A book about nothing might seem like one of those postcards showing "Harvard Square at Night" - just an empty black rectangle. But out of the dusty obscurity of the history of numbers, Harvard mathematician Robert Kaplan has drawn a finely crafted illumination.
Ranging widely from ancient Sumer to Einstein and Wittgenstein in this century, the author meditates on the invention of zero as a philosophical as well as a mathematical concept.
Strictly speaking, of course, humans did not "invent" zero, any more than the counting numbers. But the notion of zero as an arithmetic placeholder made computation far easier. Without a positional notation, the rules for simple addition or multiplication become a mysterious art. What is XLIII + XXIV? As the author notes, "no attempt to line the two up will ever automatically produce the answer LXVII."
Today, the decimal Hindu-Arabic number system is learned so early that it seems like the most natural and obvious way to represent numbers. In its most basic form, it is the binary code that underlies all our computer software languages.
It was not always thus, of course. The earliest recorded number systems, from Sumer and Babylon, were based on the number 60. A survivor of this archaic counting system exists today: We measure 60 minutes to an hour and 360 degrees in a circle.
Initially, it appears, the number 1 was a single wedge, incised into clay with the tip of a three-sided stylus. The number 60 was a bigger wedge, which inevitably must have led to chaos if the scribe was rushed or just cooking the books.
Kaplan says it was "utter confusion - until someone came up with the brilliant idea (or was it a makeshift or compromise that just worked its way into practice, as these things do?) of making the place where the wedges are written stand for their value." The next problem was how to mark an empty place. The great historical puzzle at the center of this tale is why it took thousands of years for someone to figure out that you could put an empty circle to show the absence of a value.
The modern representation of zero first appears around A.D. 876, on a stone tablet located in a garden dedicated to Vishnu by the people of the city of Gwalior in India. Kaplan hints broadly that the Indians got the idea from the Greeks over the passes from Asia Minor, brought by the conquering troops of Alexander the Great.
The charm of this volume is that the reader can never again dismiss nothing as unimportant. Deeply informed, lucidly written, this engaging work is a thought-provoking inquiry into a significant topic in the history of human thought.
*Frederick Pratter is a freelance writer in Missoula, Mont.
(c) Copyright 1999. The Christian Science Publishing Society