Spatial memory distortions for the shapes of walked paths occur in violation of physically experienced geometry.

An important question regards the nature of our spatial memories for the paths that we have walked and, in particular, whether such distortions might violate the topological properties of the shape of the paths (i.e., creating an intersection when two paths did not intersect or vice versa). To investigate whether and how this might occur, we tested humans in situations in which they walked simple paths and idiothetic and visual cues either matched or mismatched, with the mismatching cues creating the greatest potential for topological distortions. Participants walked four-segment paths with 90° turns in immersive virtual reality and pointed to their start location when they arrived at the end of the path. In paths with a crossing, when the intersection was not presented, participants pointed to a novel start location suggesting a topological distortion involving non-crossed paths. In paths without a crossing, when a false intersection was presented, participants pointed to a novel start location suggesting a topological distortion involving crossed paths. In paths without crossings and without false intersections, participants showed reduced pointing errors that typically did not involve topological distortions. Distortions more generally, as indicated by pointing errors to the start location, were significantly reduced for walked paths involving primarily idiothetic cues with limited visual cues; conversely, distortions were significantly increased when idiothetic cues were diminished and navigation relied primarily on visual cues. Our findings suggest that our spatial memories for walked paths sometimes involve topological distortions, particularly when resolving the competition between idiothetic and visual cues.