Alex's Adventures in Numberland - Alex Bellos [151]
The most common pattern that Quételet found in all of his research was the bell curve. It was ubiquitous when studying data about human populations. Sets of data in those days were harder to come by than they are now, so Quételet scoured the world for them with the doggedness of a professional collector. For example, he came across a study published in the 1814 Edinburgh Medical Journal containing chest measurements of 5738 Scottish soldiers. Quételet drew up a graph of the numbers and showed that the distribution of chest sizes traced a bell curve with a mean of about 40 inches. From other sets of data he showed that the heights of men and women also plot a bell curve. To this day, the retail industry relies on Quételet’s discoveries. The reason why clothes shops stock more mediums than they do smalls and larges is because the distribution of human sizes corresponds roughly to the bell curve. The most recent data on the shoe sizes of British adults, for example, throws up a very familiar shape:
British shoe sizes.
Quételet died in 1874. A decade later, this side of the Channel, a 60-year-old man with a bald pate and fine Victorian whiskers could frequently be seen on the streets of Britain gawping at women and rummaging around in his pocket. This was Francis Galton, the eminent scientist, conducting fieldwork. He was measuring female attractiveness. In order to discreetly register his opinion on passing women he would prick a needle in his pocket into a cross-shaped piece of paper, to indicate whether she was ‘attractive’, ‘indifferent’ or ‘repellent’. After completing his survey he compiled a map of the country based on looks. The highest-rated city was London and the lowest-rated was Aberdeen.
In ‘Cutting a Round Cake on Scientific Principles’ Galton marked intended cuts as broken straight lines, and cuts as solid lines. This method minimizes exposing the insides of the cake to become dry, which would happen if one cuts a slice in the traditional (and, he concludes, ‘very faulty’) way. In the second and third stages the cake is to be held together with an elastic band.
Galton was probably the only man in nineteenth-century Europe who was even more obsessed with gathering data than Quételet was. As a young scientist, Galton took the temperature of his daily pot of tea, together with such information as the volume of boiling water used and how delicious it tasted. His aim was to establish how to make the perfect cuppa. (He reached no conclusions.) In fact, an interest in the mathematics of afternoon tea was a lifelong passion. When he was an old man he sent the diagram above to the journal Nature, which shows his suggestion of the best way to cut a tea-cake in order to keep it as fresh as possible.
Oh, and since this is a book with the word ‘number’ in its title, it would be unsporting for me at this juncture not to mention Galton’s ‘number forms’ – even if they have little to do with the subject of this chapter. Galton was fascinated that a substantial number of people – he estimated 5 percent – automatically and involuntarily envisaged numbers as mental maps. He coined the term number form to describe these maps, and wrote that they have a ‘precisely defined and constant position’ and are such that individuals cannot think of a number ‘without referring to its own particular habitat in their mental field of view’. What is especially interesting about number forms is that they generally show up very peculiar patterns. Instead of a straight line, which might be expected, they often involve rather peculiar twists and turns.
Four examples of Galton’s ‘number forms’: curious spatial representations of numbers.
Number forms have the whiff of Victorian freakishness, perhaps evidence of repressed emotions or overindulgence in opiates. Yet a century later they are researched in academia, recognized as a type of synaesthesia, which is the neurological phenomenon that occurs