The Black Swan

by Nassim Nicholas Taleb

  Yet we automatically, spontaneously associate chance with these Platonified games. I find it infuriating to listen to people who, upon being informed that I specialize in problems of chance, immediately shower me with references to dice. Two illustrators for a paperback edition of one of my books spontaneously and independently added a die to the cover and below every chapter, throwing me into a state of rage. The editor, familiar with my thinking, warned them to “avoid the ludic fallacy,” as if it were a well-known intellectual violation. Amusingly, they both reacted with an “Ah, sorry, we didn’t know.”

  Those who spend too much time with their noses glued to maps will tend to mistake the map for the territory. Go buy a recent history of probability and probabilistic thinking; you will be showered with names of alleged “probability thinkers” who all base their ideas on these sterilized constructs. I recently looked at what college students are taught under the subject of chance and came out horrified; they were brainwashed with this ludic fallacy and the outlandish bell curve. The same is true of people doing PhD’s in the field of probability theory. I’m reminded of a recent book by a thoughtful mathematician, Amir Aczel, called Chance. Excellent book perhaps, but like all other modern books it is grounded in the ludic fallacy. Furthermore, assuming chance has anything to do with mathematics, what little mathematization we can do in the real world does not assume the mild randomness represented by the bell curve, but rather scalable wild randomness. What can be mathematized is usually not Gaussian, but Mandelbrotian.

  Now, go read any of the classical thinkers who had something practical to say about the subject of chance, such as Cicero, and you find something different: a notion of probability that remains fuzzy throughout, as it needs to be, since such fuzziness is the very nature of uncertainty. Probability is a liberal art; it is a child of skepticism, not a tool for people with calculators on their belts to satisfy their desire to produce fancy calculations and certainties. Before Western thinking drowned in its “scientific” mentality, what is arrogantly called the Enlightenment, people prompted their brain to think—not compute. In a beautiful treatise now vanished from our consciousness, Dissertation on the Search for Truth, published in 1673, the polemist Simon Foucher exposed our psychological predilection for certainties. He teaches us the art of doubting, how to position ourselves between doubting and believing. He writes: “One needs to exit doubt in order to produce science—but few people heed the importance of not exiting from it prematurely. … It is a fact that one usually exits doubt without realizing it.” He warns us further: “We are dogma-prone from our mother’s wombs.”

  By the confirmation error discussed in Chapter 5, we use the example of games, which probability theory was successful at tracking, and claim that this is a general case. Furthermore, just as we tend to underestimate the role of luck in life in general, we tend to overestimate it in games of chance.

  “This building is inside the Platonic fold; life stands outside of it,” I wanted to shout.

  Gambling with the Wrong Dice

  I was in for quite a surprise when I learned that the building too was outside the Platonic fold.

  The casino’s risk management, aside from setting its gambling policies, was geared toward reducing the losses resulting from cheaters. One does not need heavy training in probability theory to understand that the casino was sufficiently diversified across the different tables to not have to worry about taking a hit from an extremely lucky gambler (the diversification argument that leads to the bell curve, as we will see in Chapter 15). All they had to do was control the “whales,” the high rollers flown in at the casino’s expense from Manila or Hong Kong; whales can swing several million dollars in a gambling bout. Absent cheating, the performance of most individual gamblers would be the equivalent of a drop in the bucket, making the aggregate very stable.

  I promised not to discuss any of the details of the casino’s sophisticated surveillance system; all I am allowed to say is that I felt transported into a James Bond movie—I wondered if the casino was an imitation of the movies or if it was the other way around. Yet, in spite of such sophistication, their risks had nothing to do with what can be anticipated knowing that the business is a casino. For it turned out that the four largest losses incurred or narrowly avoided by the casino fell completely outside their sophisticated models.

  First, they lost around $100 million when an irreplaceable performer in their main show was maimed by a tiger (the show, Siegfried and Roy, had been a major Las Vegas attraction). The tiger had been reared by the performer and even slept in his bedroom; until then, nobody suspected that the powerful animal would turn against its master. In scenario analyses, the casino had even conceived of the animal jumping into the crowd, but nobody came near to the idea of insuring against what happened.

  Second, a disgruntled contractor was hurt during the construction of a hotel annex. He was so offended by the settlement offered him that he made an attempt to dynamite the casino. His plan was to put explosives around the pillars in the basement. The attempt was, of course, thwarted (otherwise, to use the arguments in Chapter 8, we would not have been there), but I shivered at the thought of possibly sitting above a pile of dynamite.

  Third, casinos must file a special form with the Internal Revenue Service documenting a gambler’s profit if it exceeds a given amount. The employee who was supposed to mail the forms hid them, instead, for completely unexplainable reasons, in boxes under his desk. This went on for years without anyone noticing that something was wrong. The employee’s refraining from sending the documents was truly impossible to predict. Tax violations (and negligence) being serious offences, the casino faced the near loss of a gambling license or the onerous financial costs of a suspension. Clearly they ended up paying a monstrous fine (an undisclosed amount), which was the luckiest way out of the problem.

