1192 THE STRUCTURE OF EVOLUTIONARY THEORY
In a third category, D'Arcy Thompson then considers geometrically regular growth
patterns of more complex creatures in cases where an observed order might record
the operation of a simple building principle plausibly regulated by direct mechanical
production—as in his most famous chapter on the logarithmic spiral (mainly in
molluscan shells, but also for unicellular forams and ruminant horns) as the paradigm
curve that increases in size without changing its shape; and his largely derivative
discussion of phyllotaxis, with obedience to the Fibonacci series explained not as a
Pythagorean mystery, but as an automatic consequence of initiating each new spiral
in a radiating series by setting its founding element into the largest available space at
the generating center.
But when, in a final set of cases, D'Arcy Thompson must discuss the complex
features of "higher" metazoan phyla that cannot be reduced to consequences of single
principles in growth—in other words, the difficult problems of morphology that have
always been regarded as paramount to the enterprise—he makes much less headway,
and largely confines his attention to "peripheral" questions, including the ordering of
differences among forms as expressions of relatively simple transformation gradients
(but leaving the core form as an unexplained "primitive term" or "given" in the
analysis), and the correlation of obviously ecophenotypic or epigenetic modifications
(the healing of broken bones, for example) with forces acting upon the object during
this secondary modification. (We shall see (pp. 1196-1200) how his inability to treat
the shared properties of complex taxonomic Bauplane as more than unexplained
inputs into his theory of transformation scuttles any hope that his system might enjoy
controlling, or even general, application as a theory of biological form.)
To illustrate how D'Arcy Thompson applies his central argument across this
empirical range, we should consider his own favored principle of surface/ volume
ratios as an exemplar because the fundamental property of size itself establishes a
basic prediction for testing the efficacy of physical forces. Allometric "corrections"
and accommodations can only proceed so far, and small creatures should therefore be
predominantly shaped by forces acting on surfaces, and large animals by forces
acting on volumes. Creatures of intermediate size might record a "tug of war,"
displaying the work of both sets. I therefore consider three famous examples of
sensible correlations with increasing size.
- For tiny creatures living fully in the realm of surficial forces, D'Arcy
Thompson documents the conformity of many organisms (across a wide taxonomic
spectrum) to the shape of "such unduloids as develop themselves when we suspend
an oil-globule between two unequal rings, or blow a soap-bubble between two
unequal pipes" (p. 247). (Obviously, D'Arcy Thompson must identify, in each case,
the specific organic constraint corresponding to the two terminal rings of unequal size
in his physical models. In one case, for example, he writes (p. 247) that "the surface
of our Vorticella bell finds its terminal supports, on the one hand in its attachment to
its narrow stalk, and on the other in the thickened ring from which spring its
circumoral cilia.")