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

by M. Mitchell Waldrop

In every case, groups of agents seeking mutual accommodation and self-consistency somehow manage to transcend themselves, acquiring collective properties such as life, thought, and purpose that they might never have possessed individually. Furthermore, these complex, self-organizing systems are adaptive, in that they don't just passively respond to events the way a rock might roll around in an earthquake.

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. The edge of chaos is where life has enough stability to sustain itself and enough creativity to deserve the name of life.

They believe that they are forging the first rigorous alternative to the kind of linear, reductionist thinking that has dominated science since the time of Newton—and that has now gone about as far as it can go in addressing the problems of our modern world. They believe they are creating, in the words of Santa Fe Institute founder George Cowan, "the sciences of the twenty-first century." This is their story.

Why did the VHS video system run away with the market, even though Beta was technically a little bit better? Because a few more people happened to buy VHS systems early on, which led to more VHS movies in the video stores, which led to still more people buying VHS players, and so on. Them that has gets.

brought along for just such a moment: 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.

Such self-organizing structures are ubiquitous in nature, said Prigogine. A laser is a self-organizing system in which particles of light, photons, can spontaneously group themselves into a single powerful beam that has every photon moving in lockstep. A hurricane is a self-organizing system powered by the steady stream of energy coming in from the sun, which drives the winds and draws rainwater from the oceans. A living cell—although much too complicated to analyze mathematically—is a self-organizing system that survives by taking in energy in the form of food and excreting energy in the form of heat and waste. 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.

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.

Did British colonists flock to cold, stormy, rocky shores of Massachusetts Bay because New England had the best land for farms? No: They came because Massachusetts Bay was where the Pilgrims got off the boat, and the Pilgrims got off the boat there because the Mayflower got lost looking for Virginia. Them that has gets—and once the colony was established, there was no turning back. Nobody was about to pick up Boston and move it someplace else. Increasing returns, lock-in, unpredictability, tiny events that have immense historical consequences—"These properties of increasing-returns economics shocked me at first," says Arthur. "But when I recognized that each property had a counterpart in the nonlinear physics I was reading, I got very excited. Instead of being shocked, I became fascinated." Economists had actually been talking about such things for generations, he learned. But their efforts had always been isolated and scattered.

Old Economics New Economics •Decreasing returns •Much use of increasing returns •Based on 19th-century physics (equilibrium, stability, deterministic dynamics) •Based on biology (structure, pattern, self-organization, life cycle) •People identical •Focus on individual life; people separate and different •If only there were no externalities and all had equal abilities, we'd reach Nirvana •Externalities and differences become driving force. No Nirvana. System constantly unfolding. •Elements are quantities and prices •Elements are patterns and possibilities •No real dynamics in the sense that everything is at equilibrium •Economy is constantly on the edge of time. It rushes forward, structures constantly coalescing, decaying, changing. •Sees subject as structurally simple •Sees subject as inherently complex •Economics as soft physics •Economics as high-complexity science

Increasing returns isn't an isolated phenomenon at all: the principle applies to everything in high technology. Look at a software product like Microsoft's Windows, he says. The company spent $50 million in research and development to get the first copy out the door. The second copy cost it—what, $10 in materials? It's the same story in electronics, computers, pharmaceuticals, even aerospace. (Cost for the first B2 bomber: $21 billion. Cost per copy: $500 million.) High technology could almost be defined as "congealed knowledge," says Arthur. "The marginal cost is next to zilch, which means that every copy you produce makes the product cheaper and cheaper." More than that, every copy offers a chance for learning: getting the yield up on microprocessor chips, and so on. So there's a tremendous reward for increasing production—in short, the system is governed by increasing returns. Among high-tech customers, meanwhile, there's an equally large reward for flocking to a standard. "If I'm an airline buying a Boeing jet," says Arthur, "I want to make sure I buy a lot of them so that my pilots don't have to switch." By the same token, if you're an office manager, you try to buy all the same kind of personal computer so that everyone in the office can run the same software. The result is that high technologies very quickly tend to lock in to a relatively few standards: IBM and Macintosh in the personal computer world, or Boeing, McDonnell Douglas, and Lockheed in commercial passen...

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. So by advocating increasing returns, Arthur was innocently treading into a minefield.

It ought to be a place, in short, that could educate the kind of scientist that had proved all too rare after World War II: "a kind of twenty-first-century Renaissance man," says Cowan, "starting in science but able to deal with the real messy world, which is not elegant, which science doesn't really deal with."

