Unlock the Geometry


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D’Arcy Wenthworth Thompson, On Growth And Form, 1917

Unlike the majority of biologists and naturalists of his time, that were only enthusiastic about the attributes of precedents of that particular form,  D’Arcy Thompson was working on the numerical explanations trying to define the forms of living things and physical phenomena in the light of mathematics.

On Growth and Form, notable mathematician and biologist demonstrates that the growth and form of any species of animal or plant can be interpreted through relatively simple mathematical equations. He suggests that biological growth and form has to  follow physical laws, and that one can see the materialization of these universal laws by analyzing common features in the form of different organisms. His “theory of transformation”  argues that a species evolves into another one not through a series of minor alterations in diverse body parts but through a large-scale transformation of the entire form.

Most of the transformations that stands as proof of his theory are specific cases of generic transformation which are obtained by the method of ‘conjugate functions’ and equivalent to the projection of the original figure on a new plane deforming coordinates with four different techniques that are; uniform linear functions where x-y axes are extended proportionally,  non-uniform or logarithmic definitions, simple shear where some set of parameters stay the same while others change in length as well as in orientation and radial deformation around a focus point that exposes similar characteristics with todays parametric system.

As to construct examples for his arguments he uses linear and non-linear functions to show how the corresponding bones of similar species are adapted to their particular functions, with his tactfully drawn illustrations of morphed images of the skulls of related species, reckoning primates and humans.

Thompson introduces maths as a formative apparatus simulating how the structures of the organic world mimic patterns in the inorganic existences. Thus originating the scientific explanation of the word ‘morphogenesis’, commonly used in biology to define the biological process that results in developing the shape of an organisms. He defines it as task of comparison of related forms rather than in the precise definition of each one.

He proposes structuralism by using scientific data of the physical forces when imposing biological forms, but biological forms aren’t necessarily obliged to make sense in scientific formulas at all times. That is why his examples could be considered as ‘ideal’ states of organisms.

The reading could be perceived as a poetic exposition praising the marvels of nature not only because of his profound use of language but the way he implements scientifically data in history with ideas ahead of its time and that the study of science of living things is not solely dependent on mathematics nor it should be considered as an inexplicable divinely created phenomenality.

Possible personal research:

Is it possible to adapt the mathematical formulas that are used to define the ‘shapes’ of a building not only into the ‘form’ but also into the potential states of  ’growth’ or ‘transformation’ of a building within time? Can buildings be designed to think and adapt to the nature not only within their rigid and predefined structures but as an expanding system inside the infrastructure of the future cities without any further human intervention?


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