7

Tyranny of the Dragon King

DIDIER SORNETTE LOOKED AT THE DATA AGAIN. He rubbed his forehead thoughtfully. The pattern was unmistakable. Something was about to happen — something big. He was sure of it, even though predicting such things was notoriously difficult. He leaned back and looked out the window of his office at the University of California, Los Angeles, geophysics institute. Such a tremor could have substantial consequences. The question, though, was what to do about it. Should he issue a warning? Would anyone believe him? And even if anyone did, what could be done?

It was late summer 1997. Sornette had been working on this theory for years now, though the idea of applying it in the present context was new. Still, he had had ample time to test it with historical data. In each instance, before a major event, he had seen this same characteristic pattern. It looked like a wavy line, but with the oscillations getting faster and faster over time, the peaks becoming closer and closer to one another as though they were all trying to bunch up around the same point. The critical point. Sornette had found, both theoretically and experimentally, that these patterns should be robust enough to make predictions, to project when the critical point would occur. The same pattern appeared all over the place: before earthquakes, before avalanches, before certain kinds of materials exploded. But this time it was different. This time, Sornette actually saw the pattern in advance. It was the difference between realizing a prediction was possible — a risk-free endeavor — and actually making it. But Sornette was confident. He would be willing to bet on this.

He picked up the phone and called his colleague Olivier Ledoit. Ledoit was a young faculty member at the Anderson Graduate School of Management at UCLA. Sornette told his friend what he had found. The data showed that a critical event was coming. Earth-shattering, perhaps, but not geological: this event would be a potentially dramatic crash of the world’s financial markets. Sornette could even say when it would happen. His calculations put it at the end of October, just a few months away.

Sornette had been working his way into finance for several years, but even so he was still a physicist. Ledoit knew the financial industry and could help him figure out the next steps. The two settled on a plan. First, they would file their warning with the authorities. Sornette and his postdoctoral researcher at UCLA, another geophysicist-cum-economist named Anders Johansen, wrote a notice and sent it to the French patent office. No one would believe them now, of course — none of the traditional methods of analyzing markets pointed to instability. And if they waited until after the crash, no one would believe them either, though for a different reason: their voices would be lost among the thousands of economists and investors who would insist they had seen this coming. The patent filing would be their insurance policy, their proof that they really had made the prediction, over a month before the crash. The notice was filed on September 17, 1997. It predicted a market crash in late October of that same year.

The second step? Profit. It’s easy to make money when markets are rising. But in many ways, a market crash is an even more dramatic profit opportunity, if you can see it coming. There are several ways to make money off a crash, but the simplest way is buying put options. The options I discussed earlier are known as call options. You buy the right to purchase a stock at some fixed price, called the strike price, at some time in the future. If the market value of the stock goes above the strike price, you profit, because you have the right to buy the stock at the strike price, and then sell it at the higher market price, pocketing the difference. Of course, if the price doesn’t go up, that’s OK too. You’re only out the money spent on the option, and not the higher price of the stock itself. Put options work in essentially the opposite way. You buy the right to sell a stock at a specific price. In this case, you profit if the price of the stock falls below the strike price, because you can buy the stock at the market price and sell it at the higher strike price, again pocketing the difference.

Recall that far-out-of-the-money options are options that will be valuable only if the market takes a dramatic swing. Since dramatic market swings tend to be unlikely, far-out-of-the-money options tend to be very inexpensive (because the people selling them believe they carry little risk). When markets crash, however, these far-out-of-the-money put options can become very valuable indeed, with almost no initial cost. And if you know when the market is going to crash, you can walk away with enormous profits accrued over a very short time — just a few days, say — with relatively little risk. It sure beats buy-and-hold. The problem, of course, is predicting the unpredictable.

Imagine inflating a balloon. You start with a limp piece of rubber. In this uninflated state, the balloon is stretchy and very difficult to tear. You could poke it and prod it any way you like, even with a very sharp knife, and unless you stretch the balloon out first, the knife is unlikely to puncture it. A pin would do no damage at all. Now begin to blow air into it. After a few puffs, the balloon starts to expand. The pressure from the air inside is pushing the walls of the balloon out, just enough to give the surface a roughly spherical shape. The material still has considerable give. Depending on how much air has been pumped in, a very sharp knife might now slice the rubber, but the balloon certainly won’t pop, even if you manage to puncture it. A puncture would allow the air inside to leak, but it wouldn’t be very dramatic.

As you blow more air into the balloon, however, it becomes increasingly sensitive to outside effects. A fully inflated balloon is liable to pop from the slightest brush with a tree branch or a bit of concrete — a tap from a pin is certain to make it explode. Indeed, if you keep blowing air into a balloon, you can make it burst by touching it with your fingertips, or by simply blowing in another mouthful of air. Once the balloon is primed, it doesn’t take much to produce a very dramatic effect: the balloon shreds into tiny pieces faster than the speed of sound.

