1202 THE STRUCTURE OF EVOLUTIONARY THEORY
Thompson emphasizes that "there is no argument against the theory of evolutionary
descent" (1942, p. 1094) in such a concept, but he also maintains that this view of
life's conformity to ordinary physical principles suggests a wide and radical range of
non-Darwinian implications, including the rejection of Darwin's views on
imperfection of the geological record, a defense of saltational transition between
Bauplane (contrasted with potential continuity of taxonomic order within), and a
solution to the problem of life's inhomogeneous occupation of potential morphospace
as an organic incarnation of real mathematical discontinuities in the geometry of
nature.
There is one last lesson, which coordinate geometry helps us to learn.... In the
study of evolution, and in all attempts to trace the descent of the animal
kingdom, fourscore years' study of the Origin of Species has had an unlooked-
for and disappointing result. ...
This failure to solve the cardinal problem of evolutionary biology is a very
curious thing... We used to be told, and were content to believe, that the old
record was of necessity imperfect—we could not expect it to be otherwise; the
story was hard to read because every here and there a page had been lost or
torn away... But there is a deeper reason. When we begin to draw
comparisons between our algebraic curves and attempt to transform one into
another, we find ourselves limited by the very nature of the case...
An algebraic curve has its fundamental formula, which defines the family
to which it belongs ... With some extension of the meaning of parameters, we
may say the same of the families, or genera, or other classificatory groups of
plants and animals... We never think of "transforming" a helicoid into an
ellipsoid, or a circle into a frequency-curve. So it is with the forms of animals.
We cannot transform an invertebrate into a vertebrate, nor a coelenterate into
a worm, by any simple and legitimate deformation...
A "principle of discontinuity," then, is inherent in all our classifications,
whether mathematical, physical or biological; and the infinitude of possible
forms, always limited, may be further reduced and discontinuity further
revealed ... The lines of the spectrum, the six families of crystals, Dalton's
atomic law, the chemical elements themselves, all illustrate this principle of
discontinuity. In short, nature proceeds from one type to another among
organic as well as inorganic forms; and these types vary according to their
own parameters, and are defined by physico-mathematical conditions of
possibility. In natural history Cuvier's "types" may not be perfectly chosen nor
numerous enough, but types they are; and to seek for stepping-stones across
the gaps between is to seek in vain, forever. ...
Our geometrical analogies weigh heavily against Darwin's conception of
endless small continuous variations; they help to show that discontinuous
variations are a natural thing, that "mutations"—or sudden changes, greater or
less—are bound to have taken place, and new