The Mathematics of Art

Recently a quote by Milton Glazer came to my attention. Essentially he said that art that seeks its power and relevance by linking itself to popular culture loses the eternal and universal elements that must be present in a work to be considered true art.
I’m not sure I agree, after all medieval and renaissance art contains rich symbols that while, no doubt recognizable to the audiences of the time, now require art historians to interpret for us. Today’s art that integrates elements of the hip-hop culture will have art historians available in the future to interpret them for audiences of the future.
What was far more interesting to me in what he said was that he felt there were elements that exist that can be integrated into a work of art that make would make the work universal and eternal. What could these elements be?
Oddly, the first thing that comes to mind for me is geometry.
There are many things that contribute to art being eternal and universal, for example; Nature, the emotional response to color, subconscious archetypes (by this I refer to Joseph Campbell and Karl Jung’s writings) and craftsmanship. Recently I have been studying the Mandala, the sacred art of Tibet. A Mandala achieves harmony through the careful application of universal geometric laws. The most basic shape of the Mandala is the circle, a symbol of wholeness and completeness. Inside of this circle, representing realms and roads, walls and gates are lines, squares, rectangles and triangles, all drawn with mathematical perfection. This perfection resonates with the human mind, a pattern-seeking organ, and contributes to the physical beauty and the spiritual impact of the Mandala.

For more on teaching the art of the Mandala:
http://www.mathforum.org/~sarah/shapiro/
http://www.darthmouth.edu/~matc/math5.pattern/lesson1art.html

Looking also at classic Greek sculpture and Renaissance painting.
For the Greek, the idealizations expressed mathematics were the means to salvation, to some Greek philosophers, mathematics was key to surmounting the world (seen as impure and irredeemably flawed) and achieving unity with the divine (pure and perfect). In art this translated to a emphasis on matematical harmony with geometric principles that were seen as revealing divine perfection. In Greek Scupture this ideal was achieved by a harmonization of the various features, limbs and body shape to the principles of geometry. The Greek understanding of mathematics as the language of the universe, the means of understanding the mind of God and the foundation of all that was ideal and beautiful found an expression in their sculpture. Today the mathematics of Greek sculpture can easily be seen by taking a protractor and set of triangles to a sculpture and plotting out the relationships. For more on Greek sculpture and architecture and geometry: http://milan.milanovic.org/math/english/golden/golden4.html

Geometry could be said to be the thing that distinguishes Medieval painting from Renaissance. Very early on in the Renaissance we have a painter, Piero della Francesca, claiming that “the visible world could be reduced to mathematical order by the principles of perspective and solid geometry.” Much of this was directly attributable to a renewed interest in the classical Greek and Roman world, as texts, that had been lost to Western Europe began to be translated from the Arab world. This new knowledge created a revolution in many areas of endeavor besides art, but I believe that the greater beauty and compelling nature of Renaissance art is due to the work of bringing composition into harmony with geometry and thus, into the harmony the human minds seeks and sees in proper geometric proportions.

For more on the mathematics of Renaissance painting:
http://www.yale.edu/ynhti/curriculum/units/1986/3/86.03.08.x.html
So important is geometric proportion to harmony of composition, that intentionally breaking the harmony, i.e. introducing shapes that disrupt the geometry is a way of introducing aggression and danger to a painting. The shape and the disruption of harmony and the resulting emotional distress is so strong and pronounced that this technique does exist only in representational art but is present in the best of Abstract Expressionism, where color , shape and abstract geometry are the tools the artist is using to communicate in his work.

Read our May essay: The Importance of School Art Competitions
Read our January essay : Art History and the Internet
Read our March essay: Ink Jet Printers and the Color Wheel:
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