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The Emerging Science at the Edge of Order and Chaos



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About The Book

Why did the stock market crash more than 500 points on a single Monday in 1987? Why do ancient species often remain stable in the fossil record for millions of years and then suddenly disappear? In a world where nice guys often finish last, why do humans value trust and cooperation? At first glance these questions don't appear to have anything in common, but in fact every one of these statements refers to a complex system. The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order.
Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.


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 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 mind, he had shut up about it and gone on to other things.

But now, reading Prigogine, it all came flooding back to him. Positive feedback, increasing returns -- maybe these things did happen in the real economy. Maybe they explained the liveliness, the complexity, the richness he saw in the real-world economy all around him.

Maybe so. 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? (The name QWERTY is spelled out by the first six letters along the top row.) Is this the most efficient way to arrange the keys on a typewriter keyboard? Not by a long shot. An engineer named Christopher Scholes designed the QWERTY layout in 1873 specifically to slow typists down; the typewriting machines of the day tended to jam if the typist went too fast. But then the Remington Sewing Machine Company mass-produced a typewriter using the QWERTY keyboard, which meant that lots of typists began to learn the system, which meant that other typewriter companies began to offer the QWERTY keyboard, which meant that still more typists began to learn it, et cetera, et cetera. To them that hath shall be given, thought Arthur -- increasing returns. And now that QWERTY is a standard used by millions of people, it's essentially locked in forever.

Or consider the Beta versus VHS competition in the mid-1970s. Even in 1979 it was clear that the VHS videotape format was well on its way to cornering the market, despite the fact that many experts had originally rated it slightly inferior to Beta technologically. How could this have happened? Because the VHS vendors were lucky enough to gain a slightly bigger market share in the beginning, which gave them an enormous advantage in spite of the technological differences: the video stores hated having to stock everything in two different formats, and consumers hated the idea of being stuck with obsolete VCRs. So everyone had a big incentive to go with the market leader. That pushed up VHS's market share even more, and the small initial difference grew rapidly. Once again, increasing returns.

Or take this endlessly fascinating business of patterns. Pure neoclassical theory tells us that high-tech firms will tend to distribute themselves evenly across the landscape: there's no reason for any of them to prefer one location over another. But in real life, of course, they flock to places like California's Silicon Valley and Boston's Route 128 to be near other high-tech firms. Them that has gets -- and the world acquires structure. 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. Imagine spilling a little water onto the surface of a highly polished tray, he says; it beads up into a complex pattern of droplets. And it does so because two countervailing forces are at work. There is gravity, which tries to spread out the water to make a very thin, fiat film across the whole surface. That's negative feedback. And there is surface tension, the attraction of one water molecule to another, which tries to pull the liquid together into compact globules. That's positive feedback. It's the mix of the two forces that produces the complex pattern of beads. Moreover, that pattern is unique. Try the experiment again and you'll get a completely different arrangement of droplets. Tiny accidents of history -- infinitesimal dust motes and invisible irregularities in the surface of the tray -- get magnified by the positive feedback into major differences in the outcome.

Indeed, thought Arthur, that probably explains why history, in Winston Churchill's phrase, is just one damn thing after another. Increasing returns can take a trivial happenstance -- who bumped into whom in the hallway, where the wagon train happened to stop for the night, where trading posts happened to be set up, where Italian shoemakers happened to emigrate-and magnify it into something historically irreversible. Did a certain young actress become a superstar on the basis of pure talent? Hardly: the luck of being in a single hit movie sent her career into hyperdrive on name recognition alone, while her equally talented contemporaries went nowhere. Did British colonists flock to cold, stormy, rocky shores of Massachusetts Bay because New England had the best land for farms? No: They came because Massachusetts Bay was where the Pilgrims got off the boat, and the Pilgrims got off the boat there because the Mayflower got lost looking for Virginia. Them that has gets -- and once the colony was established, there was no turning back. Nobody was about to pick up Boston and move it someplace else.

