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[[Image:Müller-Lyer illusion.svg|thumb|the Müller-Lyer optical illusion with arrows. Both set of arrows are exactly the same, the bottom one shows how the arrows are of the exact same length.|200px]]
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[[Image:Müller-Lyer illusion.svg|thumb|Two sets of arrows that exhibit the Müller-Lyer optical illusion. The set on the bottom shows that all the shafts of the arrows are of the same length.|200px]]
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The '''Müller-Lyer illusion''' is an [[optical illusion]] consisting of a stylized arrow. When viewers are asked to place a mark on the figure at the midpoint, they invariably place it more towards the "tail" end. It was devised by [[Franz Carl Müller-Lyer]] (1857 &ndash; 1916), a German sociologist, in 1889.<ref>Müller-Lyer, FC (1889), "Optische Urteilstäuschungen"; ''Archiv für Physiologie Suppl.'' 263–270.</ref><ref>Brentano, F (1892), "Über ein optisches Paradoxen", ''Zeitschrift für Psychologie'', 3:349–358.</ref><ref>Müller-Lyer, FC (1894), "Über Kontrast und Konfluxion", ''Zeitschrift für Psychologie'', IX p 1 / X p 421.</ref>
   
The '''Müller-Lyer illusion''' is an [[optical illusion]] consisting of nothing more than an arrow. When viewers are asked to place a mark on the figure at the mid-point, they invariably place it more towards the "tail" end. Another variation consists of two arrow-like figures, one with both ends pointing in, and the other with both ends pointing out. When asked to judge the lengths of the two lines, which are equal, viewers will typically claim that the inward pointing pair is longer. One possible explanation is that one sees the lines as three-dimensional, such as the outgoing and ingoing corners of a room. Another possible explanation is that the line with arrows pointing inwards may simply appear longer because the arrows themselves extend past the line.
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A variation of the same illusion (and the most common form in which it is seen today, see figure) consists of a set of arrow-like figures. Straight line segments of equal length comprise the "shafts" of the arrows, while shorter line segments (called the fins) protrude from the ends of the shaft. The fins can point inwards to form an arrow "head" or outwards to form an arrow "tail". The line segment forming the shaft of the arrow with two tails is perceived to be longer than that forming the shaft of the arrow with two heads.
   
The illusion is not cross-cultural. Non-Western subjects, and particularly subjects whose day-to-day surroundings are usually not rectangular (few buildings, doors, walls) are much less likely to be affected by it (Segall, et al., 1963).
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==Variation in perception{{anchor|Variation in Perception}}==
   
==The perspective explanation==
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It has been shown that perception of the Müller-Lyer illusion varies across cultures and age groups.
One possible explanation states that the Müller-Lyer illusion occurs because the visual system processes that judge depth and distance assume in general that the “angles in” configuration corresponds to an object which is closer, and the “angles out” configuration corresponds to an object which is far away. Basically, there seems to be a simple heuristic that takes those configurations as 90º angles. This heuristic speeds up the interpretation process, but gives rise to many optical illusions in unusual scenes.
 
