How many of you like HP41C calculators?

From: William R. Buckley <wrb_at_wrbuckley.com>
Date: Thu Nov 20 22:55:51 2003

> >From: ard_at_p850ug1.demon.co.uk
> >>
> >> In the case of Turing closure, the notion is much broader.
> Turing closure
> >> refers
> >> to the ability of a system to perform any and all computations
> that can be
> >> expressed. Now, there are problems with this notion, since
> Godel has shown
> >> that some expressible computations in fact can not be
> computed. Still, the
> >> general notion is: all that can be computed is computable upon
> a TM, and a
> >> TM
> >> is capable of computing all computations.
> >
> >Care to explain this in a way which is not either self-contradictory
> >('There are functions that can't be computed, but a Turing machine can
> >computer all functions) or tautological ('A Turing machine can compute
> >all functions that can be computed on a Turing machine')?
> >
> >-tony
> >
>
> Hi
> I believe that Turing proved that if it can be calculated
> by a computer, it can be computed on a Turning machine. It
> is the reverse that may not be true since the computer may
> not be flexable enough. Turing didn't make comments as to
> how large a Turing machine was to do this, only that it could.
> Dwight

No, Turing showed that if it can be computed, it is computable
on a TM. There is no machine existing, no machine which may
exist, that can compute a computation which is not also
computable on a TM.

William R. Buckley
Received on Thu Nov 20 2003 - 22:55:51 GMT