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:
And YOU HAVE BEEN DUPLICATED.
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:
http://kof.physto.se/theses/helena-master.pdf
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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