next section Theoretical horopter for the claim that this has been the case of a mistaken identity for about 200 years. In 1838, Charles Wheatstone invented the stereoscope, allowing him to explore the empirical horopter. He found that there were many points in space that yielded single vision; this is very different from the theoretical horopter, and subsequent authors have similarly found that the empirical horopter deviates from the form expected on the basis of simple geometry. Recently, plausible explanation has been provided to this deviation, showing that the empirical horopter is adapted to the statistics of retinal disparities normally experienced in natural environments. In this way, the visual system is able to optimize its resources to the stimuli that are more likely to be experienced. Theoretical Binocular Horopter Later Hermann von Helmholtz and Ewald Hering worked out the exact shape of the horopter almost at the same time. Their descriptions identified two components for the horopter for symmetrical fixation closer than infinity. The first is in the plane which contains the fixation point (wherever it is) and the two nodal points of the eye. Historically the geometric locus of horopteric points in this plane was taken to be a circle (the Vieth-Müller circle) going from one nodal point to the other in space and passing through the fixation point, until Howarth (2011) noted that it was only the portion of the circle containing the fixation point that made the same angle at the two eyes. The second component is a line (the Prévost–Burckhardt line) which is perpendicular to this arc in the median plane, cutting it at the point midway between the two eyes (which may, or may not, be the fixation point). This horopter geometry of an arc in the fixation plane and a perpendicular line remains approximately fixed relative to the eye centers as long as the eyes are fixating somewhere on these two lines. When the eyes are fixated anywhere off these two lines, the theoretical horopter takes the form of a twisted cubic passing through the fixation point and asymptoting to the two lines at their extremes. (Under no conditions does the horopter become either a cylinder through the Vieth-Müller circle or a torus centered on the nodal points of the two eyes, as is often popularly assumed.) If the eyes are fixating anywhere at infinity, the Vieth-Müller circle has infinite radius and the horopter