What makes a balloon pop? In some sense, it’s an external cause: a tree branch or a pin, or perhaps the pressure from your fingers as you hold it. But these very same influences, under most circumstances, have little or no effect on the balloon. The balloon needs to be inflated, or even overinflated, for the external cause to take hold. Moreover, the particular external cause doesn’t much matter — it’s far more important that the balloon be highly inflated when it is pricked. In fact, the external cause of a popped balloon isn’t what makes the balloon pop at all. It’s the internal instability in the balloon’s state that makes it susceptible to an explosive pop.

The bursting of a balloon is one of a variety of phenomena known as ruptures. Ruptures occur in all sorts of materials when they are put under stress. A rupture can often be thought of as a straw-that-broke-the-camel’s-back effect: the stress on a substance, such as high internal pressure (caused, for instance, by the air in a balloon, or the gas in a soda can that has been shaken up — or the accumulated weight on a camel’s back), leads to instabilities that in turn make the material vulnerable to explosive events. These explosions, sometimes called critical events, are the ruptures. Just as when a balloon bursts, a rupturing material changes its state very rapidly, releasing a substantial amount of energy in the process. Events that might otherwise have little effect, like a pin breaking the surface of an only partially inflated balloon, tend to cascade, building into something larger.

No one has done more to improve our understanding of ruptures than Didier Sornette. He has been stunningly prolific. Still in his early fifties, he has published more than 450 scientific articles in just thirty years. He has also written four books, one on physics, two on finance, and one on Zipf’s law, the unusual distribution that first attracted Mandelbrot’s attention. But even more remarkable than the amount of work he has produced is its range. Most physicists, even the most successful, work in a handful of closely connected areas. Acquiring expertise in a new area is difficult, and for most people, once or twice is often enough for a lifetime.

But Sornette has made contributions to more than a dozen fields, ranging from material science to geophysics, to decision theory (a branch of economics and psychology), to financial markets, even to neuroscience (he has done considerable work on the origin and prediction of epileptic seizures). He thinks of himself as a scientist in the broadest sense, as someone conversant in the sciences at large. He studied physics as a young man, not because he believed he wanted to devote his life to the field, but because he thought of physics as a kind of mother science. He likes to quote the philosopher Descartes, who in his magnum opus Discourse on Method wrote that the sciences are like a tree: metaphysics is the roots, physics is the trunk, and everything else is the branches. (Nowadays, Sornette is more modest about his training. He thinks of his background in physics as an excellent preparation for approaching many problems but says that the intellectual challenges of fields like economics and biology are at least an order of magnitude more difficult than those posed by physics.) Despite the variety of topics, however, much of Sornette’s work involves identifying patterns endemic to the structures of complex systems and using these patterns to predict critical phenomena: ruptures, quakes, crashes.

One of Sornette’s earliest scientific projects involved ruptures in Kevlar, a synthetic fiber developed in 1965 by Du Pont (and heir to the nylon tradition described earlier). It is a famously strong substance, used in the bulletproof vests worn by police and soldiers, and even as a replacement for steel in suspension bridge cables. It is stronger at very cold temperatures than at room temperature, and it is largely stable at extremely high heat, at least for short periods. It’s a marvel of modern chemistry.

These properties have made Kevlar a very attractive material for all sorts of high-tech applications. It was one of these — space flight — that led Sornette to become involved in Kevlar research. Initially, the space race was a two-sided affair, between the United States and the Soviet Union. But by the mid-1960s, the leaders of several Western European nations began to realize that Europe couldn’t rely on the largesse of the superpowers to further European economic, military, and scientific interests in space. At first, Europe’s entry into the space race was slow and scattered, but then in 1975, the various nascent organizations that had been formed over the previous decade combined into what is now the European Space Agency. By this time, the space race had begun to slow, with further escalation proving too costly for both superpowers. This left an opportunity for the new European agency to rapidly catch up and assert itself as a dominant force in the space industry. A principal part of the new European initiative was a series of cutting-edge rockets called Ariane, designed as satellite delivery mechanisms.

In 1983, the still-young European Space Agency began developing a new variety of Ariane rocket, the Ariane 4, to launch commercial satellites, particularly communication satellites. (It was enormously successful — at one stage, it was used for roughly half of all commercial satellites launched worldwide.) The new rocket was designed by the French space agency, CNES, but manufactured by private contractors. It was one of these private contractors, a firm called Aérospatiale, that contacted Sornette.

Rockets, including the Ariane, often require several substances that need to be kept under very high pressure in order for combustion to occur. The chemicals are stored in vessels called pressure tanks — essentially, high-tech water balloons intended to maintain the necessary high pressures without bursting under the strain. The researchers at Aérospatiale who contacted Sornette were studying the behavior of pressure tanks that would be used in the Ariane 4. These tanks were made out of Kevlar. Usually, the tanks were strong, even at very high pressures. Except when they suddenly exploded. The group at Aérospatiale was trying to determine the conditions under which this would happen.

