The Moon Illusion is an optical illusion , by the moon and sun in the horizon close look larger than in higher altitude on the firmament , though to the absence of physical or astronomical cause. The cause of this perceptual psychological phenomenon has not been finally clarified.
In relation to the viewing angle of the thumb of an outstretched hand, the viewing angle of the moon actually corresponds to the smallest lunar disc shown in the picture on the right, regardless of the position , even if most people would rather guess the size of the largest moon disc shown on the left. The apparent diameter of the moon (see also angle estimation ) is 31 arc minutes , i.e. about 0.5 degrees . Three to four lunar disks placed side by side appear at the same viewing angle as the width of the outstretched thumb, which is around 1.5 to 2 degrees depending on the width of the thumb and the length of the arm.
The first indications of the phenomenon of the moon deception can be found on clay tablets from the royal libraries of Nineveh and Babylon (6th century BC). Ptolemy (around 150 AD) wrongly suspected magnifying properties of the atmosphere . Alhazen (Abu Ali al-Hasan ibn al-Haitham, 965 to approx. 1040) stated that the moon has the same size both on the horizon and at the zenith, and already wrote of the flattened firmament (see below ) as the cause of the perception delusion . Even Leonardo da Vinci , Johannes Kepler and René Descartes dealt with the Moon illusion. This optical illusion has been studied by scientific psychology of perception for over 100 years. However, the phenomenon has still not been clearly clarified, and there are contradictions in the various explanations. The explanations currently most recognized and supported by many experiments are those of the incorrectly estimated distance with the flattened firmament and the principle of comparison objects.
It is often wrongly assumed that the illusion is a result of the "reddening" - due to Rayleigh scattering , much more blue than red light is scattered from the atoms and molecules of the earth's atmosphere from the bundle of rays from the sun and moon near the horizon, directed towards the observer that a larger proportion of red light reaches the eye of the observer. Nor is it a consequence of refraction . A change in size caused by refraction or reddening should also be visible on a photograph, but this is not the case.
The flattened firmament
Angle of vision and size perception
Correct information about its actual distance from the observer is essential for correct perception of the size of an object . The human brain unconsciously “calculates” the actual size of the object ( Emmert's law ) from the size of the image (the angle of vision ) of an object on the retina and the knowledge of its distance , by using the experience that an object is nearby produces a larger image on the retina than the same, more distant object. Since changes to the ground during the movement on its elliptical orbit by only about 10%, and in one night thus remains below one percent, it must be in the alleged significant increase in the size of the moon at sunrise and sunset to one the distance of the moon illusion act .
Perceptual delusions with regard to size usually arise when an unconscious incorrect assessment of the distance is present: An object (D) at a fixed distance (f), which creates an image of size (A) on the retina and incorrectly underestimates its distance (e ) is perceived as smaller or as just as large (C) as it should be in order to generate the size (A) on the retina at this underestimated smaller distance (see the sketch above). An example of this is the high moon or the so-called “toy car effect”: If you look down from a high tower, the distance is underestimated for lack of experience and the cars below are perceived as smaller, like toy cars.
Conversely: An object (C) at a fixed distance (e), which creates an image of the size (B) on the retina, and whose distance is incorrectly overestimated (f), is perceived as larger or just as large (D) how it would have to be in order to generate the size (B) on the retina at this overestimated greater distance (see sketch). An example of this is the moon near the horizon, the "moon illusion": Since there are many more objects (trees, houses, hills etc. - more "depth information") between the moon on the horizon and the viewer than between the moon up in the sky and the viewer, the Distance incorrectly assessed as larger, but if the distance is larger and the image on the retina is the same size, the object would have to be larger, and thus the moon or the sun on the horizon is also perceived larger.
Due to the depth information (trees, houses, etc.) when looking horizontally to the horizon and the lack of depth information when looking up, the firmament , on which the moon, sun and also the stars appear to be, has a flattened shape. If the image on the retina of the eye is of the same size in real terms , the apparently more distant moon is perceived larger on the horizon and the apparently less distant moon is smaller when it is higher.
