Black Swan 7 PDF

Species Density Mother Nature does not like too much connectivity and globalization —(biological, cultural, or economic). One of the privileges I got as a result of the book was meeting Nathan Myhrvold, the type of person I wish were cloned so I could have one copy here in New York, one in Euro...

Species Density Mother Nature does not like too much connectivity and globalization —(biological, cultural, or economic). One of the privileges I got as a result of the book was meeting Nathan Myhrvold, the type of person I wish were cloned so I could have one copy here in New York, one in Europe, and one in Lebanon. I started meeting with him regularly; every single meeting has led to a big idea, or the rediscovery of my own ideas through the brain of a more intelligent person—he could easily claim co- authorship of my next book. The problem is that, unlike Spyros and those very few others, he does not have his conversations while walking (though I met him in excellent restaurants). Myhrvold enlightened me about an additional way to interpret and prove how globalization takes us into Extremistan: the notion of species density. Simply, larger environments are more scalable than smaller ones —allowing the biggest to get even bigger, at the expense of the smallest, through the mechanism of preferential attachment we saw in Chapter 14. We have evidence that small islands have many more species per square meter than larger ones, and, of course, than continents. As we travel more on this planet, epidemics will be more acute—we will have a germ population dominated by a few numbers, and the successful killer will spread vastly more e ectively. Cultural life will be dominated by fewer persons: we have fewer books per reader in English than in Italian (this includes bad books). Companies will be more uneven in size. And fads will be more acute. So will runs on the banks, of course. Once again, I am not saying that we need to stop globalization and prevent travel. We just need to be aware of the side e ects, the trade-o s —and few people are. I see the risks of a very strange acute virus spreading throughout the planet. The Other Types of Redundancy The other categories of redundancy, more complicated and subtle, explain how elements of nature exploit positive Black Swans (and have an additional toolkit for surviving negative ones). I will discuss this very brie y here, as it is mostly behind my next work on the exploitation of Black Swans, through tinkering or the domestication of uncertainty. Functional redundancy, studied by biologists, is as follows: unlike organ redundancy—the availability of spare parts, where the same function can be performed by identical elements—very often the same function can be performed by two di erent structures. Sometimes the term degeneracy is used (by Gerald Edelman and Joseph Gally). There is another redundancy: when an organ can be employed to perform a certain function that is not its current central one. My friend Peter Bevelin links this idea to the “spandrels of San Marco,” after an essay by Steven Jay Gould. There, the necessary space between arches in the Venetian cathedral of San Marco has led to art that is now central to our aesthetic experience while visiting the place. In what is now called the spandrel effect, an auxiliary o shoot of a certain adaptation leads to a new function. I can also see the adaptation as having a dormant potential function that could wake up in the right environment. The best way to illustrate such redundancy is with an aspect of the life story of the colorful philosopher of science Paul Feyerabend. Feyerabend was permanently impotent from a war injury, yet he married four times, and was a womanizer to the point of leaving a trail of devastated boyfriends and husbands whose partners he snatched, and an equally long one of broken hearts, including those of many of his students (in his day, certain privileges were allowed to professors, particularly amboyant professors of philosophy). This was a particular achievement given his impotence. So there were other parts of the body that came to satisfy whatever it was that made women attached to him. Mother Nature initially created the mouth to eat, perhaps to breathe, perhaps for some other function linked to the existence of the tongue. Then new functions emerged that were most probably not part of the initial plan. Some people use the mouth and tongue to kiss, or to do something more involved to which Feyerabend allegedly had recourse. Over the past three years I became obsessed with the notion that, under epistemic limitations—some opacity concerning the future— progress (and survival) cannot take place without one of these types of redundancy. You don’t know today what may be needed tomorrow. This con icts very sharply with the notion of teleological design we all got from reading Aristotle, which has shaped medieval Arabic-western thought. For Aristotle, an object had a clear purpose set by its designer. An eye was there to see, a nose to smell. This is a rationalistic argument, another manifestation of what I call Platonicity. Yet anything that has a secondary use, and one you did not pay for, will present an extra opportunity should a heretofore unknown application emerge or a new environment appear. The organism with the largest number of secondary uses is the one that will gain the most from environmental randomness and epistemic opacity! Take aspirin. Forty years ago, aspirin’s raison d’être was its antipyretic (fever-reducing) e ect. Later it was used for its analgesic (pain-reducing) e ect. It has also been used for its anti-in ammatory properties. It is now used mostly as a blood thinner to avoid second (or rst) heart attacks. The same thing applies to almost all drugs—many are used for secondary and tertiary properties. I have just glanced at the desk in my business, nonliterary o ce (I separate the functional from the aesthetic). A laptop computer is propped up on a book, as I like to have some incline. The book is a French biography of the ery Lou Andreas Salomé (Nietzsche’s and Freud’s friend) that I can very safely say I will never read; it was selected for its optimal thickness for the task. This makes me re ect on the foolishness of thinking that books are there to be read and could be replaced by electronic les. Think of the spate of functional redundancies provided by books. You cannot impress your neighbors with electronic les. You cannot prop up your ego with electronic les. Objects seem to have invisible but signi cant auxiliary functions that we are not aware of consciously, but that allow them to thrive—and on occasion, as with decorator books, the auxiliary function becomes the principal one. So when you have a lot of functional redundancies, randomness helps on balance, but under one condition—that you can bene t from the randomness more than you can be hurt by it (an argument I call more technically convexity to uncertainty). This is certainly the case with many engineering applications, in which tools emerge from other tools. Also, I am currently absorbed in the study of the history of medicine, which struggled under this Aristotelian illusion of purpose, with Galen’s rationalistic methods that killed so many people while physicians thought they were curing them. Our psychology conspires: people like to go to a precise destination, rather than face some degree of uncertainty, even if bene cial. And research itself, the way it is designed and funded, seems to be teleological, aiming for precise results rather than looking for maximal exposures to forking avenues. I have given more complicated names to this idea, in addition to convexity, like optionality—since you have the option of taking the freebie from randomness—but this is still work in progress for me. The progress coming from the second type of randomness is what I call tinkering, or bricolage, the subject of my next book. Distinctions Without a Difference, Differences Without a Distinction  Another bene t of duplication. I have, throughout this book, focused on the absence of practical distinctions between the various notions of luck, uncertainty, randomness, incompleteness of information, and fortuitous occurrences using the simple criterion of predictability, which makes them all functionally equal. Probability can be degrees of belief, what one uses to make a bet, or something more physical associated with true randomness (called “ontic,” on which later). To paraphrase Gerd Gigerenzer, a “50 percent chance of rain tomorrow” in London might mean that it will rain half the day, while in Germany it will mean that half the experts think it will rain, and (I am adding), in Brooklyn, that the betting market at the bar is such that one would pay 50 cents to get a dollar if it rains. For scientists, the treatment is the same. We use the same equation to describe a probability distribution, regardless of whether the probability is a degree of belief or something designed by Zeus, who, we believe, calls the shots. For us probabilists (persons who work with probability in a scienti c context), the probability of an event, however it may be de ned, is, simply, a weight between 0 and 1, called the measure of the set concerned. Giving di erent names and symbols would be distracting and would prevent the transfer of analytical results from one domain to another. For a philosopher, it is altogether another matter. I had two lunches with the (analytical) philosopher Paul Boghossian, three years apart, one upon the completion of the rst edition of The Black Swan, the second upon the completion of this essay. During the rst conversation he said that, from a philosophical point of view, it is a mistake to con ate probability as a measure of someone’s rational degree of belief with probability as a property of events in the world. To me, this implied that we should not use the same mathematical language, say, the same symbol, p, and write down the same equation for the di erent types of probabilities. I spent three years wondering if he was right or wrong, whether this was a good redundancy. Then I had lunch with him again, though in a better (and even more friendly) restaurant. He alerted me to a phrase philosophers use: “distinction without a di erence.” Then I realized the following: that there are distinctions philosophers use that make sense philosophically, but do not seem to make sense in practice, but that may be necessary if you go deeper into the idea, and may make sense in practice under a change of environment. For consider the opposite: di erences without a distinction. They can be brutally misleading. People use the same term, measuring, for measuring a table using a ruler, and for measuring risk—when the second is a forecast, or something of the sort. And the word measuring conveys an illusion of knowledge that can be severely distorting: we will see that we are psychologically very vulnerable to terms used and how things are framed. So if we used measuring for the table, and forecasting for risk, we would have fewer turkeys blowing up from Black Swans. Mixing vocabulary has been very common in history. Let me take the idea of chance again. At some point in history the same Latin word, felix (from felicitas) was used to designate both someone lucky and someone happy. (The con ation of happiness and luck was explainable in an antique context: the goddess Felicitas represented both.) The English word luck comes from the Germanic Glück, happiness. An ancient would have seen the distinction between the two concepts as a waste, since all lucky people seem happy (not thinking that one could be happy without being lucky). But in a modern context we need to extricate luck from happiness—utility from probability—in order to perform any psychological analysis of decision making. (True, it is hard to disentangle the two from observing people making decisions in a probabilistic environment. People may be so fearful of bad things that may happen to them that they tend to overpay for insurance, which in turn may make us mistakenly think that they believe the adverse event has a high probability.) So we can see now that the absence of such