Нассим Талеб - The Black Swan. The Impact of the Highly Improbable

THE POET OF RANDOMNESS

It was a melancholic afternoon when I smelled the old books in Benoît Mandelbrot’s library. This was on a hot day in August 2005, and the heat exacerbated the musty odor of the glue of old French books bringing on powerful olfactory nostalgia. I usually succeed in repressing such nostalgic excursions, but not when they sneak up on me as music or smell. The odor of Mandelbrot’s books was that of French literature, of my parents’ library, of the hours spent in bookstores and libraries when I was a teenager when many books around me were (alas) in French, when I thought that Literature was above anything and everything. (I haven’t been in contact with many French books since my teenage days.) However abstract I wanted it to be, Literature had a physical embodiment, it had a smell, and this was it.

The afternoon was also gloomy because Mandelbrot was moving away, exactly when I had become entitled to call him at crazy hours just because I had a question, such as why people didn’t realize that the 80/20 could be 50/01. Mandelbrot had decided to move to the Boston area, not to retire, but to work for a research center sponsored by a national laboratory. Since he was moving to an apartment in Cambridge, and leaving his oversize house in the Westchester suburbs of New York, he had invited me to come take my pick of his books.

Even the titles of the books had a nostalgic ring. I filled up a box with French titles, such as a 1949 copy of Henri Bergson’s Matière et mémoire , which it seemed Mandelbrot bought when he was a student (the smell!).

After having mentioned his name left and right throughout this book, I will finally introduce Mandelbrot, principally as the first person with an academic title with whom I ever spoke about randomness without feeling defrauded. Other mathematicians of probability would throw at me theorems with Russian names such as “Sobolev,” “Kolmogorov,” Wiener measure, without which they were lost; they had a hard time getting to the heart of the subject or exiting their little box long enough to consider its empirical flaws. With Mandelbrot, it was different: it was as if we both originated from the same country, meeting after years of frustrating exile, and were finally able to speak in our mother tongue without straining. He is the only flesh-and-bones teacher I ever had—my teachers are usually books in my library. I had way too little respect for mathematicians dealing with uncertainty and statistics to consider any of them my teachers—in my mind mathematicians, trained for certainties, had no business dealing with randomness. Mandelbrot proved me wrong.

He speaks an unusually precise and formal French, much like that spoken by Levantines of my parents’ generation or Old World aristocrats. This made it odd to hear, on occasion, his accented, but very standard, colloquial American English. He is tall, overweight, which makes him look baby-faced (although I’ve never seen him eat a large meal), and has a strong physical presence.

From the outside one would think that what Mandelbrot and I have in common is wild uncertainty, Black Swans, and dull (and sometimes less dull) statistical notions. But, although we are collaborators, this is not what our major conversations revolve around. It is mostly matters literary and aesthetic, or historical gossip about people of extraordinary intellectual refinement. I mean refinement, not achievement. Mandelbrot could tell stories about the phenomenal array of hotshots he has worked with over the past century, but somehow I am programmed to consider scientists’ personae far less interesting than those of colorful erudites. Like me, Mandelbrot takes an interest in urbane individuals who combine traits generally thought not to coexist together. One person he often mentions is Baron Pierre Jean de Menasce, whom he met at Princeton in the 1950s, where de Menasce was the roommate of the physicist Oppenheimer. De Menasce was exactly the kind of person I am interested in, the embodiment of a Black Swan. He came from an opulent Alexandrian Jewish merchant family, French and Italian–speaking like all sophisticated Levantines. His forebears had taken a Venetian spelling for their Arabic name, added a Hungarian noble title along the way, and socialized with royalty. De Menasce not only converted to Christianity, but became a Dominican priest and a great scholar of Semitic and Persian languages. Mandelbrot kept questioning me about Alexandria, since he was always looking for such characters.

True, intellectually sophisticated characters were exactly what I looked for in life. My erudite and polymathic father—who, were he still alive, would have only been two weeks older than Benoît M.—liked the company of extremely cultured Jesuit priests. I remember these Jesuit visitors occupying my chair at the dining table. I recall that one had a medical degree and a PhD in physics, yet taught Aramaic to locals in Beirut’s Institute of Eastern Languages. His previous assignment could have been teaching high school physics, and the one before that was perhaps in the medical school. This kind of erudition impressed my father far more than scientific assembly-line work. I may have something in my genes driving me away from bildungsphilisters .

Although Mandelbrot often expressed amazement at the temperament of high-flying erudites and remarkable but not-so-famous scientists, such as his old friend Carleton Gajdusek, a man who impressed him with his ability to uncover the causes of tropical diseases, he did not seem eager to trumpet his association with those we consider great scientists. It took me a while to discover that he had worked with an impressive list of scientists in seemingly every field, something a name-dropper would have brought up continuously. Although I have been working with him for a few years now, only the other day, as I was chatting with his wife, did I discover that he spent two years as the mathematical collaborator of the psychologist Jean Piaget. Another shock came when I discovered that he had also worked with the great historian Fernand Braudel, but Mandelbrot did not seem to be interested in Braudel. He did not care to discuss John von Neuman with whom he had worked as a postdoctoral fellow. His scale was inverted. I asked him once about Charles Tresser, an unknown physicist I met at a party who wrote papers on chaos theory and supplemented his researcher’s income by making pastry for a shop he ran near New York City. He was emphatic: “un homme extraordinaire,” he called Tresser, and could not stop praising him. But when I asked him about a particular famous hotshot, he replied, “He is the prototypical bon élève , a student with good grades, no depth, and no vision.” That hotshot was a Nobel laureate.

THE PLATONICITY OF TRIANGLES

Now, why am I calling this business Mandelbrotian, or fractal, randomness? Every single bit and piece of the puzzle has been previously mentioned by someone else, such as Pareto, Yule, and Zipf, but it was Mandelbrot who a) connected the dots, b) linked randomness to geometry (and a special brand at that), and c) took the subject to its natural conclusion. Indeed many mathematicians are famous today partly because he dug out their works to back up his claims—the strategy I am following here in this book. “I had to invent my predecessors, so people take me seriously,” he once told me, and he used the credibility of big guns as a rhetorical device. One can almost always ferret out predecessors for any thought. You can always find someone who worked on a part of your argument and use his contribution as your backup. The scientific association with a big idea, the “brand name,” goes to the one who connects the dots, not the one who makes a casual observation—even Charles Darwin, who uncultured scientists claim “invented” the survival of the fittest, was not the first to mention it. He wrote in the introduction of The Origin of Species that the facts he presented were not necessarily original; it was the consequences that he thought were “interesting” (as he put it with characteristic Victorian modesty). In the end it is those who derive consequences and seize the importance of the ideas, seeing their real value, who win the day. They are the ones who can talk about the subject.