How Babies Learn to Move: An Applied Riemannian Geometry Theory of the Development of Visually-Guided Movement Synergies

Planning a multi-joint minimum-effort coordinated human movement to achieve a visual goal is computationally difficult: (i) The number of anatomical elemental movements of the human body greatly exceeds the number of degrees of freedom specified by visual goals; and (ii) the mass–inertia mechanical load about each elemental movement varies not only with the posture of the body but also with the mechanical interactions between the body and the environment. Given these complications, the amount of nonlinear dynamical computation needed to plan visually-guided movement is far too large for it to be carried out within the reaction time needed to initiate an appropriate response. Consequently, we propose that, as part of motor and visual development, starting with bootstrapping by fetal and neonatal pattern-generator movements and continuing adaptively from infancy to adulthood, most of the computation is carried out in advance and stored in a motor association memory network. From there it can be quickly retrieved by a selection process that provides the appropriate movement synergy compatible with the particular visual goal. We use theorems of Riemannian geometry to describe the large amount of nonlinear dynamical data that have to be pre-computed and stored for retrieval. Based on that geometry, we argue that the logical mathematical sequence for the acquisition of these data parallels the natural development of visually- guided human movement.