precision made the language of the ancients quite confusing to us; but to the ancients, the distinction would have been a redundancy. A SOCIETY ROBUST TO ERROR I will only very brie y discuss the crisis of 2008 (which took place after the publication of the book, and which was a lot of things, but not a Black Swan, only the result of fragility in systems built upon ignorance —and denial—of the notion of Black Swan events. You know with near certainty that a plane own by an incompetent pilot will eventually crash). Why brie y? Primo, this is not an economics book, but a book on the incompleteness of knowledge and the e ects of high-impact uncertainty —it just so happens that economists are the most Black-Swan-blind species on the planet. Secundo, I prefer to talk about events before they take place, not after. But the general public confuses the prospective with the retrospective. The very same journalists, economists, and political experts who did not see the crisis coming provided abundant ex- post analyses about its inevitability. The other reason, the real one, is that the crisis of 2008 was not intellectually interesting enough to me— there is nothing in the developments that had not happened before, at a smaller scale (for example, banks losing in 1982 every penny they ever made). It was merely a nancial opportunity for me, as I will discuss further down. Really, I reread my book and saw nothing to add to the text, nothing we had not already encountered at some point in history, like the earlier debacles, nothing I had learned from. Alas, nothing. The corollary is obvious: since there is nothing new about the crisis of 2008, we will not learn from it and we will make the same mistake in the future. And the evidence is there at the time of writing: the IMF continues to issue forecasts (not realizing that previous ones did not work and that the poor suckers relying on them are—once again—going to get in trouble); economics professors still use the Gaussian; the current administration is populated with those who are bringing model error into industrial proportion, making us rely on models even more than ever before.* But the crisis provides an illustration for the need for robustness, worth discussing here. Over the past twenty- ve hundred years of recorded ideas, only fools and Platonists (or, worse, the species called central bankers) have believed in engineered utopias. We will see in the section on the Fourth Quadrant that the idea is not to correct mistakes and eliminate randomness from social and economic life through monetary policy, subsidies, and so on. The idea is simply to let human mistakes and miscalculations remain confined, and to prevent their spreading through the system, as Mother Nature does. Reducing volatility and ordinary randomness increases exposure to Black Swans—it creates an arti cial quiet. My dream is to have a true Epistemocracy—that is, a society robust to expert errors, forecasting errors, and hubris, one that can be resistant to the incompetence of politicians, regulators, economists, central bankers, bankers, policy wonks, and epidemiologists. We cannot make economists more scienti c; we cannot make humans more rational (whatever that means); we cannot make fads disappear. The solution is somewhat simple, once we isolate harmful errors, as we will see with the Fourth Quadrant. So I am currently torn between (a) my desire to spend time mulling my ideas in European cafés and in the tranquility of my study, or looking for someone who can have a conversation while walking slowly in a nice urban setting, and (b) the feeling of obligation to engage in activism to robustify society, by talking to uninteresting people and being immersed in the cacophony of the unaesthetic journalistic and media world, going to Washington to watch phonies in suits walking around the streets, having to defend my ideas while making an e ort to be smooth and hide my disrespect. This proved to be very disruptive to my intellectual life. But there are tricks. One useful trick, I discovered, is to avoid listening to the question of the interviewer, and answer with whatever I have been thinking about recently. Remarkably, neither the interviewers nor the public notices the absence of correlation between question and answer. I was once selected to be one of a group of a hundred who went to Washington to spend two days discussing how to solve the problems of the crisis that started in 2008. Almost all the biggies were included. After an hour of meeting, and during a speech by the prime minister of Australia, I walked out of the room because my pain became intolerable. My back would start hurting upon looking at the faces of these people. The center of the problem is that none of them knew the center of the problem. This makes me convinced that there is a unique solution for the world, to be designed along very simple lines of robustness to Black Swans—it will explode otherwise. So now I am disengaged. I am back in my library. I am not even experiencing any frustration, I don’t even care about how forecasters can blow up society, and I am not even capable of being annoyed by fools of randomness (to the contrary), perhaps thanks to another discovery linked to a particular application of the study of complex systems, Extremistan, and that science of long walks. * Lehman Brothers was a nancial institution with great-looking o ces that abruptly went bust during the crisis of 2008. * Empiricism is not about not having theories, beliefs, and causes and e ects: it is about avoiding being a sucker, having a decided and preset bias about where you want your error to be—where the default is. An empiricist facing series of facts or data defaults to suspension of belief (hence the link between empiricism and the older skeptical Pyrrhonian tradition), while others prefer to default to a  characterization or a theory. The entire idea is to avoid the confirmation bias (empiricists prefer to err on the side of the discon rmation/falsi cation bias, which they discovered more than fteen hundred years before Karl Popper). * Clearly the entire economics establishment, with about a million people on the planet involved in some aspect of economic analysis, planning, risk management, and forecasting, turned out to be turkeys owing to the simple mistake of not understanding the structure of Extremistan, complex systems, and hidden risks, while relying on idiotic risk measures and forecasts—all this in spite of past experience, as these things have never worked before. II WHY I DO ALL THIS WALKING, OR HOW SYSTEMS BECOME FRAGILE Relearn to walk—Temperance, he knew not—Will I catch Bob Rubin? Extremistan and Air France travel ANOTHER FEW BARBELLS Again, thanks to the exposure the book has received, I was alerted to a new aspect of robustness in complex systems … by the most unlikely of sources. The idea came from two tness authors and practitioners who integrated the notions of randomness and Extremistan (though of the Gray Swan variety) into our understanding of human diet and exercise. Curiously, the rst person, Art De Vany, is the same one who studied Extremistan in the movies (in Chapter 3). The second, Doug McGu , is a physician. And both can talk about tness, particularly Art, who, at seventy-two, looks like what a Greek god would like to look like at forty- two. Both were referring to the ideas of The Black Swan in their works and connecting to it; and I had no clue. I then discovered to my great shame the following. I had spent my life thinking about randomness; I had written three books on dealing with randomness (one technical); I was prancing about as the expert in the subject of randomness from mathematics to psychology. And I had missed something central: living organisms (whether the human body or the economy) need variability and randomness. What’s more, they need the Extremistan type of variability, certain extreme stressors. Otherwise they become fragile. That, I completely missed.* Organisms need, to use the metaphor of Marcus Aurelius, to turn obstacles into fuel—just as re does. Brainwashed by the cultural environment and by my education, I was under the illusion that steady exercise and steady nutrition were a good thing for one’s health. I did not realize that I was falling into evil rationalistic arguments, the Platonic projection of wishes into the world. Worse, I had been brainwashed though I had all the facts in my head. From predator-prey models (the so-called Lotka-Volterra type of population dynamics), I knew that populations will experience Extremistan-style variability, hence predators will necessarily go through periods of feast and famine. That’s us, humans—we had to have been designed to experience extreme hunger and extreme abundance. So our food intake had to have been fractal. Not a single one of those promoting the “three meals a day,” “eat in moderation” idea has tested it empirically to see whether it is healthier than intermittent fasts followed by large feasts.† But Near Eastern religions (Judaism, Islam, and Orthodox Christianity) knew it, of course—just as they knew the need for debt avoidance—and so they had fast days. I also knew that the size of stones and trees was, up to a point, fractal (I even wrote about that in Chapter 16). Our ancestors mostly had to face very light stones to lift, mild stressors; once or twice a decade, they encountered the need to lift a huge stone. So where on earth does this idea of “steady” exercise come from? Nobody in the Pleistocene jogged for forty-two minutes three days a week, lifted weights every Tuesday and Friday with a bullying (but otherwise nice) personal trainer, and played tennis at eleven on Saturday mornings. Not hunters. We swung between extremes: we sprinted when chased or when chasing (once in a while in an extremely exerting way), and walked about aimlessly the rest of the time. Marathon running is a modern abomination (particularly when done without emotional stimuli). This is another application of the barbell strategy: plenty of idleness, some high intensity. The data shows that long, very long walks, combined with high-intensity exercise outperform just running. I am not talking about “brisk walks” of the type you read about in the Health section of The New York Times. I mean walking without making any e ort. What’s more, consider the negative correlation between caloric expenditure and intake: we hunted in response to hunger; we did not eat breakfast to hunt, hunting accentuated our energy de cits. If you deprive an organism of stressors, you a ect its epigenetics and gene expression—some genes are up-regulated (or down-regulated) by contact with the environment. A person who does not face stressors will not survive should he encounter them. Just consider what happens to someone’s strength after he spends a year in bed, or someone who grows up in a sterile environment and then one day takes the Tokyo subway, where riders are squeezed like sardines. Why am I using evolutionary arguments? Not because of the optimality of evolution, but entirely for epistemological reasons, how we should deal with a complex system with opaque causal links and complicated interactions. Mother Nature is not perfect, but has so far proven smarter than humans, certainly much smarter than biologists. So my approach is to combine evidence-based research (stripped of biological theory), with an a priori that Mother Nature has more authority than anyone. After my “Aha!” ash, I embarked on an Extremistan barbell lifestyle under the guidance of Art De Vany: long, very long, slow, meditative (or conversational) walks in a stimulating urban setting, but with occasional (and random) very short sprints, during which I made myself angry imagining I was chasing the bankster Robert Rubin with a big stick, trying to catch him and bring him to human justice. I went to weight- lifting facilities in a random way for a completely stochastic workout— typically in hotels, when I was on the road. Like Gray Swan events, these were very, very rare, but highly consequential weight-lifting periods, after a day of semistarvation, leaving me completely exhausted. Then I would be totally sedentary for weeks