Topology is the branch of mathematics that seeks to understand and describe spatial relations. A number of studies have examined the human perception of topology — in particular, whether adults and young children perceive and differentiate objects based on features like closure, boundedness, and emptiness. Topology is about more than ‘wholes and holes’, however; it also offers an efficient language for representing network structure. Topological maps, common for subway systems across the world, are an example of how effective this language can be. Inspired by this idea, here we examine ‘intuitive network topology’. We show that people readily differentiate objects based on several different features of topological networks, and that people both remember and match objects in accordance with their topology features, as well.

This work is published in Journal of Experimental Psychology: General.

There are many ways to describe and represent the visuospatial world. A space can be described by its Euclidean properties: the size of objects, the angles of boundaries, the distances between them. A space can also be described in non-spatial terms: one could explain the layout of a city by the order of its streets, without any metric information. Somewhere in between, topological representations capture coarse relational structure without precise Euclidean detail, offering a relatively efficient, low-dimensional way of capturing spatial content. Here, we ask whether people quickly and automatically perceive topological structure. In six experiments, we show that differences in simple topological features influence a range of visual tasks from object matching to number estimation to visual search. We discuss the possibility that topological forms are a kind of visual primitive that supports visuospatial representation.

This work is currently under review.

In ongoing work, we are exploring how children reason about topological relations, and how this relates to core knowledge of other spatial domains, like geometry.

This work is currently in preparation.