Because of the flattened shape of the firmament, the individual stars of a constellation (for example the constellation Swan ) are perceived as being further apart, so the whole constellation appears larger when it is near the horizon than when it is at the zenith: and it becomes continuous smaller if, for example, it approaches the zenith in the course of a night from the east horizon. There is this continuous and linear change in size depending on the position in the sky with the constellations, but not so clearly with the moon or the sun. The apparent change in size of the sun and moon - in contrast to the perception of size in the constellations - is only noticeable near the horizon.
The explanation principle of the flattened firmament speaks in favor of the fact that this is the only way to explain the apparent continuous change in size of the constellations, while the principle of comparison objects (see below) can better explain why a change in the size of the sun and moon is only perceived near the horizon.
The principle of comparison objects also contributes to the apparent change in size: Because the moon is seen on the horizon in comparison with objects that appear small due to the great distance, such as trees or houses that are far away, it appears larger there than when it is standing tall in the horizon Comparison with the large firmament is seen or in comparison to comparatively large-looking tree tops in the immediate vicinity.
However, the moon is perceived as very large on the horizon even if there are no smaller objects for comparison, e.g. B. in the desert or by the sea. The horizon is very far away because of the unobstructed view, and there is a lot of perspective depth information. This contradicts the exclusive explanation of the phenomenon through smaller comparison objects and should rather be seen as evidence of the principle of the overestimated distance.
In addition, there is the following paradox : The moon, perceived larger because of the apparently larger distance "on the horizon", seems to be closer again because of its unusual size. This paradox could be resolved as follows: The illusions are mixed here according to two principles of distance perception :
- more things (depth information and perspective) in between mean a greater distance,
- a larger object is closer.
Variable perception area
In this hypothesis, the visual system is equated with a data channel. While the image on the retina can contain a great deal of information, the further neural processing of the image for perception represents a bottleneck: only a certain amount of information can be transmitted and processed per second, i.e. only a limited number of image elements can be identified. These can be used to display or perceive a larger or smaller section of the image, but a smaller section shows more detailed information, as the image elements are then packed more densely. A larger section in turn has the advantage of an overview. If one also assumes that the selected image section - whether large or small (left in the image) - is projected onto a kind of internal monitor or a memory of constant size in the visual system (right), then the moon illusion is represented as follows:
Due to the limited channel capacity, only a section of the retinal image is processed for perception. If the captured area is small, the identified image elements convey a high level of detail. A single object makes up a large proportion of this area and therefore appears large, including the moon. With a large angle of perception, the resolution is correspondingly lower, and everything appears correspondingly smaller - as it is projected onto the same surface. The “inner monitor”, which is always the same size, symbolizes the idea that the visual system always uses its full data capacity when viewing a large as well as a small area in order to capture a comparable number of characteristic details in both cases.
Goüye (1700) already suspected that the perception of size is related to the dissolution of details. He compares the moon behind trees and branches to a column that appears thicker when it has grooves. Lühr (1898) and Cornish (1937) expressed the idea that visual perception is concentrated on a limited but variable area. While Lühr discusses constellations low or high in the sky, Cornish justifies a different perception of the size of the sun on the horizon with its shape (flat or high).
Experiments to measure the perceived size of a bright circular disk were carried out by Erna Schur or by Lloyd Kaufman and Irvin Rock. While Schur found a strong increase in perception in the horizontal direction of view compared to the vertical, even with nearby terrestrial stimuli, Kaufmann and Rock report that a virtual circular disc appeared larger in the vertical direction of view when the natural horizon was faded into the line of sight via a mirror.
In evolutionary time periods, the brain has learned to automatically focus on a smaller area on the horizon in order to identify structures as early as possible that promised food or protection or also betrayed competition and predators. A large-scale acquisition - with renouncing high resolution - was chosen when it is z. B. was about assessing the weather or finding a flock of birds somewhere in the wide sky.
An unusually large celestial body can be observed on the horizon when it, as the dominant light source, highlights the details in its area sharply and with high contrast. The endeavor of the visual system to resolve small objects particularly well because of the good visibility conditions prevailing there, results in the setting of a correspondingly small angle of perception, which then automatically enlarges the moon (or the sun). In the case of earthly objects, the magnification effect is not so noticeable, because one sees them constantly from different distances and thus also of different sizes, while in celestial bodies with their always the same extent an apparent change in size is more noticeable.
