So there are aspects of the pool table and its wider environment that are relevant to the control of rolling. These are represented by the feedback function and disturbances in the closed loop diagram of each of the agents. What about the other features of the pool table and the environment and their physical and dynamic relationship with one another? In other words, without a model of the environment in the simulation, how do we know a priori which are going to come up as part of each agent’s feedback function and their impact as disturbances on one another in real time? When I helped our coder to build a baseball catching simulation environment, the hardest bit was the formula that simulated (in a simplified way of course) the physics of the pitch, the ball and the agent,so that we could both view this from a bird’s eye perspective AND so the data was going to the agent from its first-person perspective for the PCT model. Note that this simulated physical world was not presumed to occur in any agent; it is in the computer; and it is forged purely for the goal of making a computer simulation; it is not needed for actually catching balls in real life. As Bill proposed, it is part of the assumptions of PCT that we do not need to know, objectively, or even model the physical world; however this luxury is not afforded to a computer coder tasked with building a simulation, IMO!
This is a very long post so I’ll just reply to the things that I think are important (to me anyway).
Bill made the feedback function, k.e, linear and static (constant) for didactic purposes. But k.e can certainly be non-linear, as demonstrated in my “What is Size” demo. And k.e can vary. One of Bill’s earliest publications –A Feedback Model for Behavior: Application to a Rat Experiment (1971); reprinted in the book Living Control Systems (1989) – describes how control theory explains the effect of varying the feedback function in an operant conditioning experiment. And I’ve developed tracking tasks where k.e varies throughout the task, demonstrating how PCT explains the effect of these variations on control.
The firing rate signals (p, r and e), as well as the perceptual and output functions (k.i and k.o) that transform physical variables into firing rates, are the theoretical part of the control theory model. This theory is built to explain observed behavior, which, most importantly, are controlled variables (q.i). Thus, the conversion of physical variables into neural signals (and vice versa) is theoretical. But, since the PCT model of behavior has been so successful, we expect to eventually observe this transformation in studies of control (which, I believe, is what Henry Yin and his students have been doing).
There is no such stipulation in PCT, which has successfully been used to explain the controlling done by living control systems in the laboratory and the field.
The effect of disturbance and system output on q.i (the controlled variable) are represented by different environmental functions because they affect q.i via different environmental paths. Just look at a simple tracking task. The effect of the disturbance, k.d, on q.i (the distance between cursot and target) is mediated solely through the electronics of the computer program; the effect of system output, k.e, on q,i is mediated by both the electronics of the computer program AND the physics of the path from hand movement (system output, q.o) to computer electronics via mouse or keypad.
I will skip a lot here. I’m not sure what point is being made but it involves dimensional analysis which, I think, is made moot by understanding that the signals and functions of the model control system are theory aimed at explaining the behavior of the physical (behavioral) variables that are observed.
I think the “environmental segments” you speak of are the tools, such as cranes and computers, that are invented and manufactured by groups of people and manifestly increase the effectiveness and reliability of our control of things like the height of the buildings we can build and the speed of calculations we can do. I agree that “disclosing and enabling this mastery” is an important task for PCT. But I think this can best be achieved by following the scientific path set out by Bill Powers – and described in my book The Study of Living Control Systems (SCLS) – for getting a scientific understanding of the controlling done by living control systems. SCLS describes how the knowledge we get about the controlling done by individual organisms can contribute to our understanding of what you call “collective control” and what I call “social control”
I’m not sure what you mean to say here. Why do you think we have to know a priori which aspects of the environment are going to come up as part of each agent’s feedback function and how they might impact as distutrbances?
My experience is that we only have to know which aspects of the environment are relevant to any particular example of behavior (controlling) before building a simulation (I prefer the term “model”) of it. This includes knowing how the feedback function and disturbances change over time so that these variations can be included in the simulation.