and hang around cafés. Even the duration of the workouts remained random—but most often very short, less than fteen minutes. I followed the path that minimized boredom, and remained very polite with gym employees who described my workouts as “erratic.” I put myself through thermal variability as well, exposed, on occasion, to extreme cold without a coat. Thanks to transcontinental travel and jet lag, I underwent periods of sleep deprivation followed by excessive rest. When I went to places with good restaurants, for instance Italy, I ate in quantities that would have impressed Fat Tony himself, then skipped meals for a while without su ering. Then, after two and a half years of this apparently “unhealthy” regimen, I saw signi cant changes in my own physique on every possible criterion—the absence of unnecessary adipose tissue, the blood pressure of a twenty-one-year-old, and so on. I also have a clearer, much more acute mind. So the main idea is to trade duration for intensity—for a hedonic gain. Recall the reasoning I presented in Chapter 6 about hedonic e ects. Just as people prefer large but sudden losses to small but regular ones, just as one becomes dulled to pain beyond a certain threshold, so unpleasant experiences, like working out without external stimuli (say in a gym), or spending time in New Jersey, need to be as concentrated and as intense as possible. Another way to view the connection to the Black Swan idea is as follows. Classical thermodynamics produces Gaussian variations, while informational variations are from Extremistan. Let me explain. If you consider your diet and exercise as simple energy de cits and excesses, with a straight calorie-in, calorie-burned equation, you will fall into the trap of misspecifying the system into simple causal and mechanical links. Your food intake becomes the equivalent of lling up the tank of your new BMW. If, on the other hand, you look at food and exercise as activating metabolic signals, with potential metabolic cascades and nonlinearities from network e ects, and with recursive links, then welcome to complexity, hence Extremistan. Both food and workouts provide your body with information about stressors in the environment. As I have been saying throughout, informational randomness is from Extremistan. Medicine fell into the trap of using simple thermodynamics, with the same physics envy, and the same mentality, and the same tools as economists did when they looked at the economy as a web of simple links.* And both humans and societies are complex systems.  But these lifestyle ideas do not come from mere self-experimentation or some quack theory. All the results were completely expected from the evidence-based, peer-reviewed research that is available. Hunger (or episodic energy de cit) strengthens the body and the immune system and helps rejuvenate brain cells, weaken cancer cells, and prevent diabetes. It was just that the current thinking—in a way similar to economics—was out of sync with the empirical research. I was able to re- create 90 percent of the bene ts of the hunter-gatherer lifestyle with minimal e ort, without compromising a modern lifestyle, in the aesthetics of an urban setting (I get extremely bored in nature and prefer walking around the Jewish quarter of Venice to spending time in Bora Bora).* By the same argument we can lower 90 percent of Black Swan risks in economic life … by just eliminating speculative debt. The only thing currently missing from my life is panic, from, say, nding a gigantic snake in my library, or watching the economist Myron Scholes, armed to the teeth, walk into my bedroom in the middle of the night. I lack what the biologist Robert Sapolsky calls the bene cial aspect of acute stress, compared to the deleterious one of dull stress— another barbell, for no stress plus a little bit of extreme stress is vastly better than a little bit of stress (like mortgage worries) all the time. Some have argued that my health bene ts come from long walks, about ten to fteen hours a week (though nobody has explained to me why they would count as workouts since I walk slowly), while others claim that they come from my few minutes of sprinting; I’ve had the same problem explaining the inseparability of the two extremes as I did explaining economic deviations. If you have acute stressors, then periods of rest, how can you separate the stressors from the recovery? Extremistan is characterized by both polar extremes, a high share of low impact, a low share of high impact. Consider that the presence of concentration, here energy expenditure, necessitates that a high number of observations do not contribute to anything except to the dilution. Just as the condition that makes market volatility explained by bursts (say one day in ve years represents half the variance) requires that most other days remain exceedingly quiet. If one in a million authors makes half the sales, you need a lot of authors to sell no books. This is the turkey trap I will discuss later: philistines (and Federal Reserve chairpersons) mistake periods of low volatility (caused by stabilization policies) for periods of low risk, not for switches into Extremistan. Welcome to Gray Extremistan. Do not tamper too much with the complex system Mother Nature gave you: your body. Beware Manufactured Stability By a variant of the same reasoning we can see how the fear of volatility I mentioned earlier, leading to interference with nature so as to impose “regularity,” makes us more fragile across so many domains. Preventing small forest res sets the stage for more extreme ones; giving out antibiotics when it is not very necessary makes us more vulnerable to severe epidemics—and perhaps to that big one, the grand infection that will be resistant to known antibiotics and will travel on Air France. Which brings me to another organism: economic life. Our aversion to variability and desire for order, and our acting on those feelings, have helped precipitate severe crises. Making something arti cially bigger (instead of letting it die early if it cannot survive stressors) makes it more and more vulnerable to a very severe collapse—as I showed with the Black Swan vulnerability associated with an increase in size. Another thing we saw in the 2008 debacle: the U.S. government (or, rather, the Federal Reserve) had been trying for years to iron out the business cycle, leaving us exposed to a severe disintegration. This is my argument against “stabilization” policies and the manufacturing of a nonvolatile environment. More on that, later. Next, I will discuss a few things about the Black Swan idea that do not appear to easily penetrate consciousness. Predictably. * There is a di erence between stressors and toxic exposure that weakens organisms, like the radiation I discussed in Chapter 8 with the story of the rats. † There is a sociology-of-science dimension to the problem. The science writer Gary Taubes has convinced me that the majority of dietary recommendations (about lowering fats in diets) stand against the evidence. I can understand how one can harbor beliefs about natural things without justifying them empirically; I fail to understand beliefs that contravene both nature and scienti c evidence. * The nancial equations used by the villains for the “random walk” is based on heat di usion. * The argument often heard about primitive people living on average less than thirty years ignores the distribution around that average; life expectancy needs to be analyzed conditionally. Plenty died early, from injuries; many lived very long—and healthy—lives. This is exactly the elementary “fooled by randomness” mistake, relying on the notion of “average” in the presence of variance, that makes people underestimate risks in the stock market. III MARGARITAS ANTE PORCOS* How to not sell books in airports—Mineral water in the desert— How to denigrate other people’s ideas and succeed at it Let me start again. The Black Swan is about consequential epistemic limitations, both psychological (hubris and biases) and philosophical (mathematical) limits to knowledge, both individual and collective. I say “consequential” because the focus is on impactful rare events, as our knowledge, both empirical and theoretical, breaks down with those— the more remote the events, the less we can forecast them, yet they are the most impactful. So The Black Swan is about human error in some domains, swelled by a long tradition of scientism and a plethora of information that fuels con dence without increasing knowledge. It covers the expert problem—harm caused by reliance on scienti c- looking charlatans, with or without equations, or regular noncharlatanic scientists with a bit more con dence about their methods than the evidence warrants. The focus is in not being the turkey in places where it matters, though there is nothing wrong in being a fool where that has no e ect. MAIN ERRORS IN UNDERSTANDING THE MESSAGE I will brie y state some of the di culties in understanding the message and the ideas of this book, typically perpetrated by professionals, though, surprisingly, less by the casual reader, the amateur, my friend. Here is a list. 1) Mistaking the Black Swan (capitalized) for the logical problem. (Mistake made by U.K. intellectuals—intellectuals in other countries do not know enough analytical philosophy to make that mistake.)* 2) Saying the maps we had were better than having no maps. (People who do not have experience in cartography, risk “experts,” or worse, employees of the Federal Reserve Bank of the United States.) This is the strangest of errors. I know few people who would board a plane heading for La Guardia airport in New York City with a pilot who was using a map of Atlanta’s airport “because there is nothing else.” People with a functioning brain would rather drive, take the train, or stay home. Yet once they get involved in economics, they all prefer professionally to use in Extremistan the measures made for Mediocristan, on the ground that “we have nothing else.” The idea, well accepted by grandmothers, that one should pick a destination for which one has a good map, not travel and then nd “the best” map, is foreign to PhDs in social science. 3) Thinking that a Black Swan should be a Black Swan to all observers. (Mistake made by people who have not spent a lot of time in Brooklyn and lack the street smarts and social intelligence to realize that some people are suckers.) 4) Not understanding the value of negative advice (“Don’t do”) and writing to me to ask me for something “constructive” or a “next step.” (Mistake usually made by chairmen of large companies and those who would like someday to become such chairmen.)† 5) Not understanding that doing nothing can be much more preferable to doing something potentially harmful. (Mistake made by most people who are not grandmothers.) 6) Applying to my ideas labels (skepticism, fat tails, power laws) o a supermarket shelf and equating those ideas with inadequate research traditions (or, worse, claiming it was dealt with by “modal logic,” “fuzzy logic,” or whatever the person has vaguely heard of). (Mistake made by those with graduate degrees from both coasts.) 7) Thinking that The Black Swan is about the errors of using the bell curve, which supposedly everyone knew about, and that the errors can be remedied by substituting a number from the Mandelbrotian in place of another. (Mistake made by the pseudoscienti c brand of tenured nance professors, like, say, Kenneth French.) 8) Claiming that “we knew all this” and “there is nothing new” in my idea during 2008, then, of course, going bust during the crisis. (Mistake made by the same type of tenured nance professors as before, but these went to work on Wall Street, and are now broke.) 9) Mistaking my idea for Popper’s notion of falsi cation—or taking any of my ideas and tting them in a prepackaged category that sounds familiar. (Mistakes mostly made by sociologists, Columbia University political science professors, and others trying to be multidisciplinary intellectuals and learning buzzwords from Wikipedia.) 10) Treating probabilities (of future states) as measurable, like the temperature or your sister’s weight. (People who did a PhD at MIT or something like that, then went to work somewhere, and now spend time reading blogs.) 