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Koestler described the more general process (would apply to maths too) in The Act of Creation like this:

Awareness of a problem

Research

Incubation period

Insight/intuition

Checking

Bertrand Russell said that when younger he'd tried to solve problems in maths by continual work on them - to the point of exhaustion and frustration. Later he realised that if, after some work, he just left it for a while, a possible solution would pop into his mind to be checked out.


Maybe it's because I'm a Londoner - that I moved to Nice.

by Ted Welch (tedwelch-at-mac-dot-com) on Wed Oct 30th, 2013 at 10:44:33 AM EST
[ Parent ]
Which sounds all lovely and noble. Sort of like a product label for artisan cheese, with maidens dancing through the countryside after their cows. Leaves out a lot of of sweat and stink and drool and sour milk.
by Colman (colman at eurotrib.com) on Wed Oct 30th, 2013 at 10:48:45 AM EST
[ Parent ]

And sour grapes ? :-) Clearly even the first could be a long, painful process, revealing a problem in one's work which had already taken a lot of sweat and which one thought was correct. The research could be difficult and lead up blind alleys. There is, of course, no guarantee that a correct insight would arrive - a common occurrence and rather sickening.

Maybe it's because I'm a Londoner - that I moved to Nice.
by Ted Welch (tedwelch-at-mac-dot-com) on Wed Oct 30th, 2013 at 11:11:23 AM EST
[ Parent ]
There's a joke about maths lecturers using "clearly" to mean "after an awful lot of boring grind".
by Colman (colman at eurotrib.com) on Wed Oct 30th, 2013 at 11:42:48 AM EST
[ Parent ]

I saw a TV version: a lecturer writes some symbols on a board and says: "So it's obvious that ..."  Very long pause - "Er, so it's obvious that ...."

Maybe it's because I'm a Londoner - that I moved to Nice.
by Ted Welch (tedwelch-at-mac-dot-com) on Wed Oct 30th, 2013 at 03:37:39 PM EST
[ Parent ]
How much math have you actually done, Ted?

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Wed Oct 30th, 2013 at 11:43:41 AM EST
[ Parent ]
Oh here we go again (as in the discussion of String theory): "You're not an expert, you're not allowed to talk about this". I referred to maths in the most general way, Koestler's account of the creative process was supposed to apply, in general, to all areas. If you think it mistaken in relation to maths, give us the benefit of your expert opinion. I quoted Russell on his experience of working on maths which illustrated the importance of the incubation stage. If you have anything significant to contribute please do so.  

Maybe it's because I'm a Londoner - that I moved to Nice.
by Ted Welch (tedwelch-at-mac-dot-com) on Wed Oct 30th, 2013 at 03:24:51 PM EST
[ Parent ]

By the way, is TBG allowed to have a 'take" on "recent physics" - as a mere "outsider" ?

Maybe it's because I'm a Londoner - that I moved to Nice.

by Ted Welch (tedwelch-at-mac-dot-com) on Wed Oct 30th, 2013 at 03:39:55 PM EST
[ Parent ]
That from Koestler and Russell sounded just like Feynman's "method" for solving problems:

  1. write que question on the board
  2. think real hard
  3. write the answer

or Dirac's quip that "to understand an equation means to be able to write down the solution without calculating".

Which is fun and all, but was just (especially in Feynman's case) intended as a joke and definitely not reflective of the amount of hard work both men devoted to their problem-solving.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Thu Oct 31st, 2013 at 05:41:41 AM EST
[ Parent ]

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
[ Parent ]
I shall ask our artisan cheese maiden about this, this evening at our food distribution.

Though my intuition tells me she's surely no maiden.

by afew (afew(a in a circle)eurotrib_dot_com) on Wed Oct 30th, 2013 at 11:58:59 AM EST
[ Parent ]
Have you moved on from that intuition to the incubation phase?

Index of Frank's Diaries
by Frank Schnittger (mail Frankschnittger at hot male dotty communists) on Wed Oct 30th, 2013 at 06:05:52 PM EST
[ Parent ]

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