Le 20-oct.-06, à 06:46, Stathis Papaioannou a écrit :

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>
>
> 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).
I must go. We can come back on this (but it is obviously a bit more
technical),
Bruno
http://iridia.ulb.ac.be/~marchal/
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