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.

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