  Fourth, there was a spate of other dangerous scenes, such as the kidnapping of the casino owner’s daughter, which caused him, in order to secure cash for the ransom, to violate gambling laws by dipping into the casino coffers.

  Conclusion: A back-of-the-envelope calculation shows that the dollar value of these Black Swans, the off-model hits and potential hits I’ve just outlined, swamp the on-model risks by a factor of close to 1,000 to 1. The casino spent hundreds of millions of dollars on gambling theory and high-tech surveillance while the bulk of their risks came from outside their models.

  All this, and yet the rest of the world still learns about uncertainty and probability from gambling examples.

  WRAPPING UP PART ONE

  The Cosmetic Rises to the Surface

  All of the topics in Part One are actually only one. You can think about a subject for a long time, to the point of being possessed by it. Somehow you have a lot of ideas, but they do not seem explicitly connected; the logic linking them remains concealed from you. Yet you know deep down that all these are the same idea. Meanwhile, what Nietzsche calls bildungsphilisters,* or learned philistines, blue collars of the thinking business, tell you that you are spread out between fields; you reply that these disciplines are artificial and arbitrary, to no avail. Then you tell them that you are a limousine driver, and they leave you alone—you feel better because you do not identify with them, and thus you no longer need to be amputated to fit into the Procrustean bed of the disciplines. Finally, a little push and you see that it was all one single problem.

  One evening I found myself at a cocktail party in Munich at the apartment of a former art historian who had more art books in its library than I thought existed. I stood drinking excellent Riesling in the spontaneously formed English-speaking corner of the apartment, in the hope of getting to a state where I would be able to start speaking my brand of fake German. One of the most insightful thinkers I know, the computer entrepreneur Yossi Vardi, prompted me to summarize “my idea” while standing on one leg. It was not too convenient to stand on one leg after a few glasses of perfumed Riesling, so I failed in my improvisation. The next da
y I experienced staircase wit. I jumped out of bed with the following idea: the cosmetic and the Platonic rise naturally to the surface. This is a simple extension of the problem of knowledge. It is simply that one side of Eco’s library, the one we never see, has the property of being ignored. This is also the problem of silent evidence. It is why we do not see Black Swans: we worry about those that happened, not those that may happen but did not. It is why we Platonify, liking known schemas and well-organized knowledge—to the point of blindness to reality. It is why we fall for the problem of induction, why we confirm. It is why those who “study” and fare well in school have a tendency to be suckers for the ludic fallacy.

  And it is why we have Black Swans and never learn from their occurrence, because the ones that did not happen were too abstract. Thanks to Vardi, I now belonged to the club of single-idea people.

  We love the tangible, the confirmation, the palpable, the real, the visible, the concrete, the known, the seen, the vivid, the visual, the social, the embedded, the emotionally laden, the salient, the stereotypical, the moving, the theatrical, the romanced, the cosmetic, the official, the scholarly-sounding verbiage (b******t), the pompous Gaussian economist, the mathematicized crap, the pomp, the Académie Française, Harvard Business School, the Nobel Prize, dark business suits with white shirts and Ferragamo ties, the moving discourse, and the lurid. Most of all we favor the narrated.

  Alas, we are not manufactured, in our current edition of the human race, to understand abstract matters—we need context. Randomness and uncertainty are abstractions. We respect what has happened, ignoring what could have happened. In other words, we are naturally shallow and superficial—and we do not know it. This is not a psychological problem; it comes from the main property of information. The dark side of the moon is harder to see; beaming light on it costs energy. In the same way, beaming light on the unseen is costly in both computational and mental effort.

  Distance from Primates

  There have been in history many distinctions between higher and lower forms of humans. For the Greeks, there were the Greeks and the barbarians, those people of the north who uttered amorphous sentences similar, to the Attic ear, to an animal’s shrieks. For the English, a higher form of life was the gentleman’s—contrary to today’s definition, a gentleman’s life was practiced through idleness and a code of behavior that included, along with a set of manners, the avoidance of work beyond the necessities of comfortable subsistence. For New Yorkers, there are those with a Manhattan zip code and those with such a thing as a Brooklyn or, worse, Queens address. For the earlier Nietzsche, there was the Apollonian compared to the Dionysian; for the better-known Nietzsche, there was the Übermensch, something his readers interpret however it suits them. For a modern stoic, a higher individual subscribes to a dignified system of virtue that determines elegance in one’s behavior and the ability to separate results from efforts. All of these distinctions aim at lengthening the distance between us and our relatives among other primates. (I keep insisting that, when it comes to decision making, the distance between us and these hairy cousins is far shorter than we think.)

