Chapter 1

The Irish Idea of a Hero

Sitting alone at his table by the bar, Brian Arthur stared out the front window of the tavern and did his best to ignore the young urban professionals drifting in to get an early start on Happy Hour. Outside, in the concrete canyons of the financial district, the typical San Francisco fog was turning into a typical San Francisco drizzle. That was fine by him. On this late afternoon of March 17, 1987, he wasn't in the mood to be impressed with brass fittings, ferns, and stained glass. He wasn't in a mood to celebrate Saint Patrick's Day. And he most definitely wasn't in a mood to carouse with ersatz Irishmen wearing bits of green on their pinstripes. He just wanted to silently sip his beer in frustrated rage. Stanford University Professor William Brian Arthur, native son of Belfast, Northern Ireland, was at rock bottom.

And the day had started so well.

That was the irony of it all. When he'd set out for Berkeley that morning, he'd actually been looking forward to the trip as a kind of triumphal reunion: local boy makes good. He'd really loved his years in Berkeley, back in the early 1970s. Perched on the hillsides north of Oakland, just across the bay from San Francisco, it was a pushy, vital, alive kind of place full of ethnics and street people and outrageous ideas. Berkeley was where he'd gotten his Ph. D. from the University of California, where he'd met and married a tall blonde doctoral student in statistics named Susan Peterson, where he'd spent his first "postdoc" year in the economics department. Berkeley, of all the places he'd lived and worked ever since, was the place he wanted to come home to.

Well now he was coming home, sort of. The event itself wouldn't be a big deal: just lunch with the chairman of the Berkeley economics department and one of his former professors there. But it was the first time he'd come back to his old department in years, and certainly the first time he'd ever done so feeling like an academic equal. He was coming back with twelve years of experience working all over the globe and a major reputation as a scholar of human fertility in the Third World. He was coming back as the occupant of an endowed chair of economics at Stanford -- the sort of thing that rarely gets handed out to anyone under age fifty. At age forty-one, Arthur was coming back as someone who had made it in academia. And who knew? The folks at Berkeley might even start talking about a lob offer.

Oh yes, he'd really been high on himself that morning. So why hadn't he, years ago, just stuck to the mainstream instead of trying to invent a whole new approach to economics? Why hadn't he played it safe instead of trying to get in step with some nebulous, half-imaginary scientific revolution?

Because he couldn't get it out of his head, that's why. Because he could see it almost everywhere he looked. The scientists barely seemed to recognize it themselves, most of the time. But after three hundred years of dissecting everything into molecules and atoms and nuclei and quarks, they finally seemed to be turning that process inside out. Instead of looking for the simplest pieces possible, they were starting to look at how those pieces go together into complex wholes.

He could see it happening in biology, where people had spent the past twenty years laying bare the molecular mechanisms of DNA, and proteins, and all the other components of the cell. Now they were also beginning to grapple with the essential mystery: how can several quadrillion such molecules organize themselves into an entity that moves, that responds, that reproduces, that is alive?

He could see it happening in the brain sciences, where neuroscientists, psychologists, computer scientists, and artificial intelligence researchers were struggling to comprehend the essence of mind: How do those billions of densely interconnected nerve cells inside our skulls give rise to feeling, thought, purpose, and awareness?

He could even see it happening in physics, where the physicists were still trying to come to terms with the mathematical theory of chaos, the intricate beauty of fractals, and the weird inner workings of solids and liquids. There was profound mystery here: Why is it that simple particles obeying simple rules will sometimes engage in the most astonishing, unpredictable behavior? And why is it that simple particles will spontaneously organize themselves into complex structures like stars, galaxies, snowflakes, and hurricanes -- almost as if they were obeying a hidden yearning for organization and order?

The signs were everywhere. Arthur couldn't quite put the feeling into words. Nobody could, so far as he could tell. But somehow, he could sense that all these questions were really the same question. Somehow, the old categories of science were beginning to dissolve. Somehow, a new, unified science was out there waiting to be born. It would be a rigorous science, Arthur was convinced, just as "hard" as physics ever was, and just as thoroughly grounded in natural law. But instead of being a quest for the ultimate particles, it would be about flux, change, and the forming and dissolving of patterns. Instead of ignoring everything that wasn't uniform and predictable, it would have a place for individuality and the accidents of history. Instead of being about simplicity, it would be about -- well, complexity.

And that was precisely where Arthur's new economics came in. Conventional economics, the kind he'd been taught in school, was about as far from this vision of complexity as you could imagine. Theoretical economists endlessly talked about the stability of the marketplace, and the balance of supply and demand. They transcribed the concept into mathematical equations and proved theorems about it. They accepted the gospel according to Adam Smith as the foundation for a kind of state religion. 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. And now he believed he'd found the way to do that, using a principle known as "increasing returns" -- or in the King James translation, "To them that hath shall be given." Why had high-tech companies scrambled to locate in the Silicon Valley area around Stanford instead of in Ann Arbor or Berkeley? Because a lot of older high-tech companies were already there. Them that has gets. 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.

