Into the void

The Book of Nothing

John D Barrow <em>Jonathan Cape, 380pp, £16.99</em>

ISBN 0224059629


Nothing comes of nothing was a fundamental tenet of medieval philosophy - a battle cry used by theologians to chase away the spectre of atomism and, they believed, of atheism. The void has long been associated with Godlessness. The very idea is, to say the least, unheimlich. Editors of newspapers, periodicals and TV stations, however, have long since proved this metaphysical assumption false, as journalists around the world conjure from thin air crises, controversies, scandals and trends, to fill what would otherwise be terrifyingly blank sheets of paper and TV screens.

It is not only journalists; we all find ourselves talking about nothing from time to time - about nothing in particular, that is. We fill awkward silences, putting our tongues on automatic, repeating what we have heard others say. We seldom discuss the thing itself. But mathematicians are different. When mathematicians talk about nothing, they mean it. They take nothing seriously. They study it, and they write books about it.

I remember with painful clarity the strange sensations produced during maths lessons by prolonged exposure to the notion of zero, and by its dazzling corollary, infinity. You will say it was an adolescent, hormonal thing - but divide any number by zero and you get infinity; divide any number by infinity and you get zero. Contemplate these mathematical operations: they are somehow thrilling and nauseating at the same time. Not feeling giddy yet? Did you know there are infinities of different size? Yes, some infinities are bigger than others. Only one infinity is infinitely large. These ideas have a similar effect on me to some of Bridget Riley's perception-warping paintings: you need the stomach for them.

The worst thing about those maths lessons was that, while I struggled to cope with the dizzyingly unstable sense of futility induced by such concepts, the maths teacher carried on as if we were counting out baskets of apples together. It was like being at a nightmare dinner party: several of the guests had died in their seats, yet the host continued to serve food and make small talk as if nothing untoward had happened. Perhaps this was done out of politeness. Or perhaps the host simply could not find the right words to express his sense of . . . of what? Of the uncanniness, anxiety and fear we all must feel when confronted with our human propensity suddenly to cease existing, at any time of day or night. The void lies within us all.

Personal annihilation can neither be predicted nor controlled. It doesn't make a pretty prospect, and anything that reminds us of this - our inalienable right to become nothing, nil, a void - is apt to make us turn away. It is a difficult thing to bear in mind. Which, I suppose, is why c'est toujours les autres qui meurent, as Marcel Duchamp obligingly reminds us by means of the inscription on his gravestone.

The startling story of the west's intellectual struggle with the concept of zero is told with admirable elegance and clarity by both John D Barrow, in The Book of Nothing, and Charles Seife, in Zero: the biography of a dangerous idea. Barrow's book is richer in historical detail, while Seife has the keener eye for logical paradox and excels in communicating the ways in which people have felt threatened by the concept of zero.

Advances in mathematical reasoning have often seemed unreasonable by the standards of common sense. Extending the number scale backwards through zero and into negative territories is a case in point - Descartes absolutely hated the idea. At other times, reality appears to be most accurately described by means of operations that make no sense, even to mathematicians. Calculus depends intimately on the concepts of zero and infinity, and was logically incoherent - literal nonsense - for more than a hundred years after its invention. The philosopher Bishop George Berkeley ridiculed it as depending on "the ghosts of departed quantities". But physicists kept on using it because it gave out the correct answers. Their "irrational" faith was right: calculus was rendered logically coherent around the time of the French revolution. It is the only language the physical world understands, and scientists speak it to this day.

It took the Hindus, whose culture was rich in conceptions of emptiness and negativity, to help the world exploit the full mathematical potential of zero. They created the positional notation - which we still use today - in which just ten symbols can represent an infinity of values. This system depends, in part, on the symbol for zero having equal status with the other nine. It allows written figures to function as a kind of calculating machine, like an abacus in ink: add a nought to a row of digits in the Indian system and you increase the size of the number by a factor of ten. The addition, subtraction, multiplication and division of large numbers can then be accomplished piecemeal, by performing a series of small, recursive, easily handled calculations.

For non-mathematicians, there is a more general lesson here: only once the existence of real negations was accepted could physicists even begin to develop adequate descriptions of the physical world. Similarly, the outcome of some of our most persistent political debates may be determined by whether we accept or reject the notion of real negation. In both cases, the conservatives seem always to be best served by denying the reality of negation - perhaps because, without it, as Parmenides realised a long time ago, there can be no change.

One example: deny the reality of negation, and injustice can quickly be made to seem chimerical. Take poverty, for instance. Everyone agrees that if you limit a person's resources, you limit his or her potential to flourish as a human being. Everyone also agrees that resources are finite. What right and left disagree about is whether or not negations are real. Deny the reality of negation, and the word "poverty" can signify only a positive condition - a degree of wealth smaller than some degrees of wealth, but greater than others. Such comparisons of wealth have no more than subjective significance. Non-lethal poverty, therefore, is a variety of envy - not a political problem at all. Admit the reality of negation, however, and suddenly poverty becomes real - a lack of access to the resources necessary to an individual's flourishing, as understood by that society.

Got a concept of human flourishing that does not involve driving everywhere, anyone?

John Binias's first novel, Theory of Flesh, is published by Macmillan

This article first appeared in the 30 October 2000 issue of the New Statesman, Divorce your husband and watch him get rich