On Thu, Apr 29, 2010 at 11:24 PM, Brent Meeker <[email protected]> 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. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
