 In Helmholtz’s early work, and in some later essays, perceptual space is a mental generalization of our orientation with respect to objects in space. We learn the general properties of space by discovering what spatial properties do not change when objects move, and when we move relative to the objects. The insight that the spatially relevant properties of objects are the properties that remain invariant when objects change position, or when we change position relative to the objects, is fundamental to Helmholtz’s later work on topology.