Interesting post! I think you’re right that entanglement is “a thing”, and that there isn’t a clean pre-existing concept that encapsulates it. For instance the idea of information rate/Shannon entropy is missing the concept of what the information is about; in a video feed of a chess game the pixels representing the pieces are far more important than the pixels representing the table.
To add to your set of candidates for formalising the idea of minimum entanglement: I started going down a similar track in my sequence about Interface-bound agents, and ended up finding ideas from Control theory quite useful. For instance, there is the concept of (Hamilton-Jacobi) reachability analysis, which deals with whether a target state of a system (e.g. a self-driving car reaching a destination) is reachable from an initial state. You could potentially treat this target state as “the task being completed” (or “the unsafe state being avoided”), and fiddle with <something representing allowed actions> and <something representing input information> and find the boundary at which the target state is unreachable.
E.g. in the self-driving car case: You could suppose an agent that can provide steering input at 1 Hz vs 10 Hz (representing lower and higher entanglement in your verbiage). You might show that at 1 Hz it’s impossible to avoid unsafe states because the external environment can dynamically evolve faster than the agent can react (another car can steer into them), but at 10 Hz it is possible. This would establish a minimum entanglement somewhere in that range.
Ty! The point about control and reachability makes sense, and sounds like it might be a part of the right story here. It will still need some tweaks or additions though. For example, we would intuitively expect that a self-driving car without any cameras or sensors isn’t entangled enough to do its job. But in terms of reachability, everything is still fine—the car could give the right set of commands that would get it safely across town, so the safe states are technically reachable.
Interesting post! I think you’re right that entanglement is “a thing”, and that there isn’t a clean pre-existing concept that encapsulates it. For instance the idea of information rate/Shannon entropy is missing the concept of what the information is about; in a video feed of a chess game the pixels representing the pieces are far more important than the pixels representing the table.
To add to your set of candidates for formalising the idea of minimum entanglement: I started going down a similar track in my sequence about Interface-bound agents, and ended up finding ideas from Control theory quite useful. For instance, there is the concept of (Hamilton-Jacobi) reachability analysis, which deals with whether a target state of a system (e.g. a self-driving car reaching a destination) is reachable from an initial state. You could potentially treat this target state as “the task being completed” (or “the unsafe state being avoided”), and fiddle with <something representing allowed actions> and <something representing input information> and find the boundary at which the target state is unreachable.
E.g. in the self-driving car case: You could suppose an agent that can provide steering input at 1 Hz vs 10 Hz (representing lower and higher entanglement in your verbiage). You might show that at 1 Hz it’s impossible to avoid unsafe states because the external environment can dynamically evolve faster than the agent can react (another car can steer into them), but at 10 Hz it is possible. This would establish a minimum entanglement somewhere in that range.
Ty! The point about control and reachability makes sense, and sounds like it might be a part of the right story here. It will still need some tweaks or additions though. For example, we would intuitively expect that a self-driving car without any cameras or sensors isn’t entangled enough to do its job. But in terms of reachability, everything is still fine—the car could give the right set of commands that would get it safely across town, so the safe states are technically reachable.