Proof of Illusion
A widespread misconception, dating back at least to the time of Aristotle (4th century BC), is that the Moon's larger size at the horizon is due to a magnification effect created by the Earth's atmosphere. However, astronomical refraction at the horizon only slightly reduces the observed size, making the Moon slightly flattened along the vertical axis.
There is currently no consensus on whether the Moon appears larger at the horizon due to a larger perceived angular size or a larger perceived physical size, that is, whether it appears closer or larger.
In general, a complete explanation of this feature of human perception still does not exist. In 2002, Helen Ross and Cornelis Plug published the book The Mystery of the Moon Illusion, in which, after considering various theories, they concluded: “No theory has won.” The authors of the collection “Moon Illusion”, published in 1989 under the editorship of M. Hershenson, came to the same decision.
There are many different theories to explain the moon illusion. Only the main ones are listed below.
Theory about the role of eye convergence
In the 1940s, Boring (1943; Holway & Boring, 1940; Taylor & Boring, 1942) and in the 1990s, Suzuki (1991, 1998) proposed an explanation for the Moon illusion, according to which the apparent size of the Moon depends on the degree convergence of the observer's eyes. That is, the illusion of the Moon is the result of increased impulses towards convergence of the eyes that arise in the observer when he looks up (to look at the Moon at its zenith), and the eyes themselves tend to diverge. Because eye convergence is a sign of object proximity, an object high in the sky appears smaller to an observer.
In one experiment, Holway and Boring (1940) asked subjects to compare their perceived size of the Moon with one of a disk of light projected onto a screen next to them. In the first series of the experiment, the subjects sat on a chair. While observing the Moon near the horizon (at the observer's eye level), they chose a disk that was significantly larger in size than the one they selected when observing the Moon at its zenith (raising their eyes at an angle of 30°). In the second series, the subjects watched the Moon while lying on the table. When they lay on their backs and looked at the Moon at its zenith, or when they were forced to throw their heads back and look up to see the Moon on the horizon from a supine position, the results were the opposite. The Moon near the horizon seemed smaller to them than the Moon at its zenith.
Opponents of this hypothesis argue that the illusion of an enlarged Moon quickly fades with an increase in the height of the luminary above the horizon, when the need to throw back the head and raise the eyes up does not yet arise.
The theory of apparent distance
The theory of apparent distance was first described by Cleomedes around 200 AD. e. The theory suggests that the Moon near the horizon appears larger than the Moon in the sky because it appears farther away. The human brain sees the sky not as a hemisphere, which it actually is, but as an oblate dome. Watching clouds, birds and airplanes, a person sees that they decrease as they approach the horizon. Unlike terrestrial objects, the Moon, when near the horizon, has approximately the same apparent angular diameter as at the zenith, but the human brain tries to compensate for perspective distortions and assumes that the Moon's disk must be physically larger.
Experiments conducted in 1962 by Kaufman & Rock showed that visual cues are a significant factor in creating an illusion (see Ponzo illusion). The moon on the horizon appears at the end of a sequence of landscape objects, trees and buildings, which tells the brain that it is very far away. As landmarks move away from the field of view, the large-looking Moon becomes smaller.
Opponents of this theory point to the presence of an illusion even when observing the luminary through a dark filter, when the objects surrounding it are indistinguishable.
Relative size theory
According to relative size theory, perceived size depends not only on the size on the retina, but also on the sizes of other objects in the visual field that we observe simultaneously. When observing the Moon close to the horizon, we see not only the Moon, but also other objects, against the background of which the Earth’s satellite appears larger than it actually is. When the Moon is in the sky, the vast expanses of the sky make it look smaller.
This effect was demonstrated by psychologist Hermann Ebbinghaus. The circle surrounded by small circles represents the Moon at the horizon and small objects surrounding it (trees, poles, etc.), and the circle surrounded by larger objects represents the Moon in the sky. Even though both center circles are the same size, many people think that the right circle in the picture is larger. Anyone can check this effect by taking some large object (for example, a table) out of the room into the yard. In an open space it will look clearly smaller than indoors.
Opponents of this theory point out that airplane pilots also observe this illusion, although there are no ground objects in their field of vision.
