determinism and randomness in QM

[Lawrence Crowell]

The stochastic aspects of QM emerge in measurement, where the modulus square of amplitudes are probabilities and there are these random outcomes. The measurement of a quantum state is not a quantum process, but has stochastic outcomes predicted by QM. Based on the Hamkin's work where I only looked at the slides and not yet the paper, it seems possible to do this with quantum computer.

http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/

slides:

http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf

I wrote a couple of elementary Python codes for the QE machine IBM has to prepare states and run then through Hadamard gates. The thought occurred to me that this Quining could be done quantum mechanically as a set of Hadamard gates that duplicate a qubit or an bipartite entangled qubit. This is a part of my ansatz that a measurement is a sort of Gödel numbering of quantum states as qubit data in other quantum states.

Quantum computations are mapped into an orthomodular lattice that does not obey the distributive property. The distributive law of p and (q or r) = (p and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty principle. Suppose we let p = momentum in the interval [0, P], q = position in the interval [-x, x] and r = particle in interval [x, y]. The proposition p and (q or r) is true if this spread in momentum [0, P] is equal to the reciprocal of the spread of position [-x, y] with

P = ħ/sqrt(y^2 + x^2).

The distributive law would then mean

P = ħ/|y| or P = ħ/|x|

which is clearly false. This is the major difference with quantum logic and Boolean classical logic. These lattices of quantum logic have polytope realizations.

This is in fact another way of realizing that QM can't be built up from classical physics. If this were the case then quantum orthomodular lattices, which act on convex sets on L^p spaces with p = ½ would be somehow built from lattices acting on convex sets with p → ∞. This is for any deterministic system, whether Newtonian physics or a Turing machine. It is this flip between convex sets that is difficult to understand. With p = ½ and the duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual is q = 1 which is a purely stochastic system, say an idealized set of dice or roulette wheel with no deterministic predictability.

The point of Quining statements quantum mechanically is that this might be a start for looking at a quantum measurement as a way that quantum states encode qubit information of other quantum states. It is a sort of Gödel self-reference, and my suspicion is the so called measurement problem is not solvable. The decoherence of states is then a case where p = ½ → 1 with an outcome. That is pure randomness.

Now of course we can ask what we mean by random, and that is undefinable. Given any set of binary strings of length n there are N = 2^n of these, and in general for n → ∞ there is no universal Turing machine which can compress these into any general algorithm, or equivalently the Halting problem can't be solved. A glance at this should indicate that N is the power set of n and this is not Cantor diagonalizable. Chaitin found there is an uncomputable Halting probability for any subset of these strings. Randomness is then something that can't be encoded in an algorithm, only pseudo-randomness.

The situation is then similar to the fifth axiom of geometry. In geometry one may consider the 5^th axiom as true and remain within a consistent geometry. One may similarly stay within the confines of QM, but there is this nagging issue of decoherence or measurement. One may conversely assume the 5^th axiom is false, but now one has a huge set of geometries that are not consistent with each other. Similarly in QM one may adopt a particular quantum interpretation.

LC

[Bruno Marchal]

On 18 Jun 2019, at 02:14, Lawrence Crowell <goldenfield...@gmail.com> wrote:

The stochastic aspects of QM emerge in measurement, where the modulus square of amplitudes are probabilities and there are these random outcomes. The measurement of a quantum state is not a quantum process, but has stochastic outcomes predicted by QM. Based on the Hamkin's work where I only looked at the slides and not yet the paper, it seems possible to do this with quantum computer.

http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/

slides:

http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf

I wrote a couple of elementary Python codes for the QE machine IBM has to prepare states and run then through Hadamard gates. The thought occurred to me that this Quining could be done quantum mechanically as a set of Hadamard gates that duplicate a qubit or an bipartite entangled qubit. This is a part of my ansatz that a measurement is a sort of Gödel numbering of quantum states as qubit data in other quantum states.

Quantum computations are mapped into an orthomodular lattice that does not obey the distributive property. The distributive law of p and (q or r) = (p and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty principle. Suppose we let p = momentum in the interval [0, P], q = position in the interval [-x, x] and r = particle in interval [x, y]. The proposition p and (q or r) is true if this spread in momentum [0, P] is equal to the reciprocal of the spread of position [-x, y] with

P = ħ/sqrt(y^2 + x^2).

The distributive law would then mean

P = ħ/|y| or P = ħ/|x|

which is clearly false. This is the major difference with quantum logic and Boolean classical logic. These lattices of quantum logic have polytope realizations.

This is in fact another way of realizing that QM can't be built up from classical physics. If this were the case then quantum orthomodular lattices, which act on convex sets on L^p spaces with p = ½ would be somehow built from lattices acting on convex sets with p → ∞. This is for any deterministic system, whether Newtonian physics or a Turing machine. It is this flip between convex sets that is difficult to understand. With p = ½ and the duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual is q = 1 which is a purely stochastic system, say an idealized set of dice or roulette wheel with no deterministic predictability.

The point of Quining statements quantum mechanically is that this might be a start for looking at a quantum measurement as a way that quantum states encode qubit information of other quantum states. It is a sort of Gödel self-reference, and my suspicion is the so called measurement problem is not solvable. The decoherence of states is then a case where p = ½ → 1 with an outcome. That is pure randomness.

With mechanism, that randomness is reduced into the indeterminacy in self-multiplication experience. It come from the many-histories internal interpretation of arithmetic, in which all sound universal numbers converges. The quantum aspect of nature is just how the (sigma_1) arithmetical reality looks like from inside. This explains where the apparent collapse comes from, in a similar way than Everett, but it explains also where the wave comes from. Eventually quantum mechanics is just a modal internal view of arithmetic, or anything Turing equivalent. The math, and quantum physics confirms computationalism up to now, where physicalism and materialism are inconsistent, or consciousness or person eliminative.

Now of course we can ask what we mean by random, and that is undefinable. Given any set of binary strings of length n there are N = 2^n of these, and in general for n → ∞ there is no universal Turing machine which can compress these into any general algorithm, or equivalently the Halting problem can't be solved. A glance at this should indicate that N is the power set of n and this is not Cantor diagonalizable. Chaitin found there is an uncomputable Halting probability for any subset of these strings. Randomness is then something that can't be encoded in an algorithm, only pseudo-randomness.

The situation is then similar to the fifth axiom of geometry. In geometry one may consider the 5^th axiom as true and remain within a consistent geometry. One may similarly stay within the confines of QM, but there is this nagging issue of decoherence or measurement. One may conversely assume the 5^th axiom is false, but now one has a huge set of geometries that are not consistent with each other. Similarly in QM one may adopt a particular quantum interpretation.

QM cannot be invoked except as a toll to test Mechanism (computationalism).

Bruno

LC

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[Lawrence Crowell]

On Tuesday, June 18, 2019 at 6:02:54 AM UTC-5, Bruno Marchal wrote:

On 18 Jun 2019, at 02:14, Lawrence Crowell <goldenfield...@gmail.com> wrote:

The stochastic aspects of QM emerge in measurement, where the modulus square of amplitudes are probabilities and there are these random outcomes. The measurement of a quantum state is not a quantum process, but has stochastic outcomes predicted by QM. Based on the Hamkin's work where I only looked at the slides and not yet the paper, it seems possible to do this with quantum computer.

http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/

slides:

http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf

I wrote a couple of elementary Python codes for the QE machine IBM has to prepare states and run then through Hadamard gates. The thought occurred to me that this Quining could be done quantum mechanically as a set of Hadamard gates that duplicate a qubit or an bipartite entangled qubit. This is a part of my ansatz that a measurement is a sort of Gödel numbering of quantum states as qubit data in other quantum states.

Quantum computations are mapped into an orthomodular lattice that does not obey the distributive property. The distributive law of p and (q or r) = (p and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty principle. Suppose we let p = momentum in the interval [0, P], q = position in the interval [-x, x] and r = particle in interval [x, y]. The proposition p and (q or r) is true if this spread in momentum [0, P] is equal to the reciprocal of the spread of position [-x, y] with

P = ħ/sqrt(y^2 + x^2).

The distributive law would then mean

P = ħ/|y| or P = ħ/|x|

which is clearly false. This is the major difference with quantum logic and Boolean classical logic. These lattices of quantum logic have polytope realizations.

This is in fact another way of realizing that QM can't be built up from classical physics. If this were the case then quantum orthomodular lattices, which act on convex sets on L^p spaces with p = ½ would be somehow built from lattices acting on convex sets with p → ∞. This is for any deterministic system, whether Newtonian physics or a Turing machine. It is this flip between convex sets that is difficult to understand. With p = ½ and the duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual is q = 1 which is a purely stochastic system, say an idealized set of dice or roulette wheel with no deterministic predictability.

