Hi Natesh,
sorry about the names! I am a slave of rhymes, and tend to map together all what sounds similar. Actually it's even worse, I also cluster faces together. By all means, I must learn to represent information more injectively...
Yes, sure, as I see it, it may well happen in the brain of the observer. There are many possible settings, which I discuss below. But in all settings, ascribing agency (as I understand it) requires an entropy-reducing mapping. If the mapping is not injective, it may still be interesting or useful for the observer, and he or she may still make a valuable acquisition in their life by learning the mapping. But I can hardly relate this operation with perceiving a system that seeks to achieve a "goal". For me, a goal is something that tends to be reached irrespective of factors that tend do interfere with its accomplishment. That is why I require the non-injectivity: the putative obstacles are a collection of input conditions, that are supposed to be overcome by the goal-seeking agent.
Now for the variable settings.
One option is: I am the observer, and I receive information of the behavior of some external system (say, a replicating DNA molecule outside me), and by defining the system under study in some specific way, I conclude that there is some goal-oriented behavior in the process.
Another option is: I am given some information which I represent in my head, and I perform a certain computation with that information, for example, the AND gate you mention. The computation happens inside my head. But I also have observers inside my head, that monitor what other parts of my head are doing. For one such observer, what the other end of the brain is doing, acts as "external" (in all computations except for self-awareness, which is the last part of my essay). One such observer can assign agency (if it wants to!) to the computation, and conclude that the AND gate (inside my head!) "tends" to reduce the numbers 1, 2, 3 to the digit 0 (or whichever implementation we choose). A weird goal for an agent, but why not.
All I am claiming is: goal-directed behavior does not exist without an observer that tends to see things in a very particular way: as non-injective mappings. I am not claiming that this is the only thing that can be learned by a plastic system (one-to-one mappings can also be learned). I am not claiming that the only thing that can be done with a non-injective mapping is to arrogate it with agency and goals. There are many more things happening in the world that may be good to learn, as well as in the brain of the observer. And there are many more computations to do, other arrogating agency. My only point is: if we see a goal (inside or outside us), then we have trained ourselves to interpret the system in the right manner for the goal to emerge. The goal is not intrinsic to nature, it is a way of being seen.
Not much, just one tiny point. Or perhaps, just a definition. If you look through the essays, there are as many definitions of "goal", "agent" and "intention" as authors...
> my main contribution is tying it all together in a physical sense
Yes, and that is precisely why it is so great! And perhaps you are right, within your framework, what so far has been presented as a mere description of the critical brain, now can be seen as the natural consequence when certain physical conditions are assumed. I do appreciate that.
Anyhow, time to rest! buenas noches!
inés.