Alex's Adventures in Numberland - Alex Bellos [18]
Some cultures count using more of their bodies than just fingers and toes. At the end of the nineteenth century an expedition of British anthropologists reached the islands of the Torres Strait, the stretch of water that separates Australia from Papua New Guinea. There they discovered a community that started with ‘right hand little finger’ for 1, ‘right hand ring finger’ for 2 and this continued through the fingers to ‘right wrist’ for 6, ‘right elbow’ for 7 and on through the shoulders, sternum, left arm and hand, feet and legs, ending at ‘right foot little toe’ for 33. Subsequent expeditions and research uncovered many communities in the region with similar ‘body-tally’ systems.
In this Chinese system, each finger has nine points, representing the digits 1 to 9 for each order of magnitude, so the right hand can express any number up to 105– 1 when the other hand touches the relevant points. Swapping hands, the numbers continue to 1010– 1. A ‘zero’ point is not needed on any finger, since when there are no values relating to that finger it is simply left alone by the other hand.
Perhaps the most curious is the Yupno, the only Papuan people for whom each individual owns a short melody that belongs to them like a name, or signature tune. They also have a counting system that enumerates the nostrils, eyes, nipples, belly button and climaxes in 31, for ‘left testicle’, 32, ‘right testicle’ and 33, ‘penis’. While one can ponder the significance of 33 in the three great monotheistic religions (the age when Christ died, the length of King David’s reign and the number of individual beads on a Muslim prayer string), what is particularly intriguing about the Yupno’s phallic number is that they are actually very coy about it. They refer to the number 33 euphemistically in phrases such as ‘the man thing’. Researchers were unable to discover whether women use the same terms, since they are not supposed to know the number system and refused to answer questions. The upper limit in Yupno is 34, which they call ‘one dead man’.
Base-ten systems have been used in the West for thousands of years. Despite their harmoniousness with our bodies, however, many have questioned whether they are the most sensible base for counting. In fact, some have argued that their physical provenance makes them an actively bad choice. King Charles XII of Sweden dismissed base ten as the product of ‘rustic and simple people’ fumbling around with their fingers. In modern Scandinavia, he believed, a base was needed ‘of more convenience and greater use’. So, in 1716, he ordered the scientist Emanuel Swedenborg to devise a new counting system with a base of 64. He arrived at this formidable number due to the fact that it was derived from a cube, 4 × 4 × 4. Charles, who fought – and lost – the Great Northern War, believed that military calculations, such as measuring the volume of a box of gunpowder, would be made easier with a cube number as a base. Yet his brainwave, wrote Voltaire, ‘could prove only that he loved the extraordinary and the difficult’. Base 64 requires 64 unique names (and symbols) for numbers – an absurdly inconvenient system. Swedenborg therefore simplified the system to base eight and came up with a new notation in which 0, 1, 2, 3, 4, 5, 6, 7 were renamed o, l, s, n, m, t, f, u. In this system, therefore l + l = s, and m × m = so. (The words for the new numbers, however, were rather wonderful. The powers of 8, which would have been written lo, loo, looo, loooo and