Humans can obtain an unambiguous perception of depth and 3-dimensionality with 1 eye or when viewing a pictorial image of a 3-dimensional scene. However, the perception of depth when viewing a real scene with both eyes is qualitatively different: There is a vivid impression of tangible solid form and immersive negative space. This perceptual phenomenon, referred to as "stereopsis," has been among the central puzzles of perception since the time of da Vinci. After Wheatstone's invention of the stereoscope in 1838, stereopsis has conventionally been explained as a byproduct of binocular vision or visual parallax. However, this explanation is challenged by the observation that the impression of stereopsis can be induced in single pictures under monocular viewing. Here I propose an alternative hypothesis that stereopsis is a qualitative visual experience related to the perception of egocentric spatial scale. Specifically, the primary phenomenal characteristic of stereopsis (the impression of "real" separation in depth) is proposed to be linked to the precision with which egocentrically scaled depth (absolute depth) is derived. Since conscious awareness of this precision could help guide the planning of motor action, the hypothesis provides a functional account for the important secondary phenomenal characteristics associated with stereopsis: the impression of interactability and realness. By linking stereopsis to a generic perceptual attribute, rather than a specific cue, it provides a potentially more unified account of the variation of stereopsis in real scenes and pictures and a basis for understanding why we can perceive depth in pictures despite conflicting visual signals.