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