by
Nassim Nicholas Taleb
I was somewhat disappointed by this book, after having devoured Fooled by Randomness a number of years ago. Many of the ideas presented here were embellishments of those presented in a more concise way (and with fewer name-dropping literary allusions) in that earlier, better book.
My main gripe with this book was the distracting omnipresence of the author and his insistence on letting me know about the fact he is well-read, well-traveled, and has his strong likes and dislikes. I found the latter annoying, especially his rather dogmatic and categorical dismissal of my profession (psychiatry) which seems silly, if for no other reason he is lumping together psychoanalysts, behavioralists, and psychopharmacologists into one rather overcrowded boat (which he then torpedoes without sufficient explanation). There is far more empirical evidence to support the treatment of depression and of anxiety disorders, for example, than there is for many medical conditions. I share his reservations about psychoanalysis, however, but feel he could be more generous in his criticism. Yes, we should beware the Black Swan and the narrative fallacy, but that does not mean we should not or must not try to make sense of our world, however imperfectly.
I was also disappointed that he spent so much time pounding the table about the "fraud" of Gaussian assumptions and their inapplicability to wars, financial time series, and social sciences, that he left little room for solutions. I would have liked to see more exploration of his ideas about insuring a portfolio with put options or replacing long positions with call options (some simple profit-loss curves showing the capping off of losses at 15% would have been useful). I cannot agree with the author more on this point (I believe options are poorly misunderstood by a public that does not appreciate their ability to mathematically cap potential losses, something impossible with any other investment) and was look forward to more on this topic. The idea of not running to catch a train and using a "venture capital" approach to the high risk portion of your portfolio was disappointing thin gruel after slogging through his heavy-handed denunciation of financial fraudsters.
Regarding fraud, I personally believe it's a bit strong of a word to use. Fraud to me connotes conscious awareness of the untruth of what one is saying, and requires a deliberate intent to deceive. I am not sure that someone who incorrectly believes that stock market returns are normally distributed, for example, is engaging in fraud as much as group think or intellectual laziness. As is true of so much of what passes for wisdom in the financial industry, most people never really bother to test their most basic assumptions empirically. Of course, this failure to do one's homework is what creates opportunities for those of us who do ours.
I also think he overstates the importance of prediction. The strange thing about the stock market is that one need not predict with any degree of precision (thankfully, since there is a large random element) but one only has to get the general, aggregate direction right, while capping losses (using, for example, options). The other unique aspect to the stock market is that long-term predictions are much easier to make than short-term predictions (which is not true for weather patterns, river flooding, etc.). I cannot tell you where the stock market will close tomorrow (although I can tell you it's about 50% likely to be higher than lower), but I can tell you that it has an 85% probability of being higher a decade from now, and about 100% probability of being significantly higher 30 years from now, the average investment lifetime of most of us. As Jeremy Siegel points out in his fantastic book, Stocks for the Long Run, the stock market has a remarkably stable LONG-TERM average real (after-inflation) return of just above 7%, no matter what long-term period you examine over the past 250 years. In fact, even if someone were able to predict that stocks would underperform their historical average, in most of those time periods, stocks still outperformed bonds, cash, and gold.
The point is that when you buy stocks, you are becoming a proportional business owner and you get the underlying growth of the economy plus a kicker which probably represents the chronic mispricing of stocks. Anyone who waded in when they went on sale about a year ago (I write this in February, 2011) would have gotten almost a 100% return.
Prediction, in other words, is not necessary for long-term wealth accumulation. His points are well-taken that we should insure our portfolios, but it is erroneous to assume that we need to be able to predict their rate of growth.
There were a few distracting factual errors. English, for example, is NOT the official language of the Swiss military, so eavesdropping on a conversation to hear accented English, as the author suggests, would be disappointing, and decimation means a 10% reduction not annihilation. He misrepresented the literature on the treatment of depression at one point, and of course his entire diatribe against the "narrative fallacy" is badly undercut by his heavy use of stories and anecdotes. I do not believe that free will eliminates our ability to make meaningful predictions about mass, aggregate, population-level behavior, even if our ability to predict any individual behavior is very poor; for example, I know that handgun owners are twice as likely to kill themselves as non-owners but would be unable to predict which of a million households will suffer suicide, although I may be able to divide the households into high, moderate, and low risk, which in the end is helpful even if I cannot predict.
