Human navigation in curved spaces.

Navigation and representations of the spatial environment are central to human survival. It has often been debated whether spatial representations follow Euclidean principles, and a number of studies challenged the Euclidean hypothesis. Two experiments examined the geometry of human navigation system using true non-Euclidean environments, i.e., curved spaces with non-Euclidean geometry at every point of the space. Participants walked along two legs in an outbound journey, then pointed to the direction of the starting point (home). The homing behavior was examined in three virtual environments, Euclidean space, hyperbolic space, and spherical space. The results showed that people's responses matched the direction of Euclidean origin, regardless of the curvature of the space itself. Moreover, participants still responded as if the space were Euclidean when a learning period was added for them to explore the spatial properties of the environment before performing the homing task to ensure violations of Euclidean geometry were readily detected. These data suggest that the path integration / spatial updating system operates on Euclidean geometry, even when curvature violations are clearly present.