Explaining the Müller-Lyer illusion has not been easy for psychologists.

One of the more popular explanations is the so-called "carpentered world" hypothesis. The idea is that in Western civilization, we are used to seeing lots of ruler-straight lines due to the dominating style of design and architecture - we live in a carpentered world of square houses, rectangular doors etc. Thus when a Westerner sees Müller-Lyer-type lines, the brain unconsciously interprets them as if they were the inside or the outside of a rectangular walled building.

This is a bit hard to explain verbally - or to represent in ASCII - but look at m_turner's diagrams (above) at 90 degrees on, and you should see it. The line in the second row is like the far corner of a room you're standing in, and the lines coming off each end are the floor and ceiling. The line in the third row, meanwhile, is the outside of a building, and the lines facing back from it are the walls receding away from you.

The brain sees that both lines look the same length, but it says to itself - if one of them is a far corner, it must be further away, so if it looks the same length, it must really be longer. All this happens before you finally perceive the conscious image, so you see the "far corner" line as being longer.

In 1963, Segall et al.1 tested this theory by showing the illusion to people from seventeen different cultures - three of "European" heritage (although actually from South Africa and North America) and fourteen non-European (mainly African). Susceptibility to the illusion can be tested by a simple device which allows you to adjust the length of one of the lines so that it looks the same length as the other. The non-Europeans came out less susceptible, and this was taken as support for the carpentered world hypothesis.

However in the same year, Pollack2 noted that susceptibility also decreases with age. He suggested that this was due to older people's decreased ability to detect contour. In 1967, Pollack and Silvar3 extended this to ethnicity and hypothesised that Europeans are more susceptible than darker-skinned people because they have less retinal pigmentation, and thus a greater ability to detect contour.

However support for the carpentered world hypothesis re-emerged in 1973 with a carefully-controlled study by Stewart4. The Müller-Lyer illusion, and a related illusion known as Sander5 (in which two lines of the same length in a parallelogram appear different), were presented to black and white children in urban Illinois, and black children in urban and rural Zambia. Stewart found that the American children were equally susceptible regardless of race, whereas among the black Zambian children, susceptibility was higher in the urban environment.

This is clear support for the carpentered world hypothesis, although crucially it cannot explain why the illusion persists when the arrows at the end of the lines are replaced by circles, which surely do not fool the brain into thinking of the edge of a building. Thus the debate continues.

1 - Segall, M.H., Campbell, D.T. and Herskovits, M.J. (1963) "Cultural differences in the perception of geometric illusions", Science, 193, pp.769-71.
2 - Pollack, R.H. (1963) "Contour detectability thresholds as a function of chronological age", Perceptual and Motor Skills, 17 pp.411-17.
3 - Pollack, R.H. and Silvar S.D. (1967) "Magnitude of the Müller-Lyer illusion in children as a function of pigmentation of the Fundus oculi", Psychonomic Science, 8, pp.83-4.
4 - Stewart, V.M. (1973) "Tests of the 'carpentered world' hypothesis by race and environment in America and Zambia", International Journal of Psychology, 8, pp.83-94.

5 - The Sander illusion, along with Müller-Lyer and various others, can be viewed at http://humanities.lit.nagoya-u.ac.jp/illusion/gallery/NVEG/index_e.html. (Update: this link appears to be dead.)

All references provided by Cardwell, M.C. (2000) Psychology for A Level, London: HarperCollins.

Is the Müller-Lyer Illusion Just a Visual Phenomenon?

*This is a write-up of an experiment that I and my fellow students conducted. This is my own interpretation of the findings. The introduction, however, was given to us by our supervisior.*

The Müller-Lyer illusion has been known for a great many years to effect the visual perception of the length of a line. But in the 1930s it was found to effect the perception of a line in the medium of touch. This finding has been demonstrated experimentally by Over (1968) and Suzuki and Arashida (1992). The purpose of this experiment was to attempt to verify their findings. It was found that using their touch sense, participants overestimated the length of the Müller-Lyer figure with outward directed fins, and underestimated the length of the figure with inwardly directed fins.

