There are truths common to every human life as elusive as why people fall in love. One is the idea of nothingness, the proposition of zero. Robert Kaplan fell wild-mad in love with zero and has done something about it. The result is his "The Nothing that Is: A Natural History of Zero" (Oxford, 256 pages, $22).
This book is a journey of discovery -- an effort to uncover and make understandable the roots of zero, and a speculation about the future of mathematics.
Kaplan starts out: "If you look at zero you see nothing; but look through it and you will see the world. For zero brings into focus the great, organic sprawl of mathematics, and mathematics in turn the complex nature of things."
By "things," he means all things -- animal, vegetable, mineral. Beyond those, most importantly, he means the abstract: the inclusive concept, if you will, of being, without which there can be no nothingness.
The book tells a story -- a history of what is known of the evolution of mathematics. It begins with still-preserved markings on baked clay tablets, cuneiform done by Sumerians, in Mesopotamia, about 5,000 years ago.
The key concept of the Sumerian genius was "positional notation." Huh? Well, take the year 1999. Without positional notation, the 1 would be a one, not a thousand. The first 9 would be a nine, not a nine-hundred; the second would be a nine, not a ninety.
Ultimately, it was that concept that freed those who knew how to use it to perceive and manage big numbers -- and thus to organize society, to conduct trade. To go figure.
Zero, the concept of expressing nothingness as a declared value, did not come easily. It seems to have evolved in the mind of a Babylonian about 700 B.C. The Greeks wrestled, rather badly, with the need for it, and the Romans, with their X's and V's and the like did no better. The Mayans apparently discovered a zero concept, but it was lost to rest of the world when their isolated civilization consumed itself in bloody excesses.
It was in India that scholars began treating nothingness as an actual number, between 500 and 800 A.D. It spread back to Europe, though for a considerable while there the idea was considered satanic, and treated with attendant fear and scorn.
Kaplan is respectful of several explanations of the origin of zero being expressed as a circular mark, but leans sharply toward India. Indians used counting boards for calculating, as did many other societies. But the Indians covered theirs with sand, and when a counter was removed, it left an O-shaped absence.
The book's full of such speculations. But the whole pulls together, coherently and thoroughly entertainingly, a tale and a thesis: That the development of what today is regarded as modern civilization would have been stymied, dead in the water, if human imagination had not risen to what now seems the necessity of conceiving the concept of zero.
The word "zero" itself emerged through Italian, with, of course, Latin roots -- words related to the modern term "zephyr," Mediterranean breezes that disappear into nothing as they move northward.
The math saga continues today, with lots to come. Already, mathematics has led humankind to figuring and bookkeeping, essential to the evolution of trade, commerce, engineering, and all science and technology. Kaplan insists it has barely begun its journey toward understanding.
Even his worst sentences are clear, clean and direct. His best are as poetic as: "There is a far more fearsome embodiment of zero: the guilt-ridden certainty of one's own utter worthlessness. The self-damned knew even in childhood the etymology of their naughtiness: it derived from being nought."
There are, inevitably, bits and pieces of mathematics in the text, but from the outset Kaplan promises that none of it is beyond the grasp of anyone who managed a passing grade in high school algebra and geometry. To my eye and mind, he keeps that promise.
Kaplan lives in Cambridge, Mass., and has been on faculties all over the place, including Harvard. He has taught Greek and Sanskrit, philosophy and philology, German and -- I would guess his favorite -- "Inspired Guessing." He's a scholar of Chinese and an enthusiast of cricket. With blissful comfort, he cites Archimedes and Ernest Zermelo, Gertrude Stein and George Gershwin, Wallace Stevens and Sylvia Plath.
Thus, Kaplan is a splendid specimen of the living polymath: a person with extraordinarily wide-ranging knowledge.
As to "polymath," the word first came into use in the early 17th century and is derived, as Kaplan would know in his sleep, from the Greek word polumathes, literally "someone with much learning," which in turn derives from manthanein "to learn," which is also the source of the English word mathematics.
Polymaths are a wonderful life form. We live in an era of massive specialization of both education and learning. Today, that is hideously accompanied by academic savaging of classic knowledge and wisdom. Buffeted by those tides, polymaths are a mortally endangered species. Yet they are irreplaceable guides to personal culture. Personal culture is the main thing worth mentioning that distinguishes humans from barn owls.
Go out today and find a polymath and offer support. Have you hugged one lately?
Or, that failing, get this book. Read it. Think long and hard and sweetly about what the human mind is for: The gift of thinking, the joy and fulfillment of searching for truth.
Pub Date: 10/24/99