This points toward a more general class of questions: when, and to what extent, does it all add up to normality? We learned the high-level ideal gas laws long before we learned the low-level molecular theory, but we knew the low-level had to at least be consistent with that high-level structure. What low-level structures did that constraint exclude? More generally: to what extent does our knowledge of the high-level model structure constrain the possible low-level structures?
One good class of structure for these sorts of questions is causal structure: to what extent does high-level causal structure constrain the possible low-level causal structures? I’ll probably have a post on that soon-ish.
Doesn’t high-level structure entail statistical averages and not necessarily Boltzmann brains in the low-level structure? Like—what of the nonequilibrium statistical mechanics?
Problem is, we didn’t know beforehand (i.e. in 1800) that the high-level things we saw (like temperatures, heat flow, etc) had anything to do with statistical averages. One could imagine an alternative universe running on different physics, where heat really is a fluid and yet macroscopically it behaves a lot like heat in our universe. If we imagine all the difference ways things could have turned out to work, given only what we knew in 1800, where does that leave us? What low-level structure is implied by the high-level structure?
Doesn’t high-level structure entail statistical averages and not necessarily Boltzmann brains in the low-level structure? Like—what of the nonequilibrium statistical mechanics?
Problem is, we didn’t know beforehand (i.e. in 1800) that the high-level things we saw (like temperatures, heat flow, etc) had anything to do with statistical averages. One could imagine an alternative universe running on different physics, where heat really is a fluid and yet macroscopically it behaves a lot like heat in our universe. If we imagine all the difference ways things could have turned out to work, given only what we knew in 1800, where does that leave us? What low-level structure is implied by the high-level structure?