On Sat, May 1, 2010 at 3:31 PM, Rex Allen <rexallen...@gmail.com> wrote:

> On Thu, Apr 29, 2010 at 11:24 PM, Brent Meeker <meeke...@dslextreme.com>
> wrote:
> > But if the universe arose from a quantum fluctuation, it would
> necessarily
> > start with very low entropy since it would not be big enough to encode
> more
> > than one or two bits at the Planck scale.  If one universe can start that
> > way then arbitrarily many can.  So then it is no longer clear that the
> > evolved brain is less probable than the Boltzmann brain.
> I asked Sean about the application of probability to the Boltzmann
> brain scenario on his blog:
> > "So, in chapter 10 you rule out the possibility of the eternal
> > recurrence scenario based on the low probability of an observer of our
> > type (human) being surrounded by a non-equilibrium visible universe
> > compared to the probability being a “boltzmann brain” human observer
> > who pops into existence to find himself surrounded by chaos.
> >
> > As you say, in the eternal recurrence scenario there should be far far
> > more of the later than of the former.
> >
> > Okay. So, my question:
> >
> > If the recurrences are really eternal, then shouldn’t there be
> > infinitely many of BOTH types of observers? Countably infinite?
> >
> > And aren’t all countably infinite sets of equal size?
> >
> > So in an infinite amount of time we would accumulate one countably
> > infinite set of our type of observer. And over that same amount of
> > time we’d could also accumulate another countably infinite set of the
> > “Boltzmann Brain” type of observer.
> >
> > The two sets would be of the same size…countably infinite. Right?
> >
> > So probabilistic reasoning wouldn’t apply here, would it?
> >
> > Especially not in a “block” universe where we don’t even have to wait
> > for an infinite amount of time to pass."
> AND, here was his reply:
> >  Sean Says:
> > January 27th, 2010 at 9:49 am
> >
> > Rex, this is certainly a good problem, related to the “measure” issue
> > that cosmologists are always talking about. Yes, in an eternal
> > universe there are countably infinite numbers of “ordinary” observers
> > and freak (thermal-fluctuation) observers. But the frequency of the
> > latter — the average number in any particular length of time — is much
> > larger. We generally assume that this is enough to calculate
> > probabilities, although it’s hardly an airtight principle.

And he says something similar in the book, but adds that he thinks it's
plausible that "ordinary observers" in the early low-entropy growth of baby
universes will be more probable than Boltzmann brains with false memories.
>From pages 363-364:

'This version of the multiverse will feature both isolated Boltzmann brains
lurking in the empty de Sitter regions, and ordinary observers found in the
aftermath of the low-entropy beginnings of the baby universes. Indeed, there
should be an infinite number of both types. So which infinity wins? The
kinds of fluctuations that create freak observers in an equilibrium
background are certainly rare, but the kinds of fluctuations that create
baby universes are also very rare. It's not enough to draw fun pictures of
universes branching off in both directions of time; we need to understand
things at a quantitative level well enough to make reliable predictions. The
state of the art, I have to admit, isn't up to that task just yet. But it's
certainly plausible that a lot more observers arise as the baby universes
grow and cool toward equilibrium than come about through random fluctuations
in empty space.'


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