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The Boltzmann brain hypothesis states that a big-bang-causing entropy fluctuation is larger than a brain-causing entropy fluctuation, therefore, you are much more likely to be a BB rather than a wet brain. But this doesn't make sense to me (maybe I don't understand?) because when $10^{80}$ particles fluctuate into one location, they will ALWAYS create a big bang whereas when $10^{22}$ particles fluctuate into one location, they will create a BB only one out of every ($10^{22}$)! times. The chance of $10^{80}$ particles fluctuating into one location seems absurdly more likely than the chance of $10^{22}$ particles fluctuating into a specific pattern.

The way I see it, there are four events, and their respective rarities, to compare here:

  • the event where $10^{22}$ particles fluctuate into one location (event rarity a)

  • the event where $10^{22}$ particles fluctuate into my BB (event rarity b),

  • the event where $10^{80}$ particles fluctuate into one location (event rarity c)

  • the event where $10^{80}$ particles evolve into my WB (event rarity d).

I don't understand why BBH says $(a \times b) > (c \times d)$

What am I not understanding here?

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  • $\begingroup$ IMHO the Boltzmann Brain hypothesis is wild speculation. Nobody knows what would, physically, constitute a Boltzmann brain. Nobody knows what makes a big bang happen. Nobody knows how to calculate the probability that a human-class brain will emerge via evolution on an Earth-like planet. We do know that evolution is vastly more efficient at producing organized structures than random association of atoms is. $\endgroup$ – S. McGrew Nov 11 '18 at 16:14
  • $\begingroup$ "We do know that evolution is vastly more efficient at producing organized structures than random association of atoms is." That's why I only stated an inequality. $\endgroup$ – EternalPropagation Nov 11 '18 at 16:44
  • $\begingroup$ Yup, I'm agreeing with you. $\endgroup$ – S. McGrew Nov 11 '18 at 21:28
  • $\begingroup$ I don't think you are. My view is that it is virtually impossible to be a Boltzmann brain. We can actually use this inequality to infer an upper bound on the probability of a big bang occurring which can infer the size of the universe; the less likely the BB, the more room there is for a large universe. This also implies no aliens; if observers are likely, why didn't we occur in a small universe? $\endgroup$ – EternalPropagation Nov 11 '18 at 23:00
  • $\begingroup$ I agree (for what that matters!) that a Boltzmann brain is essentially impossible. However, we don't have a clue how a Boltzmann brain would be structured, so estimates of its probability of existence are pretty much meaningless. And, consequently, any calculations based on a value for the probability of a Boltzmann brain would be pretty much meaningless. By the way, I don't quite understand d. Surely you don't mean a wet brain containing 10^80 particles. That would be rather large. $\endgroup$ – S. McGrew Nov 12 '18 at 1:01

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