When the slab rests ... on the edge AB ... it stands in its most stable position ... So long as it is merely tilted it will fall back on being left alone, and its position when merely tilted corresponds to a simple deviation. But when it is pushed with sufficient force, it will tumble on to the next edge, BC, into a new position of stability. It will rest there, but less securely than in its first position; moreover its range of stability will no longer be disposed symmetrically. A comparatively slight push from the front will suffice to make it tumble back, a comparatively heavy push from behind is needed to make it tumble forward. ... If, however, the slab is at length brought to rest on the edge CD . . . the next onward push, which may be very slight, will suffice to topple it over into an entirely
5-1. Galton's own illustration of his model of the polyhedron. Note how the themes of saltation, or facet flipping, and constraint in strictly limited pathways available for change arise from a similar geometric basis in this mode of depiction.
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new system of stability; in other words, a “sport” comes suddenly into existence.
In Galton's own conception, the polyhedron embodies four major implications that assert and codify the power of formalist constraint as an evolutionary agent of change (not just an impediment), while controverting the essential Darwinian claim that natural selection alone builds new forms in a creative and accumulative fashion.
1. Occasional large variations (sports) are more important for evolution than omnipresent, normally distributed small variation. This substitution of big for small forces a major compromise, and may even represent a fatal weakness, in Darwin's theory of natural selection.
Galton first introduced his polyhedron to question Darwin's key claim for insensible gradation in evolutionary continuity. (Galton, of course, did not deny continuity, but he wished to substitute a series of jumps — facet flipping, if you will — for Darwin's smoothness): “It is shown by Mr. Darwin, in his great theory of 'The Origin of Species,' that all forms of organic life are in some sense convertible into one another, for all have, according to his views, sprung from common ancestry.... Yet the changes are not by insensible gradations; there are many, but not an infinite number of intermediate links; how is the law of continuity to be satisfied by a series of changes in jerks?” (1884 edition, p. 369).
In a later article on “Discontinuity in evolution,” Galton posed the fundamental question of change in Darwin's favored style: “By what steps did A change into B? Was it necessarily through the accumulation of a long succession of alterations, individually so small as to be almost imperceptible, though large and conspicuous in the aggregate, or could there ever have been abrupt changes?” (1894, p. 363). Acknowledging the criterion of relative frequency for resolving debates in natural history, Galton correctly notes that Darwin did catalog exceptions, but only to log their peripheral character and to assert the domination of gradualistic accretion by natural selection leading to adaptation:
Notwithstanding a multitude of striking cases of the above description collected by Darwin, the most marked impression left on the mind by the sum of all his investigations was the paramount effect of the accumulation of a succession of petty differences through the influence of natural selection. This is certainly the prevalent idea among his successors at the present day, with the corollary that the Evolution of races and species has always been an enormously protracted process. I have myself written many times during the last few years in an opposite sense to this.
Galton then strongly asserts that most evolutionary novelty, in opposition to Darwin, probably arises per saltum: “Many, if not most breeds, have had their origin in sports” (p. 365). Galton bases his rationale on the argument that continuous, small-scale Darwinian variability, though omnipresent, cannot [Page 347] be effective because regression toward the mean precludes accumulation in favored directions. Galton introduces the term “transilience” (literally “going between,” and recently revived by Templeton, 1982, for a different mechanism in the same spirit) to describe his favored concept of non-Darwinian saltatory variation, or facet flipping:
No variation can establish itself unless it be of the character of a sport, that is, by a leap from one position of organic stability to another, or as we may phrase it, through “transilient” variation. If there be no such leap the variation is, so to speak, a mere blend or divergence from the parent form, towards which the offspring in the next generation will tend to regress; it may therefore be called a “divergent” variation.... I am unable to conceive the possibility of evolutionary progress except by transiliences, for, if they were merely divergences, each subsequent generation would tend to regress backwards towards the typical center (p. 368).
2. Internal factors establish a hierarchy of stabilities, discontinuous in origin, and explaining differing degrees of divergence among typical forms.
The nonhomogeneity of morphospace seems so “obviously” intrinsic to nature (lions close to tigers, with a big jump separating all cats from dogs and wolves) that we rarely consider the puzzles thereby raised. Once evolution itself becomes paradigmatic, simple inheritance and descent become the obvious, first-level reason for ordering the resemblances portrayed in our taxonomic hierarchies. But simple descent does not solve all problems of “clumping” in phenotypic space; we still want to know why certain forms “attract” such big clumps of diversity, and why such large empty spaces exist in conceivable, and not obviously malfunctional, regions of potential morphospace. The functionalist and adaptationist perspective (see Dobzhansky, 1958, quoted herein on p. 527, for a particularly striking metaphor of this view) ties this clumping to available environments, and to shaping by natural selection. Structuralists and formalists wonder if some clumping might not record broader principles, at least partly separate from a simple history of descent with adaptation — principles of genetics, of development, or of physical laws transcending biological organization.
