One of the classic stories of experimental probability comes from the internment camps of World War II. John Kerrich, a South African mathematician, was interned in the Hald camp in Denmark as he had the misfortune to visit Copenhagen at exactly the wrong time. As Freedman, Pisani, and Purves, Statistics (4th ed, p. 273), put it, “to pass the time he carried out a series of experiments in rpobability theory. One experiment involved tossing a coin 10,000 times.” In June of 1945, after the war in Europe ended, he published a little book entitled “An Experimental Introduction to the Theory of Probability”, so-called because it includes the results of many rather long experiments in the flipping of coins, the selection of balls from urns, and so on. The coin-flipping experiment opens the book. I suppose now we would have probability textbooks that take the same approach but using simulated results from a random number generator instead of the results of actual experiments. I’m also reminded of the story of how Stanislaw Ulam invented the Monte Carlo method — he was playing solitaire while sick and realized that although it would be tremendously difficult to calculate the probability of winning, it would be easy to determine it by repeated play. Indeed this seems to have been in the air around that time; the Wikipedia article cites Ulam asking the same question in 1946.
However it is not the purpose of this post to comment on this book. I have a copy of this book in my hands right now but I have not read it. But I just want to quote from Kerrich’s preface (p. 6):
It is hoped that students of these pages will never have to reject any of the ideas given here, no matter how much they may refine them as their knowledge of the subject grows.
Kerrich has previously told us that he is teaching to a “very mixed class of students and colleagues”, some of whom are well-grounded in mathematics and some of whom are not. I feel that this echoes, more elegantly, a statement I’m fond of making about teaching at different levels. In high school we lie to the students and we don’t tell them that we’re lying. In college we lie to them and tell them that we’re lying. In graduate school we don’t lie to them.