Quantitative comparison of different theories based on experimental data
Specially designed experiments allowed quantitatively compare the influence of various factors proposed to explain the illusion. In particular, observer's head lift(the theory about the role of eye convergence) affects the change in size, but very weakly (the apparent change in size is 1.04 times), the change colors or brightness the lunar disk has virtually no effect on the apparent size, and presence of a horizon line or its optical model (the theory of apparent distance and relative size) leads to an apparent change in the size of the disk by 1.3 - 1.6 times, and the exact magnitude of the change depends on the features of the landscape.
Notes
Links
- NASA - Solstice Moon Illusion (English)
- Astronomy Picture of the Day (English) (September 26, 2007). Retrieved December 9, 2012.
- The Moon Illusion, An Unsolved Mystery. (English)
- The Moon Illusion Explained
| Moon | ||
|---|---|---|
| Peculiarities |  |
|
| Orbit | ||
| Surface | ||
| Selenology | ||
| Study | ||
| Other | ||
Wikimedia Foundation. 2010.
You've probably noticed that when the full Moon "sits" on the horizon, it appears much larger, one and a half times larger, than when it rises high into the sky. The same phenomenon occurs when observing the Sun, planets and constellations. However, if you measure the angular dimensions of the Moon at the horizon and high in the sky, then these values will coincide - its projections on the retina in both cases will be equal. It turns out that the sizes of the high and low Moon are the same, but our brain perceives them differently. Why is this happening?
The Moon illusion has always aroused great interest, and many scientists have tried to explain it.
One might think that this is due to changes in the angular size of the Moon at different points in its orbit. As we know, the lunar orbit has the shape of an ellipse, which means that being at perigee (the closest point of the orbit to the Earth ~ 364,000 km), the Moon slightly increases its angular dimensions, and accordingly being at the apogee (the farthest point of the orbit ~ 406,000 km ), its angular dimensions are smaller. The percentage difference between the distances at apogee and perigee is on average 10%.
But even this insignificant 10% cannot explain why the Moon appears huge to us at the horizon. The angular dimensions of the full Moon fluctuate between 0.6 degrees (at perigee) and 0.5 degrees (at apogee), but this difference will occur within the month, and not during the night, when the Moon rises.
In fact, the size of the lunar disk above the horizon is 1.5% smaller than in the sky, since the distance to the observer is 1 Earth radius greater. Also, due to atmospheric refraction, the size of the Moon along the vertical axis decreases.
There are many different theories explaining the moon illusion, but scientists have not been able to come to a consensus. The following explanations seem to us most plausible:
1) The “Ponzo illusion,” named after Mario Ponzo, who proved it in 1913, says that a person judges the size of an object by its background. Ponzo drew two identical segments against the background of two converging lines, like a railway track stretching into the distance. Ponzo drew two identical segments against the background of an image of a railway track stretching into the distance. The top section appears larger because it overlaps the rails, unlike the bottom section, which is between the rails. Likewise, when the Moon is low, trees and houses appear smaller compared to the Moon, which in turn appears larger than it really is.
2) According to the relative size theory, perceived size depends not only on the size on the retina, but also on the sizes of other objects in the visual field that we observe simultaneously. When observing the Moon close to the horizon, we see not only the Moon, but also other objects, against the background of which the Earth’s satellite appears larger than it actually is. When the Moon is in the sky, the vast expanses of the sky make it look smaller.
This effect was demonstrated by psychologist Hermann Ebbinghaus. The circle surrounded by small circles represents the Moon at the horizon and small objects surrounding it (trees, poles, etc.), and the circle surrounded by larger objects represents the Moon in the sky. Even though both center circles are the same size, many people think that the right circle in the picture is larger.
The easiest way to dispel the illusion of the effect is to hold a small object (for example, a coin) at arm's length, while closing one eye. By comparing the size of an object with a large Moon near the horizon and a small Moon in the sky, you can see that the relative size does not change. You can also make a pipe out of a sheet of paper and look through it only at the Moon, without surrounding objects - the illusion will disappear.
So don’t be deceived when others claim that the full moon is too big today. Just admire the beautiful landscape with the Moon rising from the horizon!
Based on free Internet materials.
). In fact, the angular size of the Moon is practically independent of its height above the horizon. The illusion also occurs when observing the Sun and constellations. Evidence of the phenomenon has been preserved since ancient times and recorded in various sources of human culture (for example, in chronicles). There are currently several different theories to explain this illusion.
