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The Black Swan

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Book notes for "The Black Swan", The Impact of the Highly Improbable by Nassim Nicholas Taleb


Last annotated on January 13, 2017

What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. location 346

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability.\* A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives. location 350

Go ask your portfolio manager for his definition of "risk," and odds are that he will supply you with a measure that excludes the possibility of the Black Swan-hence one that has no better predictive value for assessing the total risks than astrology (we will see how they dress up the intellectual fraud with mathematics). This problem is endemic in social matters. location 364

The more unexpected the success of such a venture, the smaller the number of competitors, and the more successful the entrepreneur who implements the idea. The same applies to the shoe and the book businesses-or any kind of entrepreneurship. The same applies to scientific theories-nobody has interest in listening to trivialities. The payoff of a human venture is, in general, inversely proportional to what it is expected to be. location 386

We will see that, contrary to social-science wisdom, almost no discovery, no technologies of note, came from design and planning-they were just Black Swans. The strategy for the discoverers and entrepreneurs is to rely less on top-down planning and focus on maximum tinkering and recognizing opportunities when they present themselves. location 407

The person who imposed locks on cockpit doors gets no statues in public squares, not so much as a quick mention of his contribution in his obituary. "Joe Smith, who helped avoid the disaster of 9/11, died of complications of liver disease." Seeing how superfluous his measure was, and how it squandered resources, the public, with great help from airline pilots, might well boot him out of office. Vox clamantis in deserto. He will retire depressed, with a great sense of failure. He will die with the impression of having done nothing useful. location 444

This is an essay expressing a primary idea; it is neither the recycling nor repackaging of other people's thoughts. An essay is an impulsive meditation, not science reporting. I apologize if I skip a few obvious topics in this book out of the conviction that what is too dull for me to write about might be too dull for the reader to read. location 495

if my employer, First Boston, and the financial system survived until year-end, I would get the equivalent of a fellowship. This is sometimes called "f*** you money," which, in spite of its coarseness, means that it allows you to act like a Victorian gentleman, free from slavery. It is a psychological buffer: the capital is not so large as to make you spoiled-rich, but large enough to give you the freedom to choose a new occupation without excessive consideration of the financial rewards. It shields you from prostituting your mind and frees you from outside authority-any outside authority. location 884

I stayed in the quant and trading businesses (I'm still there), but organized myself to do minimal but intense (and entertaining) work, focus only on the most technical aspects, never attend business "meetings," avoid the company of "achievers" and people in suits who don't read books, and take a sabbatical year for every three on average to fill up gaps in my scientific and philosophical culture. To slowly distill my single idea, I wanted to become a fl芒neur, a professional meditator, sit in caf茅s, lounge, unglued to desks and organization structures, sleep as long as I needed, read voraciously, and not owe any explanation to anybody. location 897

If you are a prostitute, you work by the hour and are (generally) paid by the hour. Furthermore, your presence is (I assume) necessary for the service you provide. If you open a fancy restaurant, you will at best steadily fill up the room (unless you franchise it). In these professions, no matter how highly paid, your income is subject to gravity. Your revenue depends on your continuous efforts more than on the quality of your decisions. Moreover, this kind of work is largely predictable: it will vary, but not to the point of making the income of a single day more significant than that of the rest of your life. In other words, it will not be Black Swan driven. location 980

If you are dealing with quantities from Extremistan, you will have trouble figuring out the average from any sample since it can depend so much on one single observation. The idea is not more difficult than that. In Extremistan, one unit can easily affect the total in a disproportionate way. In this world, you should always be suspicious of the knowledge you derive from data. This is a very simple test of uncertainty that allows you to distinguish between the two kinds of randomness. Capish? What you can know from data in Mediocristan augments very rapidly with the supply of information. But knowledge in Extremistan grows slowly and erratically with the addition of data, some of it extreme, possibly at an unknown rate. Wild location 1110

