MATHEMATICS ELSEWHERE: An Exploration of Ideas Across Cultures

MATHEMATICS ELSEWHERE: An Exploration of Ideas Across Cultures. By Marcia Ascher. Princeton Univ. Press. 207 pp. $24.95

I’m probably not the only one who’s going to throw an "End of the World" party on December 21, 2012, the day that the 5,125-year cycle of the Mayan "long count" calendar ends. The Maya themselves never thought that the end of the long count would mark the end of the world, but some modern New Agers fear the apocalypse when the last hour of the last day on the Mayan calendar ticks away.

Whereas the Western calendar (like most other modern calendars) is linear—the numbered years get greater and greater without end—the Mayan calendar is cyclical, resetting every 5,125 years. The Maya perceived something as basic as the passage of time from a totally different viewpoint. In Mathematics Elsewhere, Ascher, a professor emerita of mathematics at Ithaca College, seeks to enter the mathematical mindsets of other cultures through the Mayan calendar, the Marshall Islanders’ intricate maps, the Tongan system of social ranking, the ornate flour figures that Tamil women would draw on their thresholds, and a number of other customs. The result is both fascinating and frustrating.

At times, the book provides a compelling glimpse into another civilization. For example, one chapter describes how the Marshall Islanders, who live on tiny islands scattered across a million square kilometers of the Pacific, were able to navigate vast stretches of seemingly featureless ocean. Ascher delves deeply into the islanders’ once-mysterious methods, including the frail-looking frameworks of palm ribs lashed together with coconut fibers that guided canoes from island to island, and the training of the navigators (lying in their outriggers, they learned to sense the interplay of wind, water, and land).

By depicting "some mathematical ideas of people in traditional or small-scale cultures," Ascher aims to contribute to "a global and humanistic history of mathematics." But while the practices in the book are describable by mathematics, there is, with few exceptions, little evidence that they reflect a different type of mathematical thought than Westerners’. Just because Marshall Islanders represented ocean swells rather than physical distances on their maps doesn’t mean that they had a fundamentally different view of relationships in space, nor does our ability to represent Tamil drawings by a mathematical formalism known as an "L-system" mean that Tamil matrons implicitly understood formal systems and recursive algorithms.

When there is a clear mathematical conclusion to be drawn—for example, that the Maya used zero some centuries before it appeared in Europe—Ascher curiously shies away from it. This is particularly disappointing because the Mayan and other calendars give her the strongest case for seeing a different type of mathematics in another culture— cyclical calendars may have forced a few cultures’ timekeepers to explore rudimentary ideas in mathematical group theory, a subject that didn’t captivate the West until later.

Despite the weak mathematics, Mathematics Elsewhere provides interesting snapshots of different cultures. Perhaps it should have been titled simply Elsewhere.

—Charles Seife