  I propose that if you want a simple step to a higher form of life, as distant from the animal as you can get, then you may have to denarrate, that is, shut down the television set, minimize time spent reading newspapers, ignore the blogs. Train your reasoning abilities to control your decisions; nudge System 1 (the heuristic or experiential system) out of the important ones. Train yourself to spot the difference between the sensational and the empirical. This insulation from the toxicity of the world will have an additional benefit: it will improve your well-being. Also, bear in mind how shallow we are with probability, the mother of all abstract notions. You do not have to do much more in order to gain a deeper understanding of things around you. Above all, learn to avoid “tunneling.”

  A bridge here to what is to come. The Platonic blindness I illustrated with the casino story has another manifestation: focusing. To be able to focus is a great virtue if you are a watch repairman, a brain surgeon, or a chess player. But the last thing you need to do when you deal with uncertainty is to “focus” (you should tell uncertainty to focus, not us). This “focus” makes you a sucker; it translates into prediction problems, as we will see in the next section. Prediction, not narration, is the real test of our understanding of the world.

  * My colleague Mark Spitznagel found a martial version of the ludic fallacy: organized competitive fighting trains the athlete to focus on the game and, in order not to dissipate his concentration, to ignore the possibility of what is not specifically allowed by the rules, such as kicks to the groin, a surprise knife, et cetera. So those who win the gold medal might be precisely those who will be most vulnerable in real life. Likewise, you see people with huge muscles (in black T-shirts) who can impress you in the artificial environment of the gym but are unable to lift a stone.

  * What Nietzsche means by this term are the dogma-prone newspaper readers and opera lovers who have cosmetic exposure to culture and shallow depth. I extend the term here to the philistine hiding in academia who lacks in erudition out of lack of curiosity and is closely centered on his ideas.

  When I ask people to name three recently implemented technologies that most impact our world today, they usually propose the computer, the Internet, and the laser. All three were unplanned, unpredicted, and unappreciated upon their discovery, and remained unappreciated well after their initial use. They were consequential. They were Black Swans. Of course, we have this retrospective illusion of their partaking in some master plan. You can create your own lists with similar results, whether you use political events, wars, or intellectual epidemics.

  You would expect our record of prediction to be horrible: the world is far, far more complicated than we think, which is not a problem, except when most of us don’t know it. We tend to “tunnel” while looking into the future, making it business as usual, Black Swan–free, when in fact there is nothing usual about the future. It is not a Platonic category!

  We have seen how good we are at narrating backward, at inventing stories that convince us that we understand the past. For many people, knowledge has the remarkable power of producing confidence instead of measurable aptitude. Another problem: the focus on the (inconsequential) regular, the Platonification that makes the forecasting “inside the box.”

  I find it scandalous that in spite of the empirical record we continue to project into the future as if we were good at it, using tools and methods that exclude rare events. Prediction is firmly institutionalized in our world. We are suckers for those who help us navigate uncertainty, whether the fortune-teller or the “well-published” (dull) academics or civil servants using phony mathematics.

  From Yogi Berra to Henri Poincaré

  The great baseball coach Yogi Berra has a saying, “It is tough to make predictions, especially about the future.” While he did not produce the writings that would allow him to be considered a philosopher, in spite of his wisdom and intellectual abilities, Berra can claim to know something about randomness. He was a practitioner of uncertainty, and, as a baseball player and coach, regularly faced random outcomes, and had to face their results deep into his bones.

  In fact, Yogi Berra is not the only thinker who thought about how much of the future lies beyond our abilities. Many less popular, less pithy, but not less competent thinkers than he have examined our inherent limitations in this regard, from the philosophers Jacques Hadamard and Henri Poincaré (commonly described as mathematicians), to the philosopher Friedrich von Hayek (commonly described, alas, as an economist), to the philosopher Karl Popper (commonly known as a philosopher). We can safely call this the Berra-Hadamard-Poincaré-Hayek-Popper conjecture, which puts structural, built-in limits to the enterprise of predicting.

  “The future ain’t what it used to be,” Berra later said.* He seems to have been right: the gains in our ability to model (and predict) the world may be dwarfed by the increases in its complexity�
��implying a greater and greater role for the unpredicted. The larger the role of the Black Swan, the harder it will be for us to predict. Sorry.

  Before going into the limits of prediction, we will discuss our track record in forecasting and the relation between gains in knowledge and the offsetting gains in confidence.

  * Note that these sayings attributed to Yogi Berra might be apocryphal—it was the physicist Niels Bohr who came up with the first one, and plenty of others came up with the second. These sayings remain, however, quintessential Berraisms.

  Chapter Ten

  THE SCANDAL OF PREDICTION

  Welcome to Sydney—How many lovers did she have?—How to be an economist, wear a nice suit, and make friends—Not right, just “almost” right—Shallow rivers can have deep spots

  One March evening, a few men and women were standing on the esplanade overlooking the bay outside the Sydney Opera House. It was close to the end of the summer in Sydney, but the men were wearing jackets despite the warm weather. The women were more thermally comfortable than the men, but they had to suffer the impaired mobility of high heels.