[FOM] Re: The Myth of Hypercomputation

[Toby Ord]

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 (which would be a simple translation of the CTT), but allow 
non-human-verifiable processes, so long as they are 'finite'. Could you 
elaborate on some reasons for holding this? If someone built a machine 
that used some 'infinite' process to determine the answer to any given 
halting problem (and output the answer on a printed page, for 
concreteness...) would you simply not accept its answers? What if those 
answers had been used and checked, with no errors noticed by the most 
powerful classical computers for the last 1000 years? What if current 
physics (which, say, had stabilised for 1000 years) showed how it 
worked and let you understand how it worked? If we had some proof that 
no such machine could exist, then I would join you in doubting that 
this machine did what physics (or its history) claimed, but you are not 
denying that it could be built, just that it could not be trusted.

Elaborations would be most welcome,
Toby Ord.