The examples could be multiplied endlessly. Arthur had convinced himself that increasing returns pointed the way to the future for economics, a future in which he and his colleagues would work alongside the physicists and the biologists to understand the messiness, the upheaval, and the spontaneous self-organization of the world. He'd convinced himself that increasing returns could be the foundation for a new and very different kind of economic science.

Unfortunately, however, he hadn't had much luck convincing anybody else. Outside of his immediate circle at Stanford, most economists thought his ideas were -- strange. Journal editors were telling him that this increasing-returns stuff "wasn't economics." In seminars, a good fraction of the audience reacted with outrage: how dare he suggest that the economy was not in equilibrium! Arthur found the vehemence baffling. But clearly he needed allies, people who could open their minds and hear what he was trying to tell them. And that, as much as any desire for a homecoming, was the reason he'd gone to Berkeley.

So there they had all been, sitting down to sandwiches at the faculty club. Tom Rothenberg, one of his former professors, had asked the inevitable question: "So, Brian, what are you working on these days?" Arthur had given him the two-word answer just to get started: "Increasing returns." And the economics department chairman, Al Fishlow, had stared at him with a kind of deadpan look.

"But -- we know increasing returns don't exist."

"Besides," jumped in Rothenberg with a grin, "if they did, we'd have to outlaw them!"

And then they'd laughed. Not unkindly. It was just an insider's joke. Arthur knew it was a joke. It was trivial. Yet that one sound had somehow shattered his whole bubble of anticipation. He'd sat there, struck speechless. Here were two of the economists he respected most, and they just -- couldn't listen. Suddenly Arthur had felt naive. Stupid. Like someone who didn't know enough not to believe in increasing returns. Somehow, it had been the last straw.

He'd barely paid attention during the rest of the lunch. After it was over and everyone had said their polite good-byes, he'd climbed into his faded old Volvo and driven back over the Bay Bridge into San Francisco. He'd taken the first exit he could, onto the Embarcadero. He'd stopped at the first bar he found. And he'd come in here to sit amidst the ferns and to give some serious thought to getting out of economics entirely.

Somewhere around the bottom of his second beer, Arthur realized that the place was beginning to get seriously noisy. The yuppies were arriving in force to celebrate the patron saint of Ireland. Well, maybe it was time to go home. This certainly wasn't accomplishing anything. He got up and walked out to his car; the foggy drizzle was still coming down.

Home was in Palo Alto, thirty-five miles south of the city in the suburban flats around Stanford. It was sunset when he finally pulled into the driveway. He must have made some noise. His wife, Susan, opened the front door and watched him as he was walking across the lawn: a slim, prematurely gray man who doubtless looked about as fed up and bedraggled as he felt.

"Well," she said, standing there in the doorway, "how did it go in Berkeley? Did they like your ideas?"

"It was the pits," said Arthur. "Nobody there believes in increasing returns."

Susan Arthur had seen her husband returning from the academic wars before. "Well," she said, trying to find something comforting to say, "I guess it wouldn't be a revolution, would it, if everybody believed in it at the start?"

Arthur looked at her, struck speechless for the second time that day. And then he just couldn't help it. He started to laugh.

The Education of a Scientist

When you're growing up Catholic in Belfast, says Brian Arthur, speaking in the soft, high cadences of that city, a certain rebelliousness sets in naturally. It wasn't that he ever felt oppressed, exactly. His father was a bank manager and his family was solidly middle class. The only sectarian incident that ever involved him personally came one afternoon as he was walking home in his parochial school uniform: a bunch of Protestant boys started pelting him with bits of brick and stone, and one piece of brick hit him in the forehead. (He could hardly see for the blood pouring into his eyes -- but he damn well threw that brick back.) Nor did he really feel that the Protestants were devils; his mother was a Protestant who converted to Catholicism when she married. He never even felt especially political. He tended to be much more interested in ideas and philosophy.

No, the rebelliousness is just something you pick up from the air. "The culture doesn't equip you to lead, but to undermine," he says. Look at whom the Irish admire: Wolfe Tone, Robert Emmet, Daniel O'Connell, Padraic Pearse. "All the Irish heroes were revolutionaries. The highest peak of heroism is to lead an absolutely hopeless revolution, and then give the greatest speech of your life from the dock -- the night before you're hanged.

"In Ireland," he says, "an appeal to authority never works."

In an odd sort of way, Arthur adds, that streak of Irish rebelliousness is what got him started in his own academic career. Catholic Belfast tended to be rather contemptuous of intellectuals. So, of course, he became one. In fact, he can remember wanting to be a "scientist" as early as age four, long before he knew what a scientist was. The idea just seemed deliciously exotic and mysterious. And yet, having gotten that idea in his head, young Brian was nothing if not determined. At school he plunged into engineering and physics and hard-edged mathematics as soon as he could. And in 1966 he had taken first-class honors in electrical engineering at Queen's University in Belfast. "Oh, I suppose you'll end up a wee professor somewhere," said his mother, who was in fact very proud; no one in her generation of the family had ever even attended a university.

