The nature of intuition

From an excellent blog post by Emanuel Derman. Derman contrasts Kahneman's use of "intuition" as quick insight with the physicist or mathematician's use of "intuition" to describe deep understanding operating at a subconscious level.

Kahneman’s "intuition" = a quick guess; I mean by intuition the insight that can come only after long mental struggles.

Kahneman is concerned with the biases of intuition. I am impressed with its occasional glimpses of absolute essence. Think Newton, Ampere, Maxwell, Einstein, Feynman, Spinoza or Freud or Schopenhauer maybe … That kind of intuition plays a major role in the discovery of nature’s truths.

Intuition is comprehensive. It unifies the subject with the object, the understander with the understood, the archer with the bow. Intuition isn’t easy to come by, but is the result of arduous struggle.

In both physics and finance the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform that intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. ...

THE INSIGHTFUL KEYNES ON THE GREAT NEWTON SEES INTUITION THE WAY I DO:

I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection. . . . His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one’s mind and apply all one’s powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary—“so happy in his conjectures,” said De Morgan, “as to seem to know more than he could possibly have any means of proving.”

Wigner on Einstein's intuition versus von Neumann's raw intellectual power:

I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed me.

... But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jansci's brilliance, he never produced anything as original.

See also Ulam:

[p.81] When we talked about Einstein, Johnny [von Neumann] would express the usual admiration for his epochal discoveries which had come to him so effortlessly ... But his admiration seemed mixed with some reservations, as if he thought, "Well, here he is, so very great," yet knowing his limitations. [ See also Feyerabend on the giants. ] ... I once asked Johnny whether he thought that Einstein might have developed a sort of contempt for other physicists, including even the best and most famous ones -- that he had been deified and lionized too much... Johnny agreed... "he does not think too much of others as possible rivals in the history of physics of our epoch."