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Kip Thorne

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Simplicity is the touchstone in finding new physical laws. ... If it's elegant, then it's a rough rule of thumb: you're on the right track.
--
in Does Physical Reality Go Beyond?, Closer to Truth TV Series (Cosmos).

 
Kip Thorne

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What we call thought (1) is itself an orderly thing, and (2) can only be applied to material, i.e. to perceptions or experiences, which have a certain degree of orderliness. This has two consequences. First, a physical organization, to be in close correspondence with thought (as my brain is with my thought) must be a very well-ordered organization, and that means that the events that happen within it must obey strict physical laws, at least to a very high degree of accuracy. Secondly, the physical impressions made upon that physically well-organized system by other bodies from outside, obviously correspond to the perception and experience of the corresponding thought, forming its material, as I have called it. Therefore, the physical interactions between our system and others must, as a rule, themselves possess a certain degree of physical orderliness, that is to say, they too must obey strict physical laws to a certain degree of accuracy.
PHYSICAL LAWS REST ON ATOMIC STATISTICS AND ARE THEREFORE ONLY APPROXIMATE

 
Erwin Schrodinger
 

The elegant simplicity of the three per cents.

 
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Elegant as simplicity, and warm
As ecstasy.

 
William Cowper
 

Well, [Kepler] reminded me of myself – the little man running desperately in circles, trying to find an explanation for the world, for his place in it, to find a plausible system, to account for reality – and never finding it. Finding lots of rules and laws which are very important, but never actually finding his own way into what it is to be in the world – very much an existentialist before his time, I think.

 
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Elegance is necessarily unnatural, only achieveable at great expense. If you just do something, it won't be elegant, but if you do it and then see what might be more elegant, and do it again, you might, after an unknown number of iterations, get something that is very elegant.

 
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