On Tuesday, March 10, 2020 at 8:34:20 AM UTC-5, Bruno Marchal wrote:
>
>
> On 10 Mar 2020, at 12:44, Lawrence Crowell <goldenfield...@gmail.com
> <javascript:>> wrote:
>
> On Monday, March 9, 2020 at 4:57:24 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 5 Mar 2020, at 12:42, ronaldheld <ronal...@gmail.com> wrote:
>>
>> Any comments, especially from Bruno, and the Physicalists?
>>
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>> <2003.01807.pdf>
>>
>>
>>
>> The paper is quite interesting, but I will have to deepen my
>> understanding of Black Hole (and GR) to better appreciate it.
>>
>> There are some preliminary point were “I disagree” (or the universal
>> machine disagree) but they might not be relevant, with respect to the
>> paper, but relevant to the plausible link you make between the paper and
>> physicalism.
>>
>> Typically, the first sentence of the paper is “physicalist”, which is not
>> astonishing in this context. Susskind says that the original Church-Turing
>> thesis may be regarded as a principle of physics (which it is not).
>>
>> This can be shown inconsistant with the mechanist assumption in Cognitive
>> Science (not in physics). Indeed, with mechanism, a priori, the physical
>> reality should be able to compute more than a Turing machine. The physical
>> reality can simulate “real” random oracle, for examples, and any physical
>> object requires the entire universal dovetailing to be determined. That
>> entails non cloning, and a priori much more computability abilities (random
>> oracle, “white rabbits”, infinite sum on infinitely histoiries, the full
>> set of true sigma_1 sentences, but also non computable Pi_1 truth
>> pertaining to the distribution of accessible states, etc.
>> That is so true, that Mechanism must explain the apparent computability
>> of nature from non computable subset of the arithmetical truth. So, here,
>> implicitly the paper relies on physicalism, without the awareness that
>> eventually the physical appearances have to be explained by the statistics
>> on all computations in arithmetic, not just the “quantum one”, and the
>> quantum must be extracted from the machine’s theory of consciousness (as I
>> did). So, normally, it can be expected that the (original) Church-Turing
>> thesis (which is one half of Mechanism) might imply the falsity of the
>> quantum Church-Turing thesis (due to Deutch, and I have to think how much
>> that is related to Susskind quantum-extended Church thesis).
>>
>> This concerns only the original Church Thesis and its impact on the
>> possible physics available to arithmetical machine, and as physics is not
>> yet entirely derived neither from Arithmetic, nor from observation (cf the
>> GR + QM problems), it is hard at this stage to see how much mechanism will
>> assess or diminish the validity of Susskind’s idea on the extended Quantum
>> and physical version of CT.
>> Yet, unlike the typical use of quantum mechanics to prevent an infinite
>> computation to be realised in the physical universe, which would need
>> digital state encodable below the Planck Era (and thus hardly usable by any
>> concrete observer), the idea of Susskind is more subtle, and involves a
>> notion of “complexity” related to the interior of Black-Hole. I would need
>> here to revise (to say the least) Finkelstein derivation of GR from a
>> finitist or discrete approach to Quantum Mechanics, which is still above my
>> head … (I mentioned the interesting book by Selesnick on it sometimes ago).
>>
>> So, just to be clear:
>>
>> CT = anything computable is computable by a Turing machine (or by a
>> combinator, or by Robinson Arithmetic, or by LISP, etc.). This has a priori
>> nothing to do with physics.
>>
>> I will note s-CT for Susskind Physicalist version of CT: any thing
>> physically computable is computable by a Turing machine. (The physical
>> reality does not compute more). This is an open problem to me. It is not
>> excluded that the physical reality which emerges from all computations in
>> arithmetic might have non Turing computable components.
>>
>> Then s-ECT is the thesis that anything computable *efficiently* (i.e. in
>> polynomial time) physically, by nature, is computable in polynomial time by
>> a Turing machine. This thesis is usually believed to be wrong, as Susskind
>> says, and indeed, if that was not wrong, we would not invest in quantum
>> computing. Most people today believes that factoring (large) number cannot
>> be done in polynomial time by a Turing machine.
>>
>> qECT (Susskind notation) is the (extended) thesis that says that if
>> nature can compute efficiently something then a quantum computer can
>> compute it efficiently. That is mainly what I call the Deustch Thesis. And
>> as <I said, I do think that CT (+ YD, i.e. mechanism) entails its plausible
>> falsity.