Galton proposed his polyhedron to explain a hierarchy of stabilities as internally generated, not externally shaped by gradual natural selection. As the long quotation (p. 345) and figure indicate, Galton purposely shaped his model to encompass both small islands of stability within species (“subtypes” in his terms, and easily subject to reversion by tipping back to the primary type — as in facet BC of Fig. 5-1, which easily falls back to AB, but can move onward to a new type only by a much bigger push), and also to cover the origin of new taxa that cannot revert (the push from facet CD to any position across the long axis and its major facet AB). Of course, Galton's polyhedron does include a role for external forces like natural selection: something must push, or the polyhedron can't move at all. But selection, in this model, provides only an impetus: both discontinuity and directionality of change follow [Page 348] internal rules (completely for discontinuity, and partly for directionality by establishing channels — trajectories between facets — that must translate the impetus into actual change).
In an interesting discussion, Galton distinguishes internally enjoined positions of stability from clumping by simple descent, and he rejects the Darwinian argument that taxonomic structure records differential shaping by natural selection: “In the first place each race has a solidarity due to common ancestors and frequent interbreeding. Secondly, some may think it, though not by myself, to have been pruned into permanent shape by the long-continued action of natural selection. But, in addition to these, I have for some years past maintained that a third cause exists more potent than the other two, and sufficient by itself to mold a race, namely that of definite positions of organic stability” (1894, p. 364).
Obviously struggling with a difficult concept that eludes precise formulation, Galton seizes upon a variety of metaphors from “governments, crowds, landscapes, and even from cookery and . . . from mechanical inventions” (1889, p. 22) to argue that workable solutions may be viewed as isolated and stable islands in a sea of largely empty space (impossib
le combinations). These “nucleating points” mark physically possible places, predetermined by the structure of matter and space, not a posteriori results of natural selection working as a contingent force in local environments. (Today, of course, we would formulate this idea in Darwinian terms as “multiple adaptive peaks,” but Galton struggles with an alternate view, worthy of our respect as an interesting option, of discontinuous solutions, internally set. In Galton's mechanism, natural selection would still operate — but only in the negative role of policing, and the facilitating task of providing a push into a preset channel.) Only a few forms of government can lead to internal stability; only some landscapes cohere; only a few combinations make flavorful dishes, despite a wide range of ingredients. In a memorable defense of formalist preference for the timelessness of distinct and stable configurations, and for downplaying the role of historical specificity, Galton writes of crowds and public rituals: “Every variety of crowd has its own characteristic features. At a national pageant, an evening party, a race-course, a marriage, or a funeral, the groupings in each case recur so habitually that it sometimes appears to me as if time had no existence, and that the ceremony in which I am taking part is identical with others at which I had been present one year, ten years, twenty years, or any other time ago” (1889, p. 23). Misidentifying (as King Solomon) the Preacher of Ecclesiastes, Galton regrets the sameness that such structural ahistoricity imposes. But he cannot disparage the way of the world: “It is the triteness of these experiences that makes the most varied life monotonous after a time, and many old men as well as Solomon have frequent occasion to lament that there is nothing new under the sun” (1889, p. 24).
Morphotypes represent islands of stability, rare combinations of coherence among available parts (for history only becomes relevant by providing an inventory of availability). Natural selection may preserve these morphotypes once they form by facet flipping, but their origin must be regarded as discontinuous [Page 349] and internally mediated. The public carriages of London take discrete forms as omnibuses, hansoms, and four-wheelers. All these forms can be improved, but the boundaries of the types seem inviolable, for “the old familiar patterns cannot, as it thus far appears, be changed with advantage, taking the circumstances of London as they are.” (Galton, obviously, did not anticipate the macromutation of the internal combustion engine!) The three “islands” arose as discontinuous inventions and cannot be transformed one into the other, for intermediary steps would be structurally inviable: “A useful blend between a four-wheeler and a hansom would be impossible; it would have to run on three wheels and the half-way position for the driver would be upon its roof” (1889, p. 31). (In the old hansom, or two-wheeled cab, the driver sat on an elevated platform behind the passenger cabin, and reins to the horses ran over the roof. Drivers of four-wheeled cabs sat in front.)
3. The positions of stability, for both subtypes (discontinuities within species) and types, are not honed by natural selection, but internally preset as rare configurations of coherence among parts. The causal basis of stable form must therefore be explained by internal integrity, not by adaptation.
In his first formulation (1869, 1884 edition, p. 370), Galton proposed an internal, correlational basis for morphological stability: “It is easy to form a general idea of the conditions of stable equilibrium in the organic world where one element is so correlated with another that there must be an enormous number of unstable combinations for each that is capable of maintaining itself unchanged, generation after generation.”
