I just bumped into this article from News.com
The article says that if you see the dancer turning clockwise, then your brain’s right hemisphere is more dominant. If you see it counter-clockwise, then your left hemisphere is the more dominant part.
Commonly, people would see the dancer turning counter-clockwise.
There are also some people who could concentrate and change the turning of the dancer from clockwise to counter-clockwise and vice-versa.

Here are the functions of the brain depending on its orientation:
| LEFT BRAIN FUNCTIONS |
RIGHT BRAIN FUNCTIONS |
| uses logic |
uses feeling |
| detail oriented |
“big picture” oriented |
| facts rule |
imagination rules |
| words and language |
symbols and images |
| present and past |
present and future |
| math and science |
philosophy & religion |
| can comprehend |
can “get it” (i.e. meaning) |
| knowing |
believes |
| acknowledges |
appreciates |
| order/pattern perception |
spatial perception |
| knows object name |
knows object function |
| reality based |
fantasy based |
| forms strategies |
presents possibilities |
| practical |
impetuous |
| safe |
risk taking |
This happened to me. Sometimes I see it clockwise then sometimes counter-clockwise.
Sometimes, if I look away and concentrated, it would turn to what I direction I wanted it to turn.
Maybe this is because I am somewhat ambidextrous.
I was left-handed when I was a child but I was forced by my father to write using my right-hand (he told me that I will be spanked by my teacher if she sees me writing using my left hand).
Up until now, there are activities wherein I sometimes use my right hand, sometimes the left.
Note:
My officemate Orly says that if you see the girl tumbling rather than turning, it means that you don’t have a brain at all !! 
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