citing particularly apt applications in physics, such as determining the orbits of planets. "But (math) hasn't worked out so well in other areas...traditional mathematics has not been well used in biology. We might not be using the right building blocks for our models or descriptions of things."
The dearth of good math-based models prompted Wolfram to spend the past 15 years building the cellular automata concept so that "mathematics can be used like a microscope pointed at various objects various flora and fauna. After all, look at all the stuff that's happening from one black box (or cell)."
That cellular automata can mimic forms in nature is evidence of "a very robust phenomena," Wolfram said. "Something very basic and fundamental is at work."
He pointed to the sequence of prime numbers, or the digits flowing forth from calculations of pi as something science has heretofore regarded as "a nuisance, or a distraction or a bug of some sort not an important basic phenomenon." But the apparent randomness of these numbers has at least one satisfying aspect: the more complicated things look, the more we are likely to ascribe "naturalness" to them.
"We want (model) systems whose behavior we can readily predict and see," Wolfram said, "but nature operates under no such constraint." What models of natural systems can mathematics potentially evoke, he wondered? "I happen to think all of the universe and physics, but that's another lecture."
The most convincing evidence of his thesis were comparisons of mollusk shell pigmentation patterns, and even shell shapes, with patterns and shapes generated by cellular automata. The shells, it could be seen, "seem to be sampling simple cellular automata rules randomly...All cases get sampled in nature," Wolfram asserted.
Leaf shapes, too, in their huge diversity, can be mimicked by cellular automata. By dissecting leaf pods, Wolfram constructed models based on their branching, size and angles, then applied cellular automata to approximate a virtual forest of recognizable leaf types.
Wolfram claims no more than insight into how nature makes its choices, and leaves further exploration of how cellular automata may benefit biology to interested biologists. But he did offer some consolation: those provoked by the power of his models are invited to visit his web site (wolframscience.com) to tinker with a program launched there just recently A New Kind of Science: Explorer. "It's really best to learn on one's own," he counseled.
Up to Top