>
> 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
> relative SSSA versus absolute SSSA (Marchal's terms). Can we all agree
> that given the absolute SSSA, there is no justification for QS? >>
>
> My understanding of the "Strong" Self Sampling Assumption is shaky, but I
> think I agree with the above statement. I would find it clearer if it could
> be rephrased as follows: If the number of branching in the MW is absolute
> then there is no justification for QS.
>
> This is the crux of the matter.
>
> Jaques Mallah's position is summarized in his words:
> << Your total measure would be reduced, so there would be less
> observers with that name in the ensemble, and the total number of
> observers would be less. >>
>
> Clearly Jacques views the number of branches in the MW as absolute and
> limited. If you do QS and trim a few branches you just end up with less
> branches. The more stringent the QS conditions (winning a $1million or a
> $1billion or having Elvis Presley come back to life) the smaller the number
> of branches you end up in. And if you make the conditions too stringent you
> may end up with nothing. No more of you.
>
> If however, the number of branches does not change no matter where you are in
> the MW -- according to a kind of a super Cosmological Principle -- then no
> matter how many times you commit QS, you still have the same number of
> branches left. This, I think, is the "relative" SSSA that Wei Dai and Marchal
> are talking about. Adding branches or subtracting branches has no impact on
> the probability of your future existence. And it is precisely in the
> discussion of probability in this environment that some of the hottest
> discussions with Jacques have taken place.
>
> So which is it? absolute and limited number of branches or relative and
> unlimited?
>
> I think that the discussion hinges around the size of the MW. If the size is
> finite, then there is no question, in my mind that Jacques is right. The
> number of branches is finite and QS just trims the MW tree (or network). If
> however, the MW is infinite, then the answer is more difficult.
>
> Imagine the MW to be infinite aleph1 just like the number of points on a
> line. In this environment the super Cosmological Principle I mentioned above
> applies: no matter how many times you cut that line, the number of points on
> any segment is still aleph1. This number is like the speed of light: a
> physical constant of that world: aleph1, independent of the observer's
> position -- or line segment.
>
> So one condition for justifying QS is having an infinite MW. -- I am not sure
> what is the lowest of Cantor's infinities would correspond to a sufficient
> condition.
>
> A second condition is that the number of branches "cut" by QS should be
> infinitely smaller than the infinity of the MW. (ie Aleph QS < Aleph MW)
>
> I would like to add that on purely philosopical grounds I can only conceive
> of an absolute infinitely large MW, larger than all of Cantor's infinities --
> because any other size would have to be arbitrary and therefore have a reason
> to be so. And this limited MW would end up being just one instance of many
> other MW in a larger MMW.
>
> 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.
> As the idea of the MW matured in my mind, I have become convinced that while
> the MW is absolutely infinite, it is possible to avoid the nihilist
> philosophy of Friedrich Nietzsche and evolve an ethic of the many worlds. In
> fact the JUSTIFICATION FOR QS COULD BE TURNED ON ITS HEAD as I have pointed
> out in my last post. Beautifully said in the 23rd psalm: "The Lord is my
> shepherd, I shall not want...the shadow of the valley of death (the MW)... I
> shall fear no evil... .my cup runneth over" The knowledge that we are
> immortal and that all stings and arrows are temporary can give us a new
> perspective on the world.
>
> George Levy
>
>
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
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Received on Tue Jun 22 1999 - 15:59:27 PDT