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Saturday, January 3, 2009

The sum of human emotion

Man doing maths
Anger, relief and disappointment - that's what sums can do
Tears, tantrums and murder. Far from being a cold and rational exercise, maths can provoke the full range of human emotions, explains Professor Ian Stewart.

In these days when wearing your heart on your sleeve is seen as qualifying you to be a true human being, rather than some robotic control freak, scientists and mathematicians are often viewed as being far too rational to be truly human.

Especially mathematicians, who spend all their days doing boring sums in some remote world of the intellect.

Some news, guys: it's not true.

Not just that we don't spend our time doing sums, but also we possess entirely normal human emotions - and express them.

Agreed, mathematicians are seldom seen bursting into tears or shouting in the streets, but that's mostly because mathematicians are seldom seen. Or, more to the point, seldom noticed, because there are hundreds of thousands of mathematically qualified people in British society, working in a huge range of jobs.

Shouting matches

And it's true that the way mathematics is usually presented strips out the emotional element - but the same goes for banking, architecture, whatever.

Anyone who has ever been to a mathematics conference, or sat in a mathematics department common room, notices very quickly that not only are mathematicians emotionally committed to their subject, but the emotions often run high. Shouting matches are not unusual.

The only time mathematics has driven me to tears was when I was 10

There is an important difference, however: when two mathematicians are arguing at the tops of their voices, eventually one of them says: "Oops, sorry, I've just seen why you're right." And the two are once more the best of friends and go off to the pub together.

One of the great emotional TV moments for mathematics was John Lynch's wonderful programme about Andrew Wiles's solution to Fermat's Last Theorem, a famous problem that had baffled mathematicians for 350 years.

Relating how his epoch-making solution very nearly collapsed because of a logical error, Wiles is on the verge of tears. The entire programme shows how committed mathematicians are to their research; how solving a problem becomes a kind of personal quest.

Dorothy Parker once said that the movie actress Katharine Hepburn ran "the gamut of emotions from A to B". Mathematicians may not quite manage A to Z, but they get a good way into the alphabet - joy, sadness, a sense of beauty, anger, relief, worry, disappointment.

Maths lecture on the BBC
Hold back the tears

Even a casual glance at the lives of some of the subject's greats should dispel the notion of mathematicians as ultra-rational calculating machines. Leopold Kronecker's dislike of Georg Cantor's new theory of infinite numbers drove Cantor to a nervous breakdown.

Évariste Galois combined dramatic work on the equation of the fifth degree with even more dramatic involvement in French revolutionary politics, culminating in a duel over a woman in which he was killed.

David Hilbert was incandescent with rage when Kurt Gödel drove a coach and horses through his massive programme to put all of mathematics on sound logical foundations. This was no surprise: Hilbert had devoted years to the project, and had made what seemed to be a lot of progress. Then it all came tumbling down.

The only time mathematics has driven me to tears was when I was 10. There's a lot of evidence that people understand maths much more easily when it is formulated in a social context.

Abstract puzzles involving cards with letters on one side and numbers on the other baffle most of us, but the same question can be instantly obvious when posed in terms of under-age drinking in a pub.

Quite a few psychologists now think that the rational mind cannot exist without an underlying emotional mind

My problem was the exact opposite: I was being asked to solve question of the type: "When Fred is half as old as Emily was when Arthur was born, how many dogs does it take to change a light bulb in three days?"

Write it as algebra, and I could solve it at the drop of a hat. But I was having real problems turning the social story into symbols.

My subject has, however, driven me to the use of distinctly strong language when my beautiful solution that I have been working on for weeks turns out to be riddled with holes.

The emotion of frustration is very familiar to any research mathematician, being the normal state of affairs about 99% of the time. The deep emotion of joy when a solution finally presents itself makes all of the frustration endurable.

Beautiful sunset

There can even be humour in mathematics, and I'm not referring to jokes: the actual maths may be genuinely funny. For example a breakthrough in my current research relies upon dividing both sides of an equation by zero. Ordinarily this is a no-go area, leading to nonsense.

But in my particular problem, you can sensibly divide by zero provided you start not with zero alone, but by two zeros multiplied together. I laughed out loud when I saw how it worked. Mind you, I don't expect you to be equally amused - you have to be emotionally involved in the problem, and frustrated by not being allowed to do what you want, to find it funny.

The word 'calculating' has several meanings

Quite a few psychologists now think that the rational mind cannot exist without an underlying emotional mind. You have to be committed to being rational. Only then can you override your fervent desire for certain things to be true, and accept that they're not.

What makes us human is not raw emotion: we share that with many animals. More refined emotion, such as a feeling of awe at a beautiful sunset, is another matter.

But to me, the real essence of humanity is to experience emotions, but not to let them take over completely if that's a bad idea.

Professor Ian Stewart is author of Taming the Infinite: The Story of Mathematics, published by Quercus

Original here

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