350 THE STRUCTURE OF EVOLUTIONARY THEORY
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."
- 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: