The Müller-Lyer Illusion is named after its creator, Franz Carl Müller-Lyer (1857 - 1916), a German psychiatrist and sociologist, who first published the illusion in the physiology journal Archiv für Anatomie und Physiologie, Physiologische Abteilung in 1889.

The Müller-Lyer Illusion is one among a number of illusions where a central aspect of a simple line image – e.g. the length, straightness, or parallelism of lines – appears distorted in virtue of other aspects of the image – e.g. other background/foreground lines, or other intersecting shapes. These are sometimes called ‘geometrical-optical illusions’ - and you can search for others in the Illusions Index.

There have been a number of attempts to explain how the Müller-Lyer illusion works. The following discussion will focus first on the original arrowhead version, before moving on to other versions. The three most discussed attempts to explain how the illusion works are: (i) ‘misapplied size constancy scaling’ – the arrowheads engage the part of the visual system that deals with depth cues in retinal images, and results in the line with the outward-pointing arrowheads being perceived as longer because it is processed as being further away (Gregory 1997); (ii) ‘conflicting cues’ – the arrowheads are perceived as contributing to the length of the lines, and the longer overall shape of the line with the outward-pointing arrowheads causes the appearance of greater length of that line (Day 1989); (iii) ‘confusion’ – the inter-tip distance between the relevant arrowheads influences perceived length. So, for the line with the inward-pointing arrowheads, the distance between the tips of the arrowheads at opposite ends of the line is shorter than the distance between the tips of the outward-pointing arrowheads of the other line, thus causing the illusion (Sekuler and Erlebacher 1971).

One version of the Müller-Lyer that seems to support the misapplied size constancy scaling hypothesis embeds the illusion in an image representing a room with relevant perspectival depth:
Perhaps the most unique contribution made by the Müller-Lyer illusion to debates in cognitive science is with regards to the modularity of mind. On the hypothesis that the mind is modular, a mental module is a kind of semi-independent department of the mind which deals with particular types of inputs, and gives particular types outputs, and whose inner workings are not accessible to the conscious awareness of the person – all one can get access to are the relevant outputs. For example, even though one knows that, with the Müller-Lyer illusion, the lines are of same lengths, it still appears as if they are not; the module, or modules, that make up the relevant parts of the visual system continue to output the ‘different length’ appearance, despite one’s conscious awareness that this is incorrect. Although the details and the implications of the modularity of the mind are widely debated, that there are modules in some sense or other is now widely accepted, but this was not always so. And the Müller-Lyer illusion was one of the central examples employed in supporting the hypothesis that human minds are at least partly modular (see Fodor 1983 for the classic statement of the argument for modularity which employs the Müller-Lyer illusion as the central example). For an examination of this general issue, see Macpherson (2012).

Relatedly, there has been much discussion of whether the illusion is only seen by people who have been raised in ‘carpentered environments’ which contain lots of right-angles (e.g. many urban environments). This hypothesis is supported by studies which purport to show that those living in less rectilinear environments (e.g. many rural environments) are less susceptible to the illusion (e.g. Segall et al. 1963). Others have investigated alternative factors such as differences in eye pigmentation between ethnicities, and gender, race, or age differences (Pollack 1963; Pollack and Silvar 1967; Jahoda 1971; Stewart 1973). Whether such differences cause a change in susceptibility to the illusion is controversial.

One interesting line of investigation in the above debates involves testing whether different versions of the illusion, such as the circle-heads variant illustrated below, produce the purported effects. If, for example, the circle-heads variant (reproduced below) produces the illusory effect in populations raised in rectilinear environments, then this might count against the ‘carpentered world’ hypothesis (as well as perhaps, the misapplied size constancy scaling hypothesis), as the illusion would have been shown to persist in the relevant groups in the absence of rectilinear cues. A recent, prominent discussion of these issues can be found in McCauley and Henrich (2006).