Later in 1966 that same determination had led him across the Irish Sea to England and the University of Lancaster, where he started graduate studies in a highly mathematical form of engineering known as operations research -- basically, a set of techniques for calculating such things as how to organize a factory to get the most output for the least input, or how to keep a fighter jet under control when it is buffeted by unexpected forces. "At the time, British industry was in terrible shape," says Arthur. "I thought that maybe through science we could reorganize it and sort it out."

And in 1967, after the professors at Lancaster had proved insufferably stuffy and condescending -- "Well," says Arthur, doing his best imitation of bored British snobbery, "it's nice to have an Irishman in the department; it adds a little colour" -- he left for America and the University of Michigan in Ann Arbor. "From the moment I set foot here, I felt right at home," he says. "This was the sixties. The people were open, the culture was open, the scientific education was second to none. In the United States, anything seemed possible."

The one thing that wasn't possible in Ann Arbor, unfortunately, was ready access to the mountains and the sea, both of which Arthur loved. So he arranged to finish his Ph.D. work at Berkeley starting in the fall of 1969. And to support himself in the summer beforehand he applied for a job with McKinsey and Company, one of the top management consulting companies in the world.

That was a piece of incredibly good fortune. Arthur didn't realize until later just how lucky he was; people were clamoring to be hired at McKinsey. But it turned out that the company liked his operations research background and the fact that he knew German. They needed someone to work out of the Düsseldorf office. Was he interested?

Was he? Arthur had the time of his life. The last time he'd been in Germany he'd worked at a blue-collar summer job at 75 cents an hour. Now here he was, twenty-three years old, advising the board of directors of BASF on what to do with an oil and gas division or a fertilizer division worth hundreds of millions of dollars. "I learned that operating at the top was just as easy as operating at the bottom," he laughs.

But it was more than just an ego trip. Basically, McKinsey was selling modern American management techniques (a concept that didn't sound as funny in 1969 as it would have fifteen years later). "Companies in Europe at that time typically had hundreds of subdivisions," he says. "They didn't even know what they owned." Arthur discovered that he had a real taste for wading into messy problems like this and coming to grips with them firsthand. "McKinsey was genuinely first-rate," he says. "They weren't selling theories and they weren't selling fads. Their approach was to absolutely revel in the complexity, to live with it and breathe it. The McKinsey team would stay with a company for five or six months or more, studying a very complicated set of arrangements, until somehow certain patterns became clear. We'd all sit around on the edge of our desks and someone would say, 'This must be happening because of that,' and someone else would say, 'Then that must be so.' Then we'd go out and check it. And maybe the local executive would say, 'Well, you're almost right, but you forgot about such and such.' So we'd spend months clarifying and clarifying, until the issues were all worked out and the answer spoke for itself."

It didn't take very long for Arthur to realize that, when it came to real-world complexities, the elegant equations and the fancy mathematics he'd spent so much time on in school were no more than tools -- and limited tools at that. The crucial skill was insight, the ability to see connections. And that fact, ironically, was what led him into economics. He remembers the occasion vividly. It was shortly before he was due to leave for Berkeley. He and his American boss, George Taucher, were driving one evening through West Germany's Ruhr Valley, the country's industrial heartland. And as they went, Taucher started talking about the history of each company they passed -- who had owned what for a hundred years, and how the whole thing had built up in an absolutely organic, historical way. For Arthur it was a revelation. "I realized all of a sudden that this was economics." If he ever wanted to understand this messy world that fascinated him so much, if he ever wanted to make a real difference in people's lives, then he was going to have to learn economics.

So Arthur headed to Berkeley after that first summer on an intellectual high. And in total innocence, he announced that economics was what he would study.

Actually, he had no intention of completely shifting fields at this late date. He'd already finished most of his requirements for a Ph.D. in operations research at Michigan; the only remaining hurdle was to complete a dissertation, the large piece of original research with which a Ph.D. candidate supposedly demonstrates that he or she has mastered the craft. But he had more than enough time to do that: the University of California was insisting that he hang around Berkeley for another three years to fulfill its residency requirements. So Arthur was welcome to spend his extra time taking all the economics courses he could.

He did. "But after the McKinsey experience, I was very disappointed," he says. "This was nothing like the historical drama I'd been so fascinated with in the Ruhr Valley." In the lecture halls of Berkeley, economics seemed to be a branch of pure mathematics. "Neoclassical" economics, as the fundamental theory was known, had reduced the rich complexity of the world to a narrow set of abstract principles that could be written on a few pages. Whole textbooks were practically solid with equations. The brightest young economists seemed to be devoting their careers to proving theorem after theorem after theorem -- whether or not those theorems had much to do with the world. "This extraordinary emphasis on mathematics surprised me," says Arthur. "To me, coming from applied mathematics, a theorem was a statement about an everlasting mathematical truth -- not the dressing up of a trivial observation in a lot of formalism."

