Hi George,
You ask us very interesting and difficult questions. I intend to comment
some of these questions as soon as possible, which means November because
I am too much buzy now.
Nevertheless it could help me (us) if you could be a little more explicit
when you say that Jacques Mallah and most of us have a differerent use of
the Leibnitzian identity principle.
I guess you remember that in my ``pure comp" approach it is important to
distinguish 1-person and 3-person points of view (POV). In particular
there
are a lot of situations where the 1-person POVs are indistinguishable and
are
identified, although they are 3-person-distinguishable. This change the
probability of the 1-person experience, but not the nature itself of the
experience. I think I agree with Jacques Mallah on these points, although
I
still believe that from his own premisses imortality cannot be avoided (so
clearly there is a need to make things clearer).
Bruno
---- Original Message -------
>I think one of the essential difference between Jacques' point of view and
>some of the rest of us (James?, Bruno?, Russell?, Gilles? and myself) is
>that
>Jacques does not accept the principle of identity of indistinguishable and
>we
>do. This principle, I think, was first enounciated by Leibniz. Depending if
>it is accepted or not, it leads to very different conclusions regarding how
>consciousness is affected by the branching of the wave function. Other
>issues
>involve absolutism or relativism of measure and the linkage between worlds
>and consciousness. I will explore this issues in the following questions
>which may be the basis for further discussion.
>
>First Question. The principle of identity of indistinguishable applied to
>the
>wave function.
>Is it possible for two (local) portions of the universal wave function
>originating from different (local) pasts, to "merge" that is to become
>identical. The output merged "measure" of this process would then be the sum
>of the two input "measures."
>So if the first input portion is X and the second input portion is Y then
>the
>resulting wave would be X+Y. (This question ignores the Self Sampling issues)
>I assume that "measure" is in some way related (or identical) to the
>probability = Square(|X +Y|) of the wave function.
>
>Second Question. Is there really branching?
>I am not sure if the branching and merging processes are at all possible in
>the first place or just an artifact of the way we look at the wave function.
>If the wave function is mapped in Wheeler's phase space, then, assuming
>purely deterministic laws, is it true to say that two trajectories in this
>space could never cross (or merge except in the limit)? and for the same
>reasons, could never branch? (I think this question is related to the
>Lyapunov stability theorem) How is this absence of branching and merging
>reconciled with the branching (and merging) that we take for granted in the
>MWI?
>
>Third Question. The principle of identity of indistinguishable applied to
>consciousness.
>Assuming that it is possible for two (local) portions of the wave function
>to
>"merge," then, is it true to say that two different consciousness
>independently expressed by these two portions, become one and same at the
>merging point?
>
>Fourth Question. Absolutism vs Relativity of measure.
>Is "measure" an absolute quantity, invariant with the observer, such as the
>distance between two points along a geodesic in space-time? Or is measure a
>relative quantity that depends on the observer, such as length, time, or
>velocity?
>I think that Jacques believes in the absolute version of measure and some of
>the rest of us, in the relative version. This question raises a hornet's
>nest
>because, and depending on the answer, it leads to different conclusions
>regarding Quantum Suicide (QS).
>
>Fifth Question. Measuring Your Own Measure.
>Can an observer observe or measure his own "measure?" How could one set up
>an
>experiment to make such a measurement? Would that experiment involve
>estimating how unlikely our world is? In other words if our world is found
>to
>be very improbable then our measure would be low, otherwise our measure
>would
>be high. The problem here is that if we assume the Plenitude to be an
>infinite set of possibilities, then any world would have a probability of
>zero. Absolutists would be satisfied with playing around with infinitesimal
>probabilities and would fight tooth and nail for maximizing those
>infinitesimals at all cost thus shunning QS as a "crackpot idea".
>Relativists
>would in a sense "RENORMALIZE" their own probability of existence by using
>the conditional probability GIVEN the existence of the self. Thus, accoding
>to them, the probability that they exist given that they exist is one. The
>Relative Self Sampling Assumption (RSSA) is the conditional probability
>given
>the self, and the Absolute Self Sampling Assumption (ASSA) is the plain
>probability.
>
>Sixth Question. Linkage between worlds and consciousness.
>I am here venturing in an area in which I know very little. However, I think
>it relates to the controversy betweenby David Lewis,"On the Plurality of
>Worlds," and Saul Kripke, a colleague of Lewis at Princeton University, who
>is the champion of ersatz modal realism. Is a particular consciousness
>linked
>to a single world, or is it kind of "spread out" like a quantum cloud over
>a multiplicity of worlds, for example like an electron is spread out in a
>probabilistic wave? (In fact maybe the quantum wave IS THE CONSCIOUSNESS
>WAVE). In other words, does consciousness have extension across worlds?
>Related to this question is the issue of how much difference is required
>between two consciousness for them to cease to be identical. In other words
>what is the TOLERANCE required by Leibniz principle of identity of
>indistinguishable. How can we define this tolerance? Is this difference
>physical or psychological? Is this tolerance defined by Planck's constant?
>Or
>is it defined by a "Turing type" test in which the difference is significant
>to an individual ONLY IF HE PERCEIVES IT TO BE SIGNIFICANT? Who is the
>observer for the "Turing type" test? The Self? Others?
>
>Again, as in previous issues, I think that some of us have championed the
>one
>consciousness - one world system and others have supported the one
>consciousness - multi-world system. And each point of view leads to
>radically
>different conclusions regarding QS.
>
>
>I have raised many questions, I think enough work to keep busy far into the
>next millenium. Forgive me if I attributed to you beliefs that you do not
>have. In the absence of a firm index of ideas with champions and challengers
>I find it difficult to know exactly what you are thinking.
>
>George Levy
>
>
Received on Thu Sep 30 1999 - 06:23:58 PDT
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