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Full House Follies

Review of Full House: The Spread of Excellence from Plato to Darwin by Stephen Jay Gould (NY: Harmony Books, 1996) Published in Origins & Design 18, no. 1

This little book is intended to correct the popular impression that “progress and increasing complexity” are characteristics of life’s course on Earth. Progress has, in the twentieth century, already been punched silly; but paleontologists seem genuinely more complex than paramecia, a point that Gould concedes, if only for reasons of professional pride. His doubts arise whenever the twig of a trend is taken as typical or representative. The underlying error evidently runs deep. “[W]e are still suffering,” he writes, “from a legacy as old as Plato, a tendency to abstract a single idea or average as the ‘essence’ of a system, and to devalue or ignore variation among the individuals that constitute the full population” (40).

If essentialism is the affliction, evolution is the remedy. “Darwin’s revolution,” Gould believes, “should be epitomized as the substitution of variation for essence as the central category of natural reality,” (42). The revolution complete, there will be individuals and their variances out there where the central categories lie. Nothing else. This seems for all the world like nominalism, a doctrine current in Twelfth century Paris, where Abelard may be seen stealing kisses from Helo├»se, drab Darwin dutifully waiting his turn at bat. Gould is off by centuries; his essential quarrel, of course, is with Aristotle and the doctrine of real essences.

No matter, I would ordinarily say, drawing down the curtain of charity. Like paleontology, philosophy is an acquired taste. But having been tempted by philosophy, Gould is tempted again by statistics, prompting me to yank that curtain up again. Witness thus his discussion of normal distributions, the familiar bell-shaped curve. “We regard the normal distribution as canonical,” Gould writes, “because we tend to view systems as having idealized ‘correct’ values, with random variations on either sideanother consequence of lingering Platonism” (52).

I am afraid that Plato, poor pooch, has nothing to do with it. Whatever the Form of the Good may be, it is not constructed by counting noses. We regard the normal distribution as canonical because it is canonical, a fact readily demonstrated in elementary texts, the distribution of distributions itself following a bell shaped curve. Perhaps that curtain had better stay up. Although drawn incorrigibly to the Big Picture, the focal plane of Gould’s attention is best adapted to short distances. Ted Williams was the last of the big-time hitters, his 1941 record now receding into memory and myth. Why should this be, Gould asks? It is not clear that in a world bursting with sin and suffering this question cries out for an answer, but the question illustrates a trend, and trends are what tend to interest Gould.

The disappearance of the four-hundred hitter might suggest that in baseball, as in so much else, things have gotten worse. In fact, Gould argues, play has in general improved, those rumpy players now scampering across the field better-conditioned and surely better-paid than their stubble-chinned predecessors. It is this circumstance, curiously enough, that provides Gould with an answer to his question.

What follows as the standard of play improves? Nothing on average, better hitters encountering better fielders, their simultaneous improvements canceling one another. But athletic performance is bounded by a wall marking the limitations of the human body. Batters may hit so far, and no further; there are some balls that no ballboy ever shags. The wall stands to the right of the bell curve measuring athletic performance like the north face of Anapurna, grim, forbidding and uncrossable. As play improves, the bell curve shifts itself closer to the wall. Variations shrink, the right tail of the curve steepening. Without such steepening, the curve would cross the wall into the forbidden zone. The disappearance of the four-hundred hitter now follows inexorably, if only because his room for maneuver has been vacated, the batter squeezed between better competition and the wall.

This is an elegant analysis, but one that tempts Gould anew into the badlands of metaphysics. “Hitting 400,” Gould concludes, “is not a thing, but the right tail of the full house for variations of batting averages.” With this, who would quarrel, but then who has ever been persuaded that a batting average is a thing? The assimilation of a very particular batting average to the full house of variations is a mistake as well. An average is a number; the full house a curve embodying a multitude of points and so a continuum of numbers. Trends arise when specific points on the curve are tracked.