He couldn't help but feel that the theory was just too neat by half. It wasn't the mathematical rigor he objected to. He loved mathematics. After all those years of studying electrical engineering and operations research, moreover, he'd acquired considerably more background in mathematics than most of his economics classmates. No, what bothered him was the weird unreality of it all. The mathematical economists had been so successful at turning their discipline into ersatz physics that they had leached their theories clean of all human frailty and passion. Their theories described the human animal as a kind of elementary particle: "economic man," a godlike being whose reasoning is always perfect, and whose goals are always pursued with serenely predictable self-interest. And just as physicists could predict how a particle will respond to any given set of forces, economists could predict how economic man will respond to any given economic situation: he (or it) will just optimize his "utility function."

Neoclassical economics likewise described a society where the economy is poised forever in perfect equilibrium, where supply always exactly equals demand, where the stock market is never jolted by surges and crashes, where no company ever gets big enough to dominate the market, and where the magic of a perfectly free market makes everything turn out for the best. It was a vision that reminded Arthur of nothing so much as the eighteenth century Enlightenment, when philosophers saw the cosmos as a kind of vast clockwork device kept in perfect running order by the laws of Sir Isaac Newton. The only difference was that the economists seemed to see human society as a perfectly oiled machine governed by the Invisible Hand of Adam Smith.

He just couldn't buy it. Granted, the free market was a wonderful thing, and Adam Smith had been a brilliant man. In fairness, moreover, neoclassical theorists had embroidered the basic model with all sorts of elaborations to cover things like uncertainty about the future, or the transfer of property from one generation to the next. They had adapted it to fit taxation, monopolies, international trade, employment, finance, monetary policy -- everything economists thought about. But none of that changed any of the fundamental assumptions. The theory still didn't describe the messiness and the irrationality of the human world that Arthur had seen in the valley of the Ruhr -- or, for that matter, that he could see every day on the streets of Berkeley.

Arthur didn't exactly keep his opinions to himself. "I think I annoyed several of my professors by showing a great deal of impatience with theorems, and by wanting to know about the real economy," he says. He also knew he was hardly alone in those opinions: he could hear the grumbling in the hallways of any economics meeting he went to.

And yet, there was also a part of Arthur that found the neoclassical theory breathtakingly beautiful. As an intellectual tour de force it ranked right up there with the physics of Newton or Einstein. It had the kind of hard-edged clarity and precision that the mathematician in him couldn't help responding to. Moreover, he could see why a previous generation of economists had welcomed it so enthusiastically. He'd heard horror stories about what economics was like when they were coming of age. Back in the 1930s, the English economist John Maynard Keynes had remarked that you could put five economists in a room and you'd get six different opinions. And from all reports, he was being kind. The economists of the 1930s and 1940s were long on insight, but they were often a trifle weak on logic. And even when they weren't, you'd still find that they came to very different conclusions on the same problem: it turns out they were arguing from different, unstated assumptions. So these major wars would be fought out between different factions over government policies or theories of the business cycle. The generation of economists who crafted the mathematical theory in the 1940s and 1950s were the Young Turks of their day, a pack of brash upstarts determined to clean out the stables and make economics into a science as rigorous and as precise as physics. And they had come remarkably close; the Young Turks who had achieved it -- Kenneth Arrow of Stanford, Paul Samuelson of MIT, Gerard Debreu of Berkeley, Tjalling Koopmans, and Lionel McKenzie of Rochester, among others -- had deservedly gone on to become the Grand Old Men, the new establishment.

Besides, if you were going to do economics at all -- and Arthur was still determined to do economics -- what other theory were you going to use? Marxism? Well, this was Berkeley, and Karl Marx certainly had his followers. But Arthur wasn't one of them: so far as he was concerned, this business of class struggle proceeding in scientifically predictable stages was just plain silly. No, as the gambler once said, the game may be crooked, but it's the only game in town. So he kept on with his courses, determined to master the theoretical tools he couldn't quite believe in.

All this time, of course, Arthur had been working on his Ph.D. dissertation for operations research. And his adviser, mathematician Stuart Dreyfus, had proved to be both an excellent teacher and a kindred spirit. Arthur remembers stopping by Dreyfus's office to introduce himself shortly after he arrived at Berkeley in 1969. He met a long-haired bead-wearing graduate student coming out. "I'm looking for Professor Dreyfus," said Arthur. "Could you tell me when he's due back?"

"I'm Dreyfus," said the "student," who was in fact about forty.

Dreyfus reinforced all the lessons that Arthur had learned at McKinsey, and provided an ongoing antidote to the economics classes. "He believed in getting to the heart of a problem," says Arthur. "Instead of solving incredibly complicated equations, he taught me to keep simplifying the problem until you found something you could deal with. Look for what made a problem tick. Look for the key factor, the key ingredient, the key solution." Dreyfus would not let him get away with fancy mathematics for its own sake.

