Late Biologist Gould Used Math to Clarify Arguments
June 1 -- Stephen Jay Gould, the eminent evolutionary biologist and stylish essayist who died last month, used mathematics to elucidate many ideas, both in and out of science.
Gould's was a wide-ranging and impassioned voice of reason that will be keenly missed. One aspect of his work that particularly appealed to me was his use of simple mathematical observations and analogies to help clarify his multifarious arguments.
Baseball, Bacteria, and the Complexity of Life
Gould was, for example, famously interested in baseball, bacteria, and the complexity of life and characteristically managed to connect them in an enlightening and non-trivial way. Consider his explanation for the disappearance of the .400 hitter in baseball in his book, Full House, The Spread of Excellence.
He argued that the absence of such hitters in recent decades was not due to any decline in baseball ability but rather to a gradual decrease in the disparity between the worst and best players, both pitchers and hitters. When almost all players are as athletically gifted as they are now, the distribution of batting averages shows less variability. The result is that .400 averages are now very scarce. Players' athletic prowess is close to the "right wall" of ultimate human excellence in baseball.
Leading to bacteria and complexity, Gould next asked his readers to consider an imaginary country in which initially every adult receives an annual salary of $100. Assume that every few years each person's salary is either adjusted upward by $100 (say 45 percent of the time) or downward by the same amount (say 55 percent of the time) with the proviso that no one's salary ever declines below $100, the minimum wage.
After a number of generations the largest salary in the country will likely be quite a bit larger than $100 and the average will rise somewhat as well. This is because there is, at first, only one direction for salaries to grow; there is a "left wall" below which salaries can't decline. Although the $100 salary becomes less common over time, it nonetheless remains the most common salary.
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