from my brother-in-law, who does research in cognitive psychology:

As far as I can tell, it's an optical illusion that is in the same class as the necker cube, an illusion that I'm sure you are all familiar with, even if you don't know it by name. Both of these are "bi-stable images" (or, in the case of the ballerina, a bi-stable movie, I guess), that your brain can interpret in one of two ways. If you are looking at the cube, with a little practice, you can force it to switch between the two interpretations pretty easily. I suspect that a forced switch will be harder with the ballerina because it's a moving image, but it should be possible. I've found that if I focus just on her planted foot, I can get the rotation to change directions almost at will.

How does it work? The key is that what you are looking at is essentially a two-dimensional image (I was going to say it was a flat image, but that's clearly not the case...) of the ballerina. There are no depth cues and no 3D shading. It is as if you are looking at the projected shadow of a twirling ballerina, if that makes sense. With that in mind, think about it this way: Imagine the ballerina is facing exactly sideways (right or left, doesn't matter). Then imagine that she spins, say, 45 degrees. First, think about what she would look like if she was spinning toward you. Then think about what she would look like if she was spinning away from you. Remember that all you have to look at is a shadow - you can't see a face or any other front/back distinctions. What you should realize is that if she spins 45 degrees "away" or 45 degrees "towards" you, the resulting image is exactly the same. Spin her another 45 degrees (so she's now rotated 90 degrees), and she will either be facing you or she will have her back to you, but again, since it's just a shadow, the image is exactly the same... What it boils down to is that with a 2D projected image (of a ballerina, of a motorcycle, anything, really, there's nothing special about the image they chose), you do not have enough information to tell the direction of rotation. They add the shadow of the feet to make the image more interesting, but again, there's no real rotational information there.

Since you don't have enough information, your mind could choose between two equally likely interpretations (hence the "bi-stable image" name). So when you look at it, your brain picks one interpretation, and then typically sticks with it until it is pushed to reinterpret the image (either by looking away for a while, or really trying to convince yourself that the image is going the other way or, I don't know, whatever else works).

As far as the right-brain, left-brain stuff goes, I don't put any real scientific faith in that terminology. Yes, certain functions like language skills and spatial processing are more localized to one side of the brain than the other. However, calling someone "left brained" or "right brained" should be viewed as an easy label to use to indicate if someone is more creative or more analytical, but it's more like saying that they are "introverted" or "extroverted" than it is a statement about their neuroanatomy.

Does the spin direction of the image reveal your brain-sidedness? I highly doubt it. I can't think of any reason that such a test would be diagnostic.

-- He's way smart.