What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing 2D space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which capture angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments, using a simple visual-matching paradigm, show that (a) representational format is recoverable from the errors that observers make in simple spatial tasks, (b) human-made errors spontaneously favor a polar coordinate system of representation, and (c) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence as well as work on spatial representation at other spatial scales.

This work is published in Psychological Science.

Mental representations are the essence of cognition. Yet to understand how the mind works, one must understand not just the content of mental representations (i.e., what information is stored) but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a “case study” of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly “redundant” formats may support the flexible spatial behavior observed in humans and that researchers should approach the study of all mental representations with this possibility in mind.

This work is published in Perspectives on Psychological Science.

Does the mind rely on similar systems of spatial representation for both perception and action? Here, we assessed the format of location representations in two simple spatial localization tasks. In one task, participants simply remembered the location of an item based solely on visual input. In another, participants remembered the location of a point in space based solely on kinesthetic input. Participants’ recall errors were more consistent with the use of polar coordinates than Cartesian coordinates in both tasks. Moreover, measures of spatial bias and performance were correlated across modalities. In a subsequent study, we tested the flexibility with which people use polar coordinates to represent space; we show that the format in which the information is presented to participants influences how that information is encoded and the errors that are made as a result. We suggest that polar coordinates may be a common means of representing location information across visual and motor modalities, but that these representations are also flexible in form.

This work is published in Psychonomic Bulletin & Review.