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

by M. Mitchell Waldrop

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. The edge of chaos is where life has enough stability to sustain itself and enough creativity to deserve the name of life. The edge of chaos is where new ideas and innovative genotypes are forever nibbling away at the edges of the status quo, and where even the most entrenched old guard will eventually be overthrown.

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.

U.S. policy-makers ought to be very careful about their economic assumptions regarding, say, trade policy vis-à-vis Japan. “If you’re using standard theory you can get it very badly wrong,” he says.

“Every democratic society has to solve a certain problem,” says Arthur: “If you let people do their own thing, how do you assure the common good? In Germany, that problem is solved by everybody watching everybody else out the windows. People will come right up to you and say, ‘Put a cap on that baby!’” In England, they have this notion of a body of wise people at the top looking after things. “Oh, yes, we’ve had this Royal Commission, chaired by Lord So-and-So. We’ve taken all your interests into account, and there’ll be a nuclear reactor in your backyard tomorrow.” But in the United States, the ideal is maximum individual freedom—or, as Arthur puts it, “letting everybody be their own John Wayne and run around with guns.” However much that ideal is compromised in practice, it still holds mythic power. But increasing returns cut to the heart of that myth. If small chance events can lock you in to any of several possible outcomes, then the outcome that’s actually selected may not be the best. And that means that maximum individual freedom—and the free market—might not produce the best of all possible worlds.

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.

all complex adaptive systems anticipate the future.

In short, complex adaptive systems are characterized by perpetual novelty. Multiple agents, building blocks, internal models, perpetual novelty—taking all this together, said Holland, it’s no wonder that complex adaptive systems were so hard to analyze with standard mathematics.

What captivated him wasn’t that science allowed you to reduce everything in the universe to a few simple laws. It was just the opposite: that 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.”

“By the middle of this century,” he wrote, “mankind had acquired the power to extinguish life on Earth. By the middle of the next century, he will be able to create it. Of the two, it is hard to say which places the larger burden of responsibility on our shoulders. Not only the specific kinds of living things that will exist, but the very course of evolution itself will come more and more under our control.”

If entropy is always increasing, he asked himself, and if atomic-scale randomness and disorder are inexorable, then why is the universe still able to bring forth stars and planets and clouds and trees? Why is matter constantly becoming more and more organized on a large scale, at the same time that it is becoming more and more disorganized on a small scale? Why hasn’t everything in the universe long since dissolved into a formless miasma?

“Evolution thrives in systems with a bottom-up organization, which gives rise to flexibility,” says Farmer. “But at the same time, evolution has to channel the bottom-up approach in a way that doesn’t destroy the organization. There has to be a hierarchy of control—with information flowing from the bottom up as well as from the top down.” The dynamics of complexity at the edge of chaos, he says, seems to be ideal for this kind of behavior.

“If we’re deep in the ordered regime,” he says, “then everybody is at a peak in fitness and we’re all mutually consistent—but these are lousy peaks.” Everybody is trapped in the foothills, so to speak, with no way to break loose and head for the crest of the range. In terms of human organizations, it’s as if the jobs are so subdivided that no one has any latitude; all they can do is learn how to perform the one job they’ve been hired for, and nothing else. Whatever the metaphor, however, it’s clear that if each individual in the various organizations is allowed a little more freedom to march to a different drummer, then everyone will benefit. The deeply frozen system will become a little more fluid, says Kauffman, the aggregate fitness will go up, and the agents will collectively move a bit closer to the edge of chaos.

“Religions try to impose rules of morality by writing them on stone tablets,” he says. “We do have a real problem now, because when we abandon conventional religion, we don’t know what rules to follow anymore. But when you peel it all back, religion and ethical rules provide a way of structuring human behavior in a way that allows a functioning society. My feeling is that all of morality operates at that level. It’s an evolutionary process in which societies constantly perform experiments, and whether or not those experiments succeed determines which cultural ideas and moral precepts propagate into the future.” If so, he says, then a theory that rigorously explains how coevolutionary systems are driven to the edge of chaos might tell us a lot about cultural dynamics, and how societies reach that elusive, ever-changing balance between freedom and control.

You have to talk about systems that remain continuously dynamic, and that are embedded in environments that themselves are continuously dynamic.” Stability, as John Holland says, is death; somehow, the world has to adapt itself to a condition of perpetual novelty, at the edge of chaos. “I still haven’t found the right words for that,” says Cowan. “Just recently I was toying with the title of Havelock Ellis’s book, The Dance of Life. But that isn’t quite right. It isn’t a dance. There’s not even a given tempo. So if anything we’re getting back to Heraclitus: ‘Everything Moves.’