Evidently if you see the dancer spinning clockwise, you use more of your right brain (logic and empiricism) and if you see it spinning counterclockwise you use more of your left brain (art, philosophy)
http://www.news.com.au/heraldsun/story/0,21985,22556281-661,00.html
http://www.news.com.au/heraldsun/story/0,21985,22556281-661,00.html