We know that if a balloon is inflated sufficiently, it will nearly always pop when pricked with a sharp pin. Other substances, though, can be trickier to figure out. Materials like Kevlar will eventually rupture from the strain of high-pressure contents, but determining precisely when, or why, is a surprisingly difficult problem. When substances like Kevlar are put under significant stress, tiny fractures begin to appear. Sometimes these fractures combine and grow into slightly larger fractures. Sometimes these slightly larger fractures grow into still-larger fractures, and so on, until you get a very large fracture. These fractures follow a pattern we have already seen: they are fractals, where the tiniest fractures look just like the larger ones. The difficulty is that tiny fractures don’t affect the behavior of the pressure tanks, whereas the largest fractures can be disastrous. But it’s hard to say what makes a large fracture different from a small one, at least in terms of the fractures’ causes. A large fracture is just a small one that never stopped growing; very large, disruptive fractures are no different in kind from the very small benign ones.

This relationship between large and small fractures posed a major problem for the rocket scientists. It meant that even under ordinary working conditions, when the Kevlar was usually stable, there was always a chance that a normal tiny fracture would spontaneously grow into a major one and destroy the rocket. Any given fracture, even the very smallest ones, had the capacity to become explosive. When Sornette joined the team, the other scientists were at a loss. To put these pressure tanks to good use, they needed to figure out how to use them safely — that is, they needed to figure out the conditions under which ruptures would occur. But this seemed an impossible task. The ruptures seemed, quite simply, random.

Until Sornette noticed a pattern.

Normally, the parts of a pressure tank are more or less independent, like workers in the nineteenth century, before collective bargaining. If you kick a pressure tank, for instance, there might be some vibrations, but these will die off pretty quickly, and even if you manage to put a dent in the part of the tank where your foot made contact (unlikely), you won’t do any damage to the rest of the tank. Likewise, if a small fracture appears under these circumstances, it won’t produce a rupture. This is a bit like when you try to pop an only partially inflated balloon: a pin doesn’t have much of an effect.

Sometimes, though, the various parts of the material begin to conspire with one another. They display a kind of herding effect. This can happen for various reasons: heat, say, or pressure, or other external effects. When this occurs, it’s almost as if the various parts of the material have unionized. A kick in one place can ripple through a whole tank, with small localized influences leading to dramatic effects, much as a pinprick in one place can make an inflated balloon tear itself apart. This kind of conspiracy is sometimes called self-organization, because no matter how random and uncorrelated the materials are to begin with, if they are placed under stress, they will begin to coordinate their activity. It’s as though the bits and pieces of material begin to stir under pressure, gradually deciding to join together in common cause.

Sornette didn’t come up with the notion of self-organization, though he has done as much work on the theory as anyone. Instead, he realized something slightly different. He finally understood how a small labor strike differs from a catastrophic one. All strikes are caused by the same sorts of sparks: an egregious injury; an unfair termination; cut wages. You might think that there’s no way of telling which such events will lead to a nationwide walkout. A large strike looks like a small strike that, for whatever reason, simply didn’t stop. So, too, with the microfractures that, under some circumstances, seem to explode into ruptures that tear a material apart. But the biggest strikes require something more than just a spark: they require a labor movement, with a high degree of structure and a capacity for coordinated action. They require a mechanism for system-wide feedback and amplification, something to transform an otherwise small event into a large one. In other words, if you want to predict a major strike, don’t look for the grievances. Those are always there. Look for the unions. Look for telltale patterns of self-organization. Coordination, rather than the pinpricks, is what really leads to critical events. And Sornette would take that insight straight to the bank.

Sornette was born in Paris but raised in the southeast of France, in a town called Draguignan on the French Riviera. Draguignan is about an hour by car from Saint-Tropez, the beautiful Mediterranean resort town famous as a jet-set vacation spot. Through high school, Sornette would often go to Saint-Tropez to sail and wind-surf. Once he graduated, he moved up the coast to Nice where he enrolled in a preparatory school to study for the grande école admissions exam. (It was at a similar kind of school in Lyon, a couple of hundred miles north, that Mandelbrot hid from the Nazis during World War II.) Sornette performed extremely well on his exams and was admitted to the most prestigious of the grandes écoles, École Normale Supérieure.

He received his doctorate in 1981, at the young age of twenty-four — and was immediately given a tenured position at the University of Nice. His earliest work was in an area of physics known as condensed matter — the study of matter under extreme conditions. But he began to branch out the following year, when he began his obligatory military service. He spent these years working at a government military contractor called Thomson-Sintra (keeping his academic position all the while). It was during this period, working on research for the military, that Sornette first began to study chaos theory and complex systems, subjects that would later provide much of the foundation for his interdisciplinary work.

