On 29 Mar 2012, at 21:47, meekerdb wrote:

On 3/29/2012 12:02 PM, Bruno Marchal wrote:

On 29 Mar 2012, at 20:08, meekerdb wrote:

On 3/29/2012 10:14 AM, Bruno Marchal wrote:

I will ask you to do the "hairsplitting" about that "YOU", that you are using here, so as to convince me and others that it refutes indeed the indeterminacy about the first person experience displayed in the WM duplication thought experience (UDA step 3).

Given that we both agree that we don't die in that experience, and given that you are the one claiming that there is no indeterminate outcome, I will ask to give us an algorithm predicting the result of the future self-localization experience.

The outcome is deterministic just like Everett's QM is deterministic. And it has the same problems being given a probabilistic interpretation as EQM. If you duplicated a coin in the transporter experiment the question, "Where will you expect to find the coin." has the same problems as "Where do you expect to find yourself". The implication is that "self" is not a unique 'thing' (as for example a soul is assumed to be) but is process that can be realized in different media.

I agree. But the experience is lived as unique, so we can follow Plotinus in using the term soul for the owner of the 1-view, that is, the knower. From its pov, it is not duplicable, in the trivial sense that the duplication is never part of his experience.

You don't know that. It's an assumption based on the idea that conscious experience is something a certain physical body, a brain, does. But if conscious experience is a process then it is certainly possible to create a process that is aware of being in both Washington and Moscow at the same time.

Or you are just a giant with one foot in W and one foot in M. But that's not relevant for the issue I was talking about, where complete brain are reconstituted separately in the two places.

Think of a brain wired via RF links to eyeballs in M and W. Or The Borg of Star Trek. Of course that experience would be strange and we would tend to say, "Yes but it's still one consciousness." So then the question becomes what do you mean by not experiencing duplication? Is it a mere tautology based on how you define 'consciousness'?

I do not define consciousness, and for the reasoning I am using an approximate notion of first person (the content of the diary which is transported in the teleportation or duplication device. And yes, it makes the "non experiencing of duplication", and the "non experiencing of reconstitution delays" obvious. That was the goal.

He would not know if we did not give him the protocol.
mathematically, this is related to the fact that no machine can know which machine she is, already seen clearly by Post and (re)intuited by Benacerraf, and "intuited" by the machine itself, accepting the Theaetetus' definition of knowledge.

I am not sure the problem of probability is identical in QM and COMP. In QM, Everett showed that the P = A^2 principle does not depend on the choice of the base,

I don't think that's correct. 'A' is the amplitude of the projection on certain basis determined by what is measured. Yes the Born rule can be applied whatever basis is chosen, but the projection produces different A's.

No problem with this.

so that A can be considered as measuring the relative proportion of possible accessible relative realities. This does not work with finite multiverse, but it works with infinite multiverse,

But infinite multiple worlds create a measure problem. That's one of Adrian Kent's points.

In all case of multiplication, be it through comp or QM, there is a measure problem. With comp, the mind-body problem is transformed into a justification of the physical laws through a measure problem.

and Gleason theorem justifies the unicity of the measure,

I'm not sure what you mean by that?

Gleason’s theorem, formulated and proved by Andrew M. Gleason in 1957, is a state- ment about measures on Hilbert spaces of dimension at least three. The theorem states that the only possible probability measures on such spaces are measures µ of the form µ(a) = Tr(ρPa ), where ρ is a positive semi-definite self-adjoint operator of unit trace, and
where Pa is a pro jection operator for pro jection onto the subspace a.
Postulating that any orthogonal basis in some Hilbert space corresponds to a measure- ment and that quantum systems can be represented by such spaces, we can understand the pro jection operators as representing yes-no observables a1 , commuting pro jectors cor- responding to yes-no questions that can be simultaneously answered (or asked). Any (measurable) property a of the system is then uniquely associated with a subspace (which could be one-dimensional i.e. a vector) of the system’s Hilbert space - within this frame- work, Gleason’s statement is one about the probability of obtaining a given outcome when making a measurement on a quantum system. The theorem is of profound importance to modern physics due to its strong implications for how probabilities can be introduced into quantum mechanics. Put another way, it is a statement about the validity and uniqueness
of the quantum probability rule.

Quoted from a Student thesis which is rather good:


If I remember well, Everett uses it to "solve" the measure problem. At the time of my reading I was pretty convinced that, once we assume comp explicitly, Gleason theorem solves the QM measure problem. If the Z1* and X1* "material hypostases" are close enough to some quantum logic, then such a solution can be extended to comp.

for sufficiently complex physical reality (meaning the Hilbert space have to be of dimension bigger than 2. So in my opinion, the Born rule is already explained.

With COMP, as I argue, we have to justify the wave itself (assuming QM is correct) from the relative number relations and personal points of view (as done in AUDA, for the logic of "measure one").

Yes, that would be a signal accomplishment.

My point is a modal point. I am not interested in solving the comp measure problem, only in the proof that comp makes *obligatory* to reduce the mind-body problem into that measure problem on machine/ numbers dream. Comp is used only to reformulate the mind body problem. A believer in comp can already believe that physics has been reduced into machine's bio-psycho-theology (and thus in computer science, and in number theory). That is done.

To extract physics might take 5 years or 500 years. Still, quantum logic has already been extracted, which is something I did not expect to live in my lifetime. But as I said, some serious optimization of the Z and X logic must be provided to verify if the arithmetical quantum logics coming from the mathematical 1 and 3 pov (based on the self-reference logics G and G*) are close enough to apply Gleason theorem or to find its arithmetical equivalent. A disproof of this would lead to a refutation of comp, or to an experimental refutation of comp.



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