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in the Popular Press

"It All Adds Up": Review of *Science and an African Logic,* by Helen Verran. Reviewed by Margarget Wertheim. *CalendarLive on latimes.com,* 23 December 2001.

Helen Verran taught mathematics and science to teachers at Obafemi Awolowo University in Ife-Ife, Nigeria, between 1979 and 1986. There "she found that her African pupils would often approach mathematical problems in what, to her Western-trained eyes, seemed highly unorthodox ways. It turns out that the Yoruba language has a particularly flexible way of representing numbers. Although in English and in other Western languages, any given number has a unique verbal representation, in Yoruba there will be many ways of speaking a large number---for the number 19,669, for example, Verran lists no fewer than seven distinct ways. Each variation is a verbal encoding of a different arithmetic pattern: ((20,000 x 1) - 400) + (-1 - 10 + (20 x 4)) = 19,669 or (20,000 - 1,000) + (-100 + (200 x 4)) - (1 + 30) = 19,669." The flexibility is due to the fact that, unlike our system based on the number 10, the Yoruba language recognizes three bases: 10, 5, and 20. Verran's two key insights are that the Yoruba traditionally had no written form for their numbers (numbers were always verbal and never abstract) and that their understanding of numbers is based on the body (reflecting the human arrangement of fingers and toes). The reviewer praises Verran's book *Science and an African Logic* as "a major contribution to the debate" about how humans think of numbers that "will no doubt keep philosophers arguing for years to come."

*--- Annette Emerson*