If the universe is infinite and chaotic, it will pass through all possible states, which includes all possible combinations of atoms and all possible observers. It follows from Poincaré recurrence theorem.
Even very improbable observers can appear as Boltzmann brains. Basically, it follows from the law of large numbers: if there are infinitely many tries, then any finite number will appear. Therefore, we need to add a constrain that observer’s mind is finite.
I’m not sure that follows. It could depend on the structure of the universe. While many or most states are reached there could be unreached areas due to being outside of attractors. Even a random walk in three dimensions doesn’t reach all points.
This objection may works for some strange astrophysical object, like cubic-size stars. If we limit our idea of observers to the finite (and not too large) size Turing machines, it seems unlikely. Any such observer could appear via random generating of a file.
I think by adding in the constraint of turning machines, you increase the complexity and thus reduce the likelihood, not increase it. Now you require Turing machines in the first place.
What is a “possible” observer? Why would an “infinite” universe contain all of them?
By analogy, there are infinitely many real numbers in the interval [0,1]. But not all real numbers are in that interval.
If the universe is infinite and chaotic, it will pass through all possible states, which includes all possible combinations of atoms and all possible observers. It follows from Poincaré recurrence theorem.
Even very improbable observers can appear as Boltzmann brains. Basically, it follows from the law of large numbers: if there are infinitely many tries, then any finite number will appear. Therefore, we need to add a constrain that observer’s mind is finite.
I’m not sure that follows. It could depend on the structure of the universe. While many or most states are reached there could be unreached areas due to being outside of attractors. Even a random walk in three dimensions doesn’t reach all points.
This objection may works for some strange astrophysical object, like cubic-size stars. If we limit our idea of observers to the finite (and not too large) size Turing machines, it seems unlikely. Any such observer could appear via random generating of a file.
I think by adding in the constraint of turning machines, you increase the complexity and thus reduce the likelihood, not increase it. Now you require Turing machines in the first place.
Turing machines are rather universal thing which will appear many times everywhere, so I don’t see how it reduces the likelihood.
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I don’t see a problem here, I will win in another branch of MWI. Or I miss something?