Transforming Species Through Mathematics

In 1917 the great Scottish zoologist D'Arcy Thompson wrote a book called On Growth and Form, in the last chapter of which he introduced his famous 'method of transformations'. * He would draw an animal on graph paper, and then he would distort the graph paper in a mathematically specifiable way and show that the form of the original animal had turned into another, related animal. You could think of the original graph paper as a piece of rubber, on which you draw your first animal. Then the transformed graph paper would be equivalent to the same piece of rubber, stretched or pulled out of shape in some mathematically defined way. For example, he took six species of crab and drew one of them, Geryon, on ordinary graph paper (the undistorted sheet of rubber). He then distorted his mathematical 'rubber sheet' in five separate ways, to achieve an approximate representation of the other five species of crab.

D'Arcy Thompson showed how one species could be transformed into another by sketching it on graph paper and distorting it.