The Müller-Lyer illusion, illustrated below, robustly leads observers to judge that a line with outgoing fins (on the top) is longer than a comparison line with ingoing fins (on the bottom), despite the fact that the lines are objectively identical.



Figure 1 -- The top figure is “outward directed”, the bottom is “inward directed”

This illusion has primarily been studied in the visual modality, but Revesz (1934, cited by Fry 1975) was the first to note that this illusion also occurred in touch. There are several explanations as to why the Müller-Lyer illusion occurs (Over 1968). Gregory (1963) proposed that the illusion occurs due to “inappropriate constancy scaling”: the fins are perceived as representing a perspective view and the viewers judgement of the line is modified to take this into account. The outgoing fin is perceived to be further away, and the line length is increased to compensate for the apparent distance. Over (1967) argued that such an explanation would not account for the occurrence of a haptic version of the illusion, as depth information would not be conveyed by touch. However, Frisby & Davies (1971) argued that Gregory’s explanation would hold if participants were using visualisation in order to complete the haptic version of the task.

Illusions in touch have been investigated using an active and a passive technique. In the active technique participants trace over the figure with their fingers, in the passive technique they simply rest their fingers on the total figure. Over (1968) reports that the passive illusion is less marked than the active version of the illusion, which raises the possibility that different processes are involved in creating what is apparently the same illusion. This study uses the active technique, which eliminates the problems, identified by Over, of poor spatial acuity of the skin and rapid adaptation to stimulus remaining in contact with the skin.

Following Suzuki and Arashida (1992) this study tested whether the illusion did exist in touch. It provided a more stringent test of the illusion by comparing the inward and outward versions with a standard line stimulus with horizontal fins. Suzuki and Arashida compared inward fin stimuli directly with outward fin stimuli maximising the possibility of an illusion. It will also compare the visual illusion with the haptic version. A strong version of the visualisation claim would predict no difference in the extent of the illusion between visual and haptic modalities.


30 participants took part in the experiment. The participants were selected from first year Psychology students at the University of Oxford, and as such, had ages in the range of 18 or 19. There were 20 female and 10 male participants.

The stimuli used in the experiment were two series of Müller-Lyer figures embossed on card so that they were both visible and tactile. One series had outward fins, and the other inward directed fins. The angle of these fins was 135° for the outward directed fins, 45° for the inward, therefore being offset to the same degree, but in perpendicular directions (see Figure 1, above). The fins were 1cm in length, and the length of each series of stimuli went from 5.0cm to 9.0cm in 0.2cm intervals (21 stimuli in each series). The standard stimulus, to which the comparison stimuli just described were compared, was 7.0cm in length and had fins at 90° to the line (see Figure 2).


Figure 2 -- Standard stimulus

The stimuli were presented using the “method of limits”. Stimuli were presented in size sequence, starting from a shorter length than the standard stimulus and working up in ascending order for the first trial. On the second trial, the stimuli were presented in descending order from a longer length than the comparison. Participants were required to say if they thought the stimulus was a “longer”, “shorter”, or “the same” length on each trial. The stimuli were presented until the participant decided that the length of the comparison was the same as the standard. If the participant shifted their judgement of length between consecutive trials (i.e., went straight from “longer” to “shorter”, or “shorter” to “longer”, skipping the “equal” option), then it was assumed that the intermediate value was “equal”.

There were two parts to the experiment – one testing the tactile abilities, the other the visual abilities. In the testing for tactile discrimination ability, participants were given the standard stimulus and comparison stimulus in front of them. They then had to compare them using touch. To prevent measuring tactics, participants were not allowed to touch both stimuli at the same time, and only allowed to use one finger. They were required to use their dominant hand, and, naturally, participants had to carry out the test with their eyes closed so that only the touch sense was being used to judge length.

