The Black Swan

by Nassim Nicholas Taleb

  The success of movies depends severely on contagions. Such contagions do not just apply to the movies: they seem to affect a wide range of cultural products. It is hard for us to accept that people do not fall in love with works of art only for their own sake, but also in order to feel that they belong to a community. By imitating, we get closer to others—that is, other imitators. It fights solitude.

  This discussion shows the difficulty in predicting outcomes in an environment of concentrated success. So for now let us note that the division between professions can be used to understand the division between types of random variables. Let us go further into the issue of knowledge, of inference about the unknown and the properties of the known.

  SCALABILITY AND GLOBALIZATION

  Whenever you hear a snotty (and frustrated) European middlebrow presenting his stereotypes about Americans, he will often describe them as “uncultured,” “unintellectual,” and “poor in math” because, unlike his peers, Americans are not into equation drills and the constructions middlebrows call “high culture”—like knowledge of Goethe’s inspirational (and central) trip to Italy, or familiarity with the Delft school of painting. Yet the person making these statements is likely to be addicted to his iPod, wear blue jeans, and use Microsoft Word to jot down his “cultural” statements on his PC, with some Google searches here and there interrupting his composition. Well, it so happens that America is currently far, far more creative than these nations of museumgoers and equation solvers. It is also far more tolerant of bottom-up tinkering and undirected trial and error. And globalization has allowed the United States to specialize in the creative aspect of things, the production of concepts and ideas, that is, the scalable part of the products, and, increasingly, by exporting jobs, separate the less scalable components and assign them to those happy to be paid by the hour. There is more money in designing a shoe than in actually making it: Nike, Dell, and Boeing can get paid for just thinking, organizing, and leveraging their know-how and ideas while subcontracted factories in developing countries do the grunt work and engineers in cultured and mathematical states do the noncreative technical grind. The American economy has leveraged itself heavily on the idea generation, which explains why losing manufacturing jobs can be coupled with a rising standard of living. Clearly the drawback of a world economy where the payoff goes to ideas is higher inequality among the idea generators together with a greater role for both opportunity and luck—but I will leave the socioeconomic discussion for Part Three and focus here on knowledge.

  TRAVELS INSIDE MEDIOCRISTAN

  This scalable/nonscalable distinction allows us to make a clear-cut differentiation between two varieties of uncertainties, two types of randomness.

  Let’s play the following thought experiment. Assume that you round up a thousand people randomly selected from the general population and have them stand next to one another in a stadium. You can even include Frenchmen (but please, not too many out of consideration for the others in the group), Mafia members, non-Mafia members, and vegetarians.

  Imagine the heaviest person you can think of and add him to that sample. Assuming he weighs three times the average, between four hundred and five hundred pounds, he will rarely represent more than a very small fraction of the weight of the entire population (in this case, about a half of a percent).

  You can get even more aggressive. If you picked the heaviest biologically possible human on the planet (who yet can still be called a human), he would not represent more than, say, 0.6 percent of the total, a very negligible increase. And if you had ten thousand persons, his contribution would be vanishingly small.

  In the utopian province of Mediocristan, particular events don’t contribute much individually—only collectively. I can state the supreme law of Mediocristan as follows: When your sample is large, no single instance will significantly change the aggregate or the total. The largest observation will remain impressive, but eventually insignificant, to the sum.

  I’ll borrow another example from my friend Bruce Goldberg: your caloric consumption. Look at how much you consume per year—if you are classified as human, close to eight hundred thousand calories. No single day, not even Thanksgiving at your great-aunt’s, will represent a large share of that. Even if you tried to kill yourself by eating, that day’s calories would not seriously affect your yearly consumption.

  Now, if I told you that it is possible to run into someone who weighs several thousand tons, or stands several hundred miles tall, you would be perfectly justified in having my frontal lobe examined, or in suggesting that I switch to science-fiction writing. But you cannot so easily rule out extreme variations with a different brand of quantities, to which we turn next.

  The Strange Country of Extremistan

  Consider by comparison the net worth of the thousand people you lined up in the stadium. Add to them the wealthiest person to be found on the planet—say, Bill Gates, the founder of Microsoft. Assume his net worth to be close to $80 billion—with the total capital of the others around a few million. How much of the total wealth would he represent? 99.9 percent? Indeed, all the others would represent no more than a rounding error for his net worth, the variation of his personal portfolio over the past second. For someone’s weight to represent such a share, he would need to weigh fifty million pounds!

  Try it again with, say, book sales. Line up a thousand authors (or people begging to get published, but calling themselves authors instead of waiters), and check their book sales. Then add the living writer who (currently) has the most readers. J. K. Rowling, the author of the Harry Potter series, with several hundred million books sold, will dwarf the remaining thousand authors with, say, collectively, a few hundred thousand readers at most.