Arthur took Dreyfus's lessons to heart. "It was both good and bad," he says a bit sadly. Later on, his ideas on increasing returns might have gone down better with traditional economists if he'd hidden them in a thicket of mathematical formalism. In fact, colleagues urged him to do so. He wouldn't. "I wanted to say it as plainly and as simply as I could," he says.

In 1970 Arthur went back to Düsseldorf for a second summer with McKinsey and Company, and found it to be just as enthralling as the first. Sometimes he wonders if he should have kept up his contacts there and become a big-time international consultant after he graduated. He could have afforded a very luxurious lifestyle.

But he didn't. Instead he found himself being drawn to an economics specialty that focused on a problem even messier than industrial Europe: Third World population growth.

Of course, it didn't hurt that this specialty gave him the opportunity to go back and forth for study at the East-West Population Institute in Honolulu, where he could keep a surfboard ready for action on the beaches. But he was quite serious about it. This was the early 1970s, and the population problem was looming large. Stanford biologist Paul Ehrlich had just written his apocalyptic best-seller The Population Bomb. The Third World was full of newly independent former colonies struggling to achieve some kind of economic viability. And economists were full of theories about how to help them. The standard advice at the time tended to place a heavy reliance on economic determinism: to achieve its "optimum" population, all a country had to do was give its people the right economic incentives to control their reproduction, and they would automatically follow their own rational self-interest. In particular, many economists were arguing that when and if a country became a modern industrial state -- organized along Western lines, of course -- its citizenry would naturally undergo a "demographic transition," automatically lowering their birthrates to match those that prevailed in European countries.

Arthur, however, was convinced that he had a better approach, or at least a more sophisticated one: analyze population control in terms of "time-delayed" control theory, the subject of his Ph.D. dissertation. "The problem was one of timing," he says. "If a government manages to cut back on births today, it will affect school sizes in about 10 years, the labor force in 20 years, the size of the next generation in about 30 years, and the number of retirees in about 60 years. Mathematically, this is very much like trying to control a space probe far out in the solar system, where your commands take hours to reach it, or like trying to control the temperature of your shower when there's a half-minute delay between adjusting the tap and the hot water reaching you. If you don't take that delay into account properly, you can get scalded."

In 1973, Arthur included his population analysis as the final chapter in his dissertation: an equation-filled tome entitled Dynamic Programming as Applied to Time-Delayed Control Theory. "It was very much an engineering approach to the population problem," he says, looking back on it ruefully, "It was all just numbers." Despite all his experience with McKinsey and Dreyfus, and despite all his impatience with overmathematized economics, he was still feeling the same impulse that had led him into operations research in the first place: let's use science and mathematics to help run society rationally. "Most people in development economics have this kind of attitude," he says. "They're the missionaries of this century. But instead of bringing Christianity to the heathen, they're trying to bring economic development to the Third World."

What brought him back to reality with a jolt was going to work for a small New York think tank known as the Population Council. He arrived in 1974, after he had completed his doctorate and spent a year as a "postdoc" researcher in the Berkeley economics department. Physically, the Population Council was about as far from the Third World as you could get: it was set up in a Park Avenue skyscraper under the chairmanship of John D. Rockefeller III. But it did fund serious research into contraception, family planning, and economic development. And most important, from Arthur's point of view, it had a policy of getting its researchers away from their desks and out into the field as much as possible.

"Brian," the director would ask, "how much do you know about population and development in Bangladesh?"

"Very little."

"How would you like to find out?"

Bangladesh was a watershed for Arthur. He went there in 1975 with demographer Geoffrey McNicoll, an Australian who had been a fellow graduate student at Berkeley and who had been responsible for bringing Arthur to the Population Council in the first place. They arrived in the first plane permitted to land in the aftermath of a coup; they could still hear machine guns firing as they touched down. Then they proceeded into the countryside, where they acted like investigative reporters: "We talked to headmen in the villages, women in the villages, everyone. We interviewed and interviewed to understand how the rural society worked." In particular, they tried to find out why rural families were still producing an average of seven children apiece, even when modern birth control was made freely available -- and even when the villagers seemed perfectly well aware of the country's immense overpopulation and stagnant development.

"What we found was that the terrible predicament of Bangladesh was the outcome of a network of individual and group interests at the village level," says Arthur. Since children could go to work at an early age, it was a net benefit to any individual family to have as many children as possible. Since a defenseless widow's relatives and neighbors might very well come in and take everything she possessed, it was in a young wife's interest to have as many sons as possible as quickly as possible, so that she would have grown sons to protect her in her old age. And so it went: "Patriarchs, women who were trying to hold onto their husbands, irrigation communities -- all these interests combined to produce children and to stagnate development."