With those caveats, I present some selected excerpts from the book, along with (in a few cases) some editorial comments:
Before the discovery of Australia, people in the Old World were convinced that all swans were white, an unassailable belief as it seemed completely confirmed by empirical evidence. The sighting of the first black swan might have been an interesting surprise for a few ornithologists (and others extremely concerned with the coloring of birds), but that is not where the significance of the story lies.
It illustrates a severe limitation to our learning from observations or experience and the fragility of our knowledge. One single observation can invalidate a general statement derived from millennia of confirmatory sightings of millions of white swans. All you need is one single (and, tam told, quite ugly) black bird.
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Reading the newspaper can actually decrease your knowledge of the world.
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Black Swan logic makes what you don't know far more relevant than what you do know.
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The inability to predict outliers implies the inability to predict the course of history, given the shore of these events in the dynamics of evenly But we act as though we ore able to predict historical events, or, even worse, as if we ore able to change the course of history We produce thirty-year projections of serial security deficits and oil prices without realizing that we cannot even predict these for next summer-our romul olive prediction errors for political and er000mie events ore so monstrous that every time I look at the empirical record hove to pinch myself to verify that I am not dreaming What is surprising is not the magnitude of our forecast errors, but our obscure of awareness of it. This is all the more worrisome when we engage in deadly conflicts: wars are fundamentally unpredictable (and we do not know it). Owing to this misunderstanding of the causal chains between phony and odious, we con easily trigger Block Swans thanks to aggressive ignorance- like a child playing with o chemistry kit
Our inability to predict in environments subjected to the Block Swan, coupled with o general lock of the awareness of this stole of affairs, means that certain professionals, while behaving they ore experts, ore in fort nob Based on their empirical record, they do not know more about their subject matter than the general population, but they ore much better at narrating-or, worse, at smoking you with complicated mathematical models They ore also more likely to wear a tie.
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What did people learn from the 9/11 episode? Did they learn that some events, owing to their dynamics, stand largely outside the realm of the predictable? No. Did they learn the built-in defect of conventional wisdom? No. What did they figure out? They learned precise rules for avoiding Islamic prototerrorists and tall buildings.
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We do not spontaneously learn that we don't learn that we don't learn... Who is more valuable, the politician who avoids a war or the one who starts a new one (and is lucky enough to win)? ... Everybody knows that you need more prevention than treatment, but few reward acts of prevention.
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We remember the martyrs who died for a cause we knew about, never those no less effective in their contribution but whose cause we were never aware of - precisely because they were successful.
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One can find similar ideas among several disconnected branches of thinking. The earliest were (as usual) the empirics, whose bottom-up, theory-free, "evidence-based" medical approach was mostly associated with Philnus of Cos, Serapion of Alexandria, and Glaucias of Tarentum, later made skeptical by Menodotus of Nicomedia, and currently well-known by its vocal practitioner, our friend the great skeptical philosopher Sextus Empiricus. Sextus who, we saw caner, was perhaps the first to discuss the Black Swan. The empirics practiced the "medical art" without relying on reasoning; they wanted to benefit from chance observations by making guesses, and experimented and tinkered until they found something that worked. They did minimal theorizing. Their methods are being revived today as evidence-based medicine, after two millennia of persuasion. Consider that before we knew of bacteria, and their role in diseases, doctors rejected the practice of hand washing because it mode no sense to them, despite the evidence of a meaningful decrease in hospital deaths. Ignaz Semmelweis, the mid-nineteenth-century doctor who promoted the idea of hand washing, wasn't vindicated until decades after his death.
Academic Libertarianism
To borrow from Warren Buffett, don't ask the barber if you need a haircut-and don't ask an academic if what he does is relevant.
If I can predict all of your actions, under given circumstances, then you may not be as free as you think you are. You are an automaton responding to environmental stimuli. You are a slave of destiny. And the illusion of free will could be reduced to an equation that describes the result of interactions among molecules. It would be like studying the mechanics of a clock: a genius with extensive knowledge of the initial conditions and the causal chains would be able to extend his knowledge to the future of your actions. Wouldn't that be stifling?
