>
> Thank you Jacques for your detailed reply to my post asking about your
> concept of measure.
>
> In a message dated Mon, 23 Aug 1999, Russel Standish wrotes:
>
> > Now this implies that an individual's measure decreases the older that
> > individual gets. This is the basis of Jacques' argument against
> > QTI. In absolute SSA, an individual concious being is a sample from
> > the set of all observer moments. There is no time, one just is. Under
> > this picture, one could never expect to be all that old.
>
> > Under relative SSA, there is time. Each observer moment is connected
> > to a range (presumably infinite) of future observer moments. The
> > relative SSA predicts that the observer will see at the next instant
> > of time an observer moment with the greatest measure, subject to its
> > lying in the future of the current observer moment. That measure may
> > be fantastically small (eg just prior to a fatal crash) - it just has
> > to be the largest from that set.
>
> and Jaques Mallah replies:
> > No. If every observer sees all future moments, then the amount of
> >consciousness does not decrease with time, and thus the measure stays
> > constant over time. This has the consequence that, for a given observer,
> >over most of his lifetime he will find himself to be very old. It may
> >seem that I am mixing in the ASSA when I say that, therefore, the fact
> >that we do not find ourselves old is evidence against the RSSA. The truth
> >is I can not avoid this way of thinking any more than I could believe that
> >1+1=3.
> >>
>
> It seems to me that you have made the assumption that the MWI only deals with
> "splitting" of the observer and not the "merging". This leads to the
> conclusion that under the Relative SSA the measure keeps increasing and we
> find ourselves to be very old in the most probable worlds.
>
> However, if we include merging of the observer, then we could end up with a
> Relative SSA in which measure is conserved.
Why is this relevant?
>
> This said, I find it difficult to talk about increase and decrease and making
> comparisons of the measure when the quantity in question is infinite.
>
> Measure is not finite. This would violate the principle of plenitude and it
> would require a reason for measure to be any particular size.
Remember we are restricting our attention to a self-aware subsystem
(eg one called Russell Standish) of the Quantum Mechanics subsystem of
the everything universe. The principle of plenitude can only apply to
the whole everything universe, not to well defined subsystems like the
MWI.
Now the measure of Russell Standish is a finite quantity, and is
calculated by the formula m_{RS}(t) = <\Psi(t)|P_{RS}|\Psi(t)>, where
\Psi(t) is the wavefunction of the multiverse, and P_{RS} is the
projection operator corresponding to Russell Standish. It doesn't
matter that we don't exactly know what \Psi(t) or P_{RS} are - however
they do exist as part of the MWI mathematical structure.
>
> If measure is infinite and no comparisons can be made in the measure between
> different branches, then flying rabbits are as likely as anything else and
> the concept of the most probable future has no meaning.
>
> This implies that in the physical world, measure must be infinite and some
> kind of comparison must be feasible.
>
> There is a need for bridging the gap between our loss in our ability to order
> infinities (ie: Aleph0 = 2 Alephs0 = 100Alephs0 - unless one compares
> infinites of different levels) and the comparisons ability allowed by the
> process of limits: ie (2X)/X <> X/X as X -> infinity.
>
> There may be a connection to the class of numbers called Surreals invented by
> Conway and the class called Hyperreal invented by Abraham Robinson.
> Interestingly enough, Conway defines his surreal, using a "branching"
> process, in which new numbers are inserted at each branch, and become the
> origins of more branches. (see Infinity and the Mind by Rudy Rucker page 89).
> These numbers can be added and multiplied together, and therefore compared.
> This is where the surreal and hyperreal numbers could be applicable.
>
> George
>
>
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
----------------------------------------------------------------------------
Received on Thu Aug 26 1999 - 18:26:15 PDT