  Humans are extremely swift learners. We are able to grasp highly abstract
notions, whether they come from art perception or pure mathematics. Current
machine learning techniques demonstrate astonishing results in extracting
patterns in information. Yet the abstract notions we possess are more than just
statistical patterns in the incoming information. Sensorimotor theory suggests
that they represent functions, laws, describing how the information can be
transformed, or, in other words, they represent the statistics of sensorimotor
changes rather than sensory inputs themselves. The aim of our work is to
suggest a way for machine learning and sensorimotor theory to benefit from each
other so as to pave the way toward new horizons in learning. We show in this
study that a highly abstract notion, that of space, can be seen as a collection
of laws of transformations of sensory information and that these laws could in
theory be learned by a naive agent. As an illustration we do a one-dimensional
simulation in which an agent extracts spatial knowledge in the form of
internalized ("sensible") rigid displacements. The agent uses them to encode
its own displacements in a way which is isometrically related to external
space. Though the algorithm allowing acquisition of rigid displacements is
designed \emph{ad hoc}, we believe it can stimulate the development of
unsupervised learning techniques leading to similar results.