Matters that seem to belong to Mediocristan (subjected to what we call type 1 randomness): height, weight, calorie consumption, income for a baker, a small restaurant owner, a prostitute, or an orthodontist; gambling profits (in the very special case, assuming the person goes to a casino and maintains a constant betting size), car accidents, mortality rates, "IQ" (as measured). Matters that seem to belong to Extremistan (subjected to what we call type 2 randomness): wealth, income, book sales per author, book citations per author, name recognition as a "celebrity," number of references on Google, populations of cities, uses of words in a vocabulary, numbers of speakers per language, damage caused by earthquakes, deaths in war, deaths from terrorist incidents, sizes of planets, sizes of companies, stock ownership, height between species (consider elephants and mice), financial markets (but your investment manager does not know it), commodity prices, inflation rates, economic data. The Extremistan list is much longer than the prior one. location 1117

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. location 1214

The following point further illustrates the absurdity of confirmation. If you believe that witnessing an additional white swan will bring confirmation that there are no black swans, then you should also accept the statement, on purely logical grounds, that the sighting of a red Mini Cooper should confirm that there are no black swans. Why? Just consider that the statement "all swans are white" is equivalent to 'all nonwhite objects are not swans.' What confirms the latter statement should confirm the former. Therefore a mind with confirmation-bent would infer that the sighting of a nonwhite object that is not a swan should bring such confirmation. location 1555

We learn from repetition-at the expense of events that have not happened before. Events that are nonrepeatable are ignored before their occurrence, and overestimated after (for a while). After a Black Swan, such as September 11, 2001, people expect it to recur when in fact the odds of that happening have arguably been lowered. We like to think about specific and known Black Swans when in fact the very nature of randomness lies in its abstraction. location 1890

This may indeed apply to all concentrated businesses: when you look at the empirical record, you not only see that venture capitalists do better than entrepreneurs, but publishers do better than writers, dealers do better than artists, and science does better than scientists (about 50 percent of scientific and scholarly papers, costing months, sometimes years, of effort, are never truly read). The person involved in such gambles is paid in a currency other than material success: hope. location 2104

your happiness depends far more on the number of instances of positive feelings, what psychologists call "positive affect," than on their intensity when they hit. In other words, good news is good news first; how good matters rather little. So to have a pleasant life you should spread these small "affects" across time as evenly as possible. Plenty of mildly good news is preferable to one single lump of great news. location 2112

Like a friend, you accept it the way it is; you do not judge it. Montaigne was asked "why" he and the writer Etienne de la Bo茅tie were friends-the kind of question people ask you at a cocktail party as if you knew the answer, or as if there were an answer to know. It was typical of Montaigne to reply, "Parce que c'茅tait lui, parce que c'茅tait moi" location 2129

some business bets in which one wins big but infrequently, yet loses small but frequently, are worth making if others are suckers for them and if you have the personal and intellectual stamina. But you need such stamina. You also need to deal with people in your entourage heaping all manner of insult on you, much of it blatant. location 2220

Nero engaged in a strategy that he called "bleed." You lose steadily, daily, for a long time, except when some event takes place for which you get paid disproportionately well. No single event can make you blow up, on the other hand-some changes in the world can produce extraordinarily large profits that pay back such bleed for years, sometimes decades, sometimes even centuries. location 2227

He made sure, after a long string of losses, that they did not think he was apologetic-indeed, paradoxically, they became more supportive that way. Humans will believe anything you say provided you do not exhibit the smallest shadow of diffidence; like animals, they can detect the smallest crack in your confidence before you express it. The trick is to be as smooth as possible in personal manners. It is much easier to signal self-confidence if you are exceedingly polite and friendly; you can control people without having to offend their sensitivity. The problem with business people, Nero realized, is that if you act like a loser they will treat you as a loser-you set the yardstick yourself. There is no absolute measure of good or bad. location 2247

When he worked as a trader for an investment bank, Nero had to face the typical employee-evaluation form. The form was supposed to keep track of "performance," supposedly as a check against employees slacking off. Nero found the evaluation absurd because it did not so much judge the quality of a trader's performance as encourage him to game the system by working for short-term profits at the expense of possible blowups-like banks that give foolish loans that have a small probability of blowing up, because the loan officer is shooting for his next quarterly evaluation. So one day early in his career, Nero sat down and listened very calmly to the evaluation of his "supervisor." When Nero was handed the evaluation form he tore it into small pieces in front of him. He did this very slowly, accentuating the contrast between the nature of the act and the tranquillity with which he tore the paper. The boss watched him blank with fear, eyes popping out of his head. Nero focused on his undramatic, slow-motion act, elated by both the feeling of standing up for his beliefs and the aesthetics of its execution. The combination of elegance and dignity was exhilarating. He knew that he would either be fired or left alone. He was left alone. location 2254

