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

by M. Mitchell Waldrop

But when it came to instability and change in the economy—well, they seemed to find the very idea disturbing, something they’d just as soon not talk about. But Arthur had embraced instability. Look out the window, he’d told his colleagues. Like it or not, the marketplace isn’t stable. The world isn’t stable. It’s full of evolution, upheaval, and surprise. Economics had to take that ferment into account.

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.

“What struck me,” he says, “was that if you went into one of these Alpine villages, it would have these ornate, Tyrolean roofs and balustrades and balconies, with characteristic pitches to the roofs, characteristic gables, and characteristic shutters on the windows. But rather than thinking that this was a nice jigsaw puzzle picture, I realized that there was not a single part of the village that wasn’t there for a purpose, and interconnected with the other parts. The pitches of the roofs had to do with what would keep the right amount of snow on the roof for insulation in the winter. The degree of overhang of the gables beyond the balconies had to do with keeping snow from falling on the balconies. So I used to amuse myself looking at the villages, thinking that this part has this purpose, that part has that purpose, and they were all interconnected.”

A love letter to systems

If the gas is off, then nothing happens. Just as the second law predicts, the soup will sit there at room temperature, in equilibrium with its surroundings. 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.

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.

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. And

Of course, they didn’t call it negative feedback. The dying-away tendency was implicit in the economic doctrine of “diminishing returns”: the idea that the second candy bar doesn’t taste nearly as good as the first one, that twice the fertilizer doesn’t produce twice the yield, that the more you do of anything, the less useful, less profitable, or less enjoyable the last little bit becomes. But

Arthur could see that the net effect was the same: just as negative feedback keeps small perturbations from running away and tearing things apart in physical systems, diminishing returns ensure that no one firm or product can ever grow big enough to dominate the marketplace. When people get tired of candy bars, they switch to apples or whatever. When all the best hydroelectric dam sites have been used, the utility companies start building coal-fired plants.

The more he thought about it, in fact, the more Arthur came to realize what an immense difference increasing returns would make to economics. Take efficiency, for example. Neoclassical theory would have us believe that a free market will always winnow out the best and most efficient technologies. And, in fact, the market doesn’t do too badly. But then, Arthur wondered, what are we to make of the standard QWERTY keyboard layout, the one used on virtually every typewriter and computer keyboard in the Western world?

In fact, Arthur suddenly realized, that’s why you get patterns in any system: a rich mixture of positive and negative feedbacks can’t help producing patterns.

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 passenger aircraft.

“In the real world, outcomes don’t just happen,” he says. “They build up gradually as small chance events become magnified by positive feedbacks.”

One of those who was influenced by the book was Francis Crick, who deduced the molecular structure of DNA along with James Watson in 1953—using data obtained from x-ray crystallography, a kind of submicroscopic imaging technique developed by physicists decades earlier.

(The name “linear” refers to the fact that if you plot such an equation on graph paper, the plot is a straight line.)

Our brains certainly aren’t linear: even though the sound of an oboe and the sound of a string section may be independent when they enter your ear, the emotional impact of both sounds together may be very much greater than either one alone. (This is what keeps symphony orchestras in business.)

Nor is the economy really linear. Millions of individual decisions to buy or not to buy can reinforce each other, creating a boom or a recession. And that economic climate can then feed back to shape the very buying decisions that produced it.

And the mathematical expression of that property—to the extent that such systems can be described by mathematics at all—is a nonlinear equation: one whose graph is curvy.

The passage of a water wave down a shallow canal, for example, turned out to have profound connections to certain subtle dynamics in quantum field theory: both were examples of isolated, self-sustaining pulses of energy called solitons. The Great Red Spot on Jupiter may be another such soliton. A swirling hurricane bigger than Earth, it has sustained itself for at least 400 years.

The self-organizing systems championed so vociferously by the physicist Ilya Prigogine were also governed by nonlinear dynamics; indeed, the self-organized motion in a simmering pot of soup turned out to be governed by dynamics very similar to the nonlinear formation of other kinds of patterns, such as the stripes of a zebra or the spots on a butterfly’s wings.