Proof of Illusion
A widespread misconception, dating back at least to the time of Aristotle (4th century BC), is that the larger size of the Moon at the horizon is due to the magnification created by the Earth's atmosphere. In fact, astronomical refraction at the horizon, on the contrary, slightly reduces the observed vertical size of the Moon and does not affect the horizontal size. As a result, the lunar disk near the horizon appears flattened.
There is another factor due to which the angular size of the Moon near the horizon is slightly less than when it is at its zenith. As the Moon moves from the zenith to the horizon, the distance from it to the observer increases by the value of the Earth's radius, and its apparent size decreases by 1.7%.
In addition, the angular size of the Moon varies slightly depending on its position in orbit. Since its orbit is noticeably elongated, at perigee (the point of the orbit closest to the Earth), the angular size of the Moon is 33.5 arc minutes, and at apogee it is 12% smaller (29.43 arc minutes). These minor changes are not related to the apparent multiple magnification of the Moon at the horizon: it represents a perceptual error. Measurements using a theodolite and photographs of the Moon at various heights above the horizon show a constant size, about half a degree, and the projection of the lunar disk onto the retina of the observer's naked eye always has a size of about 0.15 mm.
The easiest way to demonstrate the illusory nature of the effect is to hold a small object (for example, a coin) at arm's length, while closing one eye. By comparing the size of an object with a large Moon near the horizon and a small Moon high in the sky, you can see that the relative size does not change. You can also make a pipe out of a sheet of paper and look through it only at the Moon, without surrounding objects - the illusion will disappear.
Possible explanations for the illusion
The size of an object we see can be determined either through its angular size (the angle formed by the rays entering the eye from the edges of the object) or through its physical size (real size, for example in meters). These two concepts are different from the point of view of human perception. For example, the angular sizes of two identical objects placed at a distance of 5 and 10 meters from the observer differ by almost two times, however, as a rule, it does not seem to us that the nearest object is twice as large. Conversely, if a more distant object has the same angular size as a closer one, we will perceive it as twice as large (Emmert's law).
There is currently no consensus on whether the Moon appears larger at the horizon because of its larger perceived angular size or its larger perceived physical size, that is, whether it appears closer or larger.
In general, a complete explanation of this feature of human perception still does not exist. In 2002, Helen Ross and Cornelis Plug published the book The Mystery of the Moon Illusion, in which, after considering various theories, they concluded: “No theory has won.” The authors of the collection “Moon Illusion”, published in 1989 under the editorship of M. Hershenson, came to the same decision.
There are many different theories to explain the moon illusion. Only the main ones are listed below.
Theory about the role of eye convergence
In the 1940s, Boring (1943; Holway & Boring, 1940; Taylor & Boring, 1942) and in the 1990s, Suzuki (1991, 1998) proposed an explanation for the Moon illusion, according to which the apparent size of the Moon depends on the degree convergence of the observer's eyes. That is, the illusion of the Moon is the result of increased impulses towards convergence of the eyes that arise in the observer when he looks up (to look at the Moon at its zenith), and the eyes themselves tend to diverge. Because eye convergence is a sign of object proximity, an object high in the sky appears smaller to an observer.
In one experiment, Holway and Boring (1940) asked subjects to compare their perceived size of the Moon with one of a disk of light projected onto a screen next to them. In the first series of the experiment, the subjects sat on a chair. While observing the Moon near the horizon (at the observer's eye level), they chose a disk that was significantly larger in size than the one they selected when observing the Moon at its zenith (raising their eyes at an angle of 30°). In the second series, the subjects watched the Moon while lying on the table. When they lay on their backs and looked at the Moon at its zenith, or when they were forced to throw their heads back and look up to see the Moon on the horizon from a supine position, the results were the opposite. The Moon near the horizon seemed smaller to them than the Moon at its zenith.
Opponents of this hypothesis argue that the illusion of an enlarged Moon quickly fades with an increase in the height of the luminary above the horizon, when the need to throw back the head and raise the eyes up does not yet arise.
The theory of apparent distance
The theory of apparent distance was first described by Cleomedes around 200 AD. e. The theory suggests that the Moon near the horizon appears larger than the Moon in the sky because it appears farther away. The human brain sees the sky not as a hemisphere, which it actually is, but as an oblate dome. Watching clouds, birds and airplanes, a person sees that they decrease as they approach the horizon. Unlike terrestrial objects, the Moon, when near the horizon, has approximately the same apparent angular diameter as at the zenith, but the human brain tries to compensate for perspective distortions and assumes that the Moon's disk must be physically larger.
