Explaining the moon illusion.

An old explanation of the moon illusion holds that various cues place the horizon moon at an effectively greater distance than the elevated moon. Although both moons have the same angular size, the horizon moon must be perceived as larger. More recent explanations hold that differences in accommodation or other factors cause the elevated moon to appear smaller. As a result of this illusory difference in size, the elevated moon appears to be more distant than the horizon moon. These two explanations, both based on the geometry of stereopsis, lead to two diametrically opposed hypotheses. That is, a depth interval at a long distance is associated with a smaller binocular disparity, whereas an equal depth interval at a smaller distance is associated with a larger disparity. We conducted experiments involving artificial moons and confirmed the hypothesis that the horizon moon is at a greater perceptual distance. Moreover, when a moon of constant angular size was moved closer it was also perceived as growing smaller, which is consistent with the older explanation. Although Emmert's law does not predict the size-distance relationship over long distances, we conclude that the horizon moon is perceived as larger because the perceptual system treats it as though it is much farther away. Finally, we observe that recent explanations substitute perceived size for angular size as a cue to distance. Thus, they imply that perceptions cause perceptions.