Alex's Adventures in Numberland - Alex Bellos [152]
But Galton’s principal passion was measuring. He built an ‘anthropometric laboratory’ – a drop-in centre in London, where members of the public could come to have their height, weight, strength of grip, swiftness of blow, eyesight and other physical attributes measured by him. The lab compiled details on more than 10,000 people, and Galton achieved such fame that Prime Minister William Gladstone even popped by to have his head measured. (‘It was a beautifully shaped head, though low,’ Galton said.) In fact, Galton was such a compulsive measurer that even when he had up very ng obvious to measure he would find something to satisfy his craving. In an article in Nature in 1885 he wrote that while present at a tedious meeting he had begun to measure the frequency of fidgets made by his colleagues. He suggested that scientists should henceforth take advantage of boring meetings so that ‘they may acquire the new art of giving numerical expression to the amount of boredom expressed by [an] audience’.
Galton’s research corroborated Quételet’s in that it showed that the variation in human populations was rigidly determined. He too saw the bell curve everywhere. In fact, the frequency of the appearance of the bell curve led Galton to pioneer the word ‘normal’ as the appropriate name for the distribution. The circumference of a human head and the size of the brain all produced bell curves, though Galton was especially interested in non-physical attributes such as intelligence. IQ tests hadn’t been invented at the time, so Galton looked for other measures of intelligence. He found them in the results of the admission exams to the Royal Military Academy at Sandhurst. The exam scores, he discovered, also conformed to the bell curve. It filled him with a sense of awe. ‘I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the [bell curve],’ he wrote. ‘The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason.’
Galton invented a beautifully simple machine that explains the mathematics behind his cherished curve, and he called it the quincunx. The word’s original meaning is the pattern of five dots on a die, and the contraption is a type of pinball machine in which each horizontal line of pins is offset by half a position from the line above. A ball is dropped into the top of the quincunx, and then it bounces between the pins until it falls out the bottom into a rack of columns. After many balls have been dropped in, the shape they make in the columns where they have naturally fallen resembles a bell curve.
The quincunx.
Using probability, we can understand what is going on. First, imagine a quincunx with just one pin and let us say that when a ball hits the pin the outcome is random, with a 50 percent chance that it bounces to the left and a 50 percent chance of it bouncing to the right. In other words, it has a probability of of ending up one place to the left and a probability of of being one place to the right.
Now, let’s add a second row of pins. The ball will either fall left and then left, which I will call LL, or LR or RL or RR. Since moving left and then right is equivalent to staying in the same position, the L and R together cancel each other out (as does the R and L together), so there is now of a chance the ball will end up one place to the left, chance it will be in the middle and it will be to the right.
Repeating this for a third row