Psychologists, particularly Richard Gregory, explain the Müller-Lyer illusion using the concept of 'misapplied size constancy'. This explanation suggests the illusion works because the fins on the lines are interpreted as depth cues.
The line with the outward-pointing fins (>---<) resembles the outside corner of a building, which appears to be jutting out towards us. The line with the inward-pointing fins (<--->) resembles the inside corner of a room, which appears to be receding away from us.
Because we perceive the 'inside corner' line as being further away, our brain applies size constancy and scales it up, making it appear longer than the 'outside corner' line, even though the retinal images of the lines are the same length.
Richard Gregory's constructivist theory of perception provides the most common explanation for the Müller-Lyer illusion. He argued that perception is an active process of 'hypothesis testing' based on past knowledge and experience. In a world filled with buildings (a 'carpentered world'), we learn to interpret angles as depth cues. The fins-in figure looks like the far corner of a room, while the fins-out figure looks like the near corner of a building. Our brain uses this depth information and applies size constancy scaling. If two objects cast the same size image on our retina, but one is perceived as being further away, our brain concludes the further object must be larger. This is 'misapplied' constancy because the depth cues are on a 2D surface, leading to the illusion.
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