I was reading through Scott Aaronson's notes (pdf), but I can't make sense of his discussion about Boltzmann brains on p61. Specifically the fact that it says:
But the problem is worse. Since in an eternal universe, you would have inﬁnitely many Boltzmann-brain doppelgängers, any observer with your memories and experiences seems inﬁnitely more likely to be a Boltzmann brain, than to have arisen via the “normal” processes of Darwinian evolution and so on starting from a Big Bang!
I don't understand what this last statement follows from and it seems very unintuitive.
A Boltzmann-doppelgänger brain arising by chance seems very improbable since that would require the formation of a brain with a full brain state, i.e. essentially all the individual atoms/molecules appearing in the exact (or at least close enough) configuration. In other words, a very high level of organization. Whereas the Big Bang scenario merely assumes a hydrogen/helium cloud and that the basic laws of nature are in place. This seems to be a much simpler object as a starting point and hence much more probable. This starting point, once it has occurred (maybe due to chance) then evolves (through the relatively simple laws of nature) into the state we have now, and gives rise to processes like natural selection etc. which eventually bring about intelligent life and the very high level of organization in the brain. Evolution through natural selection, while fundamentally also depending on stochastic events, seems much more probable since natural selection guides the process, allowing it to "tune in" on the target state, rather than there being a requirement of the target state just emerging in one step as with the Boltzmann-doppelgänger. Another argument is that the human brain, while seemingly a very complex structure, is probably the result (as part of fetus/child development) from a much simpler process, described in the human DNA. Like how a seemingly complex fractal can emerge from a simple equation. Hence, it seems a much easier way of producing a brain by chance is to produce this simpler mechanism by chance "and let it run" until it forms a brain, rather than demanding that a full brain itself appears by chance as in the Boltzmann case.
But given Scott Aaronson is very smart there must be something about this I'm missing. Because I'm reading the statement as saying that the Boltzmann-doppelgänger are more probable than the big bang, but to me it seems the converse is true.