After six weeks in Bangladesh, Arthur and McNicoll returned to the United States to digest the information they had and to do further research in the anthropology and sociology journals. One of Arthur's first stops was Berkeley, where he dropped by the economics department in search of a reference. While he was there, he remembers, he happened to flip through a list of the latest course offerings. They were pretty much the same courses he had taken himself not so long ago. "But I had this very strange impression, as if I'd been off center a bit, that economics had changed in the year I'd been away. And then it dawned on me: economics hadn't changed. I had." After Bangladesh, all those neoclassical theorems that he'd worked so hard to learn seemed so -- irrelevant. "Suddenly I felt 100 percent lighter, like a great weight had been lifted from me. I didn't have to believe this anymore! I felt it as a great freedom."

Arthur and McNicoll's eighty-page report, published in 1978, became something of a classic in social science -- and was immediately banned in Bangladesh. (Much to the chagrin of the elite in Dacca, the capital, the authors had pointed out that the government had essentially no control of anything outside the capital; the countryside was essentially being run by local feudal godfathers.) But in any case, says Arthur, other missions for the Population Council in Syria and Kuwait only reinforced the lesson: the quantitative engineering approach -- the idea that human beings will respond to abstract economic incentives like machines -- was highly limited at best. Economics, as any historian or anthropologist could have told him instantly, was hopelessly intertwined with politics and culture. Perhaps the lesson was obvious, says Arthur, "But I had to learn it the hard way."

That insight likewise led him to abandon any hope of finding a general, deterministic theory of human fertility. Instead he began to conceive of fertility, as part of a self-consistent pattern of folkways, myths, and social mores -- a pattern, moreover, that was different for each culture. "You could measure something like income or childbearing in one country, and find that another country had the same levels of one, and totally different levels of the other. It would be a different pattern." Everything interlocked, and no piece of the puzzle could be considered in isolation from the others: "The number of children interacted with the way their society was organized, and the way their society was organized had a lot to do with the number of children they had."

Patterns. Once he had made the leap, Arthur found that there was something about the concept that resonated. He had been fascinated by patterns all his life. Given a choice he would always take the window seat on airplanes, so he could look out on the ever-changing panoram of finding a general, deterministic theory of human fertility. Instead he began to conceive of fertility, as part of a self-consistent pattern of folkways, myths, and social mores -- a pattern, moreover, that was different for each culture. "You could measure something like income or childbearing in one country, and find that another country had the same levels of one, and totally different levels of the other. It would be a different pattern." Everything interlocked, and no piece of the puzzle could be considered in isolation from the others: "The number of children interacted with the way their society was organized, and the way their society was organized had a lot to do with the number of children they had."

Patterns. Once he had made the leap, Arthur found that there was something about the concept that resonated. He had been fascinated by patterns all his life. Given a choice he would always take the window seat on airplanes, so he could look out on the ever-changing panorama below. He would generally see the same elements everywhere he went: rock, earth, ice, clouds, and so on. But these elements would be organized into characteristic patterns that might go on for half an hour. "So I asked myself the question, why does that geological pattern exist? Why is there a certain texture of rock formations and meandering rivers, and then half an hour later there's a totally different pattern?"

Now, however, he began to see patterns everywhere he went. In 1977, for example, he left the Population Council for a U.S.-Soviet think tank known as IIASA: the International Institute for Applied Systems Analysis. Created by Brezhnev and Nixon as a symbol of detente, it was housed in Maria Theresa's magnificent eighteenth-century "hunting lodge" in Laxenburg, a small village about ten miles outside of Vienna. It was also, as Arthur quickly determined, within ready driving distance from the ski slopes of the Tyrolean Alps.

"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."

What also struck him, he says, was that just across the Italian border in the Dolomite Alps, the villages were suddenly not Tyrolean at all. It was no one thing that you could point to. It was just that myriad variant details added up to a totally different whole. And yet the Italian villagers and the Austrian villagers were coping with essentially the same problem of snowfall. "Over time," he says, "the two cultures had arrived at mutually self-consistent patterns that are different."

Epiphany on the Beach

Everyone has a research style, says Arthur. If you think of a research problem as being like a medieval walled city, then a lot of people will attack it head on, like a battering ram. They will storm the gates and try to smash through the defenses with sheer intellectual power and brilliance.

But Arthur has never felt that the battering ram approach was his strength. "I like to take my time as I think," he says. "So I just camp outside the city. I wait. And I think. Until one day -- maybe after I've turned to a completely different problem -- the drawbridge comes down and the defenders say, 'We surrender.' The answer to the problem comes all at once."

In the case of what he later came to call increasing returns economics, he had been camped for quite a long time. McKinsey. Bangladesh. His general disillusionment with standard economics. Patterns. None of it was quite the answer. But he can vividly remember when the drawbridge began to open.

