> On 15 Mar 2020, at 16:39, Lawrence Crowell <[email protected]>
> wrote:
>
> On Sunday, March 15, 2020 at 4:47:10 AM UTC-5, Bruno Marchal wrote:
>
>> On 14 Mar 2020, at 22:42, Lawrence Crowell <[email protected]
>> <javascript:>> wrote:
>>
>> On Saturday, March 14, 2020 at 5:23:53 AM UTC-5, Bruno Marchal wrote:
>>
>>> On 12 Mar 2020, at 14:07, Lawrence Crowell <[email protected] <>>
>>> wrote:
>>>
>>> On Wednesday, March 11, 2020 at 11:21:55 PM UTC-5, [email protected]
>>> <http://aol.com/> wrote:
>>> You're ignoring quantum and photonic computing??!!
>>>
>>>
>>> No, quantum computing does not even map NP problems into P. I does not get
>>> around incompleteness results of Turing and Goedel.
>>
>> That’s right. In fact super-hyper-machine does not escape incompleteness and
>> can even be super-hyper-incomplete.Using the infinite to escape Gödel
>> incompleteness does not work, or becomes trivial.
>>
>> I will consider admitting the infinite in the ontology the day I got an
>> infinite salary :)
>>
>> Even the induction axioms are not allowed in the ontology, despite being the
>> main axiom about what is an observer.
>>
>> Quantum computing (and I guess photonic computing) does not violate the
>> Church-Turing thesis. David Deustch saw this clearly already in its main
>> quantum computability paper.
>>
>> Bruno
>>
>>
>>
>> Quantum computers obey the CT thesis. What might be called black hole
>> computers the same holds. Quantum gravitation is the same, and my essay on
>> FQXi explores this.
>
>
> You might recall us the link. I tend to agree with you. Of course we don’t
> know, as we have not yet a coherent theory of gravitation and quantum
> mechanics. But it is not good practice to speculate on the wrongness of a
> theory to satisfy some philosophical desire, like Penrose seems to have done.
> Gödel’s theorem and the quantum theory are until now rather strong evidence
> that mechanism is true. But then the theory of everything, unifying all
> forces, (love included!) is very simple, and any Turing complete first order
> theory, without induction, nor axiom of infinity will do the job. Physics is
> “machine independent” as we say in computer science.
>
> Bruno
>
>
> This is from a post I wrote on Hossenfelder's blog:
>
> Superdeterminism has characteristics very similar to hypercomputation. A
> hyper-Turing machine is one able to circumvent the restrictions of the
> Gödel-Turing uncomputability limit. A sort of Zeno machine may illustrate
> this. If I were to flip a switch at one second, then flip again at ½ second,
> then flip again at ¼ second and so forth, what is the state of the switch
> after 2 seconds? Well the rapid increase in energy required to oscillate the
> switch means that even if the switch does not fly apart it will face an
> energy limit where it is a black hole. Hence, at least from the outside
> general relativity appears to spoil the dream of circumventing Gödel and
> Turing.
>
> What if we go into the black hole? The inner event horizon is in the pure
> eternal solution continuous with I^∞. This would permit a sort of Zeno
> computation to be observed. This means one could in principle witness this
> end of switch toggling. So, if that switch is toggled or not toggled with
> each half-partitioned integral of time any possible algorithm can be computed
> and its output logged. However, this idealism is spoiled by quantum
> mechanics, for the black hole will emit Hawking radiation and the inner
> horizon is no longer continuous with I^∞. Thus, quantum mechanics rescues
> Gödel and Turing, where both QM and GR appear to respect the Church-Turing
> thesis of computation so computed outputs are from first order primitive
> recursive algorithms.
I agree, except on some minute vocabulary use, but I will not bother you with
this, unless necessary at some point.
Note that a universal machine can compute/emulate all algorithms, but of course
not decide all provability question, and less so semantical question, but not
less than us, apparently.
>
> As Peter Shor keeps harping on superdeterminism, with its real nesting of
> fractal loops or orbits, implies a vast or even infinite number of degrees of
> freedom. This does appear to be a serious minefield to go through, However,
> if these are nonlocal they are not real degrees of freedom that communicate
> information. They respect the no-signaling theorem of QM. If we could really
> output all of these nested loops or paths this would be a sort of
> hypercomputation. But we can’t, I illustrate this with the Matiyasevich
> theorem in the uncomputability of p-adic sets,
I know (and teaches) Matiyasevic’s result that the diophantine polynomial
equations are Turing Universal, and thus that Hilbert 10th problem is
undedicadable (assuming CT). But I am not aware he worked on the p-adic
numbers. If you have a link?