   
Neural nets in the visual system of (western) human beings learn how to make a very efficient interpretation of 3D scenes. That is why, when somebody goes away from us, we do not see him getting shorter. And when we stretch one arm and look at the two hands we do not see one hand smaller than the other. We should not forget that, as visual illusions show us quite clearly, what we see is an image created in our brain. Our brain projects the image of the smaller hand to its correct distance in our internal 3D model. This is what is called the size constancy mechanism.
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Segall, Campbell and Herskovitz<ref>Cultural Differences in the Perception of Geometric Illusions Author(s): Marshall H. Segall, Donald T. Campbell, Melville J. Herskovits Source: Science, New Series, Vol. 139, No. 3556 (February 22, 1963), pp. 769-771</ref> compared susceptibility to four different visual illusions in three population samples of Caucasians, twelve of Africans, and one from the Philippines. For the Müller-Lyer illusion, the mean fractional misperception of the length of the line segments varied from 1.4% to 20.3%. The three European-derived samples were the three most susceptible samples, while the [[Bushmen|San foragers]] of the Kalahari desert were the least susceptible.
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==History==
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Around the turn of the century, [[W. H. R. Rivers]] had noted that natives of the Australian [[Murray Island, Queensland|Murray Island]] were less susceptible to the Muller-Lyer illusion.<ref>Rivers 1901: The measurement of visual illusion ''Rep. Brit. Ass., p.&nbsp;818''</ref> Rivers suggested that this difference may be due to Europeans living in more rectilinear environments. Similar results were also observed by John Berry in his work on [[Eskimo]] groups (1968, 1971).
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.<ref>{{citation
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| title= Ecology, perceptual development and the M{\"u}ller-Lyer illusion
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| author=Berry, JW
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| journal=British Journal of Psychology
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| volume=59
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| number=3
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| pages=205–210
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| year=1968}}</ref>
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In 1965, following a debate between
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[[Donald T. Campbell]] and [[Melville J. Herskovits]] on whether culture can influence such basic aspects of perception such as the length of a line, they suggested that their student [[Marshall Segall]] investigate the problem. In their definitive paper of 1966, they investigated seventeen cultures and showed that people in different cultures differ substantially on how they experience the Müller-Lyer stimuli. They write<ref>http://psycnet.apa.org/psycinfo/1967-05876-000</ref>
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: European and American city dwellers have a much higher percentage of rectangularity in their environments than non-europeans and so are more susceptible to that illusion.
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  +
They also used the word "[[Carpentered environments|carpentered]]" for the environments that Europeans mostly live in - characterized by straight lines, right angles, and square corners.
  +
  +
These conclusions were challenged in later work by [[Gustav Jahoda]], who tested members of
  +
an African tribe living in a traditional rural environment vs. members
  +
of same group living in African cities. Here, no significant
  +
difference in susceptibility to the M-L illusion was found. Subsequent work by Jahoda suggested that [[retinal pigmentation]] may have a role in the differing perceptions on this illusion,<ref>
  +
{{cite article
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| title=Retinal pigmentation, illusion susceptibility and space perception
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| author=Jahoda, Gustav
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| journal=International Journal of Psychology
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| volume=6
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| number=3
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| pages=199--207
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| year=1971
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}}</ref> and this was verified later by Pollack (1970). It is believed now that not "carpenteredness", but the density of pigmentation in the eye is related to susceptibility to the M-L illusion. Dark-skinned people often have denser eye pigmentation.<ref>Cole, Michael; Barbara Means;
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Comparative Studies of How People Think: An Introduction, 1986. [http://books.google.com/books?id=thLR-f10WoMC&pg=PA42&lpg=PA42|gbook]</ref>
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A later study was conducted by Ahluwalia<ref>An intra-cultural investigation of susceptibility to "perspective" and "non-perspective" spatial illusions, Br. J. of Psychol., 1978, 69, 233-241</ref> on children and young adults from Zambia. Subjects from rural areas were compared with subjects from urban areas. The subjects from urban areas were shown to be considerably more susceptible to the illusion, as were younger subjects. While this by no means confirms the carpentered world hypothesis as such, it provides evidence that differences in the environment can create differences in the perception of the Müller-Lyer illusion, even within a given culture.
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Experiments have been reported<ref name="nakamura">{{cite web |first=Noriyuki |last=Nakamura et al. |url=http://psycnet.apa.org/index.cfm?fa=main.doiLanding&uid=2006-09888-010 |title=Perception of the Standard and the Reversed Müller-Lyer Figures in Pigeons (Columba livia) and Humans (Homo sapiens) |publisher=Journal of Comparative Psychology. 2006 August Vol 120(3) 252-261 |accessdate=2008-07-25}}</ref> suggesting that pigeons perceive the standard Müller-Lyer illusion, but not the reversed. Experiments on parrots have also been reported with similar results.<ref name="pepperberg">{{cite web |first=Irene |last=Pepperberg et al. |url=http://www.alexfoundation.org/pdf/irene_pdf/PerceptionAlexML.pdf |title=The Müller-Lyer illusion is processed by a Grey Parrot (Psittacus erithacus) |publisher=Perception 37:765-781 |accessdate=2011-07-30}}</ref>
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==The perspective explanation==
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[[Image:Mueller lyer.svg|thumb|right|The Müller-Lyer effect in a non-illusion]]
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One possible explanation, given by [[Richard Gregory]],<ref>Richard L. Gregory, ''Eye and Brain'', McGraw Hill, 1966.</ref> states that the Müller-Lyer illusion occurs because the visual system processes that judge depth and distance assume in general that the "angles in" configuration corresponds to an object which is closer, and the "angles out" configuration corresponds to an object which is far away. Basically, there seems to be a simple [[heuristic]] that takes those configurations as 90° angles. This heuristic speeds up the interpretation process, but gives rise to many optical illusions in unusual scenes. A recent report<ref>The Müller-Lyer illusion explained by the statistics of image–source relationships Catherine Q. Howe and Dale Purves* PNAS January 25, 2005 vol. 102 no. 4 1234-1239</ref> by Catherine Howe and Dale Purves summarizes current thinking on Gregory's ideas:
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<blockquote>Although Gregory's intuition about the empirical significance of the Müller-Lyer stimulus points in the right general direction (i.e., an explanation based on past experience with the sources of such stimuli), convex and concave corners contribute little if anything to the Müller-Lyer effect.</blockquote>
   
