The Fruitful Facets of Galton's Polyhedron 411
In a statement reminiscent of D'Arcy Thompson (see p. 1179), Bateson
expresses his hopes for mathematical analysis in morphology:
It is in the geometrical phenomena of life that the most hopeful field for the
introduction of mathematics will be found. If anyone will compare one of
our animal patterns, say that of a zebra's hide, with patterns known to be of
a purely mechanical production, he will need no argument to convince him
that there must be an essential similarity between the processes by which
the two kinds of patterns were made... Patterns mechanically produced
are of many and very diverse kinds. One of the most familiar examples, and
one presenting some especially striking analogies to organic patterns, is that
provided by the ripples of a mackerel sky, or those made in a flat sandy
beach by the wind or the ebbing tide. With a little research we can find
among the ripple marks, and in other patterns produced by simple physical
means, the closest parallels to all the phenomena of striping as we see them
in our animals... We cannot tell what in the zebra corresponds to the wind
or the flow of the current, but we can perceive that in the distribution of the
pigments... a rhythmical disturbance has been set up which has produced
the pattern we see; and I think we are entitled to the inference that in the
formation of patterns in animals and plants mechanical forces are operating
which ought to be, and will prove to be, capable of mathematical analysis
(1913, p. 36).Though Bateson never found his underlying vibrations, his faith in their
existence as bearers of heredity fueled his primary anti-Darwinian argument for
discontinuous variation, and consequent evolution by internally generated
saltation:
When the essential analogy between these various classes of phenomena is
perceived, no one will be astonished at, or reluctant to admit, the reality of
discontinuity in variation, and if we are as far as ever from knowing the
actual causation of pattern we ought not to feel surprised that it may arise
suddenly or be suddenly modified in descent. Biologists have felt it easier
to conceive the evolution of a striped animal like a zebra from a self
colored type like a horse ... as a process involving many intergradational
steps; but so far as the pattern is concerned, the change may have been
decided by a single event, just as the multitudinous and ordered rippling of
a beach may be created or obliterated at one tide (1913, pp. 36-37).Bateson remained obstinate, and no closer to a solution, as the chromosomal
theory became a foundation of modern biology. In 1924, he wrote to the great
mathematician G. H. Hardy: "We have had some absurd attempts— mostly from
biometricians—to apply mathematics to biology, but as I said my hope is still that I
may live to see mathematics applied to biology properly. The most promising place
for a beginning, I believe, is the mechanism of pattern."