Bio Mirror / Memory, Motor Control, and Embodiment
Motor Cortex and the Degrees-of-Freedom Problem
More joints than any task requires, and yet movement is stereotyped. Something is choosing within the null space.
The structure
Primary motor cortex projects to spinal motor circuits, partly through direct corticomotoneuronal connections in primates. It is somatotopically organized, though the map is far messier than the classical homunculus suggests, with overlapping representations better described as encoding movements than muscles. Premotor and supplementary motor areas sit upstream, and spinal circuits below implement reflexes and pattern generators that operate without cortical involvement.
The function it dictates
Motor cortex converts intended movement into descending commands, and the population code described earlier is how that intention is represented. The system faces Bernstein's degrees-of-freedom problem: the body has vastly more independent degrees of freedom than any task specifies, so an infinity of joint trajectories would accomplish a given reach. Yet movements are stereotyped — reaches follow smooth, roughly straight hand paths with bell-shaped velocity profiles across subjects. Some criterion is selecting among the available solutions, with minimum jerk and minimum end-point variance among the leading proposals. Layered control is also visible: spinal reflexes handle fast perturbations locally, without waiting for the cortex.
The mirror in AI
Overparameterized networks face the same structure: many parameter settings fit the training data equally well, and which one you land on is determined by implicit biases of the optimizer rather than by the loss. Redundancy resolved by an unstated secondary criterion is the same shape of problem, and in both cases identifying the criterion is harder than observing that one exists.
The mirror in robotics
Null-space projection on a redundant manipulator is the engineering answer to Bernstein's problem: achieve the task with the pseudoinverse, then use the remaining freedom for a secondary objective. The biological question — which secondary objective is the nervous system using? — is the same question a robotics engineer answers explicitly when they choose one, and biology has not told us its answer yet.
Biological actuators are muscles: nonlinear, fatiguing, with intrinsic spring-like properties that solve part of the control problem passively before any neural signal is involved. This is embodied computation — the mechanics do work the controller would otherwise have to do. Rigid robots with stiff geared joints have almost none of this, which is why compliant actuation is an active research area. The controller's difficulty depends on the body it controls, which is the strongest possible statement of structure dictating function.
Open questions
- What cost function does the nervous system actually minimize when selecting a trajectory?
- How much of biological motor competence is offloaded to muscle mechanics rather than computed?
Further reading
- Bernstein, The Co-ordination and Regulation of Movements (1967)
- Todorov & Jordan, "Optimal feedback control as a theory of motor coordination" (2002)