In almost all Western European languages, number words do not follow a regular pattern. In English we say twenty-one, twenty-two, twenty-three. But we don’t say tenty-one, tenty-two, tenty-three—we say eleven, twelve, thirteen. Eleven and twelve are unique constructions and even though thirteen is a combination of three and ten, the three part comes before the ten part—unlike twenty-three, in which the three part comes after the twenty part. Between ten and twenty, English is a mess.
In Chinese, Japanese and Korean, however, number words do follow a regular pattern. Eleven is written ten one. Twelve is ten two, and so on with ten three, ten four up to ten nine for 19. Twenty is two ten and 21 is two ten one. You pronounce numbers in all cases just as you see them written down. So what? Well, it does make a difference at a young age. Experiments have repeatedly shown that Asian children find it easier to learn to count than Europeans. In one study with Chinese and American four-and five-year-olds, the two nationalities performed similarly learning to count to 12, but the Chinese were about a year ahead with higher numbers. A regular system also makes arithmetic clearer to understand. A simple sum like 25 plus 32 when expressed as two ten five plus three ten two is one step closer to the answer already: five ten seven.
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We are also handicapped by how long it takes us to say numbers. In The Number Sense, Stanislas Dehaene writes down the list 4, 8, 5, 3, 9, 7, 6 and asks us to spend 20 seconds memorizing it. English speakers have a 50 percent chance of remembering the seven numbers correctly. By contrast, Mandarin Chinese speakers can memorize nine digits in this way. Dehaene says that this is because the number of digits we can hold in our heads at any one time is determined by how many we can say in a two-second loop. The Chinese words for one to nine are all concise single syllables: yi, er, san, si, wu, liu, qi, ba, jiu. They can be uttered in less than a quarter of a second each, so in a two-second span, a Chinese speaker can rattle through nine of them. English number words, by contrast, take just under a third of a second each to say (thanks to “seven,” with two syllables, and the extended syllable “three”), and so our limit in two seconds is seven. The record, however, goes to the Cantonese, whose digits are spoken with 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 Japanese use the more sonorous combination in ichi. 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 practice their kuku, I was struck by how much it sounded like a rap—the phrases were syncopated and said with great animation. 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 up-tempo rhythm because this 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 poetry of the kuku seems to embed the times tables in Japanese brains. Japanese adults told me that they know, for example, that seven times seven is forty-nine not because they remember the math but because the music of “seven seven forty nine” sounds right.
~~Here’s Looking at Euclid -by- Alex Bellos
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