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1 . One basically sophistic argument against progress holds that the word itself is too vague or subjective, and that the concept should be dropped for lack of rigor in description. This argument is a cop-out, and I will certainly not invoke such a lame defense in this book. Progress is too vague to stand by itself, but a variety of operational surrogates have been proposed—ranging from something as precise and measurable as brain size to more general, but still definable, notions as anatomical complexity (usually construed as number of parts and their degree of differentiation, assessed in various ways). I shall argue that progress as the primary thrust of life’s history cannot be defended even for these operational surrogates.
2 . Reification is an unfamiliar word, but this term describes the fallacy so well that I hasten to use (and explain) it. As coined by philosophers and social scientists in the mid-nineteenth century, reification refers to "the mental conversion of a person or abstract concept into a thing" (Oxford English Dictionary). The word comes from the Latin res, meaning "thing" (a republic, or res publica, is the people’s thing). When committing the error discussed in this book, we abstract the variation within a system into some measure of central tendency, like the mean value—and then make the mistake of reifying this abstraction and interpreting the mean as a concrete "thing"; we then compound our error by assuming that changes in the mean must, ipso facto, be read as an entity moving somewhere. Or, in another version of the same fallacy, we focus on extremes in variation and falsely reify these values as separate things, rather than treating them as an inextricable part of the entire system’s variation.
3 . I do rec
ognize, of course, that these claims also play into the Genesis Myth of former Elysian fields versus modern palaces to Mammon—but my argument hinges on distinguishing the pure Genesis Myth that batters have gotten absolutely worse from a more reasonable claim that players are just as good (or better), but that batting has become relatively harder for some reason.
4 . All bets are off when fundamentally new equipment or procedures enter the field, as in the fiberglass pole, or (God forbid) the aluminum bat, which (we may hope and pray) will never darken the doorstep of major league dugouts. Such innovations will produce sudden blips in curves of improvement. In fact, such innovations are usually better treated statistically as the beginning points of new curves.
5 . The recent disparity between the two leagues records, in large part, the introduction of the "designated hitter" to the American League alone—a permanent "pinch hitter" for the pitcher. His substitution for the pitcher doesn’t affect the decadal average per se, because I don’t include pitchers in this calculation. But the designated hitter still provokes a small general rise in the American League mean by introducing another good bat into the lineup, whereas the National League retains more relatively poor hitters in the bottom part of the order. Nonetheless, I remain an adamant opponent of the DH rule—the one vital subject in our culture that permits no middle ground. You gotta either love it or hate it!
6 . I referred to my first method as working "on the cheap" because five-highest and five-lowest represents a quicker and dirtier calculation than the full standard deviation of all players. But I knew that this shortcut would provide a good surrogate for the more accurate standard deviation because standard deviations are particularly sensitive to values farthest from the mean—a consequence of squaring the deviation of each player from the mean at one point in the calculation. Since my quick-and-dirty method relied entirely on values farthest from the mean, I knew that it would correlate closely with the standard deviation.
7 . These statistics can also be broken down to yield finer patterns that validate the hypothesis. The National League began in 1876, the American in 1901. Since the hypothesis holds that systems equilibrate through time by decelerating decrease in variation, we might predict that, from 1901 to 1930, when the American League was new but the National already in middle age, variation in American League records should decrease more rapidly than comparable measures in the National League. This pattern does indeed emerge, both for standard deviations of batting averages in my calculations, and for the history of differences in best versus worst teams in the data of Chatterjee and Yilmaz.
8 . In more complex cases involving several entities, the wall might be an "absorbing boundary" that destroys any object hitting it. No matter (so long as enough entities are left to play the game—certainly the case with life’s history). The important point is that an entity can’t penetrate the wall and continue to move in the wall ward direction—whether or not the entity bounces off or gets killed.
BY THE SAME AUTHOR
Ontogeny and Phylogeny
Ever Since Darwin
The Panda’s Thumb
The Mismeasure of Man
Hen’s Teeth and Horse’s Toes
The Flamingo’s Smile
An Urchin in the Storm
Time’s Arrow, Time’s Cycle
Illuminations (WITH R. W. PURCELL)
Wonderful Life
Bully for Brontosaurus
Finders, Keepers (WITH R. W. PURCELL)
Eight Little Piggies
Dinosaur in a Haystack
Copyright © 1996 by Stephen Jay Gould
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