>>
>> And Susskind abounds in that direction, and this without Mechanism, which
>> would make this into a yet another confirmation of Mechanism.
>>
>> With Mechanism, and assuming the existence of Black Hole, it should be
>> obvious that whatever happens in a black hole will not play a role in the
>> working of your brain. A good thing, as you will not have to ask to the
>> Doctor to emulate the interior of a black hole. But with mechanism, this
>> means that a black hole is full of "crazy virtual particles" doing
>> infinitely complex task, just because your state of mind is totally
>> independent of the”content of the black hole (without its boundary)".
>>
>> At first sight, Susskind seems convincing on this, but again, to be able
>> to asses this would require that I study much more the QM and GR of the
>> black hole. To compare with Mechanism, we have the rather complex task to
>> derive GR from QM and QM from arithmetic before, so this is a bit premature
>> (I still work hard to have a notion of space, although its shadow is there,
>> but requires the existence of large cardinal in set theory. (As I said,
>> with Mechanism, the ontology is extremely simple (Robinson arithmetic), but
>> the phenomenology is of unbounded complexity.
>>
>> So, very interesting but complex idea by Susskind, but it touches on
>> problem which are far from being treated with the mechanist hypothesis. If
>> I progress in my understating of Finkelstein, I might say more later. The
>> paper confirms that there is something in the holographic idea, and when
>> you compactify a universal dovetailing, you get a sort of similar
>> principle, given that the first person experience are determined only on
>> its “boundary”.
>>
>> Bruno
>>
>
> From the perspective of a physicist who knows some things about Gödel’s
> theorem and even Löb’s theorem I think in one sense you use language or
> metaphysics that is a bit outside of science.
>
>
>
> My main point is to illustrate that when we assume the Mechanist
> hypothesis in the cognitive science, then the question of
> metaphysics/theology becomes problem in mathematics and physics, and, in
> particular, that the assomption of (Digital) Mechanism is empirically
> testable.
>
> My interest is in the mind-body problem. What I claim/explain is that if
> we take seriously the digital mechanist thesis (in cognitive science, not
> in physics!) then the mind-body problem is reduced into the problem of
> deriving the physical laws entirely from
> computer-science/arithmetic/"machine-theology”. More on this later,
> probably.
>
>
>
>
>
> Terms such as physicalists are not used, and materialism sometimes comes
> up and it is not clear to me how this deviates from the term physicalist.
>
>
>
> Materialism is only a “naïve” version of phyicalism. You can equate them
> without problem, until we need, or not, to make a nuance.
>
> Materialism is the belief in primary matter (the idea that there is really
> matter out there whose appearance cannot be explained without assuming its
> existence).
>
> Physicalism is the belief that physics is the fundamental science, and
> here to, this means that we have to assume some physical theory, (but not
> necessarily some primary matter).
>
> That describes basically the theological, and metaphysical paradigm since
> 1500 years, with of course some exceptions, but usually they are not well
> seen.
>
> The antic greek used the Dream Argument to show that no experimentation at
> all can prove an ontological existence, be it a god or some Aristotelian
> primate matter. With the digital mechanism hypothesis, that “dream
> argument” and similar can be made rigorous.
>
>
>
>
>
>
> The first of Gödel’s theorem comes in with looking at a list of
> observations of a quantum system, such as a list of probabilities on the
> abscissa and actual measurements on the ordinate.
>
>
> There is some typo error? Gödel has never assumed nor study quantum
> mechanics. Bad tongues said that, when old, and living near Einstein, in
> Princeton, he was told by Einstein to not open his mouth on quantum
> Mechanics. That is why Gödel will only use General relativity to tickle
> Einstein…
>
> The first theorem of Gödel is an easy consequence of the Church-Turing
> thesis (as Kleene saw, and Webb wrote an entire book around this). Somehow
> E. Post discovered this in the 1920s. Gödel’s proof avoid carefully both
> the notion of machine, and the notion of Truth.
> Eventually, in 1936, Gödel will be OK with both Turing notion of machine,
> and Tarski’s notion of Truth. And understood them probably better than most
> people. Gödel understood that the thesis of Turing and Church, also
> proposed by ¨Post and Kleene, is just incredible. But he missed the digital
> mechanist of mind, and of course its immaterialist consequences.
>
>
>
>
>
> This can then be used to perform the Cantor diagonal trick, which flips
> the outcome, and this is then not predicable. The inability to predict the
> outcome of a particular measurement of a quantum system can then be
> expressed according to a Cantor diagonal argument. This then leads to a
> form of the incomputable nature of QM.
