# Thompson, D'Arcy Wentworth (1860–1948)

D'Arcy Thompson was a Scottish naturalist and polymath. Thompson held a professorial chair at
St. Andrews and Dundee, Scotland, for the amazing period of 64 years, a
record for tenure unlikely ever to be broken. Although he wrote more than
300 scientific articles and books, his reputation is based primarily on
his efforts to reduce biological phenomena to mathematics in his magnum
opus *On Growth and Form* (1917).^{1} In this book, full of
marvelous sketches of such things as Nautilus shells and honeycombs, Thompson
claimed that much about animals and plants could be understood by the laws
of physics, as mirrored in the structures and patterns of mathematics. His
most novel idea was to show how mathematical functions could be applied
to the shape of one organism to continuously transform it into other, physically
similar organisms. One memorable example is the squeezing and stretching
of a rectangular Cartesian grid that transforms the fish species *Scarus
sp*. to the species *Pomacanthus*. Thompson used the same principle
to transform skulls of baboons into those of other primates, and to show
how corresponding bones like the shoulder blade are related in different
species. Thompson acquired a local reputation as a mild eccentric; indeed,
older inhabitants of St. Andrews still recall seeing him strolling about
town with a parrot on his shoulder.

D'Arcy Thompson used mostly linear and quadratic maps to compare different
life forms. Linear maps between two shapes require four coefficient variables,
while quadratic maps use 10 variables. Thompson wrote in *On Growth and
Form*, "I know that in the study of material things number, order, and
position are the threefold clue to exact knowledge: and that these three,
in the mathematician's hands, furnish the first outlines for a sketch of
the Universe." Doubtless, if he were alive today, he would be heavily into
"morphing" – the digital technique that allows a computer to do exactly
the same kind of transformation of one object to another, but vastly more
efficiently.

## Reference

1. Thompson, d'Arcy W. *On Growth and Form*. Cambridge: Cambridge
University Press, 1917. (Dover reprint edition, 1992.)