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.

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