An article by Richard Lewontin in the current New York Review, on the life and work of Stephen Jay Gould, concludes with the observation that "[w]hat was most extraordinary about him, however, was the unresisting ease with which he faced his own imminent extinction." This may remind those of us who have treasured Gould's popular science writings of one of his most personal personal essays, "The Median Isn't the Message," on, of all things, probability and statistics.
Gould's serious health troubles began in 1982, when he was diagnosed with abdominal mesothelioma. In the essay he relates how, after surgery, he asked the oncologist where he might find the best technical literature on his disease, a rare cancer linked to asbestos exposure. He was told that "the medical literature contained nothing really worth reading."
Soon as he could walk, Gould was punching "mesothelioma" into a search program at the medical library of Harvard University, where he taught. The basic information was discouraging and probably shed light on the reticence of his usually frank oncologist: the disease "was incurable, with a median mortality of only eight months after discovery." He was of course crushed--until, after a few minutes, his mind began to work again.
"Median mortality of eight months after discovery," Gould realized, did not necessarily mean he would probably be dead inside of one year. It only meant that, of all the people receiving his diagnosis, half were dead eight months later. What about the half that weren't? To illustrate his line of optimistic--and, in this case, clear--thinking, consider the statement that the median income of a certain population is $50,000 per year. That means that half of all people in the population earn less than $50,000. It says nothing about the actual incomes of the other half. For both income and period of survival, zero is necessarily a lower limit, so one is justified in saying, for example, that half of all people diagnosed with Gould's disease survive for from zero to eight months. But there is no upper limit. A median mortality of eight months after discovery does not preclude the possibility that those surviving for more than eight months live relatively normal lives for years (just as a median income of $50,000 does not preclude the possibility that, of those in the upper half of the distribution, most earn several times $50,000).
When graphed, income and survival periods after mesothelioma is discovered have generally the same shape. They are right-skewed, which is to say that they rise very steeply close to the vertical axis and, having reached a peak a bit to the left of the median, gradually taper off and approach the horizontal axis, with decreasing slope, as one proceeds farther and farther away from zero. The message, one might say, is not the median, but the difference between the median and the mean.
Gould's mesothelioma had been detected early, and he enjoyed access to superior medical care. He made a full recovery and lived until May 20, 2002, when he died of a different cancer. The median mortality for mesothelioma is eight months but he survived for almost twenty years.
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