I think the boundary factorization into active and passive is wrong.
Are you sure? The informal description I gave for A and P allow for the active boundary to be a bit passive and the passive boundary to be a bit active. From the post:
the active boundary, A — the features or parts of the boundary primarily controlled by the viscera, interpretable as “actions” of the system— and the passiveboundary, P — the features or parts of the boundary primarily controlled by the environment, interpretable as “perceptions” of the system.
There’s a question of how to factor B into a zillion fine-grained features in the first place, but given such a factorization, I think we can define A and P fairly straightforwardly using Shapley value to decide how much V versus E is controlling each feature, and then A and P won’t overlap and will cover everything.
Oh yeah, oops, that is what it says. Wasn’t careful, and was responding to reading an old draft. I agree that the post is already saying roughly what I want there. Instead, I should have said that the B=AxP bijection is especially unrealistic. Sorry.
Why is it unrealistic? Do you actually mean it’s unrealistic that the set I’ve defined as “A” will be interpretable at “actions” in the usual coarse-grained sense? If so I think that’s a topic for another post when I get into talking about the coarsened variables Vc,Ac,Pc,Ec…
I mean, the definition is a little vague. If your meaning is something like “It goes in A if it is more accurately described as controlled by the viscera, and it goes in P if it is more accurately described as controlled by the environment,” then I guess you can get a bijection by definition, but it is not obvious these are natural categories. I think there will be parts of the boundary that feel like they are controlled by both or neither, depending on how strictly you mean “controlled by.”
Thanks, Scott!
Are you sure? The informal description I gave for A and P allow for the active boundary to be a bit passive and the passive boundary to be a bit active. From the post:
There’s a question of how to factor B into a zillion fine-grained features in the first place, but given such a factorization, I think we can define A and P fairly straightforwardly using Shapley value to decide how much V versus E is controlling each feature, and then A and P won’t overlap and will cover everything.
Oh yeah, oops, that is what it says. Wasn’t careful, and was responding to reading an old draft. I agree that the post is already saying roughly what I want there. Instead, I should have said that the B=AxP bijection is especially unrealistic. Sorry.
Why is it unrealistic? Do you actually mean it’s unrealistic that the set I’ve defined as “A” will be interpretable at “actions” in the usual coarse-grained sense? If so I think that’s a topic for another post when I get into talking about the coarsened variables Vc,Ac,Pc,Ec…
I mean, the definition is a little vague. If your meaning is something like “It goes in A if it is more accurately described as controlled by the viscera, and it goes in P if it is more accurately described as controlled by the environment,” then I guess you can get a bijection by definition, but it is not obvious these are natural categories. I think there will be parts of the boundary that feel like they are controlled by both or neither, depending on how strictly you mean “controlled by.”
Forcing the AxP bijection is an interesting idea, but it feels a little too approximate to my taste.