D’Arcy Wentworth Thompson: On Growth and Form. 1917 Chapter XVII: On the Theory of Transformations, or the Comparison of Related Forms.  

www.darcythompson.org accessed on 23.11.13

  In this chapter, Wentworth continues with the study of the inter-relations of growth and form, and the part which physical forces play in this interaction. He explain the theory of Transformation using mathematical methods like the plane coordinate system to describe and define the form of organisms. He talks about how you can start describing the shape of an object using words of common speech, but at the end you will use the language of mathematics, mixing words and symbols, which are characters of geometry, to reach the definition of “form”. Even with limitations and controlled and regulated freedom, it is possible to reach mathematical analysis to mathematical synthesis, this will allow you to discover homologies or identities between the organism and its forms. Wentworth talks about the dynamical relations between mathematics and form, and how you need to understand these concepts in order to know the forces which gave rise to them. In the representation of form and comparison of kindred forms you can always see in the representative diagrams that these forces are in equilibrium; but when you talk about magnitude and direction, you always will be able to recognize how one form turns into another. Composite nature and laws of math are bound to underline growth and form, but these methods peculiar fit to interpret them. Even than mathematical methods and use of symbols are used in almost all sciences, they have made slow progress in the morphology of living things, one of the most important reason is the psychological, because the study of living things is by nature and training, and the habit of mind is alien to that of the theoretical mathematician. Neglect and suspicion of mathematical methods in organic morphology is due, even when we seem to discern a regular mathematical figure in an organism which we so recognize merely resembles, but is never entirely explained by, its mathematical analogue. Wentworth concludes that the details in which the figure differs from its mathematical prototype are more important and interesting than the features in which it agrees and that there is no essential difference between organic form and the manifested in portions of inanimate matter. He made a critic to the study of Darwinian evolution because it has not taught us the actual links between animals group; is in this moment when he talks about one of the most important points in the chapter, that no one straight line of descent, or of consecutive transformation, exists. Is when Wentworth talks about the Principle of Discontinuity, he says that this principle is imposing not only by mathematical, physical or biological actions, but also by mutations or sudden changes that no one can explain or expect it and are destined to repeat themselves. During the talk with the other members that had read the lecture and the final debate with the questions session, we all had different points of view and main ideas of this lecture, at the end we agreed that the explain of theory of transformation using mathematical methods to describe and define the form of organism was the main topic, and with the final debate several new ideas and some doubts emerge, like if the theory of Darwinian evolution is wrong, which theory could explain the origin of human race? And if the mathematical method only works into a certain level to explain evolution and similitudes, how it can be completed in order to make it more exactly?  Possible topic After the reading of the lecture, one of the possible topic for my personal research could be about how these mathematical methods and systems could be applied into an specific architecture style or period, to be able of make comparisons, general ideas and obtain similitudes from one building or project to another, with the final objective of create a catalogue of styles and guides ideas that are repeated and how these theory and concepts functions as primary bases for the next periods