 Poincaré argued that the mind quickly realises that it can compensate for certain kinds of motions that it sees. If a glass comes towards you, you can walk backwards in such a way that the glass seems unaltered. You can do the same if it tilts or rotates. We come to master a store of these compensating motions, and we realise that we can follow one with another and the result will be a third compensating motion. On this basis we come to distinguish displacements (both our bodily displacements and displacements of objects) from other kinds of change, i.e., alterations for which we cannot generate compensating motions, such as the motion of the wine in the glass as it swirls around, or a change in its colour. Most importantly, the displacements form a mathematical structure called a group. In this way the mind comes to form the concept of a rigid body motion, and we elaborate a clear conceptual understanding of space on the basis of the group of motions.