Which Way Is the Dancer Spinning?

Courtesy of Marginal Revolution, take a look at this dancer. Is she spinning clockwise or counter-clockwise?

For me there is no question: the answer is clockwise. For my wife, the image is without question spinning counter-clockwise. Our babysitter, April, sometimes sees her clockwise and sometimes the opposite. This little dancer offers a powerful lesson regarding how things we conceive as incontrovertible facts are often highly subjective.

Just for fun, list your college major, your occupation, and which way the dancer spins for you. We’ll tally the data and see what we find.

We will give a piece of Freakonomics schwag to one randomly chosen person among the first two hundred commenters who provide the correct data.

And separately, how did someone invent this dancer? How did they figure out that some people would see her spin one way and others would see the opposite? If you know the answer to this question, please tell us and we’ll also offer you schwag.


Quick note of an anomaly: Out of my peripheral vision, the dancer appears to twirl counter-clockwise! If I stare off to the side/below, I'm aware of the dancer spinning counter-clockwise. Crazy!


Computer Science

Counter-clockwise most of the time, but it suddenly switched to clockwise while I was staring at it (trying to imagine how anyone could possibly see it as clockwise when it was clearly counter-clockwise). Then I couldn't get it to go back to spinning the other way without looking away and doing something else and then coming back to it.


Biology major and Mastres in Public Health, currently homemaker, but in the past I have been an epidemiologist and science teacher. I started out only able to see her spinning counter-clockwise, but if I unfocus my eyes and only stare at her arms for about 15 seconds, I can get her to switch directions.

My husband is an Engineer and an MBA, he can see both as well, but he needs to focus on her head to get her to change directions.


Finance & Economics

Kristen C.

Major: Graphic Design
I saw it clockwise at first but after staring at it it switches back and forth often.


Engineering, Economics

Will W

Applied Mathematics

The first time I glanced at it I saw it spinning clockwise. After looking away at the screen to talk to my roommate, I noticed that it was spinning counterclockwise. After blinking and turning away from the screen for 2 minutes, I managed to make it go back again to clockwise.



Chem E/EE
Electrical Engineer

Nat Filippini

My computer major was computer science and I have been an insurance agent for 32 years following 12 years as a systems programmer. I see the dancer spinning clockwise although I was able to reverse it momentarily.


Major: Software Engineering
Occupation: Undergrad Student
Clockwise only


Dancer spins counter clockwise
major: biology


music major, teacher, clockwise.


biochemistry major, student, first clockwise but now I can see it either way


I'm surprised there are so few good explanations. My favorite is 586. Good job, Steve. To reiterate: EACH frame is ambiguous. The dancer's outstretched leg can be interpreted as either - right leg, therefore behind when she's facing left, for counterclockwise rotation; or left leg, therefore in front of her when she's facing left, for clockwise rotation. To (try to) be fair, this is essentially what Adam from post 255 meant.

Another point is that once you think of her as rotating one way, it is easiest to switch to another perspective if you have some time to do it. This can happen in two ways:
1) By obstructing the figure and observing only the shadow (better yet - shadow of only the outstretched foot) one effectively buys half a rotation of time to readjust and reinterpret the shadow of outstretched foot as passing behind/in front of the other foot. Such "obstruction technique" has been suggested by several people.

2) If there is a pause in the gif animation when it has to loop from the last frame to the first. A "pause" has been mentioned by a couple of posters.

Finally, a elaborate on Adam's post 255 -

It's not quite true that ANYTHING will do. The perception switch (cos(wt) cos(-wt) in your language) induces a mirror reflection on the object. If the object is symmetric (like a point) or can be reasonably interpreted both ways (like a dancer), you get an illusion. If the object only makes sense in one "handedness" the other interpretation will seem wrong. So when you are drawing such an illusion you need to make sure each frame looks reasonable in both mirror pair interpretations. I think shadow problems that a couple of people pointed out come from just this - in some frames one of the two interpretations gives slightly wrong, or at least less natural, shadow pattern.

The reason you get cosine in your description is initial conditions - when the object is fully to the right and you want this to be time 0 you get cos(wt) or cos(-wt). If you choose time 0, say, when she is in the middle the equation you get sin(wt)= sin(-wt+pi), so rotation in other direction is still equivalent, but with a timeshift of pi. Other start times give other phase shifts.




Major: Chinese Studies

Job: Sales Manager

Counterclockwise at first sight, no problem to change directions.


It eventually did change though. Disconcerting!

Jed Christiansen

Major: Aerospace Engineering (undergrad)
Masters in Decision Sciences (Operational Research)

Job: Consulting (I'm a former US Navy submarine officer, too)

Direction: Clockwise


Double major (economics and business), investment banker. Clockwise and counterclockwise, at will.

CC Abnet

Clockwise, but staring could get her to change directions. Although, I didn't even notice her spinning at first, must be hind brain thinking.

michelle pitts

college history major. insurance agent. clockwise and counter wise.