Gould has confused the shadow of one distinction for the substance of another. If he could have continued to play unaged, Ted Williams would have seen his batting average drop year by year, even though he stood forever in the sunshine of his youth. Batting averages are relative to the circumstances of play. In this, a man may be diminished without changing, his relative decline nonetheless marking a real trend. Not so in the case of height or weight. No man becomes fat because other men have grown thin. It is this distinction between relative and absolute properties that is the cynosure of Gould’s concerns. The contrast between variations and trends that Gould means to collapse remains healthy as a horse. “Darwin’s revolution will be completed,” Gould writes, “when we smash the pedestal of human arrogance and own the plain implications of evolution for life’s nonpredictable non-directionality”(29). A great many biologists seem keen to smash that pedestal, seeing forever an ape’s haunted eyes peering from every human face; but the more that Darwinian thought shows that life is going nowhere, the less it explains about where life has gone, the net effect akin to division by zero. Writing about the evolution of the horse, Gould juxtaposes evolutionary fable to the fossil record. High school textbooks propose that, desiring an increase in stature, the rabbit-sized Eohippus (but not curiously enough, the rabbit-sized rabbit), commenced his move up through the evolutionary ranks, one incremental step after the other. This might suggest a trend, the familiar museum displays showing the beasts getting bigger and better, with even their coats becoming glossier over time.

The fossil record shows something different: rather a thick bush, with horse-like species entering the record at one time, leaving it at another. The high school progression is an artifact; a great many intermediates are absent from the record, their trace only a doleful dotted line. The facts are discrete. There is no hint of gradual change, no hint either of selective advantages accumulating. “Throughout the history of horses,” Gould recounts (quoting Prothero and Shubin’s well-known monograph), “the species are well-marked and static over millions of years.”

All this confirms Gould in his conviction that variations are crucial and trends an epiphenomena; but having in this case destroyed the notion of an evolutionary progression, Gould runs the risk of destroying the notion of an evolutionary explanation as well. The stratigraphic charts make the heresy irresistible. There is variance, to be sure, but no change in variance, and so no evident trend. Why imagine that there is anything to the record beyond what one seesone damn horse after the other? If the horses are going nowhere, not so the Foraminfera–single-celled creatures, protozoa, in fact, that popped into existence at the beginning of the Cretaceous some 136 million years ago. Starting out small, some species increased in size, at least until an obliging mass extinction served to reduce the population, with essentially the same story replayed during the earlier and later Cenozoic eras. The statistics reflect a bell-shaped curve, but one that is skewed in the directing of increasing size.

An effect demands a cause. Why the skewing? The classical Darwinian explanation involves a trip of three steps: random variations, followed by natural selection, followed in turn by biological change. Gould proposes to cut out the middleman entirely, moving from random variations to biological change wholesale.

What is given, then, are Foraminfera with an inherent variability, a repertoire of potential changes. As the Cretaceous commences, they are, those protozoa, collected by a wall marking the lower limits of their size. Thereafter, they simply drift, taking themselves to whatever place their variations allow. The wall functions to enforce a principle of elastic reflection; as protozoa hit the wall, they bounce forward. This serves to impart a preferred direction to their drifting, the simple structure of a stochastic set-up producing a simulacrum of a trend. Some species get bigger over time simply because they have the chance. “Size increase,” Gould writes, “is really random evolution away from small size, not directed evolution toward large size” (162).

Such is Gould’s theory of expanding stochastic variation. It is a theory that suggests again to Gould the enduring reality of variations, the trends in this case arising from a failure to properly distinguish passive from driven systems. The driven systems move forward with a vengeance, natural selection on the classical view positively hustling species over an adaptive landscape; the passive systems just sit there and drift. This distinction seen, trends tend to dwindle and disappear, leaving behind only the Foraminfera, smiling enigmatically, like so many cats. Does the combination of drift and bounce suffice in the case of Foraminfera to explain their increase in size? We cannot be sure. Size has been measured by a single numerical parameter; this lends a false plausibility to a picture of driftfalse because lacking analytical precision. Foraminfera never become large as whales. Their variations are bounded. How so? And by what? The mechanism of variation that allows Foraminfera to increase in size, too, is left largely in the dark, with no coordination drawn between what the Foraminfera do and how they do it. The statistical pattern that Gould sees among the Foraminfera he sees again in life as a whole. There is no progress in the evolutionary record; indeed, no overall trends. Life is dominated by bacteria, the little bugs slithering through every interstice and filling every conceivable crevice, the bacterial mode remaining unchanged over time, stable as a rock and about as interesting. There is, Gould acknowledges, the fact that “the most complex creature has tended to increase in elaboration through time,” (169), but increasing complexity reflects nothing more than the same pattern seen locally among the Foraminfera as they increase in size. The mean measuring complexity increases, the mode does not; whatever trends are tending reflect “changes in variation rather than things moving somewhere” (168).