Robert Oppenheimer, Enrico Fermi, Niels Bohr, John von Neumann, Hans Bethe, Richard Feynman, Eugene Wigner—one observer at the time called them the greatest gathering of intellects since ancient Athens.

Manhattan Project

If this institute were just a one-man show, he felt, then it wasn’t going anywhere. After thirty years as an administrator, he was convinced that the only way to make something like this happen was to get a lot of people excited about it. “You have to persuade very good people that this is an important thing to do,” he says. “And by the way, I’m not talking about a democracy, I’m talking about the top one-half of one percent. An elite. But once you do that, then the money is—well, not easy, but a smaller part of the problem.”

He was driven by an omnivorous curiosity. He had been known to turn to strangers sitting next to him on an airplane and grill them about their life stories for hours.

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.”

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.

Carruthers, for one, spent the weekend in heaven. “Here was a collection of many of the most creative people in the whole world, in many fields, he says. “And they turned out to have a lot to say to each other. They basically had the same world view, in the sense that they all seemed to feel that ‘emerging syntheses’ really meant a restructuring of science—that the overlapping themes of different parts of science would be put together in a new way.

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.

Kauffman was nothing if not affable. But then, so was Arthur; he was in a mood to love everybody that morning. The two men found themselves hitting it off immediately. “Stu is an immensely warm person,” says Arthur, “someone you feel you have to hug—and I don’t go around hugging people.

Indeed, said Arthur, this process is an excellent example of what he meant by increasing returns: once a new technology starts opening up new niches for other goods and services, the people who fill those niches have every incentive to help that technology grow and prosper. Moreover, this process is a major driving force behind the phenomenon of lock-in: the more niches that spring up dependent on a given technology, the harder it is to change that technology—until something very much better comes along.

If innovations result from new combinations of old technologies, then the number of possible innovations would go up very rapidly as more and more technologies became available. In fact, he argued, once you get beyond a certain threshold of complexity you can expect a kind of phase transition analogous to the ones he had found in his autocatalytic sets. Below that level of complexity you would find countries dependent upon just a few major industries, and their economies would tend to be fragile and stagnant.

“If all you do is produce bananas, nothing will happen except that you produce more bananas.” But if a country ever managed to diversify and increase its complexity above the critical point, then you would expect it to undergo an explosive increase in growth and innovation—what some economists have called an “economic takeoff.”

The existence of that phase transition would also help explain why trade is so important to prosperity, Kauffman told Arthur. Suppose you have two different countries, each one of which is subcritical by itself. Their economies are going nowhere. But now suppose they start trading, so that their economies become interlinked into one large economy with a higher complexity. “I expect that...

This was the part of autocatalysis that really captivated Arthur. It had the same qualities that had so fascinated him when he first read about molecular biology: upheaval and change and enormous consequences flowing from trivial-seeming events—and yet with deep law hidden beneath.

“There is a remarkable certainty among molecular biologists that all the answers will be found by understanding specific molecules,” says Kauffman. “There is a great reluctance to study how a system works. For example, the concept of an attractor strikes them as gobbledygook.”

But the physicists were nonetheless disconcerted at how seldom the economists seemed to pay attention to the empirical data that did exist. Again and again, for example, someone would ask a question like “What about noneconomic influences such as political motives in OPEC oil pricing, and mass psychology in the stock market? Have you consulted sociologists, or psychologists, or anthropologists, or social scientists in general?” And the economists—when they weren’t curling their lips at the thought of these lesser social sciences, which they considered horribly mushy—would come back with answers like Such noneconomic forces really aren’t important”; “They are important, but they are too hard to treat”; “They aren’t always too hard to treat, and in fact, we’re doing so in specific cases”; and “We don’t need to treat them because they’re automatically satisfied through economic effects.”