[[Image:Mueller_lyer.svg|thumb|left|160px|The Müller-Lyer effect in a non-illusion]]
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[[Neural net]]s in the visual system of human beings learn how to make a very efficient interpretation of [[Three-dimensional space|3D]] scenes. That is why when somebody goes away from us, we do not perceive them as getting shorter. And when we stretch one arm and look at the two hands we do not perceive one hand smaller than the other. We should not forget that, as visual illusions show us quite clearly, what we see is an image created in our brain. Our brain projects the image of the smaller hand to its correct distance in our internal 3D model. This is what is called the [[size constancy]] mechanism.
   
In the Müller-Lyer illusion, the visual system detects the depth cues, which are usually associated with 3D scenes, and incorrectly decides it is a 3D drawing. Then the size constancy mechanism makes us see an erroneous length of the object which, for a true perspective drawing, would be more far away.
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In the Müller-Lyer illusion, the visual system would in this explanation detect the depth cues, which are usually associated with 3D scenes, and incorrectly decide it is a 3D drawing. Then the size constancy mechanism would make us see an erroneous length of the object which, for a true [[Perspective (visual)|perspective]] drawing, would be farther away.
   
In the perspective drawing in the figure, we see that in usual scenes the heuristic works quite well. The length of the rug should obviously be considered shorter than the length of the wall in the back.
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In the perspective drawing in the figure, we see that in usual scenes the heuristic works quite well. The width of the rug should obviously be considered shorter than the length of the wall in the back.
   
 
==See also==
 
==See also==
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==References==
 
==References==
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{{reflist|2}}
 
* McGraw, K. O., & Stanford, J. (1994). The apparent distance of interior and exterior corners: A test of Gregory's misapplied size constancy explanation for the Mueller-Lyer illusion. ''[[Journal of General Psychology]], 121,'' 19-26.
 
* McGraw, K. O., & Stanford, J. (1994). The apparent distance of interior and exterior corners: A test of Gregory's misapplied size constancy explanation for the Mueller-Lyer illusion. ''[[Journal of General Psychology]], 121,'' 19-26.
   
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*[http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer Illusion]<br>
 
*[http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer Illusion]<br>
 
*[http://www.mind.duke.edu/files/sites/purves/pub/1181623288.pdf The Müller-Lyer illusion explained by the statistics of image–source relationships]
 
*[http://www.mind.duke.edu/files/sites/purves/pub/1181623288.pdf The Müller-Lyer illusion explained by the statistics of image–source relationships]
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*[http://www.visualstatistics.net/Scaling/Mueller-Lyer/Mueller-Lyer%20Illusion.html The misplaced illusion? The case of the Mueller-Lyer perceptual incongruity figure.]
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*[http://sites.google.com/site/nakamuranoriyuki2010/home_e NAKAMURA Noriyuki (Müller-Lyer Illusion in pigeons)]
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*[http://www.rit.edu/cla/gssp400/muller/muller.html The Muller-Lyer Illusion explained by Rochester Institute of Technology]
   
