This is excellent! Very well done, I would love to see more work like this.
I have a whole bunch of things to say along separate directions so I’ll break them into separate comments. This first one is just a couple minor notes:
For the universe section, the universe doesn’t push “toward” maxent, it just wanders around and usually ends up in maxent states because that’s most of the states. The basin of attraction includes all states.
Regarding “whether dynamical systems theory explicitly studies attractors that operate along a subset of the system’s dimensions”, I believe there’s an old theorem that the long-term behavior of dynamical systems on a compact space is always ergodic on some manifold within the space. That manifold has a name which I don’t remember, which is probably what you want to look for.
Does “ergodic on some manifold” here mean it approaches every point within the manifold, as in the ergodicity assumption, or does it mean described by an ergodic function? I realize the latter implies the former, but what I am driving at is the behavior vs. the formalism.
This is excellent! Very well done, I would love to see more work like this.
I have a whole bunch of things to say along separate directions so I’ll break them into separate comments. This first one is just a couple minor notes:
For the universe section, the universe doesn’t push “toward” maxent, it just wanders around and usually ends up in maxent states because that’s most of the states. The basin of attraction includes all states.
Regarding “whether dynamical systems theory explicitly studies attractors that operate along a subset of the system’s dimensions”, I believe there’s an old theorem that the long-term behavior of dynamical systems on a compact space is always ergodic on some manifold within the space. That manifold has a name which I don’t remember, which is probably what you want to look for.
Does “ergodic on some manifold” here mean it approaches every point within the manifold, as in the ergodicity assumption, or does it mean described by an ergodic function? I realize the latter implies the former, but what I am driving at is the behavior vs. the formalism.
Not sure.