A rchive Date
[ 20-02-2005 ]
Category
[ International Relations ]
sub-Categoy
[ Education ]
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['I met Calculus and it was magic'
When the brains for maths were handed out I was not at the back of the queue; I wasn't even in it. Five years of grammar school tuiton resulted in a miserable scrape through O-level maths and to this day I remain clueless about such things as axioms, commutative law and symmetry paths.
So it was with some anxiety that I went off to interview an eminent professor about his new book The Maths Gene. The book has a helpful subtitle Why Everyone Has It But Most People Don't Use It, and the author claims that mathematicians have a key secret that enables them to do maths with apparent ease. After struggling through it, I have to say this "key secret" still eludes me but mathematicians come out as a uniformly dotty lot. One of the leading mathematical brains of the 20th century, Norbert Wiener, went home one evening from the Massachusetts Institute of Technology to the house out of which his family had just moved. He asked a little girl standing outside if she knew where the previous occupants had gone.
"Yes, daddy," she replied. "Mummy sent me to fetch you."
Dr Keith Devlin, senior researcher at the Center for the Study of Language and Information at Stanford University and Dean of the School of Science at St Mary's College, California looks relatively sane. He seems to know where his family lives (the Oakland Hills above San Francisco bay) and wears his hair in a fetching swept-back 50s rocker style.
Dr Devlin is 53 and, thankfully, is not Californian or we really would be speaking different languages. He is from Hull and has retained his accent, although based for 15 years in California where he has tripled his salary. He tells me how at 15, he was turned on to maths, having previously been one of the last in his class to learn his times table.
"In the early Sixties everyone was science mad. I wanted to be a nuclear scientist and save the world. I got into physics, which gave me a motive to do maths. Then," he says, with reverence, "I met Calculus. It was magic."
I've never met this chap Calculus. We tried a blind date once but failed to recognise each other. So how can Devlin polish up my maths?
"There's not an easy answer to that," he says. "The key is to create a reality about maths. You can go through the motions of dealing with symbols but it will be meaningless."
I am looking a bit as I used to during school maths lessons - fidgety, puzzled - so Devlin tries an analogy. "If music were taught using musical notation but never by playing music, the rules would make no sense.
"A mathematician appreciates maths as if it were a soap opera. If you drew a chart showing the complexity of relationships in a soap show, it would be much more complex than maths. The trick in maths is to make those abstract things real. If fantasy fiction such as The Hobbit is level 3 of abstraction, maths is one step beyond."
He cites Brazilian street boys who were recorded doing amazing feats of maths while selling goods from their stalls. When asked to do the calculations on paper they did much worse. "It is the same when cooks are asked to scale down the quantities in recipes. In context, they score 98 per cent; using just numbers, they score only 35 to 50 per cent."
His argument is that the same features of the brain which enable us to use language facilitate maths. He says the main activity that prepared the human brain to do maths is keeping track of interpersonal relationships in complex societies.
Number sense is innate. Experiments have shown that babies only a few days old can discriminate between two and three objects. Animals can also differentiate numerically. In one experiment Serengeti lions were played tapes of roaring lions. If the opposing team had more members than their group, they retreated, otherwise they stood their ground.
"Children of some nationalities have an edge. In Chinese and Japanese, words are much more closely tied to numbers." In these tongues 11 becomes ten-one and 21 is two-ten-one. At four years old the average Chinese child can count to 40, while 15 is the norm for a British child.
His theory is that we all have the potential to do well at least at GCSE-level maths. This would be made much easier by one-to-one coaching: "Once you miss something, you'll never get on." Berkeley College PhD students achieved phenomenal results working closely with underprivileged children in an area of California that had formerly achieved low passes in maths.
Maths also needs to be fun. Devlin made a $4 million TV series for the US, Life by the Numbers (which the BBC has declined to buy). In it he shows how maths is used in the real world, for example, to make digital effects in movies, or to calculate the minute gradations of performances needed to win a gold medal at the Olympic Games.
The embryonic mathematician must not only want to do maths, but must also enter a level of consciousness unknown to other thinkers. "When we have visitors my wife, Jan, will sometimes shake me because I drift off into the problem I'm trying to solve and it looks rude."
Once you get past the basic stages of maths, it becomes easier, says Devlin, and less like what we associate with the subject. He explains how Euclid proved that prime numbers go on into infinity. It seems to have as much to do with philosophy as maths.
Remarkably when Devlin explained it, I could understand: it was pure logic. "If you understand that, you could at least do A level. Many of my undergraduate students just don't get it."
The book is for the "thinking person" and Devlin is working on a more basic guide. He thinks that there are "more PhD mathematicians in the world" than are needed. But there are not enough people with a good general level of mathematical ability.
Yet he admits that he cannot balance his chequebook and says that "when I grade exams my secretary checks my addition".
Non-mathematicians, he says, spend their time in the valleys. Once you start climbing the mountains, it grows easier, "if you can cope with the rarefied atmosphere".
Euclid may be my new best friend, but I still haven't much hope of getting past base camp, where I puff and pant with other maths no-hopers. I will leave the Olympian heights to Devlin and others of his ilk.
The Maths Gene, by Keith Devlin, is published by Weidenfeld & Nicolson
Keith Devlin, a Hull-born professor now resident in California, tells Moira Petty that you do not have to be a genius to understand maths ]
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