Half a century before Poincaré saw the bell curve in bread, another mathematician was seeing it wherever he looked. Adolphe Quételet has good claim to being the world’s most influential Belgian. (The fact that this is not a competitive field in no way diminishes his achievements.) A geometer and astronomer by training, he soon became sidetracked by a fascination with data—more specifically, with finding patterns in figures. In one of his early projects, Quételet examined French national crime statistics, which the government started publishing in 1825. Quételet noticed that the number of murders was pretty constant every year. Even the proportion of different types of murder weapon—whether it was perpetrated by a gun, a sword, a knife, a fist, and so on—stayed roughly the same. Nowadays this observation is unremarkable—indeed, the way we run our public institutions relies on an appreciation of, for example, crime rates, exam pass rates and accident rates, which we expect to be comparable every year. Yet Quételet was the first person to notice the quite amazing regularity of social phenomena when populations are taken as a whole. In any one year it was impossible to tell who might become a murderer. Yet in any one year it was possible to predict fairly accurately how many murders would occur. Quételet was troubled by the deep questions about personal responsibility this pattern raised and, by extension, about the ethics of punishment. If society was like a machine that produced a regular number of murderers, didn’t this indicate that murder was the fault of society and not the individual?
Quételet’s ideas transformed the use of the word statistics, whose original meaning had little to do with numbers. The word was used to describe general facts about the state; as in the type of information required by statesmen. Quételet turned statistics into a much wider discipline, one that was less about statecraft and more about the mathematics of collective behaviour. He could not have done this without advances in probability theory, which provided techniques to analyse the randomness in data. In Brussels in 1853 Quételet hosted the first international conference on statistics.
Quételet’s insights on collective behaviour reverberated in other sciences. If by looking at data from human populations you could detect reliable patterns, then it was only a small leap to realize that populations of, for example, atoms also behaved with predictable regularities. James Clerk Maxwell and Ludwig Boltzmann were indebted to Quételet’s statistical thinking when they came up with the kinetic theory of gases, which explains that the pressure of a gas is determined by the collisions of its molecules travelling randomly at different velocities. Though the velocity of any individual molecule cannot be known, the molecules overall behave in a predictable way. The origin of the kinetic theory of gases is an interesting exception to the general rule that developments in the social sciences are the result of advances in the natural sciences. In this case, knowledge flowed in the other direction.
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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.
