IT IS EASIER TO DISPROVE THAN TO PROVE. The “Black Swan†figure of speech comes from a famous example which is used to illustrate inference. Take the proposition: “All swans are white.†Any number of white swans won’t prove the proposition; a single black swan will disprove it. For Taleb, the Long Term Capital Management crisis disproves the belief that risks can be confidently estimated by traditional techniques. He also points out that we can be a lot more certain about what isn’t true than we can be about what is true.
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I have yet to read Taleb, but I think the Black Swan example focuses a lot more than is warranted on whether the probability of something is zero. Logicians love to address that question because that is perhaps the only one you can answer without evidence. Historians and lawyers are attracted to the question because if something never happens, you don’t have to try to describe just how rare or likely the event is. But for many purposes we have to come up with an estimate of how often something happens. This is related to Deirdre McCloskey’s argument that to say that A has an effect on B may not mean much if the effect is trivial. Similarly, to say that A may happen may not mean much if A happens very rarely. As I understand it, the theory of statistical mechanics says that in any object — a brick, for example — a huge number of molecules move around at random. The random movements usually cancel out, so the brick stays put. But there is a very small probability that that the huge number of random movements could happen to go in the same direction for a moment and the brick would shoot up in the air or in some other direction. The same thing could happen to you or me for that matter. The odds are extremely long against this happening. [Could one publish, say in a science fiction magazine, a story in which Pauline is rescued from the railroad track because all her molecules got lucky?] The probability that the brick may jump is not zero, but it is so low that we can ignore that possibility.
I think that this means that it is slightly beside the point to say that it is easier to disprove that all swans are white than to prove it. If we’re scared of black swans, then showing that the probability of a black swan is not zero may not help us very much. We need more information to decide what to do.
I take it that when Taleb says that conventional statistical techniques may not help much with risk analysis, he is referring to those that address the mean height of a person rather than the probability that someone will be seven feet tall. As a student I came across the title of a book from the 1930’s, the Statistics of Extremes, by a man named Emile Gumbel. It turns out that Margo’s father, Roger Keeney, published as a graduate student an article with Gumbel. As I understand it, one reason, aside from general left-wing politics, that Gumbel had to leave Nazi Germany was his statistical analyses of Nazi political murders.