[FOM] Re: A Newtonian computing design

Timothy Y. Chow tchow at alum.mit.edu
Tue Feb 17 13:35:07 EST 2004

Toby Ord wrote:
> Perhaps Harvey Friedman's suggestion (in another post) can do more to
> convince you here. If this alleged hypercomputer was used to test a
> slew of halting problems whose answers we knew but were very hard won
> (does the TM that halts if and only if Fermat's Last Theorem is true
> halt?) then this would count as testing the theory in this domain.

This would not surmount the barrier between finite and infinite.  Let's
return to the distinction I made, between systems that admit a finite
simulation and systems that don't.  If we follow one of Harvey
Friedman's suggestions and remove all infinities, then certainly, I
have no objection.  On the other hand, if we are investigating something
like the consistency of ZFC + "there exists a measurable cardinal," and
we have not figured out how to do a finite simulation of the Newtonian
system and are relying on extrapolated properties of the Newtonian system
arbitrarily far below the limit where we can measure, then no amount of
verification of Newton's laws in the verifiable realm allows us to
extrapolate beyond what we can experimentally verify.

> > 2. It avoids the recursive/non-recursive issue, which I have
> > argued is a complete red herring, leading to protracted and
> > irrelevant arguments about various Church-Turing theses.
> I don't understand. Surely it is important whether or not one can solve
> the halting problem. That is the type of thing I am interested in when
> I study hypercomputation. This is the crux of the matter and not
> peripheral.

Well, if I haven't succeeded in conveying my objection with the articles
I have posted so far, then I think I probably need to write a much more
extended article (or talk with you in person) to express my meaning
successfully.  However, the one-sentence summary is that I believe that
"whether we can solve the halting problem physically" is not a physically
meaningful question if the word "solving" is used here with the same
epistemological connotation of [physical] certainty, because there is
no way that we finite human beings can experimentally verify that a
hypercomputer correctly solves the halting problem in the same sense
that we can experimentally verify the result of a finite computation.

> Yes, but do you see that you are ruling out what is at question here?

Indeed, that is precisely my point.  I don't want to ask non-questions.

> > The new slogan might be less sensational, which might be bad if the
> > main
> > goal is to capture the attention of journalists and of funding sources.
> This seems a little unfair.

It was supposed to be a joke, but as it apparently didn't come off that
way, I apologize and retract the statement.


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