Confidence Counts
The Mathematical Brain by Brian Butterworth
Macmillan, 446pp, £20: Rating: 4/5Was Einstein's brain physically different, or did he just exercise it well? One man who has thought about it more than most is Brian Butterworth, who claims in a fascinating new book that there is indeed a physical sector of the brain, the number module, which is part of our genetic inheritance. Butterworth argues that the evidence for some sort of awareness of numbers, some sort of ability to answer the question: "how many?" goes back in human prehistory to well before the first art or the first written representations of language. The evidence also exists in the responses of newborn babies.
Thrust a white card with two black dots on it in front of a day-old baby. Replace the card with one on which the two dots are more widely spaced and the baby shows some interest, but soon gets bored. When a card appears with three dots, the baby perks up. Not because it's a different card, but because the most important factor in renewing the baby's interest is the change in the number of dots.
Nor is the phenomenon limited to humans: a pride of lionesses in the Serengeti National Park show an ability to count the number of intruders - to calculate whether their own group is larger or smaller, and plan accordingly whether to fight or run. Butterworth has also looked at people incapacitated by strokes or by degenerative brain diseases. People like Signor Strozzi, a market trader in northern Italy who, after a stroke, was unable to add two and two. Or Frau Huber, a farmer from Austria, who recovered from an operation to remove a brain tumour from her left parietal lobe - where Butterworth locates the number module - capable of talking and doing her times tables, but unable to add up. She was unable to make sense of numbers.
So is this yet another attempt to explain human difference in terms of the genetic coding which we receive? Not at all. "Everyone counts" is the central, democratic and enthusiastically-delivered message. There is good evidence that almost all of us are able, from birth, to take in at a glance if there are one, two, three or four in a collection of objects. Even for adults, it takes longer to establish the number of objects when there are more than four. This awareness of number is the foundation-stone from which subsequent mathematical ability is built. So why are some people more gifted than others? Why are some countries better at fostering numeracy than others? The answer, Butterworth argues, lies not in nature but in nurture. Just as Einstein's brain has been found to have unusually densely packed cells in the left parietal lobe, so musicians have been shown to have a bigger and more elaborately connected motor cortex - the region of the brain that controls hand and finger movements - than non-musicians. This is not a sign that these people are predisposed towards music, but simply that practice makes perfect.
The more we find out about the brain, the more we discover its flexibility. It directs more cells towards those parts that are in most use. When pianists stop practising, their motor cortices go on a diet. So does this mean we should be force-feeding maths to our children? Butterworth gives short shrift to the modern fad for rote learning, arguing that what matters is not whether children learn their tables, or whether they use calculators instead, but whether they understand, and enjoy, what they are doing. On the one hand, he says, there is a vicious circle: "Lack of understanding leads to confusion, confusion to anxiety, avoidance, and no further learning." On the other, a virtuous circle, where increased confidence leads to the inclination to practise more. Einstein starts here.
John Yandell
© Guardian Media Group plc. 1999
Numbers, their human psychology and cultural history. Restores to numerals - those Indo-Islamic signs the medieval west adopted to record transactions computed on the abacus - a depth of character and long back-stories. Four, eight and nine have dark meaningful pasts, 60 acquired in Babylon its power over the division of time and angles of space and thus over the dimensions of the known universe; the total sum of the Yupno of Papua New Guinea, who figure by naming body parts in sequence, is 33, signifying the penis (Yupno woman don't count). Mega.
Vera Rule
© Guardian Media Group plc. 2000
