Bas says:

I've downloaded the image to my computer and opened it in Windows Picture Viewer, this slowed the rotation down a bit. It made it a lot easier to see what happens. It also makes it a lot easier to consciously change the rotation.

Mark(p.s.) says:

I loved the optical illusion! Thanks for publishing it. I really was amused/laughed when the image reversed direction in my brain.

Chris says:

It seems to me that the direction of motion of at least some rigid 3-D objects must be determinable from their 2-D projections.

As you point out, the coin's direction of rotation is not determinable, but notice that a coin is symmetrical about the x,y and z axes -- these symmetries introduce a lot of ambiguity. Notice also that we have the tendency, when imagining rotating 3-D objects, to rotate them about whatever axes of symmetry they have.

So imagine we take a 3-D object which has no symmetries, e.g. a seashell. Just going on my intuition here, it should be possible to determine the direction of rotation of the shell, since you can disambiguate local motion-away and local motion-towards by examining the changes occurring at other points on the shell. For any given 2-D silhouette, there is exactly one 3-D specification of the shell that could have generated that silhouette, and so the position in space (and thus the direction of motion) of the seashell is uniquely determined.

Another object to try imagining is a cactus with two arms pointing out in different (not opposite) radial directions from the central stalk. With only one cactus arm it is not possible to disambiguate the position of the cactus, but when you take into account the position of the second arm, then you can figure out exactly where the cactus is.

PostScripts

[1] It took me forever to think of an object with no symmetries ... everything in my physical environment is symmetrical in one way or another!

[2] There is an assumption in my reasoning, which is that you have to know, in the first place, that the shell is, in fact, a shell. i.e. you have to know in the abstract its 3-D structure. But I think for the case of the spinning silhouette, we all know the general structure of the human body.

[3] When you block out the top of the spinning silhouette, you introduce an additional symmetry into the 3-D object (like removing one arm from the two-armed cactus), and thus introduce ambiguity ... so maybe that's why you can then switch the direction of rotation in your mind and then 'extend' that direction back into the original object.

[4] I have the feeling that this kind of issue is the basis for entire branches of mathematics. Although I'm not sure of the terminology, the question is something like: "how many different trajectories of points A can be projected into substructure B such that some continuity property of the original trajectory is preserved?", and then the number of solutions will depend on the number of redundancies or symmetries within the trajectory in A, relative to the axis of projection.

[5] This line of reasoning is all based on my imagination of a spinning cactus and a spinning shell ... so of course I could be totally wrong :)

Bill Beaty says:

She STILL hasn't reversed. :(

The shadow definitely has clockwise chirality. For example, look at the toes. In order for the foot to reverse, we'd have to believe that we were observing her foot from below, not from above. Yet the detail of the top of the toes as the toes sweep to the far left could only be visible from above.

Only if my personal psychophysics should become fatigued and decide to ignore all the small cues like the one above... THEN I would finally perceive the CCW rotation. Perhaps I haven't et stared at the screen for long enough.

Vaughan says:

Hi Chris,

I think you're right, as a spinning asymmetrical image would have one side looming towards you and the other vanishing into the distance to indicate direction of spin.

One of the ambiguities in this figure is that you can't rely on other depth cues. e.g. from the still image above you can interpret it either that her arm is on the near side of her body, or the far side. Same goes for the outstretched leg.

How this is related to such a striking reversal effect, I haven't quite thought through yet!

prowler says:

wow that was awesome :D it didn't work for me at first, so i did what the description says, and concentrated on the shadow ... sure enough, in 10 seconds i saw the CCW movement!

of course i couldn't get it back to CW, so i looked away from the monitor for 3-4 secs and then returned and it was in CW again.

unleashed004 says:

Hi Chris- I was reading your comments and your reasoning is interesting, but flawed. The reason we experience the illusion is that the mind extrapolates the shadow into a 3-D object. The 3-D object could be either of two mirror images. We just don't know which mirror image to select. In fact, ANY object, regardless of its symmetry or non-symmetry can be transformed by reflection and will produce the same shadow when rotating in the opposite direction as the original.

Basically just imagine reflecting the rotating object itself in a mirror - the reflected object will produce the same shadow but will be spinning in the opposite direction to produce the shadow.

Our shillouhette is a perfect example of this in action - when spining clockwise, her right arm is outstretched and her head is tilted to her right. When spinning CCW, her left arm is outstretched and her head is tilted to her left. The two objects that we can extrapolate from the shadow are mirror images of each other.

Most people see the clockwise rotation initially because we tend to perceive the feet as being closer to the observer when they are lower in the field of vision (as in everyday life).