The Nothing That Is: A Natural History of Zero, by Robert Kaplan.2000, Oxford University Press, 198 Madison Avenue, New York, New York 10016, paperback, 225pp, $9.95. ISBN 0-19-514237-3. (800)-445-9714 or http://www.oup.com/
Just when it might seem that nothing new could be written about zero, and that all puns on it were exhausted, along comes a book that happily does a lot of the former and, mercifully, little of the latter. Robert Kaplan’s book, The Nothing That Is: A Natural History of Zero, is a fascinating view of the concept and numeral from many angles.
We learn that the Sumerians, who partially used positional notation based on 1, 10, and 60, employed something like zero at the center of their numbers. Next we see that the Greeks never used the zero in the way we do but that they still constructed large numbers and built beautiful buildings geometrically. When the author introduces the Greeks, he begins his discussion on the origin of the shape of the modern numeral and establishes why it is a hollow oval. Later, about halfway through the book, he tells us that the Arabs supplied its name sifr, a translation of the Hindu word for nothing. The Hindus are given credit for incorporating the concept into arithmetic within the decimal system; the Chinese do not get it and the author takes pains to explain why. On the way there are excursions into the life of the Maya – they too used zero – and we get a clear description of their astronomic calculations and calendar that alone is worth buying this book for.
The author traverses ground well known to math historians, with a richness of language and expression that can be illuminating, irksome, novel, and massively entertaining. The reader might occasionally groan under the semantic weight of phrases like "philology captured ontogeny in taking its time to recognize negatives" or "the gallimaufry of numbers", but will also be rewarded by the vast range of ideas and people that are presented. We learn about the links to Mayan gods and their human sacrifices, the contribution of Fibonacci, fractional exponents, sections of Florentine contract law, Pierre de Fermat, Leibniz and Newton, the Bernoullis, theology, astronomy, logic, and the hypothesis of Gödel. There is an elegant exposition on graphs and the limit-based definition of the derivative. The final chapters are philosophic essays centering on such concepts as: the vacuum in nature, eugenics and non-existence, all are delivered with rich expression and imagery. Ultimately we become aware that "…each of us singly and together has entertained an angel unawares."
The author writes for a general audience but one with plenty of time to sit, read, and absorb the material. If in retirement, put down that copy of War and Peace for something truly amusing and educative. This is a history for people with brains.
Austin Lobo, Professor, Washington College, Chestertown, MD