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.
Part Two
DEATH AND HORSES:
Two CASES
for THE PRIMACY
OF VARIATION
Before presenting my central examples of baseball and life, I offer two cases to illustrate my contention that our culture encodes a strong bias either to neglect or ignore variation. We tend to focus instead on measures of central tendency, and as a result we make some terrible mistakes, often with considerable practical import.
4
Case One: A Personal Story
Where any measure of central tendency acts as a harmful abstraction, and variation stands out as the only meaningful reality
In 1982, at age forty, I was diagnosed with abdominal mesothelioma, a rare and "invariably fatal" form of cancer (to cite all official judgments at the time). I was treated and cured by courageous doctors using an experimental method that can now save some patients who discover the disease in an early stage.
The cancer survivors’ movement has spawned an enormous literature of personal testimony and self-help. I value these books, and learned much from them during my own ordeal. Yet, although I am a writer by trade, and although no experience could possibly be more intense than a long fight against a painful and supposedly incurable disease, I have never felt any urge or need to describe my personal experiences in prose. Instead, as an intensely private person, I view such an enterprise with horror. In all the years then and since, I have been moved to write only one
short article about this cardinal portion of my life.
I accept and try to follow the important moral imperative that blessings must be returned with efforts of potential use to others. I am therefore enormously grateful that this article has been of value to people, and that so many readers have requested copies for themselves, or for a friend with cancer. But I did not write my article either from compulsion (as a personal testimony) or from obligation (to the moral requirement cited above). I wrote my piece, The Median Is Not the Message, from a different sort of intellectual need. I believe that the fallacy of reified variation—or failure to consider the "full house" of all cases—plunges us into serious error again and again: my battle against cancer had begun with a fine example of practical benefits to be gained by avoiding such an error, and I could not resist an urge to share the yarn.
We have come a long way from the bad old days, when cancer diagnoses were scrupulously hidden from most patients—both for the lamentable reason that many doctors regarded deception as a preferred pathway for maintaining control, and on the compassionate (if misguided) assumption that most people could not tolerate a word that conveyed ultimate horror and a sentence of death. But we cannot overcome obstacles with ignorance: consider what Franklin D. Roosevelt could have contributed to our understanding of disability if he had not hidden his paralysis with such cunning care, but had announced instead that he did not govern with his legs.
American doctors, particularly in intellectual centers like Boston, now follow what I regard as the best strategy for this most difficult subject: any information, no matter how brutal, will be given upon request (as compassionately and diplomatically as possible, of course); if you don’t want to know, don’t ask. My own doctor made only one departure from this sensible rule—and I forgave her immediately as soon as I faced the context. At our first meeting, after my initial surgery, I asked her what I could read to learn more about mesothelioma (for I had never heard of the disease). She replied that the literature contained nothing worth pursuing. But trying to keep an intellectual from books is about as effective as that old saw about ordering someone not to think about a rhinoceros. As soon as I could walk, I staggered over to the medical school library and punched mesothelioma into the computer search program. Half an hour later, surrounded by the latest articles, I understood why my doctor had erred on the side of limited information.
All the literature contained the same brutal message: mesothelioma is incurable, with a median mortality of eight months following diagnosis. A hot topic of late, expressed most notably in Bernie Siegel’s best-selling books, has emphasized the role of positive attitude in combating such serious diseases as cancer. From the depths of my skeptical and rationalist soul, I ask the Lord to protect me from California touchie-feeliedom. I must, nonetheless, express my concurrence with Siegel’s important theme, though I hasten to express two vital caveats. First, I harbor no mystical notions about the potential value of mental calm and tenacity. We do not know the reasons, but I am confident that explanations will fall within the purview of scientific accessibility (and will probably center on how the biochemistry of thought and emotion feed back upon the immune system). Second, we must stand resolutely against an unintended cruelty of the positive attitude" movement—insidious slippage into a rhetoric of blame for those who cannot overcome their personal despair and call up positivity from some internal depth. We build our personalities laboriously and through many years, and we cannot order fundamental changes just because we might value their utility: no button reading "positive attitude" protrudes from our hearts, and no finger can coerce positivity into immediate action by a single and painless pressing. How dare we blame someone for the long-standing constitution of their tendencies and temperament if, in an uninvited and unwelcome episode of life, another persona might have coped better? If a man dies of cancer in fear and despair, then cry for his pain and celebrate his life. The other man, who fought like hell and laughed to the end, but also died, may have had an easier time in his final months, but took his leave with no more humanity.