11) Spending energy on the di erence between ontic and epistemic randomness—true randomness, and randomness that arises from incomplete information—instead of focusing on the more consequential di erence between Mediocristan and Extremistan. (People with no hobby, no personal problems, no love, and too much free time.) 12) Thinking I am saying “Do not forecast” or “Do not use models,” rather than “Do not use sterile forecasts with huge error” and “Do not use models in the Fourth Quadrant.” (Mistake made by most people who forecast for a living.) 13) Mistaking what I say for “S**t happens” rather than “this is where s**t happens.” (Many former bonus earners.)* Indeed, the intelligent, curious, and open-minded amateur is my friend. A pleasant surprise for me was to discover that the sophisticated amateur who uses books for his own edi cation, and the journalist (unless, of course, he was employed by The New York Times), could understand my idea much better than professionals. Professional readers, less genuine, either read too quickly or have an agenda. When reading for “work” or for the purpose of establishing their status (say, to write a review), rather than to satisfy a genuine curiosity, readers who have too much baggage (or perhaps not enough) tend to read rapidly and e ciently, scanning jargon terms and rapidly making associations with prepackaged ideas. This resulted early on in the squeezing of the ideas expressed in The Black Swan into a commoditized well-known framework, as if my positions could be squeezed into standard skepticism, empiricism, essentialism, pragmatism, Popperian falsi cationism, Knightian uncertainty, behavioral economics, power laws, chaos theory, etc. But the amateurs saved my ideas. Thank you, reader. As I wrote, missing a train is only painful if you are running after it. I was not looking to have a bestseller (I thought I had already had one with my previous book, and just wanted to produce a real thing), so I had to deal with a spate of harrying side e ects. I watched as the book was initially treated, owing to its bestseller status, like the non ction “idea books,” journalistic through and through, castrated by a thorough and “competent” copy editor, and sold in airports to “thinking” businessmen. Giving these enlightened Bildungsphilisters, commonly called idea-book readers, a real book is like giving vintage Bordeaux to drinkers of Diet Coke and listening to their comments about it. Their typical complaint is that they want diet-book-style “actionable steps” or “better forecasting tools,” satisfying the pro le of the eventual Black Swan victim. We will see further that, in an ailment similar to con rmation bias, charlatans provide the much demanded positive advice (what to do), as people do not value negative advice (what not to do). Now, “how not to go bust” does not appear to be valid advice, yet, given that over time only a minority of companies do not go bust, avoiding death is the best possible—and most robust—advice. (It is particularly good advice after your competitors get in trouble and you can go on legal pillages of their businesses.)* Also, many readers (say, those who work in forecasting or banking) do not often understand that the “actionable step” for them is to simply quit their profession and do something more ethical. In addition to playing into our mental biases, and telling people what they want to hear, these “idea books” often have an abhorrent de nitive and investigative tone to their messages, like the reports of management consultants trying to make you believe that they told you more than they actually did. I came up with a simple compression test using a version of what is called Kolmogorov complexity, a measure of how much a message can be reduced without losing its integrity: try to reduce a book to the shortest length possible without losing any of its intended message or aesthetic e ects. My friend the novelist Rolf Dobelli (he does not seem to like to walk slowly and drags me on hikes in the Alps), an owner of a rm that abstracts books and sells the summaries to busy businesspeople, convinced me that his rm has a lofty mission, as almost all business books can be reduced to a few pages without any loss of their message and essence; novels and philosophical treatments cannot be compressed.  So a philosophical essay is a beginning, not an end. To me the very same meditation continues from book to book, compared to the work of a non ction writer, who will, say, move to another distinct and journalistically con ned topic. I want my contribution to be a new way of viewing knowledge, the very beginning of a long investigation, the start of something real. Indeed, I am glad at the time of writing, a few years into the life of the book, to see the idea spread among thoughtful readers, inspiring like-minded scholars to go beyond it and seeding research in epistemology, engineering, education, defense, operations research, statistics, political theory, sociology, climate studies, medicine, law, aesthetics, and insurance (though not so much in the area in which The Black Swan found Black Swan–style near instant vindication, economics). I was lucky that it only took a couple of years (and a severe nancial crisis) for the Republic of Letters to realize that The Black Swan was a philosophical tale. How to Expunge One’s Crimes My ideas went through two distinctive stages after the release of the book. In the rst, as the book hit the bestseller list in almost every single country where it was published, many social scientists and nance practitioners fell into the trap of refuting me with the sole argument that I was selling too many books and that my book was accessible to readers; hence it could not re ect original and systematic thought, it was just a “popularization,” not worth reading let alone commenting upon. The rst change of regime came with the release of my more di cult mathematical, empirical, and scholarly work in a dozen articles in a variety of journals in an attempt to expiate my crime of having sold too many books.* Then, silence. Still no refutation at the time of this writing; indeed, my paper on the Fourth Quadrant in the International Journal of Forecasting (which I simplify in this essay) produced incontrovertible evidence that most (perhaps all) “rigorous” papers in economics using fancy statistics are just hot air, partaking of a collective scam (with di usion of responsibility), unusable for any form of risk management. Clearly, so far, in spite of a few smear campaigns, or, rather, attempts at a smear campaign (typically conducted by former Wall Street persons or Diet Coke drinkers), nobody has managed to present a formal (or even informal) refutation of the idea—neither of the logical-mathematical arguments nor of the empirical arguments. But meanwhile I gured out something valuable in the packaging of the Black Swan idea. Just as in Fooled by Randomness I had argued (initially from personal experience) that a “70 percent chance of survival” is vastly di erent from a “30 percent chance of death,” I found out that telling researchers “This is where your methods work very well” is vastly better than telling them “This is what you guys don’t know.” So when I presented to what was until then the most hostile crowd in the world, members of the American Statistical Association, a map of the four quadrants, and told them: your knowledge works beautifully in these three quadrants, but beware of the fourth one, as this is where the Black Swans breed, I received instant approval, support, o ers of permanent friendship, refreshments (Diet Coke), invitations to come present at their sessions, even hugs. Indeed, that is how a series of research papers started using my work on where the Fourth Quadrant is located, etc. They tried to convince me that statisticians were not responsible for these aberrations, which come from people in the social sciences who apply statistical methods without understanding them (something I veri ed later, in formal experiments, to my great horror, as we will see further down). The second change of regime came with the crisis of 2008. I kept getting invited to debates, but I stopped obliging, as it became hard for me to hear complicated arguments and restrain a smile, sometimes a smirk. Why a smile? Well, the vindication. Not the intellectual vindication of winning an argument, no: academia, I discovered, does not change its mind voluntarily, except perhaps in some real sciences such as physics. It was a di erent feeling: it is hard to focus on a conversation, especially when it is mathematical, when you have just personally earned several hundreds of times the annual salary of the researcher trying to tell you that you are “wrong,” by betting against his representation of the world. A Desert Crossing For I had undergone a di cult psychological moment, after the publication of The Black Swan, what the French call traversée du désert, when you go through the demoralizing desiccation and disorientation of crossing a desert in search of an unknown destination, or a more or less promised land. I had a rough time, shouting “Fire! Fire! Fire!” about the hidden risks in the system, and hearing people ignore the content and instead just criticize the presentation, as if they were saying “your diction in shouting ‘Fire!’ is bad.” For example, the curator of a conference known as TED (a monstrosity that turns scientists and thinkers into low-level entertainers, like circus performers) complained that my presentation style did not conform to his taste in slickness and kept my lecture on Black Swans and fragility o the Web. Of course, he subsequently tried to claim credit for my warnings voiced before the crisis of 2008.* Most of the arguments o ered were that “times are di erent,” invoking “the great moderation” by one Ben Bernanke (chairman of the Federal Reserve at the time of writing) who fell for the turkey-before- Thanksgiving trap of not understanding that moving into Extremistan comes through a drop in daily volatility. Also when I was railing against models, social scientists kept repeating that they knew it and that there is a saying, “all models are wrong, but some are useful”—not understanding that the real problem is that “some are harmful.” Very harmful. As Fat Tony would say, “Tawk is cheap.” So Mark Spitznagel and I restarted the business of “robustifying” clients against the Black Swan (helping people get closer to the barbell of Chapter 11). We were convinced that the banking system was going to collapse under the weight of hidden risks—that such an event would be a white swan. It was moving from gray to white in color as the system was accumulating risks. The longer we had to wait for it, the more severe it would be. The collapse took place about a year and a half after the publication of the book. We had been expecting it and betting against the banking system for a long time (and protecting clients by making them Black Swan robust), but the reception of the Black Swan—and the absence of refutation that was not ad hominem— made us vastly more worried about the need for protection than ever before. Like Antaeus, who lost strength when separated from contact with the earth, I needed connection to the real world, something real and applied, instead of focusing on winning arguments and trying to convince people of my point (people are almost always only convinced of what they already know). Sticking my neck out in the real world, lining up my life with my ideas by getting involved in trading, had a therapeutic e ect, even apart from the vindication; just having a trade on the books gave me strength to not care. A few months before the onset of the crisis of 2008, I was attacked at a party by a Harvard psychologist who, in spite of his innocence of probability theory, seemed to have a vendetta against me and my book. (The most vicious and bitter detractors tend to be those with a competing product on the bookstore shelves.) Having a trade on allowed me to laugh at him—or, what is even worse, made me feel some complicity with him, thanks to his anger. I wonder what would have happened to the psychological state of another author, identical to me in all respects except that he had no involvement with trading and risk taking. When you walk the walk, whether successful or not, you feel more indi erent and robust to people’s opinion, freer, more real. Finally, I got something out of my debates: the evidence that Black Swan events are largely caused by people using measures way over their heads, instilling false con dence based on bogus results. In addition to my befuddlement concerning why people use measures from Mediocristan outside those measures’ applicability, and believe in them, I had the inkling of a much larger problem: that almost none of the people who worked professionally with probabilistic measures knew what they were talking about, which was con rmed as I got into debates and panels with many hotshots, at least four with “Nobels” in economics. Really. And this problem was measurable, very easily testable. You could have nance “quants,” academics, and students use and write papers and papers using the notion of “standard deviation,” yet not understand intuitively what it meant, so you could trip them up by asking them elementary questions about the nonmathematical, real conceptual meaning of their numbers. And trip them up we did. Dan Goldstein and I ran experiments on professionals using probabilistic tools, and were shocked to see that up to 97 percent of them failed elementary questions.