[FOM] FW: Constructive mathematics in Nature

[Kreinovich, Vladik]

FYI
________________________________________
>From Bas Spitters <b.a.w.spitters at gmail.com>
Subject: Constructive mathematics in Nature

Or in the words of Nature:

!!! Paradox at the heart of mathematics makes physics problem unanswerable !!!

http://www.nature.com/news/paradox-at-the-heart-of-mathematics-makes-physics-problem-unanswerable-1.18983

Scott Aaronson has a nice discussion and questions the physical relevance.
http://www.scottaaronson.com/blog/?p=2586

It seems to be a specialization to a physically relevant class of
operators of the well-known fact, due to Bishop, that all kind of
properties of the spectrum/eigenvalues of an operator need not be
computable. In fact, this was known to the numerical analysists
before.

In any case, here's the full paper.
http://arxiv.org/abs/1502.04573


Here's some related work on the nlab. The page still needs some work.
http://ncatlab.org/nlab/show/computable+physics

It is reminiscent of the discussion about unbounded operators in physics. E.g.
Douglas Bridges, Constructive mathematics and unbounded operators