In June 1986, Sornette married a young geophysicist named Anne Sauron. At the time she was a PhD student in Orléans, interested in geophysics, but after their marriage she moved to Nice, where Sornette was already established. Shortly after their wedding, Sornette secured funding for his new wife to join his research group, with him as her doctoral advisor. They focused on connecting the work Sornette had begun on ruptures to questions concerning the cause of earthquakes.

Although Sornette was officially Sauron’s advisor, their work was really a collaboration between experts in different fields. He didn’t know the first thing about earthquakes when they began working together (she, meanwhile, didn’t know anything about material rupture). But Sornette was a quick study. Together, they began to think about applying fractal geometry to the study of tectonic plates, sections of the Earth’s crust that slowly creep around the planet. Tectonic plates were originally proposed to explain the strange evidence that the continents were once connected — for example, certain varieties of plant are found only in western South America and eastern Australia — but they are now believed to be responsible for things like earthquakes (which occur when two plates collide or shift past one another), mountain ranges (which form when the plates collide, buckling at the collision site), volcanoes (which erupt at the interface between plates, where magma from below the crust can escape), and ocean trenches (the opposite of mountain ranges). The Sornettes’ work was an attempt to understand how the current geology and topography of the divide between Asia and India — a stretch of land as long across as the continental United States, spanning the Himalayas and a handful of smaller mountain ranges — could arise as a result of many small earthquakes over millions of years, as the two continents collided with one another.

Geophysicists study a broad swath of topics concerning the internal structure of planets. But their bread and butter, the research that gets funding agencies most excited, is predicting natural disasters like earthquakes and volcanoes. Earthquake prediction is a matter of particular importance, for both scientific and humanitarian reasons. It is also famously difficult, though this hasn’t stopped scientists, and before that philosophers and astrologers, from trying their hand. The ancient Roman historian Aelian, for instance, hinted that animals could accurately predict earthquakes, claiming that snakes and weasels evacuated the Greek city of Helice a few days in advance of an earthquake that devastated the region. An ancient Indian astrologer and mathematician named Varahamihira believed that earthquakes could be predicted by looking for particular cloud patterns.

In the 1960s and 1970s, the United States and the Soviet Union launched competing earthquake prediction initiatives, showering geophysicists with funds. These programs led to claims that anything from electrical storms to increased radioactivity to an absence of earthquakes could be used to predict future disasters. But the state of the art, especially in the mid-1980s, was not much better than it was when Helice succumbed in 373 B.C. (Indeed, both animal behavior and earthquake clouds remain on the list of active research programs, even today.) The ability to accurately predict earthquakes is a kind of holy grail.

Sornette began his collaboration with Aérospatiale in 1989. That same year, he and Sauron published a paper connecting self-organization, the idea behind the theory of ruptures he had been developing, to earthquakes. The analogy was quite close: the Earth’s crust could be understood as a material capable of rupture; a theory that described rupture in something like Kevlar could also, in principle, describe rupture in something like rock. The last step was simply to view catastrophic earthquakes as critical events, ruptures at the interface between tectonic plates. It was not the very first paper to link the ideas of self-organization, criticality, and earthquakes. But it was close. And it set the stage for Sornette to think of his two parallel projects — pressure tanks and earthquakes — as closely connected.

The moment of inspiration came two years later, in 1991. By this time, he and others had developed a detailed model for how fractures and cracks percolate through a material. This model accounted for how degrees of organization and coordination could serve to amplify fractures, to turn small causes into large effects. It was while thinking about this model that Sornette realized that if all of the pieces were in place for a critical event, an explosive rupture, the way in which the fractures leading up to the rupture would multiply would be affected. The idea was that a rupture would be preceded by smaller events, following a very specific, accelerating pattern. This pattern is called log-periodic because the time between the smaller events decreases in a particular way, related to the logarithm of the time. Since this pattern would occur only if the system were primed for a rupture, it counted as a signal that a critical event was about to occur. And because the pattern was one that accelerated over time, if you looked at a few of the smaller events in a row, you could determine whether they were showing the log-periodic behavior (because the time between the events would be shrinking), and you could extrapolate forward in time to figure out when the peaks would collapse into one another, thus predicting the critical event.

Sornette first sought to test the theory with the pressure tanks. Sure enough, right before a rupture, he and his collaborators observed the log-periodic pattern in vibrations of the tanks known as acoustic emissions. Basically, the tanks would start rumbling as fractures began to appear. And if the rumblings were log-periodic, a critical event was about to occur. Aérospatiale quickly patented the method for predicting when its rockets’ tanks would explode; it is still used today for forecasting and testing pressure tank failure.

