 Reichenbach has a complex discussion of visualization. He introduces Helmholtz’s idea that to visualize a geometry is to understand what experiences one would have in a world in which that geometry holds, and extends the idea to the visualization of spaces with compact topologies, where, Reichenbach argues, Euclidean geometry could be sustained but at the cost of causal anomalies. For example, in a toroidal space, travel on a geodesic would bring one back to one’s starting point, which, Reichenbach argues, would require either abandoning Euclid or else allowing “causal anomalies” in the form of duplicate worlds at regular distances from one another. (By “Euclidean” geometry, Reichenbach means here a geometry on a manifold homeomorphic to R3, since there is a complete Euclidean metric for toroidal 3-space.) Reichenbach gives other examples of causal anomalies but no general characterization. 