Complexity: The Emerging Science at the Edge of Order and Chaos

by M. Mitchell Waldrop

Dreyfus reinforced all the lessons that Arthur had learned at McKinsey, and provided an ongoing antidote to the economics classes. “He believed in getting to the heart of a problem,” says Arthur. “Instead of solving incredibly complicated equations, he taught me to keep simplifying the problem until you found something you could deal with. Look for what made a problem tick. Look for the key factor, the key ingredient, the key solution.” Dreyfus would not let him get away with fancy mathematics for its own sake.

Everyone has a research style, says Arthur. If you think of a research problem as being like a medieval walled city, then a lot of people will attack it head on, like a battering ram. They will storm the gates and try to smash through the defenses with sheer intellectual power and brilliance. But Arthur has never felt that the battering ram approach was his strength. “I like to take my time as I think,” he says. “So I just camp outside the city. I wait. And I think. Until one day—maybe after I’ve turned to a completely different problem—the drawbridge comes down and the defenders say, ‘We surrender.’ The answer to the problem comes all at once.”

Horace Freeland Judson’s The Eighth Day of Creation, a 600-page history of molecular biology. “I was enthralled,” he recalls. He read how James Watson and Francis Crick had discovered the double-helix structure of DNA in 1952. He read how the genetic code had been broken in the 1950s and 1960s. He read how scientists had slowly deciphered the intricately convoluted structures of proteins and enzymes. And as a lifetime laboratory klutz—“I’ve done miserably in every laboratory I’ve been in”—he read about the painstaking experiments that brought this science to life: the questions that made this or that experiment necessary, the months spent in planning each experiment and assembling the apparatus, and then the triumph or dejection when the answer was in hand. “Judson had the ability to bring the drama of science alive.”

The real economy was not a machine but a kind of living system, with all the spontaneity and complexity that Judson was showing him in the world of molecular biology.

Working at the Institut Pasteur in Paris in the early 1960s, the French biologists Francois Jacob and Jacques Monod had discovered that a small fraction of the thousands of genes arrayed along the DNA molecule can function as tiny switches. Turn one of these switches on—by exposing the cell to a certain hormone, for example—and the newly activated gene will send out a chemical signal to its fellow genes. This signal will then travel up and down the length of the DNA molecule and trip other genetic switches, flipping some of them on and some of them off. These genes, in turn, start sending out chemical signals of their own (or stop sending them out). And as a result, still more genetic switches will be tripped in a mounting cascade, until the cell’s collection of genes settles down into a new and stable pattern. For biologists the implications of this discovery were enormous (so much so that Jacob and Monod later shared the Nobel Prize for it). It meant that the DNA residing in a cell’s nucleus was not just a blueprint for the cell—a catalog of how to make this protein or that protein. DNA was actually the foreman in charge of construction. In effect, DNA was a kind of molecular-scale computer that directed how the cell was to build itself and repair itself and interact with the outside world. Furthermore, Jacob and Monod’s discovery solved the long standing mystery of how one fertilized egg cell could divide and differentiate itself into muscle cells, brain cells, liver ce...

Basically, Prigogine was addressing the question, Why is there order and structure in the world? Where does it come from? This turns out to be a much tougher question than it might sound, especially when you consider the world’s general tendency toward decay. Iron rusts. Fallen logs rot. Bathwater cools to the temperature of its surroundings. Nature seems to be less interested in creating structures than in tearing structures apart and mixing things up into a kind of average. Indeed, the process of disorder and decay seems inexorable—so much so that nineteenth-century physicists codified it as the second law of thermodynamics, which can be paraphrased as “You can’t unscramble an egg.” Left to themselves, says the second law, atoms will mix and randomize themselves as much as possible. That’s why iron rusts: atoms in the iron are forever trying to mingle with oxygen in the air to form iron oxide. And that’s why bathwater cools: fast-moving molecules on the surface of the water collide with slower-moving molecules in the air, and gradually transfer their energy. Yet for all of that, we do see plenty of order and structure around. Fallen logs rot—but trees also grow. So how do you reconcile this growth of structure with the second law of thermodynamics? The answer, as Prigogine and others realized back in the 1960s, lies in that innocuous-sounding phrase, “Left to themselves …” In the real world, atoms and molecules are almost never left to themselves, not completely; they ar...

If the gas is turned on with a very tiny flame, then still nothing much happens. The system is no longer in equilibrium—heat energy is rising up through the soup from the bottom of the pot—but the difference isn’t large enough to really disturb anything. But now turn the flame up just a little bit higher, moving the system just a little farther from equilibrium. Suddenly, the increased flux of heat energy turns the soup unstable. Tiny, random motions of the soup molecules no longer average out to zero; some of the motions start to grow. Portions of the fluid begin to rise. Other portions begin to fall. Very quickly, the soup begins to organize its motions on a large scale: looking down on the surface you can see a hexagonal pattern of convection cells, with fluid rising in the middle of each cell and falling along the sides. The soup has acquired order and structure. In a word, it has begun to simmer. Such self-organizing structures are ubiquitous in nature, said Prigogine.