This everything-else-is-chemistry nonsense breaks apart on the twin shoals of scale and complexity, he explains. Take water, for example. There's nothing very complicated about a water molecule: it's just one big oxygen atom with two little hydrogen atoms stuck to it like Mickey Mouse ears. Its behavior is governed by well-understood equations of atomic physics. But now put a few zillion of those molecules together in the same pot. Suddenly you've got a substance that shimmers and gurgles and sloshes. Those zillions of molecules have collectively acquired a property, liquidity, that none of them possesses alone. In fact, unless you know precisely where and how to look for it, there's nothing in those well-understood equations of atomic physics that even hints at such a property. The liquidity is "emergent." In much the same way, says Anderson, emergent properties often produce emergent behaviors. Cool those liquid water molecules down a bit, for example, and at 32°F they will suddenly quit tumbling over one another at random. Instead they will undergo a "phase transition," locking themselves into the orderly crystalline array known as ice. Or if you were to go the other direction and heat the liquid, those same tumbling water molecules will suddenly fly apart and undergo a phase transition into water vapor. Neither phase transition would have any meaning for one molecule alone. And so it goes, says Anderson. Weather is an emergent property: take your water vapor out over t...

This self-organization theme was also taken up in a quite different form by Stephen Wolfram of the Institute for Advanced Study, a twenty-five-year-old wunderkind from England who was trying to investigate the phenomenon of complexity at the most fundamental level. Indeed, he was already negotiating with the University of Illinois to found a Center for Complex Systems Research there. Whenever you look at very complicated systems in physics or biology, he said, you generally find that the basic components and the basic laws are quite simple; the complexity arises because you have a great many of these simple components interacting simultaneously. The complexity is actually in the organization—the myriad possible ways that the components of the system can interact.

In particular, the founding workshops made it clear that every topic of interest had at its heart a system composed of many, many "agents." These agents might be molecules or neurons or species or consumers or even corporations. But whatever their nature, the agents were constantly organizing and reorganizing themselves into larger structures through the clash of mutual accommodation and mutual rivalry. Thus, molecules would form cells, neurons would form brains, species would form ecosystems, consumers and corporations would form economies, and so on. At each level, new emergent structures would form and engage in new emergent behaviors. Complexity, in other words, was really a science of emergence. And the challenge that Cowan had been trying to articulate was to find the fundamental laws of emergence.

By the way, he said, he'd recently been up in New York at a meeting of the board of the Russell Sage Foundation, which gives away a lot of money for social science-type research. And while he was there he'd talked to a friend of his, John Reed, the new chief executive officer of Citicorp. Now, Reed was a pretty interesting guy, said Adams. He had just turned forty-seven, which made him one of the youngest CEOs in the country. He'd grown up in Argentina and Brazil, where his father had worked as an executive for Armour and Company. He had a bachelor's degree in liberal arts from Washington and Jefferson University, another bachelor's degree in metallurgy from MIT, and a master's degree in business from the Sloan School at MIT. He was very knowledgeable about science, and he genuinely seemed to enjoy kicking around ideas with the academic types at the Russell Sage board. Anyway, said Adams, during one of the coffee breaks he'd told Reed about the institute, as best as he could explain it, and Reed had been very interested. He certainly didn't have $100 million to give away. But he was wondering if the institute might help him understand the world economy. When it came to world financial markets, Reed had decided that professional economists were off with the fairies. Under Reed's predecessor, Walter Wriston, Citicorp had just taken a bath in the Third World debt crisis. The bank had lost $1 billion in profits in one year, and was still sitting on $13 billion of loans that mi...

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 and self-organization apply to the creation of living systems just as surely as they do to the formation of snowflakes or the appearance of convection cells in a simmering pot of soup. So the story of life is, indeed, the story of accident and happenstance, declared Kauffman. But it is also the story of order: a kind of deep, inner creativity that is woven into the very fabric of nature. "I love it," he says. "I do truly love it. My whole life has been an unfolding of this story."

"It wasn't that I didn't love philosophy. It's that I distrusted a certain facileness in it. Contemporary philosophers, or at least those of the 1950s and 1960s, took themselves to be examining concepts and the implications of concepts—not the facts of the world. So you could find out if your arguments were cogent, felicitous, coherent, and so on. But you couldn't find out if you were right. And in the end I felt dissatisfied with that."

It was a good time to be doing so: Jacob and Monod were publishing their first papers on genetic circuits in 1961 through 1963. It was the work for which they later won the Nobel Prize (and which Brian Arthur was to discover sixteen years later on the beach at Hauula). So Kauffman soon came across their work showing that any cell contains a number of "regulatory" genes that act as switches and can turn one another on and off. "That work was a revelation for all biologists. If genes can turn one another on and off, then you can have genetic circuits. Somehow, the genome has to be some kind of biochemical computer. It is the computing behavior—the orderly behavior—of this entire system that somehow governs how one cell can become different from another."

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.

"Technology A, B, and C might make possible technology D, and so on," says Arthur. "So there'd be a network of possible technologies, all interconnected and growing as more things became possible. And therefore the economy could become more complex." Moreover, these technological webs can undergo bursts of evolutionary creativity and massive extinction events, just like biological ecosystems. Say a new technology like the automobile comes in and replaces an older technology, the horse.