I can't figure out how that dancer could ever be turning counter-clockwise
It's really interesting, it almost shocks your brain when you see it the other way.
I see it clockwise naturally, the best way I've found to see the opposite direction is to look away from the image but keep it in your peripheral vision, then imagine it spinning the opposite way (it's a lot easier to make this shift when you aren't looking directly at it), then slowly move your gaze back to it keeping the new direction in mind.
It's easier to look off to the left using this page:
http://en.wikipedia.org/wiki/Spinning_Dancer