 
[[Category:Illusions (perception)]]
 
[[Category:Illusions (perception)]]
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[[Category:Muller Lyer illusion]]
 
[[Category:Optical illusions]]
 
[[Category:Optical illusions]]
   

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Müller-Lyer illusion

Two sets of arrows that exhibit the Müller-Lyer optical illusion. The set on the bottom shows that all the shafts of the arrows are of the same length.

The Müller-Lyer illusion is an optical illusion consisting of a stylized arrow. When viewers are asked to place a mark on the figure at the midpoint, they invariably place it more towards the "tail" end. It was devised by Franz Carl Müller-Lyer (1857 – 1916), a German sociologist, in 1889.[1][2][3]

A variation of the same illusion (and the most common form in which it is seen today, see figure) consists of a set of arrow-like figures. Straight line segments of equal length comprise the "shafts" of the arrows, while shorter line segments (called the fins) protrude from the ends of the shaft. The fins can point inwards to form an arrow "head" or outwards to form an arrow "tail". The line segment forming the shaft of the arrow with two tails is perceived to be longer than that forming the shaft of the arrow with two heads.

Variation in perceptionEdit

It has been shown that perception of the Müller-Lyer illusion varies across cultures and age groups.

Segall, Campbell and Herskovitz[4] compared susceptibility to four different visual illusions in three population samples of Caucasians, twelve of Africans, and one from the Philippines. For the Müller-Lyer illusion, the mean fractional misperception of the length of the line segments varied from 1.4% to 20.3%. The three European-derived samples were the three most susceptible samples, while the San foragers of the Kalahari desert were the least susceptible.

HistoryEdit

Around the turn of the century, W. H. R. Rivers had noted that natives of the Australian Murray Island were less susceptible to the Muller-Lyer illusion.[5] Rivers suggested that this difference may be due to Europeans living in more rectilinear environments. Similar results were also observed by John Berry in his work on Eskimo groups (1968, 1971). .[6]

In 1965, following a debate between Donald T. Campbell and Melville J. Herskovits on whether culture can influence such basic aspects of perception such as the length of a line, they suggested that their student Marshall Segall investigate the problem. In their definitive paper of 1966, they investigated seventeen cultures and showed that people in different cultures differ substantially on how they experience the Müller-Lyer stimuli. They write[7]

European and American city dwellers have a much higher percentage of rectangularity in their environments than non-europeans and so are more susceptible to that illusion.

They also used the word "carpentered" for the environments that Europeans mostly live in - characterized by straight lines, right angles, and square corners.

These conclusions were challenged in later work by Gustav Jahoda, who tested members of an African tribe living in a traditional rural environment vs. members of same group living in African cities. Here, no significant difference in susceptibility to the M-L illusion was found. Subsequent work by Jahoda suggested that retinal pigmentation may have a role in the differing perceptions on this illusion,[8] and this was verified later by Pollack (1970). It is believed now that not "carpenteredness", but the density of pigmentation in the eye is related to susceptibility to the M-L illusion. Dark-skinned people often have denser eye pigmentation.[9]

A later study was conducted by Ahluwalia[10] on children and young adults from Zambia. Subjects from rural areas were compared with subjects from urban areas. The subjects from urban areas were shown to be considerably more susceptible to the illusion, as were younger subjects. While this by no means confirms the carpentered world hypothesis as such, it provides evidence that differences in the environment can create differences in the perception of the Müller-Lyer illusion, even within a given culture.

