I think consistent focus might be a bit overrated, and bouncing between topics can be a nice way to learn for some people. For example, yesterday I looked at the type signature of runST in Haskell and it was completely obvious how it works and how to implement my own. I had stumbled on that weird type signature a few times before, filed it away as incomprehensible and moved on to other things. But I guess my mind was processing it in the background somehow.
That happens to me a lot with other topics as well. I get intrigued by something, play with it enough to memorize a few details without really understanding them, then forget about the whole thing for awhile, and then come back to find a deeper understanding without apparent effort. Does anyone else feel that way?
Yes, all the time. I read a book called refactor your wetware, and despite the patronizing title, it's about how our brain processes things in 'real time' but also in a sort of longer term, background data crunching sort of way and we should take advantage of this.
Have you ever you've ever had a problem you just couldn't solve, that was really hairy and beat you up all night that was suddenly trivial and obvious when you woke up the next morning? Same process, apparently. Basically your background subconscious or a lower level part of your brain goes and picks through all your knowledge that isn't readily available to your consciousness.
Absolutely. I notice it most with math. I try to reconstruct my intuition by sheer force of will, then give up in frustration because my mind will not move. When I wake up, the intuition is just there, as if something was updated or placed. It's not always overnight. Sometimes it's days or weeks, and some things I'm still working on after many years.
Actually yes. This is exactly what happens to me. Even after months, I come back and have an easier time. I think this touched on in Barbara Oakley's stuff though she seemed to criticise the extreme lengths between my learning.
My other problem is I spent tonnes of time learning and then never do anything with it. A lot of the stuff I learn often becomes useful mental models - calculus and the idea of continuity and change did this. It felt like a new way to look at the world.
The problem is you can have infinitely many ways of looking at the world but it means nothing if you don't do anything with it!
When you learn something, you can try using your newfound skills to answer questions on subreddits, mathoverflow, etc. It feels great to satisfy other people's interest and get feedback on it.
That happens to me a lot with other topics as well. I get intrigued by something, play with it enough to memorize a few details without really understanding them, then forget about the whole thing for awhile, and then come back to find a deeper understanding without apparent effort. Does anyone else feel that way?