Increasing returns, lock-in, unpredictability, tiny events that have immense historical consequences -- "These properties of increasing-returns economics shocked me at first," says Arthur. "But when I recognized that each property had a counterpart in the nonlinear physics I was reading, I got very excited. Instead of being shocked, I became fascinated." Economists had actually been talking about such things for generations, he learned. But their efforts had always been isolated and scattered. He felt as though he were recognizing for the first time that ail these problems were the same problem. "I found myself walking into Aladdin's cave," he says, "picking up one treasure after another."

By the autumn, everything had fallen into place. On November 5, 1979, he poured it ail out. At the top of one page of his notebook he wrote the words "Economics Old and New," and under them listed two columns:

Old Economics New Economics

* Decreasing returns * Much use of increasing returns

* Based on 19th-century physics * Based on biology (structure,

(equilibrium, stability, deterministic pattern, self-organization, life

dynamics) cycle)

* People identical * Focus on individual life; people

separate and different

* If only there were no externalities * Externalities and differences become

and all had equal abilities, driving force. No Nirvana.

we'd reach Nirvana System constantly unfolding

* Elements are quantities and * Elements are patterns and possibilities


* No real dynamics in the sense * Economy is constantly on the

that everything is at equilibrium edge of time. It rushes forward, structures constantly coalescing, decaying, changing.

* Sees subject as structurally simple * Sees subject as inherently complex

* Economics as soft physics * Economics as high-complexity science

And so it went, for three pages. It was his manifesto for a whole new kind of economics. After ail those years, he says, "I finally had a point of view. A vision. A solution." It was a vision much like that of the Greek philosopher Heraclitus, who observed that you can never step into the same river twice. In Arthur's new economics, the economic world would be part of the human world. It would always be the same, but it would never be the same. It would be fluid, ever-changing, and alive.

What's the Point?

To say that Arthur was bubbling over with enthusiasm for his vision would be an understatement. But it didn't take him too long to realize that his enthusiasm was less than infectious, especially to other economists. "I thought that if you did something different and important -- and I did think increasing returns made sense of a lot of phenomena in economics and gave a direction that was badly needed -- people would hoist me on their shoulders and carry me in triumph. But that was just incredibly naive."

Before the month of November was out he found himself walking in the park near IIASA's Hapsburg palace, excitedly explaining increasing returns to a visiting Norwegian economist, Victor Norman. And he was suddenly taken aback to realize that Norman, a distinguished international trade theorist, was looking at him in bafflement: What was the point of all this? He heard much the same reaction when he began to give talks and seminars on increasing returns in 1980. About hall his audience would typically be very interested, while the other half ranged from puzzled to skeptical to hostile. What was the point? And what does any of this increasing-returns stuff have to do with real economics?

Questions like that left Arthur at a loss. How could they not see it? The point was that you have to look at the world as it is, not as some elegant theory says it ought to be. The whole thing reminded him of medical practice in the Renaissance, when doctors of medicine were learned in matters of theory and rarely deigned to touch a real patient. Health was simply a matter of equilibrium back then: If you were a sanguine person, or a choleric person, or whatever, you merely needed to have your fluids brought back into balance. "But what we know from 300 years worth of medicine, going from Harvey's discovery of the circulation of the blood on through molecular biology, is that the human organism is profoundly complicated. And that means that we now listen to a doctor who puts a stethoscope to a patient's chest and looks at each individual case." Indeed, it was on]y when medical researchers started paying attention to the real complications of the body that they were able to devise procedures and drugs that actually had a chance of doing some good.

He saw the increasing-returns approach as a step down that same path for economics. "The important thing is to observe the actual living economy out there," he says. "It's path-dependent, it's complicated, it's evolving, it's open, and it's organic."

Very quickly, however, it became apparent that what was really getting his critics riled up was this concept of the economy locking itself in to an unpredictable outcome. If the world can organize itself into many, many possible patterns, they asked, and if the pattern it finally chooses is a historical accident, then how can you predict anything? And if you can't predict anything, then how can what you're doing be called science?