My own reaction to reading this chillingly pessimistic literature taught me something that I had suspected, but had not understood for certain about myself (for we cannot really know until circumstances compel an ultimate test): I do have a sanguine temperament and a positive attitude. I confess that I did sit stunned for a few minutes, but my next reaction was a broad smile as understanding dawned: "Oh, so that’s why she told me not to read any of the literature!" (My doctor later apologized, explaining that she had erred on the side of caution because she didn’t yet know me. She said that if she had been able to gauge my reaction better, she would have photocopied all the reprints and brought them to my bedside the next day.)
My initial burst of positivity amounted to little more than an emotional gut reaction—and would have endured for only a short time, had I not been able to bolster the feeling with a genuine reason for optimism based upon better analysis of papers that seemed so brutally pessimistic. (If had read deeply and concluded that I must inevitably die eight months hence, I doubt that any internal state could have conquered grief.) I was able to make such an analysis because my statistical training, and my knowledge of natural history, had taught me to treat variation as a basic reality, and to be wary of averages—which are, after all, abstract measures applicable to no single person, and often largely irrelevant to individual cases. In other words, the theme of this book—"full house," or the need to focus upon variation within entire systems, and not always upon abstract measures of average or central tendency—provided substantial solace in my time of greatest need. Let no one ever say that knowledge and learning are frivolous baubles of academic sterility, and that only feelings can serve us in times of personal stress.
I started to think about the data, and the crucial verdict of "eight months’ median mortality" as soon as my brain started functioning again after the initial shock. And I followed my training as an evolutionary biologist. Just what does "eight months median mortality" signify? Here we encounter the philosophical error and dilemma that motivated this book. Most people view averages as basic reality and variation as a device for calculating a meaningful measure of central tendency. In this Platonic world, "eight months’ median mortality" can only signify: "I will most probably be dead in eight months"—about the most chilling diagnosis anyone could ever read.
But we make a serious mistake if we view a measure of central tendency as the most likely outcome for any single individual—though most of us commit this error all the time. Central tendency is an abstraction, variation the reality. We must first ask what "median" mortality signifies. A median is the third major measure of central tendency. (I discussed the other two in the last chapter—the mean, or average obtained by adding all the values and dividing by the number of cases; and the mode, or most common value.) The median, as etymology proclaims, is the halfway point in a graded array of values. In any population, half the individuals will be below the median, and half above. If, say, in a group of five children, one has a penny, one a dime, one a quarter, one a dollar, and one ten dollars, then the kid with the quarter is the median, since two have more money and two less. (Note that means and medians are not equal in this case. The mean wealth of $2.27—the total cash of $11.36 divided by five—lies between the fourth and fifth kids, for the tycoon with ten bucks overbalances all the paupers.) We favor medians in such cases, when extension at one end of the variation drags the mean so far in that direction. For mortality in mesothelioma and other diseases, we generally favor the median as a measure of central tendency because we want to know the halfway point in a series of similar outcomes graded in time. A higher mean might seem misleading in the case of mesothelioma because one or two people living a long time (the analog of the kid with ten bucks) might drag the mean to the right and convey a false impression that most people with the disease will live for more than eight months—whereas the median correctly informs us that half the afflicted population dies
within eight months of diagnosis.
We now come to the crux of practice: I am not a measure of central tendency, either mean or median. I am one single human being with mesothelioma, and I want a best assessment of my own chances—for I have personal decisions to make, and my business cannot be dictated by abstract averages. I need to place myself in the most probable region of the variation based upon particulars of my own case; I must not simply assume that my personal fate will correspond to some measure of central tendency.
I then had the key insight that proved so life-affirming at such a crucial moment. I started to think about the variation and reasoned that the distribution of deaths must be strongly "right skewed" in statistical parlance—that is, asymmetrically extended around a chosen measure of central tendency, with a much wider spread to the right than to the left. After all, there just isn’t much room between the absolute minimum value of zero (dropping dead at the moment of diagnosis) and the median value of eight months. Half the variation must be scrunched up into this left half of the curve (see Figure 4) between the minimum and the median. But the right half may, in principle, extend out forever, or at least into extreme old age. (Statisticians refer to the ends of such distribution as "tails"—so I am saying that the left tail abuts a wall at zero survivorship, while the right tail has no necessary limit but the maximal human life span.)
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