In this question it is described that intentionally not thinking about a problem can allow the subsonscious to find an answer to the problem; this is known as incubation. I have heard and read it a few times that if you want to solve a tough problem you can read/think about it just before going to bed and let the brain come up with a solution while you sleep. (I can find no references for this at the moment, however. Sorry)
Also, there have been few cases that provided a solution during sleep. (Benzene structure is one which I remember) Is it mere chance or false advertising, or is the brain really capable of incubating on an idea during sleep?
A robotics guy I saw on TED claimed that he used to keep a notebook by the bed, so that he could jot down the ideas if any came to him during sleep.
Can one's brain incubate on an idea while sleeping? Can one train one's brain to incubate on a specific idea during sleep?