website/content/posts/solving-hard-problems.md
Anthony Wang 925d66d541
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Solving Hard Problems
2022-11-21 19:31:33 +00:00

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title date draft description type tags
Solving Hard Problems 2022-11-21T19:09:01Z true Some ramblings about solving hard problems post
life
problem-solving
puzzles
computer-science

I've always thought of myself as being bad at solving hard problems.

Well duh, they're hard problems, so of course you'd be bad at them...

But that's not entirely accurate.

I'm currently taking an abstract algebra class with weekly problem sets. The problem sets are hard. Each week, I have to solve and write up 8 or 9 problems, applying stuff I had barely learned just a few days ago. I usually spend about 6 hours on each problem set, which mainly consists of me banging my head against the wall unable to solve anything.

But every once in a while, something amazing happens: everything just clicks and I suddenly blaze through 3 or 4 problems. At that rate, I'd finish (basically speedrun) every problem set in less than 2 hours.

Of course, this is a rare occurence. Maybe it's correlated to stumbling accross a streak of easy problems?

A simliar thing happens when I'm developing Gitea federation. Again, this stuff is hard. But I sometimes make sudden large amounts of progress in tiny spurts (for instance, when I miraculously got Mastodon to Gitea federated following working back in April!). Suddenly, I find an insight that lets me fix a big problem, and then I'm right in front of another roadblock again. If this doesn't happen, I have to settle for making small incremental progress instead (this is why we had federated following in April and still no federated-anything-else in Gitea right now).

Recently, I started playing the wonderful puzzle game Antichamber (to procrastinate problem sets and Gitea federation work of course). It's a dizzingly non-Euclidean puzzle game where all the rooms make no sense at first and perfect sense once you get a flash of insight. Every time I play it, it's always the same pattern of accomplishing basically nothing and just wandering around for a while, and then suddently solving a puzzle and unlocking a new area and having a lot of fun and such, and then it's back to accomplishing nothing, and then I have to take a break and do something else and walk around. (Also, some people say they get lots of ideas when taking a walk. I think that's garbage, or at least it doesn't work for me.)

There's no way to increase the frequency of these flashes of insight and sudden productivity. I'm sure there isn't. I'm willing to bet money there isn't. But the hard part of solving hard problems is to stick with solving the problem, even when you're not accomplishing anything and just wandering around, physically or mentally, because sooner or later you'll solve the problem. It's just a matter of not getting discouraged.

For me, I've been procrastinating on Gitea federation development quite a lot of the past few months as you can see from my commit graph, because it's simply hard to convince myself to devote a few hours to thinking hard about the current issues with Gitea federation and to stumble around trying to find insights on how to fix them. It's all about getting into this correct mental state, and I'm busy enough with other things that it's way easier to just make myself work on something easier in the meantime.

I sometimes feel bad about not working enough on Gitea federation, and I often lie to myself that I'm too busy to work on it. If I really was too busy, I wouldn't have time to play Antichamber, for one 😄.

It's not that I'm bad at solving hard problems, it's that I didn't push myself to do it.

How to change that? Now that's truly a hard problem.