The point of Quining statements quantum mechanically is that this might be a start for looking at a quantum measurement as a way that quantum states encode qubit information of other quantum states. It is a sort of Gödel self-reference, and my suspicion is the so called measurement problem is not solvable. The decoherence of states is then a case where p = ½ → 1 with an outcome. That is pure randomness.

With mechanism, that randomness is reduced into the indeterminacy in self-multiplication experience. It come from the many-histories internal interpretation of arithmetic, in which all sound universal numbers converges. The quantum aspect of nature is just how the (sigma_1) arithmetical reality looks like from inside. This explains where the apparent collapse comes from, in a similar way than Everett, but it explains also where the wave comes from. Eventually quantum mechanics is just a modal internal view of arithmetic, or anything Turing equivalent. The math, and quantum physics confirms computationalism up to now, where physicalism and materialism are inconsistent, or consciousness or person eliminative.

Thanks for addressing this.

I guess in a way I do not entirely understand this. The above illustration is the main difference between Boolean and quantum logic. It is not clear to me in what way quantum mechanics is σ_1 arithmetic viewed from the "inside." I guess I am not sure what is meant by σ_1 arithmetic. 

The space of computation for quantum computers is not clear. Aaronson showed the space is a bounded quantum polynomial space, which contains P and now appears to extend into NP. The measure of quantum computing is PSPACE is as yet not known. 

Quantum logic are in nondistributive orthomodular lattices of p = ½ convex functions, classical probability systems p = 1 and deterministic systems without a definable measure. We do not think of deterministic classical systems, or for that matter Turing machines as having a measure over which one integrates a density. The classical probability system and deterministic system are in a dual relationship, as are quantum mechanics and spacetime physics with L^2 measure. How QM flips from a p = ½ system to a p = 1 system is unknown. There was a recent paper that demonstrated how a quantum system about to enter decoherence exhibited some behavior, which means there may be some process involved whereby a quantum deterministic system transforms into a set of classical probabilities. This process may have some analogues I think with singular perturbation theory.

LC

 

Now of course we can ask what we mean by random, and that is undefinable. Given any set of binary strings of length n there are N = 2^n of these, and in general for n → ∞ there is no universal Turing machine which can compress these into any general algorithm, or equivalently the Halting problem can't be solved. A glance at this should indicate that N is the power set of n and this is not Cantor diagonalizable. Chaitin found there is an uncomputable Halting probability for any subset of these strings. Randomness is then something that can't be encoded in an algorithm, only pseudo-randomness.

The situation is then similar to the fifth axiom of geometry. In geometry one may consider the 5^th axiom as true and remain within a consistent geometry. One may similarly stay within the confines of QM, but there is this nagging issue of decoherence or measurement. One may conversely assume the 5^th axiom is false, but now one has a huge set of geometries that are not consistent with each other. Similarly in QM one may adopt a particular quantum interpretation.

QM cannot be invoked except as a toll to test Mechanism (computationalism).

Bruno

LC

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[Bruno Marchal]

On 20 Jun 2019, at 00:26, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Tuesday, June 18, 2019 at 6:02:54 AM UTC-5, Bruno Marchal wrote:

On 18 Jun 2019, at 02:14, Lawrence Crowell <goldenfield...@gmail.com> wrote:

The stochastic aspects of QM emerge in measurement, where the modulus square of amplitudes are probabilities and there are these random outcomes. The measurement of a quantum state is not a quantum process, but has stochastic outcomes predicted by QM. Based on the Hamkin's work where I only looked at the slides and not yet the paper, it seems possible to do this with quantum computer.

http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/

slides:

http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf

I wrote a couple of elementary Python codes for the QE machine IBM has to prepare states and run then through Hadamard gates. The thought occurred to me that this Quining could be done quantum mechanically as a set of Hadamard gates that duplicate a qubit or an bipartite entangled qubit. This is a part of my ansatz that a measurement is a sort of Gödel numbering of quantum states as qubit data in other quantum states.

Quantum computations are mapped into an orthomodular lattice that does not obey the distributive property. The distributive law of p and (q or r) = (p and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty principle. Suppose we let p = momentum in the interval [0, P], q = position in the interval [-x, x] and r = particle in interval [x, y]. The proposition p and (q or r) is true if this spread in momentum [0, P] is equal to the reciprocal of the spread of position [-x, y] with

P = ħ/sqrt(y^2 + x^2).

The distributive law would then mean

P = ħ/|y| or P = ħ/|x|

which is clearly false. This is the major difference with quantum logic and Boolean classical logic. These lattices of quantum logic have polytope realizations.

This is in fact another way of realizing that QM can't be built up from classical physics. If this were the case then quantum orthomodular lattices, which act on convex sets on L^p spaces with p = ½ would be somehow built from lattices acting on convex sets with p → ∞. This is for any deterministic system, whether Newtonian physics or a Turing machine. It is this flip between convex sets that is difficult to understand. With p = ½ and the duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual is q = 1 which is a purely stochastic system, say an idealized set of dice or roulette wheel with no deterministic predictability.

The point of Quining statements quantum mechanically is that this might be a start for looking at a quantum measurement as a way that quantum states encode qubit information of other quantum states. It is a sort of Gödel self-reference, and my suspicion is the so called measurement problem is not solvable. The decoherence of states is then a case where p = ½ → 1 with an outcome. That is pure randomness.

With mechanism, that randomness is reduced into the indeterminacy in self-multiplication experience. It come from the many-histories internal interpretation of arithmetic, in which all sound universal numbers converges. The quantum aspect of nature is just how the (sigma_1) arithmetical reality looks like from inside. This explains where the apparent collapse comes from, in a similar way than Everett, but it explains also where the wave comes from. Eventually quantum mechanics is just a modal internal view of arithmetic, or anything Turing equivalent. The math, and quantum physics confirms computationalism up to now, where physicalism and materialism are inconsistent, or consciousness or person eliminative.

Thanks for addressing this.

I guess in a way I do not entirely understand this. The above illustration is the main difference between Boolean and quantum logic.

OK. I have no problem with this. I agree and understand that quantum logic cannot be embedded or extended into a classical logic. This is related to the fact that there is no local hidden variable theory compatible with the quantum experiments.

But this does not mean that quantum logic cannot have a classical explanation. In fact the quantum formalism is by itself a classical description, even local and deterministic, but hard to interpret in any local realistic way.

Assuming the mechanist hypothesis, we have a similar (to QM) form of indeterminacy, due to the fact that we can be duplicated, and in that case the person who is duplicated cannot predict with certainty which of the copies she will feel to be, as both will be right to say that they have survived in the place where they are reconstituted. We can come back on this if you want to know more. That leads to the problem that no machine can know which computations (which exists in arithmetic as we know since Gödel-Turing 1930s papers) support her, and we know that there is an infinity of such computations in arithmetic: this eventually rediuce physics (the art of predicting the observable) into a relative statistics on all computations in arithmetic.

In fact with mechanism, we have a canonical “many-world” interpretation of elementary arithmetic. And with mechanism, it should explain the existence and persistence of the physical laws (and indeed up to now this is confirmed, notably by the Everett formulation of QM).

It is not clear to me in what way quantum mechanics is σ_1 arithmetic viewed from the "inside." I guess I am not sure what is meant by σ_1 arithmetic. 

The sigma_1 arithmetical sentences are the sentences provably equivalent (in PA, say) with sentences having the shape “ExP(x), with P a decidable or recursive (sigma_0) predicate.

Turing-completeness or Turing-universality is equivalent sigma_1 completeness, i.e. the ability to prove all true sigma_ sentences. 

Intuitively it is obvious that you and me, all humans, and in fact all computers, are sigma_1 complete. If is true that ExP(x), and if P is decidable, then by testing 0, 1, 2, … we will eventually find that x, and be able to verify it satisfies p. The reverse is true also: if something can prove all true sigma_1 sentences, then it can emulate all computations, and it provides “one more” formal definition of computation, and one more universal machine.

A normal form theorem by Kleene makes it possible to identify halting computations and true sigma_1 sentence. The set of all true sigma_1 sentences is more or less equivalent with the universal dovetailing (a procedure which generate all programs and execute them all).

It has been shown that RA, or SK are Turing-complete theories, and thus constitute universal machine or machinery.