In fact, wrote Prigogine in one article, it’s conceivable that the economy is a self-organizing system, in which market structures are spontaneously organized by such things as the demand for labor and the demand for goods and services. Arthur sat up immediately when he read those words. “The economy is a self-organizing system.” That was it! That was precisely what he had been thinking ever since he’d read The Eighth Day of Creation, although he hadn’t known how to articulate it. Prigogine’s principle of self-organization, the spontaneous dynamics of living systems—now Arthur could finally see how to relate all of it to economic systems.

In mathematical terms, Prigogine’s central point was that self-organization depends upon self-reinforcement: a tendency for small effects to become magnified when conditions are right, instead of dying away. It was precisely the same message that had been implicit in Jacob and Monod’s work on DNA. And suddenly, says Arthur, “I recognized it as what in engineering we would have called positive feedback.” Tiny molecular motions grow into convection cells. Mild tropical winds grow into a hurricane. Seeds and embryos grow into fully developed living creatures. Positive feedback seemed to be the sine qua non of change, of surprise, of life itself.

Very quickly, however, it became apparent that what was really getting his critics riled up was this concept of the economy locking itself in to an unpredictable outcome. If the world can organize itself into many, many possible patterns, they asked, and if the pattern it finally chooses is a historical accident, then how can you predict anything? And if you can’t predict anything, then how can what you’re doing be called science? Arthur had to admit that was a good question. Economists had long ago gotten the idea that their field had to be as “scientific” as physics, meaning that everything had to be mathematically predictable. And it was quite some time before even he got it through his head that physics isn’t the only kind of science. Was Darwin “unscientific” because he couldn’t predict what species will evolve in the next million years? Are geologists unscientific because they can’t predict precisely where the next earthquake will come, or where the next mountain range will rise? Are astronomers unscientific because they can’t predict precisely where the next star will be born? Not at all. Predictions are nice, if you can make them. But the essence of science lies in explanation, laying bare the fundamental mechanisms of nature. That’s what biologists, geologists, and astronomers do in their fields. And that’s what he was trying to do for increasing returns.

Even more distressing was his sense that things were only getting worse for the younger generation of scientists. Judging from what he’d seen of the ones coming through Los Alamos, they were impressively bright and energetic—but conditioned by a culture that was enforcing more and more intellectual fragmentation all the time. Institutionally (as opposed to politically), universities are incredibly conservative places. Young Ph.D.’s don’t dare break the mold. They have to spend the better part of a decade in the desperate pursuit of tenure in an existing department, which means that they had better be doing research that the department’s tenure committee will recognize. Otherwise, they’re going to hear something like, “Joe, you’ve been working hard over there with the biologists. But how does that show you’re a leader over here in physics?” Older researchers, meanwhile, have to spend all their waking hours in the desperate pursuit of grants to pay for their research, which means that they had better tailor their projects to fit into categories that the funding agencies will recognize. Otherwise, they’re going to hear something like, “Joe, this is a great idea—too bad it’s not our department.” And everybody has to get papers accepted for publication in established scholarly journals—which are almost invariably going to restrict themselves to papers in a recognized specialty.

In part because of their computer simulations, and in part because of new mathematical insights, physicists had begun to realize by the early 1980s that a lot of messy, complicated systems could be described by a powerful theory known as “nonlinear dynamics.” And in the process, they had been forced to face up to a disconcerting fact: the whole really can be greater than the sum of its parts. Now, for most people that fact sounds pretty obvious. It was disconcerting for the physicists only because they had spent the past 300 years having a love affair with linear systems—in which the whole is precisely equal to the sum of its parts. In fairness, they had had plenty of reason to feel this way. If a system is precisely equal to the sum of its parts, then each component is free to do its own thing regardless of what’s happening elsewhere. And that tends to make the mathematics relatively easy to analyze. (The name “linear” refers to the fact that if you plot such an equation on graph paper, the plot is a straight line.) Besides, an awful lot of nature does seem to work that way. Sound is a linear system, which is why we can hear an oboe playing over its string accompaniment and recognize them both. The sound waves intermingle and yet retain their separate identities. Light is also a linear system, which is why you can still see the Walk/Don’t Walk sign across the street even on a sunny day: the light rays bouncing from the sign to your eyes are not smashed to the ground by su...

