The Black Swan

by Nassim Nicholas Taleb

  Optimization is a case of sterile modeling that we will discuss further in Chapter 17. It had no practical (or even theoretical) use, and so it became principally a competition for academic positions, a way to make people compete with mathematical muscle. It kept Platonified economists out of the bars, solving equations at night. The tragedy is that Paul Samuelson, a quick mind, is said to be one of the most intelligent scholars of his generation. This was clearly a case of very badly invested intelligence. Characteristically, Samuelson intimidated those who questioned his techniques with the statement “Those who can, do science, others do methodology.” If you knew math, you could “do science.” This is reminiscent of psychoanalysts who silence their critics by accusing them of having trouble with their fathers. Alas, it turns out that it was Samuelson and most of his followers who did not know much math, or did not know how to use what math they knew, how to apply it to reality. They only knew enough math to be blinded by it.

  Tragically, before the proliferation of empirically blind idiot savants, interesting work had been begun by true thinkers, the likes of J. M. Keynes, Friedrich Hayek, and the great Benoît Mandelbrot, all of whom were displaced because they moved economics away from the precision of second-rate physics. Very sad. One great underestimated thinker is G.L.S. Shackle, now almost completely obscure, who introduced the notion of “unknowledge,” that is, the unread books in Umberto Eco’s library. It is unusual to see Shackle’s work mentioned at all, and I had to buy his books from secondhand dealers in London.

  Legions of empirical psychologists of the heuristics and biases school have shown that the model of rational behavior under uncertainty is not just grossly inaccurate but plain wrong as a description of reality. Their results also bother Platonified economists because they reveal that there are several ways to be irrational. Tolstoy said that happy families were all alike, while each unhappy one is unhappy in its own way. People have been shown to make errors equivalent to preferring apples to oranges, oranges to pears, and pears to apples, depending on how the relevant questions are presented to them. The sequence matters! Also, as we have seen with the anchoring example, subjects’ estimates of the number of dentists in Manhattan are influenced by which random number they have just been presented with—the anchor. Given the randomness of the anchor, we will have randomness in the estimates. So if people make inconsistent choices and decisions, the central core of economic optimization fails. You can no longer produce a “general theory,” and without one you cannot predict.

  You have to learn to live without a general theory, for Pluto’s sake!

  THE GRUENESS OF EMERALD

  Recall the turkey problem. You look at the past and derive some rule about the future. Well, the problems in projecting from the past can be even worse than what we have already learned, because the same past data can confirm a theory and also its exact opposite! If you survive until tomorrow, it could mean that either a) you are more likely to be immortal or b) that you are closer to death. Both conclusions rely on the exact same data. If you are a turkey being fed for a long period of time, you can either naïvely assume that feeding confirms your safety or be shrewd and consider that it confirms the danger of being turned into supper. An acquaintance’s unctuous past behavior may indicate his genuine affection for me and his concern for my welfare; it may also confirm his mercenary and calculating desire to get my business one day.

  FIGURE 3

  A series of a seemingly growing bacterial population (or of sales records, or of any variable observed through time—such as the total feeding of the turkey in Chapter 4).

  FIGURE 4

  Easy to fit the trend—there is one and only one linear model that fits the data. You can project a continuation into the future.

  FIGURE 5

  We look at a broader scale. Hey, other models also fit it rather well.

  FIGURE 6

  And the real “generating process” is extremely simple but it had nothing to do with a linear model! Some parts of it appear to be linear and we are fooled by extrapolating in a direct line.*

  So not only can the past be misleading, but there are also many degrees of freedom in our interpretation of past events.

  For the technical version of this idea, consider a series of dots on a page representing a number through time—the graph would resemble Figure 1 showing the first thousand days in Chapter 4. Let’s say your high school teacher asks you to extend the series of dots. With a linear model, that is, using a ruler, you can run only a straight line, a single straight line from the past to the future. The linear model is unique. There is one and only one straight line that can project from a series of points. But it can get trickier. If you do not limit yourself to a straight line, you find that there is a huge family of curves that can do the job of connecting the dots. If you project from the past in a linear way, you continue a trend. But possible future deviations from the course of the past are infinite.

  This is what the philosopher Nelson Goodman called the riddle of induction: We project a straight line only because we have a linear model in our head—the fact that a number has risen for 1,000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1,001.

  Let’s say that you observe an emerald. It was green yesterday and the day before yesterday. It is green again today. Normally this would confirm the “green” property: we can assume that the emerald will be green tomorrow. But to Goodman, the emerald’s color history could equally confirm the “grue” property. What is this grue property? The emerald’s grue property is to be green until some specified date, say, December 31, 2006, and then blue thereafter.