* Emre Soyer and Robin Hogarth subsequently took the point and tested it in the use of an abhorrent eld called econometrics (a eld that, if any scienti c scrutiny was applied to it, would not exist)—again, most researchers don’t understand the tools they are using. Now that the book’s reception is o my chest, let us move into more analytical territory. * In Latin: “pearls before swine.” * Most intellectuals keep attributing the black swan expression to Popper or Mill, sometimes Hume, in spite of the quote by Juvenal. The Latin expression niger cygnus might even be more ancient, possibly of Etruscan origin. † One frequent confusion: people believe that I am suggesting that agents should bet on Black Swans taking place, when I am saying that they should avoid blowing up should a Black Swan take place. As we will see in section IV, I am advocating omission, not commission. The di erence is enormous, and I have been completely swamped by people wondering if one can “bleed to death” making bets on the occurrence of Black Swans (like Nero, Giovanni Drogo, or the poor scientist with a rich brother-in-law). These people have made their choice for existential reasons, not necessarily economic ones, although the economics of such a strategy makes sense for a collective. * If most of the people mixed up about the message appear to be involved in economics and social science, while a much smaller share of readers come from those segments, it is because other members of society without such baggage get the book’s message almost immediately. * For instance, one anecdote that helps explain the crisis of 2008. One Matthew Barrett, former Chairman of Barclays Bank and Bank of Montreal (both of which underwent blowups from exposures to Extremistan using risk management methods for Mediocristan) complained, after all the events of 2008 and 2009, that The Black Swan did not tell him “what should I do about that?” and he “can’t run a business” worrying about Black Swan risks. The person has never heard of the notion of fragility and robustness to extreme deviations—which illustrates my idea that evolution does not work by  teaching, but destroying. * So far, about fourteen scholarly (but very, very boring) articles. (They are boring both to read and to write!) The number keeps growing, though, and they are being published at a pace of three a year. Taleb (2007), Taleb and Pilpel (2007), Goldstein and Taleb (2007), Taleb (2008), Taleb (2009), Taleb, Goldstein and Spitznagel (2009), Taleb and Pilpel (2009), Mandelbrot and Taleb (2010), Makridakis and Taleb (2010), Taleb (2010), Taleb and Tapiero (2010a), Taleb and Tapiero (2010b), Taleb and Douady (2010), and Goldstein and Taleb (2010). * Although his is a bit extreme, this phoniness is not uncommon at all. Many intellectually honest people I had warned, and who had read my book, later blamed me for not telling them about the crisis—they just could not remember it. It is hard for a newly enlightened pig to recall that he has seen a pearl in the past but did not know what it was. * Dan Goldstein and I have been collaborating and running experiments about human intuitions with respect to di erent classes of randomness. He does not walk slowly. IV ASPERGER AND THE ONTOLOGICAL BLACK SWAN Are nerds more blind to swans? Social skills in Extremistan—On the immortality of Dr. Greenspan If The Black Swan is about epistemic limitations, then, from this de nition, we can see that it is not about some objectively de ned phenomenon, like rain or a car crash—it is simply something that was not expected by a particular observer. So I was wondering why so many otherwise intelligent people have casually questioned whether certain events, say the Great War, or the September 11, 2001, attack on the World Trade Center, were Black Swans, on the grounds that some predicted them. Of course the September 11 attack was a Black Swan to those victims who died in it; otherwise, they would not have exposed themselves to the risk. But it was certainly not a Black Swan to the terrorists who planned and carried out the attack. I have spent considerable time away from the weight- lifting room repeating that a Black Swan for the turkey is not a Black Swan for the butcher. The same applies to the crisis of 2008, certainly a Black Swan to almost all economists, journalists, and nanciers on this planet (including, predictably, Robert Merton and Myron Scholes, the turkeys of Chapter 17), but certainly not to this author. (Incidentally, as an illustration of another common mistake, almost none of those—very few—who seemed to have “predicted” the event predicted its depth. We will see that, because of the atypicality of events in Extremistan, the Black Swan is not just about the occurrence of some event but also about its depth and consequences.) ASPERGER PROBABILITY This consideration of an objective Black Swan, one that would be the same to all observers, aside from missing the point completely, seems dangerously related to the problem of underdevelopment of a human faculty called “theory of mind” or “folk psychology.” Some people, otherwise intelligent, have a de ciency of that human ability to impute to others knowledge that is di erent from their own. These, according to researchers, are the people you commonly see involved in engineering or populating physics departments. We saw one of them, Dr. John, in Chapter 9. You can test a child for underdevelopment of the theory of mind using a variant of the “false-belief task.” Two children are introduced. One child puts a toy under the bed and leaves the room. During his absence, the second child—the subject—removes it and hides it in a box. You ask the subject: Where, upon returning to the room, will the other child look for the toy? Those under, say, the age of four (when the theory of mind starts developing), choose the box, while older children correctly say that the other child will look under the bed. At around that age, children start realizing that another person can be deprived of some of the information they have, and can hold beliefs that are di erent from their own. Now, this test helps detect mild forms of autism: as high as one’s intelligence may be, it can be di cult for many to put themselves in other people’s shoes and imagine the world on the basis of other people’s information. There is actually a name for the condition of a person who can be functional but su ers from a mild form of autism: Asperger syndrome. The psychologist Simon Baron-Cohen has produced much research distinguishing between polar extremes in people’s temperament with respect to two faculties: ability to systematize, and ability to empathize and understand others. According to his research, purely systematizing persons su er from a lack of theory of mind; they are drawn to engineering and similar occupations (and when they fail, to, say, mathematical economics); empathizing minds are drawn to more social (or literary) professions. Fat Tony, of course, would fall in the more social category. Males are overrepresented in the systematizing category; females dominate the other extreme. Note the unsurprising, but very consequential fact that people with Asperger syndrome are highly averse to ambiguity. Research shows that academics are overrepresented in the systematizing, Black-Swan-blind category; these are the people I called “Locke’s madmen” in Chapter 17. I haven’t seen any formal direct test of Black Swan foolishness and the systematizing mind, except for a calculation George Martin and I made in 1998, in which we found evidence that all the nance and quantitative economics professors from major universities whom we tracked and who got involved in hedge fund trading ended up making bets against Black Swans, exposing themselves to blowups. This preference was nonrandom, since between one third and one half of the nonprofessors had that investment style at the time. The best known such academics were, once again, the “Nobel”-crowned Myron Scholes and Robert C. Merton, whom God created so that I could illustrate my point about Black Swan blindness.* They all experienced problems during the crisis, discussed in that chapter, that brought down their rm Long Term Capital Management. Note that the very same people who make a fuss about discussions of Asperger as a condition not compatible with risk-bearing and the analysis of nonexplicit o -model risks, with its corresponding dangers to society, would be opposed to using a person with highly impaired eyesight as the driver of a school bus. All I am saying is that just as I read Milton, Homer, Taha Husain, and Borges (who were blind) but would prefer not to have them drive me on the Nice–Marseilles motorway, I elect to use tools made by engineers but prefer to have society’s risky decisions managed by someone who is not a ected with risk-blindness. FUTURE BLINDNESS REDUX Now recall the condition, described in Chapter 12, of not properly transferring between past and future, an autism-like condition in which people do not see second-order relations—the subject does not use the relation between the past’s past and the past’s future to project the connection between today’s past and today’s future. Well, a gentleman called Alan Greenspan, the former chairman of the U.S. Federal Reserve Bank, went to Congress to explain that the banking crisis, which he and his successor Bernanke helped cause, could not have been foreseen because it “had never happened before.” Not a single member of congress was intelligent enough to shout, “Alan Greenspan, you have never died before, not in eighty years, not even once; does that make you immortal?” The abject Robert Rubin, the bankster I was chasing in Section II, a former secretary of the Treasury, used the same argument— but the fellow had written a long book on uncertainty (with, ironically, my publisher and the same sta used for The Black Swan).* I discovered (but by then I was not even surprised) that no researcher has tested whether large deviations in economics can be predicted from past large deviations—whether large deviations have predecessors, that is. This is one of the elementary tests missing in the eld, as elementary as checking whether a patient is breathing or whether a lightbulb is screwed in, but characteristically nobody seems to have tried to do it. It does not take a lot of introspection to gure out that big events don’t have big parents: the Great War did not have a predecessor; the crash of 1987, in which the market went down close to 23 percent in a single day, could not have been guessed from its worst predecessor, a one-day loss of around 10 percent—and this applies to almost all such events, of course. My results were that regular events can predict regular events, but that extreme events, perhaps because they are more acute when people are unprepared, are almost never predicted from narrow reliance on the past. The fact that this notion is not obvious to people is shocking to me. It is particularly shocking that people do what are called “stress tests” by taking the worst possible past deviation as an anchor event to project the worst possible future deviation, not thinking that they would have failed to account for that past deviation had they used the same method on the day before the occurrence of that past anchor event.