It was in April 1979. His wife, Susan, was in a state of exhaustion after finishing her Ph.D. in statistics, and Arthur had arranged for an eight-week sabbatical from IIASA so that they could take a much-needed rest together in Honolulu. For himself, he made it a partial working vacation. From nine in the morning until three in the afternoon he would go over to the East-West Population Institute to work on a research paper while Susan continued to sleep -- literally fifteen hours a day. Then in the late afternoon they would drive up to Hauula beach on the north side of Oahu: a tiny, almost deserted strip of sand where they could body-surf and lie around drinking beer, eating cheese, and reading. It was here, one lazy afternoon shortly after they arrived, that Arthur had opened up the book he had 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. He read how scientists had slowly deciphered the intricately convoluted structures of proteins and enzymes. And as a lifetime laboratory klutz -- "I've done miserably in every laboratory I've been in" -- he read about the painstaking experiments that brought this science to life: the questions that made this or that experiment necessary, the months spent in planning each experiment and assembling the apparatus, and then the triumph or dejection when the answer was in hand. "Judson had the ability to bring the drama of science alive."

But what really galvanized him was the realization that here was a whole messy world -- the interior of a living cell -- that was at least as complicated as the messy human world. And yet it was a science. "I realized that I had been terribly unsophisticated about biology," he says. "When you're trained the way I was, in mathematics and engineering and economics, you tend to view science as something that only applies when you can use theorems and mathematics. But when it came to looking out the window at the domain of life, of organisms, of nature, I had this view that, somehow, science stops short." How do you write down a mathematical equation for a tree or a paramecium? You can't. "My vague notion was that biochemistry and molecular biology were just a bunch of classifications of this molecule or that. They didn't really help you understand anything."

Wrong. On every page, Judson was proving to him that biology was as much a science as physics had ever been -- that this messy, organic, non-mechanistic world was in fact governed by a handful of principles that were as deep and profound as Newton's laws of motion. In every living cell there resides a long, helical DNA molecule: a chain of chemically encoded instructions, genes, that together constitute a blueprint for the cell. The genetic blueprints may be wildly different from one organism to the next. But in both, the genes will use essentially the same genetic code. That code will be deciphered by the same molecular code-breaking machinery. And that blueprint will be turned into proteins and membranes and other cellular structures in the same molecular workshops.

To Arthur, thinking of all the myriad forms of life on Earth, this was a revelation. At a molecular level, every living cell was astonishingly alike. The basic mechanisms were universal. And yet a tiny, almost undetectable mutation in the genetic blueprint might be enough to produce an enormous change in the organism as a whole. A few molecular shifts here and there might be enough to make the difference between brown eyes and blue, between a gymnast and a sumo wrestler, between good health and sickle-cell anemia. A few more molecular shifts, accumulating over millions of years through natural selection, might make the difference between a human and a chimpanzee, between a fig tree and a cactus, between an amoeba and a whale. In the biological world, Arthur realized, small chance events are magnified, exploited, built upon. One tiny accident can change everything. Life develops. It has a history. Maybe, he thought, maybe that's why this biological world seems so spontaneous, organic, and -- well, alive.

Come to think of it, maybe that was also why the economists' imaginary world of perfect equilibrium had always struck him as static, machinelike, and dead. Nothing much could ever happen there; tiny chance imbalances in the market were supposed to die away as quickly as they occurred. Arthur couldn't imagine anything less like the real economy, where new products, technologies, and markets were constantly arising and old ones were constantly dying off. The real economy was not a machine but a kind of living system, with all the spontaneity and complexity that Judson was showing him in the world of molecular biology. Arthur had no idea yet how to use that insight. But it fired his imagination.

He kept reading: there was more. "Of all the drama in the book," says Arthur, "what appealed to me most was the work of Jacob and Monod." Working at the Institut Pasteur in Paris in the early 1960s, the French biologists Francois Jacob and Jacques Monod had discovered that a small fraction of the thousands of genes arrayed along the DNA molecule can function as tiny switches. Turn one of these switches on -- by exposing the cell to a certain hormone, for example -- and the newly activated gene will send out a chemical signal to its fellow genes. This signal will then travel up and down the length of the DNA molecule and trip other genetic switches, flipping some of them on and some of them off. These genes, in turn, start sending out chemical signals of their own (or stop sending them out). And as a result, still more genetic switches will be tripped in a mounting cascade, until the cell's collection of genes settles down into a new and stable pattern.

For biologists the implications of this discovery were enormous (so much so that Jacob and Monod later shared the Nobel Prize for it). It meant that the DNA residing in a cell's nucleus was not just a blueprint for the cella catalog of how to make this protein or that protein. DNA was actually the foreman in charge of construction. In effect, DNA was a kind of molecular-scale computer that directed how the cell was to build itself and repair itself and interact with the outside world. Furthermore, Jacob and Monod's discovery solved the long standing mystery of how one fertilized egg cell could divide and differentiate itself into muscle cells, brain cells, liver cells, and all the other kinds of cells that make up a newborn baby. Each different type of cell corresponded to a different pattern of activated genes.

