08 March 2008

Music To My Ears, and Eyes

I'm telling you, Julie Rehmeyer is fast becoming one of my favorite science writers. Her Science News Math Trek piece this week follows up on a paper by music theorist Dmitri Tymoczko that represents musical chords in hyperdimensional geometries. Even cooler than Rehmeyer's very accessible written description of the work, though, are the accompanying videos (1 2). It turns out that Tymoczko's techniques explain some of what goes on harmonically in Chopin's E-minor prelude, and the videos capture the effect beautifully.

Still, I was initially skeptical about Tymoczko's ideas in the last graph:

What's particularly amazing, Tymoczko says, is that the mathematics needed to describe these spaces wasn't even developed in Chopin's time. Nevertheless, he says, "it is unquestionable that he had some cognitive representation of the space. So there was this period of history where the only way Chopin could express this abstract knowledge was through music. His knowledge of four-dimensional geometry was most efficiently expressed through piano pieces."

I'm not sure I share Tymoczko's certainty that Chopin knew anything about what we would call four-dimensional geometry, abstractly or otherwise. But the more I watch these videos, the less I doubt that he "had some cognitive representation" of some idea that Tymoczko's merely learning another way of exploring. I doubt he'll be able to fully grasp whatever that idea is any more meaningfully than Chopin could, but it's hard to fault either for trying, and in the meantime we all get to bask in the beauty.

Sorry to get all heavy on you. I think today's Daily Office reading sort of puts you in the mindset to want to ponder these things: "For now we see in a mirror, dimly, but then we will see face to face. Now I know only in part; then I will know fully, even as I have been fully known."


I've been warned by a psychologist friend about the strength of the science in some of these fMRI studies, but I nonetheless thought this piece was also interesting. Douglas Adams would be pumped about the music & math/science vibes in this week's Science News coverage.


Congrats to the Badgers for clinching sole possession of the Big Ten Championship today at Northwestern. Speaking of Northwestern, I stumbled across this post from a Northwestern student giving online dating a go. Good writer, interesting stuff.

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