Natural Order - Complexity - Visions of the Whole

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The universe started out from the formless miasma of the Big Bang. And ever since then it's been governed by an inexorable tendency toward disorder, dissolution, and decay, as described by the second law of thermodynamics. Yet the universe has also managed to bring forth structure on every scale: galaxies, stars, planets, bacteria, plants, animals, and brains. How? Is the cosmic compulsion for disorder matched by an equally powerful compulsion for order, structure, and organization? And if so, how can both processes be going on at once?

At first glance, about the only thing that these questions have in common is that they all have the same answer: "Nobody knows." Some of them don't even seem like scientific issues at all. And yet, when you look a little closer, they actually have quite a lot in common. For example, every one of these questions refers to a system that is complex, in the sense that a great many independent agents are interacting with each other in a great many ways. Think of the quadrillions of chemically reacting proteins, lipids, and nucleic acids that make up a living cell, or the billions of interconnected neurons that make up the brain, or the millions of mutually interdependent individuals who make up a human society.

In every case, moreover, the very richness of these interactions allows the system as a whole to undergo spontaneous self-organization. Thus people trying to satisfy their material needs unconsciously organize themselves into an economy through myriad individual acts of buying and selling; it happens without anyone being in charge or consciously planning it. The genes in a developing embryo organize themselves in one way to make a liver cell and in another way to make a muscle cell. Flying birds adapt to the actions of their neighbors, unconsciously organizing themselves into a flock. Organisms constantly adapt to each other through evolution, thereby organizing themselves into an exquisitely tuned ecosystem. Atoms search for a minimum energy state by forming chemical bonds with each other, thereby organizing themselves into structures known as molecules. 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. They actively try to turn whatever happens to their advantage. Thus, the human brain constantly organizes and reorganizes its billions of neural connections so as to learn from experience (sometimes, anyway). Species evolve for better survival in a changing environment—and so do corporations and industries. And the marketplace responds to changing tastes and lifestyles, immigration, technological developments, shifts in the price of raw materials, and a host of other factors.

Finally, every one of these complex, self-organizing, adaptive systems possesses a kind of dynamism that makes them qualitatively different from static objects such as computer chips or snowflakes, which are merely complicated. Complex systems are more spontaneous, more disorderly, more alive than that. At the same time, however, their peculiar dynamism is also a far cry from the weirdly unpredictable gyrations known as chaos. In the past two decades, chaos theory has shaken science to its foundations with the realization that very simple dynamical rules can give rise to extraordinarily intricate behavior; witness the endlessly detailed beauty of fractals, or the foaming turbulence of a river. And yet chaos by itself doesn't explain the structure, the coherence, the self-organizing cohesiveness of complex systems.

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. 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 where centuries of slavery and segregation suddenly give way to the civil rights movement of the 1950s and 1960s; where seventy years of Soviet communism suddenly give way to political turmoil and ferment; where eons of evolutionary stability suddenly give way to wholesale species 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.

Complexity, adaptation, upheavals at the edge of chaos—these common themes are so striking that a growing number of scientists are convinced that there is more here than just a series of nice analogies. 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. (Seminars were held in what used to be the chapel.) The researchers who gather there are an eclectic bunch, ranging from pony-tailed graduate students to Nobel laureates such as Murray Gell-Mann and Philip Anderson in physics and Kenneth Arrow in economics. But they all share the vision of an underlying unity, a common theoretical framework for complexity that would illuminate nature and humankind alike. They believe that they have in hand the mathematical tools to create such a framework, drawing from the past twenty years of intellectual ferment in such fields as neural networks, ecology, artificial intelligence, and chaos theory. They believe that their application of these ideas is allowing them to understand the spontaneous self-organizing dynamics of the world in a way that no one ever has before— with the potential for immense impact on the conduct of economics, business, and even politics. 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.

COMPLEXITY

Master of the Game winners by lottery, with the highest probability of winning going to the highest bidders. The chosen classifiers would post their messages, and the cycle would repeat.  Complex? Holland couldn't deny it. As things stood, moreover, the auction simply replaced arbitrary conflict resolution strategies with arbitrary plausibility values. But assuming for the moment that the system could. somehow learn these plausibility values from experience, then the auction would eliminate the central arbiter and give Holland exactly what he wanted. Not every classifier could win: the bulletin board was big, not infinite. Nor would the race always go to the swift: even Elvis might get a chance to post his message if he got a lucky break. But on the average, control over the system's behavior would automatically be given to the strongest and most plausible hypotheses, with off-the-wall hypotheses appearing just often enough to give the system a little spontaneity. And if some of those hypotheses were inconsistent, well, that shouldn't be a crisis but an opportunity, a chance for the system to learn from experience which ones are more plausible.

