Q_Goest said:
Let’s talk about what these models are for a minute because I think the philosophy of why they are the way they are is being overlooked.
It's great that you are willing to get into the details of a defence of your view. And my reply is that you are missing the wood for the trees

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What you are highlighting here is simply the fact that allowing a system to go to global equilbrium allows you then quite properly to drop the global causes from your model because now you are only interested in what can change - the local variables, the local fluctuations, the local events. This is what reductionist modelling is all about.
It is right there in Newton's three laws of motion. The first two laws atomised the notion of local action into a force and a mass. Mass could have intrinsic motion which was inertial, and that made any globally observable change in motion the result of an atomistic force (a force vector).
So already in the first two laws, Newton's great reductionist simplification was to equilibrate away the global spacetime backdrop. Taken the greek atomist's notion of the void, he said the background exists, but it is causally inert. It is simply an equilbrated or unchanging stage upon which there is a localised play of atoms - atoms of mass and atoms of force.
Then to make this highly reduced view of reality fly, he had to introduce his third law of action~reaction. For every forceful action, there is an equal and opposite forceful reaction - a little matching localised anti-vector.
Patently the reaction vector is not actually a symmetric entity. Instead it sums up all the contextual constraints that are found to impinge on the locale. If you push against the wall, then it is not just several square inches of wall that pushes back. It is the building, the planet to which it is attached, the gravity fields which affect the planet, etc.
The third law is the local equilbrium correction! The first two laws removed the generalised background and the third quietly accounts for any disturbances of the global state by localising it to another linear and atomistic event - a reaction vector.
So this is the "philosophy" of physics - or at least the highly successful modelling strategy on which all mechanical thinking is based. Equilibrate away the global causes, the context that constrains, and you can then just describe reality in terms of local atomistic entities and local forceful changes. Just treat reality as a collection of actions happening in a mute void.
Now FEA just repeats the same exercise. If you can't equilibrate away the whole global story at once, then break the job up into a suitably grained set of compartments. Create localised equilibration stories that add up with suitably low error to give you a globally equilibrated model.
Does this then say that global downward acting constraints don't exist? Or that reductionist modelling finds ever more clever ways around them?
Now this thread was about the neurology of freewill. (Not modelling neurons with FEA).
The kind of systems that FEA is suitable for modelling is stuff like fluid dynamics. This is the non-living world where global constraints are holonomic. We are safe to presume the constraints or boundary conditions are at equilbrium and unchanging. Locally the aircraft wing may be subject to some complexity due to emergent turbulent features. But generally temperature, pressure, material strengths, viscosity, are a stable backdrop to the model.
There is not a local~global interaction so that for example the flex of the wing causes a tropical storm that sends a bolt of lightning that changes the material strength of the wing, or even just causes a dramatic pressure drop in the vicinity of the wing. No, the FEA analysis rules out interactions across scale by choice.
But for living systems, we are now talking about systems that have non-holonomic constraints. They do have the informational machinery (such as genes, words, membranes, action potentials, etc) to control their own boundary conditions or downwards acting constraints.
So to model living systems, we have to model that ability to change the global constraints - for meaningful reasons. Which is why I keep challenging you to reply to the literature on top-down selective attention and its power to reshape local neural receptive fields.
You would rather keep the discussion focused on the most reductionist models of single neurons that you can find. And yes, you can take what a receptor pore does and model it as an isolated mechanical device sitting in a stable equilibrium world utterly unlike the real world of a receptor pore. It will tell you something about the local degrees of freedom that the device might have. But it cannot then tell you anything about the kinds of global constraints that act on those degrees of freedom. You literally cannot in principle see them.
Now you can do a Blue Brain exercise and throw a lot of devices together and
simulate - see what kind of global organisation arises to constrain a network of artificial neurons. If you have built your simulation with local components that can change their behaviour (as is familiar with neural nets with nodes that can adapt their local weights), then you can start to get a realistic development of local~global interactions.
But a simulation is NOT a model. The results you are celebrating are the observable output, not an axiomatic input. You are demonstrating an effect, not a cause.
A proper model in this context would be one where you have a handle on both the bottom-up and top-down sources of causality and so can compute the outcomes directly - predict the observable state rather than merely discover it post-hoc.
So this is why systems modelling is different from reductionist modelling. Reductionism wants to deal only in local causation (and so finds ways to equilibrate away any global effects to make them a "void" - an unchanging backdrop). Systems modelling recognises that global constraints can be an active part of the mix and so seeks to include them in the model.
This is of course very difficult to do as yet. In fact it could be another 20 to 30 years before we have the real breakthroughs in this area. Everyone thought fractals, chaos theory and non-linear dynamics was some kind of mathematical modelling revolution. But that was just a first ripple of the change that could come.