The Black Swan: The Impact of the Highly Improbable

by Nassim Nicholas Taleb

We, members of the human variety of primates, have a hunger for rules because we need to reduce the dimension of matters so they can get into our heads. Or, rather, sadly, so we can squeeze them into our heads. The more random information is, the greater the dimensionality, and thus the more difficult to summarize. The more you summarize, the more order you put in, the less randomness. Hence the same condition that makes us simplify pushes us to think that the world is less random than it actually is.

National traits” might be great for movies, they might help a lot with war, but they are Platonic notions that carry no empirical validity—yet, for example, both the English and the non-English erroneously believe in an English “national temperament.”)

do not forbid myself from using the word cause, but the causes I discuss are either bold speculations (presented as such) or the result of experiments, not stories.

Pasteur said, and, like all great discoverers, he knew something about accidental discoveries. The best way to get maximal exposure is to keep researching. Collect opportunities—on that, later. To predict the spread of a technology implies predicting a large element of fads and social contagion, which lie outside the objective utility of the technology itself (assuming there is such an animal as objective utility).

If you know about the discovery you are about to make in the future, then you have almost made it.

you know a set of basic parameters concerning the ball at rest, can compute the resistance of the table (quite elementary), and can gauge the strength of the impact, then it is rather easy to predict what would happen at the first hit. The second impact becomes more complicated, but possible; you need to be more careful about your knowledge of the initial states, and more precision is called for. The problem is that to correctly compute the ninth impact, you need to take into account the gravitational pull of someone standing next to the table (modestly, Berry’s computations use a weight of less than 150 pounds). And to compute the fifty-sixth impact, every single elementary particle of the universe needs to be present in your assumptions!

Randomness, in the end, is just unknowledge. The world is opaque and appearances fool us.

Furthermore, this trade-off between volatility and risk can show up in careers that give the appearance of being stable, like jobs at IBM until the 1990s. When laid off, the employee faces a total void: he is no longer fit for anything else. The same holds for those in protected industries. On the other hand, consultants can have volatile earnings as their clients’ earnings go up and down, but face a lower risk of starvation, since their skills match demand—fluctuat nec mergitur (fluctuates but doesn’t sink). Likewise, dictatorships that do not appear volatile, like, say, Syria or Saudi Arabia, face a larger risk of chaos than, say, Italy, as the latter has been in a state of continual political turmoil since the second war. I learned about this problem from the finance industry, in which we see “conservative” bankers sitting on a pile of dynamite but fooling themselves because their operations seem dull and lacking in volatility.

you need to put a portion, say 85 to 90 percent, in extremely safe instruments, like Treasury bills—as safe a class of instruments as you can manage to find on this planet. The remaining 10 to 15 percent you put in extremely speculative bets, as leveraged as possible (like options), preferably venture capital–style portfolios.fn3 That way you

The average will be medium risk but constitutes a positive exposure to the Black Swan. More technically, this can be called a “convex” combination. Let us see how this can be implemented in all aspects of life.

But the idea behind Pascal’s wager has fundamental applications outside of theology. It stands the entire notion of knowledge on its head. It eliminates the need for us to understand the probabilities of a rare event (there are fundamental limits to our knowledge of these); rather, we can focus on the payoff and benefits of an event if it takes place.

What is the most likely breakdown of their respective incomes? In Mediocristan, the most likely combination is half a million each. In Extremistan, it would be $50,000 and $950,000. The situation is even more lopsided with book sales. If I told you that two authors sold a total of a million copies of their books, the most likely combination is 993,000 copies sold for one and 7,000 for the other. This is far more likely than that the books each sold 500,000 copies. For any large total, the breakdown will be more and more asymmetric.

Gaussian approach in variables for which there is a rational reason for the largest not to be too far away from the average. If there is gravity pulling numbers down, or if there are physical limitations preventing very large observations, we end up in Mediocristan. If there are strong forces of equilibrium bringing things back rather rapidly after conditions diverge from equilibrium, then again you can use the Gaussian approach. Otherwise, fuhgedaboudit. This is why much of economics is based on the notion of equilibrium: among other benefits, it allows you to treat economic phenomena as Gaussian.

We are either blind, or illiterate, or both. That nature’s geometry is not Euclid’s was so obvious, and nobody, almost nobody, saw it. This (physical) blindness is identical to the ludic fallacy that makes us think casinos represent randomness.

Well, from the data. So we need the data to tell us what the probability distribution is, and a probability distribution to tell us how much data we need. This causes a severe regress argument. This regress does not occur if you assume beforehand that the distribution is Gaussian. It happens that, for some reason, the Gaussian yields its properties rather easily.

scholar who applies such methodology resembles Locke’s definition of a madman: someone “reasoning correctly from erroneous premises.”

But political, social, and weather events do not have this handy property, and we patently cannot predict them, so when you hear “experts” presenting the problems of uncertainty in terms of subatomic particles, odds are that the expert is a phony. As a matter of fact, this may be the best way to spot a phony.

am skeptical about confirmation—though only when errors are costly—not about disconfirmation. Having plenty of data will not provide confirmation, but a single instance can disconfirm.

Half the people I know call me irreverent (you have read my comments about your local Platonified professors), half call me fawning (you have seen my slavish devotion to Huet, Bayle, Popper, Poincaré, Montaigne, Hayek, and others). Half the time I hate Nietzsche, the other half I like his prose.

For consider the opposite: differences 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.

we know their effect, 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 fiction 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.

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.

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 effects.

This gave me the idea of using the approach “This is where your tools work,” instead of the “This is wrong” approach I was using before. The change in style is what earned me the hugs and supply of Diet Coke and helped me get my message across. David’s comments also inspired me to focus more on iatrogenics, harm caused by the need to use quantitative models.

However, as I said, recommendations of the style “Do not do” are more robust empirically. How do you live long? By avoiding death. Yet people do not realize that success consists mainly in avoiding losses, not in trying to derive profits.

Let’s consider medicine (that sister of philosophy), which only started saving lives less than a century ago (I am generous), and to a lesser extent than initially advertised in the popular literature, as the drops in mortality seem to arise much more from awareness of sanitation and the (random) discovery of antibiotics rather than from therapeutic contributions.