Arthur had to admit that was a good question. Economists had long ago gotten the idea that their field had to be as "scientific" as physics, meaning that everything had to be mathematically predictable. And it was quite some time before even he got it through his head that physics isn't the only kind of science. Was Darwin "unscientific" because he couldn't predict what species will evolve in the next million years? Are geologists unscientific because they can't predict precisely where the next earthquake will come, or where the next mountain range will rise? Are astronomers unscientific because they can't predict precisely where the next star will be born?

Not at all. Predictions are nice, if you can make them. But the essence of science lies in explanation, laying bare the fundamental mechanisms of nature. That's what biologists, geologists, and astronomers do in their fields. And that's what he was trying to do for increasing returns.

Not surprisingly, arguments like that didn't convince anyone who didn't want to be convinced. On one occasion at IIASA in February 1982, for example, as Arthur was answering questions from the audience after a lecture on increasing returns, a visiting U.S. economist got up and demanded rather angrily, "Just give me one example of a technology that we are locked in to that isn't superior to ifs rivals!"

Arthur glanced at the lecture hall clock because he was running out of time, and almost without thinking said, "Oh! The clock."

The clock? Well, he explained, ail out clocks today have hands that move "clockwise." But under his theory, you'd expect there might be fossil technologies, buried deep in history, that might have been just as good as the ones that prevailed. It's just that by chance they didn't get going. "For ail I know, at some stage in history there may have been clocks with hands that went backward. They might have been as common as the ones we have now."

His questioner was unimpressed. Another distinguished U.S. economist then got up and snapped, "I don't sec that ifs locked in anyway. I wear a digital watch."

To Arthur, that was missing the point. But time was up for that day. And besides, it was just a conjecture. About three weeks later, however, he received a postcard from his IIASA colleague James Vaupel, who had been vacationing in Florence. The postcard showed the Florence Cathedral clock, which had been designed by Paolo Uccello in 1443 -- and which tan backward. (It also displayed all 24 hours.) On the flip side, Vaupel had simply written, "Congratulations!"

Arthur loved the Uccello clock so much that he made a transparency of it so he could show it in overhead projectors in all his future lectures on lock-in. It always produced a reaction. Once, in fact, he was showing the clock transparency during a talk at Stanford when an economics graduate student leaped up, flipped the transparency over so that everything was reversed, and said triumphantly, "You sec! This is a hoax! The clock actually goes clockwise!" Fortunately, however, Arthur had been doing a little research into clocks in the meantime, and he had another transparency of a backward clock with a Latin inscription. He put this transparency up, and said, "Unless you assume this is mirror writing done by Leonardo da Vinci, you have to accept that these clocks go backways."

Actually, by that point Arthur was able to give his audiences any number of lock-in examples. There were Beta-versus-VHS and QWERTY, of course. But there was also the strange case of the internal combustion engine. In the 1890s, Arthur discovered, when the automotive industry was still in its infancy, gasoline was considered the least-promising power source. Its chief rival, steam, was well developed, familiar, and sale; gasoline was expensive, noisy, dangerously explosive, hard to obtain in the right grade, and required a new kind of engine containing complicated new parts. Gasoline engines were also inherently less fuel-efficient. If things had been different and if steam engines had benefited from the same ninety years of development lavished on gasoline engines, we might now be living with considerably less air pollution and considerably less dependence on foreign oil.

But gasoline did win out -- largely, Arthur found, because of a series of historical accidents. In 1895, for example, a horseless-carriage competition sponsored by the Chicago Times-Herald was won by a gasoline-powered Duryea -- one of only two cars to finish out of six starters. This may have been the inspiration for Ransom Olds's 1896 patent of a gasoline engine that he subsequently mass-produced in the "Curved-Dash Olds." This allowed gasoline power to overcome its slow start. Then in 1914 there was an outbreak of hoof-and-mouth disease in North America, leading to the withdrawal of horse troughs -- which were the only places where steam cars could fill up with water. By the time the Stanley brothers, makers of the Stanley Steamer, were able to develop a condenser and boiler system that did hot need to be refilled every thirty or forty miles, it was too late. The steam car never recovered. Gasoline power quickly became locked in.

