The WSJ has a good article about research linking daydreaming and “Eureka” moments. One interesting thing I noticed is that the brain works harder during daydreaming than working on complicated problems. Another is the fact that there is a brief period of calming activity just before an insight is made – almost as if the brain is trying to clear out the competing ideas and focus in on the right one.
I think that there is an explanation for this finding in a 1977 study (warning: PDF link) by Nisbett and Wilson where people were asked to tie two ropes together that were hanging from the ceiling. The ropes were just far enough apart so that if you grabbed one you couldn’t reach the other. In the control group very few people got the answer. But in the experimental group an experimenter accidentally nudged one of the ropes, turning it into a pendulum. In this group, within seconds most of the people immediately solved the problem by doing the same thing. When asked how they came to the right answer, nearly none of them could say where the idea came from.
So my theory is that in our daydream we see something that points us toward a solution to a problem that we’re concentrating on. It’s kind of like in a movie or TV show where the character will be listening to a story or will see something and then get a blank look on their face and then get a spontaneous new idea that solves the problem. The movie The Hangover has one of those moments in it and is very funny, in case you are looking for something to do. Maybe that’s where my stroke of insight came from and I just don’t remember it.