Monday, December 28, 2009

Symmetry and the Monome

I was just in Cambridge, MA over Christmas and happened to walk into the mathematics section at the Harvard Book Store. There was a book on Symmetry called "Symmetry" by Marcus De Sautoy. Not only is it an absorbing read into how symmetry works and its role in the world, but it's also an interesting journey into the life and work and mind of a mathematician.

I was amazed to read that all 17 possible types of plane symmetry are represented in the patterns and designs on the walls of the Alhambra in Grenada, Spain. I was just there a few years back and it's one of my favorite architectural wonders. It wasn't until hundreds of years later that it was mathematically proven that 17 was the limit and there will never be an 18th type.

The human mind is a master of pattern recognition. In fact, we are very very good at noticing differences in patterns but not so good at absolute measurement. For example we can look at two very similar shades of a color and detect minute differences but we can't look at one color and know absolutely that is was this shade or the other without two to compare. This is a capability encoded in the way our mind works. It is essentially a pattern comparison and recognition machine.

This brings me to something important in the world of music. Symmetry and the language of patterns is extremely important to music as well. The mind loves patterns but also likes the challenge of finding patterns that are not obvious. If we present a pattern that is too symmetrical or too perfect or too obvious, it is not always pleasing to us and we grow bored quickly. The Japanese knew this and added imperfections to perfect things. The word for this was "Wabi-sabi" - "The aesthetic is sometimes described as one of beauty that is "imperfect, impermanent, and incomplete" (according to Leonard Koren in his book Wabi-Sabi: for Artists, Designers, Poets and Philosophers) quoted from Wikipedia".

I believe that this striving of the mind to make patterns and recognize patterns as well as cause and effect is also why the monome is so interesting and attractive. Applications on the monome are written to change a blank slate grid of lighted buttons into patterns that represent how we interact with music, video and other applications of the monome. The mind not only strives to understand the patterns of this interaction but also the cause and effect of hitting a button and a light appearing. This makes it a perfect human interface. It is imperfect by design, and that makes it perfect.


  1. This is a great, thought provoking post. I love wabi-sabi! 17 types of symmetry? Really? I wish I knew more math. Nice. I love limits like that. It sounds like the title of a mystical treatise: "The 17 Symmetries and the Mystical Craft of Monomial Music of the Spheres." Peace.

  2. very interesting. makes me want to visit the alhambra.