The Black Swan: The Impact of the Highly Improbable

I sat down and discussed this with the great man, and it became, as usual, a linguistic game. In Chapter 9 I presented the distinction economists make between Knightian uncertainty (incomputable) and Knightian risk (computable); this distinction cannot be so original an idea to be absent in our vocabulary, and so we looked for it in French. Mandelbrot mentioned one of his friends and prototypical heroes, the aristocratic mathematician Marcel-Paul Schützenberger, a fine erudite who (like this author) was easily bored and could not work on problems beyond their point of diminishing returns. Schützenberger insisted on the clear-cut distinction in the French language between hasard and fortuit. Hasard, from the Arabic az-zahr, implies, like alea, dice—tractable randomness; fortuit is my Black Swan—the purely accidental and unforeseen. We went to the Petit Robert dictionary; the distinction effectively exists there. Fortuit seems to correspond to my epistemic opacity, l’imprévu et non quantifiable; hasard to the more ludic type of uncertainty that was proposed by the Chevalier de Méré in the early gambling literature. Remarkably, the Arabs may have introduced another word to the business of uncertainty: rizk, meaning property.

I repeat: Mandelbrot deals with gray swans; I deal with the Black Swan. So Mandelbrot domesticated many of my Black Swans, but not all of them, not completely. But he shows us a glimmer of hope with his method, a way to start thinking about the problems of uncertainty. You are indeed much safer if you know where the wild animals are.

Chapter Seventeen: LOCKE’S MADMEN, OR BELL CURVES IN THE WRONG PLACES [59]

What?—Anyone can become president—Alfred Nobel’s legacy—Those medieval days

I have in my house two studies: one real, with interesting books and literary material; the other nonliterary, where I do not enjoy working, where I relegate matters prosaic and narrowly focused. In the nonliterary study is a wall full of books on statistics and the history of statistics, books I never had the fortitude to burn or throw away; though I find them largely useless outside of their academic applications (Carneades, Cicero, and Foucher know a lot more about probability than all these pseudosophisticated volumes). I cannot use them in class because I promised myself never to teach trash, even if dying of starvation. Why can’t I use them? Not one of these books deals with Extremistan. Not one. The few books that do are not by statisticians but by statistical physicists. We are teaching people methods from Mediocristan and turning them loose in Extremistan. It is like developing a medicine for plants and applying it to humans. It is no wonder that we run the biggest risk of all: we handle matters that belong to Extremistan, but treated as if they belonged to Mediocristan, as an “approximation.”

Several hundred thousand students in business schools and social science departments from Singapore to Urbana-Champaign, as well as people in the business world, continue to study “scientific” methods, all grounded in the Gaussian, all embedded in the ludic fallacy.

This chapter examines disasters stemming from the application of phony mathematics to social science. The real topic might be the dangers to our society brought about by the Swedish academy that awards the Nobel Prize.

Only Fifty Years

Let us return to the story of my business life. Look at the graph in Figure 14. In the last fifty years, the ten most extreme days in the financial markets represent half the returns. Ten days in fifty years. Meanwhile, we are mired in chitchat.

Clearly, anyone who wants more than the high number of six sigma as proof that markets are from Extremistan needs to have his head examined. Dozens of papers show the inadequacy of the Gaussian family of distributions and the scalable nature of markets. Recall that, over the years, I myself have run statistics backward and forward on 20 million pieces of data that made me despise anyone talking about markets in Gaussian terms. But people have a hard time making the leap to the consequences of this knowledge.