[In the following review, Glazier and Gunaratne offer a positive assessment of Chaos, which they praise as energetic and skillfully written.]

About 20 years ago, researchers in a variety of fields, ranging from economics and biology to mathematics and physics, began to question the assumption that complex behavior springs from random and essentially inexplicable causes. Often they were working on unfashionable or interdisciplinary topics and their results were studiously ignored by more mainstream researchers. However, starting about 10 years ago, and largely due to the efforts of mathematicians and theoretical physicists, these disparate groups began to recognize that they were all pursuing fundamentally similar problems describable in terms of the same set of unifying concepts. James Gleick's fascinating book [Chaos] is a history of the development of these ideas, now known generically as chaos.

Gleick makes a convincing case that the theory of chaos has begun a revolution in our understanding of nature comparable to that engendered by quantum mechanics, with “sensitive dependence on initial conditions” playing the role of the uncertainty principle. However, though the initial inspiration for the two movements came at roughly the same time, they developed at different rates. At the turn of the century, the mathematician Henri Poincaré provided the basic formalism necessary to understand complexity. The biologist D'Arcy Thompson in his great book On Growth and Form (1917) proposed that, independent of detailed causes, systems tend to group themselves into broad classes whose behaviors should be explicable in terms of simple mathematical models. Alan Turing in 1952 claimed that morphogenesis and the formation of complex structures were legitimate subjects for physical inquiry. Nevertheless, for some 60 years mainstream physics focused on a reductionist understanding of the basic constituents of matter rather than on an understanding of complexity. Only recently, with the success of the theory of critical phenomena, has the more holistic approach become widely acceptable.

In Thompson's view the understanding of form is visual and metaphoric, often closer to the process by which an artist imposes meaning on nature than to traditional analytic techniques. Researchers on chaos have followed both approaches, some studying the behavior of bifurcations of differential equations, others turning to computational modeling and simulation. The legitimation of computer models as a vehicle for understanding is one of the hallmarks of chaos research.

The theory of chaos has had many successes in treating specific systems, but its most revolutionary contribution has been to effect a change in attitude. It has vastly increased the scope of subjects deemed suitable for investigation. One no longer dismisses complex and irregular behaviors as uninteresting or noisy; instead, one seeks for simple explanations. In this view the future of physics lies in the exploration of complex phenomena: the formation of patterns, the origin of turbulence, the functions of the brain and more. More traditional physicists may find the message threatening, but chaos presents the first real possibility that physics can be extended to the nonequilibrium complexity of the everyday world. One may draw an analogy between the development of chaos research and the birth of physics itself, in which seemingly disparate facts from a variety of fields were united to create a new science.

Gleick, a science writer for The New York Times, understands his subject and has a gift for simple, nonmathematical explanations that are accurate and insightful. Chaos is a scholarly book. Gleick's explanations of phase space and Poincaré sections should be read by all physicists. He has interviewed essentially everyone in the US who contributed to the development of the field, and he switches from discipline to discipline with apparent effortlessness. Even specialists may find that he has extended their knowledge of the boundaries of their fields.

Chaos is also a lively book, and one that is beautifully written. In fact, like any good novel, it is almost impossible to put down. Each chapter focuses on one or a few researchers and discusses their work as part of their lives. Some are fine musicians, some writers, some polymaths, some mountain-climbers. They all seem to share a love for art and culture that has allowed them to escape the restrictive patterns of thought that characterize their disciplines. Among this great range of personalities, as expected, some are attractive and some not. Gleick presents them fairly, without romanticization but always with respect. The portraits will ring true to those who know the subjects. The book is full of vignettes and stories that make both the scientists and the process of science come alive. The frustrations and setbacks are presented in as much detail as the triumphs. Particularly attractive is the chapter devoted to Edward Lorenz, the significance of whose work was not recognized for 15 years because of its extraordinary novelty.

To write a history of current events is a difficult task. It calls for evaluating the importance of individual pieces of research when their long-term significance is still unclear. This sort of judgment is very personal, and we agree with most of Gleick's choices. But we do have a few reservations. We would have liked to see a chapter on Hamiltonian chaos and on the contributions of the great Russian theorists Vladimir I. Arnol'd, Andrei N. Kolmogorov and R. L. Stratonovich. Though Gleick continually refers to the importance of Russian research, a sketch of one of these men and his work, even at second hand, would have rounded out the presentation. Neither the discoverers of fractals—Georg Cantor, Felix Hausdorff, Gaston Julia and Pierre Fatou—nor the important topic of pattern formation are sufficiently discussed. An experimentalist will search in vain for a mention of Geoffrey Taylor, whose work inspired much of the current experimental research on hydrodynamic chaos. Overall, however, these are minor quibbles and it is the breadth and evenhandedness of Gleick's presentation that make a lasting impression.

Science books that are accurate, nontechnical and exciting are extremely rare. Gleick's book is worthwhile reading for every physicist, chaos specialist or not. It cogently addresses many of the problems, both scientific and philosophical, that face contemporary physics. Since it is eminently readable and uses no mathematics it would be an excellent text to use in a history or philosophy of science class to introduce nonspecialists to the excitement of physics. The illustrations are familiar but well chosen, and Gleick provides information allowing one to duplicate many of the basic computations on a home computer. One could scarcely ask for a better popularization of contemporary research. It will be interesting to look back in ten years to see how Gleick's judgments have fared.