Is a sleepy brain a creative brain?
Do you sometimes come out with slightly off the wall ideas when you feel tired and sleepy? I know I do and have always done. I've always called it a 'loosening of the lobe'. The fore parts of you brain - the frontal lobes - are responsible for planning and keeping you on task with analytical problem solving, as well as other things. It seems that, according to this report in Scientific American, when you are sleepy, this inhibition relaxes a bit and allows unrelated information to float around more freely. In these experiments, although there was no time of day effect for analytical tasks, people were consistently better at the creative tasks at "non-optimal" times of day. That is, when they were sleepy.
So, those ideas you get when you're falling asleep? It seems like that's our most creative stuff - thoughts that would normally get filtered out are allowed to mix together to maybe generate other, novel ideas and solutions in these precious hours. Prepare that notebook and pen before your head hits the pillow.