* These people have PhDs in economics; some are professors—one of them is the chairman of the Federal Reserve (at the time of writing). Do advanced degrees make people blind to these elementary notions? Indeed, the Latin poet Lucretius, who did not attend business school, wrote that we consider the biggest objeect of any kind that we have seen in our lives as the largest possible item: et omnia de genere omni / Maxima quae vivit quisque, haec ingentia fingit. PROBABILITY HAS TO BE SUBJECTIVE† This raises a problem that is worth probing in some depth. The fact that many researchers do not realize immediately that the Black Swan corresponds mainly to an incomplete map of the world, or that some researchers have to stress this subjective quality (Jochen Runde, for instance, wrote an insightful essay on the Black Swan idea, but one in which he felt he needed to go out of his way to stress its subjective aspect), takes us to the historical problem in the very de nition of probability. Historically, there have been many approaches to the philosophy of probability. The notion that two people can have two di erent views of the world, then express them as di erent probabilities remained foreign to the research. So it took a while for scienti c researchers to accept the non-Asperger notion that di erent people can, while being rational, assign di erent probabilities to di erent future states of the world. This is called “subjective probability.” Subjective probability was formulated by Frank Plumpton Ramsey in 1925 and Bruno de Finetti in 1937. The take on probability by these two intellectual giants is that it can be represented as a quanti cation of the degree of belief (you set a number between 0 and 1 that corresponds to the strength of your belief in the occurrence of a given event), subjective to the observer, who expresses it as rationally as he wishes under some constraints. These constraints of consistency in decision making are obvious: you cannot bet there is a 60 percent chance of snow tomorrow and a 50 percent chance that there will be no snow. The agent needs to avoid violating something called the Dutch book constraint: that is, you cannot express your probabilities inconsistently by engaging in a series of bets that lock in a certain loss, for example, by acting as if the probabilities of separable contingencies can add up to more than 100 percent. There is another di erence here, between “true” randomness (say the equivalent of God throwing a die) and randomness that results from what I call epistemic limitations, that is, lack of knowledge. What is called ontological (or ontic) uncertainty, as opposed to epistemic, is the type of randomness where the future is not implied by the past (or not even implied by anything). It is created every minute by the complexity of our actions, which makes the uncertainty much more fundamental than the epistemic one coming from imperfections in knowledge. It means that there is no such thing as a long run for such systems, called “nonergodic” systems—as opposed to the “ergodic” ones. In an ergodic system, the probabilities of what may happen in the long run are not impacted by events that may take place, say, next year. Someone playing roulette in the casino can become very rich, but, if he keeps playing, given that the house has an advantage, he will eventually go bust. Someone rather unskilled will eventually fail. So ergodic systems are invariant, on average, to paths, taken in the intermediate term—what researchers call absence of path dependency. A nonergodic system has no real long-term properties—it is prone to path dependency. I believe that the distinction between epistemic and ontic uncertainty is important philosophically, but entirely irrelevant in the real world. Epistemic uncertainty is so hard to disentangle from the more fundamental one. This is the case of a “distinction without a di erence” that (unlike the ones mentioned earlier) can mislead because it distracts from the real problems: practitioners make a big deal out of it instead of focusing on epistemic constraints. Recall that skepticism is costly, and should be available when needed. There is no such thing as a “long run” in practice; what matters is what happens before the long run. The problem of using the notion of “long run,” or what mathematicians call the asymptotic property (what happens when you extend something to in nity), is that it usually makes us blind to what happens before the long run, which I will discuss later as preasymptotics. Di erent functions have di erent preasymptotics, according to speed of convergence to that asymptote. But, unfortunately, as I keep repeating to students, life takes place in the preasymptote, not in some Platonic long run, and some properties that hold in the preasymptote (or the short run) can be markedly divergent from those that take place in the long run. So theory, even if it works, meets a short-term reality that has more texture. Few understand that there is generally no such thing as a reachable long run except as a mathematical construct to solve equations; to assume a long run in a complex system, you need to also assume that nothing new will emerge. In addition, you may have a perfect model of the world, stripped of any uncertainty concerning the analytics of the representation, but have a small imprecision in one of the parameters to input in it. Recall Lorenz’s butter y e ect of Chapter 11. Such minutely small uncertainty, at the level of the slightest parameter, might, because of nonlinearities, percolate to a huge uncertainty at the level of the output of the model. Climate models, for instance, su er from such nonlinearities, and even if we had the right model (which we, of course, don’t), a small change in one of the parameters, called calibration, can entirely reverse the conclusions. We will discuss preasymptotics further when we look at the distinctions between di erent classes of probability distributions. I will say for now that many of these mathematical and philosophical distinctions are entirely overblown, Soviet-Harvard-style, top-down, as people start with a model and then impose it on reality and start categorizing, rather than start with reality and look at what ts it, in a bottom-up way. Probability on a Thermometer  This distinction, misused in practice, resembles another de cient separation discussed earlier, between what economists call Knightian risk (computable) and Knightian uncertainty (uncomputable). This assumes that something is computable, when really everything is more or less incomputable (and rare events more so). One has to have a mental problem to think that probabilities of future events are “measurable” in the same sense that the temperature is measurable by a thermometer. We will see in the following section that small probabilities are less computable, and that this matters when the associated payo s are consequential. Another de ciency I need to point out concerns a strangely unrealistic and unrigorous research tradition in social science, “rational expectations,” in which observers are shown to rationally converge on the same inference when supplied with the same data, even if their initial hypotheses were markedly di erent (by a mechanism of updating called Bayesian inference). Why unrigorous? Because one needs a very quick check to see that people do not converge to the same opinions in reality. This is partly, as we saw in Chapter 6, because of psychological distortions such as the con rmation bias, which cause divergent interpretation of the data. But there is a mathematical reason why people do not converge to the same opinion: if you are using a probability distribution from Extremistan, and I am using a distribution from Mediocristan (or a di erent one from Extremistan), then we will never converge, simply because if you suppose Extremistan you do not update (or change your mind) that quickly. For instance, if you assume Mediocristan and do not witness Black Swans, you may eventually rule them out. Not if you assume we are in Extremistan. To conclude, assuming that “randomness” is not epistemic and subjective, or making a big deal about the distinction between “ontological randomness” and “epistemic randomness,” implies some scienti c autism, that desire to systematize, and a fundamental lack of understanding of randomness itself. It assumes that an observer can reach omniscience and can compute odds with perfect realism and without violating consistency rules. What is left becomes “randomness,” or something by another name that arises from aleatory forces that cannot be reduced by knowledge and analysis. There is an angle worth exploring: why on earth do adults accept these Soviet-Harvard-style top-down methods without laughing, and actually go to build policies in Washington based on them, against the record, except perhaps to make readers of history laugh at them and diagnose new psychiatric conditions? And, likewise, why do we default to the assumption that events are experienced by people in the same manner? Why did we ever take notions of “objective” probability seriously? After this foray into the psychology of the perception of the dynamics of time and events, let us move to our central point, the very core of our program, into what I have aggressively called the most useful problem in philosophy. The most useful, sadly. * Robert Merton, the villain of Chapter 17, a person said to be of a highly mechanistic mind (down to his interest in machinery and his use of mechanical metaphors to represent uncertainty), seems to have been created for the sole purpose of providing an illustration of dangerous Black Swan foolishness. After the crisis of 2008, he defended the risk taking caused by economists, giving the argument that “it was a Black Swan” simply because he did not see it coming, therefore, he said, the theories were ne. He did not make the leap that, since we do not see these events coming, we need to be robust to them. Normally, such people exit the gene pool; academic tenure holds them a bit longer. * The argument can actually be used to satisfy moral hazard and dishonest (probabilistically disguised) pro teering. Rubin had pocketed more than $100 million from Citigroup’s earning of pro ts from hidden risks that blow up only occasionally. After he blew up, he had an excuse—“It never happened before.” He kept his money; we, the taxpayers, who include schoolteachers and hairdressers, had to bail the company out and pay for the losses. This I call the moral hazard element in paying bonuses to people who are not robust to Black Swans, and who we knew beforehand were not robust to the Black Swan. This beforehand is what makes me angry. * It is indeed the absence of higher order representation—the inability to accept statements like “Is my method for assessing what is right or wrong right or wrong?”—that, we will see in the next section, is central when we deal with probability, that causes Dr. Johns to be suckers for measures and believe in them without doubting their beliefs. They fail to understand the metaprobability, the higher order probability—that is, the probability that the probability they are using may not be True. † The nontechnical reader should skip the rest of this section. V (PERHAPS) THE MOST USEFUL PROBLEM IN THE HISTORY OF MODERN PHILOSOPHY Small may not be the idea, after all—Where to find the powder room—Predict and perish—On school buses and intelligent textbooks I am going to be blunt. Before The Black Swan (and associated papers) most of epistemology and decision theory was, to an actor in the real world, just sterile mind games and foreplay. Almost all the history of thought is about what we know, or think we know. The Black Swan is the very first attempt (that I know of) in the history of thought to provide a map of where we get hurt by what we don’t know, to set systematic limits to the fragility of knowledge—and to provide exact locations where these maps no longer work.  