  The riddle of induction is another version of the narrative fallacy—you face an infinity of “stories” that explain what you have seen. The severity of Goodman’s riddle of induction is as follows: if there is no longer even a single unique way to “generalize” from what you see, to make an inference about the unknown, then how should you operate? The answer, clearly, will be that you should employ “common sense,” but your common sense may not be so well developed with respect to some Extremistan variables.

  THAT GREAT ANTICIPATION MACHINE

  The reader is entitled to wonder, So, NNT, why on earth do we plan? Some people do it for monetary gain, others because it’s “their job.” But we also do it without such intentions—spontaneously.

  Why? The answer has to do with human nature. Planning may come with the package of what makes us human, namely, our consciousness.

  There is supposed to be an evolutionary dimension to our need to project matters into the future, which I will rapidly summarize here, since it can be an excellent candidate explanation, an excellent conjecture, though, since it is linked to evolution, I would be cautious.

  The idea, as promoted by the philosopher Daniel Dennett, is as follows: What is the most potent use of our brain? It is precisely the ability to project conjectures into the future and play the counterfactual game—“If I punch him in the nose, then he will punch me back right away, or, worse, call his lawyer in New York.” One of the advantages of doing so is that we can let our conjectures die in our stead. Used correctly and in place of more visceral reactions, the ability to project effectively frees us from immediate, first-order natural selection—as opposed to more primitive organisms that were vulnerable to death and only grew by the improvement in the gene pool through the selection of the best. In a way, projecting allows us to cheat evolution: it now takes place in our head, as a series of projections and counterfactual scenarios.

  This ability to mentally play with conjectures, even if it frees us from the laws of evolution, is itself supposed to be the product of evolution—it is as if evolution has put us on a long leash whereas other animals live on the very short leash of immediate dependence on their environment. For Dennett, our brains are “anticipation machines;” for him the human mind and consciousness a
re emerging properties, those properties necessary for our accelerated development.

  Why do we listen to experts and their forecasts? A candidate explanation is that society reposes on specialization, effectively the division of knowledge. You do not go to medical school the minute you encounter a big health problem; it is less taxing (and certainly safer) for you to consult someone who has already done so. Doctors listen to car mechanics (not for health matters, just when it comes to problems with their cars); car mechanics listen to doctors. We have a natural tendency to listen to the expert, even in fields where there may be no experts.

  * Most of the debate between creationists and evolutionary theorists (of which I do not partake) lies in the following: creationists believe that the world comes from some form of design while evolutionary theorists see the world as a result of random changes by an aimless process. But it is hard to look at a computer or a car and consider them the result of aimless process. Yet they are.

  * Recall from Chapter 4 how Algazel and Averroës traded insults through book titles. Perhaps one day I will be lucky enough to read an attack on this book in a diatribe called The White Swan.

  * Such claims are not uncommon. For instance the physicist Albert Michelson imagined, toward the end of the nineteenth century, that what was left for us to discover in the sciences of nature was no more than fine-tuning our precisions by a few decimal places.

  * There are more limits I haven’t even attempted to discuss here. I am not even bringing up the class of incomputability people call NP completeness.

  * This idea pops up here and there in history, under different names. Alfred North Whitehead called it the “fallacy of misplaced concreteness,” e.g., the mistake of confusing a model with the physical entity that it means to describe.

  * These graphs also illustrate a statistical version of the narrative fallacy—you find a model that fits the past. “Linear regression” or “R-square” can ultimately fool you beyond measure, to the point where it is no longer funny. You can fit the linear part of the curve and claim a high R-square, meaning that your model fits the data very well and has high predictive powers. All that off hot air: you only fit the linear segment of the series. Always remember that “R-square” is unfit for Extremistan; it is only good for academic promotion.

  Chapter Twelve

  EPISTEMOCRACY, A DREAM

  This is only an essay—Children and philosophers vs. adults and nonphilosophers—Science as an autistic enterprise—The past too has a past—Mispredict and live a long, happy life (if you survive)

  Someone with a low degree of epistemic arrogance is not too visible, like a shy person at a cocktail party. We are not predisposed to respect humble people, those who try to suspend judgment. Now contemplate epistemic humility. Think of someone heavily introspective, tortured by the awareness of his own ignorance. He lacks the courage of the idiot, yet has the rare guts to say “I don’t know.” He does not mind looking like a fool or, worse, an ignoramus. He hesitates, he will not commit, and he agonizes over the consequences of being wrong. He introspects, introspects, and introspects until he reaches physical and nervous exhaustion.

  This does not necessarily mean that he lacks confidence, only that he holds his own knowledge to be suspect. I will call such a person an epistemocrat; the province where the laws are structured with this kind of human fallibility in mind I will call an epistemocracy.

  The major modern epistemocrat is Montaigne.

