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. The details of the mathematics don't matter, although they are fascinating. What you can clearly see is that it doesn't take much to transform one crab into another. D'Arcy Thompson himself wasn't very interested in evolution, but it is easy for us to imagine what the genetic mutations would have to do in order to bring about changes like this. That doesn't mean we should think of Geryon, or any other one of these six crabs, as being ancestral to the others. None of them was, and in any case that is not the point. The point is that whatever the ancestral crab looked like, transformations of this kind could change any one of these six species (or a putative ancestor) into any other.
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