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There is a story featuring Henri Poincaré and an unscrupuolous baker. Every day Poincaré bought a piece of bread which should have weighted 1 kg. After an year, the mathematician brought the baker to the judge: he weighted all the pieces of bread and found out that the average weight was just 950g. The baker was then fined. The story goes on: next year Poincaré sued the baker again. Now the average weight was more or less 1 Kg, but he showed that the distribution of weights was not a Gaussian curve but rather its tail. This meant, concluded Poincaré, that the baker chose the heaviest pieces of bread to give him, but he kept baking lighter pieces of bread.

The anecdote may be found in Leonard Mlodinov, The Drunkard's Walk, who in turn cites Bart Holland, What Are the Chances? pp. 41–42. I read both passages, but I think the story was made up. Poincaré could have done this, but would it have been able to convince a judge that his reasoning is correct?

Does anybody know some actual sources for the story?

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  • $\begingroup$ I prefer the puzzles based on a baker who produces loaves of infinite length :-) $\endgroup$ – Carl Witthoft Apr 30 '18 at 13:12
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It is interesting that even many of those who retell the anecdote immediately disown it "The following anecdote about him is probably fabricated, but it makes an interesting probability problem", says Actuarial Outpost. Oloffson who like Mlodinov even put it into his book (p.203), writes "Although the anecdote illustrates a clever way to use probabilities to detect cheating, I doubt that it is true. What Frenchman who has just bought a loaf of bread would go home and weigh it?" Laurie Snell from Dartmouth even mentions a themed exhibit at Boston Science Museum, but alas... no attribution.

The story appears to be made up, and recently. The earliest mention I could find is from 2000, on Everything2's collection of equally "credible" anecdotes, like Gauss's fast addition of numbers from 1 to 100.

There is no agreement even on whether the following normal distribution quote belongs to Poincare:"Everyone believes in it: experimentalists believing that it is a mathematical theorem, mathematicians believing that it is an empirical fact". And that one at least occurs in his book. According to Cramer, it is Lippman's, and Poincare only quoted it.

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    $\begingroup$ I've heard exactly the same sentence "Everyone believes..." but about the Law of Large Numbers, not about normal distribution. And of course I do not believe that Poincare sued a baker:-) $\endgroup$ – Alexandre Eremenko Apr 25 '18 at 2:56

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