>
>
>
> The non computability related to I-reciting an outcome does not comes from
> Gödel or Turing, which shows limitations in the long run, or all theories
> about any universal machine or being.
>
> With mechanism, the non computability for an outcome comes from the first
> person indeterminacy, which is related partially to Gödel, even made clear
> by Penrose error and then correction, which is that Gödel’s theorem cannot
> be sued to show that we are not machine, but it can be used to show that no
> machine can know which machine she is, and still less which computations
> execute her, among an infinity of computations (which exists in the
> arithmetical reality).
>
>
>
>
> This then leads to the observation that measurements in QM require that if
> one is to measure a spin in the z direction this means any prior knowledge
> of spin in the x direction is to be lost. In general relativity there are
> also event horizons that restrict knowledge one can have of the quantum
> state of a black hole. Jacobson showed how spacetime can be viewed from
> statistical mechanics as composed of a distribution of states. An event
> horizon is also a surface of reduced dimension that has quantum
> information. Raamsdonk also illustrated how spacetime can be looked at as
> due to large N-entanglement. So the loss of knowledge of a quantum spin in
> one direction in a measurement along another is in a general setting much
> the same as the red shifting of information from n event horizon that
> restricts access to information.
>
>
>
> Intersting, and perhaps exploitable, for the mechanist mind body problem.
>
>
>
>
>
> This then suggests with the Cantor diagonalization that the relationship
> between stochasticity and its dual in determinism has an incomputable
> relationship between quantum and spacetime physics. For stochasticity a p =
> 1 in a convex set with a dual q = ∞ and 1/p + 1/q = 1 there is are associated
> L^2 systems for p = q = 2, or 1/p = 1/q = ½, which are relativity as a
> metric space and QM as a system of probabilities determined by the square
> of amplitudes.
>
>
>
> I am not sure of how to get this by the diagonal (in the style of Kleene,
> Cantor). You might need to be more precise about your suggestion, at least
> for me. Keep also in mind that once we reduce the mind-body problem to the
> derivation of physics from arithmetic, we can no more assume anything in
> physics, nor even in analysis, or geometry. All those domain must be
> entirely justified from only, say, Kxy = x and Sxyz = xz(yz), or by the
> laws ofd addition and multiplication on the natural numbers. In fact from
> any universal machinery, or from any universal machine “introspection”.
>
> Bruno
>
>
The core idea there is given by Szangolies in
https://arxiv.org/abs/1805.10668 , where the details are therein. The goal
is to derive the full CHSH theorem, which is a variant of
Bells’ theorem on how QM violates classical inequalities. There is a
polytope associated with CHSH, which I think bears a certain relationship
to Kirwan polytopes for entanglement measures and Hamming distance.
The CHSH polytope is based on the relationship
I_{chsh} = A_1×B_1 + A_1×B_2 + A_2×B_1 - A_2×B_2,
for Alice and Bob experiments with two outcomes. This curiously is a type
of metric that can be interpreted as pseudo-Euclidean. This is also a
measure of entropy, for it may be expressed according to conditional
probabilities. An arbitrary two-qubit state after Schmidt decomposition can
always be written as
|ψ_n⟩ = c_0|n_+, n_+⟩ + c_1|n_−, n_−⟩.
We choose the measurement settings in the following way
A_1 = m_1·σ, A_2 = m_2·σ,
B_1 = (1/√2)(m_1·σ + m_2·σ), B_2 = (1/√2)(m_1·σ − m_2·σ).
Here n, m_1 and m_2 are the unit vectors perpendicular to each other. Now
find the expectation value of the CHSH operator in the state |ψ_n⟩. We get
⟨ψ_n|I_{chsh}|ψ_n⟩ = 2√2C.
The expectation of I then has this bound.
For measures along the x and z directions this polytope has 16 vertices.
The Kirwan polytope is a pure z, or x if one prefers, lattice. This lattice
is either a sublattice or an additional lattice in a 24-cell. The 24-cell
In fact I think it is both. The 24-cell is the root space for the F4
exceptional group that is a stabilizer with G2 in E8.
I am in communications with Szangolies with respect to these problems. This
appears to be a fascinating prospect, where Gödel’s theorem means there is
no dynamics or computational determinism for how quantum states becomes
classical or equivalently what a particular outcome is. Spacetime is a
classical system, and as composed of large N-entanglements it is something
that is emergent by entirely spontaneous means.
LC
>
>
>
> LC
>
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