Consciousness. Inspiration and Invention. Penrose, Emperor’s New Mind, page 418 Poincar é ’s experience:
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What is striking about this example (and numerous others cited by Hadamard) is that this complicated and profound idea apparently came to Poincaré in a flash, while his conscious thoughts seemed to be quite elsewhere, and that they were accompanied by this feeling of certainty that they were correct – as indeed, later calculation proved them to be. It should be made clear that the idea itself would not be something at all easy to explain in words. I imagine that it would have taken him something like an hour-long seminar, given to experts, to get the idea properly across. Clearly it could enter Poincaré’s consciousness, fully formed, only because of the many long previous hours of deliberate conscious activity, familiarizing him with many different aspects of the problem at hand. Yet, in a sense, the idea that Poincaré had while boarding the bus was a ‘single’ idea, able to be fully comprehended in one moment! Even more remarkable was Poincaré’s conviction of the truth of the idea, so that subsequent detailed verification of it seemed almost superfluous.
Penrose: It seems to me that this accords with a putting-up/shooting-down scheme of things. The putting-up seems to be unconscious (‘I have nothing to do with it’) though, no doubt, highly selective, while the shooting-down is the conscious arbiter of taste (‘those which please me I keep …’). The globality of inspirational thought is particularly remarkable in Mozart’s quotation (‘it does not come to me successively … but in its entirety’) and also in Poincaré’s (‘I did not verify the idea; I should not have had time’).