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Jonathan Ericson, William Warren; Rips and folds in virtual space: Ordinal violations in human spatial knowledge. Journal of Vision 2009;9(8):1143. doi: 10.1167/9.8.1143.
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At one extreme, human spatial knowledge might preserve Euclidean properties of metric distance and angle; at the other, it might preserve topological relations such as neighborhood or graph structure. To investigate this question, participants learn one of two virtual environments: (1) a Wormhole maze that violates Euclidean structure by introducing two “wormholes” that seamlessly transport a participant between locations, and (2) a Euclidean control maze. We probe their spatial knowledge using a shortcut task. Participants walked in a virtual environment while wearing a head-mounted display (63° H × 53° V), and head position was recorded with a sonic/inertial tracker (70 ms latency). During training, they learned the locations of nine objects by exploring the maze and then walking from Home to each object, sufficient to learn their metric locations via vector subtraction. On test trials, participants walked from Home to starting object A, the maze disappeared, and they took a direct shortcut to the remembered location of target object B. In the Euclidean maze, participants tend to walk toward the metric target location, on average, although shortcuts are highly variable in both mazes. In the Wormhole maze, from some starting points participants tend to walk toward the metric location of target B on average, whereas from other starting points they walk through a wormhole to an alternative location B'. Such “rips” and “folds” in spatial knowledge even create reversals in the ordinal relations among objects. Participants are generally unaware of these inconsistencies, even though they are in principle detectable. The results suggest that spatial knowledge may preserve some local metric properties, enabling rough shortcuts, but is globally non-Euclidean. It might be characterized by a weighted graph in which the weights are globally inconsistent.
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