On 11/22/2012 9:55 AM, Bruno Marchal wrote:


On 22 Nov 2012, at 00:20, Stephen P. King wrote:

On 11/19/2012 10:06 AM, Bruno Marchal wrote:

On 19 Nov 2012, at 15:43, Stephen P. King wrote:

On 11/19/2012 9:16 AM, Bruno Marchal wrote:
On 19 Nov 2012, at 02:12, Russell Standish wrote:

On Sun, Nov 18, 2012 at 07:48:57PM -0500, Stephen P. King wrote:
Hi Russell,

  I agree with this view, especially the part about the
compatibility of bases leading to a 'sharing of realities' that then
gives rise to an illusion of a single classical reality; I just
phrase the concepts differently. My question to you is how 'simple'
can an observer be, as a system? It seems to me that even particles
could be considered as observers. I buy Chalmers' argument for
panpsychism.


I doubt that very much, ...

Me too, as "pan" assumed some physical reality and thus contradict comp, which is assumed also.
Dear Bruno,

Why are you not considering the 'pan' to cover a plurality of 1p that are observing or otherwise interacting and communicating with each other as a 'physical reality"?

There are two physical reality notions: the one which we infer from observation and logic, like F = ma, F = km1m2/r^2, etc.
And the one explained by comp. We have to compare them to test comp.

Dear Bruno,

    How exactly does the comparison occur?

By comparing the logic of the observable inferred from observation (the quantum logic based on the algebra of the observable/linear positive operators) and the logic obtained from the arithmetical quantization, which exists already.


Dear Bruno,

How does the comparison occur? I will not ask what or who is involved, only how. What means exists to compare and contrast a pair of logics?


Comp seems to necessitate all possible physical worlds in an equiprobable way.

?

    Does not comp require all possible 1p to exist?


There is a deep problem with notions of priors as it seems that we cannot escape from the problem of subjectivity as we see in the (so-called) anthropic principle: each observer will necessarily find itself in a world what has laws compatible with its existence. It seems to me that /the observational act itself is a breaking of the perfect symmetry of equiprobability of possible worlds/.

?




But this claim implies violence to the idea of a 3p.
I found at http://higgo.com/qti/Mallah.htm an exchange between Mallah and Standish that seems to illustrate this problem:

*"**Russell Standish: *The predictions can easily depend of the 'picture' but must be consistent with each other. Let me give a simple example: In one picture, observer A decides to measure the spin of an electron in the x direction. In the other, observer B decides to measure the spin of the electron in the y direction. Observer A will see the spin of the electron aligned with x axis, and Observer B will see it aligned with the y axis. Both observations are correct in the first person picture of that observer. /A "person" with the third person perspective, sees observers A and B as inhabiting separate `worlds' of a multiverse, each with appropriate measure that can be computed from Quantum Mechanics./

*Jacques Mallah: *On the contrary, this is a textbook example of the way I said it works. The theory predicts some measure distribution of observers; an individual observer sees an observation drawn from that distribution. There are no different sets of predictions for different pictures, just the measure distribution and the sample from it.

*Russell Standish: *It sounds to me like you don't think the prediction changes according to what the observer chooses to observe? An electron cannot have its spin aligned with the x axis and the y axis at the same time. Once the experimenter has chosen which direction to measure the spin, the history of that particular is observer is constrained by that fact, and the predictions of QM altered accordingly. This is true both in MWI and the Copenhagen interpretation, and is the "spooky" nature of QM. I used to think that QM gave predictions in terms of distributions, and that because one didn't see isolated particles, rather ensembles of such particles, I didn't see a problem. The properties of an ensemble are well defined. However, the ability of experimenters to isolate a single particle, such as a photon, or an atom, means we have to take this "spookiness" seriously."

The idea of a 3p cannot be applied consistently to the notion of a 'person' or observer if one is considering the 1p of observers in separate 'worlds' of a multiverse unless, for example, A and B have observables that mutually commute and thus have some chance of being mutually consistent and capable of being integrated into a single narrative. I think that this problem is being overlooked because the problem of Satisfiability is being ignored.


?







I hope that we can agree that there is at least an illusion of a physical world that 'we' - you, me, Russell, .... can consider... Is it necessarily inconsistent with comp?

? ? ?

Not at all. The whole point of UDA is in explaining why the physical reality is unavoidable for the dreaming numbers, and how it emerges from + and * (in the "number base"). It is indeed a first person plural product, with the persons being all Löbian machines, etc.

I am coming at the idea of a 'physical reality' as an emergent structure and not some pre-defined ordering.

Good.






Comp gives the complete algorithm to extract bodies and physical laws, making comp testable, even if that is technically difficult,

I claim that it is not even technically difficult; it is impossible for the simple reason that there does not exist a unique Boolean algebra for all possible 1p.

? (I agree such BA does not exist, but this is exactly what we need to find a measure theorem à-la Gleason). We need a sufficiently good quantum logic, and up to now the comp quantum logic fits rather well.


Gleason's theorem is interesting: http://en.wikipedia.org/wiki/Gleason%27s_theorem

"For a Hilbert space of dimension 3 or greater, the only possible measure of the probability of the state associated with a particular linear subspace a of the Hilbert space will have the form Tr(?(a) W), the trace of the operator product of the projection operator ?(a) and the density matrix W for the system."

We sidestep the problem of how we define the transition from pure states to density matrices. Andrew's discussion might be seen as addressing this...




Why? Because it cannot be proven to be satisfiable(aka globally self-consistent) by any finite sequence of algorithms. Completeness and consistency for such cannot be assumed a priori.

?

    Do you ever address the question of satisfyability?




but up to now, it fits remarkably, and that would not have been the case without QM. That would not have the case if "p->[]<>p" was not a theorem of the Z1* logics (matter).

Your reasoning is correct only because you are assuming the impossible to be true a priori: that there exists a solution to the Satisfiability problem

It exists. "Satisfability" is non tractable, not insoluble. The first persons don't care "waiting exponential time" by the invariance of first person experience on delays.

Of course, but an infinite BA requires eternity (infinitely many steps) to solve its satisfiability problem. I am not claiming non-solubility; I am pointing out that the computation of satisfiability must run to obtain a solution, otherwise it is false to claim that the solution is accessible. It is a profound mistake to claim that the existence of the largest prime number defines the exact sequence of numerals that would enumerate that prime number. Similarly, the mere possibility of satisfiability of a BA cannot be used to argue about the particular distribution of propositions of the BA. You are considering first persons in the eternal and ideal case, but that does not connect omniscient machines to finite human brains. This is the challenge to Plato and Parmenides, how do we bridge between the Realm of Truth and the world of appearances? We could make claims forever but showing a proof requires physical effort. There are no shortcuts to knowledge. You seem to be OK with the idea that knowledge can obtain 'for free'. Perhaps I am mistaken, but it seems that you are assuming the impossible to be real.



*and* that it is accessible for any finitely expressible logical structure.

It is accessible, but then I don't see at all the relevance of this.

    Please explain how it is accessible.



--
Onward!

Stephen

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