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Open Access Publications from the University of California

Arc Length as a Geometric Constraint for Psychological Spaces


Many cognitive models assume that stimuli can be represented as points in a latent psychological space. However, it has been difficult to provide these spaces with a geometric structure where the distance between items accurately reflects their subjective dissimilarity. In this paper, we propose a new method to give psychological spaces a geometric structure by equating the amount of change undergone by a stimulus with the arc length of a curve in psychological space. We then assess our method with a categorization experiment where participants classified continuously changing visual stimuli according to their rate of change. Our results indicate that individuals’ judgements are well predicted by arc length, suggesting that it may be a promising geometric constraint for psychological spaces in other contexts.

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