Try holding up your fingers to represent the number three. The result is more informative than you might expect, as Brian Butterworth demonstrates in "The Mathematical Brain" (Papermac, 446 pages, published in US as "What Counts", Free Press). If you flourished your index, middle and ring fingers, he states, you are from Northern Europe or one of its former colonial outposts; if instead you raised your thumb, index and middle fingers, then you hail from the Mediterranean.
This simple test shows that cultural difference plays an important role in the ways people formulate numbers. So is numeracy solely a learnt skill? Certainly not, argues Butterworth, who is a neuropsychologist: his invigorating book fleshes out an idea that number knowledge is innate and universal, a basic capability to be ranked alongside seeing and feeling.
According to his hypothesis, we are born with a mathematical toolkit genetically hardwired into our brains, which Butterworth calls the Number Module. Its operation is automatic, enabling us "to categorize the world in terms of numerosities - the number of things in a collection." A baby, for instance, will have no idea of what pineapples are, but should be able to identify that there are two of them. More advanced abilities, from puzzling over restaurant bills to solving Fermat's last theorem, are built onto this starting-point, and the scale of their development depends mainly on cultural factors.
Butterworth sets out his case by first exploring the origins of number perception. It is a dazzling tour, stretching back to prehistoric times, in which he elucidates the etymology of number words, the emergence of Arabic numerals and the use of body-parts as counting aids. Non-linguistic methods of keeping score are embedded in the terms many people use to describe numbers: indeed, "score" is one such example, as is "digit".
In subsequent steps, he attempts to isolate the part of the brain in which the Number Module might reside. This involves work with individuals who suffer from forms of number-blindness: a stroke sufferer, for example, who could only count to four. Similar examples of localised brain damage allow him to isolate a particular lobe, which in turn leads him to discuss why some people loathe maths and others love it. Forcing blank-eyed children to learn multiplication tables by rote, it turns out, is not the best way to stimulate further interest in the world of numbers. Butterworth's book is itself the perfect panacea for anyone to whom maths is a distant or unpleasant memory. Despite its complexities, he handles his subject matter with great deftness and good humour, while his argument sweeps in epic style from mathematical habits around the globe to the inner working of the brain's hemispheres.
Ludovic Hunter-Tilney
© The Financial Times, 2000
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