When I started this blog, I figured I’d mostly write about math topics, but lots of other things have crept in. A big one is music.
There’s general agreement that math skills and music skills overlap in some deep way, but for a long time I had a hard time putting my finger on exactly where (perhaps because I have pretty good math skills, but am very deficient in music skills). The applications of math in music theory (arithmetic mod 12; going up an octave = doubling the frequency of a sound wave = cutting the length of a vibrating guitar string in half on a fretboard) are very nice, but I never felt like they were getting to the heart of the matter.
Here’s what finally got me there. It’s hard to define exactly what math is, but here’s one definition I’ve gotten to like over the years (I believe it’s due to Andy Gleason):
Mathematics is the science of order and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations.
I.e., it’s not just about numbers! There’s also geometry (finding order in space), functions and correspondences (finding order by finding rules that relate one kind of thing to another), and a lot more. It’s an inclusive, generous definition, by which I mean that it lets many notions in, and helps explain how, and to what extent, those notions are actually mathematical.
Not accidentally, it echoes Varese’s equally generous definition of music:
Music is organized sound.
Finding order, organizing things, organizing sound. When you think about it that way, of course music is mathematical.