The Story of O
By Steven Robert Allen
JANUARY 24, 2000:
The Nothing That Is: A Natural History of Zero by Robert Kaplan (Oxford), hardcover, $22
Zero. Nothing. Void. The curvature of the earth as it travels around the sun. The collar around a mangy dog's neck. The God of Death to the Maya. The impression left by a round stone after it's lifted from the sand. A concept without which modern mathematics  that most reliable of tools for weighing and tabulating the parameters of the universe  would be fundamentally impossible.
More than anything else, Kaplan's book is a flight of fancy through the wide, gaping ohhhhh of zero. As he writes in the introduction: "Look at zero and you see nothing; but look through it and you will see the world." Certainly this is true for Kaplan, a professor of mathematics at Harvard who founded the Math Circle, a program designed to foster the enjoyment of pure mathematics. In this volume, the author communicates his overwhelming enthusiasm for the symbol and concept that we numberphobic civilians all too often take for granted. Anyone who truly considers the ramifications of the mighty zero is likely to come away with a deep respect for this nothing that is. After all, without zero it would be impossible to ask such mindbending riddles as this: If four people are in a room and seven people leave it, how many must enter the room before it is empty? Answer: three.
No wonder mathematicians are such great fun at parties.
The Nothing That Is begins with a look at the sketchy historical roots of zero. Kaplan seems to be partial to the theory of a Greek origin for the number, but he acknowledges that both Babylon and India have strong claims to the honor. Most of this section of the book is admittedly based on conjecture, because zero's past, as is perhaps fitting for such a mysterious number, is remote and sparsely documented. In these pages, Kaplan ponders what early mathematicians might have been thinking as they slowly progressed toward the discovery and understanding of zero. In doing so, he shows how the story of zero reveals truths not only about mathematics but about the subtleties of human thought and invention.
In a separate chapter, Kaplan considers the Mayan zero, which was developed independently of other cultures. From the beginning the idea of zero was integral to the Mayan calendar and had an apocalyptic impact on the Mayan world view. In many ways, this wasn't so different from the impact zero had on the rest of the world.
The author explores zero's influence in various areas of mathematics, from algebra to calculus, and then explains the impact of zero on such disciplines as physics, theology and philosophy. Those who tend to shy away from books filled with equations will be relieved to discover that these musings are comprehensible to anyone who has had high school algebra and geometry. Even if you're out of practice, in most cases Kaplan does a decent job of carefully guiding the reader through his various mathematical puzzles.
The biggest problem with this book is Kaplan's penchant for strained poetics. Though his enthusiasm and awe are contagious, the subject matter is fascinating enough to be explained minus awkward linguistic ornamentation. Kaplan's wordiness all too often gets in the way of a clear exposition of his story and ideas. Furthermore, he uses zero as a springboard for some questionable musings. At one point Kaplan's free association even leads him to express some inane thoughts on American patriotism. The book would have been better if it had been told in simpler, more straightforward prose.
Despite these excesses, the book succeeds in transmitting Kaplan's love of pure, absolute nothing to the skeptical reader. "Picture the soapbubbles a child floats on the summer air," Kaplan writes. "Small and large, each is a perfect world, with colors sliding like continents over its surface." Likewise, zero is its own perfect world, only made more magnificent in that it cannot be seen or felt or even easily imagined.
In the final chapter, Kaplan opts for a bit of metaphysics to close out his little book of nothing. He asks us to ask ourselves why the universe exists at all. Why is there something rather than nothing? Why do you exist rather than not exist? The power of zero, you see, is everywhere. Just a little something to think about, John Boy, as you're drifting off to sleep.