In the visual trials, participants were presented with the standard and comparison stimuli, but one at a time so that direct comparisons could not be made between them.

The starting point from which the stimuli were presented was different in each trial and picked randomly. This was to ensure that the participants were judging the length of the comparison stimuli based on perceptual input rather than counting up to the correct length stimulus.

The mean of the ascending trial and the descending trial was calculated to produce the point of subjective equality. This was done for each for the four trials (tactile, inward fins, tactile outward fins, visual inward fins, and visual outward fins) for comparison to the point of objective equality, or the 7cm standard.


The data were analysed using a one-sample t-test. The mean point of subjective equality (PSE) for the tactile trial for the inward finned figure (hereby referred to as “tactile in”) was 7.31cm with t(29) = 3.787, p = 0.001, while the mean PSE for the “tactile out” was 6.83cm with t(29) = -2.772, p = 0.010. These are both statistically significant at the 0.05 level (i.e., there is less than a 1-in-20 chance the findings are incorrect). The mean PSE for the “visual in” trial was 7.25cm while for the “visual out” trial it was 6.71cm. Both give significant results at the 0.05 level (both have p < 0.001).

Then paired sample t-tests were carried out on the data. The first pair tested was "tactile in" and "tactile out". There was significant difference between the two means. The same was true of the "visual in" and "visual out" pairing. Next, "tactile in" was compared to "visual in" and there was no significant difference between the means. Nor was there any significant difference between the "tactile out" and "visual out" pairing.


The experiment found that not only did the Müller-Lyer illusion works as anticipated for vision, its effect is found in the tactile sense as well. The results support the findings of Over, and Suzuki and Arashida, that is, that the inward fins produce overestimation in the tactile sense, while the outward fins produce an underestimation. The direct parallel to the optic version of the illusion is therefore borne out in the results of this experiment.

An explanation for this effect still remains largely unresolved. The evidence here does not contradict Over’s suggestion that Gregory’s “inappropriate constancy scaling” explanation does not apply to the tactile version of the Müller-Lyer illusion. However, there is nothing here that overtly points to Over’s account being correct, but it seems likely that some explanation that avoids an appeal from the visual system’s functioning will turn out to be a good one. It is important to point out that Frisby & Davies’ visualisation hypothesis cannot be rejected on the testimony of this study.

Perhaps there is some truth in both potential explanations (we often find that the truth lies in the middle ground). Maybe the illusion works in the media of both touch and vision due to processes in sensory association cortex in the brain. As such, the participant may not be visualising in the exact sense that Frisby & Davies imply, but just associating what they are touching with some constructed visual representation. It is very likely that the participants had seen the illusion before (since it is so commonly seen), so it may have been relatively easy to construct a visual representation. There is the interesting question of whether blind participants would display the same effects as the sighted participants used in this study. Perhaps they would not be able to associate what they are feeling with some kind of visual representation – particularly if they have been blind from birth or a very young age. This is certainly an avenue for further study and could provide an answer to why this effect occurs.

There is no scope in this study to spot any age trends, but there should not be much variance across the adult population. There may be some revealing results from studying infants, as they may not have developed certain brain functions that are key to the outcome of the experiment

This study has, however, succeeded in demonstrating that the Müller-Lyer illusion works for touch, supporting the findings of Over, and Suzuki and Arashida.


Frisby, J.P. & Davies, I.R.L. (1971). Is the haptic Müller Lyer a visual phenomenon? Nature, 231, 463-465.

Fry C.L. (1975). Tactual Illusions. Perceptual and Motor Skills, 40, 955-960.

Over, R. (1967). Haptic Illusions and inappropriate constancy scaling. Nature 214, 629.

Over, R. (1968). Explanations of geometrical illusions. Psychological Bulletin 70 (6) 545-562.

Suzuki, K. & Arashida, R. (1992). Geometrical haptic illusions revisited: Haptic illusions compared with visual illusions. Perception and Psychophysics, 52 (3), 329-335

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