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Moon illusion

Moon illusion

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The Moon illusion is an optical illusion
Optical illusion
An optical illusion is characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source...

 in which the Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 appears larger near the horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...

 than it does while higher up in the sky
The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...

. This optical illusion also occurs with the sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and star constellations
In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....

. It has been known since ancient times, and recorded by numerous different cultures. The explanation of this illusion is still debated.

Proof of illusion

A popular belief, stretching back at least to Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 in the 4th century B.C., holds that the Moon appears larger near the horizon due to a real magnification
Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called "magnification"...

 effect caused by the Earth's atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. This is not true: although the atmosphere does change the perceived color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

 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 from the observer by up to one Earth radius and also because of atmospheric refraction, which makes the image of the Moon slightly smaller in the vertical axis. (Note that between different full moons, the Moon's angular diameter
Angular diameter
The angular diameter or apparent size of an object as seen from a given position is the “visual diameter” of the object measured as an angle. In the vision sciences it is called the visual angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its...

 can vary from 33.5 arc minutes at perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...

 to 29.43 arc minutes at apogee—a difference of over 10%. This is because of the ellipticity of the Moon's orbit.)

The angle that the full Moon subtends at an observer's eye can be measured directly with a theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...

 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.

Possible explanations

In the Book of Optics
Book of Optics
The Book of Optics ; ; Latin: De Aspectibus or Opticae Thesaurus: Alhazeni Arabis; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Muslim scholar Alhazen .-See also:* Science in medieval Islam...

 (1011-1022 C.E.), Ibn al-Haytham argued that vision occurs in the brain, and that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. Arguing against Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

's refraction theory, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. With the Moon, however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon
Roger Bacon
Roger Bacon, O.F.M. , also known as Doctor Mirabilis , was an English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through empirical methods...

, John Pecham and Witelo
Witelo was a friar, theologian and scientist: a physicist, natural philosopher, mathematician. He is an important figure in the history of philosophy in Poland...

 based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.

For over 100 years, research on the Moon illusion has been conducted by vision scientists who invariably have been psychologists specializing in human perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...

. 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 [is in opposition to] at the eye, corresponding to the proportion of the field of vision that it occupies) or physical size (its real size measured in, say, metres). As far as human perception is concerned, these two concepts are quite distinct. For example, if two small, identical, and familiar objects are placed at distances of five and ten metres 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

An apparent distance theory evidently was first clearly described by Cleomedes around AD 200. 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 airplanes in the sky, those near the horizon are typically further 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 retina
The vertebrate retina is a light-sensitive tissue lining the inner surface of the eye. The optics of the eye create an image of the visual world on the retina, which serves much the same function as the film in a camera. Light striking the retina initiates a cascade of chemical and electrical...

l 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
Perspective (visual)
Perspective, in context of vision and visual perception, is the way in which objects appear to the eye based on their spatial attributes; or their dimensions and the position of the eye relative to the objects...

, 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
Ponzo illusion
The Ponzo illusion is a geometrical-optical illusion that was first demonstrated by the Italian psychologist Mario Ponzo in 1913. He suggested that the human mind judges an object's size based on its background. He showed this by drawing two identical lines across a pair of converging lines,...

, Depth perception
Depth perception
Depth perception is the visual ability to perceive the world in three dimensions and the distance of an object. Depth sensation is the ability to move accurately, or to respond consistently, based on the distances of objects in an environment....

, linear perspective, Texture gradient
Texture gradient
Texture gradient is the distortion in size which closer objects have compared to objects farther away. It also involves groups of objects appearing denser as they move farther away...

.) 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
Ponzo illusion
The Ponzo illusion is a geometrical-optical illusion that was first demonstrated by the Italian psychologist Mario Ponzo in 1913. He suggested that the human mind judges an object's size based on its background. He showed this by drawing two identical lines across a pair of converging lines,...

, people do not perceive one line to actually be farther away than another either, or that everything on the horizon is perceived as further away, out of the habit that this is true for every object ever seen there (average-altitude clouds are about 100 times further away at the horizon than when overhead).

Relative size hypothesis

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
Ebbinghaus illusion
The Ebbinghaus illusion or Titchener circles is an optical illusion of relative size perception. In the best-known version of the illusion, two circles of identical size are placed near to each other and one is surrounded by large circles while the other is surrounded by small circles; the first...

 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, to many people the lower one looks larger.

Angle of regard hypothesis

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.

Historical References to the Moon Illusion

Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

 refers to the moon illusion in his 1781 text the Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...

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."

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