  Try it also with academic citations (the mention of one academic by another academic in a formal publication), media references, income, company size, and so on. Let us call these social matters, as they are man-made, as opposed to physical ones, like the size of waistlines.

  In Extremistan, inequalities are such that one single observation can disproportionately impact the aggregate, or the total.

  So while weight, height, and calorie consumption are from Mediocristan, wealth is not. Almost all social matters are from Extremistan. Another way to say it is that social quantities are informational, not physical: you cannot touch them. Money in a bank account is something important, but certainly not physical. As such it can take any value without necessitating the expenditure of energy. It is just a number!

  Note that before the advent of modern technology, wars used to belong to Mediocristan. It is hard to kill many people if you need to slaughter them one at the time. Today, with tools of mass destruction, all it takes is a button, a nutcase, or a small error to wipe out the planet.

  Look at the implication for the Black Swan. Extremistan can produce Black Swans, and does, since a few occurrences have had huge influences on history. This is the main idea of this book.

  Extremistan and Knowledge

  While this distinction (between Mediocristan and Extremistan) has severe ramifications for both social fairness and the dynamics of events, let us see its application to knowledge, which is where most of its value lies. If a Martian came to earth and engaged in the business of measuring the heights of the denizens of this happy planet, he could safely stop at a hundred humans to get a good picture of the average height. If you live in Mediocristan, you can be comfortable with what you have measured—provided that you know for sure that it comes from Mediocristan. You can also be comfortable with what you have learned from the data. The epistemological consequence is that with Mediocristan-style randomness it is not possible* to have a Black Swan surprise such that a single event can dominate a phenomenon. Primo, the first hundred days should reveal all you need to know about the data. Secondo, even if you do have a surprise, as we saw in the case of the heaviest human, it would not be consequential.

  If you are dealing with quantities from Extremistan, you will have trouble f
iguring out the average from any sample since it can depend so much on one single observation. The idea is not more difficult than that. In Extremistan, one unit can easily affect the total in a disproportionate way. In this world, you should always be suspicious of the knowledge you derive from data. This is a very simple test of uncertainty that allows you to distinguish between the two kinds of randomness. Capish?

  What you can know from data in Mediocristan augments very rapidly with the supply of information. But knowledge in Extremistan grows slowly and erratically with the addition of data, some of it extreme, possibly at an unknown rate.

  Wild and Mild

  If we follow my distinction of scalable versus nonscalable, we can see clear differences shaping up between Mediocristan and Extremistan. Here are a few examples.

  Matters that seem to belong to Mediocristan (subjected to what we call type 1 randomness): height, weight, calorie consumption, income for a baker, a small restaurant owner, a prostitute, or an orthodontist; gambling profits (in the very special case, assuming the person goes to a casino and maintains a constant betting size), car accidents, mortality rates, “IQ” (as measured).

  Matters that seem to belong to Extremistan (subjected to what we call type 2 randomness): wealth, income, book sales per author, book citations per author, name recognition as a “celebrity,” number of references on Google, populations of cities, uses of words in a vocabulary, numbers of speakers per language, damage caused by earthquakes, deaths in war, deaths from terrorist incidents, sizes of planets, sizes of companies, stock ownership, height between species (consider elephants and mice), financial markets (but your investment manager does not know it), commodity prices, inflation rates, economic data. The Extremistan list is much longer than the prior one.

  The Tyranny of the Accident

  Another way to rephrase the general distinction is as follows: Mediocristan is where we must endure the tyranny of the collective, the routine, the obvious, and the predicted; Extremistan is where we are subjected to the tyranny of the singular, the accidental, the unseen, and the unpredicted. As hard as you try, you will never lose a lot of weight in a single day; you need the collective effect of many days, weeks, even months. Likewise, if you work as a dentist, you will never get rich in a single day—but you can do very well over thirty years of motivated, diligent, disciplined, and regular attendance to teeth-drilling sessions. If you are subject to Extremistan-based speculation, however, you can gain or lose your fortune in a single minute.

  Table 1 summarizes the differences between the two dynamics, to which I will refer in the rest of the book; confusing the left column with the right one can lead to dire (or extremely lucky) consequences.

  TABLE 1

  Mediocristan Extremistan

  Nonscalable Scalable

  Mild or type 1 randomness Wild (even superwild) or type 2 randomness

  The most typical member is mediocre The most “typical” is either giant or dwarf, i.e., there is no typical member

  Winners get a small segment of the total pie Winner-take-almost-all effects

  Example: audience of an opera singer before the gramophone Today’s audience for an artist

  More likely to be found in our ancestral environment More likely to be found in our modern environment

  Impervious to the Black Swan Vulnerable to the Black Swan

  Subject to gravity There are no physical constraints on what a number can be

  Corresponds (generally) to physical quantities, i.e., height Corresponds to numbers, say, wealth

  As close to utopian equality as reality can spontaneously deliver Dominated by extreme winner-take-all inequality

