The Book of Nothing

  • John D. Barrow
Pantheon: 2001. 370 pp. $27.50
Credit: DAVID NEWTON

It must have been all those noughts at the end of last year's date that started people writing about zero. In 1999 we had Robert Kaplan's The Nothing That Is: A Natural History of Zero (Penguin), in 2000 we had Charles Seife's Zero: The Biography of a Dangerous Idea (Souvenir), and now we have John Barrow's The Book of Nothing. It's like standing at a bus stop. For 1,000 years nothing arrives and then you get three books on zero coming along together.

Kaplan's book was content to examine the history of zero and its position in a mathematical framework. The other two take the exploration of the idea out of the domain of pure mathematics and into the modelling of the physical Universe. This makes for a livelier story and expands the interest of the topic away from the purely arithmetic. Of these two, Barrow's book is the more authoritative and tells the story more persuasively. As with all popular books on modern physics, the approach is of necessity non-mathematical, and many of the arguments proceed by analogy. In these cases it is Barrow's arguments that are the more convincing.

All three books tell the story of how zero was invented several times, finally impinging on Western mathematics from its incarnation in Indian and Islamic culture in time to spark the Renaissance. We can only join Pierre-Simon Laplace in acknowledging: “The ingenious method of expressing every possible number using a set of 10 symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance are no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost among useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond two of the greatest men of Antiquity: Archimedes and Apollonius.”

Barrow includes an account of the parallel development of zero by the Mayan civilization of Central America and numbers his chapters with Mayan 'glyphs' (gargoyle-like stylistic faces used as numerical symbols).

The connection between zero and the nothingness at the heart of Barrow's book is made by way of that most slippery of concepts, the empty set. Nineteenth-century mathematicians were able to use some cunning tricks to make this most humble of sets the basis for their arithmetic. It is a curious fact that although we may worship different deities, we are all forced to use the same empty set. It is the true universal concept. No wonder that this idea, which mathematicians now accept with equanimity, caused much debate and heart-searching down the centuries among philosophers and theologians.

Early scientists, despite the reservations of the philosophers, pursued the vacuum increasingly successfully with their barometers and pumps, and the idea of an empty space seemed eminently satisfactory. But then the necessity of finding a medium to allow the propagation of various electromagnetic waves meant that theoreticians were led to fill it up again with a presumed 'ether' — an invisible, inviscid fluid permeating all space. Physicists played intricate games with this new toy. Lord Kelvin and Peter Tait knotted ethereal vortices; Simon Newcomb and John Gore invoked its properties to explain the darkness of the night sky. Theologians likened it to “The Rudder of the Universe, the Rod... in the Hand of the Almighty”.

With the benefit of hindsight, we can see that by the end of the nineteenth century the theory was running into trouble. This was the beginning of big-money science, and it was the first telecom magnate, Alexander Graham Bell, who financed the experiments that laid the ether to rest. Albert Michelson and Edward Morley found strong evidence for its non-existence, and eventually the man-in-the-street's favourite eccentric genius, Albert Einstein, devised a theory that allowed it to be dispensed with altogether and so restored the status quo for an empty vacuum. It was a pity he had to use mathematics that the man-in-the-street could not possibly understand.

Nature may not always abhor a vacuum, but theoretical physicists seem unable to leave it alone. Only a short time after Einstein had restored empty space as a concept that one could believe in, the invention of quantum mechanics made it something that was too simple to satisfy the new theories. In the most persuasive model, any so-called empty box contains innumerable pairs of virtual particles which switch themselves in and out of existence, and which contribute to the energy of that apparently empty hole. This is the zero-point or vacuum energy. Even the experimentalists joined in, and measured the tiny forces involved in the Casimir effect, one of its consequences. Barrow brings this firmly into the realms of credibility by outlining results on a nautical phenomenon noticed in the nineteenth century, when two ships wallowing near each other in a choppy sea were moved towards each other by the wave action. It turns out that this involves the same theory, albeit on a much greater scale.

Such is the way that modern physics is interconnected that these effects noticed in the 'quantum vacuum' turn out to have wide-ranging consequences even at the truly astronomical scale. Cosmologists now have to take account of this new version of empty space. Theories of how the Universe evolved in the first few moments after the Big Bang can be profoundly influenced by this concept of energetic nothingness.

In 1992, John Barrow wrote Theories of Everything: The Quest for the Ultimate Explanation (Clarendon). It is curious that a decade later the ultimate questions can be explored from the point of view of nothingness rather than everything.