Experiments conducted in 1962 by Kaufman & Rock showed that visual cues are a significant factor in creating an illusion (see Ponzo illusion). The moon on the horizon appears at the end of a sequence of landscape objects, trees and buildings, which tells the brain that it is very far away. As landmarks move away from the field of view, the large-looking Moon becomes smaller.
Opponents of this theory point to the presence of an illusion even when observing the luminary through a dark filter, when the objects surrounding it are indistinguishable.
Relative size theory
According to relative size theory, perceived size depends not only on the size on the retina, but also on the sizes of other objects in the visual field that we observe simultaneously. When observing the Moon close to the horizon, we see not only the Moon, but also other objects, against the background of which the Earth’s satellite appears larger than it actually is. When the Moon is in the sky, the vast expanses of the sky make it look smaller.
This effect was demonstrated by psychologist Hermann Ebbinghaus. The circle surrounded by small circles represents the Moon at the horizon and small objects surrounding it (trees, poles, etc.), and the circle surrounded by larger objects represents the Moon in the sky. Even though both center circles are the same size, many people think that the right circle in the picture is larger. Anyone can check this effect by taking some large object (for example, a table) out of the room into the yard. In an open space it will look clearly smaller than indoors.
Opponents of this theory point out that airplane pilots also observe this illusion, although there are no ground objects in their field of vision.
Quantitative comparison of different theories based on experimental data
Specially designed experiments allowed quantitatively compare the influence of various factors proposed to explain the illusion. In particular, raising the observer's head(the theory about the role of eye convergence) affects the change in size, but very weakly (the apparent change in size is 1.04 times), the change colors or brightness the lunar disk has virtually no effect on the apparent size, and presence of a horizon line or its optical model (the theory of apparent distance and relative size) leads to an apparent change in the size of the disk by 1.3 - 1.6 times, and the exact magnitude of the change depends on the features of the landscape.
Proof of Illusion
A widespread misconception, dating back at least to the time of Aristotle (4th century BC), is that the Moon's larger size at the horizon is due to a magnification effect created by the Earth's atmosphere. However, astronomical refraction at the horizon only slightly reduces the observed size, making the Moon slightly flattened along the vertical axis.
There is currently no consensus on whether the Moon appears larger at the horizon due to a larger perceived angular size or a larger perceived physical size, that is, whether it appears closer or larger.
In general, a complete explanation of this feature of human perception still does not exist. In 2002, Helen Ross and Cornelis Plug published the book The Mystery of the Moon Illusion, in which, after considering various theories, they concluded: “No theory has won.” The authors of the collection “Moon Illusion”, published in 1989 under the editorship of M. Hershenson, came to the same decision.
There are many different theories to explain the moon illusion. Only the main ones are listed below.
Theory about the role of eye convergence
In the 1940s, Boring (1943; Holway & Boring, 1940; Taylor & Boring, 1942) and in the 1990s, Suzuki (1991, 1998) proposed an explanation for the Moon illusion, according to which the apparent size of the Moon depends on the degree convergence of the observer's eyes. That is, the illusion of the Moon is the result of increased impulses towards convergence of the eyes that arise in the observer when he looks up (to look at the Moon at its zenith), and the eyes themselves tend to diverge. Because eye convergence is a sign of object proximity, an object high in the sky appears smaller to an observer.
In one experiment, Holway and Boring (1940) asked subjects to compare their perceived size of the Moon with one of a disk of light projected onto a screen next to them. In the first series of the experiment, the subjects sat on a chair. While observing the Moon near the horizon (at the observer's eye level), they chose a disk that was significantly larger in size than the one they selected when observing the Moon at its zenith (raising their eyes at an angle of 30°). In the second series, the subjects watched the Moon while lying on the table. When they lay on their backs and looked at the Moon at its zenith, or when they were forced to throw their heads back and look up to see the Moon on the horizon from a supine position, the results were the opposite. The Moon near the horizon seemed smaller to them than the Moon at its zenith.
Opponents of this hypothesis argue that the illusion of an enlarged Moon quickly fades with an increase in the height of the luminary above the horizon, when the need to throw back the head and raise the eyes up does not yet arise.
