What does it mean to solve a problem?
I feel like I cannot be the first person to have tried to answer this question, though a quick Google search reveals — well, that Merriam-Webster defines problem-solving as "the process or act of finding a solution to a problem," which doesn't seem particularly helpful, and that someone named Gene P. Agre wrote an article titled "What Does It Mean To Solve Problems?" in the Spring 1983 issue of the Journal of Thought.
This, at least, is worth considering. Here's a quote from the article preview (that is, the only part of Agre's article I could read without creating a JSTOR account):
Solving is an activity that brings about a result, and the identity of the concept of solving is a function of the activity-result combination.
That sounds like something I might have written myself. Let's keep going.
[...] whenever someone solves anything whatever, some form, structure or pattern is brought about out of an initial state which is disorganized, unformed, or lacks the desired characteristic.
Ah, there it is.
Problem-solving is bringing form to the unformed. Structure to the disorganized. Coherence to the incoherent.
And on the way — as both I and the scientific method will argue — a person goes from guessing to knowing.
This seems less ground-breaking than it felt when I told L about it last week. I was trying to explain what I had learned while I was practicing the piano, specifically that the reason I kept having difficulty with one of the sections of the second movement of the Mozart was because "I didn't fully know it yet. I was still guessing, which meant that it didn't always come out the same way every time. I had to get to the point where I knew exactly how I wanted to play it — wait, that's what problem-solving is, isn't it? Going from guessing to knowing?"
And then I immediately asked L whether "guessing" and "knowing" could be glossed onto Daniel Kahneman's System 1 and System 2 — that is, the two methods of thinking he describes in Thinking Fast and Slow. (System 1 assumes; System 2 assesses.) It's both an incomplete and an incorrect gloss, and I abandoned it as soon as I brought it up, but it's worth mentioning because that's where much of my System 2 thinking is right now.
Well, technically it's one step further.
If problem-solving is the process of going from guessing to knowing, then there could be an advantage to learning how to expedite that process.
Especially when you're, like, learning piano repertoire.
Is there also an advantage to learning how to de-expedite the problem-solving process? To take as much time as it takes to know, and to explore different avenues of what knowing might mean? It would seem to be the case — especially when you are considering the Big Problems (life, death, love, basically all of philosophy and religion) for which a measurable knowing doesn't necessarily exist.
How to live, after all, is a problem that should take an entire life to solve.
But I'd like to get a little more efficient at learning how to play Mozart.
With that in mind, in the past week I've discovered two piano practice techniques that have helped me accelerate the process of going from guessing to knowing, neither of which are probably all that applicable to anything else besides the type of problem-solving that involves rapid memorization, precision, and physical recall.
I'll tell you about them anyway, just in case they might be applicable to something else as well.
More tomorrow. ❤️
(Also I really should make a JSTOR account and read that whole article. Consider it on the to-do list.)