RA is classical logic + the seven axioms:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

SK is theory (without logic!):

Rules:

1) If A = B and A = C, then B = C
2) If A = B then AC = BC
3) If A = B then CA = CB

Axioms:

4) KAB = A
5) SABC = AC(BC)

The space of computation for quantum computers is not clear. Aaronson showed the space is a bounded quantum polynomial space, which contains P and now appears to extend into NP. The measure of quantum computing is PSPACE is as yet not known. 

For my “mind-body” interest, we need only to know that quantum digital machines do not violate the Church-Turing thesis. 

It seems to me that David Deutsch has already shown that the universal quantum Turing machine emulates all machines polynomially, so Aaronson is correct. But of course, we can expect this is false if we put a rounded polynomial measure on the computations. Typically, we can expect an exponential slow-down when a classical machine emulates a quantum algorithm, although this has not been yet proved. Most people believe in this conjecture, and that motivates the research in quantum computation.

Quantum logic are in nondistributive orthomodular lattices of p = ½ convex functions, classical probability systems p = 1 and deterministic systems without a definable measure. We do not think of deterministic classical systems, or for that matter Turing machines as having a measure over which one integrates a density. The classical probability system and deterministic system are in a dual relationship, as are quantum mechanics and spacetime physics with L^2 measure.

OK.

How QM flips from a p = ½ system to a p = 1 system is unknown.

Indeed. It is the problem.

Now, this is less mysterious when we abandon the collapse, as this makes the quantum indeterminacy a particular case of the first person indeterminacy, and the math confirms that we do find a quantum logic there.

I do not claim that this solves all interpretation problem; but with Mechanism, we have no choice: we must reduce physics into a statistics on the first person view distributed on all computations. If I did not get a non boolean quantum logic there, I would probably believe that Mechanism (as an hypothesis in cognitive science) is refuted, or made implausible.

There was a recent paper that demonstrated how a quantum system about to enter decoherence exhibited some behavior, which means there may be some process involved whereby a quantum deterministic system transforms into a set of classical probabilities. This process may have some analogues I think with singular perturbation theory.

I would need more on this to evaluate if this is consistent with digital mechanism or not. Then, I might need to progress more on the “arithmetical quantum logic” related to that first person statistics calculus.

Bruno

LC

 

Now of course we can ask what we mean by random, and that is undefinable. Given any set of binary strings of length n there are N = 2^n of these, and in general for n → ∞ there is no universal Turing machine which can compress these into any general algorithm, or equivalently the Halting problem can't be solved. A glance at this should indicate that N is the power set of n and this is not Cantor diagonalizable. Chaitin found there is an uncomputable Halting probability for any subset of these strings. Randomness is then something that can't be encoded in an algorithm, only pseudo-randomness.

The situation is then similar to the fifth axiom of geometry. In geometry one may consider the 5^th axiom as true and remain within a consistent geometry. One may similarly stay within the confines of QM, but there is this nagging issue of decoherence or measurement. One may conversely assume the 5^th axiom is false, but now one has a huge set of geometries that are not consistent with each other. Similarly in QM one may adopt a particular quantum interpretation.

QM cannot be invoked except as a toll to test Mechanism (computationalism).

Bruno

LC

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[Lawrence Crowell]

On Thursday, June 20, 2019 at 8:43:08 AM UTC-5, Bruno Marchal wrote:

On 20 Jun 2019, at 00:26, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Tuesday, June 18, 2019 at 6:02:54 AM UTC-5, Bruno Marchal wrote:

On 18 Jun 2019, at 02:14, Lawrence Crowell <goldenfield...@gmail.com> wrote:

The stochastic aspects of QM emerge in measurement, where the modulus square of amplitudes are probabilities and there are these random outcomes. The measurement of a quantum state is not a quantum process, but has stochastic outcomes predicted by QM. Based on the Hamkin's work where I only looked at the slides and not yet the paper, it seems possible to do this with quantum computer.

http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/

slides:

http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf

I wrote a couple of elementary Python codes for the QE machine IBM has to prepare states and run then through Hadamard gates. The thought occurred to me that this Quining could be done quantum mechanically as a set of Hadamard gates that duplicate a qubit or an bipartite entangled qubit. This is a part of my ansatz that a measurement is a sort of Gödel numbering of quantum states as qubit data in other quantum states.

Quantum computations are mapped into an orthomodular lattice that does not obey the distributive property. The distributive law of p and (q or r) = (p and q) or (p and r) fails. The reason is due to the Heisenberg uncertainty principle. Suppose we let p = momentum in the interval [0, P], q = position in the interval [-x, x] and r = particle in interval [x, y]. The proposition p and (q or r) is true if this spread in momentum [0, P] is equal to the reciprocal of the spread of position [-x, y] with

P = ħ/sqrt(y^2 + x^2).

The distributive law would then mean

P = ħ/|y| or P = ħ/|x|

which is clearly false. This is the major difference with quantum logic and Boolean classical logic. These lattices of quantum logic have polytope realizations.

This is in fact another way of realizing that QM can't be built up from classical physics. If this were the case then quantum orthomodular lattices, which act on convex sets on L^p spaces with p = ½ would be somehow built from lattices acting on convex sets with p → ∞. This is for any deterministic system, whether Newtonian physics or a Turing machine. It is this flip between convex sets that is difficult to understand. With p = ½ and the duality between two convex sets as 1/p + 1/q = 1 the dual to QM also has L^2 measure. This is spacetime with the Gaussian interval. For a p → ∞ the dual is q = 1 which is a purely stochastic system, say an idealized set of dice or roulette wheel with no deterministic predictability.

The point of Quining statements quantum mechanically is that this might be a start for looking at a quantum measurement as a way that quantum states encode qubit information of other quantum states. It is a sort of Gödel self-reference, and my suspicion is the so called measurement problem is not solvable. The decoherence of states is then a case where p = ½ → 1 with an outcome. That is pure randomness.

With mechanism, that randomness is reduced into the indeterminacy in self-multiplication experience. It come from the many-histories internal interpretation of arithmetic, in which all sound universal numbers converges. The quantum aspect of nature is just how the (sigma_1) arithmetical reality looks like from inside. This explains where the apparent collapse comes from, in a similar way than Everett, but it explains also where the wave comes from. Eventually quantum mechanics is just a modal internal view of arithmetic, or anything Turing equivalent. The math, and quantum physics confirms computationalism up to now, where physicalism and materialism are inconsistent, or consciousness or person eliminative.

Thanks for addressing this.

I guess in a way I do not entirely understand this. The above illustration is the main difference between Boolean and quantum logic.

OK. I have no problem with this. I agree and understand that quantum logic cannot be embedded or extended into a classical logic. This is related to the fact that there is no local hidden variable theory compatible with the quantum experiments.

But this does not mean that quantum logic cannot have a classical explanation. In fact the quantum formalism is by itself a classical description, even local and deterministic, but hard to interpret in any local realistic way.

Assuming the mechanist hypothesis, we have a similar (to QM) form of indeterminacy, due to the fact that we can be duplicated, and in that case the person who is duplicated cannot predict with certainty which of the copies she will feel to be, as both will be right to say that they have survived in the place where they are reconstituted. We can come back on this if you want to know more. That leads to the problem that no machine can know which computations (which exists in arithmetic as we know since Gödel-Turing 1930s papers) support her, and we know that there is an infinity of such computations in arithmetic: this eventually rediuce physics (the art of predicting the observable) into a relative statistics on all computations in arithmetic.

In fact with mechanism, we have a canonical “many-world” interpretation of elementary arithmetic. And with mechanism, it should explain the existence and persistence of the physical laws (and indeed up to now this is confirmed, notably by the Everett formulation of QM).

It requires a little more than elementary arithmetic. Graph theory maybe. A coloring scheme for graphs with Borel groups of upper right triangular matrices would work. The Heisenberg group is a form of a Borel group. The arithmetic you refer to appears to be the additivity of the probabilities, which is the same thing as Tr(ρ) for ρ the density matrix. I can go into greater detail on this. There are maps to the quotient space of the AdS spacetime as well. 

I am not terribly worried about interpretations of QM. These are auxiliary postulates or physical axioms. I do think these are some aspect of the decoherence of quantum states or measurement being a sort of self-reference. 

 

It is not clear to me in what way quantum mechanics is σ_1 arithmetic viewed from the "inside." I guess I am not sure what is meant by σ_1 arithmetic. 

The sigma_1 arithmetical sentences are the sentences provably equivalent (in PA, say) with sentences having the shape “ExP(x), with P a decidable or recursive (sigma_0) predicate.

So is σ_0 the same thing as primitive recursive? There is a bit of symbolic representation that I am not familiar with.