Actual fluctuations in viewing angle
The moon orbits the earth in an ellipse , its distance fluctuating between 363,300 and 405,500 km. The moon diameter of 3,476 km is less than 1% of these distances, which is why the radian measure of the angle you are looking for can simply be taken as the ratio of diameter to distance ( small-angle approximation ). The viewing angle is accordingly 0.491 ° to 0.548 °, which corresponds to a fluctuation of +/- 5.5% around the mean value. This margin of 11% is too small to be reliably detected with the eye without direct comparison. However, the term supermoon has stood for the particularly large full moon near the earth since the 2010s. A change in the apparent diameter from apogee to perigee of about 13%, spread over several years, is imperceptible to the human observer.
If you look at the moon at a low angle of elevation , i.e. near the horizon, you can see its contour in its distance, which is calculated from the middle to the middle of the two celestial bodies earth and moon. If, on the other hand, the moon is at its zenith , the observer is closer to it by the earth's radius of a good 6,000 km, i.e. almost 2%. Objectively, when the moon is 40 ° or higher in the sky, it is visible at a viewing angle that is more than 1% larger than it is deep on the horizon - that is insignificant, but precisely against the subjective impression.
Due to the varying refraction of the atmosphere with its gradual density , the image of the moon deep on the horizon tends to be (flat) oval distorted. The viewing angle of the height of the moon image can then be smaller at this viewing position than when the moon is higher, but the horizontal latitude remains unchanged.
- E. Bruce Goldstein: Perceptual Psychology. An introduction. Spektrum Akademischer Verlag, Heidelberg et al. 1997, ISBN 3-8274-0094-5 , p. 243 ff.
- Joachim Herrmann : Why does the moon appear larger on the horizon than at the zenith? (= Publication of the Wilhelm-Förster-Sternwarte, Berlin. 16). Wilhelm-Foerster-Sternwarte, Berlin 1962. (Also in: Kosmos 58, 1962, issue 2, , p. 3 f.).
- Maurice Hershenson (Ed.): The Moon illusion. L. Erlbaum Associates, Hillsdale NJ 1989, ISBN 0-8058-0121-9 .
- Lloyd Kaufman, James H. Kaufman: Explaining the moon illusion. In: Proceedings of the National Academy of Sciences . Volume 97, Number 1, January 2000, pp. 500-505. PMID 10618447 , PMC 26692 (free full text).
- Helen Ross, Cornelis Plug: The Mystery of The Moon Illusion. Exploring size perception. Oxford University Press, Oxford 2002, ISBN 0-19-850862-X .
- Maurice Hershenson: The Moon Illusion. Project Syndicate, A World of Ideas (March 5, 2004).
- Stephan Mayer: The flattened firmament.
- P. Goüye: Various Observations de Physique Generale. In: Histoire de l'Acad. Royale des Sciences. Année 1700. Paris 1703, p. 8.
- K. Lühr: The apparent enlargement of the stars near the horizon. In: Mitth. d. Ver. v. Friends d. Astron. and cosm. Physics. 8, 1898, pp. 31-35.
- V. Cornish: Apparent Enlargement of the Sun at the time of rising and setting. In: Nature. 140, 1937, pp. 1082-1083.
- E. Schur: Moon illusion and constancy of visual size. In: Psychological Research. 7, 1926, pp. 44-80.
- L. Kaufman, I. Rock: Scientific American. Jul 1962, pp. 120-130.
- Detailed explanation of the "moon illusion" with many photos, drawings and further links
- What is the moon illusion? ( Memento from February 19, 2015 in the Internet Archive ) with many photos
- Welf A. Kreiner: Why is the moon so big today? Open Access Repository of the University of Ulm, 2001. doi: 10.18725 / OPARU-60
- WA Kreiner: Sun, Moon and Ursa Major - an information-theoretical model for size perception. Open Access Repository of Ulm University, doi: 10.18725 / OPARU-1213
- English-language summary of various theories by DE Simanek
- Statement by Maurice Hershenson, Professor of Psychology at Brandeis University