So once again, it all came back to learning: How were the classifiers supposed to prove their worth and earn their plausibility values?
To Holland, the obvious answer was to implement a kind of Hebbian reinforcement. Whenever the agent does something right and gets a positive feedback from the environment, it should strengthen the classifiers responsible. Whenever it does something wrong, it should likewise weaken the classifiers responsible. And either way, it should ignore the classifiers that were irrelevant.

The trick, of course, was to figure out which classifiers were which. The agent couldn't just reward the classifiers that happen to be active at the moment of payoff. That would be like giving all the credit for a touchdown to the player who happened to carry the ball across the goal line—and none to the quarterback who called the play and passed him the ball, or to the linemen who blocked the other team and opened up a gap for him to run through, or to anyone who carried the ball in previous plays. It would be like giving all the credit for a victory in chess to the final move that trapped your opponent's king, and none to the crucial gambit many moves before that set up your whole endgame. And yet, what was the alternative? If the agent had to anticipate the payoff in order to reward the correct classifiers, how was it supposed to do so without being preprogrammed? How was it supposed to learn the value of these stage-setting moves without knowing about them already?

Good questions. Unfortunately, the general idea of Hebbian reinforcement was too broad-brush to provide any answers. Holland was at a loss— until one day he happened to think back on the basic economics course he'd taken at MIT from Paul Samuelson, author of the famous economics textbook, and realized that he'd almost solved the problem already. By auctioning off space on the bulletin board, he had created a kind of marketplace within the system. By allowing the classifiers to bid on the basis of their strength, he had created a currency. So why not take the next step? Why not create a full-fledged free-market economy, and allow the reinforcement to take place through the profit motive?

Why not, indeed? The analogy was obvious when you finally saw it. If you thought of the messages posted on the bulletin board as being goods and services up for sale, Holland realized, then you could think of the classifiers as being firms that produce those goods and services. And when a classifier sees a message satisfying its if-conditions and makes a bid, then you could think of it as a firm trying to purchase the supplies it needs to make its product. All he had to do to make the analogy perfect was to arrange for each classifier to pay for the supplies it used. When a classifier won the right to post its message, he decided, it would transfer some of its strength to its suppliers: namely, the classifiers responsible for posting the messages that triggered it. In the process, the classifier would then be weakened. But it would have a chance to recoup its strength and even make a profit during the next round of bidding, when its own message went on the market.

And where would the wealth ultimately come from? From the final consumer, of course: the environment, the source of all payoffs to the system. Except that now, Holland realized, it would be perfectly all right to reward the classifiers that happen to be active at the moment of payoff. Since each classifier pays its suppliers, the marketplace will see to it that the rewards propagate through the whole collection of classifiers and produce exactly the kind of automatic reward and punishment he was looking for. "If you produce the right intermediate product, then you'll make a profit," he says. "If not, then nobody will buy it and you'll go bankrupt." All the classifiers that lead to effective action will be strengthened, and yet none of the stage-setting classifiers will be neglected. Over time, in fact, as the system gains experience and gets feedback from the environment, the strength of each classifier will come to match its true value to the agent.
Holland dubbed this portion of his adaptive agent the "bucket-brigade" algorithm because of the way it passed reward from each classifier to the previous classifier. It was directly analogous to the strengthening of synapses in Hebb's theory of the brain—or, for that matter, to the kind of reinforcement used to train a simulated neural network in a computer. And when he had it, Holland knew he was almost home. Economic reinforcement via the profit motive was an enormously powerful organizing force, in much the same way that Adam Smith's Invisible Hand was enormously powerful in the real economy. In principle, Holland realized, you could start the system off with a set of totally random classifiers, so that the agent just thrashed around like the software equivalent of a newborn baby. And then, as the environment reinforced certain behaviors and as the bucket brigade did its work, you could watch the classifiers organize themselves into coherent sequences that would produce at least a semblance of the desired behavior. Learning, in short, would be built into the system from the beginning.

So, Holland was almost home—but not quite. By constructing the bucket brigade algorithm on top of the basic rule-based system, Holland had given his adaptive agent one form of learning. But there was another form still missing. It was the difference between exploitation and exploration. The bucket-brigade algorithm could strengthen the classifiers that the agent already possessed. It could hone the skills that were already there. It could consolidate the gains that had already been made. But it couldn't create anything new. By itself, it could only lead the system into highly optimized mediocrity. It had no way to explore the immense space of possible new classifiers .

This, Holland decided, was a job for the genetic algorithm. When you thought about it, in fact, the Darwinian metaphor and the Adam Smith metaphor fit together quite nicely: Firms evolve over time, so why shouldn't classifiers?

