 Poincaré conceives of our perception of objects as a combination of motor and visual impressions that are at first non-spatial. In order to classify these sensations, which only appear because of the movement of our bodies, Poincaré says we introduce “sensible space” as a category “of our understanding” that is not physical space and does not even have a metric, meaning that “it involves no idea of measurement” (Poincaré 1898). Sensible space is a necessary condition for our understanding of our place in the world, that is, for our understanding of the objects around us, their relations and how they move, but it is not a form of our sensibility, since individual sensations can exist without it (Poincaré 1898: 3). Thus sensible space can be seen as an example of a natural hypothesis. We introduce a metric to this space in order to measure distance by using the language of group theory, that is, the mathematical study of abstract algebraic structures. Groups serve as a tool of reasoning about representations of muscular sensations. We can choose a group (or sub-group) which corresponds to the geometry of Euclid, Lobachevskii or Riemann to describe space. Poincaré proposes a criterion of choice between the three possible geometries, positing