The theory of apparent distance
The theory of apparent distance was first described by Cleomedes around 200 AD. e. The theory suggests that the Moon near the horizon appears larger than the Moon in the sky because it appears farther away. The human brain sees the sky not as a hemisphere, which it actually is, but as an oblate dome. Watching clouds, birds and airplanes, a person sees that they decrease as they approach the horizon. Unlike terrestrial objects, the Moon, when near the horizon, has approximately the same apparent angular diameter as at the zenith, but the human brain tries to compensate for perspective distortions and assumes that the Moon's disk must be physically larger.
Experiments conducted in 1962 by Kaufman & Rock showed that visual cues are a significant factor in creating an illusion (see Ponzo illusion). The moon on the horizon appears at the end of a sequence of landscape objects, trees and buildings, which tells the brain that it is very far away. As landmarks move away from the field of view, the large-looking Moon becomes smaller.
Opponents of this theory point to the presence of an illusion even when observing the luminary through a dark filter, when the objects surrounding it are indistinguishable.
Relative size theory
According to relative size theory, perceived size depends not only on the size on the retina, but also on the sizes of other objects in the visual field that we observe simultaneously. When observing the Moon close to the horizon, we see not only the Moon, but also other objects, against the background of which the Earth’s satellite appears larger than it actually is. When the Moon is in the sky, the vast expanses of the sky make it look smaller.
This effect was demonstrated by psychologist Hermann Ebbinghaus. The circle surrounded by small circles represents the Moon at the horizon and small objects surrounding it (trees, poles, etc.), and the circle surrounded by larger objects represents the Moon in the sky. Even though both center circles are the same size, many people think that the right circle in the picture is larger. Anyone can check this effect by taking some large object (for example, a table) out of the room into the yard. In an open space it will look clearly smaller than indoors.
Opponents of this theory point out that airplane pilots also observe this illusion, although there are no ground objects in their field of vision.
Quantitative comparison of different theories based on experimental data
Specially designed experiments allowed quantitatively compare the influence of various factors proposed to explain the illusion. In particular, observer's head lift(the theory about the role of eye convergence) affects the change in size, but very weakly (the apparent change in size is 1.04 times), the change colors or brightness the lunar disk has virtually no effect on the apparent size, and presence of a horizon line or its optical model (the theory of apparent distance and relative size) leads to an apparent change in the size of the disk by 1.3 - 1.6 times, and the exact magnitude of the change depends on the features of the landscape.
Notes
Links
- NASA - Solstice Moon Illusion (English)
- Astronomy Picture of the Day (English) (September 26, 2007). Retrieved December 9, 2012.
- The Moon Illusion, An Unsolved Mystery. (English)
- The Moon Illusion Explained
| Moon | ||
|---|---|---|
| Peculiarities | |
|
| Orbit | ||
| Surface | ||
| Selenology | ||
| Study | ||
| Other | ||
Wikimedia Foundation. 2010.
The illusion of the Moon is manifested in the fact that when it is near the horizon, it seems to us that it is about one and a half times larger than when it is at its zenith, although its retinal images (image on the retina in the central projection) in both cases are equal. In reality, the Moon, like the Sun, occupies a much smaller portion of the visible sky than most of us realize.
The angular size of the Moon's projection onto the retina is almost exactly 0.5°. The object has an angular size close to this value, equal to approximately 6 mm and 76 cm distant from the eye. But if you hold this object at the correct distance, its size is sufficient to completely cover the projection of the Moon. The Moon illusion has always aroused great interest, and many scientists have tried to explain it. Below is a description of the most famous interpretations.
Apparent distance hypothesis
An attempt to explain the illusion of the Moon using perceptual factors was made by Ptolemy (c. 90 - c. 160), a Greek astronomer and geometer. He proposed that any object separated from the observer by filled space, including the Moon visible on the horizon surrounded by various objects, appears more distant than an object physically equally distant but separated by empty space, such as the Moon at the zenith. The images of the Moon on the retina are the same in both cases, but when the Moon is not on the horizon, it appears more distant to the observer.
That it both appears to him and is larger in size is a direct consequence of the linear relationship between apparent size and apparent distance, which we described in discussing the factors favoring the constancy of the perception of distance: perceived size is directly proportional to perceived distance.
This interdependence is illustrated in the figure. 
Thanks to the signs of perspective, the right block seems more distant than the others. Since the sign of distance “triggers the mechanism” of constancy in the perception of size, it seems to the observer that the right block is larger than the others, although they are identical.
