Abstract
Studies of motor adaptation to patterns of deterministic forces have revealed the ability of the motor control system to form and use predictive representations of the environment. One of the most fundamental elements of our environment is space itself. This article focuses on the notion of Euclidean space as it applies to common sensory motor experiences. Starting from the assumption that we interact with the world through a system of neural signals, we observe that these signals are not inherently endowed with metric properties of the ordinary Euclidean space. The ability of the nervous system to represent these properties depends on adaptive mechanisms that reconstruct the Euclidean metric from signals that are not Euclidean. Gaining access to these mechanisms will reveal the process by which the nervous system handles novel sophisticated coordinate transformation tasks, thus highlighting possible avenues to create functional human-machine interfaces that can make that task much easier. A set of experiments is presented that demonstrate the ability of the sensory-motor system to reorganize coordination in novel geometrical environments. In these environments multiple degrees of freedom of body motions are used to control the coordinates of a point in a two-dimensional Euclidean space. We discuss how practice leads to the acquisition of the metric properties of the controlled space. Methods of machine learning based on the reduction of reaching errors are tested as a means to facilitate learning by adaptively changing he map from body motions to controlled device. We discuss the relevance of the results to the development of adaptive human-machine interfaces and optimal control.