FOM: Application of reverse maths to theoretical physics
pratt at CS.Stanford.EDU
Thu Sep 16 02:29:40 EDT 1999
>From: Joe Shipman
>Another way in which we could get at mathematical truth from physics is
>if Church's thesis is false and we could set up an experiment to
>calculate a definable but noncomputable real number; the value of any
>digit beyond a certain finite level of precision would be a mathematical
>fact independent of ZFC.
Why do you need the failure of Church's thesis for this? The truth
value of Con(ZFC), as the number 0 or 1, is (as a mathematical fact)
independent of ZFC, yet is an eminently computable number not entailing
the failure of Church's thesis.
It's a much taller order to ask nature for a noncomputable real than
just one bit.
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