Is the Cerebellum a Neuronal Machine?

Ever since Eccles (1967), the authors, and most enthusiastically, Ito, have tried to get the computer community to endorse their analysis of the cerebellum by the creation of neural network models. That is how Ito (2012, ch.3) expresses how he felt at a symposium he and his co-authors had organized to get these specialist on board: "I was frustrated enough at the Salishan meeting to ask what else experimentalists would need to uncover before we would be able to understand the meaning of these wiring diagrams." I found his honesty quite disarming when he added: 
"Someone equally frustrated replied that the available diagrams were too simple to construct even a primitive radio, so more information was urgently needed before any meaningful model could be conceived." (my emphasis)

You can imagine Ito and his colleagues' relief when Marr came up with his theory that turned this "primitive radio" into a huge success!
But how justified were they in their relief? Even assuming that the cerebellum is exclusively concerned with movements, can we describe what happens in this part of the brain in computational terms, and still keep within the boundaries of biological plausibility?

Let me try a very general approach first.

Suppose I am shooting hoops, trying to get the ball in the basket without it touching anything else. You could say that I will need each time to adjust the "weights" controlling my muscles. And for that, I need visual information (which is certainly a form of feedback, as are the proprioceptive sensations provided by my body) that I can translate in new, hopefully more successful, movements. 

Let us assume that the feedback information "made me think" that I needed, shooting from the same position, to put more power in my movements. I will not bother for now with the question how we are able to fine-tune the intensity of our movements for them to be a little more or a little less intense, something we all can do, but concentrate on the fact that we can do that at all, however crudely. 
How do we control the intensity of our movements? How can we produce more (or less) neurotransmitters at the neuro-muscular junction?

The answer to this question may well be the key to fundamental brain functions.

Let us forget the (probably) unanswerable question of Will, and concentrate on the neural mechanisms that our will necessarily has to use to express itself.

Also, it would certainly be interesting to know if this ability of control is limited to the neuro-muscular junction. Can we, through sheer will, influence the quantity of neuro-transmitter produced at other locations in the brain which are more or less already under our control, and which do not involve muscles? Do such locations exist at all?

In a less speculative perspective:
Is there a neural mechanism to control neuro-transmitter release other than through sensory input?
In our example, the fact that I did not reach my goal, was reason enough to try again. Also, the feedback information somehow determined if the following release of neurotransmitters needed to be intensified, or reduced.

Let us assume that there is some kind of automatic reflex playing out. The feedback has, in this view, taken over the role of a direct stimulus capable of increasing or reducing the release.

Ever since the fetus becomes capable of movement, it keeps trying out its muscles. Babies, very often, look like they are working out while lying on their back. They are mapping their movements to their own intentions and sensations. By the time we can play basket ball, we are pretty well acquainted with our body and how much energy each movement approximately needs. I say approximately, because even familiar situations vary in infinite ways. Nowhere is this more obvious than when we are trying for very precise movements like shooting hoops. 
That is why professional sporters need to train so often. They need to learn configurations that are in principle infinite. If age did not take care of it, they would keep learning until the end of times. If the brain could use mathematical formulas, we would be all professional sporters by the age of 18 or less.

Assuming the existence of a memory mechanism, a database as it were, of specific movements and spatial configurations, neither demands geometrical computations nor a mysterious quantic gate in the brain.
Not even the direction of the change (more or less power) could be under the conscious (or unconscious for that matter) control of the brain. That would lead us into an infinite regress. The direction of change can, in this situation, only be an effect, never a cause. [One of the many reasons why neural networks keep George busy.]

We can now, I think, answer our question: we cannot control the amount of neurotransmitter used by each movement. That amount is an effect of the stimulation level of the muscle. It is a chemical reaction, also an effect, and never a primary cause (thank you Aristotle for this ancient but clear concept). 

Do we have then the memory of stimulation levels? That would bring us back to the matter of neural codes in a hurry!

Let me state my, speculative, view on this matter.

1) No, the brain has no way of registering stimulation levels other than by the intensity of the sensations we experience.
2) The neural record or memory of these sensations is therefore an abstract, clinical representation of the sensation, be it color, sound, or contraction of a muscle.
3) Sensations, including those concerning us here (more or less power to a movement), cannot be considered in isolation. Each sensation will be the result of a huge number of connections all though the brain, making its identification easier.
4) last, but certainly not least. Sensations that we feel different from each others have to be somehow kept apart. Even (3) could not explain all the fine distinctions between the many nuances of a same sensation. I am not sure it is a completely "physical" process in the usual sense. Memories must have a way, just like external or internal stimulations, to (re)produce those sensations.
5) We will have to rethink the concept of causal efficacy in a materialist perspective.
6) We should take example of the work of Weber. (see my thread The Brain: some problematic concepts)

If the cerebellum does not need to, or cannot compute movements, how can we then be sure that is has something to do with movements at all, except in a very general, indirect way?