Topological structure in human spatial representation revealed through drawing

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Abstract

Human spatial representations are often assumed to represent Euclidean properties such as length, distance, and angle. Here we test an alternative (but not mutually exclusive) possibility – that spatial memory is structured primarily around topological relations. Across four experiments, adults and children memorized simple letter-like figures and reproduced them by drawing, allowing the contents of their spatial representations to be revealed directly. Drawings showed systematic distortions of metric features, including strong biases of angles toward 90° and compression of line length towards an average value. In contrast, topologically critical features — such as T-junctions and holes — were reliably preserved, even relative to closely matched but topologically irrelevant features like L-junctions. These effects were magnified in a serial reproduction paradigm, in which participants iteratively generated new drawings from previous participant drawings: At the end of each mnemonic chain, figures converged on simplified topological structures as metric detail degraded. Similar patterns were observed in children aged five to eight years. Together, these findings suggest that basic topological relations may function as primitive building blocks of human spatial representation, with metric detail encoded secondarily.

Significance statement

The iconic map of the London Underground is one of the most famous maps in history, yet something special about it goes unnoticed: it is not a veridical representation of space. Distances are arbitrary, and angles are presented only in coarse terms. Yet the ubiquity and appeal of such maps suggests that topological representation is intuitive — as if the mind is keen to receive information in exactly this way. Here, using drawing as a tool, we show directly that the most primitive form of spatial representation appears to be a topological skeleton. Remarkably, even children as young as five represent spatial structure in topological terms, with roughly the same fidelity as adults — pointing to an underappreciated building block of spatial representation.

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