Helmholtz, Poincaré, & the creative process

In The Quark and the Jaguar, theoretical physicist Murray Gell-Mann discusses the creative process in terms of Helmholz's three stages of saturation, incubation, and illumination, and the verification stage added thereto by Poincaré. This accords quite well with “my” foursome of beginning, middle, end, check. On pp. 264-265, Gell-Mann says that he and some physicists, biologists, painters, and poets compared experiences of discovery, & that their accounts were remarkably similar. The entire passage from which I've drawn excerpts is available through Google books http://www.google.com/search?q=%22each+found+a+contradiction%22+Gell-Mann. All ellipses below are mine.

---

[...]. We had each found a contradiction between the established way of doing things and something we needed to accomplish: in art, the statement of a feeling, a thought, an insight; theoretical science, the explanation of some experimental facts in the face of an accepted “paradigm” that did not permit such an explanation.
  First, we had worked, for days or weeks or months, filling our minds with the difficulties of the problem in question and trying to overcome them. Second, there had come a time when further conscious thought was useless, even though we continued to carry the problem around with us. Third, suddenly, while we were cycling or shaving or cooking [...], the crucial idea had come. We had shaken loose from the rut we were in.
  We were all impressed with the congruence of our stories. Later on I learned that the insight about this act of creation was in fact rather old. Hermann Von Helmholtz [...] described the three stages of conceiving an idea as saturation, incubation, and illumination, in perfect agreement with what the members of our group [...] had discussed a century later.
  [...].
  In 1908, Henri Poincaré added a fourth stage, important though rather obvious -- verification. He described his own experience in developing a theory of a certain kind of mathematical function. He worked on the problem steadily for two weeks without success. One night, sleepless, it seemed to him that “ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination.” Still, he did not have the solution. But, a day or so later, he was boarding a bus [...]. “The idea came to me, without anything in my thoughts seeming to have paved the way for it, that the transformations I had used to define these functions were identical with those of non-Euclidean geometry. [...] I felt a perfect certainty. On my return to Caen, for conscience’s sake, I verified the result.”
  The psychologist Graham Wallas formally described the process in 1926, and it has been standard ever since in the relevant branch of psychology, though I think none of us at the [...] meeting had ever heard of it. I first came across it in a popular book by Morton Hunt entitled The Universe Within, from which the above translated quotations are drawn.

---

(1) In saturation, one is taking hold of the problem, taking it on. That’s the beginning.
(2) If this does not lead soon either to illumination or to dropping the problem, then there is incubation, in which, though the problem remains unsolved, one has gotten its elements sufficiently under control to process the problem without having to consciously think about it (though of course one still can so think). It may consist, as Gell-Mann points out in the passage's fuller version, in little more than unconscious stewing over established assumptions till one or another of them softens in the mind. Anyway, that’s the middle.
(3) Illumination is the eureka, the ending, the climax.
(4) Verification/falsification is the checking.
I'd say that it's a very good match. - posted by The Tetrast @ 10:25 PM [top of post] [top of page] Copyright © BenjaminðA.ðUde11.