Holland certainly wasn't surprised by this insight; he'd had the genetic algorithm in the back of his mind all along. He'd been thinking about it when he first set up the binary representation of classifiers. A classifier might be paraphrased in English as something like, "If there are two messages with the patterns 1###0#00 and 0#00####, then post the message 01110101." In the computer, however, its various parts would be concatenated together and written simply as a string of bits: "1###0#000#00####01110101." And to the genetic algorithm, that looked just like a digital chromosome. So the algorithm could be carried out in exactly the same way. Most of the time, the classifiers would merrily buy and sell in their digital marketplace as before. But every so often, the system would select a pair of the strongest classifiers for reproduction. These classifiers would reshuffle their digital building blocks by sexual exchange to produce a pair of offspring. The offspring would replace a pair of weak classifiers. And then the offspring would have a chance to prove their worth and grow stronger through the bucket-brigade algorithm.

The upshot was that the population of rules would change and evolve over time, constantly exploring new regions of the space of possibilities. And there you would have it: by adding the genetic algorithm as a third layer on top of the bucket brigade and the basic rule-based system, Holland could make an adaptive agent that not only learned from experience but could be spontaneous and creative.

And all he had to do was to turn it into a working program.

Holland started coding the first classifier system around 1977. And oddly enough, it didn't turn out to be as straightforward a job as he had hoped. "I really thought that in a couple of months I'd have something up and running that was useful to me," he says. "Actually, it was the better part of a year before I was fully satisfied."

On the other hand, he didn't exactly make things easy for himself. He coded that first classifier system in true Holland style: by himself. At home. In hexadecimal code, the same kind that he'd written for the Whirlwind thirty years earlier. On a Commodore home computer.
Holland's BACH colleagues still roll their eyes when they tell this story. The whole campus was crawling with computers: VAXs, mainframes, even high-powered graphics workstations. Why a Commodore? And hex! Almost nobody wrote in hex anymore. If you were really a hard-core computer jock trying to squeeze the last ounce of performance out of a machine, you might write in something called assembly language, which at least replaced the numbers with mnemonics like MOV, JMZ, and SUB. Otherwise, you went with a high-level language such as PASCAL, C, FORTRAN, or LISP—something that a human being could hope to understand. Cohen, in particular, remembers arguing long and hard with Holland: Who's going to believe that this thing works if it's written in alphanumeric gibberish? And even if anybody does believe you, who's going to use a classifier system if it only runs on a home computer?
Holland eventually had to concede the point—although it was well into the early 1980s before he agreed to hand over the classifier system code to a graduate student, Rick Riolo, who transformed it into a general-purpose senses the analogies, but it's more difficult to make them precise," he says. "That's another area where somebody needs to do some careful cross comparisons, analogous to the Rosetta Stone paper."

Meanwhile, says Farmer, it's even less clear whether the edge-of-chaos idea applies to coevolutionary systems. When you get to something like an ecosystem or an economy, he says, it's not obvious how concepts like order, chaos, and complexity can even be defined very precisely, much less a phase transition between them. Nonetheless, he says, there's something about the edge-of-chaos principle that still feels right. Take the former Soviet Union, he says: "It's now pretty clear that the totalitarian, centralized approach to the organization of society doesn't work very well." In the long run, the system that Stalin built was just too stagnant, too locked in, too rigidly controlled to survive. Or look at the Big Three auto makers in Detroit in the 1970s. They had grown so big and so rigidly locked in to certain ways of doing things that they could barely recognize the growing challenge from Japan, much less respond to it.

On the other hand, says Farmer, anarchy doesn't work very well, either— as certain parts of the former Soviet Union seemed determined to prove in the aftermath of the breakup. Nor does an unfettered laissez-faire system: witness the Dickensian horrors of the Industrial Revolution in England or, more recently, the savings and loan debacle in the United States. Common sense, not to mention recent political experience, suggests that healthy economies and healthy societies alike have to keep order and chaos in balance—and not just a wishy-washy, average, middle-of-the road kind of balance, either. Like a living cell, they have to regulate themselves with a dense web of feedbacks and regulation, at the same time that they leave plenty of room for creativity, change, and response to new conditions. "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.

The Growth of Complexity

In any case, says Farmer, "at a vague, heuristic level we think we know something about the domain where this interesting organizational phenominum…

Shortly before Christmas of 1989, as Brian Arthur drove west from Santa Fe with a car packed full of books and clothes for his return home to Stanford, he found himself staring straight into a spectacular New Mexico sunset that bathed the desert in a vast red glow. "I thought, 'This is too bloody romantic to be true!' " he laughs.