But pressure tanks were only the beginning. If the Sornettes were right about the close connection between material rupture and earthquakes, Didier’s discovery had enormous implications. There were all sorts of reasons for the occurrence of small earthquakes, which were the equivalent of tiny fractures in Kevlar under stress. But if catastrophic earthquakes were like ruptures, as the Sornettes had proposed, then one should be able to predict a critical earthquake by looking for the log-periodic pattern in the geophysical data. (There is a long history of people believing that small earthquakes foretell larger ones — Sornette’s approach makes this much more precise, by saying when small earthquakes are predictive.) Sornette’s methods weren’t useful for predicting anything but the critical earthquakes, the ones that resulted from underlying coordination. But these were usually the biggest earthquakes of all, the ones that leveled cities and tore continents apart. It was a tool for predicting catastrophe. The holy grail, indeed.

As September 1997 crept to an end and October began, Sornette and Ledoit began to buy far-out-of-the-money put options. Neither had a fortune to invest, but the options were cheap. Nervously, they watched as the major world indices marched along, blithely unaware that disaster was just around the bend. Sornette was confident enough to put his own money where his best science told him to. But there have been only a handful of market crashes in modern history. This pattern could have been a false alarm. Much was on the line for Sornette, both financially and intellectually.

The middle of October came and went. Sornette’s predictions were not perfectly precise — the market oscillations put the crash somewhere toward the end of October, but it was difficult to pinpoint a specific day. Each day, the probability that the crash would happen (given that it hadn’t already) increased. But this would continue for only a short while — it was theoretically possible, if unlikely, for the critical point to pass without so much as a shudder from the markets. Another week passed. Going into the weekend of October 24, there was still no crash. It was becoming nerve-racking. The end of October was here, and Sornette had nothing to show for it.

And then it happened. On Monday, October 27, 1997, the Dow Jones Industrial Average suffered its sixth-largest single-day point loss ever, down 554 points. The NASDAQ and S&P 500 indexes suffered similar losses. For the first time in its history, the New York Stock Exchange was forced to close early in order to avoid a still more severe catastrophe. On that day alone, over $650 billion vanished from New York’s financial markets. International markets fared just as poorly, with sharp declines in London, Frankfurt, and Tokyo. The Hong Kong Hang Seng index fell 14% the following night.

Sornette and Ledoit, however, made a 400% profit. They released their Merrill Lynch trading statement that November to prove it. The crash had come, just as Sornette had predicted.

Historians now explain the worldwide crash as a reverberation effect. Earlier that year, the Thai baht collapsed after the Thai government decided to stop pegging it to the U.S. dollar. Thailand carried significant foreign debt before the collapse of the currency, and afterward the country was essentially bankrupt. Thailand’s difficulties quickly spread to its neighbors, earning the nickname “Asian flu” for the crisis because of the way it moved through Southeast Asian economies, devaluing currencies and depressing equity markets throughout the region. These conditions increased uncertainty in all parts of the world’s economy, leading to unusually high variations in the prices of securities. When Asian markets fell overnight on the twenty-sixth, investors in the United States reacted strongly and amplified the crash.

One of the most striking things about the October 27 crash, and the reason it is now referred to as a “mini crash,” is that New York markets rebounded the next day. By the close of trading on the twenty-eighth, the Dow had regained 60% of the previous day’s losses. And in a striking counterpoint to closing its doors early for the first time the day before, October 28 was the first day that over a billion shares were traded on the NYSE. This kind of dramatic seesawing is telling: since the cumulative effect of the crash and rebound was a relatively modest change in prices, standard reasoning about pricing in an efficient market does not seem to apply. That is, any theory of the stock market that accounts for price changes in terms of the actual values of the companies whose stocks are being traded would predict that a crash would correspond to some dramatic change in the real-world values. But this didn’t happen. Stocks were worth more or less the same amount on October 29 as they had been on October 26, indicating that most investors didn’t think the values of the companies had changed all that much. Instead, it seems that the crash resulted from some sort of internal instability in the markets themselves.

According to Sornette and his collaborators, this is a feature that shows up in many market crashes. As he is fond of pointing out, the standard economic reasoning suggests that if bubbles are possible at all, they can end only with some dramatic news that materially changes the value of firms whose stocks are being traded. And yet, many economists agree that if you look at particular crashes, it is often very hard to identify what that piece of news could have been. Sure, there’s always some piece of bad news to associate with a market crash. But one is often stuck blaming extreme events on run-of-the-mill external causes that do not seem to change the value of the things being traded. This alone should be highly suggestive, at least to someone who is accustomed to thinking about critical phenomena in physics, because it implies that even if a piece of news is the immediate cause of a crash, there is something about the state of the market that determines whether the market actually crashes, or just closes a few points lower. And as with ruptures and earthquakes, Sornette argues, even if you cannot predict the news, you can try to identify when the market is in a precarious state. Just look for the log-periodic tremors.

