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One possible explanation, given by Richard Gregory, states that the Müller-Lyer illusion occurs because the visual system processes that judge depth and distance assume in general that the " angles in " configuration corresponds to an object which is closer, and the " angles out " configuration corresponds to an object which is far away.
Basically, there seems to be a simple heuristic that takes those configurations as 90 ° angles.
This heuristic speeds up the interpretation process, but gives rise to many optical illusions in unusual scenes.
A recent report by Catherine Howe and Dale Purves summarizes current thinking on Gregory's ideas:

2.032 seconds.