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

by M. Mitchell Waldrop

In every case, moreover, the very richness of these interactions allows the system as a whole to undergo spontaneous self-organization.

Instead, all these complex systems have somehow acquired the ability to bring order and chaos into a special kind of balance. This balance point—often called the edge of chaos—is were the components of a system never quite lock into place, and yet never quite dissolve into turbulence, either.

transformation. The edge of chaos is the constantly shifting battle zone between stagnation and anarchy, the one place where a complex system can be spontaneous, adaptive, and alive.

The movement's nerve center is a think tank known as the Santa Fe Institute, which was founded in the mid-1980s and which was originally housed in a rented convent in the midst of Santa Fe's art colony along Canyon Road.

When Arthur finished Judson's book he went prowling through the University of Hawaii bookstore, snatching up every book he could find on molecular biology. Back on the beach, he devoured them all. "I was captured," he says, "obsessed." By the time he returned to IIASA in June he was moving on pure intellectual adrenaline. He still had no clear idea how to apply all this to the economy. But he could feel that the essential clues were there.

In hindsight it was all so obvious. 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.

"The royal road to a Nobel Prize has generally been through the reductionist approach," he says—dissecting the world into the smallest and simplest pieces you can. "You look for the solution of some more or less idealized set of problems, somewhat divorced from the real world, and constrained sufficiently so that you can find a solution," he says. "And that leads to more and more fragmentation of science. Whereas the real world demands—though I hate the word—a more holistic approach." Everything affects everything else, and you have to understand that whole web of connections.

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.

More and more over the past decade, he'd begun to sense that the old reductionist approaches were reaching a dead end, and that even some of the hard-core physical scientists were getting fed up with mathematical abstractions that ignored the real complexities of the world. They

Center for Nonlinear Systems

"I said I felt that what we should look for were great syntheses that were emerging today, that were highly interdisciplinary," says Gell-Mann. Some were already well on their way: Molecular biology. Nonlinear science. Cognitive science. But surely there were other emerging syntheses out there, he said, and this new institute should seek them out.

As they walked along the roads and hillsides around the convent, Arthur couldn't help but be intrigued by Kauffman's concept of order and self-organization. The irony of it was that when Kauffman used the word "order," he was obviously referring to the same thing that Arthur meant by the word "messiness"—namely emergence, the incessant urge of complex systems to organize themselves into patterns. But then, maybe it wasn't so surprising that Kauffman was using exactly the opposite word; he was coming at the concept from exactly the opposite direction. Arthur talked about "messiness" because he had started from the icy, abstract world of economic equilibrium, in which the laws of the market are supposed to determine everything as precisely as the laws of physics. Kauffman talked about "order" because he had started from the messy, contingent world of Darwin, in which there are no laws—just accident and natural selection. But by starting from totally different places, they had arrived at essentially the same place.

science showed you how a few simple laws could produce the enormously rich behavior of the world. "It really delights me," he says. "Science and math are the ultimate in reduction in one sense. But if you turn them on their heads, and look at the synthetic aspects, the possibilities for surprise are just unending. It's a way of making the universe comprehensible at one end and forever incomprehensible at the other end."

"I'd like to be able to take themes from all over and see what emerges when I put them together," he says.

Glasperlenspiel

Hebb's cell assemblies were a bit like genes, in that they were supposed to be the fundamental units of thought. But in isolation the cell assemblies were almost nothing. A tone, a flash of light, a command for a muscle twitch—the only way they could mean anything was to link up into larger concepts and more complex behaviors.

Same goes for workers nindividually and as part of a company .

To Holland, evolution and learning seemed much more like—well, a game. In both cases, he thought, you have an agent playing against its environment, trying to win enough of what it needed to keep going. In evolution that payoff is literally survival, and a chance for the agent to pass its genes on to the next generation. In learning, the payoff is a reward of some kind, such as food, a pleasant sensation, or emotional fulfillment. But either way, the payoff (or lack of it) gives agents the feedback they need to improve their performance: if they're going to be "adaptive" at all, they somehow have to keep the strategies that pay off well, and let the others die out.

This game analogy seemed to be true of any adaptive system. In economics the payoff is in money, in politics the payoff is in votes, and on and on. At some level, all these adaptive systems are fundamentally the same. And that meant, in turn, that all of them are fundamentally like checkers or chess: the space of possibilities is vast beyond imagining. An agent can learn to play the game better—that's what adaptation is, after all. But it has just about as much chance of finding the optimum, stable equilibrium point of the game as you or I have of solving chess.

you have a system exploring its way into an immense space of possibilities, with no realistic hope of ever finding the single "best" place to be. All evolution can do is look for improvements, not perfection.

how evolution could explore this immense space of possibilities and find useful combinations of genes—without having to search over every square inch of territory.