By now the point has become familiar while remaining unpersuasive, like an advertisement for breakfast cereal. The provocative and plausible part of Gould’s thesis lies elsewherewith the idea of expanding stochastic variation. But where the doctrine is plausible, as in the case of Foraminfera, it is not provocative, and where provocative, not plausible.

Looking backwards some 3.5 billion years, Gould observes bacteria crouched by an initial wall, one marking what he calls “minimal complexity.” Movement away from the wall is movement toward increasing complexity. “As life diversified,” he writes, “only one direction stood open for expansion” (171). Some species have grown progressively more complex; but “the vaunted progress of life,” Gould writes with satisfaction, “is really random motion away from simple beginnings, not directed impetus toward inherently advantageous complexity” (173).

In coming to this conclusion, Gould has been misled by his own analogy between size and complexity. Both increasing size (among Foraminfera) and increasing complexity (in life) yield right-skewed distributionsbell-shaped curves with long right tails. Such is the statistical picture, but it is a picture that describes as well the distribution of height in human habitation since the fifteenth century. Most buildings have remained small, some have gotten bigger; and no one imagines that taller buildings arise because they have simply “wandered into a previously unoccupied domain.” This is a point to which Gould is sensitive, but the statistical tests that he invokes to distinguish passive from driven systems seem to me far too coarse to be of interest.

Expanding stochastic variation may well carry the Foraminfera to an increase in size; the problems associated with complexity are of a different order entirely. Biological objects are made of many parts and only a particular arrangement of those parts serves to realize a biological function. A probability thresholda wall, to continue Gould’s imageseparates complex objects from any mechanism of random search. No arbitrary rearrangement of the eye is apt to see; no reconfiguration of the heart to pump blood. This is to speak only at the most superficial level of analysis. An organism comprises any number of very complex systems coordinated to achieve a variety of familiar but poorly-described biological functions. Even the simplest of biological systems–the bacterial cell, in fact–suggests an exponentially increasing order of complexity, as complex structures interact with one another in ways that are themselves complex.

The great evolutionary trajectories span many dimensions and relatively short periods of time. Causes evoke effects, but effects in turn influence their causes; things are strongly non-linear and analytically intractable. The structures that result occupy points in a space that no mathematician has ever glimpsed, let alone described. The examples of complexity that Gould invokes, by way of contrast, are one dimensional and almost hopelessly trivial, a point that with a good-natured shrug, Gould himself comes close to acknowledging.

Gould is right to scruple at progress, but he has added his voice late to the chorus. Everyone else has already left off shouting. He is right again to be skeptical of traditional explanations in biology. Richard Dawkin’s The Blind Watchmaker and Daniel Dennett’s Darwin’s Dangerous Idea are books in which ignorance is made an epistemological principle. But he is wrong to suppose that the only alternative to systems driven by natural selection are systems that are not driven at all. Random mechanisms cannot in principle explain the nature of biological complexity, the doctrine of expanding stochastic variation returning evolutionary thought to the dread place from which it has always tried to flee. By endeavoring to deconstruct a distinction between trends and variances, Gould has inadvertently come to express a more profound and ultimately more explosive truth: that the issue why things in biology change as they do remains what it has always been, which is to say an abysmal mystery.

David Berlinski

Writer, Thinker, Raconteur, and Senior Fellow, Discovery Institute
David Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He is currently a Senior Fellow at Discovery Institute's Center for Science and Culture. Dr. Berlinski has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at such universities as Stanford, Rutgers, the City University of New York and the Universite de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis (IIASA) in Austria and the Institut des Hautes Etudes Scientifiques (IHES) in France.