Critical phenomena often have what physicists call universal properties. This means that you can start with two materials that look as different from one another as can be — a Kevlar tank, for instance, and tectonic plates — and find that, despite the profound differences in their microscopic details, under certain circumstances they exhibit the exact same large-scale behaviors. Both rupture, for instance, as a result of prolonged strain. If you look in detail at how the ruptures occur, you find that the differences in the microscopic details fade away and the radically different materials end up acting in more or less the same way. There are certain universal laws that seem to apply at a statistical level. You might think of these as laws that govern coordination between parts, irrespective of what the parts happen to be. It is this kind of universality that makes Sornette and his collaborators’ ideas so widely applicable. The details are often different from field to field, but the principal mechanisms are not. The same phenomena affect avalanches, forest fires, political revolutions, even epileptic seizures.

Sornette’s first foray into economics was in 1994. He coauthored a paper with another physicist in France, named Jean-Philippe Bouchaud. That same year, Sornette and Bouchaud went on to found a research company called Science & Finance, which in 2000 merged with a Parisian hedge fund management company, Capital Fund Management (CFM). Today Bouchaud is chairman and chief scientist of CFM, which has grown to be the largest hedge fund management company in France. (He is still officially a physics professor, at École Polytechnique, the grande école near Paris where Mandelbrot studied; Sornette, meanwhile, left Science & Finance in 1997.) Their joint paper showed how to price options even if the underlying stock does not follow the kind of random walk assumed by Black and Scholes. This effectively extended the theory of options pricing to more sophisticated models of price changes, including those with fat-tailed distributions. (O’Connor and Associates had already done work along these lines — but this wasn’t widely known.)

After that paper, Sornette was hooked. Over the next several years, he read more and more about traditional economics, adding what he could to problems like options pricing and risk. (Sornette prides himself on having learned to think like an economist.) Much of this early work was done in collaboration with Bouchaud, who by this time was working on finance nearly full-time.

In 1996, Sornette’s work on earthquakes earned him a part-time professor-in-residence position in UCLA’s earth and space sciences department, and at the Institute of Geophysics and Planetary Physics. By this time, though, at least half of his energy was devoted to finance. That same year, Sornette, Bouchaud, and Sornette’s postdoctoral researcher, Anders Johansen, realized that Sornette’s earlier work on predicting earthquakes and ruptures could be extended to predicting market crashes. They published a paper together in another physics journal. Amazingly, just a few months later, Sornette detected the log-periodic pattern that he had determined should presage a crash. The success of October 1997 deepened his belief that he was on to something important, and he redoubled his efforts on economics and financial modeling.

As with his theories of material rupture and earthquakes, the central idea behind Sornette’s market-crash-as-critical-event hypothesis involves collective action, or herding behavior. By itself, this is hardly surprising, as the suggestion that market crashes have something to do with mob psychology is old: in 1841, Charles Mackay wrote a book on, among other things, economic bubbles that he called Extraordinary Popular Delusions and the Madness of Crowds. There, he pointed to several historical cases in which entire countries had been taken by some sort of frenzy, leading to speculative bubbles — market conditions under which prices become entirely divorced from the value of the things being traded.

Perhaps the most striking example occurred in the Netherlands in the early seventeenth century. The subject of speculation was tulip bulbs. Tulips originated in Turkey but made their way into western Europe, via Austria, in the middle of the sixteenth century. The flowers were considered very beautiful and were highly prized by the European aristocracy, but the real money was in tulip bulbs, which could be used both to produce the flowers and to produce new bulbs. Tulips came to represent Dutch imperial power. The country’s new merchant class, made wealthy by trade in the Dutch East and West Indies, would broadcast its power and prestige with ornate flower gardens, with tulips as the centerpiece.

So tulip bulbs were a valuable commodity. But how valuable? During the 1630s, prices began to grow rapidly. By 1635, trades worth 2,500 Dutch guilders (worth roughly $30,000 in 2010 dollars) for a single bulb were recorded. Trades of 1,500 guilders were common. In contrast, a skilled laborer could expect to make about 150 guilders in a year. Around this time, foreign money began to pour into the market as outsiders tried to make a quick buck in the tulip game. The Dutch were thrilled. They took the foreign investment to mean that all of Europe was catching on to their tulip craze, and so they doubled down: ordinary people sold their belongings, mortgaged their houses, and exhausted their savings to participate in the tulip market.

Tulips bulbs are typically planted in the fall and then harvested in the late spring. But winter was the prime time for speculation because this was when would-be investors had the least information about the supply for the coming year: the old bulbs had been planted but the new bulbs and cut flowers were not yet available. It was during the winter of 1636–37 that tulip mania (as it is now called) reached its height. That winter, a single bulb sold for as much as 5,200 guilders (more than $60,000 for one tulip bulb!). And then one day in February 1637, at an otherwise ordinary tulip auction in Haarlem, the bidding stopped too soon. Apparently no one had invited the next batch of tulip fools. That day, prized tulips sold for just a fraction of what they had even one day before. Panic spread quickly, and within days prices had fallen to less than 1% of their height. Fortunes that had been made overnight vanished by morning. The Dutch economy teetered, until ultimately the government needed to intervene.

