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Through a Monitor, Darkly

Researchers like Wolfram turn their backs on the world outside the laboratory. They gaze instead through the windowpane of a computer monitor into a hypothetical universe, harnessing the power of the computer to explore the behavior of mathematical structures and complex systems.

Every computer program embodies an algorithm, or a set of instructions, that governs the way numerical data are modified by the computer, much as the laws of nature govern the way objects behave in the real world. To conduct experiments on a computer, Wolfram explains, researchers use numbers or symbols to represent objects and then manipulate them according to the rules they have established. “My work is all really based on one big idea: that everything can be expressed as a symbolic expression,” he explains. Because these kinds of simulations can be performed in a hypothetical universe rather than one bound by the laws of nature, he argues, computer experiments represent “a new kind of science.”

When Wolfram first turned his attention to complexity studies in the early 1980s, he was looking for a way to explain complex phenomena-the patterns on mollusk shells, the behavior of molecules swirling in turbulent fluid, and fluctuating prices on the stock market. “I tried to use methods from statistical mechanics and various other quite formal, sophisticated areas of physics and I was fairly disappointed that I did not get very far using these conventional methods,” Wolfram says. “It is quite plain that the [conventional] approach has been a failure for biology and studying more complex physical systems.”

Instead, he developed a computer-modeling device called cellular automata. Cellular automata are self-replicating, self-organizing groups of cells that live, die, and form patterns based on simple rules that instruct each cell to change its behavior in accordance with the behavior of neighboring cells. They provide a uniquely useful tool for scientists studying how the interaction of individual elements influences a system as a whole. As in nature, it is extraordinarily difficult to predict what pattern will result from a given set of rules. The only way to find out is to set the initial conditions and let the program run.

“I found that very simple rules, instead of producing fairly simple behavior, actually produce extremely complicated behavior,” Wolfram says. “That is a piece of intuition that many people just haven’t got yet. When you see a complicated phenomenon in nature, your instinct is to try and make a complicated model to explain it. Somehow, nature itself does not need that. People don’t understand that there are really simple experiments that can tell you really interesting things about, for example, how biological systems can be constructed.”

Scientists in a variety of fields have begun using cellular automata and other kinds of computer simulations to investigate questions traditional physics can’t answer. Physicist Per Bak at Brookhaven National Laboratory is looking into his computer for a theory that accounts for the ability of matter to organize itself into ever more complex forms. Stuart Kauffman at the Santa Fe Institute is investigating self-organizing behavior as a key to understanding the origin of life. Langton at the Santa Fe Institute is developing standardized computer programs to allow researchers to study complex systems, from a collection of single-celled animals in a pond to a group of competing companies.

But Wolfram, once again, is going his own way. In his view, much of the research into complexity is “impenetrable nonsense” with “a fair amount of rhetoric and not much science.” But when it comes to trying to explain his own work, he shares the difficulty: “I am talking about concepts that are reasonably fundamental and reasonably abstract. That means most words that describe it sound vacuous.”

Where many researchers are using complexity studies to explore biology, Wolfram says he is exploring the underlying order of the universe itself. “I wondered what would happen if we started from scratch and ignored everything that had been achieved in physics, to see what we could do,” he says. “I have spent the last 10 years doing the most obvious experiments. Of course, you often do not realize they are obvious until you have been thinking about it for years.”

Computational physics “is a great field because nothing is known, absolutely nothing,” he declares. “There is a computer universe there that just has not been looked at.”

Wolfram is somewhat sheepish about the secrecy of his work, but says he simply wants to work undisturbed by intellectual competition. Not everyone is bothered by his silence. “Maybe Stephen has a really good idea but is just being very careful about building a solid case for it,” Langton says.

Colleagues around the country say Wolfram has alluded to some of his findings in Internet exchanges with a few key researchers. “He is wrestling with what is probably the hardest question in physics-the relationship between physics and computation. That is a pretty heady topic,” says Danny Hillis, an influential computer theoretician who pioneered the concept of massive parallel processing, the basis of most new supercomputer designs.

“He has given only tantalizing hints as to what the answers he has found would be,” says Kolb at the University of Chicago. “He seems confident he is on to something.”

“He is looking for some deep connections between fundamental physics and fundamental ideas in computer science,” says Gregory J. Chaitin, a noted mathematician at IBM’s Watson Research Center. The idea that the way the universe works is analogous to the way computation works “is a very intriguing idea that a number of people have speculated on, but there has been no serious work. Maybe he won’t find anything. But maybe he will find something very interesting indeed.”

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