It reminds me of that Eureka story - how Archimedes came upon the solution of determining if the crown had pure gold in it or not in the bath.
Also reminds me of something Dien posted long time ago on the old sowpub forum - about Henri Poincare and how he researched into what made people more creative.
This is what Google tells us about Henri Poincare's ideas:
Poincaré then goes on to analyze this raw evidence. He draws the following conclusions:
1. The creations involve a period of conscious work, followed by a period of unconscious work.
2. Conscious work is also necessary after the unconscious work, to put the unconscious results on a firm footing.
4. The unconscious can present the conscious mind with something that is not fruitful, but which is nevertheless elegant or beautiful.
5. What the unconscious presents to the conscious mind is not a full and complete argument or proof, but rather "point of departure" from which the conscious mind can work out the argument in detail. The conscious mind is capable of the strict discipline and logical thinking, of which the unconscious is incapable.