## Thursday, August 1, 2013

BOX 3–1 de Moivre, the Eccentric Stranger Who Invented the Normal Curve
The normal curve is central to statistics and is the foundation of most statistical theories and procedures. If any one person can be said to have discovered this fundamental of the field, it was Abraham de Moivre. He was a French Protestant who came to England at the age of 21 because of religious persecution in France, which in 1685 denied Protestants all their civil liberties. In England, de Moivre became a friend of Isaac Newton, who was supposed to have often answered questions by saying, “Ask Mr. de Moivre—he knows all that better than I do.” Yet because he was a foreigner, de Moivre was never able to rise to the same heights of fame as the British-born mathematicians who respected him so greatly.
Abraham de Moivre was mainly an expert on chance. In 1733, he wrote a “method of approximating the sum of the terms of the binomial expanded into a series.” His paper essentially described the normal curve. The description was only in the form of a law, however; de Moivre never actually drew the curve itself. In fact, he was not very interested in it.
Credit for discovering the normal curve is often given to Pierre Laplace, a Frenchman who stayed home; or Karl Friedrich Gauss, a German; or Thomas Simpson, an Englishman. All worked on the problem of the distribution of errors around a mean, even going so far as describing the curve or drawing approximations of it. But even without drawing it, de Moivre was the first to compute the areas under the normal curve at 1, 2, and 3 standard deviations, and Karl Pearson (discussed in Chapter 13, Box 13–1), a distinguished later statistician, felt strongly that de Moivre was the true discoverer of this important concept.
In England, de Moivre was highly esteemed as a man of letters as well as of numbers, being familiar with all the classics and able to recite whole scenes from his beloved Moliére’s Misanthropist. But for all his feelings for his native France, the French Academy elected him a foreign member of the Academy of Sciences just before his death. In England, he was ineligible for a university position because he was a foreigner there as well. He remained in poverty, unable even to marry. In his earlier years, he worked as a traveling teacher of mathematics. Later, he was famous for his daily sittings in Slaughter’s Coffee House in Long Acre, making himself available to gamblers and insurance underwriters (two professions equally uncertain and hazardous before statistics were refined), who paid him a small sum for figuring odds for them.
De Moivre’s unusual death generated several legends. He worked a great deal with infinite series, which always converge to a certain limit. One story has it that de Moivre began sleeping 15 more minutes each night until he was asleep all the time, then died. Another version claims that his work at the coffeehouse drove him to such despair that he simply went to sleep until he died. At any rate, in his 80s he could stay awake only four hours a day, although he was said to be as keenly intellectual in those hours as ever. Then his wakefulness was reduced to 1 hour, then none at all. At the age of 87, after eight days in bed, he failed to wake and was declared dead from “somnolence” (sleepiness).
Sources: Pearson (1978); Tankard (1984). (Statistics for Psychology, 5th ed., Aron, A., Aron, E.N., Coups, E.J., 2009)