Why am I a Boltzmann brain?

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?

• 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. – S. McGrew Nov 11 '18 at 16:14
• "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. – EternalPropagation Nov 11 '18 at 16:44
• Yup, I'm agreeing with you. – S. McGrew Nov 11 '18 at 21:28
• 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? – EternalPropagation Nov 11 '18 at 23:00
• 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. – S. McGrew Nov 12 '18 at 1:01