But appropriate. "I had been at the institute just about eighteen months at that time," he says, "and I felt that I needed to go home—to write, and think, and get things clear in my mind. I was just loaded down with ideas. I'd felt that I was learning at Santa Fe more in a month than I would have in a year at Stanford. The experience had almost been too rich. And yet it was a wrench to leave. I felt very, very, very sad, in a good way, and very nostalgic. The whole scene—the desert, the light, the sunset—brought home to me that those eighteen months might well have been the high point of my scientific life, and they were over. That time would not be easily recaptured. I knew other people would come and follow up. I knew I could probably go back—even go back and run the economics program again in some future years. But I suspected that the institute might never be the same. I felt lucky to have been in on a golden time."
The Tao of Complexity

Three years later, sitting in his corner office overlooking the tree-shaded waldways of Stanford University, the Dean and Virginia Morrison Professor of Population Studies and Economics admits that he still hasn't gotten the Santa Fe experience completely clear in his mind. "I'm beginning to appreciate it more as time passes, " says Arthur. "But I think the story of what's been accomplished in Santa Fe is still very much unfolding."

Fundamentally, he says, he's come to realize that the Santa Fe Institute was and is a catalyst for changes that would have taken place in any case— but much more slowly. Certainly that was the case for the economics program, which continued after his departure under the joint directorship of Minnesota's David Lane and Yale's John Geanakoplos. "By about 1985," says Arthur, "it seems to me that all sorts of economists were getting antsy, starting to look around and sniff the air. They sensed that the conventional neoclassical framework that had dominated over the past generation had reached a high water mark. It had allowed them to explore very thoroughly the domain of problems that are treatable by static equilibrium analysis. But it had virtually ignored the problems of process, evolution, and pattern formation—problems where things were not at equilibrium, where there's a lot of happenstance, where history matters a great deal, where adaptation and evolution might go on forever. Of course, the field had kind of gotten stymied by that time, because theories were not held to be theories in economics unless they could be fully mathematized, and people only knew how to do that under conditions of equilibrium. And yet some of the very best economists were sensing that there had to be other things going on and other directions that the subject could go in.

"What Santa Fe did was to act as a gigantic catalyst for all that. It was a place where very good people—people of the caliber of Frank Hahn and Ken Arrow—could come and interact with people like John Holland and Phil Anderson, and over a period of several visits there realize, Yes! We can deal with inductive learning rather than deductive logic, we can cut the Gordian knot of equilibrium and deal with open-ended evolution because many of these problems have been dealt with by other disciplines. Santa Fe provided the jargon, the metaphors, and the expertise that you needed in order to get the techniques started in economics. But more than that, Santa Fe legitimized this different vision of economics. Because when word got around that people like Arrow and Hahn and Sargent and others were writing papers of this sort, then it became perfectly reasonable and perfectly kosher for others to do so."

Arthur sees evidence for that development every time he goes to an economics meeting these days. "The people who were interested in process and change in the economy were there all along," he says. Indeed, many of the essential ideas were championed by the great Austrian economist Joseph Schumpeter as far back as the 1920s and 1930s. "But my sense is that in the past four or five years, the people who think this way have gotten much more confident. They aren't apologetic any more about just being able to give wordy, qualitative descriptions of economic change. Now they're armed. They have technique. They form a growing movement that is becoming part of the neoclassical mainstream everywhere."

That movement has certainly made his own life easier, notes Arthur. His ideas on increasing returns, once virtually unpublishable, now have a following. He finds himself getting invitations to give this or that distinguished lecture in far-off places. In 1989 he was invited to write a feature article on increasing-returns economics for Scientific American. "That was one of the biggest thrills," he says. And that article, published in February 1990, helped him become a co-winner of the International Schumpeter Society's 1990 Schumpeter Prize for the best research on evolutionary economics.

For Arthur, however, the most gratifying assessment of the Santa Fe approach came in September 1989, as Ken Arrow was summarizing a big, week-long workshop that had reviewed the program's progress to date. At the time, ironically, Arthur barely heard what Arrow was saying. That l noontime, he says, as he'd headed out the front door of the convent on his way to lunch, he'd managed to trip and sprain his ankle terribly. He'd spent that whole afternoon in the convent's chapel-turned-conference room listening to the closing session of the workshop through a haze of pain, with his foot carefully wrapped by Dr. Kauffman and propped up with a bag of ice on the chair in front of him. In fact, the full impact of Arrow's words only hit him a few days later, after he'd defied all advice of doctors, colleagues, and wife and hobbled off to a long-planned conference in Irkutsk, on the shores of Lake Baikal in Siberia.

