[FOM] Re: The Myth of Hypercomputation

Piyush P Kurur ppk at imsc.res.in
Fri Feb 13 23:04:54 EST 2004

On Tue, Feb 10, 2004 at 10:11:06PM +0000, Toby Ord wrote:
> On 10 Feb 2004, at 18:25, Timothy Y. Chow wrote:
> >Upon further reflection, I think I have a partial answer to the 
> >concerns I
> >raised.  It seems to me now that the issue of extrapolating from finite
> >machines to Turing machines is actually a red herring.  I think that it
> >is the two following theses that are really at stake:
> >
> >  Finite Verification Thesis:  Computations that admit a finite 
> >physical
> >  verification (i.e., finite observations of an experiment requiring
> >  a finite amount of resources [time, energy, error control, etc.] to
> >  prepare) confer an epistemological certainty that computations that
> >  don't admit a finite physical verification cannot.
> I'm afraid that I see no reason to accept this thesis. I assume you are 
> not simply saying that the computation must be verifiable by an unaided 
> human 

	For a "hyper computer" built using a theory say T, one first needs to
be confident that T is indeed true. For this to be the case, T has to be
experimentally verified. Suppose that T predicts a fundamental constant
to have the value $\Omega$ (the halting set coded as a real number), how
are we going to check it. We consider T to be true iff apart from being
mathematically consistent should agree to all experiments. All
predictions made by this theory should be in principle verified. That is a 
fundamental problem. 


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