Among the great, unanswered questions in life: Why do we sleep? Followed by: Why do we dream when we sleep? While I don't have much insight on either of those questions, I have experienced what this article is all about. (Thanks to Ann for the link.)
For some reason, I usually have my best flashes of insight in the shower. But that could be because I don't really wake up until I've been in there for a couple minutes! However, recently a friend and I were listening to music from decades past and trying to identify who the artists were. We were doing pretty well until we came to one song. We both knew the song but, for the life of us, could not come up with who sang it. Throughout the day I thought about it off and on, making a few guesses but with no luck. After that, I pretty much forgot about it and filed it in the "I must be getting old" category. :)
My mind obviously decided to continue to puzzle over it, though. The next morning when I woke up (without benefit of an alarm, which may have helped), it was as if a switch had been flipped, and my first conscious thought was the name of the band. Okay, not earth-shaking like literally dreaming up the periodic table of elements, but not something that I have happen every day and the force with which the name popped into my head really caught my attention.
Oh, geez, look at the time. I'd better go to sleep so I can work on figuring out that chicken and egg conundrum...