The Black Swan

by Nassim Nicholas Taleb

  Pranks can be compassionate. I remember in my early trading days, at age twenty-five or so, when money was starting to become easy. I would take taxis, and if the driver spoke skeletal English and looked particularly depressed, I’d give him a $100 bill as a tip, just to give him a little jolt and get a kick out of his surprise. I’d watch him unfold the bill and look at it with some degree of consternation ($1 million certainly would have been better but it was not within my means). It was also a simple hedonic experiment: it felt elevating to make someone’s day with the trifle of $100. I eventually stopped; we all become stingy and calculating when our wealth grows and we start taking money seriously.

  I don’t need much help from fate to get larger-scale entertainment: reality provides such forced revisions of beliefs at quite a high frequency. Many are quite spectacular. In fact, the entire knowledge-seeking enterprise is based on taking conventional wisdom and accepted scientific beliefs and shattering them into pieces with new counterintuitive evidence, whether at a micro scale (every scientific discovery is an attempt to produce a micro–Black Swan) or at a larger one (as with Poincaré’s and Einstein’s relativity). Scientists may be in the business of laughing at their predecessors, but owing to an array of human mental dispositions, few realize that someone will laugh at their beliefs in the (disappointingly near) future. In this case, my readers and I are laughing at the present state of social knowledge. These big guns do not see the inevitable overhaul of their work coming, which means that you can usually count on them to be in for a surprise.

  HOW TO LEARN FROM THE TURKEY

  The überphilosopher Bertrand Russell presents a particularly toxic variant of my surprise jolt in his illustration of what people in his line of business call the Problem of Induction or Problem of Inductive Knowledge (capitalized for its seriousness)—certainly the mother of all problems in life. How can we logically go from specific instances to reach general conclusions? How do we know what we know? How do we know that what we have observed from given objects and events suffices to enable us to figure out their other properties? There are traps built into any kind of knowledge gained from observation.

  Consider a turkey that is fed every day. Every single feeding will firm up the bird’s belief that it is the general rule of life to be fed every day by friendly members of the human race “looking out for its best interests,” as a politician would say. On the afternoon of the Wednesday before Thanksgiving, something unexpected will happen to the turkey. It will incur a revision of belief.*

  The rest of this chapter will outline the Black Swan problem in its original form: How can we know the future, given knowledge of the past; or, more generally, how can we figure out properties of the (infinite) unknown based on the (finite) known? Think of the feeding again: What can a turkey learn about what is in store for it tomorrow from the events of yesterday? A lot, perhaps, but certainly a little less than it thinks, and it is just that “little less” that may make all the difference.

  The turkey problem can be generalized to any situation where the same hand that feeds you can be the one that wrings your neck. Consider the case of the increasingly integrated German Jews in the 1930s—or my description in Chapter 1 of how the population of Lebanon got lulled into a false sense of security by the appearance of mutual friendliness and tolerance.

  Let us go one step further and consider induction’s most worrisome aspect: learning backward. Consider that the turkey’s experience may have, rather than no value, a negative value. It learned from observation, as we are all advised to do (hey, after all, this is what is believed to be the scientific method). Its confidence increased as the number of friendly feedings grew, and it felt increasingly safe even though the slaughter was more and more imminent. Consider that the feeling of safety reached its maximum when the risk was at the highest! But the problem is even more general than that; it strikes at the nature of empirical knowledge itself. Something has worked in the past, until—well, it unexpectedly no longer does, and what we have learned from the past turns out to be at best irrelevant or false, at worst viciously misleading.

  FIGURE 1: ONE THOUSAND AND ONE DAYS OF HISTORY

  A turkey before and after Thanksgiving. The history of a process over a thousand days tells you nothing about what is to happen next. This naïve projection of the future from the past can be applied to anything.

  Figure 1 provides the prototypical case of the problem of induction as encountered in real life. You observe a hypothetical variable for one thousand days. It could be anything (with a few mild transformations): book sales, blood pressure, crimes, your personal income, a given stock, the interest on a loan, or Sunday attendance at a specific Greek Orthodox church. You subsequently derive solely from past data a few conclusions concerning the properties of the pattern with projections for the next thousand, even five thousand, days. On the one thousand and first day—boom! A big change takes place that is completely unprepared for by the past.

  Consider the surprise of the Great War. After the Napoleonic conflicts, the world had experienced a period of peace that would lead any observer to believe in the disappearance of severely destructive conflicts. Yet, surprise! It turned out to be the deadliest conflict, up until then, in the history of mankind.

  Note that after the event you start predicting the possibility of other outliers happening locally, that is, in the process you were just surprised by, but not elsewhere. After the stock market crash of 1987 half of America’s traders braced for another one every October—not taking into account that there was no antecedent for the first one. We worry too late—ex post. Mistaking a naïve observation of the past as something definitive or representative of the future is the one and only cause of our inability to understand the Black Swan.