"It was one of these flashes of extreme clarity you get at three in the morning," he says. "The Aeroflot jet was just coming into Irkutsk, and i there was this guy riding a bicycle down the runway, waving a light stick to show us where to taxi. And when I thought about what Arrow had said in his closing summary, it finally struck home. He said, 'I think we can safely say we have another type of economics here. One type is the standard stuff that we're all familiar with'—he was too modest to call it the Arrow-Debreu system, but he basically meant the neoclassical, general equilibrium theory—'and then this other type, the Santa Fe-style evolutionary economics.' He made it clear that, to his mind, what the program had demonstrated in a year was that this was another valid way to do economics, equal in status to the traditional theory. It wasn't that the standard formulation was wrong, he said, but that we were exploring into a new way of looking at parts of the economy that are not amenable to conventional methods. So this new approach was complementary to the standard ones. He also said that we didn't know where this new sort of economics was taking us. It was the beginnings of a research program. But he found it very interesting and exciting.
"That pleased me enormously," says Arthur. "But Arrow said a second thing also. He compared the Santa Fe program of research with the Cowles Foundation program that he had been associated with in the early 1950s. And he said that the Santa Fe approach seemed to be much more accepted at this stage, given that it's now at most two years old, than the Cowles Foundation group had been at the same point. Well, I was amazed to hear that, and tremendously flattered. Because the Cowles Foundation people were the Young Turks of their day—Arrow, Koopmans, Debreu, Klein, Hurwicz, et cetera. Four of them got Nobel Prizes, with maybe a few more to come. They were the people who mathematized economics. They were the people who had set the agenda for the following generations. They were the people who had actually revolutionized the field."

From the Santa Fe Institute's point of view, of course, this effort to catalyze a sea change in economics is only a part of its effort to catalyze the complexity revolution in science as a whole. That quest may yet prove quixotic, says Arthur. But nonetheless, he's convinced that George Cowan, Murray Gell-Mann, and the others have gotten hold of exactly the right set of issues.

"Nonscientists tend to think that science works by deduction," he says. "But actually science works mainly by metaphor. And what's happening is that the kinds of metaphor people have in mind are changing." To put it in perspective, he says, think of what happened to our view of the world with the advent of Sir Isaac Newton. "Before the seventeenth century," he says, "it was a world of trees, disease, human psyche, and human behavior. It was messy and organic. The heavens were also complex. The trajectories of the planets seemed arbitrary. Trying to figure out what was going on in the world was a matter of art. But then along comes Newton in the 1660s. He devises a few laws, he devises the differential calculus—and suddenly the planets are seen to be moving in simple, predictable orbits!

"This had an incredibly profound effect on people's psyche, right up to the present," says Arthur. "The heavens—the habitat of God—had been explained, and you didn't need angels to push things around anymore. You didn't need God to hold things in place. So in the absence of God, the age became more secular. And yet, in the face of snakes and earthquakes, storms and plagues, there was still a profound need to know that something had it all under control. So in the Enlightenment, which lasted from about 1680 all through the 1700s, the era shifted to a belief in the primacy of nature: if you just left things alone, nature would see to it that everything worked out for the common good."

The metaphor of the age, says Arthur, became the clockwork motion of the planets: a simple, regular, predictable Newtonian machine that would run of itself. And the model for the next two and a half centuries of reductionist science became Newtonian physics. "Reductionist science tends to say, 'Hey, the world out there is complicated and a mess—but look! Two or three laws reduce it all to an incredibly simple system!'

"So all that remained was for Adam Smith, at the height of the Scottish Enlightenment around Edinburgh, to understand the machine behind the economy," says Arthur. "In 1776, in The Wealth of Nations, he made the case that if you left people alone to pursue their individual interests, the 'Invisible Hand' of supply and demand would see to it that everything, worked out for the common good." Obviously, this was not the whole story:. Smith himself pointed to such nagging problems as worker alienation and exploitation. But there was so much about his Newtonian view of the: economy that was simple and powerful and right that it has dominated Western economic thought ever since. "Smith's idea was so brilliant that it just dazzled us," says Arthur. "Once, long ago, the economist Kenneth Boulding asked me, 'What would you like to do in economics?' Being young and brash, I said very immodestly, 'I want to bring economics into the twentieth century.' He looked at me and said, 'Don't you think you should bring it into the eighteenth century first?' "

In fact, says Arthur, he feels that economics in the twentieth century has lagged about a generation behind a certain loss of innocence in all the sciences. As the century began, for example, philosophers such as Russell, i, Whitehead, Frege, and Wittgenstein set out to demonstrate that all of mathematics could be founded on simple logic. They were partly right.. Much of it can be. But not all: in the 1930s, the mathematician Kurt Godel showed that even some very simple mathematical systems—arithmetic, for example—are inherently incomplete. They always contain statements that cannot be proved true or false within the system, even in principle. At about the same time (and by using essentially the same argument), the logician Alan Turing showed that even very simple computer programs can be undecidable: you can't tell in advance whether the computer will reach an answer or not. In the 1960s and 1970s, physicists got much the same message from chaos theory: even very simple equations can produce results that are surprising and essentially unpredictable. Indeed, says Arthur, that message has been repeated in field after field. "People realized that logic and philosophy are messy, that language is messy, that chemical kinetics is messy, that physics is messy, and finally that the economy is naturally messy. And it's not that this is a mess created by the dirt that's on the microscope glass. It's that this mess is inherent in the systems themselves. You can't capture any of them and confine them to a neat box of logic."

