Constructing Space: How a naive agent can learn spatial relationships by observing sensorimotor contingencies

The brain sitting inside its bony cavity sends and receives myriads of sensory inputs and outputs. A problem that must be solved either in ontogeny or phylogeny is how to extract the particular characteristics within this "blooming buzzing confusion" that signal the existence and nature of physical space, with structured objects immersed in it, among them the agent's body. The idea that spatial knowledge must be extracted from the sensorimotor flow in order to underlie perception has been considered by a number of thinkers, including Helmholtz, Poincare, Nicod, Gibson, etc. However, little work has considered how this could actually be done by organisms without a priori knowledge of the nature of their sensors and effectors. Here we show how an agent with arbitrary sensors will naturally discover spatial knowledge from the undifferentiated sensorimotor flow. The method first involves tabulating sensorimotor contingencies, that is, the laws linking sensory and motor variables. Second, further laws are created linking these sensorimotor contingencies together. The method works without any prior knowledge about the structure of the agent's sensors, body, or of the world. We show that the extracted laws endow the agent with basic spatial knowledge, manifesting itself through perceptual shape constancy and the ability to do path integration. We further show that the ability of the agent to learn all spatial dimensions depends on the ability to move in all these dimensions, rather than on possessing a sensor that has that dimensionality. This latter result suggests, for example, that three dimensional space can be learned in spite of the fact that the retinas are two-dimensional. We conclude by showing how the acquired spatial knowledge paves the way to building the notion of object.
Alexander Terekhov was born in Moscow, Russia in 1981. He received his B.S. (2003) and Ph.D. (2007) in Applied Mathematics from the Moscow State University. His early work was mainly focused on biomechanics and control of human movements. Being a postdoc at Penn State (2007-2008) he has identified the uniqueness conditions for inverse optimization problem. This result was used to develop an algorithm for cost functions identification, which was applied to various human motor activities in healthy population as well as in patients. In 2008 he switched to engineering and joined Movicom Ltd in Moscow to develop a system for aerial coverage of sport events which is being used at Winter Olympics 2014. In 2009 he has made a sharp turn in his career by switching to the perception studies, at first to haptics, where he contributed to psychophysical and neurophysiological studies, and later to sensorimotor theory in general. He is one of the main developers and popularizers of the formal sensorimotor theory of perception. Currently he works as a postdoctoral fellow at the Paris Descartes University where he studies how naive agents (biological or artificial) can learn such fundamental perceptual notions as "space', "body', "object', "tool', "color', etc.