• Email
  • Single Page
  • Print

On the Edge of Chaos

The spectacular success of Stephen Hawking’s A Brief History of Time, a shard of the true cross that has sold more than five million copies since its publication in 1988, touched off a speculative frenzy among book publishers suddenly willing to back just about any scientist-author who might duplicate Hawking’s ascent to the best-seller lists. Of these perhaps the most celebrated is Murray Gell-Mann, the Nobel laureate, theoretical physicist, and polymath who thought up and named the quark and has been described as “the smartest man in the world.”

Nevertheless, news of the book raised a few eyebrows among observes of the science-writing scene. Of Gell-Mann’s erudition there was no doubt. In addition to his mastery of physics, Gell-Mann is at home in botany, evolutionary biology, cosmology, and many other sciences. He is said to speak thirteen languages. He can discourse at length on cuisine, etymology, ethics, ornithology, South American pottery, Caucasian carpet-weaving, literature (he came across the word “quark” in Finnegans Wake), and enough else to make a complete recitation of the subjects of his expertise read like the spines of a set of encyclopedias. Certainly a book that surveyed even some of the interests of so commodious a mind would be worthy of wide attention.

His erudition aside, however, there were doubts that Gell-Mann, who had never written a popular book or even an especially well-composed nontechnical article, could reach an audience of general readers. Part of the concern had to do with his legendarily combative personality. Gell-Mann is not one of those geniuses who wears his learning lightly. He dismisses many of his colleagues as ignoramuses, and is less charitable when it comes to nonscientists. On striking up an acquaintanceship he will argue with you about everything from the street map of your home town to the pronunciation of your grandmother’s surname. He likes to steer conversation to one of the many subjects he knows well, then stage an intellectual fireworks show that leaves his audience dumbstruck with awe. This sort of thing can be a liability when it comes to popularizing science, which calls for a certain solicitude toward the anxieties of nonscientists, who are unlikely to read very far if they sense that, just as they had feared, the author is a wizard and they are hopeless dolts.

And, indeed, The Quark and the Jaguar has its flaws. It is littered with self-congratulatory phrases like, “Through the John D. and Catherine T. MacArthur Foundation, of which I am a director,” and “the World Resources Institute (which I am proud to have played a role in founding).” GellMann mentions the Santa Fe Institute, which he also helped found, so often—ten times in eleven pages, at one point—that in the book’s preface he apologizes for “what amounts to a glorification of Santa Fe” and “for what must seem like advertising” of it. At the same time Gell-Mann is disappointingly reticent about describing his own life. Early in the book we are treated to a few autobiographical glimpses: He and his older brother, Ben, took nature walks in Van Cortlandt Park and the New Dorp area of Staten Island, devoured novels and poetry and books on history, evolution, and languages, “wanted to understand the world and enjoy it, not to slice it up in some arbitrary way.” But, as Einstein did in his Autobiographical Notes, Gell-Mann soon drops this thread of personal narrative and escapes into the world of ideas, never to look back.

Nevertheless, The Quark and the Jaguar emerges as a work of considerable felicity. It can be read by anyone with an interest in science, and it has a clarity and integrity that can only be produced by sustained effort. Gell-Mann writes disarmingly in the preface that “I have never worked so hard on anything in my life,” and it shows.

The subject of The Quark and the Jaguar is twofold. The quark part concerns particle physics, the study of the most rudimentary structures in nature, while the jaguar represents complicated systems like thunderstorms, living creatures, and market economies. Gell-Mann, an inveterate birdwatcher and hiker, writes that the idea for the book came to him when he spotted a wild cat—a jaguarundi or otter cat—on a forest trail in Central America. “Meeting the jaguarundi in Belize somehow strengthened my awareness of the progress my colleagues and I had made in understanding better the relation between the simple and the complex,” he writes. “….[I]t struck me that my two worlds, that of fundamental physics and that of condors, jaguarundis, and Maya ruins, had finally come together.”

The celebrated attainments of modern science have had to do almost exclusively with simple structures. This fact has to some extent been obscured by popular reports that physicists are close to arriving at a “theory of everything.” But such a theory would be limited to interpreting fundamental interactions and explaining why subatomic particles have the mass, charge, and other characteristics that they do. It would explain “everything” in the sense that everything is made of particles. It could not predict the behavior of complex systems like jaguars and human beings. To gain such predictive power by charting the course of all the particles involved, the sometime dream of nineteenth-century science, is now seen to be impossible. One can never ascertain the locations and trajectories of all the subatomic particles in a jaguar. Nor, if provided with such information, could a scientist compute the behavior of all those particles for any significant time into the future.

