“On Growth and Form” by D’Arcy Wentworth Thomson

skull transformation

In Thomson’s book “On Growth and Form”, he looks at the way natural living things, such as vegetation and animals, and why they take the form they do by growing and changing. While at first the forms are described with words, they later are represented with mathematical and graphical drawings. Thomson admits that the mathematical analysis has its limitations since one cannot simply draw anything. However, it does have an advantage in a way we can manipulate shapes and discover new things; he places a grid and then deforms it consistently in one particular pattern, the result is a new species. Nevertheless not everything can be transformed to anything; a vertebral animal cannot be transformed to a mammal. His study of form is called “morphology”. The form goes from a static to dynamic state with the influence of forces on them. While looking at the shape we can recognize the force that transformed it, which can be for example Gravity. By understanding the form transformation vs. the forces, we can see a similarity with DeLanda in the evolution process from young to older. Thomson discuses the concept of average since the process of transformation allows you to get only an approximate result; one can get mathematical forms for shapes in general, but not for a specific case – “Keep the type in mind & leave the single cases, with all its accidents, alone”. In “On Growth and Form”, there is also the idea of Newton which says that “Nature delights in transformation”. The book is mostly about questioning and comparing the form, growth and Cartesian coordinates. According to Thomson, comparison of related forms allows us to understand better the transformation and deformation that if we saw the form alone. His method was to use Cartesian coordinates, and it can be used to study missing parts of an animal or the missing steps of the evolution process. Thomson describes Listing’s point of view of seeing a topological similarity in mammals where in the science of typology any form can be changed to any form. This concept comes behind the fact that if you breakdown different forms, we will end up with similar basic geometric shapes. However Thomson did not study this perspective. All of his experiments are limited since they are in 2D, where everything in the grid changes but keeps the same relation. His study can be applied on a 3D grid but there will be difficulty in correlating one plane into different one. Moreover, even in his 2D process, we can notice that his transformation from the initial drawing to the obtained result is not always very accurate and sometimes raises doubts about certain coordinate’s displacement; Nevertheless we should keep in mind the book was written in a time where computer analysis and parametric still did not exist, making his work an impressing read. We can notice that Thomson applied the same method as Albert Durer did on human face, but for animals.

In my personal research, I would like to experiment and apply Thomson’s theories since he was descriptive rather than experimental in his book. It is clear that he was aware of that when he said: “This book of mine has little need of preface, for indeed it is ‘all preface’ from beginning to end”. It would be to apply the study to all shapes in our daily life to follow their process and see what forces and changes they have been affected by to become transformed to what they are.