The entire notion of biography is grounded in the arbitrary ascription of a causal relation between specified traits and subsequent events. Now consider the cemetery. The graveyard of failed persons will be full of people who shared the following traits: courage, risk taking, optimism, et cetera. Just like the population of millionaires. There may be some differences in skills, but what truly separates the two is for the most part a single factor: luck. Plain luck. location 2367

A recent wave of philosophers and physicists (and people combining the two categories) has been examining the self-sampling assumption, which is a generalization of the principle of the Casanova bias to our own existence. Consider our own fates. Some people reason that the odds of any of us being in existence are so low that our being here cannot be attributed to an accident of fate. Think of the odds of the parameters being exactly where they need to be to induce our existence (any deviation from the optimal calibration would have made our world explode, collapse, or simply not come into existence). It is often said that the world seems to have been built to the specifications that would make our existence possible. According to such an argument, it could not come from luck. However, our presence in the sample completely vitiates the computation of the odds. Again, the story of Casanova can make the point quite simple-much simpler than in its usual formulation. Think again of all the possible worlds as little Casanovas following their own fates. The one who is still kicking (by accident) will feel that, given that he cannot be so lucky, there had to be some transcendental force guiding him and supervising his destiny: "Hey, otherwise the odds would be too low to get here just by luck." For someone who observes all adventurers, the odds of finding a Casanova are not low at all: there are so many adventurers, and someone is bound to win the lottery ticket. location 2575

The reference point argument is as follows: do not compute odds from the vantage point of the winning gambler (or the lucky Casanova, or the endlessly bouncing back New York City, or the invincible Carthage), but from all those who started in the cohort. location 2605

My biggest problem with the educational system lies precisely in that it forces students to squeeze explanations out of subject matters and shames them for withholding judgment, for uttering the "I don't know." Why did the Cold War end? Why did the Persians lose the battle of Salamis? Why did Hannibal get his behind kicked? Why did Casanova bounce back from hardship? In each of these examples, we are taking a condition, survival, and looking for the explanations, instead of flipping the argument on its head and stating that conditional on such survival, one cannot read that much into the process, and should learn instead to invoke some measure of randomness (randomness is what we don't know; to invoke randomness is to plead ignorance). location 2626

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. location 2844

Our human race is affected by a chronic underestimation of the possibility of the future straying from the course initially envisioned (in addition to other biases that sometimes exert a compounding effect). To take an obvious example, think about how many people divorce. Almost all of them are acquainted with the statistic that between one-third and one-half of all marriages fail, something the parties involved did not forecast while tying the knot. Of course, "not us," because "we get along so well" (as if others tying the knot got along poorly). location 2954

When you are employed, hence dependent on other people's judgment, looking busy can help you claim responsibility for the results in a random environment. The appearance of busyness reinforces the perception of causality, of the link between results and one's role in them. This of course applies even more to the CEOs of large companies who need to trumpet a link between their "presence" and "leadership" and the results of the company. I am not aware of any studies that probe the usefulness of their time being invested in conversations and the absorption of small-time information-nor have too many writers had the guts to question how large the CEO's role is in a corporation's success. location 2994

Show two groups of people a blurry image of a fire hydrant, blurry enough for them not to recognize what it is. For one group, increase the resolution slowly, in ten steps. For the second, do it faster, in five steps. Stop at a point where both groups have been presented an identical image and ask each of them to identify what they see. The members of the group that saw fewer intermediate steps are likely to recognize the hydrant much faster. Moral? The more information you give someone, the more hypotheses they will formulate along the way, and the worse off they will be. They see more random noise and mistake it for information. The problem is that our ideas are sticky: once we produce a theory, we are not likely to change our minds-so those who delay developing their theories are better off. When you develop your opinions on the basis of weak evidence, you will have difficulty interpreting subsequent information that contradicts these opinions, even if this new information is obviously more accurate. Two mechanisms are at play here: the confirmation bias that we saw in Chapter 5, and belief perseverance, the tendency not to reverse opinions you already have. Remember that we treat ideas like possessions, and it will be hard for us to part with them. location 3013

