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Finding Order Beneath Apparent Chaotic Acts


By John H. Holland

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Helix Books

259 pp., $25

There are scientists for whom the universe is a kind of cosmic puzzle. The pieces with one straight side can be lined up to form an edge of the picture. But the vast empty space in the center can be filled in only by a Kepler, a Newton, or an Einstein.

Scientists and researchers at the Santa Fe Institute in New Mexico are trying to assemble some of the most challenging pieces. Founded in the mid-1980s, the institute is a collection of Nobel Prize-winning physicists, economists, and computer scientists who share a common vision of a mathematical unity underlying seemingly disparate areas of knowledge.

John Holland, an Ann Arbor, Mich., professor and a research fellow at the institute, is one of the gurus of this new interdisciplinary enterprise. His most recent volume, "Emergence: From Chaos to Order," is a glimpse of work in progress, the effort to find a formal basis for the evolution of complex systems.

He begins by defining emergence as "this sense of much coming from little." For instance, a seed is a tiny thing, but in its wondrous compactness, it contains a complete set of instructions for the construction of a rose, a radish, or a redwood.

Similarly, the rules of chess are simple enough that an elementary school child can memorize them, but the number of possible chess games is greater than the number of particles in the universe. From evolution to economics, game theory to cosmology, the pattern recurs: a relatively small set of rules can produce structures of astonishing complexity.

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Although these emergent systems are dynamic, Hollard suggests that they change over time according to regular patterns that we can describe. He notes that "from earliest times, human endeavor has been directed toward discovering ways to channel a chaotic world."

In other words, we build models to try to understand the universe around us. Scientists use mathematical modeling as a way of creating an experimental picture of the world, a metaphor for physical structures. If their model predicts a certain outcome correctly, they gain new insights about the forces of nature.

This book is intended for the general reader, although it helps to have done some other reading in the areas of chaos theory and complexity. The book can be read either for a general overview of the concepts or as a text for the development of a mathematical definition of emergence. The math is no harder than high school algebra and set theory, and it repays close attention with an increase in mental agility.

Holland admits that his results are still at the most elementary level. "Because so many of the problems that baffle us - ranging from the control of economies to understanding consciousness - involve emergent phenomena ... one might causally infer that we've gone as far as science can take us."

He strongly disagrees, however, with those who feel we are approaching the end of science. It may be that we are ultimately limited in our scientific understanding by the fact that we live inside the universe. But, Holland argues, there is no limit to the questions we can ask.

* Frederick Pratter is a writer living in Hull, Mass.

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