[Actually, not at all. One need not predict individual behavior; only assign probabilities to aggregate behavior. I need not know which of a thousand shareholders will stampede into a stock or out of it, anymore than I need to know which of a hundred movie-goers will charge toward the exit at the smell of smoke, but if I can anticipate that on average many will, I can plan my exit from the theater appropriately.]
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.
Chapter Twelve - Epistemocracy, a Dream
Chapter Twelve - Epistemocracy, a Dream
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 nut 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, homuni 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, his not that he was ahead of his time; it would be better said that later scholars (advocating rationality) were backward.
He was thinking, ruminating fellow, and his ideas did not spring up in his tranquil study, but while on horseback He went on lung rides and came back with ideas. Montaigne was neither one of the academies 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 bees 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 Sextos Empiricus, particularly in his awareness of the need to suspend judgment.
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Just as autism is called "mind blindness," this inability to think dynamically, to position oneself with respect to a future observer, we should call "future blindness."
Prediction, Misprediction, and Happiness
I searched the literature of cognitive science for any research on "future blindness" and found nothing. But in the literature on happiness I did find an examination of our chronic errors in prediction that will make as happy. This prediction error works as follows. You are about to buy a new car. It is going to change your life, elevate your status, and make your commute a vacation... Yet you forget that the last time you bought a car, you also had the same expectations. You do not anticipate that the effect of the new car will eventually wane and that you will revert to the initial condition, as you did last time. A few weeks after you drive your new car out of the showroom, it will become dull. If you had expected this, you probably would not have bought it. You are about to commit a prediction error that you have already made. Yet it would cost so little to introspect!
Psychologists have studied this kind of misprediction with respect to both pleasant and unpleasant events. We overestimate the effects of both kinds of future events on our lives. We seem to be in a psychological predicament that makes us do so. This predicament is called "anticipated utility" by Danny Kahneman and "affective forecasting" by Dan Gilbert. The point is net so much that we tend to mispredict our future happiness, but rather that we do not learn recursively from past experiences. We have evidence of a mental black and distortions in the way we fail to learn from our past errors in projecting the future of our affective states.
We grossly overestimate the length of the effect of misfortune on our lives. You think that the loss of your fortune or current position will be devastating, but you are probably wrong. More likely, you will adapt to anything, as you probably did after past misfortunes. You may feel a sting, but it will not be as bad as you expect. This kind of misprediction may have a purpose: to motivate us to perform important acts (like buying new cars or getting rich) and to prevent us from taking certain unnecessary risks. And it is part of a more general problem: we humans are supposed to fool ourselves a little bit here and there. According to Trivers's theory of self-deception, this is supposed to orient us favorably toward the future. But self-deception is not a desirable feature outside of its natural domain. It prevents us from taking some unnecessary risks-but we saw in Chapter 6 how it does not as readily cover a spate of modern risks that we do not fear because they are not vivid, such as investment risks, environmental dangers, or long-term security.
Maximize the serendipity around you.
Indeed, we have psychological and intellectual difficulties with trial and error, and with accepting that series of small failures are necessary in life. My colleague Mark Spitznagel understood that we humans have a mental hang-up about failures: "You need to love to lose" was his motto. In fact, the reason I felt immediately at home in America is precisely because American culture encourages the process of failure, unlike the cultures of Europe and Asia where failure is met with stigma and embarrassment. America's specialty is to take these small risks for the rest of the world, which explains this country's disproportionate share in innovation. Once established, an idea or a product is later "perfected" over there. ...