the psychologist Paul Slovic asked bookmakers to select from eighty-eight variables in past horse races those that they found useful in computing the odds. These variables included all manner of statistical information about past performances. The bookmakers were given the ten most useful variables, then asked to predict the outcome of races. Then they were given ten more and asked to predict again. The increase in the information set did not lead to an increase in their accuracy; their confidence in their choices, on the other hand, went up markedly. Information proved to be toxic. location 3030

Worse yet, many financial institutions produce booklets every year-end called "Outlook for 200X," reading into the following year. Of course they do not check how their previous forecasts fared after they were formulated. The public might have been even more foolish in buying the arguments without requiring the following simple tests-easy though they are, very few of them have been done. One elementary empirical test is to compare these star economists to a hypothetical cabdriver (the equivalent of Mikhail from Chapter 1): you create a synthetic agent, someone who takes the most recent number as the best predictor of the next, while assuming that he does not know anything. Then all you have to do is compare the error rates of the hotshot economists and your synthetic agent. The problem is that when you are swayed by stories you forget about the necessity of such testing. location 3105

Jean-Philippe Bouchaud, whom I was visiting in Paris. He is a boyish man who looks half my age though he is only slightly younger than I, a matter that I half jokingly attribute to the beauty of physics. Actually he is not exactly a physicist but one of those quantitative scientists who apply methods of statistical physics to economic variables, a field that was started by Beno卯t Mandelbrot in the late 1950s. This community does not use Mediocristan mathematics, so they seem to care about the truth. They are completely outside the economics and business-school finance establishment, and survive in physics and mathematics departments or, very often, in trading houses (traders rarely hire economists for their own consumption, but rather to provide stories for their less sophisticated clients). location 3130

these brokerage-house analysts predicted nothing-a na茂ve forecast made by someone who takes the figures from one period as predictors of the next would not do markedly worse. Yet analysts are informed about companies' orders, forthcoming contracts, and planned expenditures, so this advanced knowledge should help them do considerably better than a na茂ve forecaster looking at the past data without further information. Worse yet, the forecasters' errors were significantly larger than the average difference between individual forecasts, which indicates herding. Normally, forecasts should be as far from one another as they are from the predicted number. location 3139

We humans are the victims of an asymmetry in the perception of random events. We attribute our successes to our skills, and our failures to external events outside our control, namely to randomness. We feel responsible for the good stuff, but not for the bad. This causes us to think that we are better than others at whatever we do for a living. Ninety-four percent of Swedes believe that their driving skills put them in the top 50 percent of Swedish drivers; 84 percent of Frenchmen feel that their lovemaking abilities put them in the top half of French lovers. location 3178

The unexpected has a one-sided effect with projects. Consider the track records of builders, paper writers, and contractors. The unexpected almost always pushes in a single direction: higher costs and a longer time to completion. location 3255

Don't cross a river if it is four feet deep on average. You would take a different set of clothes on your trip to some remote destination if I told you that the temperature was expected to be seventy degrees Fahrenheit, with an expected error rate of forty degrees than if I told you that my margin of error was only five degrees. The policies we need to make decisions on should depend far more on the range of possible outcomes than on the expected final number. location 3340

A five-year plan? To a fellow deeply skeptical of the central planner, the notion was ludicrous; growth within the firm had been organic and unpredictable, bottom-up not top-down. It was well known that the firm's most lucrative department was the product of a chance call from a customer asking for a specific but strange financial transaction. The firm accidentally realized that they could build a unit just to handle these transactions, since they were profitable, and it rapidly grew to dominate their activities. location 3405

Again, Poincar茅 is in a class by himself. I recall my father recommending Poincar茅's essays, not just for their scientific content, but for the quality of his French prose. location 3559