And then there was the case of nuclear power. When the United States embarked on ifs civilian nuclear power program in 1956, a number of designs were proposed: reactors cooled by gas, by ordinary "light" water, by a more exotic fluid known as "heavy" water, and even by liquid sodium. Each design had its technical advantages and disadvantages; indeed, with a perspective of thirty years, many engineers believe that a high-temperature, gas-cooled design would have been inherently safer and more efficient than the others, and may have forestalled most of the public anxiety and opposition to nuclear power. But as it happened, the technical arguments were almost irrelevent to the final choice. When the Soviets launched Sputnik in October of 1957, the Eisenhower administration was suddenly eager to get some reactor up and running -- any reactor. And at the rime, the only reactor that was anywhere near being ready was a highly compact, high-powered version of the light-water reactor, which had been developed by the Navy as a power plant for its nuclear submarines. So the Navy's design was hurriedly scaled up to commercial size and placed into operation. That led to further technical development of the light-water design, and by the mid-1960s, if had essentially displaced all the others in the United States.

Arthur recalls using the light-water reactor example in 1984 during a talk at the Kennedy School of Government at Harvard. "I was saying that here's a simple model that shows the economy can lock in to an inferior outcome, as it appears to have done with the light-water reactor. Whereupon a certain very distinguished economist stood up and shouted, 'Well, under perfect capital markets, if couldn't happen!' He gave a lot of technicalities, but basically, if you wheel up a lot of extra assumptions, then perfect capitalism would restore the Adam Smith world."

Well, maybe he was right. But six months later, Arthur gave the same talk in Moscow. Whereupon a member of the Supreme Soviet who happened to be in the audience got up and said, "What you're describing may happen in Western economies. But with perfect socialist planning this can't happen. We would arrive at the correct outcome."

Of course, so long as QWERTY, steam cars, and light-water reactors were just isolated examples, critics could always dismiss lock-in and increasing returns as something rare and pathological. Surely, they said, the normal economy isn't that messy and unpredictable. And at first Arthur suspected that they might be right; most of the time the market is fairly stable. It was only much later, as he was preparing a lecture on increasing returns for a group of postgraduate students, that he suddenly realized why the critics were also wrong. Increasing returns isn't an isolated phenomenon at ail: the principle applies to everything in high technology.

Look at a software product like Microsoft's Windows, he says. The company spent $50 million in research and development to get the first copy out the door. The second copy cost it -- what, $10 in materials? Ifs 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 -- 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 ail 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.

Now compare that with standard bulk commodities such as grain, fertilizer, or cement, where most of the know-how was acquired generations ago. Today the real costs are for labor, land, and raw materials, areas where diminishing returns can set in easily. (Producing more grain, for example, may require that farmers start to open up less productive land.) So these tend to be stable, mature industries that are described reasonably well by standard neoclassical economics. "In that sense, increasing returns isn't displacing the standard theory at all," says Arthur, "It's helping complete the standard theory. It just applies in a different domain."

What this means in practical terms, he adds, is that U.S. policy-makers ought to be very careful about their economic assumptions regarding, say, trade policy vis-à-vis Japan. "If you're using standard theory you can get it very badly wrong," he says. Several years ago, for example, he was at a conference where the British economist Christopher Freeman got up and declared that Japan's success in consumer electronics and other high-tech markets was inevitable. Just look at the country's low cost of capital, said Freeman, along with its canny investment banks, its powerful cartels, and its compelling need to exploit technology in the absence of oil and mineral resources.

"Well, I was the next speaker," says Arthur. "So I said, 'Let's imagine that Thailand or Indonesia had taken off and Japan was still languishing. Conventional economists would then be pointing to all the same reasons to explain Japan's backwardness. The low cost of capital means a low rate of return on capital -- so there's no reason to invest. Cartels are known to be inefficient. Collective decision-making means molasses-slow decision-making. Banks are not set up to take risks. And economies are hobbled if they lack oil and mineral resources. So how could the Japanese economy possibly have developed?'"

