Dear Ganesh,
I suppose, you like critical examination of your essay. I must confess that I really could not follow the mathematical derivation entirely, may be due to my own limitation. But, I will grant the concluding remarks by you based on those mathematical expressions. I read this essay twice over a fortnight.
I take the following statement as your motivation. "Open physical systems with constraints on their finite complexity, that dissipate minimally when driven by external fields, will necessarily exhibit learning and inference dynamics."
In Fig.1b, at the first stage we see the external input coming, which is mixed with the prediction of the same coming from higher level, and up goes the 'prediction error'. This is OK, but from the next stage onwards, we see that the predictive estimator (processor/comparator) receives only the prediction error from lower level, and feedback of prediction from the next higher level. A prediction from higher level cannot be compared with the prediction error that took place at the lower level, it would make no sense. A predictive estimator must receive appropriate modular value derived (or predicted) from observation from lower level in order to be able to compare or generate prediction error. I suppose the direction of flow is incorrect. In fact, a predictive estimator should generate a prediction error internally from the predictions coming from both sides, and use the error to predict for the next higher level as well as for the lower level, which must be appropriate for both sides independently. Natesh, in cases of processing systems, always take the limiting cases to test the hypothesis. For example, when the system makes first observation, at the lowest level there is no prediction coming back from the higher level to compute the error. Similarly, at the highest level no prior action to make a correction with only incoming prediction error. Furthermore, this is also to be noted, in any realistic system, a module may receive input from multiple modules and send its output to multiple modules.
"The joint system SA is a quantum system with two components." From this I also gather a classical system might not be able to achieve what a quantum system does, otherwise, there was no need to classify it as quantum. But then, later on I notice that you identify neo-cortex as S, and A as motor-cortex. I trust, you are equating neo-cortex and motor-cortex as quantum systems, a hard to gulp inference.
"Agency is the capacity of a system/entity/agent/organism to act on it's environment." And if all physical entities satisfy this definition of agency, then I do not see the need of a separate definition taking the attention of some readers on the side of psychology. Being a part of environment, any reaction to the physical context is equivalent to altering the environment. But when you say, "(I am imbuing system A with agency, but not with a specific goal or purpose)", it is as if there could be a system without agency. As you defined earlier, all physical entities are natural agents. So, by stating this, you are priming a reader with certain preconceived notion of agency. Again when you say, "The optimal encoding of R0 in SA is a trade-off between exploiting known information and exploration", where does the exploration come from? I understood that A would simply react physically as per the input from S. But this reaction is aimless. The term 'exploration' also achieves the same goal of priming the reader with certain kind of agency, reinforcing the sense. "While the state of A depends upon balancing exploration with prediction", further enhances this sense.
Even in cases where the system SA is evolving to predict the incoming input correctly, it is just a prediction of the system R, where is the purposeful goals for self sustenance or whatever coming into picture? Therefore, I suppose, one has to design an extra element in SA system such that S tries to optimize on certain parameter, to signal A to act in a particular manner. Otherwise why would S set the task of throwing a ball in any manner, let alone trying to dunk. The purpose also has to be artificially coded.
"Due to these past inputs, let the state of the system A (motor cortex) that is most likely given the prediction-exploration trade off, corresponds to the action "throw the ball." How did the first input come, and what would be any reason to throw the ball at all?
"We will define sense of agency (SA) as the pre-reflective subjective awareness that one is initiating, executing, and controlling one's own volitional actions in the world."
"Thus the joint state of SA=("see ball being thrown","throw ball") as the ball is thrown will explain the sense of agency, the awareness of an action being performed as it being performed." The association of an awareness of an action being performed to the system SA is in your/our mind. I do not see where and how exactly this sense of awareness is represented in SA. Then you rain statements like, "For example, in the case of visual perception of a face, the higher levels make predictions corresponding to say, 'seeing a face'." I can accept that the system may have representation of all the parts described, but I do not see how 'seeing a face' is represented.
The masterpiece of all statements is, "Similarly predictions made in the higher levels of the hierarchical model in SA, under the minimal dissipation hypothesis, would correspond to the higher level intention of the action-sense of agency (like say "win game" in our example)...."
As I said about your system that goals and purposes would not arise unless especially coded in the system, the same applies to all systems. In a system like brain, such a coding is achieved by the process of natural evolution in the Darwinian sense. You may quote me on any statement here.
Then comes the attribution of ownership, "Crucial to this process though, is a sense of ownership that the system will learn over time about what is within the system's control and what is beyond that." Natesh, what you could see as a logical extension from your own perspective of a relation of an actor and its acts, you assign that to the system.
"... arguments have been made for inherent intentionality in every perception event [12]. We can view the upper levels of the hierarchical model in the brain as the source of only intentions and make a strong case that intention is physical."
Imagine if we say, "intention is a specification of an information represented in a physical system", then it does not remain physical, yet it has origins in physical systems. But then, if we insist on the paradigm of 'intention is physical', then there must be a way to measure it. Though I trust what you may have meant is 'intention' arises from physical function of the universe, it does not require or depend on any non-physical phenomena.
As a concluding remark, I am going to consider a stone as a system S embedded in surrounding heat bath, the air in thermal equilibrium. A puff of wind blows that applies certain force on the stone, but the stone remains undisplaced, and no exchange of heat (energy) takes place, i.e., the stone dissipated minimum energy. In such a scenario, what learning has taken place in S that it can predict about wind? So, any development from minimum dissipation hypothesis must conform to this limiting case. I suppose, you may require some other constraint in addition.
In an exchange with Ellis, you wrote, "Thanks for a delightful exchange. I am enjoying myself!!" I consider you a system like SA, so which component of S and A is referring to itself as an enjoyer, and which component is being enjoyed? And why would both be claimed to be as oneself?
I feel favorable to consider reasonably well rating for clever usage of the terms so wisely that the reader might end up with the notion of emergence of goals from minimal dissipative hypothesis. Mr Natesh, you are a magician too.
Rajiv
