[FOM] constructivism and physics
legor at gmx.de
Sun Feb 12 19:30:46 EST 2006
Neil Tennant wrote on Wed, 8 Feb 2006 21:34:01 -0500 (EST):
> The discussion on constructivism and physics appears to be based on the
> common assumption that the constructivist's task would be to serve up as
> (constructive) theorems all those theorems that physicists might have
> occasion to apply when making predictions about, and giving explanations
> of, empirical phenomena.
It might not necessarily be related to physics, but let me remind this
Protein folding problem:
Given a stable protein as a long string over 20 amino acids identify its
unique 3D spatial structure with minimal energy.
This (obviously constructive) open problem in biology is NP-hard under most
mathematical models, and yet in "natural reality" it takes only a few
seconds to achieve the solution. Nobody knows how this is done in nature, so
people are testing genetic algorithms to approximate the natural folding
Now clearly even the longest proteins have finite length. Are there still
unknown simple mathematical solutions of NP-hard problems in large bounded
domains? Should the ultraintuitionism be reanimated?
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