Since the Japanese economy quite obviously did develop, says Arthur, he argued for a different explanation: "I said that Japanese companies weren't successful because they had some magical qualities that U.S. and European companies didn't have. They were successful because increasing returns make high-tech markets unstable, lucrative, and possible to corner -- and because Japan understood this better and earlier than other countries. The Japanese are very quick at learning from other nations. And they are very good at targeting markets, going in with huge volume, and taking advantage of the dynamics of increasing returns to lock in their advantage."

He still believes that, says Arthur. And by the same token, he suspects that one of the main reasons the United States has had such a big problem with "competitiveness" is that government policy-makers and business executives alike were very slow to recognize the winner-take-all nature of high-tech markets. All through the 1970s and well into the 1980s, Arthur points out, the federal government followed a "hands-off" policy based on a conventional economic wisdom, which did not recognize the importance of nurturing an early advantage before the other side locks in the market. As a result, high-tech industries were treated exactly the same as low-tech, bulk-commodity industries. Any "industrial policy" that might have given a boost to infant industries was ridiculed as an assault on the free market. Free and open trade on everything remained a national goal. And firms were discouraged from cooperating by antitrust regulations drawn up in an era when the world was dominated by bulk commodities. That approach has begun to change a bit in the 1990s, says Arthur. But only a bit. So he, for one, argues that it is high time to rethink the conventional wisdom in light of increasing returns. "If we want to continue manufacturing our wealth from knowledge," he says, "we need to accommodate the new rules."

Meanwhile, even as he was collecting dozens of real-world examples of increasing returns, Arthur was looking for a way to analyze the phenomenon in rigorous mathematical terms. "I'm certainly not against mathematics per se," he says. "I'm a heavy-duty user. I'm just against mathematics when it's misapplied, when it becomes formalism for its own sake." Used correctly, he says, mathematics can give your ideas a tremendous clarity. It's like an engineer who gets an idea for a device and then builds a working model. The equations can tell you which parts of your theory work and which don't. They can tell you which concepts are necessary and which aren't. "When you mathematize something you distill its essence," he says.

Besides, says Arthur, he knew that if he didn't come up with a rigorous mathematical analysis of increasing returns, the wider economics community would never regard his theory as anything more than a collection of anecdotes. Look at what had happened in every previous effort to introduce the concept. Back in 1891, the great English economist Alfred Marshall actually devoted quite a bit of space to the increasing returns in his Principles of Economics -- the book in which he also introduced the concept of diminishing returns. "Marshall thought very deeply on increasing returns," says Arthur. "But he didn't have the mathematical tools to do much with it in an analytical way. In particular, he says, Marshall recognized even then that increasing returns could lead to multiple possible outcomes in the economy, which meant that the fundamental problem for economists was to understand precisely how one solution rather than another came to be selected. And economists ever since have gotten hung up on the same point. "Wherever there is more than one equilibrium point possible, the outcome was deemed to be indeterminate," he says. "End of story. There was no theory of how an equilibrium point came to be selected. And without that, economists couldn't bring themselves to incorporate increasing returns."

Something similar happened in the 1920s, when a number of European economists tried to use increasing-returns concepts to explain why cities grew and concentrated the way they did, and why different cities (and different countries) would specialize in, say, shoes or chocolates or fine violins. The basic concepts were correct, says Arthur. But again the mathematical tools just weren't there. "In the face of indeterminacy," he says, "economics came to a halt."