To Arthur, the combination of déjà vu and excitement when he read this was overwhelming. Here it was again: patterns. An entire sprawling set of self-consistent patterns that formed and evolved and changed in response to the outside world. It reminded him of nothing so much as a kaleidoscope, where a handful of beads will lock in to one pattern and hold it -- until a slow turn of the barrel causes them to suddenly cascade into a new configuration. A handful of pieces and an infinity of possible patterns. Somehow, in a way he couldn't quite express, this seemed to be the essence of life.

When Arthur finished Judson's book he went prowling through the University of Hawaii bookstore, snatching up every book he could find on molecular biology. Back on the beach, he devoured them all. "I was captured," he says, "obsessed." By the time he returned to IIASA in June he was moving on pure intellectual adrenaline. He still had no clear idea how to apply all this to the economy. But he could feel that the essential clues were there. He continued to pour through biology texts all that summer. And in September, at the suggestion of a physicist colleague at IIASA, he started delving into the modern theories of condensed matter -- the inner workings of liquids and solids.

He was as astonished as he had been at Hauula beach. He hadn't thought that physics was anything like biology. In fact, it wasn't like biology; the atoms and molecules that the physicists usually studied were much, much simpler than proteins and DNA. And yet, when you looked at those simple atoms and molecules interacting in massive numbers, you saw all the same phenomena: tiny initial differences producing enormously different effects. Simple dynamics producing astonishingly complex behaviors. A handful of pieces falling into a near-infinity of possible patterns. Somehow, at some very deep level that Arthur didn't know how to define, the phenomena of physics and biology were the same.

On the other hand, there was one very important difference at a practical level: the systems that physicists studied were simple enough that they could analyze them with rigorous mathematics. Suddenly, Arthur began to feel right at home. If he'd had any lingering doubts before, he knew now he was dealing with science. "These were not just fuzzy notions," he says.

He found that he was most impressed with the writings of the Belgian physicist Ilya Prigogine. Prigogine, as he later discovered, was considered by many other physicists to be an insufferable self-promoter who often exaggerated the significance of what he had accomplished. Nonetheless, he was an undeniably compelling writer. And perhaps not coincidentally, his work in the field of "nonequilibrium thermodynamics" had convinced the Swedish Academy of Sciences to award him the Nobel Prize in 1977.

Basically, Prigogine was addressing the question, Why is there order and structure in the world? Where does it come from?

This turns out to be a much tougher question than it might sound, especially when you consider the world's general tendency toward decay. Iron rusts. Fallen logs rot. Bathwater cools to the temperature of its surroundings. Nature seems to be less interested in creating structures than in tearing structures apart and mixing things up into a kind of average. Indeed, the process of disorder and decay seems inexorable -- so much so that nineteenth-century physicists codified it as the second law of thermodynamics, which can be paraphrased as "You can't unscramble an egg." Left to themselves, says the second law, atoms will mix and randomize themselves as much as possible. That's why iron rusts: atoms in the iron are forever trying to mingle with oxygen in the air to form iron oxide. And that's why bathwater cools: fast-moving molecules on the surface of the water collide with slower-moving molecules in the air, and gradually transfer their energy.

Yet for all of that, we do see plenty of order and structure around. Fallen logs rot -- but trees also grow. So how do you reconcile this growth of structure with the second law of thermodynamics?

The answer, as Prigogine and others realized back in the 1960s, lies in that innocuous-sounding phrase, "Left to themselves..." In the real world, atoms and molecules are almost never left to themselves, not completely; they are almost always exposed to a certain amount of energy and material flowing in from the outside. And if that flow of energy and material is strong enough, then the steady degradation demanded by the second law can be partially reversed. Over a limited region, in fact, a system can spontaneously organize itself into a whole series of complex structures.

The most familiar example is probably a pot of soup sitting on the stovetop. 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.

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.

Arthur sat up immediately when he read those words. "The economy is a self-organizing system." That was it! That was precisely what he had been thinking ever since he'd read The Eighth Day of Creation, although he hadn't known how to articulate it. Prigogine's principle of self-organization, the spontaneous dynamics of living systems -- now Arthur could finally see how to relate all of it to economic systems.

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.

And yet, positive feedback is precisely what conventional economics didn't have, Arthur realized. Quite the opposite. Neoclassical theory assumes that the economy is entirely dominated by negative feedback: the tendency of small effects to die away. In fact, he can remember listening with some puzzlement as his economics professors back in Berkeley had hammered away on the point. 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 enjoyble 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. When enough fertilizer is enough, farmers quit applying it. Indeed, negative feedback/diminishing returns is what underlies the whole neoclassical vision of harmony, stability, and equilibrium in the economy.

But even back in Berkeley, Arthur the engineering student couldn't help but wonder: What happens if you have positive feedback in the economy? Or in the economics jargon, what happens if you have increasing returns?

"Don't worry about it," his teachers had reassured him. "Increasing-returns situations are extremely rare, and they don't last very long." And since Arthur didn't have any particular example in