Many scientists have been interested in the question of the way in which scientific discoveries are made. A popular idea is that scientists apply their powerful intellects in the straightforward, logical induction of new general principles from known facts and the logical deduction of previously unrecognized conclusions from known principles. This method is, of course, sometimes used; but much advance in knowledge results from mental processes of another sort – in large part unconscious processes.
Henri Poincaré in his essay on mathematical creation said that knowledge of mathematics and of the rules of logic is not enough to make a man a creative mathematician; he must also be gifted with an intuition that permits him to select from among the infinite number of combinations of mathematical entities already known, most of them absolutely without interest, those combinations that will lead to useful and interesting results. In illustration, he described his investigations on the nature of the Fuchsian functions, which he had discovered while working at Caen. He left Caen on a geologic excursion, and for some tine, while traveling, made no conscious effort to attack the problem; then one day, as he put his foot on the step of an omnibus, the idea suddenly came to him that the transformations that he had used to define the Fuchsian functions are identical with those of non-Euclidian geometry. Several days later he verified this discovery by detailed analysis.
From my own experience I have come to the conclusion that one way for me to have a new idea is to set my unconscious to work on a problem. This is probably what the Persian philosopher Avicenna, a thousand years ago, also did when he was unable to solve a problem. He would go to the mosque and pray for his understanding to be opened and his difficulties to be smoothed away; he probably had fixed the problem in his mind before going to the mosque, and his nature was such that his unconscious could then set to work on it.
My own experience…has suggested to me that it is possible to train the unconscious to help in the discovery of new ideas. I reached the conclusion some years ago that I had been making use of my unconscious in a well-defined way. I had developed the habit of thinking about certain scientific problems as I lay in bed, waiting to go to sleep. Sometimes I would think about the same problem for several nights in succession, while I was reading or making calculations about the problem during the day. Then I would stop working on the problem, and stop thinking about it in the period before going to sleep. Some weeks or months might go by, and then, suddenly, an idea that represented a solution to the problem or the germ of a solution to the problem would burst into my consciousness.
I think that after this training, the subconscious examined many ideas that entered my mind, and rejected those that had no interest in relation to the problem. Finally, after tens or hundreds of thousands of ideas had been examined in this way and rejected, another idea came along that was recognized by the unconscious as having some significant relation to the problem, and this idea and its relation to the problem were brought into the consciousness.
-Linus Pauling, “The Genesis of Ideas,” June 7, 1961.