Drunkard's Walk - Leonard Mlodinow [53]
THE MANUSCRIPT in which Bernoulli presented his golden theorem ends abruptly even though he promises earlier in the work that he will provide applications to various issues in civic affairs and economics. It is as if “Bernoulli literally quit when he saw the number 25,550,” wrote the historian of statistics Stephen Stigler.20 In fact, Bernoulli was in the process of publishing his manuscript when he died “of a slow fever” in August 1705, at the age of fifty. His publishers asked Johann Bernoulli to complete it, but Johann refused, saying he was too busy. That may appear odd, but the Bernoullis were an odd family. If you were asked to choose the most unpleasant mathematician who ever lived, you wouldn’t be too far off if you fingered Johann Bernoulli. He has been variously described in historical texts as jealous, vain, thin-skinned, stubborn, bilious, boastful, dishonest, and a consummate liar. He accomplished much in mathematics, but he is also known for having his son Daniel tossed out of the Académie des Sciences after Daniel won a prize for which Johann himself had competed, for attempting to steal both his brother’s and Leibniz’s ideas, and for plagiarizing Daniel’s book on hydrodynamics and then faking the publication date so that his book would appear to have been published first.
When he was asked to complete his late brother’s manuscript, he had recently relocated to Basel from the University of Groningen, in the Netherlands, obtaining a post not in mathematics but as a professor of Greek. Jakob had found this career change suspicious, especially since in his estimation Johann did not know Greek. What Jakob suspected, he wrote Leibniz, was that Johann had come to Basel to usurp Jakob’s position. And, indeed, upon Jakob’s death, Johann did obtain it.
Johann and Jakob had not gotten along for most of their adult lives. They would regularly trade insults in mathematics publications and in letters that, one mathematician wrote, “bristle with strong language that is usually reserved for horse thieves.”21 And so when the need arose to edit Jakob’s posthumous manuscript, the task fell further down the food chain, to Jakob’s nephew Nikolaus, the son of one of Jakob’s other brothers, also named Nikolaus. The younger Nikolaus was only eighteen at the time, but he had been one of Jakob’s pupils. Unfortunately he didn’t feel up to the task, possibly in part because he was aware of Leibniz’s opposition to his uncle’s ideas about applications of the theory. And so the manuscript lay dormant for eight years. The book was finally published in 1713 under the title Ars conjectandi, or The Art of Conjecture. Like Pascal’s Pensées, it is still in print.
Jakob Bernoulli had shown that through mathematical analysis one could learn how the inner hidden probabilities that underlie natural systems are reflected in the data those systems produce. As for the question that Bernoulli did not answer—the question of how to infer, from the data produced, the underlying probability of events—the answer would not come for several decades more.
CHAPTER 6
False Positives and Positive Fallacies
IN THE 1970S a psychology professor at Harvard had an odd-looking middle-aged student in his class. After the first few class meetings the student approached the professor to explain why he had enrolled in the class.1 In my experience teaching, though I have had some polite students come up to me to explain why they were dropping my course, I have never had a student feel the need to explain why he was taking it. That’s probably why I can get away with happily assuming that if asked, such a student would respond, “Because