Herding and similar phenomena — the kinds of behavior that lead to bubbles — seem to be an ever-present aspect of human psychology. No one wants to be left out, and so we tend to copy one another. Ordinarily, though, we do not act like lemmings. Even if we look to one another for guidance, we do not usually follow blindly. The question, then, is why under some circumstances herding seems to take over. How does something like tulip mania strike? When do the normal mental brakes that would keep someone from spending his entire life savings on a tulip bulb give out? Sornette doesn’t have an answer to this question, though he has developed some models that predict which circumstances will lead herding effects to become particularly strong. What Sornette can do is identify when herding effects have taken over. This amounts to identifying when a speculative bubble has taken hold in a particular market and to predicting the probability that the bubble will pop before a certain fixed time (the critical point).

Despite Sornette’s enormous productivity in finance, he resists the idea that he has “switched over” to economics. Since 2006, he has held the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology in Zürich (usually abbreviated ETH Zürich) — his first finance-related academic position — but he maintains a part-time position in geophysics at UCLA, and also a full-time appointment as a geophysicist in ETH Zürich’s physics department. He continues to write articles and supervise students in both fields. And if you ask him what prompted the change in focus of his work, since surely there was a shift in the mid-1990s when he began working on new topics, he replies, with some bewilderment, that he has always been interested in such things. After all, he is interested in everything.

Still, he does think there is something special about finance and economics. Many people go into science because of some urge to understand how the world works. But, Sornette believes, the physical world is only part of the story. He is just as interested, perhaps more interested, in how the social world works. Gravity may keep the planet in orbit, but, as the emcee in the musical Cabaret sings, money makes the world go round. And financial markets determine how money flows. As Sornette puts it, finance is the “queen, and not the maid.” It controls everything. And whatever your political position on the role of financial markets in global geopolitics, Sornette believes that the very fact that financial markets and the people who run them do have so much social power is a sufficient reason to look closely at how they work.

Since first predicting the October 1997 crash, Sornette has had a remarkable track record of identifying when market crashes will occur. He saw the log-periodic pattern in advance of the September 2008 crash, for instance, and was able to predict the timing. Similarly, the 1998 collapse in the Russian ruble that brought Long-Term Capital Management to its knees showed the signs of an impending crash — indeed, Sornette has claimed that even though the largely unanticipated Russian debt default may have triggered the market turmoil that summer, the crash showed the log-periodic precursors characteristic of herding behavior. This means that a market crash would likely have occurred during that period whether the ruble had collapsed or not. The balloon was already in a primed state; Russia’s default was just the pinprick.

He has had success predicting other crashes, as well, most notably the dot-com crash that occurred in 2000. Over several years in the late nineties, technology stocks skyrocketed. In 1998 and 1999, the technology sector of the S&P 500 index went up by a factor of four, while the index as a whole increased by just 50%. The technology-based NASDAQ index increased by almost a factor of three between 1998 and early 2000. Analysts began talking about a so-called new economy consisting of computer firms and companies whose business strategies depended entirely on the Internet. For these companies, none of the old rules applied. It didn’t matter if a firm was making any money, for instance — earnings could be negative, but the company could still be considered valuable if there was a wide expectation of success in the future. In many ways, the boom echoed earlier periods of speculation: in the 1920s, for instance, investors also spoke of a “new economy,” though then the hot tech companies were AT&T and General Electric.

Sornette started seeing the log-periodic oscillations in NASDAQ data beginning in late 1999. By March 10, 2000 — the day the NASDAQ peaked — he had enough data to say the crash was imminent, and to predict when it would occur. He put the date somewhere between March 31 and May 2. Sure enough, during the week beginning April 10, the NASDAQ fell by 25%. Tech stocks had gone the way of the tulip bulb.

The methods Sornette has used to identify bubbles and predict when crashes will occur can also be used to identify a situation that Sornette has called an anti-bubble. These are cases in which stock prices are artificially low. On January 25, 1999, for instance, Sornette posted a paper on an online physics archive claiming that, based on his observation of log-periodic patterns in the market data, the Japanese Nikkei stock index was in the midst of an anti-bubble. The paper included quite precise predictions: Sornette indicated that by the end of that year, the Nikkei would increase by 50%.

This prediction was all the more remarkable because the Japanese market was near its fourteen-year low, which it reached on January 5, 1999. All indications were that the market would continue to fall — an opinion held by most economists at the time. Nobel Prize laureate and New York Times opinion columnist Paul Krugman, for instance, wrote on January 20 that the Japanese economy was beginning to look like a tragedy, and that there simply wasn’t enough demand for a recovery. But time proved Sornette right. By the end of the year, the Nikkei had recovered, by precisely the 50% Sornette predicted.

