Drunkard's Walk - Leonard Mlodinow [64]
Laplace’s political dexterity was fortunate for mathematics, for in the end his analysis was richer and more complete than Bayes’s. With the foundation provided by Laplace’s work, in the next chapter we shall leave the realm of probability and enter that of statistics. Their joining point is one of the most important curves in all of mathematics and science, the bell curve, otherwise known as the normal distribution. That, and the new theory of measurement that came with it, are the subjects of the following chapter.
CHAPTER 7
Measurement and the Law of Errors
ONE DAY not long ago my son Alexei came home and announced the grade on his most recent English essay. He had received a 93. Under normal circumstances I would have congratulated him on earning an A. And since it was a low A and I know him to be capable of better, I would have added that this grade was evidence that if he put in a little effort, he could score even higher next time. But these were not normal circumstances, and in this case I considered the grade of 93 to be a shocking underestimation of the quality of the essay. At this point you might think that the previous few sentences tell you more about me than about Alexei. If so, you’re right on target. In fact, the above episode is entirely about me, for it was I who wrote Alexei’s essay.
Okay, shame on me. In my defense I should point out that I would normally no sooner write Alexei’s essays than take a foot to the chin for him in his kung fu class. But Alexei had come to me for a critique of his work and as usual presented his request late on the night before the paper was due. I told him I’d get back to him. Proceeding to read it on the computer, I first made a couple of minor changes, nothing worth bothering to note. Then, being a relentless rewriter, I gradually found myself sucked in, rearranging this and rewriting that, and before I finished, not only had he fallen asleep, but I had made the essay my own. The next morning, sheepishly admitting that I had neglected to perform a “save as” on the original, I told him to just go ahead and turn in my version.
He handed me the graded paper with a few words of encouragement. “Not bad,” he told me. “A 93 is really more of an A- than an A, but it was late and I’m sure if you were more awake, you would have done better.” I was not happy. First of all, it is unpleasant when a fifteen-year-old says the very words to you that you have previously said to him, and nevertheless you find his words inane. But beyond that, how could my material—the work of a person whom my mother, at least, thinks of as a professional writer—not make the grade in a high school English class? Apparently I am not alone. Since then I have been told of another writer who had a similar experience, except his daughter received a B. Apparently the writer, with a PhD in English, writes well enough for Rolling Stone, Esquire, and The New York Times but not for English 101. Alexei tried to comfort me with another story: two of his friends, he said, once turned in identical essays. He thought that was stupid and they’d both be suspended, but not only did the overworked teacher not notice, she gave one of the essays a 90 (an A) and the other a 79 (a C). (Sounds odd unless, like me, you’ve had the experience of staying up all night grading a tall stack of papers with Star Trek reruns playing in the background to break the monotony.)
Numbers always seem to carry the weight of authority. The thinking, at least subliminally, goes like this: if a teacher awards grades on a 100-point scale, those tiny distinctions must really mean something. But if ten publishers could deem the manuscript for the