Navigators learn a local graph, not a global map
It is still an unresolved issue how humans represent navigable space and use this information to relate distant locations, as when shortcuting or pointing. In the present study we compare two competing theoretical approaches to the structure of this spatial knowledge. We contrast the metric embedding of spatial information in a global reference frame (i.e., a Euclidean mental map) with models that assume only local place-to-place information (i.e., a labeled graph), which can be used to estimate shortcuts and pointing direction when needed. Two groups of participants learned a multi-corridor virtual maze by walking around a zig-zag loop that connected seven objects placed on a circle. One group experienced a possible Euclidean maze, and the other group an impossible, non-Euclidean, broken version of the maze. In the impossible environment, after walking one lap the participant was covertly teleported to the starting place again, despite having walked to a different Euclidean location. Thus, the local place-to-place metrics were globally inconsistent. During the test phase, participants pointed to targets in a clockwise or counterclockwise sequence around the circle from their current location. Whereas the possible maze group was fairly accurate, the estimates of the impossible maze group were systematically biased by the test sequence, as predicted by local place-to-place metrics. Despite being queried about the same target, participants pointed in significantly different directions, violating the metric postulates. The results suggest that human knowledge of navigable space is not a globally consistent Euclidean map, but can be characterized as a labeled graph.