Alex's Adventures in Numberland - Alex Bellos [25]
‘Freedom is the freedom to say two plus two equals four,’ wrote Winston Smith, the protagonist of George Orwell’s Nineteen Eighty-Four. Orwell was making a comment not only about freedom of speech in the Soviet Union, but also about mathematics. Two plus two is always four. No one can tell you it isn’t. Mathematical truths cannot be influenced by culture or ideology.
On the other hand, our approach to mathematics is very much influenced by culture. The selection of base ten, for example, was not premised on mathematical reasons but on physiological ones, the number of our fingers and toes. Language also shapes mathematical understanding in surprising ways. In the West, for example, we are held back by the words we have chosen to express numbers.
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, when 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 nineteen. Twenty is two ten, and twenty-one 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 when 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 such as twenty-five plus thirty-two when expressed as two ten five plus three ten two is one step closer to the answer already: five ten seven.
Not all European languages are irregular. Welsh, for example, is just like Chinese. Eleven in Welsh is un deg un (one ten one); twelve is un deg dau (one ten two), and so on. Ann Dowker and Delyth Lloyd at the University of Oxford tested the maths abilities of Welsh-and English-speaking kids from the same Welsh village. While Asian children may be better than American children because of many cultural factors, such as hours spent practising or attitudes towards maths, cultural factors can be eliminated if the children are all living in the same place. Dowker and Lloyd concluded that while general arithmetic performance was more or less equal between Welsh-and English-speakers, the Welsh-speakers did demonstrate better mathematical skills in specific areas – such as reading, comparing and manipulating two-digit numbers.
German is even more irregular than English. In German, twenty-one is einundzwanzig, or one-and-twenty, twenty-two is zweiundzwanzig, or two-and-twenty, and this continues with the unit value preceding the tens value all the way up to 99. This means that when a German says a number over 100, the digits are not pronounced in a consecutive order: three hundred and forty-five is dreihundertfünfundvierzig, or three-hundred-five-and-forty, which lists the numbers in the higgledy-piggledy form 3-5-4. Such is the level of concern in Germany that this makes numbers more confusing than they have to be, that a campaign group Zwanzigeins (Twenty-one) has been set up to push for a change to a more regular system.
And it’s not just the positioning of number words, or their irregular forms between eleven and nineteen, that puts the speakers of the main Western European languages