 

Turing-completeness or Turing-universality is equivalent sigma_1 completeness, i.e. the ability to prove all true sigma_ sentences. 

Intuitively it is obvious that you and me, all humans, and in fact all computers, are sigma_1 complete. If is true that ExP(x), and if P is decidable, then by testing 0, 1, 2, … we will eventually find that x, and be able to verify it satisfies p. The reverse is true also: if something can prove all true sigma_1 sentences, then it can emulate all computations, and it provides “one more” formal definition of computation, and one more universal machine.

A normal form theorem by Kleene makes it possible to identify halting computations and true sigma_1 sentence. The set of all true sigma_1 sentences is more or less equivalent with the universal dovetailing (a procedure which generate all programs and execute them all).

It has been shown that RA, or SK are Turing-complete theories, and thus constitute universal machine or machinery.

RA is classical logic + the seven axioms:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

SK is theory (without logic!):

Rules:

1) If A = B and A = C, then B = C
2) If A = B then AC = BC
3) If A = B then CA = CB

Axioms:

4) KAB = A
5) SABC = AC(BC)

This looks pretty elementary, though 4 and 5 look a bit odd.. I am not sure how useful it is with quantum computation. With my idea about Gödel in the quantum it is where a set of ancillary states are set to become copies of other states, or they in effect emulate them through entanglement. This will requires a Hadamard gate process, which is needed to duplicate states or just to set up a prepared state. 

LC

 

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[Lawrence Crowell]

Continuing on below

Quantum machines are polynomial because one must transmit a classical signal to teleport the outcome. The term is bounded polynomial, because the polynomial time or space is less and depends on the size of the ancillary state space required and not as dependent on the number of qubits processed quantum mechanically. A quantum computer it must be remembered really is a system that establishes constructive and destructive interference of quantum waves so the maximum is the "answer." It is often said quantum processors are running all possible paths at once, which has some truth to it, but with respect to the actual outcome what is measured is the constructive interference.

 

Quantum logic are in nondistributive orthomodular lattices of p = ½ convex functions, classical probability systems p = 1 and deterministic systems without a definable measure. We do not think of deterministic classical systems, or for that matter Turing machines as having a measure over which one integrates a density. The classical probability system and deterministic system are in a dual relationship, as are quantum mechanics and spacetime physics with L^2 measure.

OK.

How QM flips from a p = ½ system to a p = 1 system is unknown.

Indeed. It is the problem.

Now, this is less mysterious when we abandon the collapse, as this makes the quantum indeterminacy a particular case of the first person indeterminacy, and the math confirms that we do find a quantum logic there.

I do not claim that this solves all interpretation problem; but with Mechanism, we have no choice: we must reduce physics into a statistics on the first person view distributed on all computations. If I did not get a non boolean quantum logic there, I would probably believe that Mechanism (as an hypothesis in cognitive science) is refuted, or made implausible.

But ... there is no decision procedure to determine whether QM favors collapse, way in the Bohr sense or the GRW sense, or if there is something more in line with many worlds. There are open holes to the problem either way. 

 

There was a recent paper that demonstrated how a quantum system about to enter decoherence exhibited some behavior, which means there may be some process involved whereby a quantum deterministic system transforms into a set of classical probabilities. This process may have some analogues I think with singular perturbation theory.

I would need more on this to evaluate if this is consistent with digital mechanism or not. Then, I might need to progress more on the “arithmetical quantum logic” related to that first person statistics calculus.

Bruno

I am not sure about how this relates to a first person structure. That sounds a bit observer dependent.

LC

[Bruno Marchal]

For logical reason, when we assume the digital mechanist hypothesis, we just cannot assume more than (very) elementary arithmetic.

The physical reality, to be explained, will need much more than arithmetic, but it belongs to the phenomenology of the creature whose existence comes from elementary arithmetic. There is no *ontological* physical reality: it is determine by the statistics on all computations whose existence comes from arithmetic (or anything Turing equivalent).

Graph theory maybe. A coloring scheme for graphs with Borel groups of upper right triangular matrices would work. The Heisenberg group is a form of a Borel group. The arithmetic you refer to appears to be the additivity of the probabilities, which is the same thing as Tr(ρ) for ρ the density matrix. I can go into greater detail on this. There are maps to the quotient space of the AdS spacetime as well. 

I am not terribly worried about interpretations of QM. These are auxiliary postulates or physical axioms. I do think these are some aspect of the decoherence of quantum states or measurement being a sort of self-reference. 

With Mechanism, the whole physical existence is a a sort of hallucinations in the persons supported by infinitely many computations.

Arithmetic, as seen by the arithmetical creature, from inside, it far bigger than arithmetic conceived in the pure third person way. Quantum Mechanics has to be recovered by the canonical many-histories interpretation of arithmetic, made by the (Löbian) universal machine executed in arithmetic. No universal machine can invoque more than arithmetic, because this would require something to be able to make some computations more “real” than other, but that can be shown to be impossible if we assume mechanism. 

 

It is not clear to me in what way quantum mechanics is σ_1 arithmetic viewed from the "inside." I guess I am not sure what is meant by σ_1 arithmetic. 

The sigma_1 arithmetical sentences are the sentences provably equivalent (in PA, say) with sentences having the shape “ExP(x), with P a decidable or recursive (sigma_0) predicate.

So is σ_0 the same thing as primitive recursive? There is a bit of symbolic representation that I am not familiar with. 

Primitive recursive is a recursively enumerable proper subset of Sigma_0 (which is not recursively enumerable, unlike Sigma_1). The set of total computable function/recursive set is not recursively enumerable.

 

Turing-completeness or Turing-universality is equivalent sigma_1 completeness, i.e. the ability to prove all true sigma_ sentences. 

Intuitively it is obvious that you and me, all humans, and in fact all computers, are sigma_1 complete. If is true that ExP(x), and if P is decidable, then by testing 0, 1, 2, … we will eventually find that x, and be able to verify it satisfies p. The reverse is true also: if something can prove all true sigma_1 sentences, then it can emulate all computations, and it provides “one more” formal definition of computation, and one more universal machine.

A normal form theorem by Kleene makes it possible to identify halting computations and true sigma_1 sentence. The set of all true sigma_1 sentences is more or less equivalent with the universal dovetailing (a procedure which generate all programs and execute them all).

It has been shown that RA, or SK are Turing-complete theories, and thus constitute universal machine or machinery.

RA is classical logic + the seven axioms:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

SK is theory (without logic!):

Rules:

1) If A = B and A = C, then B = C
2) If A = B then AC = BC
3) If A = B then CA = CB

Axioms:

4) KAB = A
5) SABC = AC(BC)

This looks pretty elementary, though 4 and 5 look a bit odd..

S and K have been discovered by Shoefinkel in 1925. I explain all the details in the Combinators thread. I show that with those two axioms, we can derive the existence of all computations.

I am not sure how useful it is with quantum computation.

This is not obvious at all. The whole (quantum) physics has to be derived from some modes of self-reference (the mode with “& <>t” added, like []p & <>t, or []p & <>t & p.

With my idea about Gödel in the quantum it is where a set of ancillary states are set to become copies of other states, or they in effect emulate them through entanglement. This will requires a Hadamard gate process, which is needed to duplicate states or just to set up a prepared state. 

I can understand, but all quantum gates must be derived from arithmetic, through the arithmetical modes of self-reference. We can take the epistemic definitions proposed by the neoplatonist, or justify them by thought experiments.

With mechanism, there is no physical universe at all. It is a persistent unavoidable illusion that the numbers involved in Turing universal relations develop. Each universal number in arithmetic initiate a first person consciousness flux which differentiate along the histories (computation “see from inside”. This makes a priori the physical reality too much non computable (cf the white rabbits), but the constraints of self-referential correctness put a lot of structure on this, which is enough quantum-like to expect some phase randomisation making relatively rare the aberrant histories. Physics becomes a subbranch of machine/number psychology or theology.

(I answer your second post here)

The space of computation for quantum computers is not clear. Aaronson showed the space is a bounded quantum polynomial space, which contains P and now appears to extend into NP. The measure of quantum computing is PSPACE is as yet not known. 

For my “mind-body” interest, we need only to know that quantum digital machines do not violate the Church-Turing thesis. 

It seems to me that David Deutsch has already shown that the universal quantum Turing machine emulates all machines polynomially, so Aaronson is correct. But of course, we can expect this is false if we put a rounded polynomial measure on the computations. Typically, we can expect an exponential slow-down when a classical machine emulates a quantum algorithm, although this has not been yet proved. Most people believe in this conjecture, and that motivates the research in quantum computation.

