Saturday, July 2, 2011

The Language of Form - Part 1

"The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty."

- D.W. Thompson, On Growth and Form, 1917

Whether you, as an artist - or a creative, so to speak - work consciously or unconsciously, you will be dealing with the same forms, the same fundamental shapes and patterns over and over again. And these shapes are part of a language, a language that all humans - and, most likely, organisms - use to perceive and create (and, possibly, transcend) the physical world. Oddly enough, this same language is also used to construct the actual symbols we use. This includes sacred symbols, arcane symbols, and even corporate logos. Regardless of how complex a form we're dealing with, it can always be broken down into several rudimentary, or "root shapes" - a handful of basic forms - that may change in color, arrangement of mass, etc., but never meaningfully diverge from the fundamental code, the language of form this article addresses.

D. W. Thompson, 1860-1948, biologist, mathematician, and philosopher, considered organic form to be a "diagram of forces."  Many somehow convoluted his basic tenet as being anti-Darwinian and/or creationist, and therefore, his immense body of work, "On Growth and Form" is generally overlooked by contemporary theorists. My own opinion is that Thompson was grappling with the very thing that I'm attempting to discuss here and, that is, a form language. From his perspective, it is a language shared by all organisms in the expression/ construction (even) of their own anatomy. He went on to illustrate dozens of examples of how, by mapping each organism with Cartesian Coordinates, one could prove that all members of any given species were simply a deformation of one basic morphology that inadvertently applied to all of them. Another tenet that he held, was that all things physical conform to a specific order or forms because "they must". And by this, he meant that all things physical must obey this fundamental order because it is the only true order which exists... and this order is, for the most part, a self-generating, geometric order, the connective between both the macro and micro "worlds". Today, Thompson's ideas might be seen as a precursor to some of those which fall under the heading of Biophysics.

The 4 Suits of the Pelaneiron and/or Metastructures - 2007, DS

In my younger days - as a student of Sacred Geometry, that discipline which examines the metaphysical meaning of number, patterns and form - I was obsessed with this code and my obsession took many strange turns. The four symbols (above) were an example of this, initially inspired by my interest in that dense body of esoteric work referred to as the Tarot, specifically the Minor Arcana sans the "court cards". The Tarot deck of cards, whose origins are rather mysterious to begin with, have inspired countless artists. (For those interested, here is one roster here.) The point I'm trying to make - and was trying to make with my own 4 symbols - is that everything that we see and experience can, ultimately, be broken down into a code. I wrote in 1981: "After years of frustrating myself with abstract intellectualizations, and confusing myself with complex philosophies, I suddenly discovered what my unconscious mind had probably been establishing for years... that is, a theory of structure." 

This "structure", however, did not merely apply to physical construction, but forms and patterns that might transcend the 3-dimensional as we know it. Over a period of several years during the 1980's I drew around 100 geometrical images based on the 4 root shapes; specifically numerical aggregates and radiant figures that resulted in 4 interpenetrating fields. I referred to this work under the title "Temp L" (1976), then "Metastructures" (1982), and, finally, a word that "came to me" out of nowhere: The Pelaneiron (2007). (and, no, I do not consciously know what the word means, and it is not a word that can be found in any dictionary that I know of...)

There are, of course, sheerly mathematical codes, and certainly these were (explicitly) a large part of Thompson's, and (implicitly) my own system. But, generally speaking, breaking things down into actual numerical codes is a "language" that many people (myself included) find too dense and complex. It is, however, this exact type of "language" one uses in certain forms of digital art - specifically that of the "fractal", which I'll address in Part 2 of this article: Fractal, Form and Field - Inevitable Symmetries

Upper Photograph credit: Diatoms by Andrew Syred


  1. Fascinating...a universal code of form/structure that underlies the physics we inhabit -- indeed the very mathematics that we use to describe the foundation of existence......and yes, fractals come to mind very quickly.

    You bring in intriguing dissertation to the table...I hope to read more.

  2. Thanks, Bob... let's just say that I tried to bring something "to the table"; emphasis on the word: tried! ;-)