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The Moon illusion is an optical illusion which causes the Moon to appear larger near the horizon than it does higher up in the sky. This optical illusion also occurs with the Sun and star constellations. It has been known since ancient times and recorded by various cultures. The explanation of this illusion is still debated.
A popular belief, stretching back at least to Aristotle in the 4th century B.C., holds that the Moon appears larger near the horizon due to a real magnification effect caused by the Earth's atmosphere. This is not true: although the atmosphere does change the perceived color of the Moon, it does not magnify or enlarge it. In fact, the Moon appears about 1.5% smaller when it is near the horizon than when it is high in the sky, because it is farther away by nearly one Earth radius. Atmospheric refraction also makes the image of the Moon slightly smaller in the vertical direction.
The angle that the full Moon subtends at an observer's eye can be measured directly with a theodolite to show that it remains constant as the Moon rises or sinks in the sky (discounting the very small variations due to the physical effects mentioned). Photographs of the Moon at different elevations also show that its size remains the same.
A simple way of demonstrating that the effect is an illusion is to hold a small object (say, 1/4 inch wide) at arm's length (25 inches) with one eye closed, positioning it next to the seemingly large Moon. When the Moon is higher in the sky, positioning the same object near the Moon reveals that there is no change in size. This formed the basis for the title of Somerset Maugham's work 'The Moon and Sixpence'.
Note that between different full moons, the Moon's angular diameter can vary from 29.43 arc minutes at apogee to 33.5 arc minutes at perigee—an increase of around 14% in apparent diameter or 30% in apparent area. This is because of the ellipticity of the Moon's orbit.
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. This brings up the question of not why the moon appears so large when close to the ground, but why does it seem so small when in the sky.
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. 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.
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.
An apparent distance theory evidently was first clearly described by Cleomedes around 200 A.D. The theory proposes that the horizon moon looks larger than the zenith moon because it looks farther away.
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.
In 1813, Schopenhauer wrote about this, that the moon illusion is "purely intellectual or cerebral and not optical or sensuous." The brain takes the sense data that is given to it from the eye and it apprehends a large moon because "our intuitively perceiving understanding regards everything that is seen in a horizontal direction as being more distant and therefore as being larger than objects that are seen in a vertical direction." The brain is accustomed to seeing terrestrially–sized objects in a horizontal direction and also as they are affected by atmospheric perspective, according to Schopenhauer.
If we perceive the Moon to be in the general vicinity of the 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. However, the response that the horizon moon appears larger, but not closer than the zenith moon could be because the viewer's logic confounds his or her perception; because the viewer knows that the moon can't possibly be physically farther away, he or she is not consciously aware of the perception. This is reinforced by the idea that we do not consciously perceive distance and size, as spatial awareness is a subconscious, retinocortical cognition. 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).
Historically, the best-known alternative to the "apparent distance" theory has been a "relative size" theory. This states that the perceived size of an object depends not only on its retinal size, but also on the size of objects in its immediate visual environment. In the case of the Moon illusion, objects in the vicinity of the horizon moon (that is, objects on or near the horizon) exhibit a fine detail that makes the Moon appear larger, while the zenith moon is surrounded by large expanses of empty sky that make it appear smaller.
The effect is illustrated by the classic Ebbinghaus illusion shown at the right. The lower central circle surrounded by small circles might represent the horizon moon accompanied by objects of smaller visual extent, while the upper central circle represents the zenith moon surrounded by expanses of sky of larger visual extent. Although both central circles are actually the same size, the lower one looks larger to many people.
According to the "angle of regard" hypothesis, the Moon illusion is produced by changes in the position of the eyes in the head accompanying changes in the angle of elevation of the Moon. Though once popular, this explanation no longer has much support.One obvious problem with this theory is that it would suggest that changing the position of the viewer's head and thereby the relative position of the viewer's eyes when looking at the moon (for instance, lying flat on one's back when looking at a moon low in the horizon) would somehow change or remove the moon illusion. That in fact, is not the case. The moon illusion remains intact independent of the position of the viewer's head relative to the position of the moon.
Immanuel Kant refers to the Moon illusion in his 1781 text Critique of Pure Reason, when he writes that "the astronomer cannot prevent himself from seeing the moon larger at its rising than some time afterwards, although he is not deceived by this illusion". Schopenhauer (1813) was cited above. Wade (1998) shortly summarizes historical references to the Moon illusion starting with Aristotle; he lists quotes by Aristotle (~330 BC), Ptolemy (~142, 150), Ibn al-Haytham (Alhazen) (1083), John Pecham (~1280), Leonardo da Vinci (~1500), René Descartes (1637), Benedetto Castelli (1639), Pierre Gassendi (1642), Thomas Hobbes (1655), J. Rohault (1671), Nicolas Malebranche (1674), William Molyneux (1687), J. Wallis (1687), G. Berkeley (1709), J.T. Desaguliers (1736), W. Porterfield (1737), R. Smith (1738), C.N. Le Cat (1744), D. Hartley (1749), Thomas Young (1807), and Carl Friedrich Gauss (1830).
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