Drunkard's Walk - Leonard Mlodinow [75]
By the 1830s most scientists had come to believe that every measurement is a composite, subject to a great number of sources of deviation and hence to the error law. The error law and the central limit theorem thus allowed for a new and deeper understanding of data and their relation to physical reality. In the ensuing century, scholars interested in human society also grasped these ideas and found to their surprise that the variation in human characteristics and behavior often displays the same pattern as the error in measurement. And so they sought to extend the application of the error law from physical science to a new science of human affairs.
CHAPTER 8
The Order in Chaos
IN THE MID-1960S, some ninety years old and in great need of money to live on, a Frenchwoman named Jeanne Calment made a deal with a forty-seven-year-old lawyer: she sold him her apartment for the price of a low monthly subsistence payment with the agreement that the payments would stop upon her death, at which point she would be carried out and he could move in.1 The lawyer must have known that Ms. Calment had already exceeded the French life expectancy by more than ten years. He may not have been aware of Bayes’s theory, however, nor known that the relevant issue was not whether she should be expected to die in minus ten years but that her life expectancy, given that she had already made it to ninety, was about six more years.2 Still, he had to feel comfortable believing that any woman who as a teenager had met Vincent van Gogh in her father’s shop would soon be joining van Gogh in the hereafter. (For the record, she found the artist “dirty, badly dressed, and disagreeable.”)
Ten years later the attorney had presumably found an alternative dwelling, for Jeanne Calment celebrated her 100th birthday in good health. And though her life expectancy was then about two years, she reached her 110th birthday still on the lawyer’s dime. By that point the attorney had turned sixty-seven. But it was another decade before the attorney’s long wait came to an end, and it wasn’t the end he expected. In 1995 the attorney himself died while Jeanne Calment lived on. Her day of reckoning finally came on August 4, 1997, at the age of 122. Her age at death exceeded the lawyer’s age at his death by forty-five years.
Individual life spans—and lives—are unpredictable, but when data are collected from groups and analyzed en masse, regular patterns emerge. Suppose you have driven accident-free for twenty years. Then one fateful afternoon while you’re on vacation in Quebec with your spouse and your in-laws, your mother-in-law yells, “Look out for that moose!” and you swerve into a warning sign that says essentially the same thing. To you the incident would feel like an odd and unique event. But as the need for the sign indicates, in an ensemble of thousands of drivers a certain percentage of drivers can be counted on to encounter a moose. In fact, a statistical ensemble of people acting randomly often displays behavior as consistent and predictable as a group of people pursuing conscious goals. Or as the philosopher Immanuel Kant wrote in 1784, “Each, according to his own inclination follows his own purpose, often in opposition to others; yet each individual and people, as if following some guiding thread, go toward a natural but to each of them unknown goal; all work toward furthering it, even if they would set little store by it if they did know it.”3
According to the Federal Highway Administration, for example, there are about 200 million drivers in the United States.4 And according to the National Highway Traffic Safety Administration, in one recent year those drivers drove a total of about 2.86 trillion miles.5 That’s about 14,300 miles per driver. Now suppose everyone in the country had decided it would be fun to hit that same total again the following year. Let’s compare two methods that could have been used to achieve that goal. In method 1 the government institutes a rationing