Isn’t economics a good deal simpler than physics?” “Well,” Arthur replied, “in one sense it is. We call our particles ‘agents’—banks, firms, consumers, governments. And those agents react to other agents, just as particles react to other particles. Only we don’t usually consider the spatial dimension in economics much, so that makes economics a lot simpler.” However, he added, there is one big difference: “Our particles in economics are smart, whereas yours in physics are dumb.” In physics, an elementary particle has no past, no experience, no goals, no hopes or fears about the future. It just is. That’s why physicists can talk so freely about “universal laws”: their particles respond to forces blindly, with absolute obedience. But in economics, said Arthur, “Our particles have to think ahead, and try to figure out how other particles might react if they were to undertake certain actions. Our particles have to act on the basis of expectations and strategies. And regardless of how you model that, that’s what makes economics truly difficult.” Immediately,

In the natural world such systems included brains, immune systems, ecologies, cells, developing embryos, and ant colonies. In the human world they included cultural and social systems such as political parties or scientific communities.

Complex adoptive systems

First, he said, each of these systems is a network of many “agents” acting in parallel. In a brain the agents are nerve cells, in an ecology the agents are species, in a cell the agents are organelles such as the nucleus and the mitochondria, in an embryo the agents are cells, and so on. In an economy, the agents might be individuals or households. Or if you were looking at business cycles, the agents might be firms. And if you were looking at international trade, the agents might even be whole nations.

But regardless of how you define them, each agent finds itself in an environment produced by its interactions with the other agents in the system. It is constantly acting and reacting to what the other agents are doing. And because of that, essentially nothing in its environment is fixed.

Second, said Holland, a complex adaptive system has many levels of organization, with agents at any one level serving as the building blocks for agents at a higher level. A group of proteins, lipids, and nucleic acids will form a cell, a group of cells will form a tissue, a collection of tissues will form an organ, an association of organs will form a whole organism, and a group of organisms will form an ecosystem. In the brain, one group of neurons will form the speech centers, another the motor cortex, and still another the visual cortex. And in precisely the same way, a group of individual workers will compose a department, a group of departments will compose a division, and so on through companies, economic sectors, national economies, and finally the world economy.

complex adaptive systems typically have many niches, each one of which can be exploited by an agent adapted to fill that niche. Thus, the economic world has a place for computer programmers, plumbers, steel mills, and pet stores, just as the rain forest has a place for tree sloths and butterflies. Moreover, the very act of filling one niche opens up more niches—for new parasites, for new predators and prey, for new symbiotic partners. So new opportunities are always being created by the system. And that, in turn, means that it’s essentially meaningless to talk about a complex adaptive system being in equilibrium: the system can never get there. It is always unfolding, always in transition. In fact, if the system ever does reach equilibrium, it isn’t just stable. It’s dead.

And by the same token, said Holland, there’s no point in imagining that the agents in the system can ever “optimize” their fitness, or their utility, or whatever. The space of possibilities is too vast; they have no practical way of finding the optimum. The most they can ever do is to change and improve themselves relative to what the other agents are doing. In short, complex adaptive systems are characterized by perpetual novelty.

Holland’s ideas produced a shock of recognition, the kind that made more ideas start exploding in your own brain.

In the mathematical theory of games there is a theorem telling you that any finite, two-person, zero-sum game—such as chess—has an optimal solution. That is, there is a way of choosing moves that will allow each player, black and white, to do better than he would with any other choice of moves.

Equilibrium implies an endpoint. But to Holland, the essence of evolution lay in the journey, the endlessly unfolding surprise: “It was becoming more and more clear to me that the things I wanted to understand, that I was curious about, that would please me if I found out about them—equilibrium wasn’t an important part of any of them.”

But the more Holland thought about this idea of coherent, self-reinforcing clusters, the more subtle it began to seem. For one thing, you could find analogous examples almost anywhere you looked. Subroutines in a computer program. Departments in a bureaucracy. Gambits in the larger strategy of a chess game. Furthermore, you could find examples at every level of organization.

If a cluster is coherent enough and stable enough, then it can usually serve as a building block for some larger cluster. Cells make tissues, tissues make organs, organs make organisms, organisms make ecosystems—on and on. 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.

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-designed (emphasize well-designed) hierarchy is an excellent way of getting some work done without any one person being overwhelmed by meetings and memos.

As Holland thought about it, however, he became convinced that the most important reason lay deeper still, in the fact that a hierarchical, building-block structure utterly transforms a system’s ability to learn, evolve, and adapt. Think of our 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.