When I was a Zoology undergraduate at Oxford my teachers often referred to D’Arcy Wentworth Thompson’s book “On Growth and Form”. They acknowledged it as a work of undoubted erudition, but somehow they evaded any impact it might have on our studies. That was reserved for Darwin, and Darwin alone.
Returning to “on Growth and Form” after several decades it is possible to better comprehend what Thompson was trying to say. In his own words:
The fact that I set little store by certain postulates (often deemed to be fundamental) of our present day biology the reader will have discovered and I have not endeavored to conceal. But it is not for the sake of polemical argument that I have written, and the doctrines which I do not subscribe to I have only spoken of by the way
He was referring to Darwinism. What he was really interested in was how mathematics could explain biological phenomena. Thompson was a polymath, who fully understood the course of Western thought. He was aware that Pythagoras has discovered how the qualities of music could be resolved to geometrical figures, and thus sparked a revolution in Greek thought. Perhaps it was his ambition to do the same with living creatures. The beauty of mathematics and the acceptance that it is conterminous with space and coeval with time led him to say that A greater than Milton had magnified the theme and glorified Him “that sitteth upon the circle of the earth,” saying: He hath measured the waters in the hollow of his hand, and meted out heaven with the span, and comprehended the dust of the earth in a measure.Indeed, he finishes his work with a tribute to Jean Henri Fabre, of whom he says who being of the same blood and marrow with Plato and Pythagoras, saw in Number le comment et le pourquoi des choses [the how and the why of things], and found in it la clef de voute de l’Univers [the key to the vault of the universe].
The beauty that Thompson comprehended is today replaced by the drab meaninglessness that is regarded as the triumph of resolving the science of life to pure atheism. Thompson would have none of it. For him the living world reflected something vastly greater, something immensely more intelligible than an abyss of random forces. As we shall see he left unmistakable clues in “On Growth and Form” of his view of a mathematics that reflected the intelligence that lies behind the universe .