One thing this discussion made me realize is that "thinking hard" might not be a single mode of thinking.

In grad school, I had what I'd call the classic version. I stayed up all night mentally working on a topology question about turning a 2-torus inside out. I already knew you can't flip a torus inside out in ordinary R^3 without self-intersection. So I kept moving and stretching the torus and the surrounding space in my head, trying to understand where the obstruction actually lived.

Sometime around sunrise, it clicked that if you allow the move to go through infinity(so effectively S^3), the inside/outside distinction I was relying on just collapses, and the obstruction I was visualizing dissolves. Birds were chirping, I hadn't slept, and nothing useful came out of it, but my internal model of space felt permanently upgraded. That's clearly "thinking hard" in the sense.

But there's another mode I've experienced that feels related but different. With a tough Code Golf problem, I might carry it around for a week. I'm not actively grinding on it the whole time, but the problem stays loaded in the background. Then suddenly, in the shower or on a walk, a compression trick or a different representation just clicks.

That doesn't feel "hard" moment to moment. It's more like keeping a problem resident in memory long enough for the right structure to surface.

One is concentrated and exhausting, the other is diffuse and slow-burning. They're different phenomenologically, but both feel like forms of deep engagement that are easy to crowd out.

Yup, yup! There's so many different ways of thinking hard.

For me, thinking about an extremely technical TCS problem, for example, is my version of actively, tirelessly thinking hard. I'm logging a ton of observations, trying new ideas and hypotheses, using a mix of computer simulation and math to try and arrive at a concrete framing and answer.

On the other end of the specturm, I have philosophy. It's definitely a different type of hard. Most of my "Aha!" moments come from when I realize I've been strawmanning some argument, and not actually understanding what the person is saying. Why is the person saying this, relative to what, why is this a new observation, etc. Things are so amorphus and you can tweak the problem parameters in so many ways, and it's really tempting to either be too fluid and pretend you understand the thinker (because it's a subset of some conception you already have), or be too rigid and dissolve the thinker as a category error / meaningless. I've never felt the same feeling as I did when doing TCS research, but the feeling was definitely hard thinking nonetheless.

In terms of extremely nitty-gritty technical things, like linker bullshit and linux kernel programming, I'm much more familiar with, and these things are more about reading documentation (because the tool won't behave like you want it to) and iteration / testing (because... the tool won't behave like you want it to, so you need to make sure it behaves like you want it to!). This is also a type of thinking - I would call it hard as in the physiological response I have is similar to that of research in the very bad moments, but in terms of my lofty ideals, I don't want to call this hard.... it's very "accidental" complexity, but it's what I get paid to do :/

At work, you have a huge idea space to consider, both problem and solution framings, mixing in "bullshit" constraints like business ones. You also throw in the real-time aspect of it, so I can't just either armchair on a problem for a month (unlike Philosophy) or deep dive on a problem for a month (unlike research). I'm technically doing the third type of programming right now, but we'll see how long that lasts and I get put on a new project.

I'm not even sure if there's a clean demarcation between any of these. These are certainly better than brainrotting youtube though.