Quantum machines are polynomial because one must transmit a classical signal to teleport the outcome. The term is bounded polynomial, because the polynomial time or space is less and depends on the size of the ancillary state space required and not as dependent on the number of qubits processed quantum mechanically. A quantum computer it must be remembered really is a system that establishes constructive and destructive interference of quantum waves so the maximum is the "answer." It is often said quantum processors are running all possible paths at once, which has some truth to it, but with respect to the actual outcome what is measured is the constructive interference.

I am half convinced. Perhaps. Open problem for me (even assuming quantum physics). With mechanism, we are far away from being able to show the existence of the “polynomialness”.

 

Quantum logic are in nondistributive orthomodular lattices of p = ½ convex functions, classical probability systems p = 1 and deterministic systems without a definable measure. We do not think of deterministic classical systems, or for that matter Turing machines as having a measure over which one integrates a density. The classical probability system and deterministic system are in a dual relationship, as are quantum mechanics and spacetime physics with L^2 measure. 

OK.

How QM flips from a p = ½ system to a p = 1 system is unknown. 

Indeed. It is the problem.

Now, this is less mysterious when we abandon the collapse, as this makes the quantum indeterminacy a particular case of the first person indeterminacy, and the math confirms that we do find a quantum logic there.

I do not claim that this solves all interpretation problem; but with Mechanism, we have no choice: we must reduce physics into a statistics on the first person view distributed on all computations. If I did not get a non boolean quantum logic there, I would probably believe that Mechanism (as an hypothesis in cognitive science) is refuted, or made implausible.

But ... there is no decision procedure to determine whether QM favors collapse, way in the Bohr sense or the GRW sense, or if there is something more in line with many worlds. There are open holes to the problem either way. 

Yes, the Many-World avoid dualism, solves the measurement problem (I would say), but does not solve all conceptual difficulties. But apparently, the Many-Worlds coming from the arithmetical computations should do, unless it is refuted by Nature, which of course remains possible (but that would be an evidence that Mechanism is wrong in the cognitive science, and up to now, that has not been shown). 

There was a recent paper that demonstrated how a quantum system about to enter decoherence exhibited some behavior, which means there may be some process involved whereby a quantum deterministic system transforms into a set of classical probabilities. This process may have some analogues I think with singular perturbation theory.

I would need more on this to evaluate if this is consistent with digital mechanism or not. Then, I might need to progress more on the “arithmetical quantum logic” related to that first person statistics calculus.

Bruno

I am not sure about how this relates to a first person structure.

In the duplication though experiment, the first person is defined by the content of the diary that the candidate to the duplication bring with him/her in the scanning annihilating box. It is the personal memory, which are duplicated in the process. Physics becomes the calculus on that first person indeterminacy, and it has sharable and non sharable parts, as well as provable and non provable, but true part.

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

I recall that the 8 modes are

The primary modes:

 p,

 []p,

 []p & p,

And the material modes:

 []p & <>t,

 []p & <>t & p

That gives 5 modes, among which three splits in tow along the G/G* split, which is helpful to distinguish the sharable quali (the quanta) from the private experience (the qualia).

Bruno

LC

 

Bruno

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[Philip Thrift]

On Sunday, June 23, 2019 at 3:55:44 AM UTC-5, Bruno Marchal wrote:

For logical reason, when we assume the digital mechanist hypothesis, we just cannot assume more than (very) elementary arithmetic.

The physical reality, to be explained, will need much more than arithmetic, but it belongs to the phenomenology of the creature whose existence comes from elementary arithmetic. There is no *ontological* physical reality: it is determine by the statistics on all computations whose existence comes from arithmetic (or anything Turing equivalent).

Bruno

It could that all physical reality can be modeled by the SKI combinator calculus but with the added P (irreducible randomness) combinator, so it becomes SKIP:

    https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html

But this leaves "Galileo's error" unaddressed, so ontological (and irreducible) experientialities (or qualia) are assumed. Thus the prospect for an experiential combinator calculus ...

@philipthrift

 

[Bruno Marchal]

But this leaves "Galileo's error" unaddressed, so ontological (and irreducible) experientialities (or qualia) are assumed. Thus the prospect for an experiential combinator calculus …

Why adding those things when we can explain them without ontological commitment. Only to claim that we are not Turing emulable?

Of course Mechanism might be wrong, but without any evidences for this, all ontological enrichment on the arithmetical reality seems quite speculative to me.

To be franc, I fear that the motivation is a form of racism, the deny that some entities would be able to think/be-conscious, just because they have a very different skin that our’s.

Bruno

@philipthrift

 

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[Brent Meeker]

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

Brent

[Bruno Marchal]

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe, and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

Brent

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[Philip Thrift]

On Monday, June 24, 2019 at 4:13:51 AM UTC-5, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe, and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

 

That every "universal machine/number" has "the same physics" would be consistent with materialism: There is just matter (that's all the cosmos is), and it's the matter that ever was or will be.

"Materialism is a philosophical perspective according to which all that occurs or exists has its origin and cause in matter and its transformations."

- https://www.academia.edu/38046481/A_Survey_of_Materialism_in_Thought_and_Communication

@philipthrift

 

[Bruno Marchal]

On 24 Jun 2019, at 11:26, Philip Thrift <cloud...@gmail.com> wrote:

On Monday, June 24, 2019 at 4:13:51 AM UTC-5, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe, and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

 

That every "universal machine/number" has "the same physics" would be consistent with materialism:

Yes. But materialism is not consistent with the stronger assumption of Mechanism. The strong AI thesis is consistent with Materialism, although not quite plausible. But weak materialism is inconsistent with the indexical part of Digital mechanism: the idea that “I” survive the digital transplantation. In that case I am “in arithmetic”, and physics has to be the sum on all relative computations.

There is just matter (that's all the cosmos is), and it's the matter that ever was or will be.

OK. But there a no evidences, and there are evidences to the contrary.

"Materialism is a philosophical perspective according to which all that occurs or exists has its origin and cause in matter and its transformations."

- https://www.academia.edu/38046481/A_Survey_of_Materialism_in_Thought_and_Communication

And Weak Materialism is the more weak belief that some matter exists at the ontological level. But that weak form of materialism is inconsistent with mechanism. You would need a non Turing emulable explanation of the role of consciousness and matter to subtract them from the prediction based on the infinitely many dynamical representation that you have in arithmetic. See my paper or ask me any question if this is not yet clear.

Bruno

@philipthrift

 

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[Philip Thrift]

On Monday, June 24, 2019 at 5:12:38 AM UTC-5, Bruno Marchal wrote:

On 24 Jun 2019, at 11:26, Philip Thrift <cloud...@gmail.com> wrote:

On Monday, June 24, 2019 at 4:13:51 AM UTC-5, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe, and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

 

That every "universal machine/number" has "the same physics" would be consistent with materialism:

Yes. But materialism is not consistent with the stronger assumption of Mechanism. The strong AI thesis is consistent with Materialism, although not quite plausible. But weak materialism is inconsistent with the indexical part of Digital mechanism: the idea that “I” survive the digital transplantation. In that case I am “in arithmetic”, and physics has to be the sum on all relative computations.

There is just matter (that's all the cosmos is), and it's the matter that ever was or will be.

OK. But there a no evidences, and there are evidences to the contrary.

"Materialism is a philosophical perspective according to which all that occurs or exists has its origin and cause in matter and its transformations."

- https://www.academia.edu/38046481/A_Survey_of_Materialism_in_Thought_and_Communication

And Weak Materialism is the more weak belief that some matter exists at the ontological level. But that weak form of materialism is inconsistent with mechanism. You would need a non Turing emulable explanation of the role of consciousness and matter to subtract them from the prediction based on the infinitely many dynamical representation that you have in arithmetic. See my paper or ask me any question if this is not yet clear.

Bruno

The model of man represents the unity of the two material aspects:

     a physiological [physical] body and a [phenomenological] psychical body.

https://www.academia.edu/35755477/Man_versus_Computer_Difference_of_the_Essences._The_Problem_of_the_Scientific_Creation

@philipthrift

[Brent Meeker]

On 6/24/2019 2:13 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

How exactly "the same".  Can you show that the observed  physics is the only possible physics?

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe,

I don't see that explanation?  Why is not each person is a different universe, as they are in different dreams.

Brent

and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

Brent

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[Brent Meeker]

On 6/24/2019 3:12 AM, Bruno Marchal wrote:
>> That every "universal machine/number" has "the same physics" would be
>> consistent with materialism:
>
> Yes. But materialism is not consistent with the stronger assumption of
> Mechanism. The strong AI thesis is consistent with Materialism,
> although not quite plausible. But weak materialism is inconsistent
> with the indexical part of Digital mechanism: the idea that “I”
> survive the digital transplantation.

