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. It has been known since ancient times and recorded by various cultures. [1] [2] The explanation of this illusion is still debated. [2] [3] [4]
The angle that the diameter of 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. 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 pebble (say, 0.33 inches or 8.4 millimetres wide) at arm's length (25 inches or 64 centimetres) with one eye closed, positioning the pebble so that it covers (eclipses) the full Moon when high in the night sky. Then, when the seemingly very large Moon is on the horizon, the same pebble will also cover it, revealing that there has been no change in the size of the Moon.
Across different full moons, the Moon's angular diameter can vary from 29.43 arcminutes at apogee to 33.5 arcminutes at perigee—a variation of around 14% in apparent diameter or 30% in apparent area. [5] This is because of the eccentricity of the Moon's orbit.
The size of a viewed object can be measured objectively either as an angular size (the visual angle that it subtends at the eye, corresponding to the proportion of the visual field that it occupies), or as physical size (its real size measured in, say, meters). Perceived size is only loosely related to these concepts, however. 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 visual angle of the nearer object, but it is normally perceived to be the same size (a phenomenon referred to as size constancy), not as half the size. Conversely, if the more distant object did subtend the same angle as the nearer object then it is normally perceived to be twice as big.
One question concerning 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 consensus on this point. Most recent research on the Moon illusion has been conducted by psychologists specializing in human perception. The 2013 book The Moon Illusion, edited by Hershenson, offers 19 chapters written by various illusion researchers reaching different conclusions. [3] 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." [6] They argue that the size of the illusion is variable, but is usually an apparent increase in diameter of about 50 percent. The most important factor is the sight of the terrain, but there is a small contribution from other factors such as the angle of regard, posture, and eye movements.[ citation needed ]
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, [7] [8] or the difficulty of looking upwards, although interpretations of the account in the Optics are disputed. [9] Similarly Cleomedes (about 200 A.D.), in his book on astronomy, ascribed the illusion both to refraction and to changes in apparent distance. [2] In the Book of Optics (1011–1022 A.D.), Ibn al-Haytham (Alhazen) repeated refraction as an explanation, but also proposed a more detailed explanation based on intervening objects and apparent distance.
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. [10]
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 further away. Ibn al-Haytham was more specific: 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 perceived distance is too short and the Moon appears smaller than on the horizon. [2] Researchers have argued [11] that the apparent distance hypothesis is problematic scientifically because it explains perceptions as consequences of perceptions: the Moon looks further away because it looks larger. However, there are probably complex internal processes behind this relationship.
In 1813, Schopenhauer wrote about this, that the Moon illusion is "purely intellectual or cerebral and not optical or sensuous". [12] 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." [13] 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 the Moon is perceived to be in the general vicinity of the other things seen in the sky, it would be expected 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, the brain, attempting to compensate for perspective, assumes 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, comparable to the Ponzo illusion. 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 few people (perhaps about 5%) perceive the horizon Moon as being both larger and further 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 their perception; because the viewer knows that the Moon can't possibly be physically further away, they are not consciously aware of the perception. This is reinforced by the idea that the brain does not consciously perceive distance and size, as spatial awareness is a subconscious, retino cortical cognition. In line with the possibility that the reported distance of the Moon is due to logic, rather than perception, is the finding that these varying reports—with some reporting closer distances and others not—are likely due to response biases. [11] Nevertheless, the apparent distance explanation is the one most often found in textbooks.
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. [14]
The effect is illustrated by the classic Ebbinghaus illusion, where a circle appears larger when surrounded by smaller circles, than it does when surrounded by larger circles.
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. [3] Looking through one's legs at the horizon Moon does reduce the illusion noticeably, but this may be because the image on the retina is inverted. Raising the eyes or tilting the head when in an upright posture gives only a very small reduction in the illusion. [2]
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". [15] Schopenhauer (1813) was cited above. Wade [1] 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), George 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).
Ḥasan Ibn al-Haytham was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir, written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the scientific revolution by Isaac Newton, Johannes Kepler, Christiaan Huygens, and Galileo Galilei.
In visual perception, an optical illusion is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; their categorization is difficult because the underlying cause is often not clear but a classification proposed by Richard Gregory is useful as an orientation. According to that, there are three main classes: physical, physiological, and cognitive illusions, and in each class there are four kinds: Ambiguities, distortions, paradoxes, and fictions. A classical example for a physical distortion would be the apparent bending of a stick half immersed in water; an example for a physiological paradox is the motion aftereffect. An example for a physiological fiction is an afterimage. Three typical cognitive distortions are the Ponzo, Poggendorff, and Müller-Lyer illusion. Physical illusions are caused by the physical environment, e.g. by the optical properties of water. Physiological illusions arise in the eye or the visual pathway, e.g. from the effects of excessive stimulation of a specific receptor type. Cognitive visual illusions are the result of unconscious inferences and are perhaps those most widely known.
