Straight lines, 'uncurved lines', and Helmholtz's 'great circles on the celestial sphere'

Helmholtz's famous pincushioned chessboard figure has been used to make the point that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight. However, there is little agreement as to the cause of these perceptual errors. Some authors have attributed the errors to the shape of the retina, or the amount of cortex devoted to the processing of images falling on different parts of the retina, while others have taken the effects to indicate that visual space itself is curved. Helmholtz himself claimed that the 'uncurved lines on the visual globe' corresponded to 'direction circles' defined as those arcs described by the line of fixation when the eye moves according to Listing's law. Careful re-reading of Helmholtz together with some additional observations lead us to the conclusion that two other factors are also involved in the effect: (i) a lack of information about the distance of peripherally viewed objects and (ii) the preference of the visual system for seeing the pincushion squares as similar in size.