Do rotation coordinates provide the substrate for a mental protractor?

In previous studies, we have found that the accuracy in judging collinearity of lines or dots varies considerably from one subject to another as a function of the relative angle of the stimulus elements. A model of errors generally shows large excursions across several subranges of angular position. These do not appear to be motor errors, at least not ones that are well separated from perceptual mechanisms. The errors are most likely generated at primary visual cortex, or beyond. We examined and modeled accuracy in judging collinearity of dot pairs, varying the angular position of the dots through 360 degrees, the distance between the dots (stimulus span), and the distance at which the subject was required to respond (response span). Subjects manifested idiosyncratic profiles of error across angular positions, as reported previously. But across the tested range of spans, from 4 to 8 deg, the errors tended to be the same, irrespective of stimulus or response span. This suggests that the judgments are based on a radial (angular) measure of spatial position. We discuss these results in the context of proposals that the brain maps spatial position using rotation coordinates. These new data are consistent with the hypothesis that subjects use the z-axis coordinates as a mental protractor for judging angular position and collinearity.