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Quarterly Review
A Great Mind at Work
Full House: The Spread of Excellence from Plato to Darwin by Stephen Jay Gould
(Harmony Books, 1996, $14)
Reviewed by Amy S. Bouska
Attention, Syllabus Committee! This book is about the use and misuse of statistical concepts, and contains accessible examples of clear reasoning and hypothesis testing. Of course, it may be difficult to determine which exam should contain its broad range of other topics, including the size of catcher's mitts, the evolution of horses and foraminifera, men's vs. women's winning Boston Marathon times, the death of the 0.400 batting average, and the importance of bacteria.
The title of the book is taken from Gould's primary theme—that a variable system cannot be adequately described by a single parameter, such as the mean. Rather, it is necessary to view the "full house" of variation, including other descriptors such as the mode and the skewness of the distribution. He applies this assertion to two general areas: baseball and evolution.
Even for someone who is not a baseball addict, his chapters on the game and its statistics are fascinating. It is particularly interesting to watch as he develops testable hypotheses, and examines the data to either accept or reject these ideas, all the while working to support his central thesis that the current dearth of 0.400 batting averages actually represents an overall improvement in the level of play. He traces the continuing battle between pitchers and batters, concluding that both have improved so much that they are approaching the absolute limits imposed by the physics of the human body, the bat, and the baseball.
In developing his hypothesis, he examines and discards the "Genesis Myth" (batters were better in the good old days) and the "tougher competition" theory (the introduction of relief pitching, bigger fielder's gloves, and more scientific management). He argues that various changes in the rules over time (for example, in the location of the pitching mound and the size of the strike zone) have been introduced to maintain the desired parity between pitchers and hitters, that is, the desired overall batting average. Thus, the mean of the system has changed very little. He demonstrates, however, that the standard deviations of both the batting average of regular players and the winning percentage of National League teams have decreased. Based on these and other statistical compilations, he concludes that the overall level of play has changed (improved) so much that the 0.400 tail has been compressed away.
After mining the rich statistical fields of the U.S. national pastime, Gould turns to his professional practice area, evolution. Here, his assertion is that there is no general drive towards complexity over time, that is, homo sapiens is a random occurrence, not the result of an innate evolutionary bias towards "higher" organisms.
He agrees completely that the mean level of complexity (as represented in the fossil record) has increased over time. He asserts that this is the necessary result of starting with the simplest possible organisms—there has been nowhere to go but "up." However, returning again and again to the book's title, he insists that it is not the mean that is important, but rather the full distribution. While the mean and the skewness of the complexity distribution of species have increased over time, the mode of terrestrial life was and continues to be firmly bacterial.
Within the general argument, he also presents data supporting the conclusion that, even for more complex species, descendant species show no detectable trend towards increasing complexity. Gould is particularly distressed by the usual evolutionary illustrations that show, for example, small horses evolving along a clear path into today's much larger steeds. The fossil record indicates that, contrary to this simplistic idea of lineal development, equine evolution was noticeably indirect. For example, at least one step on this supposed developmental ladder had no successor species and the next step actually arose from a different branch.
Professor Gould (1941-2002) was one of the most prolific and readable of the relatively limited group of excellent scientists who write for nonscientists. In addition to his many "lay" science books, he also wrote 300 consecutive columns for Natural History magazine. However, as a MacArthur Prize Fellow and the Alexander Agassiz Professor of Zoology and Professor of Geology at Harvard, he was also a highly respected scientist. With Niles Eldredge, he developed the punctuated equilibria theory of evolution. Before his untimely death from cancer (unrelated to the mesothelioma that was diagnosed in 1982), he published The Structure of Evolutionary Theory, a 1,400-page exposition of his interpretation of evolution.
This is a truly excellent book for anyone who enjoys spying on a great mind at work in the fields of scientific thought, or who has harbored the secret dream that baseball is actually the pinnacle of evolution.