Late Biologist Gould Used Math to Clarify Arguments

A more heartening use of a mathematical notion appeared in his well-known article, "The Median Isn't the Message." There Gould discussed being diagnosed in 1982 with abdominal mesothelioma, a cancer whose median survival time is (or at least was) eight months; that is, half the people with it live less than eight months, half longer. He took comfort from the fact that the mean or average survival time might nevertheless be considerably longer than eight months. This could occur in the same way that the average home price in a neighborhood might be $1,000,000 even if the median price were just $50,000 (if, say, there were a few palatial mansions surrounded by many quite modest homes).

Gould's book, The Mismeasure of Man, is also full of mathematical observations, most devoted to undermining the foundations of I.Q. testing. He criticized disguised confusions of correlation and causation in the misapplication of statistical techniques such as factor analysis and regression analysis. In a related New Yorker piece on The Bell Curve he illuminated the I.Q. debate with a discussion on the heritability of height in impoverished villages in India. Tall fathers there, say over 5 feet, 7 inches, generally have tall sons, while short fathers there, say under 5 feet, 2 inches, generally have short sons.

Despite this undisputed heritability of height (much more so than for I.Q.), most would conclude that improved nutrition and sanitation would raise the average height of the villagers to that in the West. The conclusion: the heritability of characteristics (such as height or I.Q.) within populations is not an explanation for average differences between populations.

Being an evolutionary biologist, Gould was always conscious not merely of averages, but of variations, exceptions, and diversity. Appropriately, his writings across a wide range of disciplines were themselves various, exceptional, and diverse.

He was a rare throwback to a less myopically specialized era.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on appears the first weekend of every month.

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