The emerging science of complexity, in which Gell-Mann is a leading figure, seeks to redress this deficiency. Complexity theory is related to the betterknown study of “chaos,” a term whose ambiguity has engendered confusion. (As Gell-Mann writes, “The word has been turned into a kind of catchall expression for any sort of real or apparent complexity or uncertainty.”) The essential point about chaotic systems is that they are “nonlinear.” In linear systems, a straightforward cause leads to a straightforward effect. In nonlinear systems, “the outcome of a dynamical process is so sensitive to initial conditions that a minuscule change in the situation at the beginning of the process results in a large difference at the end,” as Gell-Mann writes. Consider water flowing out of a faucet. At low velocities the water behaves in linear fashion, flowing out in a predictable way. But if the faucet is opened wide enough, the water becomes highly turbulent and chaotic, spurting in unpredictable directions. The input is not qualitatively different from the input that previously produced a linear result—one just kept opening the faucet, a crack at a time—but the result is suddenly very different.

Between these two regimes of the simple and the complex there can arise behavior that is partly linear and partly chaotic. Cells of turbulence may appear in an otherwise smooth flow. (We’re all familiar with one result, which is to make a bathroom faucet suddenly start rapping loudly.) This twilight zone between determinism and chaos is, loosely speaking, the domain of complexity. For that reason complexity is sometimes characterized as “the edge of chaos.” If this sounds vague, there is as yet no precise definition of what exactly is meant by complexity and chaos. As Gell-Mann notes, “[I]t is not simple to define ‘simple.’ Probably no single concept of complexity can adequately capture our intuitive notions of what the word ought to mean.”

Much of the excitement about complexity theory has to do with the view that living systems dwell “on the edge of chaos,” which is to say that they retain a degree of order while flirting with chaotic nonlinearity. Cell membranes, for instance, are poised on the boundary between a solid and a liquid state. This somewhat unstable situation subjects the cells to nonlinear dynamics. A small change in the local cholesterol content, for instance, can produce disproportionately large changes in the cell. While many of these changes are harmful to the cell, some may prove to be biologically useful. Hence complexity can be biologically creative. Complexity studies could be helpful in evolutionary biology, where scientists understand the basic mechanism—natural selection operating through DNA coding—but have gained far less insight into how that mechanism has come to express itself in the particular forms we see in the myriad species of life around us.

Gell-Mann classes living creatures as “complex adaptive systems,” and analyzes them by using information theory. Complex adaptive systems, he writes,

take in information—in the form of a data stream—and find perceived regularities in that stream, treating the rest of the material as random. Those regularities are compressed into a schema, which is employed to describe the world, predict its future to some extent, and to prescribe behavior for the complex adaptive system itself. The schema can undergo changes that produce many variants, which compete with one another. How they fare in that competition depends on selection pressures, representing the feedback from the real world.

Such systems require a degree of order, but they also need enough disorder to facilitate novelty—the development of new structures and behavior patterns that enable organisms to cope with changing environmental conditions. Otherwise life would have remained relatively nondiverse. Were the environment too complex, too nonlinear, “a properly operating complex adaptive system would then be unable to find any schema, since a schema summarizes regularities and there aren’t any.” Were the environment too simple—too regular, insufficiently complex, and unpredictable—the adaptive system would have little incentive to change, and efficacious evolutionary possibilities would remain underexplored.

As a somewhat fanciful example, suppose that the solar system were less complicated, in the sense that it contained only planets and not the comets and asteroids that scientists now think caused mass extinctions. In that case life today probably would remain in the less diversified state that existed prior to the Permian or Cambrian extinction events and the explosive emergence of new species that followed. According to complexity theory, the fact that 99.9 percent of all species that ever lived are now extinct is essential to the fact that there are so many species today. By making it necessary for surviving life forms to adapt to radically changed conditions and by opening space for innovation, mass extinctions provided the chaos—the noise in the signal—that permitted innovative new designs to emerge.

This point can be illustrated by plotting the Darwinian “fitness” of various species on a topological map of three-dimensional space. By custom, relative fitness on such maps corresponds to height, and evolutionary biologists depict the species they judge best adapted as sitting atop hills and mountains, like triumphant “killer-apes” pounding their chests in the opening sequence of the film 2001. But Gell-Mann cleverly inverts this map, so that the best-adapted species occupy not mountaintops but the bottoms of wells. By putting stable ecosystems in dales rather than hills, he clarifies how complexity theory views the importance of chaos in evolution. If there is too much chaos, species that find their way to a well will soon be jolted out (by external forces such as climatic shifts and changes in food supply). If there is too little chaos, species that find themselves in the bottom of a fitness well are likely to stay there indefinitely, and the result will be a static ecosystem with inadequate room for diversity to emerge. The system requires enough order to preserve some continuity, yet enough disorder to jolt species out of fitness wells from time to time, forcing them to innovate or perish.

  • Email
  • Single Page
  • Print