The deviation between empirical corresponding points along the vertical meridians of the two retinas has often been proposed as adaptive for depth discrimination in the world. Empirical corresponding points are defined as pairs of points in the two eyes that, when stimulated, result in the same perceived direction in the world. The horopter, the intersection in space of rays projected out from these corresponding retinal points, is where depth estimates from disparity are the most accurate in the whole visual field. It has been suggested that the vertical component of this horopter tends to lie in the ground plane in many viewing situations, allowing for better visual guidance of locomotion. This is demonstrated in the figure. The projections of corresponding points along the vertical meridians can be represented as a plane containing all points in space that could stimulate these points for each eye (red and green planes). The horopter is represented by the intersection of these planes (blue line). When the eyes are in infinite gaze, in a typical observer, a horizontal shear of about 2 degrees between corresponding points results in a horopter that lies in the ground plane. According to Listing’s Law, when gaze shifts downward to fixate the ground, the eyes would rotate around an axis that is orthogonal to the two deviated vertical meridians. When such an eye movement is made, the planar projections of corresponding points into space do not move relative to the head and therefore if the head does not move, the planar projections do not move relative to the ground. Said another way, such an eye movement maintains the geometry that projects the horopter to the ground plane. We are currently investigating two aspects of this theory. The first is the prediction that the position of corresponding retinal points will vary with individual eye heights and interpupillary distances such that the horopter lies near the ground for individual observers at earth horizontal infinite gaze. The second is the prediction that declining gaze and pitching the head toward the ground, as often happens during walking, will not significantly change the location of the horopter.