By

Numbercrunching

Recently I found myself writing a poem about the experience of learning how to count. In Primary One, I was given boards with spots on them arranged in patterns a bit like those on a dice, and coloured plastic discs – ‘counters’ – to cover the spots. I was taught to count, I realised, by the recognition of pattern. So, the poem I was writing, called ‘Counters’, had brought me to this – not at first sight very momentous – thought: that pattern was involved in number from the outset.

Immediately I went to the public library and browsed through various books on arithmetic. I was not certain what I was looking for, until I found it, in a book about number theory and chaos, in which the author confirmed for me that pattern was the basis of all mathematics, and that recognising a number of dots which was not set out in a pattern was much more difficult than recognising a number of dots which was – for chimpanzees, crows and computers as well as people.

Then I remembered – though perhaps at this point imagination began to take over from memory – all the other things I did with the plastic counters. Playing tiddly-winks with them, putting them in my mouth, building them into a column which leaned towards infinity … I noticed all the titles in the Mathematics Section of the library which included the word ‘Infinity’ or the word ‘Infinite’ and I remembered the song we chanted in Primary One, about all those mad men going to Mow, wherever that was. Had nobody told them the meadow was endless, and that Mow was a totalitarian state? So I borrowed all those books about infinity from the library, went home and informed my family that I would be busy for the rest of the millennium, if not longer.

To the consternation of my children, I began to demonstrate the remarkable qualities of the Mobius strip over dinner. Topology, I argued, was the most practical of the mathematics, with its problems to do with inverted rubber gloves and tiling giant Easter eggs using only two shapes of tile, not to mention the money the American government could have saved if only they had consulted a mathematician before having all of those tiles for that N.A.S.A. space probe designed individually, at enormous cost to the taxpayer.

But already I was far beyond the mysteries of topology. What obsessed me more was the concept of number itself. Individual numbers themselves – not just whole numbers, the ones dancers used to wear on their backs in ‘Come Dancing’, the kind of numbers worn by footballers and horses, but the fractions which were made up from whole numbers, and the irrational numbers, the complex numbers, twin primes, the digits of pi. In numbers I had discovered a new fetish – much to the chagrin of my family.

During my subsequent reading I learned that Ludolf van Ceulen had spent almost a third of his life calculating the digits of pi, by the laborious Archimedes method, to the thirty-fifth digit. He had this number engraved on his tombstone, which went missing during the second world war – the fate of many Jewish tombstones at that time. Ludolf van Ceulen’s tombstone may still exist, though I don’t imagine Ludolf cares much any more. Ten years after his death, his work as a mathematician had become obsolete. Someone else had come up with a formula which made it much easier to calculate the digits of pi into the hundreds. Even now, mathematicians use computers to calculate the digits of pi into the billions, just in case this number reveals a pattern which might make us feel we can understand it.

What interests me is that these dedicated number-crunchers, human or otherwise, are still doing what Ludolf van Ceulen was doing in sixteenth-century Leyden. The thrilling thing, for me, is that their work might be equally pointless – if only it could be proved to be inherently pointless, and that pi could be shown to be by definition patternless. Similarly, twin primes are still something of a mystery to mathematicians. I find this thrilling, because it shows me that mathematics is just as speculative an endeavour as poetry.

I am presently reading a biography of Pythagoras. He wore trousers – an extraordinary thing to do in ancient Greece, amounting to a fashion statement: I am a barbarian – grew his hair long, lived in a cave, took drugs, worshipped stars and numbers, believed in reincarnation – i.e. that he had lived as both a plant and an animal – and didn’t eat beans because, structurally, the bean resembled a human foetus. He also played the kithara, a sort of prototype of the guitar, heard the music of the spheres, believed that earthquakes were caused by the restlessness of the dead, and travelled in Egypt and Babylonia, where he found out that thing about the right-angled triangle which made him so famous. Although it wasn’t his own, and had been used to demarcate reclaimed fields after flooding for centuries, Pythagoras was the first to realise its significance i.e. that the formula was indubitably the case for any right-angled triangle. In other words, he discovered and revealed something universal which could be of possible benefit to humanity – which is also, perhaps, what poets must try to do.

Mathematics. The subject might seem an eccentric one for poetry, but my ignorance of mathematics is immeasurable – though perhaps it could be measured – and the primary function of my poetry, for me, is to probe the vast areas of my ignorance. My ignorance may well be finite, but unbounded, or the converse: bounded, but infinite. My ignorance of mathematics probably looks a bit like the lemniscate, or lazy eight lying on its side, like a reclining poet, contemplating the eternal verities, or even the short-term verities, like the question of how to make a living as a sonneteer while counting syllables. Who knows what reclining poets think about when they recline? Their heads may be full of naked women, shopping lists, or numbers of syllables.

My common-law wife once said to me: ‘You don’t choose the subjects you write about – they choose you.’ She didn’t mean me personally, by ‘you’, I don’t think. She’s right – she must be, because I would never have chosen to write about something as difficult as mathematics, if I’d had the choice.

‘As difficult’ – except that mathematics isn’t difficult: I just have that preconception about it, a hangover from the way it was taught to me in school. My reading has disabused me of this preconception. Even if I can’t – or can’t be bothered – following all of the stages of a mathematical proof through to its indisputable conclusion, I can often grasp the concepts involved. And perhaps as a poet I grasp them in a slightly different way from a mathematician. I know what fractals are – those diminishing, replicating shapes which end up looking like the coastline of Scotland. I’m more taken with the problem of the travelling salesman who has to visit several towns, using as little gas as possible, by the shortest route – a problem mathematics still hasn’t been able to solve. I hope to solve it – in a poem, or a car. I understand the concept of the hypersphere, I think, though the mathematicians I have met socially have not been able to define the hypersphere to me satisfactorily. They usually begin: ‘Well, if you can imagine a sphere, okay…’ What is interesting is that they then usually have to resort to metaphor in order to convey even a hypernotion of what the hypersphere is.

Though founded on certainty, mathematics is essentially just another way of probing the uncertain, the many – though not necessarily infinite – mysteries of the universe. So it should be no surprise – though I did find it surprising – to learn that mathematicians are like artists. They intuit theorems and know that they’re true but can’t prove them. And occasionally poets write wonderful, inexplicable lines which sound absolutely right and are theorems of a kind too. In both cases the theorems are proved, or disproved, some time later – unless of course they are shown to be undecidable.

Body Parts, Brian McCabe’s poetry collection is published in paperback by Canongate at £7.99 ISBN 0 86241 877 1

Selected Stories, Brian McCabe’s short story collection is published by Argyll at £9.99 ISBN 1902831624

Copyright Brian McCabe 2005.