Stathis Papaioannou wrote:
> Bruno Marchal writes:
>
> > >> The UD is both massively parallel
> > >> and massively sequential. Recall the UD generates all programs and
> > >> executes them all together, but one step at a time. The "D" is for
> > >> dovetailing which is a technic for emulating parallelism sequentially.
> > >
> > > Given that no actual physical hardware is needed to run it, why did
> > > you choose the UD to generate all the computations rather than just
> > > saying they are all run in parallel. There is enough room in Platonia
> > > for infinite parallel virtual machines, isn't there?
> >
> >
> > This is an interesting and key question. It is also a rather difficult
> > one. To answer it we have to dig deeper on the importance and
> > miraculous aspect of Church thesis, which makes existing a universal
> > dovetailer, and which makes precise what a computational states is, and
> > why we have to postulate Arithmetical Realism, and why we have to be
> > cautious with any form of larger mathematical platonism (but such
> > platonism is not prohibited per se).
> > Now with comp, and Church thesis in particular, it can be shown that
> > the computational states can be said to exist (in the same sense than
> > numbers) and it can be defined thoroughly by the UD. If you introduced
> > infinite machines (and I agree that it is defensible that some of such
> > machine exists in Platonia) , either you will lose Church thesis, or
> > you will lose the "YES DOCTOR", at least in the form I usually gave it.
> > Your move here can be done, nevertheless, without changing the
> > mathematical structure of the hypostases, but this asks for a non
> > trivial generalization of comp, and of Church thesis in particular. I
> > would not do that unless it is needed to get the physics (and then this
> > would be a refutation of comp, or more precisely here: of Sigma_1
> > comp).
>
> The Chuch thesis concerns what can in theory be computed by a physical
> computer with unlimited resources.
Not exactly
http://plato.stanford.edu/entries/church-turing/#Bloopers
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Received on Sat Oct 21 2006 - 08:30:32 PDT