A UNIVERSAL HISTORY OF NUMBERS

Ifrah’s monumental follow-up to From One to Zero (1993) goes from one to (almost) infinity as he meticulously reviews the numbers and reckoning systems of countless tribes and cultures in a dazzling scholarly performance.

“Performance” is the operative word here, for not only does Ifrah enumerate the words and symbols used for arithmetic, but he also explains how to use each system, providing illustrations, diagrams, riddles, and puzzles. Indeed, nearly every page displays handsome numerals, counting devices, and illustrations of their use. Ifrah takes the human body as the aboriginal point of reference for most counting systems—fingers and toes producing systems using 5, 10, or 20 as a base. But 12, 60, and 360 have also been used, usually by cultures that attached more importance to the sky than to their anatomy. Ifrah gives special credit to the Mayans for their extraordinary adeptness at astronomical measurements, which calculated the length of the solar year as 365.242 days and the month at 29.53086 days. He commends India for the invention of zero—the placeholder in counting systems that use positional notation to indicate the different values, for instance, of 1, 10, and 100. A recurring theme is the intimate relation between number systems and written language. Just as the invention of alphabets allows the generation of myriad words, advanced number systems can use a limited number of symbols to represent any large number. A quibble or two: Ifrah frequently asserts that our brains cannot instantly number a collection of more than four objects, though psychologists maintain we can recognize up to seven objects without counting. And since many statements on the origins of systems and borrowings across cultures are speculative, they are subject to change in light of recent discoveries.

A must for any library—and a wonderful gift for anthropologists, ethnographers, cultural historians, and quiz kids.