Consequently, if two objects whose retinal images are equal in size appear to the observer to be located at different distances from him, the one that appears more distant will always appear larger in size. This relationship is called the apparent distance hypothesis (or the size-distance invariance hypothesis).
If we use this hypothesis to explain the illusion of the Moon, we can say that the Moon near the horizon seems to us more distant than the Moon at the zenith, and therefore larger in size. You must have already understood that we have before us a special case of constancy of size perception, namely, due to the fact that signs of distance activate the mechanism of constancy of size perception, the Moon near the horizon seems to us larger in size than the Moon at the zenith.
The apparent distance hypothesis was actively studied by Kaufman and Rock. They argued that since the Moon is very far from the observer, it is perceived by him as a large object, but as an object whose size is indeterminable. Asking observers to estimate the magnitude of a stimulus, the magnitude of which is indeterminable, by comparing it with disks located next to it, which have very specific dimensions, means asking them to compare obviously incomparable things.
Instead, Kaufman and Rock asked observers to compare the size of two artificial moons visible against the sky and select pairs of equal size. Of course, such a comparison is in its very essence similar to the comparison made in the original illusion, although in the latter the two real Moons are separated in both time and space.
Against the sky, Kaufman and Rock, using a spotlight, presented observers with a circle of light, the size of which could be changed (an artificial moon). Using a pair of searchlights, the observer was able to compare a standard circle projected at a certain point in the sky, for example, near the horizon, with a circle whose size could be changed and which was projected, for example, at a point corresponding to the zenith.
The size of the variable circle, which was “chosen” by the observer and which, in his opinion, corresponded to the size of the standard circle, was taken as a measure of the magnitude of the illusion.
The results of these experiments showed that, regardless of the degree of gaze elevation, the Moon near the horizon was perceived as significantly larger in magnitude than the Moon at its zenith. After conducting a series of experiments, the researchers came to the conclusion that the Moon near the horizon appears much more distant than the Moon at its zenith, and that this impression is created by the terrain, which is perceived by the observer as space receding into the distance.
As noted above, when discussing the role of constancy in the perception of size, if two objects have retinal images of equal size, but are located at different distances from the observer, the larger one will appear larger in size, the distance to which seems greater to the observer.
This means that from Kaufman and Rock’s ideas about apparent distance it follows that the Moon, which seems more distant to the observer, is also perceived by him as larger in size. In other words, due to the constancy of size perception, the perceived size of an object is a function of its distance from the observer. Therefore, if the retinal images are equal, the greater the apparent distance, the greater the apparent magnitude.
Criticism of the apparent distance hypothesis: the paradox of remoteness. Despite all its appeal, the apparent distance hypothesis cannot explain all the nuances of the Moon illusion. Thus, Suzuki compared judgments about light stimuli projected onto the horizon with stimuli projected at the highest point of the vault located under the dome of a planetarium immersed in complete darkness.
Despite the fact that under these conditions practically no signs of distance were available to the observer, the illusion of the Moon manifested itself quite reliably. Of more fundamental importance for the theory of apparent distance is that very often it seems to us that the Moon near the horizon is not only larger than the Moon at the zenith, but that it is also less distant from us. This phenomenon is called the paradox of remoteness, or the phenomenon of further - more - closer.
The distance paradox poses a serious problem for the apparent distance hypothesis, which is based on the idea that the Moon near the horizon appears larger to an observer because, due to the distance features associated with Terrain, it appears further away than the Moon at its zenith.
Kaufman and Rock explain the paradox of the distance of the Moon near the horizon as a seriality effect, which is the result of processing information about magnitude and distance in situations in which it is necessary to make conclusions about distance and magnitude, respectively.
In other words, conclusions about the size of the Moon and its distance from the observer are not made simultaneously or on the basis of the same set of visual features. In accordance with the hypothesis that explains the illusion of the Moon by the apparent distance and constancy of the perception of size, it seems to the observer that the Moon near the horizon is larger in size than the Moon at the zenith, because it seems to him more distant. This is the result of a direct, unintentional, almost automatic inference regarding the relationship between apparent distance and apparent size, characteristic of such a phenomenon as the constancy of the perception of size.
As for the judgment about the distance of the Moon, located near the horizon, it is the result of a deliberate, conscious decision based on its apparent size. Since it seems to the observer that the Moon near the horizon is larger in size than the Moon at the zenith, therefore, it must be closer.
