> On 23 Feb 2018, at 12:40, Lawrence Crowell <goldenfieldquaterni...@gmail.com> 
> wrote:
> 
> On Thursday, February 22, 2018 at 6:38:15 AM UTC-6, Bruno Marchal wrote:
> 
> > On 21 Feb 2018, at 20:40, Brent Meeker <meek...@verizon.net <javascript:>> 
> > wrote: 
> > 
> > 
> > 
> > On 2/21/2018 1:32 AM, Bruno Marchal wrote: 
> >> I guess you mean enumerable here. I don’t see what physical bounds have to 
> >> do with Church-Turing thesis, though. We laws suppose that the universal 
> >> machine have potentially unbounded time and space (in the non physical 
> >> computer science sense) available for them. 
> > 
> > But they are bounded in the physical sense, and not just potentially. 
> 
> But Church-Turing thesis has nothing to do with physics or the physical 
> sense. 
> 
> Then you don’t know if a machine, even in the physical world is bounded, 
> unless you make special assumption on some existing universe. 
> 
> With mechanism, there are no evidence for a physical primary universe. We 
> would have found one if we would have discover a serious discrepancy between 
> the Nature’s physics and the physics in the “head of the number”, but we have 
> tested this as far as possible, and found none. 
> 
> The relationship between the physical world and mathematics of computation is 
> something I explore here 
> <https://physics.stackexchange.com/questions/305346/is-there-something-similar-to-g%C3%B6dels-incompleteness-theorems-in-physics/305368#305368>.
>  This is in connection with the theoretical concept of hypercomputation. 
> Certain types of spacetimes called MH (Malament-Hogarth spacetimes) have the 
> physical properties that might do an end run around the limits of Godel. On 
> the other hand quantum mechanics might provide limits on that.

I know the existence of MH spacetimes, but it is not yet clear how this escapes 
Gödel incompleteness. Since Turing we know that hyper-computations do not 
escape incompleteness. It escapes PA and ZF, but it does not lead to effective 
way to emulate something not Turing emulable, but I would need more time to 
assess this, and I judge from an early draft I saw on this subject.

Then you say in your blog “Physics, on the other hand, ultimately attempts to 
model reality.” But that is the main axiom of Aristotle metaphysics which is 
doubted at the start when we realise that all computations are run in 
arithmetic. You invoke “god” in theology, which means that you don’t intent to 
do metaphysics or theology with the scientific method. When we do theology or 
metaphysics with the scientific method we must stay neutral on what could be 
the fundamental reality, especially when some work like mine give a precise 
tool to assess if the materiality is fundamental or emerging, and the results 
get so far abounds in the idea that the material reality is not the fundamental 
reality. The axioms you are using is refuted by the mechanist hypothesis, so 
you must take into account that you are postulating a “god” incompatible with 
Mechanism, but then the MH space-time is out of use in metaphysics, as it 
requires a black hole to work, and there is few evidence that we have a black 
hole in our head. 
Note that I do find the MH-space time very interesting, and it suggest we might 
exploit computationally back holes in some far future, (or not, as you are 
right that quantum mechanics makes this theoretically close to impossible), but 
even if done, it would not change the logical conclusion of Mechanism: physics 
is just not the fundamental science and physics is constructively reducible to 
machine’s self-reference theory. You have only the arithmetical reality, which 
emulates (in the sense of Church, Turing) all computations, and physics is 
given by the non computable statistics on all relative computational consistent 
extensions. Although it is not computable, the propositional part of physics is 
computable and decidable, and indeed we have recovered some quantum logics at 
the place they were mandatory. This is not just an evidence for 
computationalism it is also a very deep theoretical evidences for quantum 
mechanics being completely valid.

Bruno


> 
> LC
> 
>  
> https://physics.stackexchange.com/questions/305346/is-there-something-similar-to-g%C3%B6dels-incompleteness-theorems-in-physics/305368#305368
> 
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