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Theoretical Statistics Is Practical and Life-Giving
Theoretical Statistics Is Practical and Life-Giving

Theoretical Statistics Is Practical and Life-Giving

In “The Median Isn’t the Message,” Stephen Jay Gould (evolutionary biologist who taught at Harvard University) wrote:
My life has recently intersected, in a most personal way, two of Mark Twain’s famous quips. One I shall defer to the end of this essay. The other (sometimes attributed to Disraeli), identifies three species of mendacity, each worse than the one before – lies, damned lies, and statistics. Many people make an unfortunate and invalid separation between heart and mind, or feeling and intellect. In some contemporary traditions, abetted by attitudes stereotypically centered on Southern California, feelings are exalted as more “real” and the only proper basis for action – if it feels good, do it – while intellect gets short shrift as a hang-up of outmoded elitism. Statistics, in this absurd dichotomy, often become the symbol of the enemy. As Hilaire Belloc wrote, “Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.” This is a personal story of statistics, properly interpreted, as profoundly nurturant and life-giving. It declares holy war on the downgrading of intellect by telling a small story about the utility of dry, academic knowledge about science. Heart and head are focal points of one body, one personality.
Mr. Gould also goes on to discuss how the Platonic view that the type or kind is (most) real is false; what is true is the Aristotelian view that the individual (“variation”) is real. He says:
We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous “beginning of life” or “definition of death,” although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation. But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.
Notice how Mr. Gould is talking about kinds of things as being separate from variation, shadings, and continua. I don’t know if he’d say everything was like that, even individuals, but if so, I’d have to disagree: individuals are distinct and separate; this is given clearly (by real, immutable cause-effect relationships) in perception. Kinds of things, conceptual categories, come about only by recognizing things in their reality- and perceptually-given background of variation: tables grasped as related to but contrasted with furniture and other items in a house; trees grasped as related to but contrasted with grass and bushes; people grasped as related to but contrasted with other animals; engineers grasped as related to but contrasted with other human professions. Concepts are only ways of categorizing individuals based on cause-effect and explanatory relationships. Individuals are most real; types or kinds are real, but have a “secondary, dependent existence” to individuals.

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