The shape of space: Evidence for spontaneous but flexible use of polar coordinates in visuospatial representations (Published in Psychological Science)

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing two-dimensional space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which captures angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments utilizing a simple ‘visual matching’ paradigm show that (1) representational format is recoverable from the errors observers make in simple spatial tasks; (2) human-made errors spontaneously favor a polar coordinate system of representation; and (3) 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.