This multiplicative difficulty leading to the need for greater and greater precision in assumptions can be illustrated with the following simple exercise concerning the prediction of the movements of billiard balls on a table. I use the example as computed by the mathematician Michael Berry. If you know a set of basic parameters concerning the ball at rest, can compute the resistance of the table (quite elementary), and can gauge the strength of the impact, then it is rather easy to predict what would happen at the first hit. The second impact becomes more complicated, but possible; you need to be more careful about your knowledge of the initial states, and more precision is called for. The problem is that to correctly compute the ninth impact, you need to take into account the gravitational pull of someone standing next to the table (modestly, Berry's computations use a weight of less than 150 pounds). And to compute the fifty-sixth impact, every single elementary particle of the universe needs to be present in your assumptions! An electron at the edge of the universe, separated from us by 10 billion light-years, must figure in the calculations, since it exerts a meaningful effect on the outcome. location 3621

On discussions of free will, the deterministic nature of the mind often comes up. Yes, it might be possible to predict the workings of a mind and it follows that there is no free will. Laplace's Demon could perform such a calculation, but we cannot. Brains are therefore deterministic in principle, but not in practice. There is no free-will, but this has no concrete meaning.

But corporations can go bust as often as they like, thus subsidizing us consumers by transferring their wealth into our pockets-the more bankruptcies, the better it is for us. Government is a more serious business and we need to make sure we do not pay the price for its folly. As individuals we should love free markets because operators in them can be as incompetent as they wish. location 3675

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 made 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. Similarly it may not "make sense" that acupuncture works, but if pushing a needle in someone's toe systematically produces relief from pain (in properly conducted empirical tests), then it could be that there are functions too complicated for us to understand, so let's go with it for now while keeping our minds open. location 3710

in people's minds, the relationship between the past and the future does not learn from the relationship between the past and the past previous to it. There is a blind spot: when we think of tomorrow we do not frame it in terms of what we thought about yesterday on the day before yesterday. Because of this introspective defect we fail to learn about the difference between our past predictions and the subsequent outcomes. When we think of tomorrow, we just project it as another yesterday. location 3878

need for people to use prediction markets for improving rationality

Go to the primate section of the Bronx Zoo where you can see our close relatives in the happy primate family leading their own busy social lives. You can also see masses of tourists laughing at the caricature of humans that the lower primates represent. Now imagine being a member of a higher-level species (say a "real" philosopher, a truly wise person), far more sophisticated than the human primates. You would certainly laugh at the people laughing at the nonhuman primates. Clearly, to those people amused by the apes, the idea of a being who would look down on them the way they look down on the apes cannot immediately come to their minds-if it did, it would elicit self-pity. They would stop laughing. Accordingly, an element in the mechanics of how the human mind learns from the past makes us believe in definitive solutions-yet not consider that those who preceded us thought that they too had definitive solutions. We laugh at others and we don't realize that someone will be just as justified in laughing at us on some not too remote day. location 3882

We can get negative confirmation from history, which is invaluable, but we get plenty of illusions of knowledge along with it. location 3981

I am trying here to generalize to real life the notion of the "barbell" strategy I used as a trader, which is as follows. If you know that you are vulnerable to prediction errors, and if you accept that most "risk measures" are flawed, because of the Black Swan, then your strategy is to be as hyperconservative and hyperaggressive as you can be instead of being mildly aggressive or conservative. Instead of putting your money in "medium risk" investments (how do you know it is medium risk? by listening to tenure-seeking "experts"?), you need to put a portion, 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.鈭?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 more than, say, 15 percent. You are "clipping" 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 will be medium risk but constitutes a positive exposure to the Black Swan. More technically, this can be called a "convex" combination. location 4067

For your exposure to the positive Black Swan, you do not need to have any precise understanding of the structure of uncertainty. I find it hard to explain that when you have a very limited loss you need to get as aggressive, as speculative, and sometimes as "unreasonable" as you can be. Middlebrow thinkers sometimes make the analogy of such strategy with that of collecting "lottery tickets." It is plain wrong. First, lottery tickets do not have a scalable payoff; there is a known upper limit to what they can deliver. The ludic fallacy applies here-the scalability of real-life payoffs compared to lottery ones makes the payoff unlimited or of unknown limit. Secondly, the lottery tickets have known rules and laboratory-style well-presented possibilities; here we do not know the rules and can benefit from this additional uncertainty, since it cannot hurt you and can only benefit you.鈭?location 4105

