  The question of the nature of space around us has occupied thinkers since the
dawn of humanity, with scientists and philosophers today implicitly assuming
that space is something that exists objectively. Here we show that this does
not have to be the case: the notion of space could emerge when biological
organisms seek an economic representation of their sensorimotor flow. The
emergence of spatial notions does not necessitate the existence of real
physical space, but only requires the presence of sensorimotor invariants
called `compensable' sensory changes. We show mathematically and then in
simulations that na\"ive agents making no assumptions about the existence of
space are able to learn these invariants and to build the abstract notion that
physicists call rigid displacement, which is independent of what is being
displaced. Rigid displacements may underly perception of space as an unchanging
medium within which objects are described by their relative positions. Our
findings suggest that the question of the nature of space, currently exclusive
to philosophy and physics, should also be addressed from the standpoint of
neuroscience and artificial intelligence.
