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.

This view of life clearly presents tempting opportunities for the interpretation of human activities according to evolutionary theory. One such approach, much discussed in neuro-science these days, describes thinking as itself a form of evolutionary dynamics. Gell-Mann notes that the process of creative thinking was described by the nineteenth-century physicist Hermann von Helmholtz as consisting of three characteristic stages—saturation, incubation, and illumination. Gell-Mann and colleagues arrived at a similar conclusion. Recalling the gestation of some of their own best scientific ideas, he writes:

First, we had worked, for days or weeks or months, filling our minds with the difficulties of the problem in question and trying to overcome them. [That’s Helmholtz’s “saturation” stage.]

Second, there had come a time when further conscious thought was useless, even though we continued to carry the problem around with us. [“Incubation.”]

Third, suddenly, while we were cycling or shaving or cooking…the crucial idea had come. We had shaken loose from the rut we were in. [“Illumination.”]

This “shaking loose” smacks of the near-chaos that would be required if thinking is indeed a kind of high-speed Darwinian evolution.

The Quark and the Jaguar recounts more about the study of complexity than can be touched on here, and succeeds in casting bright shafts of light across the jumbled landscape of this new field of scientific research. If the book is not always as tidily arranged as one might wish, that is true of complexity science itself. The subjects on which active research is taking place almost always resemble the near-chaos of the artist’s studio; only later, when most of the important work is over, do they take on the complacent order of the museum.

Surprisingly, Gell-Mann flags a bit when recounting the basic outline of quark theory, which his own research did so much to establish. His great insight was that neutrons and protons, the components of atomic nuclei, are themselves composed of trios of particles, which he named quarks. Quarks are not normally found in isolation, but they have been detected in particle accelerators. The elusive “top” quark—the last of the six kinds of quarks to be found—made headlines two years ago when its existence was finally confirmed in a series of experiments at Fermilab in Illinois. Despite all the public excitement overa quarks, they are explained a bit flatly by Gell-Mann; one suspects they seem like old news to him by now.

Gell-Mann’s writing becomes more animated once he turns to the future of fundamental physics and describes the speculative “superstring” theories, in which subatomic particles are viewed as little balls of compactified hyperdimensional space. If superstring theory is correct, everything is made of space, matter having originated when, at the beginning of time, six of the original ten dimensions of space collapsed into the tiny strings of which subatomic particles are composed.

In some quarters it has become fashionable to dismiss superstring theory as unverifiable, because no feasible collider could replicate the titanic energies characteristic of the universe during the first fraction of a second of its expansion, in which the strings were born. Gell-Mann argues persuasively to the contrary, noting that there are many excellent ways of testing it. First, he writes, superstring theory “already predicts, in a suitable limit, Einstein’s general-relativistic theory of gravitation,” which forms the theoretical basis of modern cosmology. Now the theory must prove capable of accounting for the “standard model” of particle physics, which can predict the outcome of every known form of fundamental interaction in the universe, including gravitation, electromagnetism, the “strong” interactions responsible for binding protons and neutrons in the nucleus, and the “weak” interactions that are responsible for nuclear decay. In particular, superstring theory must reveal why more than a dozen constants of nature, currently derived from observation and plugged into the standard model arbitrarily, are what they are and not some other numbers.

In the process a new and larger theory should emerge, one that embraces the standard model. As Gell-Mann observes, “The properties of that larger theory, including its particle content and the constants describing the masses and interactions of the particles, can all be compared with the results of experiments.” He notes that although superstring theory belongs to a “high-mass sector” of nature (i.e., can be tested only under the high-energy conditions prevalent in the early universe) it may have effects that can be observed in the “low-mass” (low energy) universe we inhabit today. “Finally, superstring theory may have consequences for cosmology that are verifiable by astronomical observation.” After all, the big bang was in a sense the original particle physics experiment. We live in the debris it left behind, from which it may be possible to learn at least some of the lessons the experiment has to teach us. It is for instance highly interesting that most versions of superstring theory predict the existence of a particle with just the characteristics required to provide the “dark matter” that many theories and a few observations suggest comprises 99 percent of the mass of the universe.

This leads to Gell-Mann’s graceful treatment of the equally futuristic question of quantum cosmology. Most contemporary theories of cosmology are based on general relativity. Relativity views the world as a continuum ruled by cause-and-effect determinism. Quantum theory, on the other hand, views the world as divided into discrete units (“quanta”) and accepts that their behavior is to a degree nondeterministic. Since the universe began as a high-energy caldron of subatomic particles, quantum theory is crucial to cosmological investigation, at least insofar as the early universe is concerned—and to study the universe without the big bang would be like studying anatomy while ignoring embryology. A “unified” theory is needed—one that embraces both relativity and quantum physics. Superstring theory is probably the best candidate for doing so, as Gell-Mann argues, but a realized superstring theory is not yet in hand. Meanwhile, as theorists grope their way toward a coherent account of how the infant universe evolved, Gell-Mann has emerged as a point man among the pathfinders, capable of staying ahead of theorists a third his age.

