The Limited Place in Cognitive Space

How we judge the similarity between stimuli in the world is connected ultimately to how we represent them. Because of this, decisions about how we model similarity, either in terms of human behavior or patterns of neural activity, can provide key insights into how representations are structured and organized. Despite this, psychology and cognitive neuroscience continue to be dominated by a narrow range of similarity models, particularly those that characterize similarity as distance within "cognitive space." Despite the appeal of such models, their topological nature places fundamental constraints on their ability to capture relationships between objects and events in the world. To probe this, we created a stimulus set in which the predicted similarity relationships (based on an alternative model of similarity) could not be simply embedded within Euclidean space. This approach revealed that the spatial model distorts these predictions, and the perceived similarities of human observers. These findings indicate that cognitive spaces-that underlie much recent work probing both visual and conceptual representations in cognitive neuroscience-are limited in fundamental ways that restrict their theoretical and practical utility.