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 näıve 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. To illustrate the principle, consider first the sensory universe or “Merkwelt” (cf von Uexküll) of the one-dimensional agent in Fig 1. Assume (though this is not known to the agent’s brain) that its body is composed of a single photoreceptive sensor that can move laterally inside its body using a “muscle” (Fig 1A). Assume a one-dimensional environment as in Fig 1B, and assume first that it is static. If the agent were to perform scanning actions with the muscle and were to plot photoreceptor output against the photoreceptor’s actual physical position, it would obtain a plot such as Fig 1D. But it cannot do this because it has no notion, let alone any measure, of physical position, and only has knowledge of proprioception. The agent can only plot photoreceptor output against proprioception, and so obtains a distorted plot as in Fig. 1F. This “sensorimotor contingency” is all that the agent knows about. It does not know anything about the structure of its body and sensor, let alone that there is such a thing as space in which it is immersed. Indeed the agent does not need such notions to understand its world, since its world is completely accounted for by its knowledge of the sensorimotor contingency it has established by scanning. But now suppose that the environment can move relative to the agent, for example taking Fig 1B to Fig 1B’. The previously plotted sensorimotor contingency will no longer apply, and a different plot will be obtained (e.g. Fig 1F’). The agent goes from being able to completely predict the effects of its scanning actions on its sensory input, to no longer being able to do so. However, there is a notable fact which applies. Although the agent does not know this, physicists looking from outside the agent would note that if the displacement relative to the environment is not too large,