Allen Newell and Herbert Simon had been conducting a landmark study of human problem-solving since the mid-1950s.

Indeed, thought Holland, that's what this business of "emergence" was all about: building blocks at one level combining into new building blocks at a higher level. It seemed to be one of the fundamental organizing principles of the world. It certainly seemed to appear in every complex, adaptive system that you looked at. But why? This hierarchical, building-block structure of things is as commonplace as air. It's so widespread that we never think much about it. But when you do think about it, it cries out for an explanation: Why is the world structured this way? Well, there are actually any number of reasons. Computer programmers are taught to break things up into subroutines because small, simple problems are easier to solve than big, messy problems; it's simply the ancient principle of divide and conquer. Large creatures such as whales and redwoods are made of trillions of tiny cells because the cells came first; when large plants and animals first appeared on Earth some 570 million years ago, it was obviously easier for natural selection to bring together the single-celled creatures that already existed than to build big new blobs of protoplasm from scratch. General Motors is organized into several zillion divisions and subdivisions because the CEO doesn't want to have half a million employees reporting to him directly; there aren't enough hours in the day. In fact, as Herbert Simon had pointed out in the 1940s and 1950s in his studies of business organizations, a well-...

cognitive building blocks, which include such concepts as red, car, and road. Once a set of building blocks like this has been tweaked and refined and thoroughly debugged through experience, says Holland, then it can generally be adapted and recombined to build a great many new concepts—say, "A red Saab by the side of the road." Certainly that's a much more efficient way to create something new than starting all over from scratch. And that fact, in turn, suggests a whole new mechanism for adaptation in general. Instead of moving through that immense space of possibilities step by step, so to speak, an adaptive system can reshuffle its building blocks and take giant leaps.

"So if I have a process that can discover building blocks," says Holland, "the combinatorics start working for me instead of against me. I can describe a great many complicated things with relatively few building blocks."

What are the building blocks of an orgnisation. Or an eduction system?

Michael Cohen, another political scientist, specializing in the social dynamics of human organizations; and

"Think of the system as a kind of office," says Holland. "The bulletin board contains the memos that are to be processed that day, and each rule corresponds to a desk in that office that has responsibility for memos of a given kind. At the beginning of the day, each desk collects the memos for which it is responsible. And at the end of the day, each desk posts the memos that result from its activities." In the morning, of course, the cycle repeats. In addition, he says, some of the memos may be posted by detectors, which keep the system up to date about what's going on in the outside world. And still other memos may activate effectors, subroutines that allow the system to affect the outside world. Detectors and effectors are the computer analog of eyes and muscles, says Holland. So, in principle, a rule-based system can easily get feedback from its environment—one of his prime requirements.

"As I look back on it, I think Ken made the right decision," says Eugenia Singer, who had originally been disappointed at Arrow's failure to include sociologists and psychologists in the group. "He had the most highly, technically trained economists he could get. And as a result, there was a credibility that was built. The physical scientists were amazed at their technical background. They were familiar with a lot of the technical concepts, even some of the physical models. So they were able to start using common terms and building a language they could talk to each other in. But if they had gotten a lot of social scientists in there with no technical background, I'm not sure the gulf could have been crossed.

Ecosystems, economies, societies—they all operate according to a kind of Darwinian principle of relativity: everyone is constantly adapting to everyone else. And because of that, there is no way to look at any one agent and say, "It's fitness is 1.375." Whatever "fitness" means—and biologists have been arguing about that since the time of Darwin—it cannot be a single, fixed number. That's like asking if a gymnast is a better or worse athlete than a sumo wrestler; the question is meaningless because there's no common scale to measure them. Any given organism's ability to survive and reproduce depends on what niche it is filling, what other organisms are around, what resources it can gather, even what its past history has been. "That shift in viewpoint is very important," says Holland. Indeed, evolutionary biologists consider it so important that they've made up a special word for it: organisms in an ecosystem don't just evolve, they coevolve. Organisms don't change by climbing uphill to the highest peak of some abstract fitness landscape, the way biologists of R. A. Fisher's generation had it. (The fitness-maximizing organisms of classical population genetics actually look a lot like the utility-maximizing agents of neoclassical economics.) Real organisms constantly circle and chase one another in an infinitely complex dance of coevolution. On the face of it, coevolution sounds like a recipe for chaos, says Holland. At the institute, Stuart Kauffman liked to compare it to c...