> while Palmer appeals to a funny idea of uncomputability of fractal or
> recursively enumerable sets by Blum, Shub, and Smale.
OK. Unfortunately with a non standard notion of computability on the reals (or
on any rings). They ahem shown that the Mandelbrot set, for example, is
uneducable in that sense, but the question “is the (rational) Mandelbrot set
Turing universal is still an open problem.
> Hypercomputing is an interesting concept,
To be honest, I have not yet find a satisfying definition of
“hyper-computation”. It always look like computation + magic, which is not
different from Turing computability + oracle. Note that all my results go
through for the machine + oracle.
Or, in some case, hypercomputaion is more than that, but then all functions are
computable, and it is not clear if this is meant classicaly, (in which case it
is a trivial) or intutionistically, in which case we get a very restricted
subset of the Turing-computable.
> but spacetime configurations that permit it violate conditions such as
> Hawking-Penrose energy conditions or chronology protection. Quantum mechanics
> and general relativity have conditions that in some ways are equivalent. For
> instance, the no-cloning theorem of QM is equivalent to chronology
> protection, for a wormhole would permit quantum cloning of states.
That is interesting. If you can explain the relation between non-cloning
theorem (which I got from mechanism even before I heard about quantum
mechanics), that would be interesting to get some “chronology protection” in
arithmetic. It might help to fight the “white rabbits” which pullulated a
priori the arithmetical reality.
>
> For hypercomputation a spacetime with closed timelike curves would suffice as
> well. The answer to an undecidable problem could come from a time machine if
> one sends the results back in time to yourself later. Anti-de Sitter
> spacetimes permit this. Curiously AdS and de Sitter (dS) spacetimes have the
> same quantum information, for the two spacetimes share asymptotic infinity.
> The de Sitter spacetime of inflation may then have a correspondence with an
> AdS in a quantum computing system. We may think of a computer with a closed
> timelike curve CTC register plus a chronology respecting register. As the two
> are quantum states or waves they then constructively and destructively
> interfere with each other.
> <quantum computer with closed timelike curves.png>
>
>
> The CTC corresponds to the chronology violating AdS and the CR is chronology
> respecting register. The self-interference of quantum waves imprints a
> quantum computing output in the R_{ctc} and quantum information in the R_{cr}
> corresponding to it has constructive interference. This is then how quantum
> computing in quantum gravitation or cosmology may work.
Hmm… Once a machine is trapped on a loop, it can no more exploit its
universality. Now, if the loop is gigantic, that does not matter in principle,
FAPP, but it does matter in the derivation of the physical laws from the
elementary arithmetical ontology (which is need to solve the mind-body problem
in the Computationalist frame).
>
> However, event horizons protect us from observing the data stack in R_{ctc}
> and this is then not hypercomputation. In this way spacetime and in general
> classical einselected outcomes occur, but we are shielded away from knowing
> how it occurs. It is not Turing computable. If theorems of QM and those of GR
> are formally equivalent, then this carries over to superdeterminism. This
> means there is no extra information we can obtain from superdeterminism that
> beats Gödel and Turing.
I agree.
Bruno
>
> LC
>
>
>>
>> LC
>>
>>
>>>
>>> LC
>>>
>>>
>>> -----Original Message-----
>>> From: Lawrence Crowell <[email protected] <>>
>>> To: Everything List <[email protected] <>>
>>> Sent: Wed, Mar 11, 2020 10:31 am
>>> Subject: Re: Reachability for infinite -time Turing machines with long tapes
>>>
>>> On Tuesday, March 10, 2020 at 10:16:38 AM UTC-5, Philip Thrift wrote:
>>>
>>> https://arxiv.org/abs/1802. 05734 <https://arxiv.org/abs/1802.05734>
>>>
>>> @philipthrift
>>>
>>> It looks to be a version of the busy beaver problem. The scale of the
>>> problem grows beyond computable bounds.
>>>
>>> LC
>>
>>
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> <quantum computer with closed timelike curves.png>
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