The result, says Arthur, has been the revolution in complexity. "In a sense it's the opposite of reductionism. The complexity revolution began the first time someone said, 'Hey, I can start with this amazingly simple system, and look—it gives rise to these immensely complicated and unpredictable consequences. ' " Instead of relying on the Newtonian metaphor of clockwork predictability, complexity seems to be based on metaphors more closely akin to the growth of a plant from a tiny seed, or the unfolding of a computer program from a few lines of code, or perhaps even the organic, self-organized flocking of simpleminded birds. That's certainly the kind of metaphor that Chris Langton has in mind with artificial life: his whole point is that complex, lifelike behavior is the result of simple rules unfolding from the bottom up. And it's likewise the kind of metaphor that influenced Arthur in the Santa Fe economics program: "If I had a purpose, or a vision, it was to show that the messiness and the liveliness in the economy can grow out of an incredibly simple, even elegant theory. That's why we created these simple models of the stock market where the market appears moody, shows crashes, takes off in unexpected directions, and acquires something that you could describe as a personality."

While he was actually at the institute, ironically, Arthur had almost no time at all for Chris Langton's artificial life, or the edge of chaos, or the hypothetical new second law. The economics program was taking up 110 percent of his workday as it was. But what he did hear he found fascinating. It seemed to him that artificial life and the rest captured something essential about the spirit of the institute. "Martin Heidegger once said that the fundamental philosophical question is being," notes Arthur. "What are we doing here as conscious entities? Why isn't the universe just a turbulent mess of particles tumbling around each other? Why are there structure, form, and pattern? Why is consciousness possible at all?" Very few people at the institute were grappling with that problem quite as directly as Langton, Kauffman, and Farmer were. But in one way or another, says Arthur, he sensed that everyone was working on a piece of it.
Furthermore, he felt that the ideas resonated strongly with what he and his coconspirators were trying to accomplish in economics. When you look at the subject through Chris Langton's phase transition glasses, for example, all of neoclassical economics is suddenly transformed into a simple assertion that the economy is deep in the ordered regime, where the market is always in equilibrium and things change slowly if at all. The Santa Fe approach is likewise transformed into a simple assertion that the economy is at the edge of chaos, where agents are constantly adapting to each other and things are always in flux. Arthur always knew which assertion he thought was more realistic.

Like other Santa Fe folk, Arthur is hesitant when it comes to speculating about the larger meaning of all this. The results are still so—embryonic. And it's entirely too easy to come off sounding New Age and flaky. But like everyone else, he can't help thinking about the larger meaning.

You can look at the complexity revolution in almost theological terms, I he says. "The Newtonian clockwork metaphor is akin to standard Protestantism. Basically there's order in the universe. It's not that we rely on God for order. That's a little too Catholic. It's that God has arranged the world so that the order is naturally there if we behave ourselves. If we act as individuals in our own right, if we pursue our own righteous self-interest and work hard, and don't bother other people, then the natural equilibrium :, of the world will assert itself. Then we get the best of all possible worlds— the one we deserve. That's probably not quite theological, but it's the impression I have of one brand of Christianity.

"The alternative—the complex approach—is total Taoist. In Taoism there is no inherent order. 'The world started with one, and the one became two, and the two became many, and the many led to myriad things.' The universe in Taoism is perceived as vast, amorphous, and ever-changing. You can never nail it down. The elements always stay the same, yet they're always rearranging themselves. So it's like a kaleidoscope: the world is a matter of patterns that change, that partly repeat, but never quite repeat, that are always new and different.

"What is our relation to a world like that? Well, we are made of the same elemental compositions. So we are a part of this thing that is never changing and always changing. If you think that you're a steamboat and can go up the river, you're kidding yourself. Actually, you're just the captain of a paper boat drifting down the river. If you try to resist, you're not going to get anywhere. On the other hand, if you quietly observe the flow, realizing that you're part of it, realizing that the flow is ever-changing and always leading to new complexities, then every so often you can stick an oar into the river and punt yourself from one eddy to another.
"So what's the connection with economic and political policy? Well, in a policy context, it means that you observe, and observe, and observe, and occasionally stick your oar in and improve something for the better. It means that you try to see reality for what it is, and realize that the game you are in keeps changing, so that it's up to you to figure out the current rules of the game as it's being played. It means that you observe the Japanese like hawks, you stop being naive, you stop appealing for them to play fair, you stop adhering to standard theories that are built on outmoded assumptions about the rules of play, you stop saying, 'Well, if only we could reach this equilibrium we'd be in fat city.' You just observe. And where you can make an effective move, you make a move."
Notice that this is not a recipe for passivity, or fatalism, says Arthur. "This is a powerful approach that makes use of the natural nonlinear dynamics of the system. You apply available force to the maximum effect. You don't waste it. This is exactly the difference between Westmoreland's approach in South Vietnam versus the North Vietnamese approach. Westmoreland would go in with heavy forces and artillery and barbed wire and burn the villages. And the North Vietnamese would just recede like a tide. Then three days later they'd be back, and no one knew where they came from. It's also the principle that lies behind all of Oriental martial arts. You don't try to stop your opponent, you let him come at you—and then give him a tap in just the right direction as he rushes by. The idea is to observe, to act courageously, and to pick your timing extremely well."

