344 THE STRUCTURE OF EVOLUTIONARY THEORY
will, in subsequent generations, regress towards the mean, and no permanent or
directional modification can therefore accrue. Substantial change to new "types"
and taxa must occur by the occasional production of true-breeding "sports"—
discontinuous variants that do not meld to intermediacy in hybrid offspring, and
are therefore not subject to regression. In thus emphasizing "sports" for
evolutionarily efficacious variation, and stability for taxa at other times (as
regression to the mean holds continuous variants in check), Galton also became a
hero of the early Mendelians, Bateson and de Vries, particularly for his role in
formulating a general rationale for their non-Darwinian concept of saltational
origin for new species by macromutation.
Galton subsumed both non-Darwinian formalist themes of discontinuity in
effective variation and internally-generated, preferred channels of change
(constraints) in a brilliant metaphor that I have called "Galton's polyhedron" (see
Gould and Lewontin, 1979). This image had been forgotten by 20th century
biologists, but many of Galton's contemporaries discussed the model and its
implications. Mivart (1871) invoked the polyhedron as a centerpiece of the critique
that most attracted Darwin's attention and response (see Mivart, 1871, pp. 97, 113,
and 228); W. K. Brooks (1883, p. 296) cited this image in the most important
American treatise on variation, a book that strongly influenced Brooks's visiting
student, William Bateson. Bateson (1894, p. 42) then described "the metaphor
which Galton has used so well—and which may prove hereafter to be more than a
metaphor." Kellogg (1907), speaking of Galton's "familiar analogy" (p. 332),
considered the polyhedron as an ideal illustration for the key non-Darwinian
challenge of heterogenesis (saltational evolution). And de Vries (1909, p. 53)
stated that Galton's polyhedron expressed his own view of variation "in a very
beautiful way."
Galton introduced the metaphor of the polyhedron in his eugenic manifesto
and most influential book, Hereditary Genius (1869). In discussing "stability of
types" in the closing chapter on "general considerations," Galton presented his
model in an overtly material, and petrological, form:
The mechanical conception would be that of a rough stone, having, in
consequence of its roughness, a vast number of natural facets, on any one
of which it might rest in "stable" equilibrium. That is to say, when pushed it
would somewhat yield, when pushed much harder it would again yield, but
in a less degree; in either case, on the pressure being withdrawn, it would
fall back into its first position. But, if by a powerful effort the stone is
compelled to overpass the limits of the facet on which it has hitherto found
rest, it will tumble over into a new position of stability, whence just the
same proceedings must be gone through as before, before it can be
dislodged and rolled another step onwards. The various positions of stable
equilibrium may be looked upon as so many typical attitudes of the stone,
the type being more durable as the limits of its stability are wider. We also
see clearly that there is no violation of the law of continuity in the
movements of the stone, though it can only repose in certain widely
separated places (1884 edition, p. 369).