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From: Russell Standish <R.Standish.domain.name.hidden>

Date: Wed, 23 Jun 1999 08:58:14 +1000 (EST)

*>
*

*> Jaques Mallah's role is important in that he forces us to confront important
*

*> issues. However, he could more effectively communicate by "polishing" his
*

*> style. Enough said of that. Wei Dai has summarized the issue very well.
*

*>
*

*> In a message dated 99-06-19 18:29:26 EDT, Wei Dai writes:
*

*>
*

*> <<
*

*> I think the main point of disagreement between the two camps now is
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*> relative SSSA versus absolute SSSA (Marchal's terms). Can we all agree
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*> that given the absolute SSSA, there is no justification for QS? >>
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*>
*

*> My understanding of the "Strong" Self Sampling Assumption is shaky, but I
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*> think I agree with the above statement. I would find it clearer if it could
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*> be rephrased as follows: If the number of branching in the MW is absolute
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*> then there is no justification for QS.
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*>
*

*> This is the crux of the matter.
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*>
*

*> Jaques Mallah's position is summarized in his words:
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*> << Your total measure would be reduced, so there would be less
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*> observers with that name in the ensemble, and the total number of
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*> observers would be less. >>
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*>
*

*> Clearly Jacques views the number of branches in the MW as absolute and
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*> limited. If you do QS and trim a few branches you just end up with less
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*> branches. The more stringent the QS conditions (winning a $1million or a
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*> $1billion or having Elvis Presley come back to life) the smaller the number
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*> of branches you end up in. And if you make the conditions too stringent you
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*> may end up with nothing. No more of you.
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*>
*

*> If however, the number of branches does not change no matter where you are in
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*> the MW -- according to a kind of a super Cosmological Principle -- then no
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*> matter how many times you commit QS, you still have the same number of
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*> branches left. This, I think, is the "relative" SSSA that Wei Dai and Marchal
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*> are talking about. Adding branches or subtracting branches has no impact on
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*> the probability of your future existence. And it is precisely in the
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*> discussion of probability in this environment that some of the hottest
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*> discussions with Jacques have taken place.
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*>
*

*> So which is it? absolute and limited number of branches or relative and
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*> unlimited?
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*>
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*> I think that the discussion hinges around the size of the MW. If the size is
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*> finite, then there is no question, in my mind that Jacques is right. The
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*> number of branches is finite and QS just trims the MW tree (or network). If
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*> however, the MW is infinite, then the answer is more difficult.
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*>
*

*> Imagine the MW to be infinite aleph1 just like the number of points on a
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*> line. In this environment the super Cosmological Principle I mentioned above
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*> applies: no matter how many times you cut that line, the number of points on
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*> any segment is still aleph1. This number is like the speed of light: a
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*> physical constant of that world: aleph1, independent of the observer's
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*> position -- or line segment.
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*>
*

*> So one condition for justifying QS is having an infinite MW. -- I am not sure
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*> what is the lowest of Cantor's infinities would correspond to a sufficient
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*> condition.
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*>
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*> A second condition is that the number of branches "cut" by QS should be
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*> infinitely smaller than the infinity of the MW. (ie Aleph QS < Aleph MW)
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*>
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*> I would like to add that on purely philosopical grounds I can only conceive
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*> of an absolute infinitely large MW, larger than all of Cantor's infinities --
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*> because any other size would have to be arbitrary and therefore have a reason
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*> to be so. And this limited MW would end up being just one instance of many
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*> other MW in a larger MMW.
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*>
*

*> So which is it? Is the MW finite or infinite? Is QS justified?
*

This is well said, particularly with your example given as

clarification. Minor quibble, don't confuse "c" - the cardinality of

real line segments with \aleph1 - that the two are the same is a

conjecture, not proven.

In fact your argument works with discrete sets - \aleph0 works just as

well. However, quantum mechanics is a continuous theory, so i believe

reality is much more like "c".

*>
*

*> This said, I think that NOTHING justifies QS. My position however is ethical.
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*> As the idea of the MW matured in my mind, I have become convinced that while
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*> the MW is absolutely infinite, it is possible to avoid the nihilist
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*> philosophy of Friedrich Nietzsche and evolve an ethic of the many worlds. In
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*> fact the JUSTIFICATION FOR QS COULD BE TURNED ON ITS HEAD as I have pointed
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*> out in my last post. Beautifully said in the 23rd psalm: "The Lord is my
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*> shepherd, I shall not want...the shadow of the valley of death (the MW)... I
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*> shall fear no evil... .my cup runneth over" The knowledge that we are
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*> immortal and that all stings and arrows are temporary can give us a new
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*> perspective on the world.
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*>
*

*> George Levy
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*>
*

*>
*

Nice little theological example. Good for throwing at rabid

theologues!

Cheers

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 7123

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Tue Jun 22 1999 - 15:59:27 PDT

Date: Wed, 23 Jun 1999 08:58:14 +1000 (EST)

This is well said, particularly with your example given as

clarification. Minor quibble, don't confuse "c" - the cardinality of

real line segments with \aleph1 - that the two are the same is a

conjecture, not proven.

In fact your argument works with discrete sets - \aleph0 works just as

well. However, quantum mechanics is a continuous theory, so i believe

reality is much more like "c".

Nice little theological example. Good for throwing at rabid

theologues!

Cheers

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 7123

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Tue Jun 22 1999 - 15:59:27 PDT

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