Mandelbrot’s work gave some economists reason to think that markets are wildly random, exhibiting behavior that someone like Bachelier or Osborne could never have imagined. Even if Mandelbrot turned out to be wrong in the details of his proposal, he nonetheless revealed that financial markets are governed by fat-tailed distributions. There’s nothing special about extreme financial events. They are not exceptions; they are the norm — and worse, they happen all the time, for the same reason as more mundane events. Big market drawdowns, at their core, are just smaller drawdowns that didn’t stop.

If this is right, one might think that there is no way to predict catastrophes. Indeed, self-organization, one of the principal parts of the theory of critical phenomena, is usually associated with just the kind of fat-tailed distributions that make predicting extreme events so difficult. The three physicists who first introduced the notion of self-organization, Per Bak, Chao Tang, and Kurt Wiesenfeld, took their discovery as evidence that extreme events are, in principle, indistinguishable from more moderate events. The moral, they thought, was that predicting such events was a hopeless endeavor.

This concern is at the heart of hedge fund manager Nassim Taleb’s argument against modeling in finance. In his book The Black Swan, Taleb explains that some events — he calls them “black swans” — are so far from standard, normal distribution expectations that you cannot even make sense of questions about their likelihood. They are essentially unpredictable, and yet when they occur, they change everything. Taleb takes it to be a consequence of Mandelbrot’s arguments that these kinds of extreme events, the events with the most dramatic consequences, occur much more frequently than any model can account for. To trust a mathematical model in a wildly random system like a financial market is foolish, then, because the models exclude the most important phenomena: the catastrophic crashes.

Recently, Sornette introduced a new term for extreme events. Instead of black swans, he calls them “dragon kings.” He used the word king because, if you try to match plots like Pareto’s law — the fat-tailed distribution governing income disparity that Mandelbrot studied at IBM — to countries that have a monarchy, you find that kings don’t fit with the 80–20 rule. Kings control far more wealth than they ought to, even by the standards of fat tails. They are true outliers. And they, not the extremely wealthy just below them, are the ones who really exert control. The word dragon, meanwhile, is supposed to capture the fact that these kinds of events don’t have a natural place in the normal bestiary. They’re unlike anything else. Many large earthquakes are little ones that, for whatever reason, didn’t stop. These are not predictable using Sornette’s methods. But dragon-king earthquakes, the critical events, seem to require more. Like ruptures, they happen only if all sorts of things fall into place in just the right way. A good example of a dragon king is the city of Paris. France’s cities follow Zipf’s law remarkably well. The distribution of cities in France is fat-tailed, in that the very biggest cities are much bigger than the next biggest cities. But if you plot the size of French cities by their population size, as Zipf’s law would have you do, Paris is still much too big. It breaks the mold.

Taleb’s argument trades on the fact that black swans can have enormous consequences. Dragon kings are similar in their influence. They are tyrannical when they appear. But unlike black swans, you can hear them coming. Sornette does not argue that all black swans are really dragon kings in disguise, or even that all market crashes are predictable. But he does argue that many things that might seem like black swans really do issue warnings. In many cases, these warnings take the form of log-periodic precursors, oscillations in some form of data that occur only when the system is in the special state where a massive catastrophe can occur. These precursors arise only when the right combination of positive feedback and amplifying processes is in place, along with the self-organization necessary to make a bang, and not a whimper.

The Prediction Company, on the one hand, and Sornette, on the other, offer two ways in which one might fill in the gaps in the now-standard Black-Scholes-style reasoning. The Prediction Company’s methods might be thought of as local, in the sense that their strategy involved probing the fine-grained financial data produced every instant by the world’s markets for patterns that had some temporary predictive power. These patterns allowed them to build models that could be used over a short window of time to make profitable trades, even though the patterns were often fleeting. Along with these methods, they developed the tools necessary to evaluate the effectiveness of the patterns they were finding, and to tell when they had passed their prime. In a way, the Prediction Company’s approach is modest and conservative. It is easy to see why it should work, as a part of what makes markets more efficient.

Sornette, conversely, has taken a more global approach, looking for regularities that are associated with the biggest events, the most damaging catastrophes, and trying to use those regularities to make predictions. His starting point is Mandelbrot’s observation that extreme events occur more often than a normal random walk would predict; Sornette believes that catastrophic crashes happen even more than Mandelbrot proposed. In other words, even after you accept fat-tailed distributions, you still see extreme events unusually often. Sornette’s intuition, on seeing these apparent outliers, is that there must be some mechanism that, at least sometimes, amplifies the largest catastrophes. This is a riskier hypothesis — but it is one that can be tested, and so far, it seems to have passed.

If you think of Mandelbrot’s work as a revision to the early accounts of random markets, pointing out why they fail and how, then Sornette’s proposal is a second revision. It is a way of saying that, even if markets are wildly random and extreme events occur all the time, at least some extreme events can be anticipated if you know what to look for. These dragon kings can upend the entire world economy — and yet they can be studied and understood. They are the stuff of myths, but not of mystery.