## The Spinning Dancer Illusion

The Spinning Dancer is a popular optical illusion that even has its own wikipedia entry.
The illusion is the following:

The illusion was created by web designer Nobuyuki Kayahara and the question is “Which direction is the dancer spinning?” That is, is the dancer is spinning clockwise or counter-clockwise?

“If the foot touching the ground is perceived to be the left foot, the dancer appears to be spinning clockwise (if seen from above); if it is taken to be the right foot, then she appears to be spinning counterclockwise.”

A nice graphic that illustrates how the dancer can be observed as spinning in either direction is below. By simplying adding some lines to the original image you you can give direction to the dancer. The left image shows the dancer spinning clockwise, while the right image shows the dancer spinning counter-clockwise.

** Note: Some posts on Math-Fail are user-submitted and NOT verified by the admin of the site before publication. If you find this post to be distasteful, non-math related, ?or something worse?, then definitely leave a comment letting me know. Thanks very much! Mike **

1. Michael J Swart

This is cool. I’ve seen this illusion with the following question “Is she spinning right or left?” which is meaningless and I never quite understood what they meant. The question “Is she spinning clockwise or counterclockwise” makes more sense (because looking down at her is implied).

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2. Technically she is standing on her right leg and spining anti-clockwise when seen from above

Explanation: assume from the direction of the shadow that the light is on the other side of the girl than ths camera

Now, the shadow of the raised (left) foot is coming into view when the left foot is away from us… and when it comes closer, the shadow vanishes because it goes beyond the angle of view of camera

Otherwise if you think she is rotating in the clockwise direction when seen from top, you will mean she is standing on the left foot and shadow of the right leg is coming in picture when she is bringing her foot closer to the camera and vanishing when taken away.. this is wrong by physics principles..

However if you assume that is not a shadow but her reflection from a mirror like floor, then clockwise direction when seen from above would be the right answer and the anticlockwie direction a wrong one

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3. Smartie McSmartypants

Ah, but your assertions regarding shadows make 2 assumptions: a) you know which way the light is coming from and b) that her foot remains at the same height.
If the light can come from other directions, the shadows could be cast in many different ways. Also, if her foot is moving up and down relative to the floor as she rotates (which dancers often do to) then the way the shadows fall will vary.
If, on the other hand, it is a “mirror like floor”, both reflection patterns can be obtained if you throw out the assumption that the floor is level. If it has a slope, then either reflection pattern (clockwise or anti-clockwise) is possible.

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4. 1) The light source has to be on the other side of the shadow. So that is not an assumption but the inference. However, the positioning of the light source may be high or low but in either cases the shadow of the foot should be visible if it is visible on the other side.. the inclination of the light ray touching the foot (in the shadow-not-in-view case)angle will always be more in that case than for the other foot.
2) If her foot was moving up and down the it would have to be really a sufficiently high raise relative to the inclination of the ray of light touching her foot. Her motion pattern doesn’t seem to suggest that. [though it could be another illusion in itself here ;)]
3) Also if you suggest that dancers often move the foot up and down, you should also realise that a dance floor is ALWAYS level

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7. What’s troubling is that years of cognitive tuning force continuity of either one direction or the other and make it practically impossible to switch without looking away first. I understand that it’s inefficient for the illusion to remain ambiguous, but shouldn’t we at least have the capacity to consciously switch the perceived direction? Makes me feel powerless…

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8. Actually, it’s not bull at all. I thought it was on an automatic timer the first time too, but then my mom and I watched it together. She reported seeing it going one way, where as I saw it going the opposite way. And we also saw it changing at different points in time. She would say ‘OMG there it goes!!’ and I wouldn’t see it change for several more seconds.

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