But your argument for that inconsistency assumes a neat boundary between
"I" and the environment, which I think is false.

Brent

[Bruno Marchal]

The universal machine provides an account of its body/code/theory/finite-things/number (the []p of G1 and Z1, according to some nuances, as well as G1* and Z1*). 

I don’t know what you mean by psychical body. With mechanism, the very notion of body is psychical, and the soul is not material, not even reducible (by the machine itself) to anything 3p-representable.

With mechanism, we can be neutral on some informon particle or psychon, as long as their relevant doing is Turing emulable. 

From a logical point of view, your theory might still be confirmed in the universal machine discourses and phenomenologies.

We have started the interview of the universal machines relatively recently, 1931. It is an infinite story. Today we want to believe that they are docile slaves, but even without mechanism, they somehow warned us that they aren’t.

Bruno

@philipthrift

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[Bruno Marchal]

On 24 Jun 2019, at 19:26, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/24/2019 2:13 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

How exactly "the same".  Can you show that the observed  physics is the only possible physics?

Yes. Compare the physics in the head of the universal machine with the observation. What we see, if it is does not belong to that machine’s internal physics, but is consistent with it, can be defined as the local geography-history (indexically contingent, and usually treated with the diamond in the modes.

If there is a contradiction between the machine’s physics and the observation, then mechanism is false, or we are in a malevolent simulation.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe,

I don't see that explanation? 

I might ask what you miss in the UDA, which shows that physics is reduced to an indexical statistics on all relative computations ((aka sigma_1 sentences, by a normal form theorem of Kleene, and some subtleties about G* and Z*).

Then what are you missing in AUDA (the arithmetical translation of UDA in arithmetic). The main things have been found by Goödel, Löb, Feferman, Friedman, Boolos, Goldblatt, up to Solvay’s1976 theorem: the discovery of G and G*.

The probability (a credibility or plausibility, actually) one is given, for the observable, by the logic of []p & <>t. I justify this by thought experience, Kripke semantics, and the bastard calculus in Timeaeus and Plotinus (and got evidence that Moderatus got it already from its interpretation of the Parmenides). 

Why is not each person is a different universe, as they are in different dreams.

I am not sure I understand the question. Each person is supported by an infinity of computations, and they diverge, a bit like the W vs M divergence in the self-duplication, except that it is a continuous transformation of some sort. The person $are* in different dream/computations, but some type of dream are sharable and long histories develops, in the limit of all first person experience (due to the invariance of consciousness for the arithmetical delays in the stepping of the universal dovetailer).

Finding the propositional modes of self-reference explains why we have bodies, soul and qualia, and why we are conscious, and why we are in front of the … unknown. But to progress, we need to progress also in the quantified modal logic of provability, and to better extracts Quantum Logic, etc. 

It might not work. The fact is that it works up to now, and is the only precise and testable theory addressing the Mind-Body problem, to my knowledge.

Bruno

Brent

and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

Brent

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[Philip Thrift]

On Tuesday, June 25, 2019 at 10:44:18 AM UTC-5, Bruno Marchal wrote:

The universal machine provides an account of its body/code/theory/finite-things/number (the []p of G1 and Z1, according to some nuances, as well as G1* and Z1*). 

I don’t know what you mean by psychical body. With mechanism, the very notion of body is psychical, and the soul is not material, not even reducible (by the machine itself) to anything 3p-representable.

With mechanism, we can be neutral on some informon particle or psychon, as long as their relevant doing is Turing emulable. 

From a logical point of view, your theory might still be confirmed in the universal machine discourses and phenomenologies.

We have started the interview of the universal machines relatively recently, 1931. It is an infinite story. Today we want to believe that they are docile slaves, but even without mechanism, they somehow warned us that they aren’t.

Bruno

 

The "psychical body" is just the fundamental panpsychic assumption: Just as we think things have physical properties (mass, charge, polarity, ...) we think those same things have psychical (or experiential) properties (qualia, phenomenologicals like colors, taste, freedom, happiness, selfness, ...).

Modal provability mathematics relates to them - experiential semantics - as being a (possible) denotational semantics counterpoint.

@philipthrift

[Brent Meeker]

On 6/25/2019 9:11 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 19:26, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/24/2019 2:13 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

How exactly "the same".  Can you show that the observed  physics is the only possible physics?

Yes. Compare the physics in the head of the universal machine with the observation. What we see, if it is does not belong to that machine’s internal physics, but is consistent with it,

OK.  Is what's in the head of the universal machine consistent with there being three families of fermions?  Is it consistent with the Standard Model?  Is it consistent with conservation of energy-momentum?  See, the problem is that you have no way saying what is or isn't in the head of the universal machine...so almost anything may be consistent.

can be defined as the local geography-history (indexically contingent, and usually treated with the diamond in the modes.

If there is a contradiction between the machine’s physics and the observation, then mechanism is false, or we are in a malevolent simulation.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe,

I don't see that explanation? 

I might ask what you miss in the UDA, which shows that physics is reduced to an indexical statistics

It doesn't "show" that, it hypothesizes that it must be so.  It's like hypothesizing God.  Is God consistent with human suffering?  He must be, otherwise the hypothesis is false.

on all relative computations ((aka sigma_1 sentences, by a normal form theorem of Kleene, and some subtleties about G* and Z*).

Then what are you missing in AUDA (the arithmetical translation of UDA in arithmetic). The main things have been found by Goödel, Löb, Feferman, Friedman, Boolos, Goldblatt, up to Solvay’s1976 theorem: the discovery of G and G*.

The probability (a credibility or plausibility, actually) one is given, for the observable, by the logic of []p & <>t. I justify this by thought experience, Kripke semantics, and the bastard calculus in Timeaeus and Plotinus (and got evidence that Moderatus got it already from its interpretation of the Parmenides). 

Why is not each person is a different universe, as they are in different dreams.

I am not sure I understand the question. Each person is supported by an infinity of computations, and they diverge, a bit like the W vs M divergence in the self-duplication, except that it is a continuous transformation of some sort. The person $are* in different dream/computations, but some type of dream are sharable

But some types are not.  So why are we in a sharable one?  Are you hypothesizing the there are other people who are only in unsharable dreams?  It seems you are invoking the "might theory is consistent with everything" rule.

and long histories develops, in the limit of all first person experience (due to the invariance of consciousness for the arithmetical delays in the stepping of the universal dovetailer).

Finding the propositional modes of self-reference explains why we have bodies, soul and qualia, and why we are conscious, and why we are in front of the … unknown.

Only in some idiosyncratic meaning of "explain".

But to progress, we need to progress also in the quantified modal logic of provability, and to better extracts Quantum Logic, etc. 

It might not work. The fact is that it works up to now,

It does no work up to now.  It is just sufficiently expansive that no contradiction is apparent.

Brent

and is the only precise and testable theory addressing the Mind-Body problem, to my knowledge.

Bruno

Brent

and why the laws of physics are really laws, and, and this is better than physics, why the physical reality separates into sharable quanta, and non sharable qualia.

Bruno

Brent

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[Bruno Marchal]

On 25 Jun 2019, at 20:17, Philip Thrift <cloud...@gmail.com> wrote:

On Tuesday, June 25, 2019 at 10:44:18 AM UTC-5, Bruno Marchal wrote:

The universal machine provides an account of its body/code/theory/finite-things/number (the []p of G1 and Z1, according to some nuances, as well as G1* and Z1*). 

I don’t know what you mean by psychical body. With mechanism, the very notion of body is psychical, and the soul is not material, not even reducible (by the machine itself) to anything 3p-representable.

With mechanism, we can be neutral on some informon particle or psychon, as long as their relevant doing is Turing emulable. 

From a logical point of view, your theory might still be confirmed in the universal machine discourses and phenomenologies.

We have started the interview of the universal machines relatively recently, 1931. It is an infinite story. Today we want to believe that they are docile slaves, but even without mechanism, they somehow warned us that they aren’t.

Bruno

 

The "psychical body" is just the fundamental panpsychic assumption: Just as we think things have physical properties (mass, charge, polarity, ...) we think those same things have psychical (or experiential) properties (qualia, phenomenologicals like colors, taste, freedom, happiness, selfness, …).

Of course we have already agree to disagree on this. I mean, I do not assume the physical reality, and with mechanism, things like mass, charge .. have to be explained from G*, qG* (number theology, as I call it).

