FOM: Re: Application of reverse maths to theoretical physics JoeShipman at
Sun Sep 19 21:09:58 EDT 1999

In a message dated 9/18/99 1:03:47 PM Eastern Daylight Time, 
Helene.Boucher at writes:

<<    First, you need an infinite output for a noncomputable real; any
 finite string is of course computable.  So it seems a bit dicey to
 assert that there is an experiment which could determine this, or that
 a physical machine can calculate a noncomputable real, since
 presumably that would mean it would have to output an infinite number
 of digits. >>

But to get new mathematical facts independent of ZFC, you only need finitely 
many digits, because ZFC doesn't settle the value of certain individual 
digits of any definable noncomputable real.  

It needs to be a definable real so the value of one of its digits can be a 
"mathematical fact"; but I am raising the possibility of the failure of 
Church's thesis *in the context of a mathematized physical theory*.

The uncertainty principle is not an issue here because the number to be 
measured can be dimensionless (like the fine-structure consistent, or a ratio 
of two frequencies which can be measured to arbitrary precision by counting 
enough events).

-- Joe Shipman

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