DRMacIver's Notebook

Curiosity is a team sport

Curiosity is a team sport

Back in Relearning curiosity I talked about the need to talk to others about things I’m interested in. I’ve been thinking some more about this some more and run into what is, in retrospect, an obvious problem: I don’t have the first idea of how to do this, and I think this is because I’m doing something wrong prior to getting to that point.

Let me tell you about the one time I tried to do research level mathematics. The question I was interested in was this: Given a discontinuous function \(f: X \to \mathbb{R}\), where \(X\) is some topological space, how closely can it be approximated by a continuous function in the uniform norm? There is an “obvious” lower bound of \(\delta(f) = \sup\limits_{x \in X} \inf\limits_{U \ni x} \textrm{diam}(f(U)\), where \(U\) ranges over open sets. Is this lower bound tight? The answer proves to be yes, if \(X\) is paracompact. Is the converse true? i.e. if \(X\) is not paracompact, are we guaranteed that this bound is not tight?

It turns out, yes, more or less. This question had all been thoroughly explored by some German mathematician back in the 70s, which took me a while to find out because Google Scholar wasn’t really a thing I knew about back then (it did exist, but I’m not sure I knew it existed and certainly I wasn’t good at using it - this would have been 2005 or so). I can no longer find the reference, which shows how much I still care about the problem. But at the time it was a neat problem to get my teeth into.

This problem has a couple of characteristics of things that are easily interesting to me:

Firstly, the problem statement is relatively accessible. In this case that means it’s relatively accessible if you have a certain amount of mathematical knowledge, which I did, but it’s not super off into the weeds. This will not be obvious to you because I’ve made no attempt to handhold you into it and also my idea of what counts as accessible is weird, but the point is that I could start tackling the problem immediately.

Secondly, it’s pretty niche. Less niche than I thought, clearly, in that it did have a niche of people who had worked on it a while ago, it’s just that it was unfashionable. Also being unfashionable seems a common theme in my interests.

Thirdly, it’s not all that useful, and if you asked me why it was interesting I wouldn’t be able to give you a good answer (certainly not now, but probably even then). It’s just neat, in a way that I can’t really articulate or defend. It’s within arm’s length of practical things (for a pure mathematician’s notion of practical), but not itself practical. There’s no extrinsic reason to be interested in it.

Unlike most things I tend to get interested in of that nature, I did have the advantage of having a friend who I could interest in the topic. We worked on it together for a bit until we discovered the prior art and got disappointed. That doens’t happen to me much these days.

Other things I’ve been interested in over the years include random voting, test-case reduction, various interesting algorithmic problems, etc. Recently I’ve been getting into writing Wordle solvers, just for the lulz. There have probably been many others.

The crucial feature of all of these is that I noticed something interesting that seemed under-researched, picked it up, and ran with it for a bit.

Which is to say uh… I appear to be picking my interests in a manner that actively selects for things that other people are not currently interested in, and then being very surprised pikachu when this results in not having people to share my interests.

I’ve tried to get other people interested in these sometimes. If I hadn’t flamed out of my PhD, that was ostensibly the point of it - getting other people interested in test-case reduction to the degree that I was. It turns out marketing is hard. Hypothesis was a genuine opportunity to share my interests with people and collaborate on them, but unfortunately I mostly burned out on that by trying to make it do too much for me.

I can explain my interests to lots of people. I’m very good at explaining. But as I wrote about yesterday I’m increasingly feeling like my ideal working environment is working in a team, and I think a lot of the time what I want is not for people to listen to my interests, but to engage with them fully and work with me on them.

Back in Maintaining niche interests I talked about how if you’ve got niche interests you want to maintain, you probably need a community for that interest, but I think I understated the problem there. I tried to fix my increasingly lackluster level of interest in computer science by forming a computer science community, and that was a good thing for me to do but didn’t help, because what it got me was an audience for my interests, which falls very far short of partners.

And, well, if that’s actually what I want, why the hell am I working on this as an individual and trying to interest people in what I’ve done after I’ve already picked something that makes it hard?

Surely, if you want to have interests you share with people, the thing to do is to start with people you want to share interests with, and then work together with them to find and develop those interests?