Experiments have been reported[11] suggesting that pigeons perceive the standard Müller-Lyer illusion, but not the reversed. Experiments on parrots have also been reported with similar results.[12]

The perspective explanationEdit

Mueller lyer

The Müller-Lyer effect in a non-illusion

One possible explanation, given by Richard Gregory,[13] states that the Müller-Lyer illusion occurs because the visual system processes that judge depth and distance assume in general that the "angles in" configuration corresponds to an object which is closer, and the "angles out" configuration corresponds to an object which is far away. Basically, there seems to be a simple heuristic that takes those configurations as 90° angles. This heuristic speeds up the interpretation process, but gives rise to many optical illusions in unusual scenes. A recent report[14] by Catherine Howe and Dale Purves summarizes current thinking on Gregory's ideas:

Although Gregory's intuition about the empirical significance of the Müller-Lyer stimulus points in the right general direction (i.e., an explanation based on past experience with the sources of such stimuli), convex and concave corners contribute little if anything to the Müller-Lyer effect.

Neural nets in the visual system of human beings learn how to make a very efficient interpretation of 3D scenes. That is why when somebody goes away from us, we do not perceive them as getting shorter. And when we stretch one arm and look at the two hands we do not perceive one hand smaller than the other. We should not forget that, as visual illusions show us quite clearly, what we see is an image created in our brain. Our brain projects the image of the smaller hand to its correct distance in our internal 3D model. This is what is called the size constancy mechanism.

In the Müller-Lyer illusion, the visual system would in this explanation detect the depth cues, which are usually associated with 3D scenes, and incorrectly decide it is a 3D drawing. Then the size constancy mechanism would make us see an erroneous length of the object which, for a true perspective drawing, would be farther away.

In the perspective drawing in the figure, we see that in usual scenes the heuristic works quite well. The width of the rug should obviously be considered shorter than the length of the wall in the back.

See alsoEdit


ReferencesEdit

  1. Müller-Lyer, FC (1889), "Optische Urteilstäuschungen"; Archiv für Physiologie Suppl. 263–270.
  2. Brentano, F (1892), "Über ein optisches Paradoxen", Zeitschrift für Psychologie, 3:349–358.
  3. Müller-Lyer, FC (1894), "Über Kontrast und Konfluxion", Zeitschrift für Psychologie, IX p 1 / X p 421.
  4. Cultural Differences in the Perception of Geometric Illusions Author(s): Marshall H. Segall, Donald T. Campbell, Melville J. Herskovits Source: Science, New Series, Vol. 139, No. 3556 (February 22, 1963), pp. 769-771
  5. Rivers 1901: The measurement of visual illusion Rep. Brit. Ass., p. 818
  6. Berry, JW (1968), "Ecology, perceptual development and the M{\"u}ller-Lyer illusion", British Journal of Psychology 59 (3): 205–210 
  7. http://psycnet.apa.org/psycinfo/1967-05876-000
  8. Template:Cite article
  9. Cole, Michael; Barbara Means; Comparative Studies of How People Think: An Introduction, 1986. [1]
  10. An intra-cultural investigation of susceptibility to "perspective" and "non-perspective" spatial illusions, Br. J. of Psychol., 1978, 69, 233-241
  11. Nakamura et al., Noriyuki Perception of the Standard and the Reversed Müller-Lyer Figures in Pigeons (Columba livia) and Humans (Homo sapiens). Journal of Comparative Psychology. 2006 August Vol 120(3) 252-261. URL accessed on 2008-07-25.
  12. Pepperberg et al., Irene The Müller-Lyer illusion is processed by a Grey Parrot (Psittacus erithacus). Perception 37:765-781. URL accessed on 2011-07-30.
  13. Richard L. Gregory, Eye and Brain, McGraw Hill, 1966.
  14. The Müller-Lyer illusion explained by the statistics of image–source relationships Catherine Q. Howe and Dale Purves* PNAS January 25, 2005 vol. 102 no. 4 1234-1239
  • McGraw, K. O., & Stanford, J. (1994). The apparent distance of interior and exterior corners: A test of Gregory's misapplied size constancy explanation for the Mueller-Lyer illusion. Journal of General Psychology, 121, 19-26.

Further readingEdit

  • McCauley, R., & Henrich, J. (2006). Susceptibility to the Muller-Lyer Illusion, theory-neutral observation, and the diachronic penetrability of the visual input System. Philosophical Psychology, 19, 1-23. Full text

External linksEdit

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