The Fruitful Facets of Galton's Polyhedron 389
chequers originated in the form of bars at the posterior end of the wing and
then spread from behind forward (1919, p. 55).The trend, Whitman argues, is pervasive and entirely general. He presented
(1919) a remarkable vision of inexorable movement through the entire family of
pigeons, from a uniformly spotted archetype to some idealized, albinized version
of the Holy Ghost, depicted as a pure white dove in many medieval paintings:
"When we see all these stages multiplied and varied through some 400 to 500 wild
species and 100 to 200 domestic breeds, and in general tending to the same goal,
we begin to realize that they are... slowly passing phases in the progress of an
orthogenetic process of evolution, which seems to have no fixed goal this side of
an immaculate monochrome—possibly none short of complete albinism." Can one
conceive a more unpigeonlike state (in both appearance and deed)—at least in our
metaphors—than "immaculate"? To the primary spotting agent of cities throughout
the world, Whitman thus gave a higher aspiration and the promise of a purer form.
As the Psalmist wrote, "Behold, I was shapen in iniquity... Wash me, and I shall
be whiter than snow" (Psalm 51).
The hypothesized putative inexorability of this trend allowed Whitman to
explain or interpret many otherwise puzzling phenomena. He seemed most pleased
about the unification thereby provided for the two main patterns of domestic
pigeons—the empirical source of the entire study. If Darwin had been right,
Whitman argued, then the origin of Darwin's postulated ancestral pattern (two-
barred) would remain a mystery, and we would also lack any explanation for the
subsequent evolution of checkers de novo. But if the trend begins with the
turtledove pattern as ancestral, then the checkered state may be easily derived there
from, and the two-barred condition becomes just a further step in reduction and
concentration of pigment along an orthogenetic series. (This argument, of course,
leaves the origin of the turtledove pattern itself as an unexplained "primitive term,"
but methods of phyletic analysis can at least establish its ancestral status.) "We
could not explain how two bars could arise de novo in a clear gray wing surface;
but we can see how a sweeping reduction process, anteroposterior in direction,
would leave two or more rows of chequers cut to dimensions that would coalesce
in transverse bars at the posterior end of the wing" (1919, p. 61).
To cite another example of variational puzzles resolved by the orthogenetic
trend, Whitman notes that the stock dove, Columba aenas, develops weaker bars
than the domestic pigeon and never exhibits any checkers. The trend, having so far
surpassed the stage reached by domestic pigeons, no longer permits the
development of any checkers, even as an occasional variant in highly colored
individuals: "We can readily understand why the stock dove, which has, at least in
many cases, a vestigial third bar, quite like that in domestic pigeons, never appears
in chequered dress. It is moving in the other direction, and no reversal of course is
now open to it" (1919, pp. 60-61).
On the second criterion of channeled variability, Whitman cites three lines