  It would appear to a quoting dilettante—i.e., one of those writers and scholars who fill up their texts with phrases from some dead authority—that, as phrased by Hobbes, “from like antecedents flow like consequents.” Those who believe in the unconditional benefits of past experience should consider this pearl of wisdom allegedly voiced by a famous ship’s captain:

  But in all my experience, I have never been in any accident… of any sort worth speaking about. I have seen but one vessel in distress in all my years at sea. I never saw a wreck and never have been wrecked nor was I ever in any predicament that threatened to end in disaster of any sort.

  E. J. Smith, 1907, Captain, RMS Titanic

  Captain Smith’s ship sank in 1912 in what became the most talked-about shipwreck in history.*

  Trained to Be Dull

  Similarly, think of a bank chairman whose institution makes steady profits over a long time, only to lose everything in a single reversal of fortune. Traditionally, bankers of the lending variety have been pear-shaped, clean-shaven, and dress in possibly the most comforting and boring manner, in dark suits, white shirts, and red ties. Indeed, for their lending business, banks hire dull people and train them to be even more dull. But this is for show. If they look conservative, it is because their loans only go bust on rare, very rare, occasions. There is no way to gauge the effectiveness of their lending activity by observing it over a day, a week, a month, or … even a century! In the summer of 1982, large American banks lost close to all their past earnings (cumulatively), about everything they ever made in the history of American banking—everything. They had been lending to South and Central American countries that all defaulted at the same time—“an event of an exceptional nature.” So it took just one summer to figure out that this was a sucker’s business and that all their earnings came from a very risky game. All that while the bankers led everyone, especially themselves, into believing that they were “conservative.” They are not conservative; just phenomenally skilled at self-deception by burying the possibility of a large, devastating loss under the rug. In fact, the travesty repeated itself a decade later, with the “risk-conscious” large banks once again under financial strain, many of them near-bankrupt, after the real-estate collapse
of the early 1990s in which the now defunct savings and loan industry required a taxpayer-funded bailout of more than half a trillion dollars. The Federal Reserve bank protected them at our expense: when “conservative” bankers make profits, they get the benefits; when they are hurt, we pay the costs.

  After graduating from Wharton, I initially went to work for Bankers Trust (now defunct). There, the chairman’s office, rapidly forgetting about the story of 1982, broadcast the results of every quarter with an announcement explaining how smart, profitable, conservative (and good looking) they were. It was obvious that their profits were simply cash borrowed from destiny with some random payback time. I have no problem with risk taking, just please, please, do not call yourself conservative and act superior to other businesses who are not as vulnerable to Black Swans.

  Another recent event is the almost-instant bankruptcy, in 1998, of a financial investment company (hedge fund) called Long-Term Capital Management (LTCM), which used the methods and risk expertise of two “Nobel economists,” who were called “geniuses” but were in fact using phony, bell curve–style mathematics while managing to convince themselves that it was great science and thus turning the entire financial establishment into suckers. One of the largest trading losses ever in history took place in almost the blink of an eye, with no warning signal (more, much more on that in Chapter 17).*

  A Black Swan Is Relative to Knowledge

  From the standpoint of the turkey, the nonfeeding of the one thousand and first day is a Black Swan. For the butcher, it is not, since its occurrence is not unexpected. So you can see here that the Black Swan is a sucker’s problem. In other words, it occurs relative to your expectation. You realize that you can eliminate a Black Swan by science (if you’re able), or by keeping an open mind. Of course, like the LTCM people, you can create Black Swans with science, by giving people confidence that the Black Swan cannot happen—this is when science turns normal citizens into suckers.

  Note that these events do not have to be instantaneous surprises. Some of the historical fractures I mention in Chapter 1 have lasted a few decades, like, say, the computer that brought consequential effects on society without its invasion of our lives being noticeable from day to day. Some Black Swans can come from the slow building up of incremental changes in the same direction, as with books that sell large amounts over years, never showing up on the bestseller lists, or from technologies that creep up on us slowly, but surely. Likewise, the growth of Nasdaq stocks in the late 1990s took a few years—but the growth would seem sharper if you were to plot it on a long historical line. Matters should be seen on some relative, not absolute, timescale: earthquakes last minutes, 9/11 lasted hours, but historical changes and technological implementations are Black Swans that can take decades. In general, positive Black Swans take time to show their effect while negative ones happen very quickly—it is much easier and much faster to destroy than to build. (During the Lebanese war, my parents’ house in Amioun and my grandfather’s house in a nearby village were destroyed in just a few hours, dynamited by my grandfather’s enemies who controlled the area. It took seven thousand times longer—two years—to rebuild them. This asymmetry in timescales explains the difficulty in reversing time.)

  A BRIEF HISTORY OF THE BLACK SWAN PROBLEM

  This turkey problem (a.k.a. the problem of induction) is a very old one, but for some reason it is likely to be called “Hume’s problem” by your local philosophy professor.