To answer the most common “criticism” by economists and (now bankrupt) bankers I mentioned in Section III, I am not saying “S**t happens,” I am saying “S**t happens in the Fourth Quadrant,” which is as di erent as mistaking prudence and caution for paranoia. Furthermore, to be more aggressive, while limits like those attributed to Gödel bear massive philosophical consequences, but we can’t do much about them, I believe that the limits to empirical and statistical knowledge I have shown have sensible (if not vital) importance and we can do a lot with them in terms of solutions, by categorizing decisions based on the severity of the potential estimation error of the pair probability times consequence. For instance, we can use it to build a safer society—to robustify what lies in the Fourth Quadrant. LIVING IN TWO DIMENSIONS A vexing problem in the history of human thought is nding one’s position on the boundary between skepticism and gullibility, or how to believe and how to not believe. And how to make decisions based on these beliefs, since beliefs without decisions are just sterile. So this is not an epistemological problem (i.e., focusing on what is true or false); it is one of decision, action, and commitment. Clearly, you cannot doubt everything and function; you cannot believe everything and survive. Yet the philosophical treatment of the problem has been highly incomplete, and, worse, has not improved much over the centuries, if it has improved at all. One class of thinkers, say the Cartesians, or the academic skeptics some eighteen centuries before them, in their own way, started with the rejection of everything upfront, with some even more radical, such as the Pyrrhonians, rejecting so much that they even reject skepticism as too dogmatic. The other class, say the medieval Scholastics or the modern-day pragmatists, starts with the xation of beliefs, or some beliefs. While the medieval thinkers stop there, in an Aristotelian way, the early pragmatists, with the great thinker Charles Sanders Peirce, provided a ray of hope. They proposed to update and correct beliefs as a continuous work in progress (albeit under a known structure of probability, as Peirce believed in the existence and attainability of an ergodic, long-run, reachable state of convergence to truth). That brand of pragmatism (initially called pragmaticism) viewed knowledge as a rigorous interplay between anti- skepticism and fallibilism, i.e., between the two categories of what to doubt and what to accept. The application to my eld, probability, and perhaps the most sophisticated version of the program, lies in the dense, di cult, deep, and brilliant forays of Isaac Levi into decision theory with the notion of corpus of belief, doxastic commitment, distance from expectation, and credal probabilities. A ray of hope, perhaps, but still not even close. Not even remotely close to anything useful. Think of living in a three-dimensional space while under the illusion of being in two dimensions. It may work well if you are a worm, certainly not if you happen to be a bird. Of course, you will not be aware of the truncation—and will be confronted with many mysteries, mysteries that you cannot possibly clear up without adding a dimension, no matter how sophisticated you may get. And, of course, you will feel helpless at times. Such was the fate of knowledge all these centuries, when it was locked in two dimensions too simplistic to be of any use outside of classrooms. Since Plato only philosophers have spent time discussing what Truth was, and for a reason: it is unusable in practice. By focusing on the True/False distinction, epistemology remained, with very few exceptions, prisoner of an inconsequential, and highly incomplete, 2-D framework. The third missing dimension is, of course, the consequence of the True, and the severity of the False, the expectation. In other words, the payoff from decisions, the impact and magnitude of the result of such a decision. Sometimes one may be wrong and the mistake may turn out to be inconsequential. Or one may be right, say, on such a subject as the sex of angels, and it may turn out to be of no use beyond intellectual stamp collecting. The simpli ed, philistini ed, academi ed, and glori ed notion of “evidence” becomes useless. With respect to Black Swans, you act to protect yourself from negative ones (or expose yourself to positive ones) even though you may have no evidence that they can take place, just as we check people for weapons before they board a plane even though we have no evidence that they are terrorists. This focus on o -the-shelf commoditized notions such as “evidence,” is a problem with people who claim to use “rigor” yet go bust on occasion. A probabilistic world has trouble with “proof” as it is, but in a Black Swan world things are a lot worse.  Indeed, I know of almost no decision that is based on notions of True/False. Once you start examining the payo , the result of decisions, you will see clearly that the consequences of some errors may be benign, those of others may be severe. And you pretty much know which is which beforehand. You know which errors are consequential and which ones are not so much. But rst let us look at a severe problem in the derivation of knowledge about probabilities. THE DEPENDENCE ON THEORY FOR RARE EVENTS During my deserto period, when I was getting severe but entertaining insults, I found myself debating a gentleman then employed by a rm called Lehman Brothers. That gentleman had made a statement in The Wall Street Journal saying that events we saw in August 2007 should have happened once every ten thousand years. Sure enough, we had three such events three days in a row. The Wall Street Journal ran his picture and if you look at it, you can safely say, “He does not look ten thousand years old.” So where is he getting his “once in ten thousand years” probability? Certainly not from personal experience; certainly not from the records of Lehman Brothers—his rm had not been around for ten thousand years, and of course it didn’t stay around for another ten thousand years, as it went under right after our debate. So, you know that he’s getting his small probabilities from a theory. The more remote the event, the less we can get empirical data (assuming generously that the future will resemble the past) and the more we need to rely on theory. Consider that the frequency of rare events cannot be estimated from empirical observation for the very reason that they are rare. We thus need a prior model representation for that; the rarer the event, the higher the error in estimation from standard inductive methods (say, frequency sampling from counting past occurrences), hence the higher the dependence on an a priori representation that extrapolates into the space of low-probability events (which necessarily are not seen often).* But even outside of small probabilities, the a priori problem is always present. It seems salient with respect to rare events, but it pervades probabilistic knowledge. I will present two versions I have been working on with two collaborators, Avital Pilpel, a philosopher of science (he walks fast), and Raphael Douady, a mathematician (he is sometimes a good walker, when he is not busy). Epimenides the Cretan Avital Pilpel and I expressed the regress argument as follows, as the epistemic problem of risk management, but the argument can be generalized to any form of probabilistic knowledge. It is a problem of self-reference by probability measures. We can state it in the following way. If we need data to obtain a probability distribution to gauge knowledge about the future behavior of the distribution from its past results, and if, at the same time, we need a probability distribution to gauge data su ciency and whether or not it is predictive of the future, then we face a severe regress loop. This is a problem of self-reference akin to that of Epimenides the Cretan stating whether or not Cretans are liars. Indeed, it is too uncomfortably close to the Epimenides situation, since a probability distribution is used to assess the degree of truth but cannot re ect on its own degree of truth and validity. And, unlike many problems of self-reference, those related to risk assessment have severe consequences. The problem is more acute with small probabilities. An Undecidability Theorem This problem of self-reference, published with Pilpel after The Black Swan, went unnoticed as such. So Raphael Douady and I re-expressed the philosophical problem mathematically, and it appears vastly more devastating in its practical implications than the Gödel problem. Raphael is, among the people I know, perhaps the man with the greatest mathematical erudition—he may have more mathematical culture than anyone in modern times, except perhaps for his late father, Adrien Douady. At the time of writing, we may have produced a formal proof using mathematics, and a branch of mathematics called “measure theory” that was used by the French to put rigor behind the mathematics of probability. The paper is provisionally called “Undecidability: On the inconsistency of estimating probabilities from a sample without binding a priori assumptions on the class of acceptable probabilities.” It’s the Consequences … Further, we in real life do not care about simple, raw probability (whether an event happens or does not happen); we worry about consequences (the size of the event; how much total destruction of lives or wealth, or other losses, will come from it; how much bene t a bene cial event will bring). Given that the less frequent the event, the more severe the consequences (just consider that the hundred-year ood is more severe, and less frequent, than the ten-year ood; the bestseller of the decade ships more copies than the bestseller of the year), our estimation of the contribution of the rare event is going to be massively faulty (contribution is probability times e ect; multiply that by estimation error); and nothing can remedy it.* So the rarer the event, the less we know about its role—and the more we need to compensate for that de ciency with an extrapolative, generalizing theory. It will lack in rigor in proportion to claims about the rarity of the event. Hence theoretical and model error are more consequential in the tails; and, the good news, some representations are more fragile than others. I showed that this error is more severe in Extremistan, where rare events are more consequential, because of a lack of scale, or a lack of asymptotic ceiling for the random variable. In Mediocristan, by comparison, the collective e ect of regular events dominates and the exceptions are rather inconsequential—we know their e ect, and it is very mild because one can diversify thanks to the “law of large numbers.” Let me provide once again an illustration of Extremistan. Less than 0.25 percent of all the companies listed in the world represent around half the market capitalization, a less than minuscule percentage of novels on the planet accounts for approximately half of ction sales, less than 0.1 percent of drugs generate a little more than half the pharmaceutical industry’s sales—and less than 0.1 percent of risky events will cause at least half the damages and losses. From Reality to Representation* Let me take another angle. The passage from theory to the real world presents two distinct di culties: inverse problems and pre-asymptotics. Inverse Problems. Problems Recall how much more di cult it is to re-create an ice cube from the results of the puddle (reverse engineering) than to forecast the shape of the puddle. In fact, the solution is not unique: the ice cube can be of very many shapes. I have discovered that the Soviet- Harvard method of viewing the world (as opposed to the Fat Tony style) makes us commit the error of confusing the two arrows (from ice cube to puddle; from puddle to ice cube). It is another manifestation of the error of Platonicity, of thinking that the Platonic form you have in your mind is the one you are observing outside the window. We see a lot of evidence of confusion of the two arrows in the history of medicine, the rationalistic medicine based on Aristotelian teleology, which I discussed earlier. This confusion is based on the following rationale. We assume that we know the logic behind an organ, what it was made to do, and thus that we can use this logic in our treatment of the patient. It has been very hard in medicine to shed our theories of the human body. Likewise, it is easy to construct a theory in your mind, or pick it up from Harvard, then go project it on the world. Then things are very simple. This problem of confusion of the two arrows is very severe with probability, particularly with small probabilities.