The New Field of Complexity

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Complexity theory examines the systems that lie in the middle ground between the predictable and the chaotic -- in fact, right on the border between the two states. Says Edward Knapp, president of the Santa Fe Institute: "We think of a complex system as one that is probably never in equilibrium, a system with many interlocking parts that are not easily described by simple arithmetic."

One of the easiest examples to understand is sand dunes, which maintain their overall shape despite winds and sandslides. Researchers at IBM's Thomas Watson Research Center built an artificial dune, a tiny sandpile sitting on a sensitively balanced plate, to study this behavior in detail. In one experiment, they dropped 35,000 grains of sand onto the pile one by one. As the sides grew too steep -- in some cases, by only a single grain of sand -- avalanches would make the pile collapse. Then it would start growing steeper again, until it was time for the next avalanche.

This phenomenon is known as self-organized criticality -- the grains have organized themselves to slope at a certain angle, yet the arrangement is precarious because a tiny extra bit of sand can knock the whole thing down. The sandpile is not quite stable, not quite chaotic.

Complexity theorists believe more sophisticated phenomena follow the same pattern. The stock market can, without outside direction, hum along on an upward course for years and then crash 500 points in a single day. A species can survive for millions of years and then abruptly die out -- or conversely, evolve almost all at once into something entirely new. And self-reproducing organisms can somehow arise, against all odds, from a soup of simple organic chemicals.

It certainly makes intuitive sense that a simple underlying principle should explain such similar behaviors across a wide variety of systems. Indeed, complexity theorists often speak about their science "feeling" or even "tasting" right. Waldrop sometimes jokingly refers to the all- encompassing theory as "the Grand Unified Theory of Holism." The only trouble is, he says, "some people take me seriously."

The field might have remained a kind of New Age plaything for computer nerds were it not for the fact that it has stood up to a variety of tests. Some experiments have been done in the lab, as with tiny sandpiles. More often they take place inside computers. Scientists create mathematical models of real- world systems -- the stock market, an ecosystem, a group of living cells -- and let them evolve on the screen. If the computerized world behaves as the real one does, there is a good chance the underlying mathematics is valid.

By this measure, complexity works, at least roughly. Computer simulations of ( life, the best-known application of the theory, create onscreen worlds of cyber-creatures that evolve in ways that eerily parallel real life. Biophysicist Stuart Kauffman of the Santa Fe Institute says confidently, "Biological evolution proceeds at the boundary between order and chaos. If there is too much order, the system becomes frozen and cannot change. But if there is too much chaos, the system retains no memory of what went on before."