atyy said:
Is the main point that free energy minimization is essentially maximization of entropy subject to the constraint of constant of energy, so the two poles are entropy and energy, with both poles equally fundamental?
Sort of. A first clarification may be to swap the dichotomy of maximal~minimal for something more appropriate, like extremal~optimised. Otherwise the language tends to get in the way - as in dissipative structure theory where people can't decide whether they are talking about a maximum or minimum entropy production principle.
So the underlying theory, from a systems perspective is that in any situation you have the two extremal poles that separate the subject under discussion. The differentiation step. Then you have the complementary process of the synergistic mixing or integration, which is the optimisation action.
In terms of the thermodynamics of living/mindful structures - which is what we are talking about here with Friston - the opposing extremes would be complete certainty and complete uncertainty. Then the optimisation is the search for a productive balance of the two, over the spatiotemporal scales relevant to an organism. So for instance, we both want to know things for sure in a "right now" way and a "long term" way. Reducing uncertainty for one scale could increase it for the other. Therefore some kind of balance needs to be struck.
Also, uncertainty is about degrees of freedom still yet to be disposed. You can't teach an old dog new tricks, as they say. So that is another reason why a balance would want to be struck between a capacity to learn, to be creative due to uncertainty, and to be able to impose a certainty on thought and perception.
You can see I'm talking about all this in information theoretic terms. And that is the advantage of thermodynamics - its straddles the divide pretty well. So the usable energy~dissipated energy distinction in material reality can be formally equated to a certainty~uncertainty distinction in our subjective view. The maths of one can be used to describe the maths of the other.
And the relationship goes even deeper if you follow the infodynamics approach to dissipative structure because information is being used to regulate dynamics. Minds have a reason to exist - it is to control their worlds.
Anyway, the thing to get perhaps is that standard thermodynamics seems to say that the goal of reality is to entropify gradients. If a source of energy/order can be dissipated to waste heat/disorder, then it must be.
This does seem like a simple extremum principle - thou shalt maximise disorder! But it also hides the larger systems story. There have to be the two extremes to have a gradient (an initial state of order, a final state of disorder). And then the disordering has to actually happen in time. So there is an optimal rate for the process - which is the fastest possible perhaps, but as we can tell from the long history of our universe, not actually instantaneous.
Then from this baseline simpliciity, complexity can arise. Any region of the universe that is can accelerate the entropification rate can also afford a complementary measure of deceleration. Or in other words, life can arise as order (negentropy) because it is increasing the local disorder (entropy). And the way it does this is by capturing energy and turning it into stored information - the physical structure that is a body, its genes, its neural circuits.
So dissipative structure dips into the flow of entropification to build an informational self that can exist because it raises the general rate of entropification.
Now, there is a lifecycle balance to be optimised here as said. A living system is a mix of it genes and its metabolism, its information and its dynamics. It needs to be able to regulate its world, but there is a danger in trying to over-regulate.
In theoretical biology, Stan Salthe models this dilemma as the canonical lifecyle of immaturity, maturity, senescence. A gastrula is immature - lightly constrained, fast growing/entropifying, still many degrees of freedom open to it. A mature organism has a more structured balance - it no longer grows, but still repairs, still learns. Then a senescent individual is overloaded by informational constraints - it is well-adapted to its world, but in a now rigid and brittle fashion. It can no longer respond to sharp environmental perturbation and is subject to catastrophic collapse and material recyling.
Sorry, I seem to have strayed a long way from a direct answer. But I am trying to stress that there is first a rich thermodynamical basis now to life and mind science. And this base is natually a hybrid discourse as it can be talked about in both material and informational terms.
The complexity of life/mind is that it actually physically connects the material and the informational in a literal sense. It transcribes energy/matter into informational structure or memories - which are used in turn to control that realm of energy/matter (for the purposes of the second law of thermodynamics).
And then, all this fits into a systems perspective where you expect to find a causal organisation of exactly this type. You expect to find a fundamental division into complementary concepts, a differentiation that creates a spectrum of possibility, that then gets integrated to create a state of actuality.
So Friston has recognised that many of the most promising neuroscience models share something in common. Life and mind exist by playing the game of accelerating entropification. And they are by definition themselves a matching deceleration of that universal baseline entropification rate. But that can only happen by putting aside energy some place the rest of the universe cannot get at it - storing it as information, the configurational entropy of genes, neurons, cells, bodies, that can then act as material constraints on the world (via everything from the production of enzymes to the choice to reach out and stuff food in your mouth).
Now that in turns sets up the game of storing the optimal amount of information. Too much and scenescence beckons. Too little, and immature behaviour results. There has to be a balance that is optimised continually, dynamically.
Friston boils this down to the dichotomy of expectations vs surprise. And over a modestly long run (which in fact is just dealing with the mature phase of an organism's life cycle) the goal is to do the most with the least. To reduce uncertainty as much as is useful (rather than as much as is possible) while storing the least amount of information (ie: creating the most generalised anticipations).
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your geometric heart). However the evolution parameter is not time, but resolution scale. Would you consider that a dynamical system?
