Müller-Lyer Illusion

Fins that change a line's length

Two straight lines of exactly the same length: one ends in inward-pointing fins, like arrowheads (>-<), the other in outward-pointing fins, like the flights of an arrow (<->). The line with outward fins looks longer, and keeps looking longer even after you've measured them. The test above measures how strongly it works on you: set the lines to look equal a few times, and it tells you how far, and in which direction, the fins pulled your judgement.

More than one cause

The Müller-Lyer illusion has outlived well over a century of competing explanations, and the honest answer is that several effects probably add together.

The best-known account is Richard Gregory's: the fins look like corners (Gregory, 1963). Inward fins resemble the near corner of a building, its walls sloping away from you; outward fins resemble the far corner of a room, its walls coming towards you. The visual system spends its life correcting for distance, enlarging things it takes to be further away so that they keep a constant size. Applied to a flat drawing that only resembles a corner, that correction misfires, and the "far corner" line is stretched.

A related account comes from Catherine Howe and Dale Purves, who analysed large collections of images of real scenes. They argued that, in the real world, lines seen in these two kinds of context tend to come from physical objects of different lengths, and that perception reflects what such lines have most often turned out to be, rather than measuring the drawing directly (Howe & Purves, 2005).

A simpler factor also contributes: the outward fins make the whole figure bigger, and length judgements are partly pulled towards the overall extent of the shape. That's one reason the illusion survives when the fins are replaced with circles or squares, which look nothing like corners.

How the test above works

Each run has eight trials in random order. In three, you adjust the outward-fin line to match an inward-fin line; in three more, it's the other way round, so a habit of always setting the adjustable line too long or too short cancels out rather than masquerading as the illusion. The last two trials use plain lines with no fins at all. They measure your ordinary eyeballing error, which gives you something to compare the fin trials against: if the fins shift you 20% while plain lines only put you 3% out, the difference is the illusion.

A few details stop you gaming it. The adjustable line starts somewhere between 8% and 25% too long or too short, so you can't just leave the slider where it was. The two lines are also shifted sideways by different amounts, so you can't simply line up their ends by eye.

There isn't a single "normal" score to aim for. The size of the illusion depends on how the figure is drawn: it grows with longer fins and shrinks as the angle between fin and shaft widens or as the shaft is made more prominent (Dewar, 1967). The fins in this test are 20 units long at about 37° to the shaft, a fairly standard shape, so a clear effect in the classic direction is what you'd expect.

If you run the test several times, your score will probably drop. That isn't the test going wrong; it's one of the oldest findings about this illusion. Charles Judd reported in 1902 that repeated judgments steadily shrank the effect, and that flipping the figure left to right brought it straight back - evidence that people were learning to discount these particular figures rather than seeing the lines any more accurately. The test remembers your previous score on this device so you can watch it happen.

Does everyone see it?

Not to the same degree. In the 1960s, Marshall Segall and colleagues tested people from many cultures and found that some groups living in environments with few straight walls, square corners and rectangular buildings were much less affected than urban Europeans and Americans (Segall, Campbell & Herskovits, 1963). That fits the corner explanation: if the illusion comes partly from experience with built corners, less exposure should weaken it. The interpretation is still debated, since the groups also differed in education, familiarity with pictures and how they were tested, but the size of the differences was striking.

A long-lived figure

The German psychiatrist and sociologist Franz Carl Müller-Lyer published the figure in 1889, one of a wave of "geometric-optical illusions" studied in German laboratories at the time, alongside the Ebbinghaus and Ponzo effects (Müller-Lyer, 1889). It's still a standard tool in perception research because it's so easy to vary and so reliable. The Ponzo illusion and the Ebbinghaus illusion have their own tests on this site, so you can compare your scores.