Right Brain or Left Brain?

I'd imagine by now, everybody who spends much time on the internet has probably seen the dancer above... She's part of a left brain/right brain test. Allegedly, if you see her turning clockwise, you're a right-brained person, counter-clockwise is left-brained. (for all the details, click on the title to this post)

So, my question is, what if you see her spinning a different direction every time you look away for a second? Seriously. Clockwise. Counter. Clockwise.

I've always wondered about the whole left/right brain thing anyway. I mean supposedly, the right brain handles creativity, religion, etc. while the left handles math and logic. I can buy that. The part that I don't get is how everyone is supposed to fall into one or the other category, but not both.

I've always found myself in both categories. In school I took mostly art classes, and precalculus as an elective. I love logic problems, but I also like to draw paint and write. Theoretically, the folks who are good at math should also excel at sciences, but most of that is over my head.

So I've been thinking about it. Haven't there been a lot of people who have exhibited the traits of both brain sides? Probably the best example I can come up with would be Leonardo DaVinci. I mean, he was an amazing artist and also had a really good grasp on physics. Or how about Ben Franklin? Quite the creative writer. Quite the inventor. History is just littered with people who are neither right-brained nor left-brained, but seemingly both. And that's just the ones who did something notable enough (in both spheres) for us to remember them.

The way I see it, it's not A or B, but more varying degrees of both.