BOOK REVIEW / Complex interactions in the primordial soup: Complexity - M Mitchell Waldrop: Viking, pounds 9.99; Complexity - Roger Lewin: J M Dent, pounds 15.99

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BEWARE OF scientists bearing beautiful mathematical models. They are not dangerous, but can be misleading unless they describe the real world. This warning particularly applies to the seductive computer simulations associated with recent studies on the nature of complexity.

Scientists working in this new and fashionable area are interested in a whole set of problems hitherto thought intractable: why did the stock market crash on a Monday in 1987; why do some species remain stable for millions of years and then die out or change suddenly; how did the primordial soup give rise to life itself; and what is thinking? There is the fundamental belief that what all these problems have in common is the complex interaction between their component units - people in the stock exchange, molecules in cells - and that they may thus be governed by the same set of basic laws.

This is a most attractive prospect, the main proponents of which are at the Santa Fe Institute in New Mexico, and their work is the theme of both books.

A possible unifying idea in all these complex systems is that of spontaneous self-organisation, together with adaptations. Somehow, the components do not interact to produce chaos - instead, patterns emerge that make the system better adapted to the environment. If all this sounds a little vague, it is because the processes are only poorly understood: at best, some computer simulations can exhibit such properties.

Much of M Mitchell Waldrop's book is devoted to vivid biographies of the key players in this field, such as the economist Brian Arthur, who finds that his unconventional way of thinking is similar to that of the biologist Stuart Kauffman. Again, in just the way that Kauffman thinks about the origin of life, with its molecules forming a coherent, self-reinforcing web of reactions, John Holland sees the economy as a complex adaptive system. As the cell gives rise to organisms, so individual workers come together in larger structures that continue all the way up to national economies. At some deep level they hope that evolution, economics, ecology and learning are all the same. The approach of these scientists is different from that of the so-called reductionists, who attempt to dissect and study the component parts of the system. Although that method has been spectacularly successful in physics, chemistry and biology, complexity theorists are more holistic in their approach.

Such theories often strike a sympathetic note with non-scientists, but we still have to ask what they have achieved. And, in spite of the considerable hype contained in both these books, the answer is as yet - very little. They are full of hope, but nothing has been firmly established. But perhaps at such an early stage in what may be a new science one should suspend too critical an assessment.

Of course, it is not all new. And it is a serious omission that neither book gives any credit to the key paper in 1952 by the English genius Alan Turing. He showed that a homogeneous mixture of chemicals could be spontaneously self-organising and generate chemical waves. Many of his findings and ideas are used by the complexity theorists.

Waldrop's book is an excellent and scholarly account of the people and the science, though parts will be tough going for computer illiterates. Roger Lewin's book is easier, but more superficial and covers a wider range of topics, including consciousness, Gaia and embryonic development. Both authors are confident that a new science has been born. But we must remember that these problems are also being tackled by more conventional approaches. There is no reason to believe, for example, that in my own field of embryonic development these will not be successful. However, complexity theory may surprise us yet: those at the institute include the Nobel Laureates Kenneth Arrow, an economist, and the physicist Murray Gell-Mann. Meanwhile, if one asks what determines the behaviour of complex systems, the answer is . . . aah . . . um . . . rather complex.

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