An ambitious but baffling history of automatic calculation, from ancient Egyptian hieroglyphic numbers to modern computers.

Ifrah, a former math teacher and independent scholar, precedes his discussion of computation with a condensed version of his first study, *The Universal History of Numbers *(not reviewed). The first section begins with a chronology of significant events in the development of writing and numerical notation: the entries start with notched bones dating from between 35,000 and 20,000 b.c., continuing through various ancient scripts and number-systems to the spread of the “Arabic” numerals now in use. Diagrams illustrating ancient number systems are intriguing, but dauntingly technical; examples of calculation presented in mathematical transcription without verbal explanations are bound to frustrate nonmathematical readers. A chronology of algebraic calculation is also intimidating, whipping through the formulations of Gauss and Fourier with the same blithe disdain for explanations. Ifrah slows down in his discussion of non-decimal number systems, especially the binary systems that underlie the operation of modern computers; in a fascinating twist, he notes, the 17th-century logician Leibniz based his invention of binary arithmetic on a misunderstanding of the ancient Chinese hexagrams of the I-Ching. The second section, which looks at the computer’s mechanical ancestors—abacuses, clockwork calculators of the late Renaissance, and slide-rules—before tracing the development of ENIAC, the first modern electronic calculator, and its descendants, offers more dramatic episodes (including Germany’s hair-raising successes with electromechanical calculation during WWII). However, the author does little to make crucial material—the elements of set theory, polyvalent logic, or the premises of symbolic calculus—understandable for a general audience, too often lapsing into laundry lists of events or concepts without discussion of the significance of the entries. Frequent intrusions by the translator, attempting to introduce sections, recapitulate, or supply missing information, further suggest Ifrah’s impatience with nonspecialists.

Like many a software designer, the author has put plenty of information into his work, but has failed to make it user-friendly. (b&w drawings)