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I chose the spinning dancer illusion, which, seen from two different perspectives, can give the illusion that the dancer is spinning in two different directions (not at once). We can see the dancer in different ways as a result of our bistable perception, so this illusion is thus in the family of illusions that includes the Necker cube and the face-vase. We have two optic nerves, one in each eye, which meet up at the optic chiasma. Any information about the left field of your view goes to the right hemisphere of your brain, and any information about the right field of your view goes to the left hemisphere of your brain. 

In the natural world, there are usually enough context clues around the object that the object will convey only one image to each person. However, with the silhouette, those context clues are eliminated, and the brain has to make a huge number of assumptions to produce an image that makes sense to the person.

With the dancer, because there are two valid contradictory views, the brain just picks one at any given time. Sometimes it'll pick the dancer to spin counterclockwise. Sometimes clockwise. As I wrote this paragraph, the dancer flipped 3 times for me.

The counterpart of this illusion in sound is the tritone paradox, where tritones are involved. When two notes related by a half octave are played in succession, some people will hear the notes ascending while others will hear them descending.

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