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You need to put a portion [of your portfolio], say 85 to 90 percent, in extremely safe instruments, like Treasury bills-as safe a class of instruments as you can manage to find on this planet. The remaining 10 to 15 percent you put in extremely speculative bets, as leveraged as possible (like options), preferably venture capital-style portfolios. That way you do not depend on errors of risk management; no Black Swan can hurt you at all, beyond your "floor," the nest egg that you have in maximally safe investments. Or, equivalently, you can have a speculative portfolio and insure it (if possible) against losses of mere than, say, 15 percent. You are "capping" your incomputable risk, the one that is harmful to you instead of having medium risk, you have high risk on one side and no risk on the other. The average still be medium risk but constitutes a positive exposure to the Black Swan. More technically, this can be called a "convex" combination. Let us see how this can be implemented in all aspects of life …
"Nobody Knows Anything"
The legendary screenwriter William Goldman was said to have shouted "Nobody knows anything!" in relation to the prediction of movie sales Now, the reader may wonder how someone as successful as Goldman ran figure out what to do without making predictions The answer stands perceived business logic on its head. He knew that he could not predict individual events, but he was well aware that the unpredictable, namely a movie turning into a blockbuster, would benefit him immensely…
Do not waste year time trying to fight forecasters, stock analysts, economists, and social scientists, except to play pranks on them. They are considerably easy to make fun of, and many get angry quite readily. It is ineffective to moan about unpredictability: people will continue to predict foolishly, especially if they are paid for it, and you cannot put an end to institutionalized fraud. If you ever do have to heed a forecast, keep in mind that its accuracy degrades rapidly as you extend it through time, e.g., if you hear a "prominent" economist using the word equilibrium, or normal distribution, do not argue with him; just ignore him, or try to put a rat down his shirt.
The Great Asymmetry
All these recommendations have one point in common: asymmetry. Put yourself in situations where favorable consequences are much larger than unfavorable ones. Indeed, the notion of asymmetric outcomes is the central idea of this book: I will never get to know the unknown since, by definition, it is unknown. However, I can always guess how it might affect me, and I should base my decisions around that.
This idea is often erroneously called Pascal's wager, after the philosopher and (thinking) mathematician Blaise Pascal. He presented it something like this: I do not know whether God exists, but I know that I have nothing to gain from being an atheist if he does not exist, whereas I have plenty to lose if he does. Hence, this justifies my belief in God.
Pascal's argument is severely flawed theologically: one has to be naive enough to believe that God would not penalize us for false belief. Unless, of course, one is taking the quite restrictive view of a naive God. (Bertrand Russell was reported to have claimed that God would need to have created fools for Pascal's argument to work.)
But the idea behind Pascal's wager has fundamental applications outside of theology. It stands the entire notion of knowledge on its head. It eliminates the need for us to understand the probability of a rare event (there are fundamental limits to our knowledge of these); rather, we can focus on the payoff and benefits of an event if it takes place. The probabilities of very rare events are not computable; the effect of an event on us is considerably easier to ascertain (the rarer the event, the fuzzier the odds). We can have a clear idea of the consequences of an event, even if we do not know how likely it is to occur. I don't know the odds of an earthquake, but I can imagine how San Francisco might be affected by one. This idea that in order to make a decision you need to focus on the consequences (which you can know) rather than the probability (which you can't know) is the central idea of ssnccrtuiutsj. Much of my life is based on it. You can build an overall theory of decision making on this idea. All you have to do is mitigate the consequences. As I said, if my portfolio is exposed to a market crash, the odds of which I can't compute, all I have to do is buy insurance, or get out and invest the amounts I am not willing to ever lose in less risky securities.
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[Jack Green in Fire the Bastards! shows how] book reviewers anchor on other reviews and reveals powerful mutual influence, even in wording.
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Take a cross section of the dominant corporations at any particular time; many of them will be out of business a few decades later, while firms nobody ever heard of will have popped onto the scene from some garage in California or from some college dorm. Consider the following sobering statistic, Of the five hundred largest U.S. companies in 1957, only
74 were still part of [the S&P 500] 40 years later. Only a few had disappeared in mergers; the rest either shrank or went bust. Interestingly, almost all these large corporations were located in the most capitalist country on earth, the United States. The more socialist a country's orientation, the easier it was for the large corporate monsters to stick around. Why did capitalism (and not socialism) destroy these ogres? In other words, if you leave companies alone, they tend to get eaten up. Those in favor of economic freedom claim that beasty and greedy corporations pose no threat because competition keeps them in check. What I saw at the Wharton School convinced me that the real reason includes a large share of something else: chance.
[Note: This may be true for the legal abstraction called a corporation, but the executives and corporate insiders often enriched themselves massively in the process, shunting wealth from workers and shareholders into their own pockets; they companies may have failed, but the money was not returned to investors or reflowed into the system; much remained in the pockets of insiders, often the ones who oversaw the failure of the companies. Also, I am not sure this is true on a market cap basis. Most of the S&P 500 market cap is in a few companies that dominate; smaller companies are much more likely to turn over.]