Koren and Ax explain the paradox of distance as follows, i.e., the fact that the observer perceives the Moon near the horizon as larger in size and located closer to it than the Moon at the zenith.
If we accept that we are dealing with a sequence of events that begins with the “launch” of the mechanism of constancy of perception of magnitude by a sign of depth accessible to the observer and ends with a distortion of the perception of the magnitude of the Moon, it turns out that, of course, there is no paradox, and the result is quite expected.
In this case, it seems to the observer that the Moon near the horizon is larger in size, and this impression is a source of information for assessing the apparent distance. She seems closer to him because she is bigger. Two judgments are made on the basis of different initial data... Thus, in the Moon illusion, one illusory perception (the illusion of size) becomes the source of a secondary illusion (the difference in apparent distance).
Hypothesis based on eye convergence
Boring proposed an explanation for the Moon illusion based on the fact that its apparent size depends on the degree of convergence (from Lat. con - getting closer, converging) - reduction of the visual axes of the eyes in relation to the center, in which point light stimuli reflected from the object of observation fall on the corresponding places of the retinas in both eyes, due to which the elimination of double vision of the object is achieved) the eye of the observer. In other words, according to the hypothesis based on eye convergence, the Moon illusion is the result of an increase in impulses to converge the eyes that arise in the observer when he looks up, and the eyes themselves tend to diverge (divergence of the visual axes of the right and left eyes). (When an observer looks at the Moon at its zenith, this is exactly what happens.) However, since eye convergence is a sign of the proximity of an object, the observer appears to the object to be smaller in size.
One of Holway and Boring's (1940) experiments involved asking subjects to compare their perceived size of the Moon with one of a disk of light projected onto a nearby screen. Observing the Moon located near the horizon, i.e., at eye level, the subjects chose a disk that was significantly larger in size than the one they chose when observing the Moon located at. zenith, raising your eyes at an angle of 30°.
When observers lay on a flat table and from this position observed the Moon at its zenith, without raising or lowering their eyes, or when they lay on the table with their heads hanging from it and their eyes raised up to see the Moon on the horizon, the results were the opposite: The Moon near the horizon seemed smaller to the subjects than the Moon at its zenith. Similar impressions can be obtained if you look at the Moon, bending in half and sticking your head between your legs.
Boring explains the moon illusion by the convergence and divergence of the eyes that occurs when the observer raises or lowers his head. Moving the neck, head or body alone is not enough to observe this illusion. However, there is no convincing psychological process that could explain the change in visual space observed by Boring during vertical eye movements. Boring himself wrote:
No theory provides a satisfactory explanation for this phenomenon. Everything that happens is connected with the specifics of the vision mechanism... We can only assume that the efforts aimed at raising or lowering the eyes reduce the perceived size of the Moon... Since we do not know why the tension of the oculomotor muscles should affect the visually perceived size.
Alternative explanations for the moon illusion
Despite the fact that the explanation of the Moon illusion based on the hypothesis of apparent distance has the largest number of supporters, many other explanations are known, mainly of a cognitive nature. A well-known explanation is that the observer does not need to process information about apparent distance (Restle, 1970). The basic proposition of the relative size hypothesis proposed by Restle is that the perceived size of an object depends not only on the size of its retinal image, but also on the size of objects in its immediate vicinity.
The smaller these objects, the larger its apparent size. Consequently, if a decision about the size of the Moon is made by an observer based on its comparison with the objects closest to it, it seems to him that the Moon near the horizon is larger, because it is perceived by him against the backdrop of a certain landscape and at a small angle of inclination (the angle of inclination to the horizon is 1° ). When the Moon is at its zenith, it is perceived against the background of visually free space (the angle of inclination to the horizon is 90°) and therefore appears smaller.
In this case, the Moon illusion is interpreted as an example of the relativity of perceived size. The same object can be perceived differently depending on the context. It is possible that relative size may play some role, perhaps a subordinate one, in one version of the apparent distance hypothesis.
There are many other explanations for the moon illusion, and we simply do not have the opportunity to present them all. However (we do not mean “exotic” hypotheses) if there is a systematic error in the perception of the Moon, this should not surprise anyone. After all, when we make judgments about the size of the Moon, we are actually trying to estimate the size of a celestial body that is 402,250 km away and has a diameter of 3,218 km!
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