So Arthur sharpened his pencils and went to work. What he wanted was a mathematical framework that incorporated dynamics -- that showed explicitly, step by step, how the marketplace chose among the multiple possible outcomes. "In the real world, outcomes don't just happen," he says. "They build up gradually as small chance events become magnified by positive feedbacks." What he finally came up with in 1981, after many consultations with friends and colleagues, was a set of abstract equations based on a sophisticated theory of nonlinear, random processes. The equations were actually quite general, he says, and applied to essentially any kind of increasing-returns situation. Conceptually, however, they worked something like this: Suppose you are buying a car. (At the time, lots of people at IIASA were buying Volkswagens and Fiats.) And suppose, for the sake of simplicity, that there are just two models to choose from. Call them A and B. Now, you've read the brochures on both cars, says Arthur, but they're pretty similar, and you still aren't sure which to buy. So what do you do? Like any sensible person, you start asking your friends. And then it so happens, purely by chance, that the first two or three people you talk to say that they've been driving car A. They tell you that it works fine. So you decide to buy one, too.

But notice, says Arthur, there is now one more A-type driver in the world: you. And that means that the next person to come along asking about cars is just a little more likely to encounter an A-type driver. So that person will be just a little bit more likely to choose car A than you were. With enough lucky breaks like this, car A can come to dominate the market.

On the other hand, he says, suppose the breaks had gone the other way. Then you might have chosen to go with model B, and then car B would have gotten the edge and come to dominate.

In fact, says Arthur, under some conditions you can even show mathematically that with a few lucky breaks either way in the beginning, this kind of process can produce any outcome at all. The car sales might eventually come to lock in at a ratio of 40 percent A to 60 percent B, or 89 percent A to 11 percent B, or anything else. And it all works purely by chance. "Showing how chance events work to select one equilibrium point from many possible in random processes was the most challenging thing I've ever done," says Arthur. But by 1981, working in collaboration with his IIASA colleagues Yuri Ermoliev and Yuri Kaniovski of the Skorokhod School in Kiev -- "two of the best probability theorists in the world" -- he had it. The three of them published the first of their several papers on the subject in the Soviet journal Kibernetika in 1983. "Now," says Arthur, "economists could not only follow the entire process by which one outcome emerged, they could see mathematically how different sets of historical accidents could cause radically different outcomes to emerge."

And most important, he says, increasing returns was no longer, in the words of the great Austrian economist Joseph Schumpeter, "a chaos that is not under analytical control."

Violating Sacred Ground

In 1982, Arthur suddenly found IIASA to be a far less hospitable place than it had been, courtesy of the rapidly chilling Cold War. The Reagan administration, eager to avoid any further taint by association with the Evil Empire, had abruptly pulled the United States out of the organization. Arthur was sorry to go. He'd greatly enjoyed working with his Soviet colleagues, and how could you beat an office in a Hapsburg palace? But things worked out well enough, as it happens. As a stopgap, Arthur took up a one-year visiting professorship at Stanford, where his reputation for demography seemed to stand him in good stead. And shortly before his year there drew to a close he got a call from the dean: "What would it take to keep you here?"

"Well," Arthur replied, secure in the knowledge that he already had a fistful of job offers from the World Bank, the London School of Economics, and Princeton, "I see there's this endowed chair coming open...."

The dean was shocked. Endowed professorships are very prestigious. They are generally only awarded to the most distinguished researchers. In effect, they are sinecures for life. "We don't negotiate with endowed chairs!" she declared.

"I wasn't negotiating," said Arthur. "You just asked me what it would take to keep me here."

So they gave it to him. In 1983, at age thirty-seven, Arthur became the Dean and Virginia Morrison Professor of Population Studies and Economics. "My first permanent job in academia!" he laughs. He was one of the youngest endowed professors in Stanford's history.

It was a moment to savor -- which in retrospect, turned out to be a good thing. He wasn't destined to have many such moments for a long while. However much his fellow economists may have liked his work in demography, many of them seemed to find his ideas on increasing-returns economics outrageous.

To be fair, he says, many of them were also quite receptive, even enthusiastic. But it was true that his most virulent critics had almost always been Americans. And being at Stanford brought him face to face with that fact. "I could talk about these ideas in Caracas, no sweat whatever. I could talk about them in Vienna, no sweat. But whenever I talked about these ideas in the United States, there was hell to pay. People got angry at the very notion that anything like this could happen."

