> On 23 Feb 2018, at 17:15, Lawrence Crowell <goldenfieldquaterni...@gmail.com> 
> wrote:
> On Friday, February 23, 2018 at 7:06:47 AM UTC-6, Bruno Marchal wrote:
>> On 23 Feb 2018, at 12:40, Lawrence Crowell <goldenfield...@gmail.com 
>> <javascript:>> 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 <>> 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
> The MH spacetime in the case of the Kerr metric does permit an observer in 
> principle to witness an infinite stream of bits or qubits up to the inner 
> horizon r_- that is continuous with I^+ in the exterior spacetime. This means 
> due to spacetime effects one could witness the diagonalization in a Zeno 
> machine context. For instance a switch that is switched one in one second, 
> off the next half second, on in the next quarter second and so forth will 
> presumably have a final state. However, what does prevent this in a 
> fundamental way is that a switch flipped in this chirped frequency will 
> diverge in energy and become a black hole before returning a result. We could 
> of course avoid the black hole with a ball that bounces, but of course one 
> does not get an infinite number of little bounces at the end. Because of this 
> an observer could in principle witness a universal Turing machine emulate all 
> possible Turing machines. Thinking according to TMs is for me a bit simpler, 
> but this does illustrate one could get around Godel.

I am not sure the observer should not be itself implemented in the MH, and its 
first person perspective might not allow him to see the TM emulating all TMs. 
But even if it did, that would only be the implementation of a halting 
algorithm, which overcome the Turing limitations, but not the Gödel one: you 
will only get the sigma_truth completely, but “time” itself is such an oracle, 
and again, I am not sure if such an observer does not, from its personal point 
of view, have to live an infinite life to assess the result. But I have looked 
at the MH paper a long time ago, so take this with caution. Note that Gödel 
incompleteness cannot be escaped by *any* means, even infinite means, unless 
you directly refer to the semantics, which is not an effective process.

> However, quantum mechanics as I illustrate seems to throw a spanner in the 
> works. This breaks the continuity between r_- and I_+. It also means the 
> inner horizon is built from quantum fields from the exterior in ways that 
> generates a mass inflation singularity. This is interesting to ponder with 
> respect to the connection between quantum mechanics and general relativity.

Yes, very interesting. 

> In fact I think the two are simply aspects of the same thing. This means in 
> some way the incompleteness theorems of Godel are involved with the 
> foundations of physics.

Very glad to hear that. 
Note that with Mechanism, incompleteness is responsible for the whole set of 
accessible phenomenologies including the physical one, so yes, it is hoped that 
physicists will someday study incompleteness (in a more serious (valid) way 
than Penrose which has detracted many physicists from Gödel, and many logicians 
from physics). 


> LC
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