And yet, as intriguing as molecular biology and computer simulation and nonlinear science were separately, Cowan had a suspicion that they were only the beginning. It was more a gut feeling than anything else. But he sensed that there was an underlying unity here, one that would ultimately encompass not just physics and chemistry, but biology, information processing, economics, political science, and every other aspect of human affairs. What he had in mind was a concept of scholarship that was almost medieval. If this unity were real, he thought, it would be a way of knowing the world that made little distinction between biological sciences and physical sciences—or between either of those sciences and history or philosophy. Once, says Cowan, “The whole intellectual fabric was seamless.” And maybe it could be that way again.

Meanwhile, there was the matter of incorporation: if you’re going to start asking people for money, you really ought to have something besides your own personal checking account to put it into.

And so it goes, says Anderson. Weather is an emergent property: take your water vapor out over the Gulf of Mexico and let it interact with sunlight and wind, and it can organize itself into an emergent structure known as a hurricane. Life is an emergent property, the product of DNA molecules and protein molecules and myriad other kinds of molecules, all obeying the laws of chemistry. The mind is an emergent property, the product of several billion neurons obeying the biological laws of the living cell. In fact, as Anderson pointed out in the 1972 paper, you can think of the universe as forming a kind of hierarchy: “At each level of complexity, entirely new properties appear. [And] at each stage, entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry.”

One office featured a name that Arthur was very interested to see: Stuart Kauffman of the University of Pennsylvania. Arthur had briefly met Kauffman two years earlier at a conference in Brussels, where he had been immensely impressed by Kauffman’s talk on cells in a developing embryo. The idea was that the cells send out chemical messengers to trigger the development of other cells in the embryo in a self-consistent network, thus producing a coherent organism instead of just a lump of protoplasm. It was a concept that resonated strongly with Arthur’s ideas on the self-consistent, mutually supportive webs of interactions in human societies, and he remembers coming back from that conference and telling his wife, Susan, “I’ve just listened to the best talk I’ve ever heard!”

Kauffman couldn’t help it. For nearly a quarter of a century he had been a man in the grip of a vision—a vision that he found so powerful, so compelling, so overwhelmingly beautiful that he simply could not hold it in. The closest English word for it is “order.” But that word doesn’t begin to capture what he meant by it. To hear Kauffman talk about order was to hear the language of mathematics, logic, and science being used to express a kind of primal mysticism. For Kauffman, order was an answer to the mystery of human existence, an explanation for how we could possibly come to exist as living, thinking creatures in a universe that seems to be governed by accident, chaos, and blind natural law. For Kauffman, order told us how we could indeed be an accident of nature—and yet be very much more than just an accident. Yes, Kauffman always hastened to add, Charles Darwin was absolutely right: human beings and all other living things are undoubtedly the heirs of four billion years of random mutation, random catastrophes, and random struggles for survival; we are not here as the result of divine intervention, or even space aliens. But, he would emphasize, neither was Darwinian natural selection the whole story. Darwin didn’t know about self-organization—matter’s incessant attempts to organize itself into ever more complex structures, even in the face of the incessant forces of dissolution described by the second law of thermodynamics. Nor did Darwin know that the forces of order ...

Furthermore, said Holland, the control of a complex adaptive system tends to be highly dispersed. There is no master neuron in the brain, for example, nor is there any master cell within a developing embryo. If there is to be any coherent behavior in the system, it has to arise from competition and cooperation among the agents themselves.

In the spring of 1978, Langton laid out his thinking in a twenty-six-page paper entitled “The Evolution of Belief.” His basic argument was that biological and cultural evolution were simply two aspects of the same phenomenon, and that the “genes” of culture were beliefs—which in turn were recorded in the basic “DNA” of culture: language.

So before von Neumann could answer the question about machine self-reproduction, he had to reduce that process to its essence, its abstract logical form. In effect, he had to operate in the same spirit that programmers would years later when they started to build virtual machines: he had to find out what was important about self-reproduction, independent of the detailed biochemical machinery.

No, the Game of Life computer would exist entirely within the von Neumann universe, in exactly the same way that Langton’s self-reproducing pattern did. It would be a crude and inefficient computer, to be sure. But in principle, it would be right up there with Seymour Cray’s finest. It would be a universal computer, with the power to compute anything computable. Now, that’s a pretty astonishing result, says Langton—especially when you consider that only comparatively few cellular automaton rules allow it to happen. You couldn’t make a universal computer in a cellular automaton governed by Class I or II rules, because the structures they produce are too static; you could store data in such a universe, but you would have no way to propagate the information from place to place. Nor could you make a computer in a chaotic Class III automaton; the signals would get lost in the noise, and the storage structures would quickly get battered to pieces. Indeed, says Langton, the only rules that allow you to build a universal computer are those that are in Class IV, like the Game of Life. These are the only rules that provide enough stability to store information and enough fluidity to send signals over arbitrary distances—the two things that seem essential for computation. And, of course, these are also the rules that sit right in this phase transition at the edge of chaos.