Alex's Adventures in Numberland - Alex Bellos [158]
Then something else occurred to me. What about the ambient temperature? I had started my experiment at the beginning of spring. It had ended at the beginning of summer, when the weather was significantly hotter. I looked at the figures and saw that my baguette weights were lighter on the whole towards the end of the project. The summer heat, I assumed, was drying them out faster. Again, this variation could have had the effect of stretching the curve leftwards.
My experiment may have shown that baguette weights approximated a slightly distorted bell curve, yet what I had really learned was that measurement is never so simple. The normal distribution is a theoretical ideal, and one cannot assume that all results will conform to it. I wondered about Henri Poincaré. When he measured his bread did he eliminate bias due to the Parisian weather, or the time of day of his measurements? Perhaps he had not demonstrated that he was being sold a 950g loaf instead of a 1kg loaf at all, but had instead proved that from baking to measuring, a 1kg loaf reduces in weight by 50g.
The history of the bell curve, in fact, is a wonderful parable about the curious kinship between pure and applied scientists. Poincaré once received a letter from the French physicist Gabriel Lippmann, who brilliantly summed up why the normal distribution was so widely exalted: ‘Everybody believes in the [bell curve]: the experimenters because they think it can be proved by mathematics; and the mathematicians because they believe it has been established by observation.’ In science, as in so many other spheres, we often choose to see what serves our interests.
Francis Galton devoted himself to science and exploration in the way that only a man in possession of a large fortune can do. His early adulthood was spent leading expeditions to barely known parts of Africa, which brought him considerable fame. A masterful dexterity with scientific instruments enabled him, on one occasion, to measure the figure of a particularly buxom Hottentot by standing at a distance and using his sextant. This incident, it seems, was indicative of a desire to keep women at arm’s length. When a tribal chief later presented him with a young woman smeared in butter and red ochre in preparation for sex – Galton declined the offer, concerned she would smudge his white linen suit.
Eugenics was Galton’s most infamous scientific legacy, yet it was not his most enduring innovation. He was the first person to use questionnaires as a method of psychological testing. He devised a classification system for fingerprints, still in use today, which led to their adoption as a tool in police investigations. And he thought up a way of illustrating the weather, which when it appeared in The Times in 1875 was the first public weather map to be published.
That same year, Galton decided to recruit some of his friends for an experiment with sweet peas. He distributed seeds among seven of them, asking them to plant the seeds and return the offspring. Galton measured the baby seeds and compared their diameters to those of their parents. He noticed a phenomenon that initially seems counter-intuitive: the large seeds tended to produce smaller offspring, and the small seeds tended to produce larger offspring. A decade later he analysed data from his anthropometric laboratory and recognized the same pattern with human heights. After measuring 205 pairs of parents and their 928 adult children, he saw that exceptionally tall parents had kids who were generally shorter than they were, while exceptionally short parents had children who were generally taller than their parents.
After reflecting upon this, we can understand why it must be the case. If very tall parents always produced even taller children, and if very short parents always produced even shorter ones, we would by now have turned into a race of giants