But when people discuss chance (which they rarely do), they usually only look at their own luck. The luck of others counts greatly. Another corporation may luck out thanks to a blockbuster product and displace the current winners. Capitalism is, among other things, the revitalization of the world thanks to the opportunity to be lucky. Luck is the grand equalizer, because almost everyone can benefit from it. The socialist governments protected their monsters and, by doing so, killed potential newcomers in the womb.
[Note: Again, this assumes that "everyone" has a place at the table. This is simply not empirically true. Corporate insiders including managers who had nothing to do with the creation of the most successful companies profit massively from their positions in ways that ordinary investors and workers cannot. The Bush family, Koch brothers, and Prince family (owners of Blackwater) may all be competing against one another, but none will likely be impoverished if they "lose" and no one from the bottom 99% will have an opportunity to compete viably against these extremely wealthy, well-connected families. ]
Everything is transitory. Luck bath made and unmade Carthage; it both made and unmade Rome. I said earlier that randomness is bad, but it is not always so. Luck is far more egalitarian than even intelligence. If people were rewarded strictly according to their abilities, things would still be unfair-people don't choose their abilities. Randomness has the beneficial effect of reshuffling society's cards, knocking down the big guy.
Naïve Globalization
We are gliding into disorder, but not necessarily bad disorder. This implies that we will see more periods of calm and stability, with most problems concentrated into a small number of Black Swans. Consider the nature of past wars. The twentieth century was not the deadliest (in percentage of the total population), but it brought something new: the beginning of the Extremistan warfare-a small probability of a conflict degenerating into total decimation of the human race, a conflict from which nobody is safe anywhere.
[Minor quibble: decimate means to reduce by 10%, not to annihilate, which I think he intends here. A "total decimation of the human race" would still leave over 5 billion people on the planet (as of this writing).]
A similar effect is taking place in economic life. I spoke about globalization in Chapter ~ it is here, but it is not all for the good: it creates interlocking fragility, while reducing volatility and giving the appearance of stability. In other words it creates devastating Black Swans. We have never lived before under the threat of a global collapse. Financial institutions have been merging into a smaller number of very large banks. Almost all banks are now interrelated. So the financial ecology is swelling into gigantic, incestuous, bureaucratic banks (often Gaussianized in their risk measurement)-when one falls, they all fall. The increased concentration among banks seems to have the effect of making financial crisis less likely, but when they happen they are more global in scale and hit us very hard. We have moved from a diversified ecology of small banks, with varied lending policies, to a more homogeneous framework of firms that all resemble one another. True, we now have fewer failures, but when they occur ... shiver at the thought. I rephrase here: we still have fewer but more severe crises.
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Shockingly, the bell curve is used as a risk-measurement tool by those regulators and central bankers who wear dark suits and talk in a boring way about currencies.
The Increase in the Decrease
The main point of the Gaussian, as I've said, is that most observations hover around the mediocre, the average; the odds of a deviation decline faster and faster (exponentially) as you move away from the average If you must have only one single piece of information, this is the one: the dramatic increase in the speed of decline in the odds as you move away from the center, or the average. Look at the list below for an illustration of this. I am taking an example of a Gaussian quantity, such as height, and simpli~4ng it a bit to make it more illustrative Assume that the average height (men and women) is 1.67 meters, or 5' 7 inches Consider what I call a unit of deviation here as 10 cm. Let us look at increments above 1.67 meters and consider the odds of someone being that tall:
10 cm taller than the average (i.e., taller than 1.77 m, or 5 ' 10): 1 in 6.3
20 cm taller than the average (i.e., taller than 1.87 m, or 6' 2): 1 in 44
30 cm taller than the average (i.e., taller than 1.97 m, or 6' 6): 1 in 740
40 cm taller than the average (i.e., taller than 2.n7 m, or 6' 9): 1 in 32,000
50 cm taller than the average (i.e., taller than 2.17 m, or 7' 1): 1 in 3,500,000
60 cm taller than the average (i.e., taller than 2.27 m, or 7' 5): 1 in 1,000,000,000
70 cm taller than the average (i.e., taller than 2.37 m, or 7' 9): 1 in 780,000,000,000
8o cm taller than the average (i.e., taller than 2.47 m, or 8' 1): 1 in i,6oo,ooo,ooo,ooo,ooo
90 cm taller than the average (i.e., taller than 2.57 m, or 8' 5): 1 in 8,900,000,000,000,000,000
100 cm taller than the average (i.e., taller than 2.67 m, or 8' 9): 1 in 130,000,000,000,000,000,000,000
and, 110 cm taller than the average (i.e., taller than 2.77 m, or 9 ' 1): 1 in 36,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000.