As his most enduring practical legacy, Galton (1892) pioneered the use of fingerprints in identification and criminology. He also found in these “papillary ridges” an ideal example of discontinuous stable “islands” (subtypes in this case) that could not be attributed to direct natural selection. Galton extols the value of these patterns as stable and traceable throughout ontogeny: “We know nothing by observation about the persistence of any internal character, because it is not feasible to dissect a man in his boyhood, and a second or third time in his after life, whereas finger prints can be taken as often as desired” (1894, p. 366).
Fingerprints serve as ideal examples of internally generated structural islands for “they fall into three definite and widely different classes . . . transitional forms between them being rare and the typical forms being frequent, while the frequency of deviations from the several typical centers . . . correspond approximately with the normal law of frequency” (1894, pp. 366-367). Individual patterns remain stable throughout life “and are consequently not unimportant in spite of their minute character” (p. 366).
Nonetheless, the stabilization of these three typical forms cannot be attributed to natural selection:
Notwithstanding the early appearance of the patterns in fetal life and their apparent importance, they are totally independent of any quality upon which either natural selection or marriage selection can be conceived to depend. For example, I find the same general run of patterns in [Page 350] English, Welsh, Jews, Basques, Hindoos, Negroes, and men of culture, farm laborers, criminals, and idiots. I have failed to observe the slightest correlation between the patterns and any single personal quality whether physical or mental. They are therefore to be looked upon as purely local peculiarities, with a slight tendency towards transmission of inheritance (p. 366).
Galton concludes his treatment of this case with a formalist flourish: “I therefore insisted that the continual appearance of these well-marked and very distinct patterns proved the reality of the alleged positions of organic stability, and that the latter were competent to mold races without any help whatever from the process of selection, whether natural or sexual.”
4. Galton's polyhedron also highlights the theme of internally based directionality, not only of discontinuous change.
Galton often stated that his model did not deny continuity in change (1869, 1884 edition, p. 369), but only confuted the insensible character of transitions — for the polyhedron tumbles in a jerky fashion by facet flipping, and does not roll smoothly towards “better” positions. Galton's conception of change does grant a role to natural selection; some force has to push the polyhedron.
But a status as provider of an impetus scarcely fulfills Darwinian requirements for selection's power. In a metaphor for illustrating pure Darwinism, organisms may be represented as billiard balls, with natural selection as the pool cue. A perfectly round ball denotes Darwinian isotropic variation; the organism only supplies raw material, and cannot set its own direction of change. The ball's trajectory depends upon the pool cue of natural selection and the form of the surface (local environment). (The surface of this old table may be channeled and pitted, representing directions favored by external environments.) The pool cue supplies propulsion, and the ball rolls with no internal control over its own direction of motion.
But Galton's polyhedron pushes back. Absent an impetus, the polyhedron cannot tumble at all, but the pusher (the “pool cue” in Galton's model) doesn't set the direction of motion (or at least can only push effectively in a strictly limited number of trajectories set by the configuration of facets on the morphologically complex “billiard ball”). The direction of tumbling will therefore be determined as much by the internal structure of the polyhedron as by the coordinates and strength of the impetus. Only certain, internally established channels of change can be realized, even if natural selection must always initiate the tumbling of the polyhedron — a very different image from setting the smooth billiard ball in motion! In this sense, Galton's polyhedron weds the theme of directionality with the idea of discontinuity.
Galton emphasizes this dual concern in his initial presentation. Just after describing the first version of his polyhedron (the stone with many facets), he introduces another metaphor to reinforce the theme of directionality combined with facet flipping — an image that may not be so apt or fruitful as the polyhedron itself, however expressive of Galton's intent: [Page 351]<
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Now for another metaphor, taken from a more complex system of forces. We have all known what it is to be jammed in the midst of a great crowd, struggling and pushing and swerving to and fro, in its endeavor to make a way through some narrow passage. There is a dead lock; each member of the crowd is pushing, the mass is agitated, but there is no progress ... At length, by some accidental unison of effort, the dead lock yields, a forward movement is made, the elements of the crowd fall into slightly varied combinations, but in a few seconds there is another dead lock, which is relieved, after a while, through just the same process as before. Each of these formations of the crowd, in which they have found themselves in a dead lock, is a position of stable equilibrium and represents a typical attitude (1869, 1884 edition, pp. 369-370).
Formalism, as the preceding chapter documents, boasts a long and distinguished pedigree, well antedating both Darwin and any explicit discussion of evolution. Darwinism rendered many formalist concerns irrelevant, but key features of the structuralist agenda could not be encompassed, or even well addressed, by natural selection and its functionalist mechanics. Galton's polyhedron provides a strikingly apt metaphor for the two great themes of formalism that continue to demand attention within evolutionary theory, and that the Darwinism of his day could not adequately comprehend — discontinuous evolution, and internally generated pathways: in other words, saltation and channels. Both themes express the more general conception that internal properties of organisms “push back” against external selection, thereby rendering evolution, as dialectic of inside and outside — that organism, in other words, must be conceived as polyhedrons, not billiard balls.
The Structure of Evolutionary Theory Page 56