Free Alex’s Adventures in Numberland by Alex Bellos Page A

even more brevity. They can remember ten of them in a two-second period.
    While Western languages seem to be working against any mathematical ease of understanding, in Japan language is recruited as an ally. Words and phrases are modified in order to make their multiplication tables, called kuku , easier to learn. The tradition of these tables originated in ancient China, spreading to Japan around the eighth century. Ku in Japanese is nine, and the name comes from the fact that the tables used to begin at the end, with 9×9 = 81. Around 400 years ago they were changed so that the kuku now begins ‘one one is one’.
    The words of the kuku are simply:
    One one is one
    One two is two
    One three is three…
     
    This carries on to ‘One nine is nine’, and then the twos begin with:
    Two one is two
    Two two is four
     
    And so on to nine nine is eighty-one.
    So far, this seems very similar to the plain British style of reciting the times tables. In the kuku , however, whenever there are two ways to pronounce a word, the way that flows better is used. For example, the word for one can be in or ichi , and rather than starting the kuku with either in in or ichi ichi , the more sonorous combination in ichi is used. The word for eight is ha . Eight eights should be ha ha . Yet the line in the kuku for 8×8 is happa since it rolls quicker off the tongue. The result is that the kuku is rather like a piece of poetry, or a nursery rhyme. When I visited an elementary school in Tokyo and watched a class of seven-and eight-year-olds practise their kuku , I was struck by how much it sounded like a rap – the phrases were syncopated and jolly. Certainly it bore no relation to how I remember reciting my times tables at school, which was with the metronomic delivery of a steam train going up a hill. Makiko Kondo, the teacher, said that she teaches her pupils kuku with an uptempo rhythm because it makes it fun to learn. ‘First we get them to recite it, and only some time later do they come to understand the real meaning.’ The of the kuku seems to embed the times tables in Japanese brains. Adults told me that they know, for example, that seven times seven is 49 not because they remember the maths but because the music of ‘seven seven forty-nine’ sounds right.
    While the irregularities of Western number words may be unfortunate for budding arithmeticians, they are of extreme interest to mathematical historians. The French for eighty is quatre-vingts , or four-twenties, indicating that ancestors of the French once used a base-20 system. It has also been suggested that the reason why the words for ‘nine’ and ‘new’ are identical or similar in many Indo-European languages, including French ( neuf, neuf ), Spanish ( nueve, nuevo ), German ( neun, neu ) and Norwegian ( ni, ny ) is a legacy of a long-forgotten base-eight system, where the ninth unit would be the first of a new set of eight. (Excluding thumbs, we have eight fingers, which could be how such a base developed. Or possibly from counting the gaps between the fingers.) Number words are also a reminder of how close we are to the numberless tribes of the Amazon and Australia. In English, thrice can mean both three times and many times; in French, trois is three and très is very: shadows, perhaps, of our own ‘one, two, many’ past.
     
     
    Whereas certain aspects of number – such as the base, the style of numeral or the form of the words used – have differed widely between cultures, the early civilizations were surprisingly unified in the mechanics of how they counted and calculated. The general method they used is called ‘place value’ and is the principle by which different positions are used to represent different orders of number. Let’s consider what this means in the context of shepherds in medieval Lincolnshire. As I wrote earlier, they had 20 numbers from yan to piggot . Once a shepherd counted 20 sheep, he put a pebble aside and started counting from yan to