Arthur is reluctant to get into the implications of all this for policy issues. But he does remember one small workshop that Murray Gell-Mann persuaded him to cochair in the fall of 1989, shortly before he left the institute. The purpose of the workshop was to look at what complexity might have to say about the interplay of economics, environmental values, and public policy in a region such as Amazonia, where the rain forest is being cleared for roads and farms at an alarming rate. The answer Arthur gave during his own talk was that you can approach policy-making for the rain forest (or for any other subject) on three different levels.

The first level, he says, is the conventional cost-benefit approach: What are the costs of each specific course of action, what are the benefits, and how do you achieve the optimum balance between the two? "There is a place for that kind of science," says Arthur. "It does force you to think through the implications of the alternatives. And certainly at that meeting we had a number of people arguing the costs and benefits of rain forests. The trouble is that this approach generally assumes that the problems are well defined, that the options are well defined, and that the political wherewithal is there, so that the analyst's job is simply to put numbers on the costs and benefits of each alternative. It's as though the world were a railroad switch yard: We're going down this one track, and we have switches we can turn to guide the train onto other tracks." Unfortunately for the standard theory, however, the real world is almost never that well defined—particularly when it comes to environmental issues. All too often, the apparent objectivity of cost-benefit analyses is the result of slapping arbitrary numbers ; on subjective judgments, and then assigning the value of zero to the things that nobody knows how to evaluate. "I ridicule some of these cost-benefit analyses in my classes," he says. "The 'benefit' of having spotted owls is ' defined in terms of how many people visit the forest, how many will see a spotted owl, and what's it worth to them to see a spotted owl, et cetera. It's all the greatest rubbish. This type of environmental cost-benefit analysis ; makes it seem as though we're in front of the shop window of nature looking in, and saying, 'Yes, we want this, or this, or this'—but we're not inside, we're not part of it. So these studies have never appealed to me. By asking only what is good for human beings, they are being presumptuous and arrogant.

The second level of policy-making is a full institutional-political analysis, says Arthur: figuring out who's doing what, and why. "Once you start to: do that for, say, the Brazilian rain forest, you find that there are various players: landowners, settlers, squatters, politicians, rural police, road builders, indigenous peoples. They aren't out to get the environment, but they are all playing this elaborate, interactive Monopoly game, in which the environment is being deeply affected. Moreover, the political system isn't some exogenous thing that stands outside the game. The political system is actually an outcome of the game—the alliances and coalitions that form as a result of it."

In short, says Arthur, you look at the system as a system, the way a Taoist in his paper boat would observe the complex, ever-changing river. Of course, a historian or a political scientist would look at the situation this way instinctively. And some beautiful studies in economics have recently started to take this approach. But at the time of the workshop in 1989, he says, the idea still seemed to be a revelation to many economists. "In my. talk I put in a strong plea for this kind of analysis," he says. "If you really want to get deeply into an environmental issue, I told them, you have to ask these questions of who has what at stake, what alliances are likely to form, and basically understand the situation. Then you might find certain points at which intervention may be possible.
"So all of that is leading up to the third level of analysis," says Arthur. "At this level we might look at what two different world views have to say about environmental issues. One of these is the standard equilibrium viewpoint that we've inherited from the Enlightenment—the idea that there's a duality between man and nature, and that there's a natural equilibrium between them that's optimal for man. And if you believe this view, then you can talk about 'the optimization of policy decisions concerning environmental resources,' which was a phrase I got from one of the earlier speakers at the workshop.
"The other viewpoint is complexity, in which there is basically no duality between man and nature," says Arthur. "We are part of nature ourselves We're in the middle of it. There's no division between doers and done-to because we are all part of this interlocking network. If we, as humans, try to take action in our favor without knowing how the overall system will adapt—like chopping down the rain forest—we set in motion a train of events that will likely come back and form a different pattern for us to adjust to, like global climate change.

"So once you drop the duality," he says, "then the questions change. You can't then talk about optimization, because it becomes meaningless. It would be like parents trying to optimize their behavior in terms of 'us versus the kids,' which is a strange point of view if you see yourself as a family. You have to talk about accommodation and coadaptation—what would be good for the family as a whole.

