Ptolemy attempted to explain the Moon illusion through atmospheric refraction in the Almagest, and later (in the Optics) as an optical illusion due to apparent distance, although interpretations of the account in the Optics are disputed. In the Book of Optics (1011–1022 A.D.), Ibn al-Haytham (Alhazen) repeated refraction as an explanation, but also proposed an explanation based in human perception. His argument was that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer; however, since there are no intervening objects between the Earth and the Moon, the observed distance is inaccurate and the Moon appears larger on the horizon. Through additional works (by Roger Bacon, John Pecham, Witelo, and others) based on Ibn al-Haytham's explanation, the Moon illusion came to be accepted as a psychological phenomenon in the 17th century. Most recent research on the Moon illusion has been conducted by psychologists specializing in human perception. After reviewing the many different explanations in their 2002 book The Mystery of the Moon Illusion, Ross and Plug conclude "No single theory has emerged victorious". The same conclusion is reached in the 1989 book, The Moon Illusion edited by Hershenson, which offers about 24 chapters written by different illusion researchers. Angular size and physical size The "size" of an object in our view can be measured either as angular size (the angle that it subtends at the eye, corresponding to the proportion of the field of vision that it occupies) or physical size (its real size measured in, say, meters). As far as human perception is concerned, these two concepts are quite distinct. For example, if two identical, familiar objects are placed at distances of five and ten meters respectively, then the more distant object subtends approximately half the angle of the nearer object, but we do not normally perceive that it is half the size. Conversely, if the more distant object did subtend the same angle as the nearer object then we would normally perceive it to be twice as big. A central question pertaining to the Moon illusion, therefore, is whether the horizon moon appears larger because its perceived angular size seems greater, or because its perceived physical size seems greater, or some combination of both. There is currently no firm consensus on this point. Apparent distance hypothesis Clouds near the horizon are typically farther away from the viewer, while those high in the sky are closer, giving the impression of a flat, or gently curved, sky surface An apparent distance theory evidently was first clearly described by Cleomedes arou
d 200 A.D. The theory proposes that the horizon moon looks larger than the zenith moon because it looks farther away. Comparison between the size of the Moon and the size of a cloud as they move higher in the sky.[clarification needed] When we see objects such as clouds, birds, and aeroplanes in the sky, those near the horizon are typically farther away from us than those overhead. This may result in the perception of the sky itself as a comparatively flat or only gently curving surface in which objects moving towards the horizon always recede away from us. If we perceive the Moon to be in the general vicinity of those other things we see in the sky, we would expect it to also recede as it approaches the horizon, which should result in a smaller retinal image. But since its retinal image is approximately the same size whether it is near the horizon or not, our brains, attempting to compensate for perspective, assume that a low Moon must be physically larger. Extensive experiments in 1962 by Kaufman and Rock showed that a crucial causative factor in the illusion is a change in the pattern of cues to distance. (See Ponzo illusion, depth perception, linear perspective, texture gradient.) The horizon moon is perceived to be at the end of a stretch of terrain receding into the distance, accompanied by distant trees, buildings and so forth, all of which indicate that it must be a long way away, while these cues are absent from the zenith moon. Experiments by many other researchers have found the same result; namely, when pictorial cues to a great distance are subtracted from the vista of the large-looking horizon moon it looks smaller. When pictorial cues to an increased distance are added into the vista of the zenith moon, it appears larger. A potential problem for the apparent distance theory has been that very few people (perhaps about 5%) perceive the horizon moon as being both larger and farther away. Indeed most people (perhaps 90%) say the horizon moon looks both larger and closer than the zenith moon (Boring, 1962; Hershenson, 1982; McCready, 1965, 1986; Restle, 1970). Most of the rest say it looks larger and about the same distance away as the zenith moon, with a few people reporting no Moon illusion at all. Nevertheless, the apparent distance explanation is the one most often found in textbooks. Those advocating the apparent distance hypothesis might counter that in the Ponzo illusion, people do not perceive one line to actually be farther away than another either, or that everything on the horizon is perceived as farther away, out of the habit that this is true for every object ever seen there (average-altitude clouds are about 100 times farther away at the horizon than when overhead).