Arthur found the Americans' hostility both mystifying and disturbing. Some of it he put down to their well-known fondness for mathematics. After all, if you spend your career proving theorems about the existence of market equilibrium, and the uniqueness of market equilibrium, and the efficiency of market equilibrium, you aren't likely to be very happy when someone comes along and tells you that there's something fishy about market equilibrium. As the economist John R. Hicks had written in 1939, when he looked aghast at the implications of increasing returns, "The threatened wreckage is that of the greater part of economic theory."

But Arthur also sensed that the hostility went deeper than that. American economists are famous for being far more passionately devoted to free-market principles than almost anyone else in the world. At the time, in fact, the Reagan administration was busily cutting taxes, junking federal regulations, "privatizing" federal services, and generally treating free-market capitalism as a kind of state religion. And the reason for that passion, as Arthur slowly came to realize, was that the free-market ideal had become bound up with American ideals of individual rights and individual liberty: both are grounded in the notion that society works best when people are left alone to do what they want.

"Every democratic society has to solve a certain problem," says Arthur: "If you let people do their own thing, how do you assure the common good? In Germany, that problem is solved by everybody watching everybody else out the windows. People will come right up to you and say, 'Put a cap on that baby!'"

In England, they have this notion of a body of wise people at the top looking after things. "Oh, yes, we've had this Royal Commission, chaired by Lord So-and-So. We've taken all your interests into account, and there'll be a nuclear reactor in your backyard tomorrow."

But in the United States, the ideal is maximum individual freedom-or, as Arthur puts it, "letting everybody be their own John Wayne and run around with guns." However much that ideal is compromised in practice, it still holds mythic power.

But increasing returns cut to the heart of that myth. If small chance events can lock you in to any of several possible outcomes, then the outcome that's actually selected may not be the best. And that means that maximum individual freedom -- and the free market -- might not produce the best of all possible worlds. So by advocating increasing returns, Arthur was innocently treading into a minefield.

Well, he had to admit that he'd had fair warning.

It was in 1980, he recalls. He had been invited to give a series of talks on economic demography at the Academy of Sciences in Budapest. And one evening, at the bar of the Budapest Intercontinental Hotel, he found himself chatting with academician Maria Augusztinovics. Standing there with a scotch in one hand and a cigarette in the other, she was a most formidable lady. Not only had she married, in succession, most of the top economists in Hungary but she was a very perceptive economist herself. Moreover, she was an influential politician, with a post high in the Hungarian government. She was rumored to eat bureaucrats for breakfast. Arthur saw no reason to doubt it.

What are you working on these days? she asked. Arthur enthusiastically launched into a discourse about increasing returns. "It explains so many problems," he concluded, "all these processes and patterns."

Augusztinovics, who knew exactly what the philosophical stakes were for Western economists, simply looked at him with a kind of pity. "They will crucify you," she said.

"She was right," says Arthur. "The years from 1982 through 1987 were dreadful. That's when my hair turned gray."

Arthur has to admit that he brought a lot of that agony on himself. "If I had been the kind of person who forms inside allegiances in the profession, then the whole thing might have gone smoother," he says. "But I'm not an insider by nature. I'm just not a joiner."

With that Irish streak of rebelliousness, he was also not in a mood to dress up his ideas in a lot of jargon and phony analysis just to make them palatable to the mainstream. And that's what led him to make a critical tactical blunder: in the summer of 1983, when he was preparing his first paper on increasing returns for official publication, he wrote the thing in more or less plain English.

"I was convinced that I was onto something crucial in economics," he explains. "So I decided that I should write it at a very intelligible level, where it could be understood even by undergraduates, I thought that fancy mathematics would just get in the way of the argument. I also thought, 'Gee, I've published heavily mathematical papers before. I don't need to prove anything.'"

Wrong. If he hadn't known it before, he says, he learned it soon enough. Theoretical economists use their mathematical prowess the way the great stags of the forest use their antlers: to do battle with one another and to establish dominance. A stag who doesn't use his antlers is nothing. It was fortunate that Arthur circulated his manuscript informally that autumn as an IIASA working paper. The official, published version wasn't to see the light of day for another six years.

