Drunkard's Walk - Leonard Mlodinow [54]
At first the happenings confused him. Then, as most of us would, he formed a mental model to reconcile the events with the way he believed the world behaves. The theory he came up with, however, was unlike anything most of us would devise: he was the subject of an elaborate secret scientific experiment. He believed the experiment was staged by a large group of conspirators led by the famous psychologist B. F. Skinner. He also believed that when it was over, he would become famous and perhaps be elected to a high public office. That, he said, was why he was taking the course. He wanted to learn how to test his hypothesis in light of the many instances of evidence he had accumulated.
A few months after the course had run its course, the student again called on the professor. The experiment was still in progress, he reported, and now he was suing his former employer, who had produced a psychiatrist willing to testify that he suffered from paranoia.
One of the paranoid delusions the former employer’s psychiatrist pointed to was the student’s alleged invention of a fictitious eighteenth-century minister. In particular, the psychiatrist scoffed at the student’s claim that this minister was an amateur mathematician who had created in his spare moments a bizarre theory of probability. The minister’s name, according to the student, was Thomas Bayes. His theory, the student asserted, described how to assess the chances that some event would occur if some other event also occurred. What are the chances that a particular student would be the subject of a vast secret conspiracy of experimental psychologists? Admittedly not huge. But what if one’s wife speaks one’s thoughts before one can utter them and co-workers foretell your professional fate over drinks in casual conversation? The student claimed that Bayes’s theory showed how you should alter your initial estimation in light of that new evidence. And he presented the court with a mumbo jumbo of formulas and calculations regarding his hypothesis, concluding that the additional evidence meant that the probability was 999,999 in 1 million that he was right about the conspiracy. The enemy psychiatrist claimed that this mathematician-minister and his theory were figments of the student’s schizophrenic imagination.
The student asked the professor to help him refute that claim. The professor agreed. He had good reason, for Thomas Bayes, born in London in 1701, really was a minister, with a parish at Tunbridge Wells. He died in 1761 and was buried in a park in London called Bunhill Fields, in the same grave as his father, Joshua, also a minister. And he indeed did invent a theory of “conditional probability” to show how the theory of probability can be extended from independent events to events whose outcomes are connected. For example, the probability that a randomly chosen person is mentally ill and the probability that a randomly chosen person believes his spouse can read his mind are both very low, but the probability that a person is mentally ill if he believes his spouse can read his mind is much higher, as is the probability that a person believes his spouse can read his mind if he is mentally ill. How are all these probabilities related? That question is the subject of conditional probability.
The professor supplied a deposition explaining Bayes’s existence and his theory, though not supporting the specific and dubious calculations that his former student claimed proved his sanity. The sad part of this story is not just the middle-aged schizophrenic himself, but the medical and legal team on the other side.