Reflections on Sudoku, or the Impossibility of Systematizing Thought

Summary

I reflect on the Entscheidungsproblem how it relates to Sudoku solvers. It's a little weird.. The other day, to no one's surprise, I was fumbling over a programming problem. This wasn't anything satisfyingly algorithmic, but more the thing where you're evaluating a million questions on "how should I structure this system?". While I'm no design purist, I like to at least make an attempt at sketching out the problem space and think through options before I just start coding something. My rule of thumb for this is, let's call it the "10% rule" - make sure I try to think hard about a problem for 10% of the time before I start playing around with code. Writing code helps clarify many things but it's also easy to get stuck in local minimaI have the same problem when writing text, like this blog post. Put me in front of an editor and I'll pointlessly recraft sentences instead of getting the thing finished. . This rule helps keep me from getting lost too early, but I often think about whether I could do better. I'd like to say I have a systematic process I apply here. I don't. I think over one idea, then another, writing down my thoughts, but it's always hard to feel like you're making a lot of progress. It's honestly frustrating. I often wish I could "systematize" it somehow, applying some rigorous method and march towards the solution. Could I become one of those magic people who just sit down in front of a problem and watch it decompose in front of them? Over time I've accepted that is impossible. There is no person, no process, which can systematize thought. Millions of math problems elude Terence Tao despite his brilliance. Now I see these differences in aptitude as having different sets of mental tools at your disposal. The more tools you have, the better tools you have, and the better you are at applying them, then the better you get at certain problems. Maybe your background makes you better or more interested in different tools. But we can all learn new tools, and ...