This is great! The issue of timescale is interesting to me in this. I am wondering for different systems at different levels of the ergodic heirarchy, if there are certain statements you can make (when considering the relevant timescales).
Also I am wondering how this plays with the issue of observer models. When I say that some event one month from now has 30% probability, are you imagining that I have a chaotic world model that I somehow run forward many times or push a probability distribution forward in some way and then count the volume in model space that contains the event? How would that process actually work in practice (ie how does my brain do it?).
This is cool, I had never heard of the Ergodic Hierarchy before!
Related to your second point—Alex Cai showed this psychology paper to me. It found that when humans are predicting the behavior of physical systems (e.g. will this stack of blocks fall over?), in their subconscious they are doing exactly this: running the scene in their brain’s internal physics engine with a bunch of initial perturbations/randomness and selecting the majority result. Of course, predicting how a tower of blocks will topple is a lot different from predicting the probability of an event one month into the future.
This is great! The issue of timescale is interesting to me in this. I am wondering for different systems at different levels of the ergodic heirarchy, if there are certain statements you can make (when considering the relevant timescales).
Also I am wondering how this plays with the issue of observer models. When I say that some event one month from now has 30% probability, are you imagining that I have a chaotic world model that I somehow run forward many times or push a probability distribution forward in some way and then count the volume in model space that contains the event? How would that process actually work in practice (ie how does my brain do it?).
This is cool, I had never heard of the Ergodic Hierarchy before!
Related to your second point—Alex Cai showed this psychology paper to me. It found that when humans are predicting the behavior of physical systems (e.g. will this stack of blocks fall over?), in their subconscious they are doing exactly this: running the scene in their brain’s internal physics engine with a bunch of initial perturbations/randomness and selecting the majority result. Of course, predicting how a tower of blocks will topple is a lot different from predicting the probability of an event one month into the future.