So Cari shared this optical illusion with me: The Right Brain vs Left Brain. Before reading the article’s content, I’d like you to first stare at the spinning dancer and see if she’s going clockwise or counter-clockwise.
You can also see the dancer here:

Click image to start animation or view it in the gallery.
If you could comment which orientation you first saw it in, I’d like to collect some statistics.
Most people I know saw her originally as spinning clockwise, which leads me to think the right brain vs left brain thing doesn’t really make sense, since most of the people I work with I would say are logical and math/science based instead of “uses feelings”. Then again, I’ve been able to get the dancer to swap orientations, so what does that say about me? What does it say about those who can swap them easier than others?
Anyway, if you want to get her to swap, we found staring at the legs and focusing at shadow helps. Sometimes closing your eyes for a bit or looking away helps too.
What’s happening here is that there is very little hints for depth perception, so the brain doesn’t really know which leg is in front of the other. If you truly believe that the dancer is only spinning in one direction or think that the animation is really just randomly switching directions on you, I’d like to give you the following 2 images:
Clockwise:

Click image to start animation or view it in the gallery.
Counter-clockwise:

Click image to start animation or view it in the gallery.
The 2 images above contain all the frames from the original and the frames are in the exact same order, but I’ve added some lines to help with the depth perception. If you think I’ve just reversed the order, then I’d bring you to my final animation:

By having these side by side, where the middle one is the original, it is now a lot easier to switch the orientation of the original. What’s that old saying? Don’t always believe what you see? ;p
One thing I noticed that’s different between the 2 spinning orientations is that the dancer is spinning on different legs. When she’s spinning clockwise, she’s spinning on her left foot. When she’s spinning counter-clockwise, she’s spinning on her right foot.
Xyon did point out that the shadow does align correctly with the counter-clockwise spinning, and maybe that’s why they decided that people who are logical would see her spinning counter-clockwise. But the experiment seems quite lacking and no justification was really given, so I’d wouldn’t say what they’re claiming is definitive.