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D'Arcy Thompson and the theory of transformations

An Erratum to this article was published on 01 June 2006


D'Arcy Thompson was a biologist, a mathematician and a classicist. His writing was great literature as well as great science. He is primarily known for a single book — On Growth and Form — and indeed for a single chapter within it, on his 'theory of transformations', which shows how the differences between the forms of related species can be represented geometrically. This theory cries out for causal explanation, which is something the great man eschewed. Perhaps the time is close when comparative developmental genetics will be able to provide such an explanation.

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Figure 1: D'Arcy Thompson in the early 1900s and in the 1940s.
Figure 2: Transformations that are used to relate different crustaceans to each other.
Figure 3: Transformations that are used to relate different fish to each other.
Figure 4: Transformations that are used to relate human, chimpanzee and baboon skulls.


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I thank H. Arthur, U. Frank, G. McCormack and A. Panchen for scientific discussion and comments on the draft manuscript, and the library of Trinity College Dublin for the loan of copies of the first and second editions (1917 and 1942, respectively) of On Growth and Form.

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Arthur, W. D'Arcy Thompson and the theory of transformations. Nat Rev Genet 7, 401–406 (2006).

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