Full House (5 page)

After all, one kid may have a ten-dollar bill, and the other nine nothing. One dollar per kid would still be the mean value, but would such a figure accurately characterize the population? Similarly, to be serious about real cases, spin doctors for politicians in power often use mean incomes to paint dishonestly bright pictures. Suppose that, under 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"
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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 album of reality. All these images clip the wings of taxonomy and reduce the science of classification to the dullest task of keeping things neat and tidy. But these portrayals also reflect a cardinal fallacy: the assumption of a fully objective nature "out there" and visible in the same way to any unprejudiced observer (the same image that I criticized in the first section of this chapter as "Huxley’s chessboard"). If such a vision could be sustained, I suppose that taxonomy would become the most boring of all sciences, for nature would then present a set of obvious pigeonholes, and taxonomists would search for occupants and shove them in—an enterprise requiring diligence, perhaps, but not much creativity or imagination.

But classifications are not passive ordering devices in a world objectively divided into obvious categories. Taxonomies are human decisions imposed upon nature—theories about the causes of nature’s order. The chronicle of historical changes in classification provides our finest insight into conceptual revolutions in human thought. Objective nature does exist, but we can converse with her only through the structure of our taxonomic systems.

We may grant this general point, but still hold that certain fundamental categories present so little ambiguity that basic divisions must be invariant across time and culture. Not so—not for these, or for any subjects. Categories are human impositions upon nature (though nature’s factuality offers hints and suggestions in return). Consider, as an example, the "obvious" division of humans into two sexes.

We may view male versus female as a permanent dichotomy, as expressions of two alternative pathways in embryological development and later growth. How else could we possibly classify people? Yet this "two-sex model" has only recently prevailed in Western history (see Laqueur, 1990; Gould, 1991), and could not hold sway until the mechanical philosophy of Newton and Descartes vanquished the Neoplatonism of previous worldviews. From classical times to the Renaissance, a "one-sex model" was favored, with human bodies ranged on a continuum of excellence, from low earthiness to high idealization. To be sure, people might clump into two major groups, called male and female, along this line, but only one ideal or archetypal body existed, and all actual expressions (real persons) had to occupy a station along a single continuum of metaphysical advance. This older system is surely as sexist as the later "two-sex model" (which posits innate and predetermined differences of worth from the start), but for different reasons—and we need to understand this history of radically altered taxonomy if we wish to grasp the depth of oppression through the ages. (In the "one-sex model," conventional maleness, by virtue of more heat, stood near the apex of the single sequence, while the characteristic female form, through relative weakness of the same generating forces, ranked far down the single ladder.)

This book treats the even more fundamental taxonomic issue of what we designate as a thing or an object in the first place. I will argue that we are still suffering from a legacy as old as Plato, a tendency to abstract a single ideal or average as the "essence" of a system, and to devalue or ignore variation among the individuals that constitute the full population. (Just consider our continuing hang-ups about "normality." When I was a new father, my wife and I bought a wonderful book by the famous pediatrician T. Berry Brazelton. He wrote to combat every parent’s excessive fear that one standard of normality exists for a child’s growth, and that anything your particular baby does must be judged against this unforgiving protocol. Brazelton used the simple device of designating three perfectly fine pathways, each exemplified by a particular child—one hellion, one in the middle, and one shy baby who, in gentle euphemism, was labeled "slow to warm up." Even three, instead of one, doesn’t capture the richness of normal variation, but what a fine start in the right direction.)

In his celebrated analogy of the cave, Plato (in the Republic) held that actual organisms are only shadows on the cave’s wall (empirical nature)— and that an ideal realm of essences must exist to cast the shadows. Few of us would maintain such an unbridled Platonism today, but we have never put aside this distinctive view that populations of actual individuals form a set of accidents, a collection of flawed examples, each necessarily imperfect and capable only of approaching the ideal to a certain extent. One might survey this pool of accidents and form some idea of the essence by cobbling together the best parts—the most symmetrical nose from this person, the most oval eyes from a second, the roundest navel from a third, and the best-proportioned toe from a fourth—but no actual individual can stand for the category’s deeper reality.

Only by acknowledging this lingering Platonism can I understand the fatal inversion that we so often apply to calculated averages. In Darwin’s post-Platonic world, variation stands as the fundamental reality and calculated averages become abstractions. But we continue to favor the older and opposite view, and to regard variation as a pool of inconsequential happenstances, valuable largely because we can use the spread to calculate an average, which we may then regard as a best approach to an essence. Only as Plato’s legacy can I grasp the common errors about trends that make this book necessary: our misreading of expanding or contracting variation within a system as an average (or extreme) value moving somewhere.

I spoke in chapter 2 about completing Darwin’s revolution. This intellectual upheaval included many components—in part (and already accomplished among educated people during Darwin’s lifetime), the simple acceptance of evolution as an alternative to divine creation; in part (and still unfulfilled), Freud’s pedestal-smashing recognition of Homo sapiens as only a recent twiglet on an ancient and enormous genealogical bush. But, in an even more fundamental sense, Darwin’s revolution should be epitomized as the substitution of variation for essence as the central category of natural reality (see Mayr, 1963, our greatest living evolutionist, for a stirring defense of the notion that "population thinking," as a replacement for Platonic essentialism, forms the centerpiece of Darwin’s revolution). What can be more discombobulating than a full inversion, or "grand flip," in our concept of reality: in Plato’s world, variation is accidental, while essences record a higher reality; in Darwin’s reversal, we value variation as a defining (and concrete earthly) reality, while averages (our closest operational approach to "essences") become mental abstractions.

Darwin knew that he was overturning fundamental ideas with venerable Greek ancestry. During his late twenties, in a youthful notebook about evolution, he wrote a wonderful, sardonic commentary about Plato’s theory of essences—noting succinctly that the existence of innate ideas need not imply an ethereal realm of unchanging essential concepts, but may only indicate our descent from a material ancestor: "Plato says in Phaedo that our ’imaginary ideas’ arise from the preexistence of the soul, are not derivable from experience—read monkeys for preexistence."

In his poem History, Ralph Waldo Emerson records the grand legacies held by this greatest of all subjects:

I am the owner of the sphere ...
Of Caesar’s hand, and Plato’s brain,
Of Lord Christ’s heart, and Shakespeare’s strain.

These legacies are our joy and inspiration, but also our weights and impediments. Read monkeys for preexistence, and read variation as the primary expression of natural reality.