* As we showed with the undecidability theorem and the self-reference argument, in real life we do not observe probability distributions. We just observe events. So I can rephrase the results as follows: we do not know the statistical properties—until, of course, after the fact. Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations—each would extrapolate di erently outside the set of events from which it was derived. The inverse problem is more acute when more theories, more distributions can t a set of data, particularly in the presence of nonlinearities or nonparsimonious distributions.† Under nonlinearities, the families of possible models/ parametrization explode in numbers.‡ But the problem gets more interesting in some domains. Recall the Casanova problem in Chapter 8. For environments that tend to produce negative Black Swans, but no positive Black Swans (these environments are called negatively skewed), the problem of small probabilities is worse. Why? Clearly, catastrophic events will be necessarily absent from the data, since the survivorship of the variable itself will depend on such e ect. Thus such distributions will let the observer become prone to overestimation of stability and underestimation of potential volatility and risk. This point—that things have a bias to appear more stable and less risky in the past, leading us to surprises—needs to be taken seriously, particularly in the medical eld. The history of epidemics, narrowly studied, does not suggest the risks of the great plague to come that will dominate the planet. Also I am convinced that in doing what we are to the environment, we greatly underestimate the potential instability we will experience somewhere from the cumulative damage we have done to nature. One illustration of this point is playing out just now. At the time of writing, the stock market has proved much, much riskier than innocent retirees were led to believe from historical discourses showing a hundred years of data. It is down close to 23 percent for the decade ending in 2010, while the retirees were told by nance charlatans that it was expected to rise by around 75 percent over that time span. This has bankrupted many pension plans (and the largest car company in the world), for they truly bought into that “empirical” story—and of course it has caused many disappointed people to delay their retirement. Consider that we are suckers and will gravitate toward those variables that are unstable but that appear stable. Preasymptotics. Preasymptotics Let us return to Platonicity with a discussion of preasymptotics, what happens in the short term. Theories are, of course, a bad thing to start with, but they can be worse in some situations when they were derived in idealized situations, the asymptote, but are used outside the asymptote (its limit, say in nity or the in nitesimal). Mandelbrot and I showed how some asymptotic properties do work well preasymptotically in Mediocristan, which is why casinos do well; matters are di erent in Extremistan. Most statistical education is based on these asymptotic, Platonic properties, yet we live in the real world, which rarely resembles the asymptote. Statistical theorists know it, or claim to know it, but not your regular user of statistics who talks about “evidence” while writing papers. Furthermore, this compounds what I called the ludic fallacy: most of what students of mathematical statistics do is assume a structure similar to the closed structures of games, typically with a priori known probability. Yet the problem we have is not so much making computations once you know the probabilities, but nding the true distribution for the horizon concerned. Many of our knowledge problems come from this tension between a priori and a posteriori. Proof in the Flesh There is no reliable way to compute small probabilities. probabilities I argued philosophically the di culty of computing the odds of rare events. Using almost all available economic data—and I used economic data because that’s where the clean data was—I showed the impossibility of computing from the data the measure of how far away from the Gaussian one was. There is a measure called kurtosis that the reader does not need to bother with, but that represents “how fat the tails are,” that is, how much rare events play a role. Well, often, with ten thousand pieces of data, forty years of daily observations, one single observation represents 90 percent of the kurtosis! Sampling error is too large for any statistical inference about how non-Gaussian something is, meaning that if you miss a single number, you miss the whole thing. The instability of the kurtosis implies that a certain class of statistical measures should be totally disallowed. This proves that everything relying on “standard deviation,” “variance,” “least square deviation,” etc., is bogus. Further, I also showed that it is impossible to use fractals to get acceptably precise probabilities—simply because a very small change in what I called the “tail exponent” in Chapter 16, coming from observation error, would make the probabilities change by a factor of 10, perhaps more. Implication: the need to avoid exposure to small probabilities in a certain domain. We simply cannot compute them. FALLACY OF THE SINGLE EVENT PROBABILITY Recall from Chapter 10, with the example of the behavior of life expectancy, that the conditional expectation of additional life drops as one advances in age (as you get older you are expected to live a smaller number of years; this comes from the fact that there is an asymptotic “soft” ceiling to how old a human can get). Expressing it in units of standard deviations, the conditional expectation of a Mediocristani Gaussian variable, conditional on it being higher than a threshold of 0, is.8 (standard deviations). Conditional on it being higher than a threshold of 1, it will be 1.52. Conditional on it being higher than 2, it will be 2.37. As you see, the two numbers should converge to each other as the deviations become large, so conditional on it being higher than 10 standard deviations, a random variable will be expected to be just 10. In Extremistan, things work di erently. The conditional expectation of an increase in a random variable does not converge to the threshold as the variable gets larger. In the real world, say with stock returns (and all economic variables), conditional on a loss being worse than 5 units, using any unit of measure (it makes little di erence), it will be around 8 units. Conditional that a move is more than 50 units, it should be around 80 units, and if we go all the way until the sample is depleted, the average move worse than 100 units is 250 units! This extends to all areas in which I found su cient samples. This tells us that there is “no” typical failure and “no” typical success. You may be able to predict the occurrence of a war, but you will not be able to gauge its e ect! Conditional on a war killing more than 5 million people, it should kill around 10 million (or more). Conditional on it killing more than 500 million, it would kill a billion (or more, we don’t know). You may correctly predict that a skilled person will get “rich,” but, conditional on his making it, his wealth can reach $1 million, $10 million, $1 billion, $10 billion—there is no typical number. We have data, for instance, for predictions of drug sales, conditional on getting things right. Sales estimates are totally uncorrelated to actual sales—some drugs that were correctly predicted to be successful had their sales underestimated by up to 22 times. This absence of “typical” events in Extremistan is what makes something called prediction markets (in which people are assumed to make bets on events) ludicrous, as they consider events to be binary. “A war” is meaningless: you need to estimate its damage—and no damage is typical. Many predicted that the First World War would occur, but nobody really predicted its magnitude. One of the reasons economics does not work is that the literature is almost completely blind to this point. Accordingly, Ferguson’s methodology (mentioned in Chapter 1) in looking at the prediction of events as expressed in the price of war bonds is sounder than simply counting predictions, because a bond, re ecting the costs to the governments involved in a war, is priced to cover the probability of an event times its consequences, not just the probability of an event. So we should not focus on whether someone “predicted” an event without his statement having consequences attached to it. Associated with the previous fallacy is the mistake of thinking that my message is that these Black Swans are necessarily more probable than assumed by conventional methods. They are mostly less probable, but have bigger e ects. Consider that, in a winner-take-all environment, such as the arts, the odds of success are low, since there are fewer successful people, but the payo is disproportionately high. So, in a fat- tailed environment, rare events can be less frequent (their probability is lower), but they are so powerful that their contribution to the total pie is more substantial. The point is mathematically simple, but does not register easily. I’ve enjoyed giving graduate students in mathematics the following quiz (to be answered intuitively, on the spot). In a Gaussian world, the probability of exceeding one standard deviation is around 16 percent. What are the odds of exceeding it under a distribution of fatter tails (with the same mean and variance)? The right answer: lower, not higher —the number of deviations drops, but the few that take place matter more. It was puzzling to see that most graduate students get it wrong. Back to stress testing again. At the time of writing, the U.S. government is having nancial institutions stress-tested by assuming large deviations and checking the results against the capitalization of these rms. But the problem is, Where did they get the numbers? From the past? This is so awed, since the past, as we saw, is no indication of future deviations in Extremistan. This comes from the atypicality of extreme deviations. My experience of stress testing is that it reveals little about the risks—but the risks can be used to assess the degree of model error. Psychology of Perception of Deviations Fragility of Intuitions About the Typicality of the Move.Move Dan Goldstein and I ran a series of experiments about the intuitions of agents concerning such conditional expectations. We posed questions of the following sort: What is the average height of humans who are taller than six feet? What the average weight of people heavier than 250 pounds? We tried with a collection of variables from Mediocristan, including the above-mentioned height and weight, to which we added age, and we asked participants to guess variables from Extremistan, such as market capitalization (what is the average size of companies with capitalization in excess of $5 billion?) and stock performance. The results show that, clearly, we have good intuitions when it comes to Mediocristan, but horribly poor ones when it comes to Extremistan—yet economic life is almost all Extremistan. We do not have good intuition for that atypicality of large deviations. This explains both foolish risk