I deliberately left out a key qualification in that (slightly edited) statement, because I couldn’t explain it until today.
I might be missing something crucial because I don’t understand why this addition is necessary. Why do we have to specify “simple” boundaries on top of saying that we have to draw them around concentrations of unusually high probability density? Like, aren’t probability densities in Thingspace already naturally shaped in such a way that if you draw a boundary around them, it’s automatically simple? I don’t see how you run the risk of drawing weird, noncontiguous boundaries if you just follow the probability densities.
The best way to draw a boundary around the high-probability things, without worrying about simplicity, is to just write down all your observations; they have probability 1 of having been observed, and everything else has probability 0. This boundary is way too complicated; you’ve seen many things.
I might be missing something crucial because I don’t understand why this addition is necessary. Why do we have to specify “simple” boundaries on top of saying that we have to draw them around concentrations of unusually high probability density? Like, aren’t probability densities in Thingspace already naturally shaped in such a way that if you draw a boundary around them, it’s automatically simple? I don’t see how you run the risk of drawing weird, noncontiguous boundaries if you just follow the probability densities.
The best way to draw a boundary around the high-probability things, without worrying about simplicity, is to just write down all your observations; they have probability 1 of having been observed, and everything else has probability 0.
This boundary is way too complicated; you’ve seen many things.