  Total is not determined by a single instance or observation Total will be determined by a small number of extreme events

  When you observe for a while you can get to know what’s going on It takes a long time to know what’s going on

  Tyranny of the collective Tyranny of the accidental

  Easy to predict from what you see and extend to what you do not see Hard to predict from past information

  History crawls History makes jumps

  Events are distributed* according to the “bell curve” (the GIF) or its variations The distribution is either Mandelbrotian “gray” Swans (tractable scientifically) or totally intractable Black Swans

  * What I call “probability distribution” here is the model used to calculate the odds of different events, how they are distributed. When I say that an event is distributed according to the “bell curve,” I mean that the Gaussian bell curve (after C. F. Gauss; more on him later) can help provide probabilities of various occurrences.

  This framework, showing that Extremistan is where most of the Black Swan action is, is only a rough approximation—please do not Platonify it; don’t simplify it beyond what’s necessary.

  Extremistan does not always imply Black Swans. Some events can be rare and consequential, but somewhat predictable, particularly to those who are prepared for them and have the tools to understand them (instead of listening to statisticians, economists, and charlatans of the bell-curve variety). They are near–Black Swans. They are somewhat tractable scientifically—knowing about their incidence should lower your surprise; these events are rare but expected. I call this special case of “gray” swans Mandelbrotian randomness. This category encompasses the randomness that produces phenomena commonly known by terms such as scalable, scale-invariant, power laws, Pareto-Zipf laws, Yule’s law, Paretian-stable processes, Levy-stable, and fractal laws, and we will leave them aside for now since they will be covered in some depth in Part Three. They are scalable, according to the logic of this chapter, but you can know a little more about how they scale since they share much with the laws of nature.

  You can still experience severe Black Swans in Mediocristan, though not easily. How? You may forget that something is random, think that it is deterministic, then have a surprise. Or you can tunnel and miss on a source of uncertainty, whether mild or wild, owing to lack of imagination—most Black Swans result from this “tunneling” disease, which I will discuss in Chapter 9.*

  This has been a “literary” overview of the central distinction of this book, offering a trick to distinguish between what can belong in Mediocristan and what belongs in Extremistan. I said that I will get into a more thorough examination in Part Three, so let us focus on epistemology for now and see how the distinction affects our knowledge.

  * To those readers who Googled Yevgenia Krasnova, I am sorry to say that she is (officially) a fictional character.

  * I emphasize possible because the chance of these occurrences is typically in the order of one in several trillion trillion, as close to impossible as it gets.

  * It is worth mentioning here that one of the mistakes people make in the interpretation of the Black Swan idea is that they believe that Black Swans are more frequent than in our imagination. Not quite the point. Black Swans are more consequential, not necessarily more frequent. There are actually fewer remote events, but they are more and more extreme in their impact, which confuses people, as they tend to write them off more easily.

  Chapter Four

  ONE THOUSAND AND ONE DAYS, OR HOW NOT TO BE A SUCKER

  Surprise, surprise—Sophisticated methods for learning from the future—Sextus was always ahead—The main idea is not to be a sucker—Let us move to Mediocristan, if we can find it

  Which brings us to the Black Swan problem in its original form.

  Imagine someone of authority and rank, operating in a place where rank matters—say, a government agency or a large corporation. He could be a verbose political commentator on Fox News stuck in front of you at the health club (impossible to avoid looking at the screen), the chairman of a company discussing the “bright future ahead,” a Platonic medical doctor who has categorically ruled out the utility of mother’s milk (because he did not see anything special in it), or a Harvard Business School professor who does not laugh at your jokes. He takes what he knows a li
ttle too seriously.

  Say that a prankster surprises him one day by surreptitiously sliding a thin feather up his nose during a moment of relaxation. How would his dignified pompousness fare after the surprise? Contrast his authoritative demeanor with the shock of being hit by something totally unexpected that he does not understand. For a brief moment, before he regains his bearings, you will see disarray in his face.

  I confess having developed an incorrigible taste for this kind of prank during my first sleepaway summer camp. Introduced into the nostril of a sleeping camper, a feather would induce sudden panic. I spent part of my childhood practicing variations on the prank: in place of a thin feather you can roll the corner of a tissue to make it long and narrow. I got some practice on my younger brother. An equally effective prank would be to drop an ice cube down someone’s collar when he expects it least, say during an official dinner. I had to stop these pranks as I got deeper into adulthood, of course, but I am often involuntarily hit with such an image when bored out of my wits in meetings with serious-looking businesspersons (dark suits and standardized minds) theorizing, explaining things, or talking about random events with plenty of “because” in their conversation. I zoom in on one of them and imagine the ice cube sliding down his back—it would be less fashionable, though certainly more spectacular, if you put a living mouse there, particularly if the person is ticklish and is wearing a tie, which would block the rodent’s normal route of exit.*