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From: <GSLevy.domain.name.hidden>

Date: Sun, 26 Sep 1999 02:08:59 EDT

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 Sat Sep 25 1999 - 23:14:20 PDT

Date: Sun, 26 Sep 1999 02:08:59 EDT

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 Sat Sep 25 1999 - 23:14:20 PDT

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