Sunday, November 25, 2007
I've been debating whether to share this next item with everyone; I decided it would be selfish to keep it to myself. (Remember the mindless seagulls in Finding Nemo? "Mine!")
Over the years, I've wondered about the wisdom of choosing color to illustrate my ideas re: secondary qualities & the foundations of quantum theory. I continue to believe that it was the best choice to start out with, given how easy it is for us to "see" the main ideas and how most of us are highly visual in our orientation to the world.
On the other hand, sounds have a certain appeal, given that there are well-known harmonic relations, already known to Pythagoras, between what we hear and the numbers associated with the media producing those sounds. And then, there are the fascinating correspondences between the vibrating strings (and membranes!) we hear and the strings of string/M-theory theory.
Well, it turns out there are all sorts of wonderful relations (rather obvious, in retrospect*) between harmonic analysis, operator theory, spectral theory, group theory, number theory, Calabi-Yau theory & Kac-Moody algebras -- far too many for me to adequately explore in my lifetime.
The math mirrors what I've been on about regarding color all this time. I couldn't be happier -- especially so in view of the fact that one could lob a stone in any direction on a college campus and, chances are, you'd bean someone with more native mathematical ability than I'll ever have.
So ... now is the way plain. But I thought I'd better leave a trail of bread crumbs for those who come after, in case I get hit by a truck tomorrow. (Heaven forfend!)
Although I am only beginning to understand harmonic relations, the parallels with the mathematics of color seem clear enough. He wrote confidently.
I feel a bit foolish, looking back, wishing I'd looked into this business better years ago, but ...
I remember a desire to narrow my focus to one (relatively) simple phenomenon -- color vision -- and then see what sorts of math & physics might model the facts on hand ... and, as it were, before our eyes.
I always knew that, if I should be able to get those facts right regarding vision, the math ought to fall out naturally and apply, mutatis mutandis, to audition, olfaction, and so forth.
Lately, I'm beginning to think I wasn't wholly mistaken.