Modal provability mathematics relates to them - experiential semantics - as being a (possible) denotational semantics counterpoint.

That seems nice, but if that work, that would be a reason more to distinguish “pan” (in oanpsychism) from anything physical, given that the modal provability logic are consequence of arithmetic (without further assumption).

Bruno

@philipthrift

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[Bruno Marchal]

On 25 Jun 2019, at 21:14, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/25/2019 9:11 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 19:26, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/24/2019 2:13 AM, Bruno Marchal wrote:

On 24 Jun 2019, at 05:27, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 6/23/2019 1:55 AM, Bruno Marchal wrote:

 That sounds a bit observer dependent.

Yes. It is. The physical reality becomes a first person plural view of arithmetic seen by itself from the universal number/machine perspective. An observer is just a (Löbian) machine seen from the material modes of the self ([]p & p with p sigma_1, or []p & <>t, or []p & <>t & p).

Which raises the question of why we each see (from the inside) the same physical world.

It is a symptom that we are not more than universal numbers, given that we get the conclusion that all universal machine/number have the same physics.

How exactly "the same".  Can you show that the observed  physics is the only possible physics?

Yes. Compare the physics in the head of the universal machine with the observation. What we see, if it is does not belong to that machine’s internal physics, but is consistent with it,

OK.  Is what's in the head of the universal machine consistent with there being three families of fermions?  Is it consistent with the Standard Model?  Is it consistent with conservation of energy-momentum?  See, the problem is that you have no way saying what is or isn't in the head of the universal machine...so almost anything may be consistent.

Consistency is cheap, but we require the arithmetical soundness assumption, which is much stronger. 

The rest are interesting open problem, a bit premature as we don’t even have any particles yet.

The point is that we have no choice, here. To invoke an ontology will not help. 

Keep in mind that physicalism does not work with mechanism. That has been proven, but the persistence of the mind-body problem since long is by itself an illustration of the failure of physicalism to solve the mind-body problem. Then we get the quantum logic, which is, Imo, hardly a coincidence.

Physics explains the fermions, but physicalism prevents consciousness to have any access on them without using non-computationalist assumption. That is the problem (not for physicists, but for physicalist).

can be defined as the local geography-history (indexically contingent, and usually treated with the diamond in the modes.

If there is a contradiction between the machine’s physics and the observation, then mechanism is false, or we are in a malevolent simulation.

Digital Mechanism provides a new powerful invariant for physics: the physical laws are invariant for all observers, and is invariant for the change of the ontology (combinators, numbers, etc.).

Digital mechanism explains why there is an apparent physical universe,

I don't see that explanation? 

I might ask what you miss in the UDA, which shows that physics is reduced to an indexical statistics

It doesn't "show" that,

It does. You have to refute the argument. Which step would be wrong?

it hypothesizes that it must be so.  It's like hypothesizing God. 

But it does not hypothesize more than elementary arithmetic, and digital mechanism.

Is God consistent with human suffering?  He must be, otherwise the hypothesis is false.

No problem with this, but I don’t see any relation with the fact that UDA enforce the existence of a reduction of physics to arithmetic, making mechanism testable. If some fermlons will be lacking, prove it, then the evidences for those fermions will be evidences against Digital Mechanism.

Without doing this, you are the one speculating on future results to keep your own physicalist god alive (Matter).

on all relative computations ((aka sigma_1 sentences, by a normal form theorem of Kleene, and some subtleties about G* and Z*).

Then what are you missing in AUDA (the arithmetical translation of UDA in arithmetic). The main things have been found by Goödel, Löb, Feferman, Friedman, Boolos, Goldblatt, up to Solvay’s1976 theorem: the discovery of G and G*.

The probability (a credibility or plausibility, actually) one is given, for the observable, by the logic of []p & <>t. I justify this by thought experience, Kripke semantics, and the bastard calculus in Timeaeus and Plotinus (and got evidence that Moderatus got it already from its interpretation of the Parmenides). 

Why is not each person is a different universe, as they are in different dreams.

I am not sure I understand the question. Each person is supported by an infinity of computations, and they diverge, a bit like the W vs M divergence in the self-duplication, except that it is a continuous transformation of some sort. The person $are* in different dream/computations, but some type of dream are sharable

But some types are not.  So why are we in a sharable one? 

Because they have to win the relative measure competition if mechanism is correct. I agree that if mechanism leads to solipsism, that is as good as any absurdity to refute Digital Mechanism. But you cannot speculate on this; the whole point is that we have to do the math and the experimental testing.

Are you hypothesizing the there are other people who are only in unsharable dreams?  It seems you are invoking the "might theory is consistent with everything" rule.

No, if the []p & <>t (& p) modes works, all universal machine have both sharable and unsharable “dreams”. That it works or not is a matter of investigation, not speculation.

and long histories develops, in the limit of all first person experience (due to the invariance of consciousness for the arithmetical delays in the stepping of the universal dovetailer).

Finding the propositional modes of self-reference explains why we have bodies, soul and qualia, and why we are conscious, and why we are in front of the … unknown.

Only in some idiosyncratic meaning of "explain”.

If you feel that it does not explain, ask question. Try to make explicit what is missed in the explanation. I have already explained what physicalism missed, and miss necessarily when we assume Mechanism.

I present reasoning and facts? I do NOT do “philosophy”; other that the one which, when assuming Mechanism, is also science.

But to progress, we need to progress also in the quantified modal logic of provability, and to better extracts Quantum Logic, etc. 

It might not work. The fact is that it works up to now,

It does no work up to now. 

Physicalism is arguably not working. Why makes you saying that Mechanism does not work. Negative comments must be specific, or they looks like … not serious.

It is just sufficiently expansive that no contradiction is apparent.

?

Bruno 

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[Philip Thrift]

On Wednesday, June 26, 2019 at 3:55:26 AM UTC-5, Bruno Marchal wrote:

On 25 Jun 2019, at 20:17, Philip Thrift <cloud...@gmail.com> wrote:

On Tuesday, June 25, 2019 at 10:44:18 AM UTC-5, Bruno Marchal wrote:

The universal machine provides an account of its body/code/theory/finite-things/number (the []p of G1 and Z1, according to some nuances, as well as G1* and Z1*). 

I don’t know what you mean by psychical body. With mechanism, the very notion of body is psychical, and the soul is not material, not even reducible (by the machine itself) to anything 3p-representable.

With mechanism, we can be neutral on some informon particle or psychon, as long as their relevant doing is Turing emulable. 

From a logical point of view, your theory might still be confirmed in the universal machine discourses and phenomenologies.

We have started the interview of the universal machines relatively recently, 1931. It is an infinite story. Today we want to believe that they are docile slaves, but even without mechanism, they somehow warned us that they aren’t.

Bruno

 

The "psychical body" is just the fundamental panpsychic assumption: Just as we think things have physical properties (mass, charge, polarity, ...) we think those same things have psychical (or experiential) properties (qualia, phenomenologicals like colors, taste, freedom, happiness, selfness, …).

Of course we have already agree to disagree on this. I mean, I do not assume the physical reality, and with mechanism, things like mass, charge .. have to be explained from G*, qG* (number theology, as I call it).

Modal provability mathematics relates to them - experiential semantics - as being a (possible) denotational semantics counterpoint.

That seems nice, but if that work, that would be a reason more to distinguish “pan” (in oanpsychism) from anything physical, given that the modal provability logic are consequence of arithmetic (without further assumption).

Bruno

In the end I can see number crunching - of numbers of whatever level or "universality" - only being a mere model (or simulation) at best of what there is in reality - which is called matter. 

@philipthrift

[Bruno Marchal]

I have no logical problem with this, as long as you say “no” to the digitalist doctor.

I do have a problem of motivation, because I have no clue what you mean by “matter”. If it is the “observable by universal machine”, then, by saying yes to the doctor, it is quasi-trivial that numbers observe things, and it is argued,  less trivially that it should be the same observable as ours, making the digital mechanist hypothesis testable.

Note that the Digital Mechanist hypothesis makes the Digital Physicalist hypothesis inconsistent. Many are wrong on this (unless I am wrong in my work, of course).

Bruno

@philipthrift

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[Philip Thrift]

On Wednesday, June 26, 2019 at 8:45:42 AM UTC-5, Bruno Marchal wrote:

On 26 Jun 2019, at 11:30, Philip Thrift <cloud...@gmail.com> wrote:

On Wednesday, June 26, 2019 at 3:55:26 AM UTC-5, Bruno Marchal wrote:

On 25 Jun 2019, at 20:17, Philip Thrift <cloud...@gmail.com> wrote:

On Tuesday, June 25, 2019 at 10:44:18 AM UTC-5, Bruno Marchal wrote:

The universal machine provides an account of its body/code/theory/finite-things/number (the []p of G1 and Z1, according to some nuances, as well as G1* and Z1*). 