  Monsieur de Montaigne, Epistemocrat

  At the age of thirty-eight, Michel Eyquem de Montaigne retired to his estate, in the countryside of southwestern France. Montaigne, which means mountain in Old French, was the name of the estate. The area is known today for the Bordeaux wines, but in Montaigne’s time not many people invested their mental energy and sophistication in wine. Montaigne had stoic tendencies and would not have been strongly drawn to such pursuits anyway. His idea was to write a modest collection of “attempts,” that is, essays. The very word essay conveys the tentative, the speculative, and the nondefinitive. Montaigne was well grounded in the classics and wanted to meditate on life, death, education, knowledge, and some not uninteresting biological aspects of human nature (he wondered, for example, whether cripples had more vigorous libidos owing to the richer circulation of blood in their sexual organs).

  The tower that became his study was inscribed with Greek and Latin sayings, almost all referring to the vulnerability of human knowledge. Its windows offered a wide vista of the surrounding hills.

  Montaigne’s subject, officially, was himself, but this was mostly as a means to facilitate the discussion; he was not like those corporate executives who write biographies to make a boastful display of their honors and accomplishments. He was mainly interested in discovering things about himself, making us discover things about himself, and presenting matters that could be generalized—generalized to the entire human race. Among the inscriptions in his study was a remark by the Latin poet Terence: Homo sum, humani a me nil alienum puto—I am a man, and nothing human is foreign to me.

  Montaigne is quite refreshing to read after the strains of a modern education since he fully accepted human weaknesses and understood that no philosophy could be effective unless it took into account our deeply ingrained imperfections, the limitations of our rationality, the flaws that make us human. It is not that he was ahead of his time; it would be better said that later scholars (advocating rationality) were backward.

  He was a thinking, ruminating fellow, and his ideas did not spring up in his tranquil study, but while on horseback. He went on long rides and came back with ideas. Montaigne was neither one of the academics of the Sorbonne nor a professional man of letters, and he was not these things on two planes. First, he was a doer; he had been a magistrate, a businessman, and the mayor of Bordeaux before he retired to mull over his life and, mostly, his own knowledge. Second, he was an antidogmatist: he was a skeptic with charm, a fallible, noncommittal, personal, introspective writer, and, primarily, someone who, in the great classical tradition, wanted to be a man. Had he been in a different period, he would have been an empirical skeptic—he had skeptical tendencies of the Pyrrhonian variety, the antidogmatic kind like Sextus Empiricus, particularly in his awareness of the need to suspend judgment.

  Epistemocracy

  Everyone has an idea of utopia. For many it means equality, universal justice, freedom from oppression, freedom from work (for some it may be the more modest, though no more attainable, society with commuter trains free of lawyers on cell phones). To me utopia is an epistemocracy, a society in which anyone of rank is an epistemocrat, and where epistemocrats manage to be elected. It would be a society governed from the basis of the awareness of ignorance, not knowledge.

  Alas, one cannot assert authority by accepting one’s own fallibility. Simply, people need to be blinded by knowledge—we are made to follow leaders who can gather people together because the advantages of being in groups trump the disadvantages of being alone. It has been more profitable for us to bind together in the wrong direction than to be alone in the right one. Those who have followed the assertive idiot rather than the introspective wise person have passed us some of their genes. This is apparent from a social pathology: psychopaths rally followers.

  Once in a while you encounter members of the human species with so much intellectual superiority that they can change their minds effortlessly.

  Note here the following Black Swan asymmetry. I believe that you can be dead certain about some things, and ought to be so. You can be more confident about disconfirmation than confirmation. Karl Popper was accused of promoting self-doubt while writing in an aggressive and confident tone (an accusation that is occasionally addressed to this author by people who don’t follow my logic of skeptical empiricism). Fortunately, we have learned a lot since Montaigne about how to carry on the skeptical-empirical enterprise. The Black Swan asymmetry allows you to be confident about what is wrong, not about what you believe is right. Karl P
opper was once asked whether one “could falsify falsification” (in other words, if one could be skeptical about skepticism). His answer was that he threw students out of his lectures for asking far more intelligent questions than that one. Quite tough, Sir Karl was.

  THE PAST’S PAST, AND THE PAST’S FUTURE

  Some truths only hit children—adults and nonphilosophers get sucked into the minutiae of practical life and need to worry about “serious matters,” so they abandon these insights for seemingly more relevant questions. One of these truths concerns the larger difference in texture and quality between the past and the future. Thanks to my studying this distinction all my life, I understand it better than I did during my childhood, but I no longer envision it as vividly.

  The only way you can imagine a future “similar” to the past is by assuming that it will be an exact projection of it, hence predictable. Just as you know with some precision when you were born, you would then know with equal precision when you will die. The notion of future mixed with chance, not a deterministic extension of your perception of the past, is a mental operation that our mind cannot perform. Chance is too fuzzy for us to be a category by itself. There is an asymmetry between past and future, and it is too subtle for us to understand naturally.