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Sunday, September 13, 2015

Mathematical Discovery... Deconstructed


This morning's Sunday reflection from Stanislas Dehaene's "Consciousness and the Brain":
"[Jacques] Hadamard deconstructed the process of mathematical discovery into four successive stages: initiation, incubation, illumination, and verification. Initiation covers all the preparatory work, the deliberate conscious exploration of a problem. This frontal attack, unfortunately, often remains fruitless -- but all may not be lost, for it launches the unconscious mind on a quest. The incubation phase -- an invisible brewing period during which the mind remains vaguely preoccupied with the problem but shows no conscious sign of working hard on it -- can start. Incubation would remain undetected, were it not for its effects. Suddenly, after a good night's sleep or a relaxing walk, illumination occurs: the solution appears in all its glory and invades the mathematician's conscious mind. More often than not, it is correct. However, a slow and effortful process of conscious verification is nevertheless required to nail all the details down."


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