I don’t know what you mean by psychical body. With mechanism, the very notion of body is psychical, and the soul is not material, not even reducible (by the machine itself) to anything 3p-representable.

With mechanism, we can be neutral on some informon particle or psychon, as long as their relevant doing is Turing emulable. 

From a logical point of view, your theory might still be confirmed in the universal machine discourses and phenomenologies.

We have started the interview of the universal machines relatively recently, 1931. It is an infinite story. Today we want to believe that they are docile slaves, but even without mechanism, they somehow warned us that they aren’t.

Bruno

 

The "psychical body" is just the fundamental panpsychic assumption: Just as we think things have physical properties (mass, charge, polarity, ...) we think those same things have psychical (or experiential) properties (qualia, phenomenologicals like colors, taste, freedom, happiness, selfness, …).

Of course we have already agree to disagree on this. I mean, I do not assume the physical reality, and with mechanism, things like mass, charge .. have to be explained from G*, qG* (number theology, as I call it).

Modal provability mathematics relates to them - experiential semantics - as being a (possible) denotational semantics counterpoint.

That seems nice, but if that work, that would be a reason more to distinguish “pan” (in oanpsychism) from anything physical, given that the modal provability logic are consequence of arithmetic (without further assumption).

Bruno

In the end I can see number crunching - of numbers of whatever level or "universality" - only being a mere model (or simulation) at best of what there is in reality - which is called matter. 

I have no logical problem with this, as long as you say “no” to the digitalist doctor.

I do have a problem of motivation, because I have no clue what you mean by “matter”. If it is the “observable by universal machine”, then, by saying yes to the doctor, it is quasi-trivial that numbers observe things, and it is argued,  less trivially that it should be the same observable as ours, making the digital mechanist hypothesis testable.

Note that the Digital Mechanist hypothesis makes the Digital Physicalist hypothesis inconsistent. Many are wrong on this (unless I am wrong in my work, of course).

Bruno

matter = material substratum 

The existence of a material substratum was posited by John Locke, with conceptual similarities to Baruch Spinoza's substance and Immanuel Kant's concept of the noumenon (in The Critique of Pure Reason).

- https://en.wikipedia.org/wiki/Hypokeimenon

@philipthrift

[Bruno Marchal]

I would have said that Aristotle, and perhaps the ancient atomist did come up with this before.

with conceptual similarities to Baruch Spinoza's substance 

I tend to agree with you, but among my students this year I have a philosopher who like very much Spinoza, and he criticises a lot that interpretation of Spinoza. Now, he considers only Spinoza treatise “the Ethic”, and dismiss most of his other writing. I find Spinoza not enough clear on this.

and Immanuel Kant's concept of the noumenon (in The Critique of Pure Reason).

Again, I agree with you, but hereto Kant is unclear, and different readers have different opinion on this.

- https://en.wikipedia.org/wiki/Hypokeimenon

Substance is the latine for the greek Hypostasis. The word “substance" in philosophy is sometimes used for Aristotle’s primary matter, which is at the antipode of the use of “hypostasis” by the neoplatonist, where the hypostases are more like fundamental modes of view.

The "material hypostases” (sensible and intelligible matter) are more close to the modern idea of “invariant” in physics than of a material substance that things should be made-of.

 I don’t assume that type of thing. Like God, it is too much unclear to be assumed in a fundamental theory, I think. 

With the computationalist theory of mind, it does not make sense at all. Now, a departure between G* “theory of matter” and observation would be an evidence against computationalism, and so, indirectly, perhaps, an evidence for some substance, but even this is not so obvious. If Mechanism is false, we might need some infinities having a rôle in consciousness, but the notion of ontological substance remains unclear.

Bruno

@philipthrift

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[Philip Thrift]

If an ARM processor running any ARM code [ http://www.toves.org/books/arm/ ] program is ever conscious, or a computer consisting of 10^10 ARM processors running multiprocessor ARM code is ever conscious them the "computationalist theory of mind" holds. If not, it doesn't.

@philipthrift

[Bruno Marchal]

The point is that elementary arithmetic run, out of tie and space, in the precise mathematical sense of “run”, all programs, infinitely often with a precise mathematical redundancy, and once you agree that such 10^100 ARM processor are conscious, they get the same problem as us, which computations run them. By reasoning they know that below their substitution level there should be a complex statistics on *all* computations, and above, there are the laws of physics and finitely many universal neighbours. 

Keep in mind that all universal system can imitate all other universal system. That play a role in metaphysics, not in applications. 

I read a summary of a paper justifying the (rather complex and mysterious) kinetic of enzymes by the fact that some could exploits some quantum computation. That could lower down the substitution level a lot and 10^10 ARM might not been enough, if the substitution level is at the biochemical level. But again, the weak Mechanist assumption I work with is that it exists such a level (being totally neutral on it in particular).

Bruno

@philipthrift

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[Philip Thrift]

I think I meant 10^100 (vs. 10^10 I wrote, or rather size - in this case - doesn't matter). And the ARMs could be replaced by QuARMs (ARMs w/qubits). It still would not have the experientiality of biocomputers.

But the idea of computing as elementary arithmetic run, out of time and space, in the precise mathematical sense of “run”, all programs, infinitely often with a precise mathematical redundancy is certainly a 'Platonic' or immaterially pure idea of computing (and of course I call it 'fictional', but that's OK). But following Donald Rumsfeld, you compute with the computers you have (the stuff engineers can use to make ''computers' - of whatever materials, including biomaterials), not with the computers  you don't have (Platonic arithmetic).

@philipthrift

[Bruno Marchal]

On 1 Jul 2019, at 09:45, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, June 30, 2019 at 1:13:00 PM UTC-5, Bruno Marchal wrote:

On 28 Jun 2019, at 16:52, Philip Thrift <cloud...@gmail.com> wrote:

If an ARM processor running any ARM code [ http://www.toves.org/books/arm/ ] program is ever conscious, or a computer consisting of 10^10 ARM processors running multiprocessor ARM code is ever conscious them the "computationalist theory of mind" holds. If not, it doesn’t.

The point is that elementary arithmetic run, out of tie and space, in the precise mathematical sense of “run”, all programs, infinitely often with a precise mathematical redundancy, and once you agree that such 10^100 ARM processor are conscious, they get the same problem as us, which computations run them. By reasoning they know that below their substitution level there should be a complex statistics on *all* computations, and above, there are the laws of physics and finitely many universal neighbours. 

Keep in mind that all universal system can imitate all other universal system. That play a role in metaphysics, not in applications. 

I read a summary of a paper justifying the (rather complex and mysterious) kinetic of enzymes by the fact that some could exploits some quantum computation. That could lower down the substitution level a lot and 10^10 ARM might not been enough, if the substitution level is at the biochemical level. But again, the weak Mechanist assumption I work with is that it exists such a level (being totally neutral on it in particular).

Bruno

I think I meant 10^100 (vs. 10^10 I wrote, or rather size - in this case - doesn't matter). And the ARMs could be replaced by QuARMs (ARMs w/qubits). It still would not have the experientiality of biocomputers.

But the idea of computing as elementary arithmetic run, out of time and space, in the precise mathematical sense of “run”, all programs, infinitely often with a precise mathematical redundancy is certainly a 'Platonic' or immaterially pure idea of computing (and of course I call it 'fictional', but that's OK).

OK. Computation is a mathematical notion. 

But following Donald Rumsfeld, you compute with the computers you have (the stuff engineers can use to make ''computers' - of whatever materials, including biomaterials), not with the computers  you don't have (Platonic arithmetic).

Thanks God, there is still no patent for using the numbers, and you don’t have to pay taxes when using the model opens rule.

So, no need to invoke a “physical-ontological universe” to explain why a machine needs a concrete computer, relatively to itself to make a concrete computation relatively to some other universal numbers, be it a colleague, a friend, a teacher, …

The goal here is not to sell computers. But to understand where the illusion of physical computers comes from, and why that illusion is persistent.

We believe already, by computer science and Mechanism, that such illusion exist, are lawful, and gives rise to physical realities, and this in a way precise enough to be tested experimentally, and Quantum Mechanics does confirms the main features made obligatory from Mechanism.

That does not make biocomputing, and unconventional programming less interesting, but it found them on rigorous, and rather simple (conceptually) base.

Bruno 

@philipthrift

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