Don't look for the precise and the local. Simply, do not be narrow-minded. The great discoverer Pasteur, who came up with the notion that chance favors the prepared, understood that you do not look for something particular every morning but work hard to let contingency enter your working life. location 4112

If you ever do have to heed a forecast, keep in mind that its accuracy degrades rapidly as you extend it through time. location 4144

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 probabilities 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 uncertainty. Much of my life is based on it. location 4156

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. location 4374

Remember this: the Gaussian-bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while "scalables," or Mandelbrotian variations, do not have such a restriction. That's pretty much most of what you need to know. location 4506

The Gaussian family (which includes various friends and relatives, such as the Poisson law) are the only class of distributions that the standard deviation (and the average) is sufficient to describe. You need nothing else. The bell curve satisfies the reductionism of the deluded. There are other notions that have little or no significance outside of the Gaussian: correlation and, worse, regression. Yet they are deeply ingrained in our methods; it is hard to have a business conversation without hearing the word correlation. location 4592

If you're dealing with qualitative inference, such as in psychology or medicine, looking for yes/no answers to which magnitudes don't apply, then you can assume you're in Mediocristan without serious problems. The impact of the improbable cannot be too large. You have cancer or you don't, you are pregnant or you are not, et cetera. Degrees of deadness or pregnancy are not relevant (unless you are dealing with epidemics). But if you are dealing with aggregates, where magnitudes do matter, such as income, your wealth, return on a portfolio, or book sales, then you will have a problem and get the wrong distribution if you use the Gaussian, as it does not belong there. One single number can disrupt all your averages; one single loss can eradicate a century of profits. You can no longer say "this is an exception." The statement "Well, I can lose money" is not informational unless you can attach a quantity to that loss. You can lose all your net worth or you can lose a fraction of your daily income; there is a difference. location 4690

Note the central assumptions we made in the coin-flip game that led to the proto-Gaussian, or mild randomness. First central assumption: the flips are independent of one another. The coin has no memory. The fact that you got heads or tails on the previous flip does not change the odds of your getting heads or tails on the next one. You do not become a "better" coin flipper over time. If you introduce memory, or skills in flipping, the entire Gaussian business becomes shaky. location 4786

Second central assumption: no "wild" jump. The step size in the building block of the basic random walk is always known, namely one step. There is no uncertainty as to the size of the step. We did not encounter situations in which the move varied wildly. location 4795

Many people accepted my Black Swan idea but could not take it to its logical conclusion, which is that you cannot use one single measure for randomness called standard deviation (and call it "risk"); you cannot expect a simple answer to characterize uncertainty. location 4815

I have shown in the wealth lists in Chapter 15 the logic of a fractal distribution: if wealth doubles from 1 million to 2 million, the incidence of people with at least that much money is cut in four, which is an exponent of two. If the exponent were one, then the incidence of that wealth or more would be cut in two. The exponent is called the "power" (which is why some people use the term power law). Let us call the number of occurrences higher than a certain level an "exceedance"-an exceedance of two million is the number of persons with wealth more than two million. One main property of these fractals (or another way to express their main property, scalability) is that the ratio of two exceedances\* is going to be the ratio of the two numbers to the negative power of the power exponent. location 4985

Let us illustrate this. Say that you "think" that only 96 books a year will sell more than 250,000 copies (which is what happened last year), and that you "think" that the exponent is around 1.5. You can extrapolate to estimate that around 34 books will sell more than 500,000 copies-simply 96 times (500,000/250,000)-1.5. We can continue, and note that around 12 books should sell more than a million copies, here 96 times (1,000,000/250,000)-1.5. location 5022

the impact of the highly improbable. It shows the contributions of the top 1 percent and 20 percent to the total. The lower the exponent, the higher those contributions. But look how sensitive the process is: between 1.1 and 1.3 you go from 66 percent of the total to 34 percent. Just a 0.2 difference in the exponent changes the result dramatically-and such a difference can come from a simple measurement error. This difference is not trivial: just consider that we have no precise idea what the exponent is because we cannot measure it directly. All we do is estimate from past data or rely on theories that allow for the building of some model that would give us some idea-but these models may have hidden weaknesses that prevent us from blindly applying them to reality. location 5051

