Tuesday, December 23, 2008

Piero della Francesca, Symmetry

In several previous blogs (Haeckel, Calder, Jess, Merian, and Baer) I referred to artists with technical backgrounds, and to the connections between math and art. I have also quoted artists and mathematicians who sought to separate math from art: Robert Mangold, — "Abstraction is an idea. Geometry is not."; Mel Bochner, — "Happily there seems to be little or no connection between art and mathematics (math deals with abstractions, art deals with tangibilities)."; and the mathematician, G. H. Hardy — "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."

I received a Kindle for my birthday, and the first book I read was Ian Stewart's Why Beauty Is Truth: A History of Symmetry. This is a fascinating history of the idea of symmetry, how central it is to mathematics, and of the mathematicians that worked out what we currently know about the concept. (Much of the math is over my head.) In one short section Stewart explains how artists Filippo Brunelleschi and others formulated, Leonardo da Vinci applied, and Piero della Francesca perfected the mathematics of perspective, and how this fits into the continuous thread of discovery.
"In those days [during the Renaissance] mathematics and art were rather close; not just in architecture but in painting. The Renaissance artist discovered how to apply geometry to perspective. They found geometric rules for drawing images on paper that really looked like three-dimensional objects and scenes. In so doing, they invented a new and extremely beautiful kind of geometry."

Flagellation of Christ by Piero della Francesca
Galleria Nazionale delle Marche, Urbino, Italy

In the 17th century, Girard Desargues used this math to develop a new non-Euclidean, projective geometry. Desargues' contribution was a key step in the path that leads to the mathematics of higher dimensions.

So despite what Mangold, Bochner, and Hardy had to say, there is an important connection between math and art. That relation may have been strongest during the Renaissance, but continues in the math if not the art of today.

Here's one of my paintings from last year. It's one of several I did based on the idea that I could break the rules by combining multiple horizon lines in a single projective plane.

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