Mathematics Elsewhere: An Exploration across Cultures

Mathematics Elsewhere: An Exploration across Cultures by Marcia Ascher. Princeton University Press, 224 pp., $24.95. Ascher provides us with a fascinating trip around the world as she shows us how various cultures use surprisingly sophisticated mathematical techniques, though in the absence of anything like mathematical language and theory, to prognosticate the future, create unique navigational maps and astronomical and other calendars, control the social order in different ways, and form complicated symmetric designs expressing social values.

In the Caroline islands of the North Pacific and among the Yoruba people of West Africa, divination practices rely on randomization techniques, modular arithmetic, ordered sets, and specified algorithms. Among the peoples of Madagascar, again for purposes of divination, all these are used as well as techniques of Boolean algebra.

The Jewish calendar, mixing lunar and solar cycles with prohibitions involving the 7-day week and numerous religious celebrations, is heavy on calculations using complicated algorithms and modular arithmetic. Calculations based on the lunar-solar calendar of the Incas involved ordered pairs, modular arithmetic with mixed bases 18 and 20, and the equivalent of solving systems of linear congruences. The very complex and abstract Balinese calendar likewise leads to solutions of systems of linear congruences. By way of relief Ascher points out that ingenuity can obviate the need for mathematical nuances: the lunar calendar of the Trobriand Islanders (off the coast of Papua New Guinea) is periodically adjusted to fit the solar year in accordance with the biological clock of a marine annelid (a worm gear?).

The stick charts guiding Marshall Islanders accurately across hundreds of miles of open ocean in primitive sailboats without the aid of compasses don't look anything like maps to the western eye but in fact are more than maps, portraying not only the relevant geometry but also prevailing meteorological phenomena.

Social relationships among the Basques, Tongans, and the Borana of Ethiopia, all different from one another, are directed in accordance with cyclical schemes the calculations for which can be described using modular arithmetic. Complex geometrical designs, the making of which is considered necessary for the social education of Tamil Nadu women of southern India, can be described via string languages and can therefore be duplicated by computer. A very slight extension leads Ascher to fractals.

Detailed explanations of these remarkable phenomena are provided, making this book well worth studying. Although I recommend it highly, I deplore the uniform carelessness with which underlying mathematical principles are enunciated.

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