More significantly, this exponent begins to apply at some number called "crossover," and addresses numbers larger than this crossover. It may start at 200,000 books, or perhaps only 400,000 books. Likewise, wealth has different properties before, say, $600 million, when inequality grows, than it does below such a number. How do you know where the crossover point is? This is a problem. My colleagues and I worked with around 20 million pieces of financial data. We all had the same data set, yet we never agreed on exactly what the exponent was in our sets. We knew the data revealed a fractal power law, but we learned that one could not produce a precise number. But what we did know-that the distribution is scalable and fractal-was sufficient for us to operate and make decisions. location 5059

I have learned a few tricks from experience: whichever exponent I try to measure will be likely to be overestimated (recall that a higher exponent implies a smaller role for large deviations)-what you see is likely to be less Black Swannish than what you do not see. I call this the masquerade problem. Let's say I generate a process that has an exponent of 1.7. You do not see what is inside the engine, only the data coming out. If I ask you what the exponent is, odds are that you will compute something like 2.4. You would do so even if you had a million data points. The reason is that it takes a long time for some fractal processes to reveal their properties, and you underestimate the severity of the shock. location 5071

First, in assuming a scalable, I accept that an arbitrarily large number is possible. In other words, inequalities should not stop above some known maximum bound. Say that the book The Da Vinci Code sold around 60 million copies. (The Bible sold about a billion copies but let's ignore it and limit our analysis to lay books written by individual authors.) Although we have never known a lay book to sell 200 million copies, we can consider that the possibility is not zero. It's small, but it's not zero. For every three Da Vinci Code-style bestsellers, there might be one superbestseller, and though one has not happened so far, we cannot rule it out. And for every fifteen Da Vinci Codes there will be one superbestseller selling, say, 500 million copies. Apply the same logic to wealth. Say the richest person on earth is worth $50 billion. There is a nonnegligible probability that next year someone with $100 billion or more will pop out of nowhere. For every three people with more than $50 billion, there could be one with $100 billion or more. There is a much smaller probability of there being someone with more than $200 billion-one third of the previous probability, but nevertheless not zero. There is even a minute, but not zero probability of there being someone worth more than $500 billion. This tells me the following: I can make inferences about things that I do not see in my data, but these things should still belong to the realm of possibilities. There is an invisible bestseller out there, one that is absent from the past data but that you need to account for. location 5149

Also note a mental bias I encounter on the occasion: people mistake an event with a small probability, say, one in twenty years for a periodically occurring one. They think that they are safe if they are only exposed to it for ten years. location 5310

The following remark is one reason I have inordinate respect for Karl Popper; it is one of the few quotations in this book that I am not attacking. The degeneration of philosophical schools in its turn is the consequence of the mistaken belief that one can philosophize without having been compelled to philosophize by problems outside philosophy鈥? Genuine philosophical problems are always rooted outside philosophy and they die if these roots decay.鈥?[emphasis mine] These roots are easily forgotten by philosophers who "study" philosophy instead of being forced into philosophy by the pressure of nonphilosophical problems. location 5491

In the end this is a trivial decision making rule: I am very aggressive when I can gain exposure to positive Black Swans-when a failure would be of small moment-and very conservative when I am under threat from a negative Black Swan. I am very aggressive when an error in a model can benefit me, and paranoid when the error can hurt. This may not be too interesting except that it is exactly what other people do not do. location 5545

I then realized that the great strength of the free-market system is the fact that company executives don't need to know what's going on. location 7558

My main point, which I repeat in some form or another throughout Part Three, is as follows. Everything is made easy, conceptually, when you consider that there are two, and only two, possible paradigms: nonscalable (like the Gaussian) and other (such as Mandebrotian randomness). The rejection of the application of the non-scalable is sufficient, as we will see later, to eliminate a certain vision of the world. This is like negative empiricism: I know a lot by determining what is wrong. \* location 7726

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