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Feynman's joke leaves out how one gets to the stage of knowing what the problem is. This, and working on the problem, can involve lots of hard work.  Koestler notes the fact of work/study which leads to awareness of a problem in the sciences, maths, etc., or a felt need to express something in the arts. Wallas, in a model similar to Koestler's calls this the "preparation" stage. But it is a model, a sort of ideal form; he notes how, in reality, these stages can be mixed up:


In 1926, English social psychologist and London School of Economics co-founder Graham Wallas penned The Art of Thought, laying out his theory for how creativity works. Its gist, preserved in the altogether indispensable The Creativity Question (public library), identifies the four stages of the creative process -- preparation, incubation, illumination, and verification -- and their essential interplay:

In the daily stream of thought these four different stages constantly overlap each other as we explore different problems. An economist reading a Blue Book, a physiologist watching an experiment, or a business man going through his morning's letters, may at the same time be "incubating" on a problem which he proposed to himself a few days ago, be accumulating knowledge in "preparation" for a second problem, and be "verifying" his conclusions on a third problem. Even in exploring the same problem, the mind may be unconsciously incubating on one aspect of it, while it is consciously employed in preparing for or verifying another aspect. And it must always be remembered that much very important thinking, done for instance by a poet exploring his own memories, or by a man trying to see clearly his emotional relation to his country or his party, resembles musical composition in that the stages leading to success are not very easily fitted into a "problem and solution" scheme. Yet, even when success in thought means the creation of something felt to be beautiful and true rather than the solution of a prescribed problem, the four stages of Preparation, Incubation, Illumination, and the Verification of the final result can generally be distinguished from each other.

http://www.brainpickings.org/index.php/tag/arthur-koestler/

Koestler's account of creativity involves the key idea of the bisociation of matrices - the way creativity involves the integration of previously unrelated sets of ideas.

Here's a bit more on how Koestler's model applies to the development of science in general.


The Evolution of Ideas

Koestler argues that just as ontogeny reproduces phylogeny the historical progress of science mirrors on a large scale the characteristic stages of individual discovery. In the history of any research programme, we see periods of preparation, in which new data are collected and interpreted; incubation, in which alternative matrices ripen; discovery, which involves the cross-fertilisation of previously separate branches of science, mental disciplines or experimental techniques and verification and elaboration, in the synthesis is hardened into a new collective orthodoxy.

http://webprojects.eecs.qmul.ac.uk/marcusp/notes/koestler.pdf



Maybe it's because I'm a Londoner - that I moved to Nice.
by Ted Welch (tedwelch-at-mac-dot-com) on Tue Nov 5th, 2013 at 04:00:06 PM EST
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