Do you think math would have helped in any of the examples listed here? Or, generally, help you elicit your inner intuitive predictor's models?
(I agree math helps in other ways that I would call "usefully concrete" and that shares structure with the stuff in this post, but it's not really what this post is about)
I think of math as a more general problem-solving technique doing essentially what you describe in your post. "What specifically is my problem? What do I mean when I say, 'I need to eat better' or 'I'm so confused'? How can I write this down precisely, so I can know when an attempt at solving it works?"
Math has a connotation that you're solving numbers or scientific problems, but I would argue we should expand its definition to include solving problems like, "where should we go for dinner?" I think the reason humans are applying it to these problems last (through recommendation algorithms) is because the solutions are much fuzzier. Set theory is chosen to be as consistent as possible, computer programs very rarely have bit errors, even physics experiments turn out more-or-less the same each time, but what you want to eat for dinner changes every day based on a lot of factors it's difficult to be aware of, or say anything concrete about.
Seems reasonable, but, I think it is still just false that "math" is a word that means "the concept I was getting at in this post." (Certainly it's related, but, if you're smushing the above together with math, I think you're missing an important distinction)
In "What's hard about this? What can I do about that?", I talk about how, when you're facing a difficult situation, it's often useful to list exactly what's difficult about it. And then, systematically brainstorm ideas for dealing with those difficult things.
Then, the problem becomes easy.
But, there is a secret subskill necessary for this to work. The first few people I pitched "What's hard about this and what can I do about that?" to happened to already have the subskill, so I didn't notice for awhile.
The subskill is "being a useful kind of 'concrete.'"
Often, people who are ostensibly problem-solving, will say things that are either vague, or concrete but in a way that doesn't help. (This doesn't just apply to "why is this hard?", it's more general).
Here's some examples of vague things:
Here are some examples of somewhat-concrete-but-not-that-helpful things you might say, about each of those, if you were trying to ask "what's hard about that?"
Here are some more helpfully concrete things:
(I'm going to come back to "I only get ideas when I talk to other people and they basically give me the ideas", because the problem there is a bit differently shaped)
Usefully concrete things typically have at least a "who", a "what [happened]" and a "when and/or where". When you have those things, it's a lot easier to notice which followup questions are useful. Such as:
The Who/What/Where gives you enough concrete detail to start forming a model of:
This puts you in a much better position to start investigating and gathering followup data. You know who was involved, you know what situation they were in, that's specific enough to pay more attention the next time you end up in that situation.
By contrast, if I ask "why do you love sugar so much?" (as opposed to "why do you get sugar cravings in the afternoon?"), the answer-space is wider and less obviously useful. "Because... my mom fed me too much sugar and I got used to it?". "Because it tastes good?". It suggests some kind of essentialist answer instead of a mechanistic answer.
"Why do I get sugar cravings in the afternoon?" suggests that either something specifically interesting is happening in the afternoon, or, maybe it's happening a few hours earlier every day. Or, something about my biochemistry is just real "afternoon-sugar-craving" shaped, but at least that can prompt some followup questions about why is my biochemistry like that.
What's wrong with "I only get ideas when I talk to other people and they basically give me the ideas?". It's located where the problem isn't. You talk to people, you either come up with or get new ideas. Great.
(slightly fictionalized example). I recently was talking to someone who said the "only get ideas around others" sentence. I asked "what happens when you try to have ideas?". And at first they sort of shrugged and moved on without answering the question, but I asked again and they said "I... guess I don't really try to have ideas?"
And then I asked "what do you expect would happen, if you tried?"
And they said "I dunno, I wouldn't have any. It wouldn't work"
And I asked "Can you be more specific about that? What wouldn't work?". They didn't quite know how to answer the question, I tried to explain something like "what cognitive motions do you think you'd do, if you were trying to have ideas? What questions would you ask yourself? What places would you look?"
Eventually they said "okay, I guess yeah upon reflection I basically just haven't tried even at all and when I try even at all, things come up like 'I'd look for books or papers to read that might have interesting concepts I could build on' or 'I'd ask why I don't understand something that feels confusing."
In this case it was hard to get started down the journey, because there was no specific time that they might have gone and tried to generate novel ideas.
Noticing a vacuum is harder than noticing when something goes wrong. But, when you're going to try and articulate your problem, you can notice if you have failed to state a situation where the problem is occurring, and widen your search space.
(There's a similar-but-less-extreme version with Alice, Bob and Charlie. Where first, there was an opportunity to, for example, decide who was doing Task X, or write it down to remember later, or something, and they didn't notice that as an inflection point at all)
Dumb/vague solutions:
There's no way that'll actually work reliably. A somewhat better set:
The reason problem solutions should be concrete is partly so it's easier to form a plan to actually do them. i.e. who is actually doing what? When is it time to do that?
But, another reason to do it is that, if something is sufficiently concrete, your brain can actually simulate it, and then you get to leverage your fast intuitions may immediately get a sense of whether it'll work. For example, when I look at the above statements, I immediately imagine:
To deal with each of those, I'd ask "Okay, what's hard about this situation, and what can we do about it?". But, it's much easier to ask that question when you can clearly visualize the situation, and your imagined interventions on it.