Friday, October 2, 2009

Art, Mathematics, and Psychology

Thus far, I have written mostly about ongoing project developments and information pertaining to my DPP class. Meanwhile, most of my time has been spent reading, studying, and designing for Art, Technology, and Design (ATD). Essentially a crash course in graphic design, ATD is a bit like taking a linguistics class where, instead of letter-based semantics, one studies how to "read" pictures. Surprisingly, this involves a fair bit of background in psychology and mathematical principles.

The primary text is Rudolph Arnheim's "Art and Visual Perception: A Psychology of the Creative Eye," and yes, is about as dense as it sounds. Arnheim describes the various ways in which the mind processes certain qualities of an image. For instance, the relatively simple rule that Westerners "read" images from left to right--like text--is explained by delving into the functions of the left and right cerebral cortex and their related functions. He also says that we perceive objects to be stable or restless depending on a shape's imaginary structural skeleton. The restful loci in a square, for example, can be found along the diagonal, horizontal, and vertical axes passing through its imaginary center. These rules are essential to achieving balance in a composition, regardless of whether or not the observer is aware of them; we sense innately that something is imbalanced even if we cannot explain why that is so.

Similarly, certain laws of psychology--specifically those of the Gestalt school--enable us to arrive at conclusions based on how objects exist in relation to one another (part to whole). Gestalt, from the German meaning "whole" or "form," describes the concepts that make unity and variety possible in design. Each principle can be used both to group or to un-group (A or Not-A, as Derrida might put it). Ultimately, Gestalt theorists believe that the whole, in perception, is more than the sum of its parts. Their basic organizing laws, which are more or less self-explanatory are: Proximity, Similarity, Closure, Continuity, and Symmetry. Therefore, objects closer together appear grouped; objects that are similar in shape, color, or size appear grouped; etc. Within each law there exists one or more subsets, creating a hierarchy that artists then use to convey meaning. Or not. I personally feel that some of this is a bit too technical a way to explain great art, depending on the medium.

One thing that does seem inescapable, though, is the ratio 1.618 : 1. This is the mathematical principle underlying the Golden Mean, from which the golden rectangle also derives. A golden rectangle is one that can be partitioned into a square and a smaller rectangle, which has the same length to height aspect ratio as the original rectangle of 1.618 : 1. This means that the smaller rectangle can also be divided into a square and a golden rectangle, and so on. Pythagoras is credited with constructing the first golden rectangle in the 6th century B.C., although it appears to have been used by the Egyptians in the construction of the Great Pyramids. This again raises the question: To what extent are these design choices made subconsciously? Leonard Da Vinci, however, saw the golden mean as evidence of a spiritual force rather than a psychological one. In his studies of the human body, he found that the distance from the soles of a man's feet to his navel, divided by the distance between the navel and the top of his head, was 1.618: the Divine Proportion.

The recurrence of this number in nature is indeed prolific and naturally raises questions about a supreme order--or even a supreme being. In terms of art, it essentially asks us to consider whether there can exist a mathematical formula for determining beauty? Such was indeed the case for the Parthenon. Rather than continuing to explore it here in laborious prose, however, I return now to this project's roots in animation and present the short film that we watched in ATD. Not surprisingly, I particularly enjoy the bunny rabbits.


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