Full House by Stephen Jay Gould Read Free Book Online Page A

super-Reaganomic system with tax breaks only for the rich, a few millionaires add immense wealth while a vast mass of people at the poverty line either gain nothing or become poorer. The mean income may rise because one tycoon’s increase from, say, $6 million to $600 million per year may balance several million paupers. If one man gains $594 million and one hundred million people lose five dollars each (for a total of $500 million), mean income for the whole population will still rise—but no one would dare say (honestly) that the average person was making more money.
    Statisticians have developed other measure of average, or "central tendency," to deal with such cases. One alternative, called the mode, is defined as the most common value in the population. No mathematical rule can tell us which measure of central tendency will be most appropriate for any particular problem. Proper decisions rest upon knowledge of all factors in a given case, and upon basic honesty.
    Would anyone dispute a claim that modes, rather than means, provide a better understanding of all the examples presented above? The modal amount of money for the ten kids is zip. The modal income for our population remains constant (or falls slightly), while the mean rises because one tycoon makes an immense killing. The modal weight for the population of my second silly example remains at fifty pounds. The fifteen gainers increase steadily (and the mean of the whole population therefore rises), but who would deny that stability of the majority best characterizes the population as a whole? (At the very least, allow me that you cannot represent the population by the rising mean values of Figure 3 if, for whatever personal reason, you choose to focus on the gainers—and that you must identify the stability of the majority as a major phenomenon.) I be-labor this point because my second focal example, progress in the history of life, emerges as a delusion on precisely the same grounds. A few creatures have evolved greater complexity in the only direction open to variation. The mode has remained rock-solid on bacteria throughout the history of life—and bacteria, by any reasonable criterion, were in the beginning, are now, and ever shall be the most successful organisms on earth.
    Variation as Universal Reality
    I have tried to show how an apparent trend in a whole system—traditionally read as a "thing" (the population’s average, for example) moving somewhere—can represent a false reading based only on expansion or contraction of variation within the system. We make such errors either because we focus myopically upon the small set of changing extreme values and falsely read their alteration as a trend in the whole system (my first case, to be illustrated by 0.400 hitting in baseball)—or because variation can expand or contract in only one direction, and we falsely characterize the system by a changing mean value, while a stable mode suggests a radically different interpretation (my second case, to be illustrated by the chimera of progress as the primary thrust of life’s history).
    I am not saying that all trends fall victim to this error (genuine "things" do move somewhere sometimes), or that this "fallacy of reified variation" 2 exceeds in importance the two more commonly recognized errors of confusing trends with random sequences, or conflating correlation with causality. But the variational fallacy has caused us to read some of our most important, and most intensely discussed, cultural trends in an ass-backwards manner. I am also intrigued by this fallacy because our general misunderstanding or undervaluation of variation raises a much deeper issue about the basic perception of physical reality.
    We often portray taxonomy as the dullest of all fields, as expressed in a variety of deprecatory metaphors: hanging garments on nature’s coat-rack; placing items into pigeonholes; or (in an image properly resented by philatelists) sticking stamps into the