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Gaianne: ... Without intuition you get nowhere.  

But none of my colleagues would ever admit that in public.  

Why do you think is that?  

Because they were prisoners of a false image of what real maths or science was like - from their own education and the way papers are written - tidily, after the messy process of creative thinking (cf Colman below).

Koestler's "The Act of Creation" was published back in 1964 and gave many examples from science (as well as the arts) of how the creative process worked; bascially:

felt need (arts) existing problem (sciences)

initial conscious work

unconscious activity (so important to leave time for this - a very important lesson that B. Russell learnt the hard way after years of struggling to do it all consciously)

Insight/inspiration

The latter often occurred in dreams or half-awake state and often involved imagery - including in sciences - Kekule snake with tail in mouth I seem to recall - yes:

 "While researching benzene, the German chemist dreamed of a snake with its tail in its mouth. Kekulé interpreted the snake as a representation of the closed-carbon ring of benzene"

http://en.wikipedia.org/wiki/Cryptomnesia

 Einstein even said his creative "thinking" involved muscular sensations.

As this review points out, unfortunately it got a very bad review from Medawar (and probably other scientists) so not too many young scientists may have read this - a pity:

"The Act of Creation" offers a theory to account for the "Ah Ha" reaction of scientific discovery, the "Ha Ha" reaction to jokes and the "Ah" reaction of mystical or religious insight. In each case the result is produced by a "bisociation of matrices" or the intersection of lines of thought which brings together hitherto unconnected ideas and fuses them into a creative synthesis. When the lines of thought are scientic the result is a scientific discovery, when they are concerned with devotional matters the result is mystical insight and when they are on a more homely plane the result can be a joke.

The model is fleshed out with a great deal of information ranging from the religions of the world to a theory about the nervous system to account for the build-up of tension and its discharge at the puchline of a joke. Peter Medawar's review was scathing in his comments on Koestler's science, which is a shame because the book can have the desirable effect of encouraging young scientists to read far beyond the usual range of their literature.

http://www.amazon.ca/Act-Creation-Arthur-Koestler/dp/0140191917



Maybe it's because I'm a Londoner - that I moved to Nice.
by Ted Welch (tedwelch-at-mac-dot-com) on Wed Jan 2nd, 2008 at 11:43:24 AM EST
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