  People imagine us skeptics and empiricists to be morose, paranoid, and tortured in our private lives, which may be the exact opposite of what history (and my private experience) reports. Like many of the skeptics I hang around with, Hume was jovial and a bon vivant, eager for literary fame, salon company, and pleasant conversation. His life was not devoid of anecdotes. He once fell into a swamp near the house he was building in Edinburgh. Owing to his reputation among the locals as an atheist, a woman refused to pull him out of it until he recited the Lord’s Prayer and the Belief, which, being practical-minded, he did. But not before he argued with her about whether Christians were obligated to help their enemies. Hume looked unprepossessing. “He exhibited that preoccupied stare of the thoughtful scholar that so commonly impresses the undiscerning as imbecile,” writes a biographer.

  Strangely, Hume during his day was not mainly known for the works that generated his current reputation—he became rich and famous through writing a bestselling history of England. Ironically, when Hume was alive, his philosophical works, to which we now attach his fame, “fell deadborn off the presses,” while the works for which he was famous at the time are now harder to find. Hume wrote with such clarity that he puts to shame almost all current thinkers, and certainly the entire German graduate curriculum. Unlike Kant, Fichte, Schopenhauer, and Hegel, Hume is the kind of thinker who is sometimes read by the person mentioning his work.

  I often hear “Hume’s problem” mentioned in connection with the problem of induction, but the problem is old, older than the interesting Scotsman, perhaps as old as philosophy itself, maybe as old as olive-grove conversations. Let us go back into the past, as it was formulated with no less precision by the ancients.

  Sextus the (Alas) Empirical

  The violently antiacademic writer, and antidogma activist, Sextus Empiricus operated close to a millennium and a half before Hume, and formulated the turkey problem with great precision. We know very little about him; we do not know whether he was a philosopher or more of a copyist of philosophical texts by authors obscure to us today. We surmise that he lived in Alexandria in the second century of our era. He belonged to a school of medicine called “empirical,” since its practitioners doubted theories and causality and relied on past experience as guidance in their treatment, though not putting much trust in it. Furthermore, they did not trust that anatomy revealed function too obviously. The most famous proponent of the empirical school, Menodotus of Nicomedia, who merged empiricism and philosophical skepticism, was said to keep medicine an art, not a “science,” and insulate its practice from the problems of dogmatic science. The practice of medicine explains the addition of empiricus (“the empirical”) to Sextus’s name.

  Sextus represented and jotted down the ideas of the school of the Pyrrhonian skeptics who were after some form of intellectual therapy resulting from the suspension of belief. Do you face the possibility of an adverse event? Don’t worry. Who knows, it may turn out to be good for you. Doubting the consequences of an outcome will allow you to remain imperturbable. The Pyrrhonian skeptics were docile citizens who followed customs and traditions whenever possible, but taught themselves to systematically doubt everything, and thus attain a level of serenity. But while conservative in their habits, they were rabid in their fight against dogma.

  Among the surviving works of Sextus’s is a diatribe with the beautiful title Adversos Mathematicos, sometimes translated as Against the Professors. Much of it could have been written last Wednesday night!

  Where Sextus is mostly interesting for my ideas is in his rare mixing of philosophy and decision making in his practice. He was a doer, hence classical scholars don’t say nice things about him. The methods of empirical medicine, relying on seemingly purposeless trial and error, will be central to my ideas on planning and prediction, on how to benefit from the Black Swan.

  In 1998, when I went out on my own, I called my research laboratory and trading firm Empirica, not for the same antidogmatist reasons, but on account of the far more depressing reminder that it took at least another fourteen centuries after the works of the school of empirical medicine before medicine changed and finally became adogmatic, suspicious of theorizing, profoundly skeptical, and evidence-based! Lesson? That awareness of a problem does not mean much—particularly when you have special interests and self-serving institutions in play.

  Algazel

  The third major thinker who dealt with the problem was the eleventh-century Arabic-language skeptic Al-Ghazali, known in Latin as Algazel. His name for a class
of dogmatic scholars was ghabi, literally “the imbeciles,” an Arabic form that is funnier than “moron” and more expressive than “obscurantist.” Algazel wrote his own Against the Professors, a diatribe called Tahafut al falasifah, which I translate as “The Incompetence of Philosophers.” It was directed at members of the school called falasifah—the Arabic intellectual establishment was the direct heir of the classical philosophy of the academy, and they managed to reconcile it with Islam through rational argument.

  Algazel’s attack on “scientific” knowledge started a debate with Averroës, the medieval philosopher who ended up having the most profound influence of any medieval thinker (on Jews and Christians, though not on Moslems). The debate between Algazel and Averroës was finally, but sadly, won by both. In its aftermath, many Arab religious thinkers integrated and exaggerated Algazel’s skepticism of the scientific method, preferring to leave causal considerations to God (in fact it was a stretch of his idea). The West embraced Averroës’s rationalism, built upon Aristotle’s, which survived through Aquinas and the Jewish philosophers who called themselves Averroan for a long time. Many thinkers blame the Arabs’ later abandonment of scientific method on Algazel’s huge influence—though apparently this took place a few centuries later. He ended up fueling Sufi mysticism, in which the worshipper attempts to enter into communion with God, severing all connections with earthly matters. All of this came from the Black Swan problem.