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]
>> 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.
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, while Palmer appeals to a
funny idea of uncomputability of fractal or recursively enumerable sets by
Blum, Shub, and Smale.
Hypercomputing is an interesting concept, 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.
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.
[image: 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.
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.
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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