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What you're describing is well-known to mathematicians. The idea is that if you struggle hard with something (perhaps till you have to give up), your brain feels there is "unfinished business" and keeps working on the problem even when you're not consciously thinking ("grinding" in your words) about it. The second time you engage with the problem, you're primed to understand it - or understanding may just pop into your head, like an unexpected pizza delivery. A couple of examples: The great mathematician Henri Poincare was struggling with a problem on fuchsian functions. He made some progress, and then: "Just at this time, I left Caen, where I was living, to go on a geological exursion under the auspices of the Schools of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it ..." [1] "Incubation is the work of the subconscious during the waiting time, which may be several years. Illumination, which can happen in a fraction of a second, is the emergence of the creative idea into the conscious. This almost always occurs when the mind is in a state of relaxation, and engaged lightly with ordinary matters. Helholtz's ideas usually came to him when he was walking in hilly country. ... Incidentally, the relaxed activity of shaving can be a fruitful source of minor idea; I used to postpone it, when possible, till after a period of work." [2] [1] Jacques Hadamard, "The Psychology of Invention in the Mathematical Field" (p. 12--13) [2] J. E. Littlewood, "Littlewood's Miscellany" (p. 192) [A wonderful book, by the way!] |