What is the format of spatial representation?

This page contains information from the following manuscripts:

Yousif, S. R., Keil, F. C. (In press). The shape of space: Evidence for spontaneous but flexible use of polar coordinates in visuospatial representations. Psychological Science.

Yousif, S. R., Chen, Y-C., and Scholl, B. J. (2020). Systematic angular biases in the representation of visual space. Attention, Perception, & Psychophysics, 82, 3124-3143. picture_as_pdf

How do we remember and how do we see where things are? The answer may seem obvious, but in fact both behavior and perception exhibit large spatial distortions.

Consider the image below. What you can see are 3200 random dots that observers saw, one at a time, and had to place black in a different-sized shape. There were no memory demands; all that observers had to do was replace the dot. If you hover your cursor over the image, you can see each of those dots slowly move from its initial location to its final destination. Notice how distorted the responses are.

(Hover over the above image for a demo!)

Below, you can see the exact same set of points, but filtered for density. Here you can most clearly see the pattern of distortion.

(Hover over the above image for a demo!)

This kind of pattern is evident in many spatial arrangments, not just circles. Below you can see the same data for (1) a shapeless configuration (with only a central dot), (2) a square configuration, and (3) a triangle configuration. (Hover any of them to see the movement!)

(Hover over the above images for demos!)

How can we use this information to assess the format of representations? In short, people's errors on these very simple tasks contain subtle but critical clues to the latent representational format. For example, we can ask: what should be true if observers represent space in a given format? If anything is represented in an independent, two-dimensional space, then those two dimensions should be uncorrelated. Is that true for cartesian space, or polar space? We can ask whether, on average, the errors that observers make in cartesian dimensions (x vs. y) and polar dimensions (angle vs. radial distance) and correlated. If they are correlated, this would suggest that these representations are not independent, thus making that system an unlikely candidate for the representational format.

Across several experiments (including all of the data above), we show that cartesian coordinates are consistently correlated and polar coordinates are consistently uncorrelated. We believe provides a strong hint as to the true format of our most basic visuospatial representations. Below, you can see a schematic of some of our other tasks, as well as a schematic of the primary analyses.