Thanks, James Higgo, for the message below. Things do get complicated when
you try to take account of peculiar worlds which continue onwards. I'd
have thought, however, that the same argument could be run with respect to
each of those worlds:  any observers in them would be very likely to be
near annihilation, for the reasons I gave (exponential explosion until
annihilation in any branch): the fact that you don't experience the very
last moment of your lifetime is irrelevant, since it can still be the case
that you should expect that most of the branches leading forward from you
at the present moment will end in annihilation soon, and that should
influence your expectation-of-continued-life; any fact that there will be
peculiar branches which don't, and which then themselves explode
exponentially, should not lead you to expect to see a branch which does
not end soon. The point centers on what is meant by "expecting" this or
that. Take the simpler case of throwing two dice and "expecting" not to
see double-six. Against the background of Everettism, what this means is
that the range of the future branches which include double-six is only one
thirty-sixth of the total. Well, suppose you are assured that those
person-versions who throw anything other than double-six will be shot
immediately they have seen double-six landing on the table, whereas all
those who do throw double-six will continue onwards, and that while they
continue onwards they will divide up into more and more person-versions,
exponentially. It can follow from this that most of (or the greatest
range of, if we are dealing with infinite numbers) the person-versions
who will ever have had histories running through the moment of the tossing
of the dice will be person-versions in whose histories double-six appears.
None the less, the fact is that one is trying to estimate "the probability
OF SEEING double-six", i.e. the range of the double-six branches in the
branches IMMEDIATELY AHEAD of one's present moment, and not the
probability of HAVING SEEN having seen double-six in the cases of branches
existing, say, ten hours in the future. So one ought to expect not to see
double-six (whereas your argument suggests the opposite conclusion).
Note, however, that (as I think I said in my original email to you and
others) I regret not having used the simpler argument that a believer in
Everettism-with-continued-exponential-increase-in-number-of-branches
(which is, N.B., NOT Deutsch's version of Everettism, which is immune to
my argument as it has differentiations rather than increases in total
numbers) ought to believe that, e.g., it is really June 5 1999, instead of
being June 4 as his watch or the newspaper which he thought came this
morning tells him, so long as there is the slightest chance that the watch
is wrongly set or the newspaper in fact the one delivered yesterday, the
reason for this being that on June 5 there would be vastly more versions
of himself doing the observing/ wondering what day it was.   ...Will now
sign off without trying to clean up the arguments above, since (as I've
stressed to Nick Bostrom) I'm trying to get back into philosophy of
religion instead of spending the remainder of my life thinking about this
rich and complex subject. I'm pleased, though, that it has captured the
interest of you and of so many others.  All the best:  John Leslie 

On Fri, 4 Jun 1999, Higgo James wrote:

> > Dear John
> > 
> > Many thanks for sending me your papers. I read 'a difficulty'..
> > for MWI with interest. The doomsday argument has been
> > much discussed on the everything-list discussion group
> > largely due to the influence of Nick Bostrom, who runs
> > anthropic-Principle.com.  It's an intriguing idea but Standard
> > Life are still willing to bet 1 million to 1 that it is flawed.
> > 
> > But let's say that the overwhelming likelihood is that we are
> > milliseconds from annihilation. Like the vacuum collapse, this
> > only adds strength to Deutsch-style-MWI-plus-assumption-
> > that-we-only-experience-universes-in-which-we-exist (or QTI
> > for short). See http://www.higgo.com/qti.
> > 
> > From this moment on, 99.99...% of subsequent branches are
> > dead ends, due to a vacuum collapse, or perhaps simply
> > because there are no causal relationships: the branch will
> > lead to a world of random disorder. But we don't experience
> > the worlds we don't exist in, and we are still left with an
> > infinite number of worlds ahead of us. This process continues
> > ad infinitum.
> > 
> > The contributor base of the everything-list  is currently in the
> > thrall of these ideas despite Jacques Mallah's valient lone
> > efforts to dissuade us. Any fresh ideas would be very
> > welcome.
> > 
> > With best wishes,
> > James Higgo
> 

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