The limited place in cognitive space

The idea that objects can be represented within multi-dimensional ‘cognitive spaces’ remains popular within psychology and neuroscience, and yet the restrictive topology of such spaces is seldom considered. Here, we show that it is possible, even within a simple set of items, to break such models by imposing neighbourhood relations that are incompatible with a purely spatial representation. These results highlight the fundamental limits of cognitive space as a representational format for complex cognition.