"Basically, what I'm saying is not at all new to Eastern philosophy. It's never seen the world as anything else but a complex system. But it's a world view that, decade by decade, is becoming more important in the West— both in science and in the culture at large. Very, very slowly, there's been a gradual shift from an exploitative view of nature—man versus nature— to an approach that stresses the mutual accommodation of man and nature. What has happened is that we're beginning to lose our innocence, or naiveté, about how the world works. As we begin to understand complex systems, we begin to understand that we're part of an ever-changing, interlocking, nonlinear, kaleidoscopic world.

"So the question is how you maneuver in a world like that. And the answer is that you want to keep as many options open as possible. You go for viability, something that's workable, rather than what's 'optimal.' A lot of people say to that, 'Aren't you then accepting second best?' No, you're not, because optimization isn't well defined anymore. What you're trying to do is maximize robustness, or survivability, in the face of an ill-defined future. And that, in turn, puts a premium on becoming aware of nonlinear relationships and causal pathways as best we can. You observe the world very, very carefully, and you don't expect circumstances to last."

So what is the role of the Santa Fe Institute in all this? Certainly not to Y become another policy think tank, says Arthur, although there always seem to be a few people who expect it to. No, he says, the institute's role is to help us look at this ever-changing river and understand what we're seeing.

"If you have a truly complex system," he says, "then the exact patterns are not repeatable. And yet there are themes that are recognizable. In history, for example, you can talk about 'revolutions,' even though one revolution might be quite different from another. So we assign metaphors. It turns out that an awful lot of policy-making has to do with finding the appropriate metaphor. Conversely, bad policy-making almost always involves finding inappropriate metaphors. For example, it may not be appropriate to think about a drug 'war,' with guns and assaults.

"So from this point of view, the purpose of having a Santa Fe Institute is that it, and places like it, are where the metaphors and a vocabulary are ,i being created in complex systems. So if somebody comes along with a beautiful study on the computer, then you can say 'Here's a new metaphor. Let's call this one the edge of chaos,' or whatever. So what the SFI will do, if it studies enough complex systems, is to show us the kinds of patterns we might observe, and the kinds of metaphor that might be appropriate for systems that are moving and in process and complicated, rather than the metaphor of clockwork.

"So I would argue that a wise use of the SFI is to let it do science," he says. "To make it into a policy shop would be a great mistake. It would cheapen the whole affair. And in the end it would be counterproductive, because what we're missing at the moment is any precise understanding of how complex systems operate. This is the next major task in science for the next 50 to 100 years."

"I think there's a personality that goes with this kind of thing," Arthur says. "It's people who like process and pattern, as opposed to people who are comfortable with stasis and order. I know that every time in my life that I've run across simple rules giving rise to emergent, complex messiness I've just said, 'Ah, isn't that lovely!' And I think that sometimes, when other people run across it, they recoil."

In about 1980, he says, at a time when he was still struggling to articulate his own vision of a dynamic, evolving economy, he happened to read a book by the geneticist Richard Lewontin. And he was struck by a passage in which Lewontin said that scientists come in two types. Scientists of the first type see the world as being basically in equilibrium. And if untidy forces sometimes push a system slightly out of equilibrium, then they feel the whole trick is to push it back again. Lewontin called these scientists "Platonists," after the renowned Athenian philosopher who declared that the messy, imperfect objects we see around us are merely the reflections of perfect "archetypes."

Scientists of the second type, however, see the world as a process of flow and change, with the same material constantly going around and around in endless combinations. Lewontin called these scientists "Heraclitians," after the Ionian philosopher who passionately and poetically argued that the world is in a constant state of flux. Heraclitus, who lived nearly a century before Plato, is famous for observing that "Upon those who step into the same rivers flow other and yet other waters," a statement that Plato himself paraphrased as "You can never step into the same river twice."

"When I read what Lewontin said," says Arthur, "it was a moment of revelation. That's when it finally became clear to me what was going on. I thought to myself, 'Yes! We're finally beginning to recover from Newton. ' "

The Hair Shirt

Meanwhile, at about the same time that Brian Arthur was driving off into the sunset, the Heraclitian-in-chief back in Santa Fe was getting ready to call it quits. For all the undeniable success of the economics program, and for all the intellectual ferment over the edge of chaos, artificial life, and the rest, George Cowan was acutely aware that the institute's permanent endowment fund still stood at zero. And after six years, he was tired of constantly begging people for operating cash. He was tired of fretting over the economics program, lest it become the 800-pound gorilla that took over the institute. And speaking of 800-pound gorillas, he was tired of the endless contest of wills with Murray Gell-Mann to define what the Santa Fe Institute was all about—including, not incidentally, what the complexity revolution could tell us about building a more sustainable future for the human race. Cowan was just—tired. Now that he'd gotten the Santa Fe Institute up and running, he wanted to spend the time he had left in life working on the science of the institute, this strange new science of complexity. So at the first opportunity—the annual meeting of the institute's board of trustees in …

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