Poincaré and the baker: was the anecdote true?

Question

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?

Answer 1

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.

Answer 2

I first ran across this story at an exhibit in Los Angeles' Museum of Science and Industry some time before 1970, maybe as early as 1964. In the version I read there, a magistrate was involved, and the person questioning the baker's methods had some sort of civic power connection.

When you suggest that no Frenchman might have taken a loaf of bread home and weighed it, don't forget two things: a) nerds have always lived among us, and b) Paris is the home of the "Grand Prix de la Baguette de la Ville de Paris." This is a competition in which the winner, the top baguette-maker of the year, gets the honor of supplying the French presidential residence with baguettes every morning for the entire year. Mightn't it seem totally reasonable for a competitor to weigh his adversaries' loaves?

Answer 3

I think I recall reading this story as a little girl in the Time Life series of science books, in the volume on “Mathematics.” If that is the case (it’s a fifty-plus year old recollection), those books were published in the early 1960s. Perhaps there is a clue in the references at the back of the book as to the source of the story. Time Life, by the way, did not have footnotes or in-line citations in these volumes, but they did have LOTS of pictures and anecdotes that made science come alive to a pre-teen kid.