Forced perspective is a technique that employs optical illusion to make an object appear farther away, closer, larger or smaller than it actually is. It manipulates human visual perception through the use of scaled objects and the correlation between them and the vantage point of the spectator or camera. It has uses in photography, filmmaking and architecture.
Depth perception is the ability to perceive distance to objects in the world using the visual system and visual perception. It is a major factor in perceiving the world in [[three-dimensional|three dimensions]
An Ames room is a distorted room that creates an optical illusion. Likely influenced by the writings of Hermann Helmholtz, it was invented by American scientist Adelbert Ames Jr. in 1946, and constructed in the following year.
The Ponzo illusion is a geometrical-optical illusion that takes its name from the Italian psychologist Mario Ponzo (1882–1960). Ponzo never claimed to have discovered it, and it is indeed present in earlier work. Much confusion is present about this including many references to a paper that Ponzo published in 1911 on the Aristotle illusion. This is a tactile effect and it has nothing at all to do with what we now call the Ponzo illusion. The illusion can be demonstrated by drawing two identical lines across a pair of converging lines, similar to railway tracks, but the effect works also at different orientations.
The Jastrow illusion is an optical illusion attributed to the Polish-American psychologist Joseph Jastrow. This optical illusion is known under different names: Ring-Segment illusion, Jastrow illusion, Wundt area illusion or Wundt-Jastrow illusion.
Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies, also known as The Heavens.
Visual angle is the angle a viewed object subtends at the eye, usually stated in degrees of arc. It also is called the object's angular size.
Subjective constancy or perceptual constancy is the perception of an object or quality as constant even though our sensation of the object changes. While the physical characteristics of an object may not change, in an attempt to deal with the external world, the human perceptual system has mechanisms that adjust to the stimulus.
A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.
The size–weight illusion, also known as the Charpentier illusion, is named after the French physician Augustin Charpentier because he was the first to demonstrate the illusion experimentally. It is also called De Moor's illusion, named after Belgian physician Jean Demoor (1867–1941).
Emmert's law states that objects that generate retinal images of the same size will look different in physical size if they appear to be located at different distances. Specifically, the perceived linear size of an object increases as its perceived distance from the observer increases. This makes intuitive sense: an object of constant size will project progressively smaller retinal images as its distance from the observer increases. Similarly, if the retinal images of two different objects at different distances are the same, the physical size of the object that is farther away must be larger than the one that is closer.
The Chubb illusion is an optical illusion or error in visual perception in which the apparent contrast of an object varies substantially to most viewers depending on its relative contrast to the field on which it is displayed. These visual illusions are of particular interest to researchers because they may provide valuable insights in regard to the workings of human visual systems.
Convergence micropsia is a type of micropsia characterized by the reduction in apparent size of objects viewed when the eyes are more converged than they need to be for the distance of the object from the eyes.
In human visual perception, the visual angle, denoted θ, subtended by a viewed object sometimes looks larger or smaller than its actual value. One approach to this phenomenon posits a subjective correlate to the visual angle: the perceived visual angle or perceived angular size. An optical illusion where the physical and subjective angles differ is then called a visual angle illusion or angular size illusion.
Atmospheric optics is "the study of the optical characteristics of the atmosphere or products of atmospheric processes .... [including] temporal and spatial resolutions beyond those discernible with the naked eye". Meteorological optics is "that part of atmospheric optics concerned with the study of patterns observable with the naked eye". Nevertheless, the two terms are sometimes used interchangeably.
Geometrical–optical are visual illusions, also optical illusions, in which the geometrical properties of what is seen differ from those of the corresponding objects in the visual field.
The ambient optic array is the structured arrangement of light with respect to a point of observation. American psychologist James J. Gibson posited the existence of the ambient optic array as a central part of his ecological approach to optics. For Gibson, perception is a bottom-up process, whereby the agent accesses information about the environment directly from invariant structures in the ambient optic array, rather than recovering it by means of complex cognitive processes. More controversially, Gibson claimed that agents can also directly pick-up the various affordances of the environment, or opportunities for the observer to act in the environment, from the ambient optic array.
Ptolemy's Optics is a 2nd-century book on geometrical optics, dealing with reflection, refraction, and colour. The book was most likely written late in Ptolemy's life, after the Almagest, during the 160s. The work is of great importance in the early history of optics. The Greek text has been lost completely. Fragments of the work survive only in the form of a Latin translation, prepared around 1154 by Eugene of Palermo, based on an Arabic translation which was presumably based on the Greek original. Both the Arabic and the Greek texts are lost entirely, and the Latin text is "badly mangled". The Latin text was edited by Albert Lejeune in 1956. The 1996 English translation by Mark Smith is based on Lejeune's Latin text.
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