This is my first stream of consciousness writing post. I've decided to try to do this daily, or at least weekdaily, in the morning to just have a place to put ideas down on paper. I've been thinking a lot about motor control and motor learning. What are the kinds of mechanisms the brain needs to do this? Seems obvious that control theory is relevant here - should probably delve into some of that literature. There is so much neuroscience literature to look at first though, it's a bit overwhelming. The big question that seems to me to remain totally unanswered is where the learning takes place. Not where in the brain but where in the computational graph so to speak. To be able to generate the right motor commands to achieve a given goal requires you to 1. know the mapping from goal to [limb] movement, and 2. the mapping from neural activity to [limb] movement. And in fact the second mapping contains two mappings in it: 2a. from neural activity to muscle contraction, and 2b. from muscle contraction to limb movement. The hard part I guess is that mappings 1 is not unique - it is not injective (surjective? I always forget...). Mapping 2b is definitely unique, but in fact it turns out under certain conditions 2a sometimes is not unique (cf. some Science paper from early 2000's).

Mapping 1 is not unique but it is obviously constrained, particularly for easy problems. You wouldn't swing your arm around your head and throw it out in front of you just to reach for a coffee mug right in front of you - that's a massive waste of energy (and possible risk of injury). So the space of muscle movements that map on to a given motor goal are certainly a subspace highly constrained already by a reasonably obvious set of cost considerations (this solves Bernstein's famous problem if you consider that your costs are only specific to the task-relevant errors - Todorov & Jordan 2002). I think mapping 1 is also highly variable, depending on the environment. If you want to reach for an object on an elevated surface, you will probably use totally different movements if the surface you are standing on is perfectly stable or out of balance.

Let me talk about one other situation: the highly contrived experimental paradigm of making reaching within a force field. This paradigm has been studied over and over again by people like Emilio Bizzi and others in the past decade as a way of investigating motor learning, or motor "adaptation" (inevitably will be more on this distinction on another post). Now let's put it in our picture of mappings 1-2a,b. The force field leads to a change in the movement produced by a given muscle activation pattern. Well shit this is a change in mapping 2b - the only one we said was unique. So now we have a twofold problem: we need (to learn) a context-specific (non-unique) mapping 1 and (presumably unique) mapping 2b.

Do we lump them together? Which of these (or both) correspond to the famous forward models allegedly found in the cerebellum etc.? Will have to get back to you on this..

My mind keeps going to model selection when I think about this context-specific mapping idea. Are we capable of learning these models on the fly? Or do we store a learned set of them that we can switch between? If the latter, we need a method for selection. This is a famously hard problem in statistics, although maybe for reasons that are not applicable here (i.e. higher complexity = higher likelihood). More on this another time!