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But if I were seeing chaos, wouldn't I stop evaluating evidence, thus making the Boltzmann brains where I can read your post the only ones who are convinced that they're not Boltzmann brains? I don't know how to put it in more rigorous terms.
Hmm, not quite sure I understand the question? If you have all your memories (including those of reading this post) but are seeing chaos, then you basically DO know you're a Boltzmann Brain. You can know for sure one way, but not the other. So in a Boltzmann Brain universe, the vast majority of "you"s would know you were in one, but some tiny fraction of "you"s would mistakenly think you weren't (matching your current experience).
You assume that I'd keep my memories, but wouldn't them being scrambled as well be expected to go along with seeing chaos?
In a Boltzmann Brain universe, EVERY configuration exists. So sure, there would also be versions of you with scrambled memories, but we're not talking about those - you already know you're not one of them! In statistics terms, your possibility space (based on your current observation that oh-hey-I-exist) consists of all the brains that are exactly equivalent (atom-to-atom, memory-to-memory) to "you" at this instant, and the successes consist of which ones then proceed to see order. If we exist in a physics-based universe, that probability ratio is basically 1. In a Boltzmann-Brain universe, it's basically 0. I hope this makes sense, without bringing in too much formal terminology.
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