[In the following review, Carrithers offers a positive assessment of Chaos.]

In the Prologue to this fascinating account, [Chaos,] Gleick attributes to Joseph Ford this characteristic claim of the “chaos movement”: “Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability.” James Gleick adds that “of the three, the revolution in chaos applies to the universe we see and touch, to objects at human scale.” Gleick, since 1978 an editor and reporter at the New York Times, chronicles the story.

The first chapter features three papers by Edward N. Lorenz published in 1963–64. It was he who showed mathematically and graphically that long-range weather prediction is inherently impossible (rather than merely difficult), and who later gave us in 1979 “the butterfly effect,” as in “Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?” Yes; at least it may; though it might not.

The following ten chapters are in several ways a cautionary tale—of scholarly investigators in many lines of research historically and institutionally defined as disparate, needing to know about one another's works, and only very slowly (one may feel) making those longer-range connections, while meeting discouragement at the short range. This might be said to be the account of a meta-science coming into being. That meta-science defies “accepted ways of working in science,” which Gleick construes as focussing on linearity, and repeatable results within what some chaos scientists deem reductive limits; and it “makes strong claims about the universal behavior of complexity,” the “global nature of systems” featuring “orderly disorder created by simple processes.”

For example, Stephen Smale, a topologist, developed the “horseshoe” transformation for mathematically understanding the chaotic properties of dynamic systems as stretching, squeezing, folding—like taffy on the arms of a mechanical taffy-puller. Apart from contributing to the rapprochement in the 1960s of mathematicians and physicists (who had “simply despised each other” for three decades, according to Ralph Abraham), this line of work fostered computer modeling. A development of that: a graphic by Philip Marcus effectively modeled and explained the dynamic stability of the weather system which we have known as the Great Red Spot of Jupiter.

Gleick describes the confluence of working modes of ecological biologists with the making of the new science of chaos, and interprets it in a proportion worthy of a metaphysical poet: “The hitherto received mathematics of ecology is to the mathematics of Steve Smale what the Ten Commandments are to the Talmud.” The story is partly of change of heart: from the bearing that mathematically stable models were the interesting ones, to fascination with the relevance of mathematically unstable models. The story has something for everyone, including the textual editor. Smale circulated second-generation photocopies of Lorenz's paper on “Deterministic Nonperiodic Flow” sent to him by James Yorke in 1972, with the latter's return address on it. He, rather than Smale, became known as the promulgator of Lorenz. But of course the crucial point was the growing recognition of the pervasiveness, in a large sense the regularity in nature of sensitive and non-linear dependence on initial conditions. It meant that “nature” must be in Huxley's words not only queerer than we suppose but queerer than we can suppose.

Gleick might well have used Huxley's words, or the Russian formalist term defamiliarization, in describing a certain movie. Frank Hoppensteadt made a movie from each of a thousand different values of the parameter in the logistic nonlinear equation (such as x=rx[1-x]), as plotted on the graphic display screen of a very powerful computer. As the parameter increases, chaotic unpredictability develops, giving way to “fleeting bits of periodic behavior,” which on the movie of the computer screen resemble “flying through an alien landscape.”

The landscape of chaos science's nature invites celebration by a Gerard Manley Hopkins. It is more than dappled, “a geometry of the pitted, pocked, and broken up, the twisted, tangled, and intertwined,” in which, for example, the degrees of roughness or irregularity of a computer-generated coastline may look the same no matter how much the image is magnified. Such is the fractal geometry pioneered by Benoit Mandelbrot, and illustrated in the eerily beautiful picture section. Such is the geometry of “strange attractors,” that can look like stylized owl eyes or butterfly wings, “an infinitely long line in a finite area,” modelling a certain turbulence as a trajectory in phase space.

“The Ice Ages,” we learn, “may simply be a byproduct of chaos.” Sensitive dependence on initial conditions, and multiple scaling patterns recursively dependent, or, as one might uneasily say, self-referential, could well mean that climate, like nature, is not only a cluster-bound notion but a very parochial one. That is a little more than Gleick says, but he describes Mitchell Feigenbaum developing a “universal theory” of different real-world systems moving from orderly to turbulent in ways not just analogously but measurably the same. And his breakthrough, “so original and so unexpected,” was rejected by journals for two years. Yet the theory gained dissemination anyway in “the way most science is now disseminated—through lectures and pre-prints,” for him in 1976 and after.

Gleick's book, then, is a story of science itself as more complexly a matter of process than the myth of taxonomy has held, and of nature and very numbers as more a process than mythology has held (at least complex numbers). “When a geometer iterates an equation instead of solving it, the equation becomes a process instead of a description, dynamic instead of static.”

Gleick notes that “To see an image on a [computer] graphics screen does not guarantee its existence in the language of theorem and proof.” But, he adds in the kind of observation which is one of his strengths, “the numerical power of computation and the visual cues of intuition would suggest promising avenues and spare the mathematician blind alleys” in ecological shifts, in heart-beat fibrillation, and such. Intuition, play, and the spirit of competitive gaming (especially games played against the self or in some sense against the “house”) have all contributed enormously to the bizarre flowering of chaos science, itself an exotic design with its exoticism seeming to repeat at every scale. Is it mathematic or poetic justice that computer-generated fractal landscapes have proven “phenomenally realistic … in special effects for movies.” Norman Packard is quoted as remarking that “the phenomenon of chaos could have been discovered long, long ago. It wasn't, in part because this huge body of work on the dynamics of regular motion didn't lead in that direction. But if you just look, there it is.”

Look playfully? To repeat, this is in more than one sense a cautionary tale, not only of the need for communities of connection, but (overlapping that) the need for playfully imaginative viewing. “Only the most naïve scientist believes that the perfect model is the one that perfectly represents reality. Such a model would have the same drawbacks as a map as large and detailed as the city it represents. …” This book about chaos “in the new sense: orderly disorder created by simple processes,” is likewise a book about some scientists, and sectors of their disciplines, accommodating the Kuhnian notion that “You don't see something until you have the right metaphor to let you perceive it.” Is that accommodation, that boundary of interaction, a psycho-perceptual fractal boundary, with similar interfoldings at every scale? Is fractal boundary the best metaphor for perceiving interaction in a small organization between, say, professionalism and cronyism?

The question is meant to suggest something of the teasing suggestiveness of Gleick's story. Certainly he insists on a great deal. He summarizes by sketching an analytic, always already at least incipiently reductive old science in which “Simple systems behave in simple ways. … Complex behavior implies complex causes. … Different systems behave differently.” And this he contrasts with the nature, chaos-scientific, wherein “Simple systems give rise to complex behavior. Complex systems give rise to simple behavior. And most important, the laws of complexity hold universally, caring not at all for the details of a system's constituent atoms.”

Strong words. Do I hear Haldane whisper “queerer than we can suppose”? As at large, so occasionally and inevitably in small: we find assertions or predications which may seem unearned. There is a slippery use of Gustave Mahler at one point, a skewed remark about the eighteenth century by John Fowles uncritically invoked at another. To say the heart's rhythms “so precisely [measure] the difference between life and death,” to say fibrillation is a disorder “just as mental disorders … are disorders,” to speak of “ideas, emotions, and all the other artifacts of consciousness” (my emphases) seems to reduce or even beg some questions. But those questions deserve their own books. This book is delectable good news for anyone who rejoices at the mind extending its claims on the unintelligible, and anyone who believes that the most important thing coming out of the investigation arena is the investigator.