The most prestigious U.S. journal, The American Economic Review, sent the paper back in early 1984 with a letter from the editor saying, in essence, "No way!" The Quarterly Journal of Economics sent the paper back saying that its reviewers could find no technical fault, but that they just didn't think the work was worth anything. The American Economic Review, under a new editor this time, tentatively accepted the paper on its second submittal, bounced it around internally for two and a half years while demanding innumerable rewrites, and then rejected it again. And The Economic Journal in Britain simply said, "No!" (After some fourteen rewrites, the paper was finally accepted by The Economic Journal and published in March 1989 as "Competing Technologies, Increasing Returns, and Lock-In by Historical Events.")

Arthur was left in helpless rage. Martin Luther could nail his ninety-five theses to the church door of Wittenberg to be read by one and all. But in modern academia, there are no church doors; an idea that hasn't been published in an established journal doesn't officially exist. And what he found doubly frustrating, ironically, was the fact that the idea of increasing returns was finally beginning to catch on. It was becoming something of a movement in economics -- and so long as his paper was in limbo, he couldn't take part in it.

Take the economic historians, for example -- the people who did empirical studies on the history of technologies, the origin of industries, and the development of real economies. Stanford had a first-class group of them, and they had been among Arthur's earliest and most enthusiastic supporters. For years, they had suffered from the fact that neoclassical theory, if really taken seriously, says that history is irrelevant. An economy in perfect equilibrium exists outside of history; the marketplace will converge to the best of all possible worlds no matter what historical accidents intervene. And while very few economists took it quite that seriously, a lot of economics departments around the country were thinking of scrapping their required courses in economic history. So the historians liked lock-in. They liked the idea that small events could have large consequences. They saw Arthur's ideas about increasing returns as providing them with a rationale for their existence.

No one was a more effective advocate of that point of view than Arthur's Stanford colleague Paul David, who had independently published some thoughts about increasing returns and economic history back in the mid-1970s. But from Arthur's point of view, even David's support backfired. At the national meeting of the American Economics Association in late 1984, David participated in a panel discussion on "What Is the Use of History?" and used the QWERTY keyboard example to explain lock-in and path dependence to 600 economists at once. The talk created a sensation. Even the hard-core mathematical economists were impressed: here was a theoretical reason for thinking that history was important. Even the Boston Globe wrote about it. And Arthur was soon hearing people ask him, "Oh, you're from Stanford. Have you heard about Paul David's work on lock-in and path dependence?"

"It was simply dreadful," Arthur recalls. "I felt I had something to say, and I couldn't say it -- and the ideas were getting credited to other people. It appeared that I was following rather than leading. I felt like I was in some doomed fairy story."

The Berkeley debacle with Fishlow and Rothenberg in March 1987 was arguably his lowest moment -- but not by much. He began to have nightmares. "About three times a week I'd have this dream of a plane taking off -- and I was not on it. I felt I was definitely getting left behind." He seriously began to think of abandoning economics and devoting himself full time again to his demographic research. His academic career seemed to be turning to ashes.

All that kept him going was stubbornness. "I just pushed, and pushed, and pushed," he says. "I just kept believing that the system had to give somewhere."

Actually, he was right. And as it happens, he didn't have too much longer to wait.

Copyright © 1992 by M. Mitchell Waldrop

About The Author

Product Details

  • Publisher: Simon & Schuster (September 1, 1993)
  • Length: 384 pages
  • ISBN13: 9780671872342

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The Washington Post If you liked Chaos, you'll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year.

Heinz Pagels physicist I am convinced that the nations and people who master the new sciences of complexity will become the economic, cultural, and political superpowers of the next century.

The New York Times Book Review Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner....[Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.

Douglas R. Hofstadter author of Götel, Esther, Bach One comes away from Complexity both intellectually excited by ideas and emotionally involved with the people struggling to formulate them. This is a deep tale of science in the making.

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