In a short essay, Paul Graham talks about what he calls an ambient thought or "the top idea in your mind." As he observes, everyone who has "worked on difficult problems is probably familiar with the phenomenon of working hard to figure something out, failing, and then suddenly seeing the answer a bit later while doing something else. There's a kind of thinking you do without trying to. I'm increasingly convinced this type of thinking is not merely helpful in solving hard problems, but necessary. The tricky part is, you can only control it indirectly."
I think he is right on both counts:
there is a "kind of thinking you do without trying to" and