Yesterday afternoon I found myself sprawled on the couch, eyes half open, the concepts of dot product, cross product, projection and determinant swimming around in my head. It’s worth noting here both that I studied up through a MS in math and that I’m no longer a mathematician professionally. I came upon these concepts idly walking memory lane, as happens on Rosh Hashanah.
It felt great—and not just because hey, I know a lot—still got it a decade later, baby!
Doing original research in math rarely felt great when that was my task. Full of dead-ends where you think you’re about to crest a peak to a beautiful vista. An emotional tug-of-war between excitement and despair that probably didn’t help my bipolar disorder any. I often explain, post facto, that languages ended up being a better fit for me because they allow reliable, accreting progress. If I work at a language, I‘m more proficient at the end of the day than I was when I woke up, by 8 new words or a syntactic structure or maybe an inspiring target-language conversation. If I do wake up sweating at 3am—as happens—it won’t be because I recognized all the last day’s work was flawed. When I did math research, I woke up to the demoralizing poof of a good day’s thinking more often than I woke up to a fruitful new idea.
But yesterday, I knew the math I was running wasn’t going to go poof. The thinking felt like improv, where every choice is right and you just keep moving forward. It was goal-less, aimless, intensely associative, fleet, light, inconsequential. I started with a concept—a landmark on the surface of my mental model of Math World. If the flight of math had started with a problem statement, I imagine it would’ve been what a Zen koan is for the one about to sit for meditation: a jumping off point, an invitation to someplace that promises to be cool. Not a challenge demanding a solution. A problem you actively don’t bother solving, even if you know it’s an easy one and within your wheelhouse. An infinite game and a cooperative one between me and math.
One of the mini-games is how many paths forward you can generate from a single unit of math. Another is minimizing the size of your displacement while maximizing the distance wandered. If you get back to where you started, it’s a return to Cavafy’s boring Ithaca, enriched by the travels. If you set out again, in the same spirit from the same spot, oh the places you’ll go!—destination unknowable, as to Bilbo walking out his door. Any dead end reveals itself as a portal: you glide through to the next stop, no banging your head or re-pacing your steps.
I’m going to call this thing free-mathing, by analogy with free writing. It seems impossible: the internal editor is central to doing math. But I think the sense of play, openness, spontaneous generation and infinity can be likened to the state free writing wants to generate.
Free-mathing shares benefits with free writing, too: warming up the mind and getting the gunk out; lowering the activation energy for approaching the Serious Real Work that Must Be Excellent. Both mean you get in reps of concepts and skills you’ll need for a “real”, convergent-thinking math or writing task down the line, whether in five minutes or six months. Both show you what you know and actually don’t know so well as you thought you did, while being rather less critical of you when compared with a set of exam questions or the strategy of self-testing.
And why bother with this, now that I don’t “do” math anymore? I enjoy free-mathing once in a while, and now that I’ve named it maybe I’ll try it more often. I already have the permission from myself not to take my hobby math seriously. Maybe if I practice not taking things seriously there, it’ll make my writing work more approachable, too, the work I take too seriously to do it at the moment. If I freewrite and freemath and my pattern-loving brain sees the connections between the two things, maybe I’ll get more playful about serious writing. Or, supposing (ridiculously, helpfully) that Plato is right that all learning is recollection, maybe I’ll remember the lightness of play on the mind.