Space as an invention of biological organisms

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

Induced current in the presence of magnetic flux tube of small radius

The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the region of nonzero magnetic field, this current is the odd periodical function of the magnetic flux. If the region inside the magnetic tube is not forbidden for penetration of electron, the induced current is not a periodical function of the magnetic flux. However in the limit $R\to 0$, where $R$ is the radius of magnetic flux tube, this function has the universal form which is independent of the magnetic field distribution inside the magnetic tube at fixed value of the magnetic flux.Comment: 5 pages, 1 figur