## Saturday, October 11, 2008

### The Spinning Dancer's Mistery

I explain why the "spinning dancer" is perceived by the most as spinning clockwise. I will then show why the laws of perspective indicate that in fact she spins counter-clockwise.

What is "The Spinning Dancer"?

The spinning dancer is an interesting optical illusion created by Nobuyuki Kayahara. The ambivalence of the image makes some observers seeing that the dancer is spinning clockwise, while others have the impression that she is spinning counter-clockwise. This is an example of bistable optical illusion.

Some tests presented at Cognitive Daily show that the ones perceiving the dancer spinning clockwise are twice as many as the others.

Why two people out of three see the dancer spinning clockwise?

I will explain now why. The answer is based on our experience. We are accustomed to see other people from one specific angle - from about the level of their eyes. For example, in the case of the dancer, the rotating leg’s toe describes a (almost) horizontal circle. Well, at least the circle would be horizontal, if the dancer would not go up and down. Our brains tend to make the supposition that we are looking at that circle from the above, that the circle is at a lower level than our eyes. The figure below shows this:

This is also the reason why, when you look at the dancer’s reflection, you switch the to counter-clockwise mode. The reflected circle, seen from above, corresponds to the counter-clockwise spin.

Why the correct answer is that the dancer spins counter-clockwise?

Well, although the illusion is usually presented as lacking any hint for the depth, I will show you that this is not the case. If we look at the dancer’s reflection in the floor, we can see that, assuming that the circle is more or less horizontal, we obtain a clue. If we assume that the circle described by the dancer’s toe is horizontal, then its plane should be parallel to the plane containing the circle described by the reflection of the toe in the floor. But the laws of the perspective tell us that a closer object look larger than a distant one. Accordingly, the distance between the toe and its reflection should look larger when the toe is closer to the observer. In our case, this happens if the dancer is spinning counter-clockwise. Of course, this means that the observer’s point of view is somewhere near the floor, because the circle described by the toe is now perceived from below.

To give a chance to the clockwise interpretation, we can assume that the floor is very inclined, so that the circle is far from being parallel to its reflection. Even in this case, the point of view should be under the floor’s level, because the closest side of the reflected circle appears to be above the other one. But in this case, the reflection makes no sense. If it is shadow and not reflection, it should not appear upside down, when we see it from below the floor. Therefore, the only interpretation compatible with the laws of perspective is the counter-clockwise one.

It is therefore safe to affirm that the original 3d animation (perhaps created with a 3d computer graphics software like 3ds Max) from which Nobuyuki Kayahara exported the animation rotates indeed counter-clockwise.

Breaking the illusion

How many of our perceptions, how many of our beliefs, are illusions? Is there a possibility to understand that we are living in an illusory world? I not necessarily refer to the objective world as being an illusion. By definition, the illusions are subjective. Between us and the objective world, is a thick layer of more or less illusory beliefs.

To realize whether a belief is based on illusion, we can use the logic. We can check the consistency; this is the best reality test. If the laws of perspective tell us that the reflection of the dancer is not consistent with her spinning clockwise, then we can try the opposite interpretation. We can try the opposite interpretation anyway, as a mean to wonder whether our point of view is the only possible, or as a way to understand other perspectives.

The opinion of the majority cannot be taken as a reality test, or as a proof of objectiveness. Their opinion matters in politics, it matters in their personal lives, or in marketing. The opinion of the others matter for us, because we care about them. But we should not consider the opinion of the majority as our reference frame. The majority believes that the dancer is spinning clockwise, but the logic and the geometry showed us that she is spinning counter-clockwise.

Even if you are among the few that saw the dancer spinning counter-clockwise, this may be an illusion too. You can dream that you are in your bed, and when you wake up you find that you were right, but it was only an illusion. You can consider that you were not fooled by the illusion only when you not only were right, but you understood, or experienced, the reason why you are right.

An example makes the things clearer. If you simplify in the fraction 16/64 the figure 6, you obtain the correct answer 1/4. But you obtained it by pure chance; the same solution will not apply to other fractions. The way to solve the problem was completely wrong, but this does not guarantee you that the answer will be wrong too.

Let me summarize: don’t let you be fooled by the illusions, question every preconception you are tempted to adopt. Whether the preconception belongs to the majority, to a minority you trust, to a person you cherish… Even better: question every preconception of yourself. A preconception is not necessarily false, but it is based on false arguments. The logical consistency should be your first guide out of the illusion.

Peter Staack said...

Excellent summary! I've always had difficulty explaining this particular bistable optical illusions, in simple terms. Usually when I start explaining the mechanics of the illusion, people stare at me like I'm crazy.

Cristi Stoica said...

Hi Peter,
Thank you for your encouraging comment. Yes, I felt the same as you when I tried to explain using only words, that’s why I had to draw.

twoballs said...

All good but the original animation, as you can see frame by frame, spins clockwise.

Cristi Stoica said...

Any frame you take, you can perceive the ballerina in two distinct positions. The illusion works as well when you watch it frame by frame. Watching frame by frame doesn't add extra clues about the depth.

Anonymous said...

it doesnt spin it looks like its spinning but its just swinging left and right the rotation is 100% illusion caused by us making presumptions based on our experience of a 3d world. it doesnt spin clockwise or counter clockwise. just sort of pulsates left and right. the rest is done by your imagination.

joel-david-hamkins said...

What about the idea that it is not a shadow below, but a mirror image? That is, if the floor were a mirror, then the image on the floor would seem to support a clockwise interpretation, no? (And it doesn't seem unreasonable that the image was made by means of a mathematical reflection.)

joel-david-hamkins said...