ACHILLES IN THE QUANTUM UNIVERSE

The idea of the infinite has baffled thinkers since ancient times; now a top science writer tries to shed light on the concept. Morris (Cosmic Questions, 1993, etc.) begins by noting the paradoxes that arise when infinite numbers are put through standard arithmetic processes: Half of infinity remains infinite, and infinity minus 30 trillion is still infinite. Precisely because of its tendency to produce paradox, infinity has always had a shady reputation. George Cantor, the first mathematician to seriously study it, went mad. It was the suggestion of infinite worlds, rather than the heliocentric model of the solar system, that got Giordano Bruno burnt at the stake. And Newton went to great pains to find a way to explain his newly invented calculus without resorting to the infinitesimals (infinitely tiny numbers) on which its operations depend; he never quite managed the trick. Morris spends a good deal of time showing how astronomers and cosmologists have dealt with the growth of the observable universe and with the implication that the actual universe might really be infinite. Much of our modern picture of the cosmos arises from the fact that certain equations in Einstein's general relativity theory produce infinite answers—``singularities''—when the right values are plugged in. From these troublesome infinities eventually arose the concepts of the Big Bang and black holes, both of which are now considered all but confirmed by observational evidence. Morris is a clear and lively writer, with a penchant for down-to-earth examples—a useful asset in dealing with a subject so notoriously difficult. A good survey not only of infinity, but of the scientific revolutions that have grown out of our attempts to grapple with the concept.