jazz and math

Here’s a slightly rambly and somewhat pretentious post about my thoughts on the similarities between math and jazz.

I attended a lecture/Q&A session today at UMD given by the jazz bassist Linda May Han Oh. First of all, how cool is it that we have these preeminent musicians coming to UMD??? It’s not quite something I’m used to, and it feels like a rare privilege to be able to listen to these musicians live; let alone hear their thoughts and experiences, live in the same room. It’s a nice break from my life in the math building, to go from my office of chalkboards and equations to the concert hall of grand pianos and stage lights.

She started the session by having us listen to a few short clips of Mingus: “Myself When I Am Real (from Mingus Plays Piano)” and “Adagio ma non troppo (from Let My Children Hear Music)”. For me, first of all it was a blast to hear that again. I spent a lot of time listening to Let My Children Hear Music in high school, so it was somehow nostalgic to hear that again, immediately sensing the familiarity of that tune but not being able to quite place it (“ah, that’s Mingus!”) But it seemed like the point was to explain and elaborate her thoughts and approach as an improviser and composer - Mingus plays this “rough” thing on an instrument which isn’t his primary one, but comes up with this harmonic landscape that gets fleshed out into this grandiose orchestral realization on Adagio ma non troppo.

The language that she used to describe that idea was something along the lines of “exploring the architecture of sound,” which was something that immediately captured my attention. Anyone who spends some serious time studying proof-based mathematics will eventually get some notion of the idea of a mathematical “structure” - an abstraction describing the essential data of an object or concept, describing what information is changed, destroyed, or preserved under transformations. I myself became very interested in the word “system” - a word that evokes the dynamics of independent things which come together and blend into a bigger picture, structure arising from an apparent lack thereof.

And in some vague way I had noted that same thing in jazz - the circle of fifths, the sequences of 2-5-1s, all those important harmonic sequences that you learn when you first seriously study jazz, also come to bear in a similarly logical way. Improvisation - spontaneity within structure, structure within spontaneity. And when you go to a jam, you never really know how exactly things will go. Independent musicians coming together to form one sound, but everyone’s personality shines through.

The thing that struck me today was that -

“yeah, composers really DO think in this ‘mathematical’ way” -

this way of thinking of I’d only come into in the past few years -

but also the continued reaffirmation of a belief I’ve held in the back of my head since high school.

Music can be a perfect blending of the intuitive and the logical, the emotional and the technical.

That truly continues to fascinate me.

Her approach was to take this narrative, or feeling - a story about my mother, the invisible threads that bind us together - these abstract ideas; ineffably humanistic - and take that as a grounds for improvisation or composition. And the process of taking something abstract and emotional, and turning it into real sounds, real textures, real music seems amazingly cool to me. And the process of that looked like sitting in the front row of your own show, hearing and imagining the sound that you want to hear. That sort of compositional freedom also seemed so cool to me. I recall myself that when I’d try to take abstract ideas and make them into compositions, the result felt half-baked. I was reaching for sounds I couldn’t hear. There was a technical barrier.

I did ask, “how did you reach that level or get past those technical barriers?” And I pretty much knew the answer, to be honest. I realized it almost at the same time I was asking it. Of course the only way to that is to assimilate that technique into your subconscious. Hours of listening and playing, getting the sounds in your ear and under your fingers. That way, when you need them, they’re there within your grasp. And then you can use them to write stories. Build worlds. You create your own vocabulary to describe the sounds, you build the mental maps needed to create music from feelings and narratives.

I think there is something similar in mathematics. I am not so sure that mathematics is so unabashedly emotional; yet I do think that what we call “intuition” in mathematics is built by the same cognitive process. You stare at problems, you solve lots of them, you read lots of mathematics, and somehow your subconscious will intuit solutions to problems before your conscious brain does. (Indeed, I’ve found myself realizing that I can do some problem sets without really actively thinking about it now, almost on autopilot). Then, when you need them, your “bag of tricks” is ready at hand to be deployed. You build the mental maps needed to create proofs from hunches. (I guess this is what Terry Tao calls the post-rigorous stage.)

So in a sense to (only) focus on the structures and the techniques themselves feels like missing the bigger picture. The intuition you build from working with them and making them your own, coming up with your own way to feel around the space of possibilities afforded to you by those 12 notes is the prize one earns from hard work and diligent study. That feels like a kind of freedom to me. “When you understand it yourself and make it a part of yourself, there is some great happiness in doing that.” And I guess whether I was doing jazz or doing math, that’s what I wanted in a sense - and continue to want. The sheer joy of uninhibited facility with a sound or an idea, seeing how far I can take it, like riding a bike down a hill and feeling the wind blow past you.

One day I might be able to break through the barrier. More likely than not I will struggle with it for as long as I’m doing both. I think that’s the joy and the curse. There is always something new to do, some new sound to explore, some new idea to try.

So in a sense, it’s been really good to have done a bit of both music and math. It sort of prevents you from getting narrow-minded about your discipline. Surely if these two seemingly disparate things seem to share something in common, then maybe there’s more I can learn from other fields, too. (I guess it’s really not that uncommon for STEM people to also be musicians, but…)

Ok, so at the end of all that pretentious declaration, reality kicks in - and I have to just do my problem sets tomorrow. Haha. And therein lies another gap between the abstract and the concrete - the gap between the high-minded aesthetic idealism vs. the everyday grind. but that could be another blog post…