Research in Tandem (Part 2)
Today we continue our discussion about research meetings with a few concrete strategies. When I was a new graduate student, I often had long meetings with my PhD advisor and other professors that went completely over my head. Such meetings are extremely demanding: they require a broad base of shared knowledge, they involve carrying out complex calculations and spatial manipulations entirely through verbal communication, and they proceed at a meandering conversational pace that often jumps back and forth between many different approaches and perspectives.
The meta-heuristic underlying all of the following tips is: learn to play a supporting role. Every mathematician wants to be the genius who single-handedly carries the team to the finish line with insight after insight. In contrast, nobody tries to playing support. Therein lies an enormous well of untapped potential for you to contribute directly to mathematical inquiry without having the faintest clue what’s going on.
Never be afraid to interrupt the flow of conversation to walking up to the blackboard (or pulling out paper or laptop) to draw pictures and note down what’s being said. Just copying down what others are saying might not seem like much contribution, but you’ll soon learn the many benefits this practice has.
You help catch mistakes and ambiguities that were skated by in conversation. Taking notes improves your long-term memory and learning. Having visible log for the history of the meeting frees up precious working memory for you and your collaborators to forge rapidly ahead. Writing things down forces you to develop evocative notation, useful pictures, and modular lemma statements that compress amorphous heuristics into concrete, versatile building blocks. As collaborations extend over weeks, months, and years, everyone will be thanking you later for keeping notes, however half-assed they may be.
If you have nothing to contribute, the first thing you can do is take notes.
The Thirty-Six Stratagems are a compilation of aphorisms for war and politics deeply engrained into Chinese culture, of comparable influence to the Art of War. One of my favorites is 拋磚引玉, which roughly translates as “toss out a brick to lure out the jade.”
If you’re stuck – and you often will be – instead of silently waiting for others to present good ideas, present your own bad ideas. Throw this brick out as a way of baiting insights – which are the jade in this analogy – out from your peers. It’s common knowledge that the fastest way to get a question answered on the internet is to post a wrong answer. The same heuristic applies to research: if a conversation stalls, throwing out a brick. Your collaborators will rush to point out all the reasons your approach is wrong and naïve, and how to improve it. Before you know it, beautiful pieces of jade will have appeared in its place.
There is an art to tossing the right bricks. I don’t suggest yelling out “Let’s try category theory” at every turn when there’s no connection whatsoever to the current problem. Best practice for throwing bricks is akin to semi-bluffing in poker: a brick is a hand that is currently useless, but there’s still a chance it might work out on the river. You probably have bad ideas and fuzzy intuitions you’re embarrassed to share that seem very slightly relevant to the problem. Just lower your filters and babble them out.
I can’t count the number of times I’ve opened my mouth to spew out a nonsense thought that didn’t even make syntactical – let alone logical – sense, only for one of my brilliant collaborators to charitably error-correct said sentence into a useful insight. “Ah yes, of course, that’s exactly what I meant,” is usually how I continue this conversation, “But just to be pedantic, could you explain that in more detail?”
If you’re not courageous enough to present a brick as if it’s a genuine insight, preface it with a disclaimer: “So here’s an idea that definitely doesn’t work, but I’d like to figure out why.”
To be continued…