Anyone who takes on quantum cosmology must deal with the knotty issue of “observership.” Quantum physics reveals that the outcome of a single microscopic event can be interpreted in one of two mutually exclusive ways, depending on how we measure it. An electron, for instance, behaves like a particle or like a wave, depending on how the experimental apparatus is set up. Yet it cannot be both, for particles and waves have mutually exclusive characteristics. Niels Bohr, one of the founders of quantum physics, sought to resolve this paradox by including the observer in the loop. He did this by defining “phenomenon” as meaning an observed phenomenon. The electron is neither particle nor wave, Bohr maintained, until it is observed. (This, the “Copenhagen” interpretation of quantum physics, is rather like the philosophy expressed by a respected baseball umpire who, when asked upon his retirement what, exactly, differentiated a ball from a strike, replied, “Some is balls and some is strikes, but until I calls ’em, they ain’t nothing.”)

The Copenhagen interpretation, however, poses problems of its own. If a distant star explodes and its light reaches Earth millions of years later, we are asked to believe that this phenomenon, though it has by then illuminated planets orbiting billions of stars, has not actually occurred until an astronomer or amateur stargazer in Spain or Georgia happens to point a telescope in the right direction and notice it. Einstein recoiled at the notion: Do you really believe, he asked a colleague as they were strolling outside the Institute for Advanced Study, that the moon exists only if I look at it?¹

More to the point where cosmology is concerned, the Copenhagen interpretation demands that we keep an observer in the loop even when studying the big bang, when the universe was a hot quark soup and there could not have been any observers. Yet the infant universe was the scene of plenty of phenomena, including “frozen accidents”—chance occurrences that could have had different outcomes but are now irreversible—that may well have yielded not only the material composition of the universe but even the nature of its fundamental physical laws.² To insist that no observer means no phenomena, as the Copenhagen interpretation does, strikes Gell-Mann as “stupid.”³ Many scientists and philosophers of science share his view, if not his peremptory way of expressing it.

Working with the cosmologist James Hartle, Gell-Mann has sought to replace the Copenhagen interpretation with an alternative approach based on the “many worlds” interpretation of quantum physics. First put forth decades ago by the late Hugh Everett III, the many-worlds approach purports to get rid of observer-dependency by postulating that the universe divides at each quantum event. To observe that an electron is a particle is to follow one branch of the universe, in which that particular electron is particle-like. Meanwhile a second universe has branched off, in which the electron pursues a career as a wave. Thus “many worlds”—an endlessly bifurcating multiverse.

The many-worlds approach strikes many thinkers as no less counter-intuitive than the Copenhagen interpretation. As Stephen Hawking likes to say, “People object to this because they just don’t feel themselves spliting,”⁴ Gell-Mann agrees. “We consider Everett’s work to be useful and important, but we believe that there is much more to be done,” he writes. Rather than “many worlds,” Gell-Mann and Hartle prefer to speak of “many alternative histories of the universe.” Their universe is depicted as a branching tree of fantastic complexity—far more tangled than the South American jungles in which Gell-Mann goes birdwatching—but for Gell-Mann it is less confusing to speak of alternative historical interpretations of the universe than to think that each of the many worlds actually exists. “To use the language we recommend is to address the familiar notion that a given system can have different possible histories, each with its own probability,” he writes. “It is not necessary to become queasy trying to conceive of many ‘parallel universes,’ all equally real.” Whether this tack will succeed in scotching the perplexities of quantum observership remains to be seen.

For many readers the best thing about The Quark and the Jaguar is not so much its discussion of technical issues as the way it conveys something of the excitement and majesty of the quantitative, scientific way of looking at things. Certainly Gell-Mann’s passion for living things helps to explain the bare-bones equations that scare so many people away from science. In a characteristic passage, Gell-Mann notes that the ornithologist Charles Munn, studying feeding flocks in a tropical forest in Peru, found that they typically are accompanied by “sentinel” birds that call out to warn of approaching raptors. Sometimes the sentinels make false calls: “The fake alarm often permitted the sentinel to grab a succulent morsel that another member of the flock might otherwise have eaten.

“Careful observation,” Gell-Mann writes, “revealed that the sentinels were practicing deception about 15 percent of the time and often profiting by it…. Presumably, if the percentage were much higher, the signals would not be accepted by the rest of the flock (recall the story The Boy Who Cried “Wolf”), and if it were much lower, the opportunity for the sentinel to obtain extra food by lying would be partially or wholly wasted.

“I am intrigued by the challenge of deriving by some kind of mathematical reasoning the figure of about 15 percent,” he continues. “In a plausible model, might it come out one divided by two pi? When I asked that question of Charles Bennett [the UCLA ecologist], he was reminded of something his father had told him about Royal Canadian Air Force units based in England during the Second World War. They found it useful, when sending out a fighter and a bomber together, to attempt occasionally to deceive the Luftwaffe by positioning the fighter below the bomber rather than above. After a good deal of trial and error, they ended up following that practice at random one time in seven“—in other words, about 15 percent of the time. I don’t know whether Gell-Mann the birdwatcher sees tongues in trees, but there is something more than a little charming in the notion that he sees birds as mathematicians.