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By Root 774 0

challenges, mathematicians, social scientists, and biologists have embarked since the sixteenth century on serious attempts to tackle uncertainties methodically. Following the establishment of the field of statistical mechanics, and faced with the realization that the very foundations of physics—in the form of quantum mechanics—are based on uncertainty, physicists of the twentieth and twenty-first centuries have enthusiastically joined the battle. The weapon researchers use to combat the lack of precise determinism is the ability to calculate the odds of a particular outcome. Short of being capable of actually predicting a result, computing the likelihood of different consequences is the next best thing. The tools that have been fashioned to improve on mere guesses and speculations—statistics and probability theory—provide the underpinning of not just much of modern science, but also a wide range of social activities, from economics to sports.

We all use probabilities and statistics in almost every decision we make, sometimes subconsciously. For instance, you probably don’t know that the number of fatalities from automobile accidents in the U.S. was 42,636 in 2004. However, had that number been, say, 3 million, I’m sure you would have known about it. Furthermore, this knowledge would have probably caused you to think twice before getting into the car in the morning. Why do these precise data on road fatalities give us some confidence in our decision to drive? As we shall see shortly, a key ingredient to their reliability is the fact that they are based on very large numbers. The number of fatalities in Frio Town, Texas, with a population of forty-nine in 1969 would hardly have been equally convincing. Probability and statistics are among the most important arrows for the bows of economists, political consultants, geneticists, insurance companies, and anybody trying to distill meaningful conclusions from vast amounts of data. When we talk about mathematics permeating even disciplines that were not originally under the umbrella of the exact sciences, it is often through the windows opened by probability theory and statistics. How did these fruitful fields emerge?

Statistics—a term derived from the Italian stato (state) and statista (a person dealing with state affairs)—first referred to the simple collection of facts by government officials. The first important work on statistics in the modern sense was carried out by an unlikely researcher—a shopkeeper in seventeenth century London. John Graunt (1620–74) was trained to sell buttons, needles, and drapes. Since his job afforded him a considerable amount of free time, Graunt studied Latin and French on his own and started to take interest in the Bills of Mortality—weekly numbers of deaths parish by parish—that had been published in London since 1604. The process of issuing these reports was established mainly in order to provide an early warning signal for devastating epidemics. Using those crude numbers, Graunt started to make interesting observations that he eventually published in a small, eighty-five-page book entitled Natural and Political Observations Mentioned in a Following Index, and Made upon the Bills of Mortality. Figure 32 presents an example of a table from Graunt’s book, where no fewer than sixty-three diseases and casualties were listed alphabetically. In a dedication to the president of the Royal Society, Graunt points out that since his work concerns “the Air, Countries, Seasons, Fruitfulness, Health, Diseases, Longevity, and the proportion between the Sex and Ages of Mankind,” it is really a treatise in natural history. Indeed, Graunt did much more than merely collect and present the data. By examining, for instance, the average numbers of christenings and burials for males and females in London and in the country parish Romsey in Hampshire, he demonstrated for the first time the stability of the sex ratio at birth. Specifically, he found that in London there were thirteen females born for every fourteen males and in Romsey fifteen females for sixteen males.