Note that soon after, I believe, 22 deviations, or 220 cm taller than the average, the odds reach a googol, which is 1 with 100 zeroes behind it.
The point of this list is to illustrate the acceleration. Look at the difference in odds between 60 and 70 cm taller than average: for a mere increase of four inches, we go from one in 1 billion people to one in 780 billion! As for the jump between 70 and 80 cm: an additional 4 inches above the average, we go from one in 780 billion to one in 1.6 million billion!
This precipitous decline in the odds of encountering something is what allows you to ignore outliers. Only one curve can deliver this decline, and it is the bell curve (and its nonscalable siblings)
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One of the most misunderstood aspects of a Gaussian is its fragility and vulnerability in the estimation of tail events. The odds of a 4 sigma move are twice that of a 4.15 sigma. The odds of a 20 sigma are a trillion times higher than those of a 21 sigma! It means that a small measurement error of the sigma will lead to a massive underestimation of the probability. We can be a trillion times wrong about some events.
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Let us return to the story of my business life. Look at the graph in Figure 14. in the last fifty years, the ten most extreme days in the financial markets represent half the returns. Ten days in fifty years. Meanwhile, we are mired in chitchat.
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I can't figure out whether the war is going to degenerate into something even more severe. Looking into the outcome of the war, with all my relatives, friends, and property exposed to it, I face true limits of knowledge. Can someone explain to me why I should care about subatomic particles that, anyway, converge to a Gaussian? People can't predict how long they will be happy with recently acquired objects, how long their marriages will last, how their new jobs will turn out, yet it's subatomic particles that they cite as "limits of prediction." They're ignoring a mammoth standing in front of them in favor of matter even a microscope would not allow them to see. I worry less about small failures, more about large, potentially terminal ones. I worry far more about the "promising" stock market, particularly the "safe" blue chip stocks, than I do about speculative ventures-the former present invisible risks, the latter offer no surprises since you know how volatile they are and can limit your downside by investing smaller amount.
I worry less about advertised and sensational risks, more about the more vicious hidden ones I worry less about terrorism than about diabetes, less about matters people usually worry about because they are obvious worries, and more about matters that lie outside our consciousness and common discourse (I also have to confess that I do not worry a lot - I try to worry about matters I can do something about) I worry less about embarrassment than about missing an opportunity.
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I once received another piece of life-changing advice… My classmate in Paris, the novelist-to-be Jean-Olivier Tedesco, pronounced, as he prevented me from running to catch a subway, "I don't run for trains."
Snub your destiny. I have taught myself to resist running to keep on schedule. This may seem a very small piece of advice, but it registered. In refusing to run to catch trains, I have felt the true value of elegance and aesthetics in behavior, a sense of being in control of my time, my schedule, and my life. Missing a train is only painful if you run after it! Likewise, not matching the idea of success others expect from you is only painful if that's what you are seeking.
You stand above the rat race and the pecking order, not outside of it, if you do so by choice. Quitting a high-paying position, if it is your decision, will score a bigger payoff than the utility of the money involved (this may sound crazy, but I've tried it and it works). This is the first step toward the stoic's throwing a four-letter word at fate. You have far more control over your life if you decide on your criterion by yourself.
Mother Nature has given ns some defense mechanisms: as in Aesop's fable, one of these is our ability to consider that the grapes we cannot (or did not) reach are sour. But an aggressively stoic prior disdain and rejection of the grapes is even more rewarding. Be aggressive; be the one to resign, if you have the guts. It's more difficult to be a loser in a game you set up yourself. In Black Swan terms, this means that you are exposed to the improbable only if you let it control you. You always control what you do; so make this your end.
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