From the Sun Herald (via Mark Bernstein) is this neat animated gif. If you see it turning clockwise, you're right-brained (meaning you use more of the right brain than the left), and if counterclockwise, left-brained. Weird, isn't it?

This illusion definitely fits with my experience, according to the Sun Herald's list of differences below: That is, I'm oriented toward logic, details, facts, words and language, math and science, practicality, and playing it safe. I seldom take risks or act impetuously. I was 48 before I got married! And although I'm good in math, geometry was my weakest area in math. I'm not quite so sure about lacking imagination, however. Of course, these are tendencies, not absolutes, but still, it's weird to me that one's brain-side dominance affects how you see this figure turn. I wonder how this might affect learning.

LEFT BRAIN FUNCTIONS
uses logic
detail oriented
facts rule
words and language
present and past
math and science
can comprehend
knowing
acknowledges
order/pattern perception
knows object name
reality based
forms strategies
practical
safe

RIGHT BRAIN FUNCTIONS
uses feeling
"big picture" oriented
imagination rules
symbols and images
present and future
philosophy & religion
can "get it" (i.e. meaning)
believes
appreciates
spatial perception
knows object function
fantasy based
presents possibilities
impetuous
risk taking

Update: Stephen Downes says that it's not a matter of right- or left-brain dominance because

You can learn to see the dancer spin both ways - it has to do with where you focus your attention.

I've asked in a comment on how that works. Let's see if he will respond. Even so, if one has to learn how to do something to go against the brain's natural preference, then apparently something brain-related is occurring whether or not it's a brain hemisphere dominance. Perhaps, Stephen can comment on that, too. For right now, I tried looking in different ways but could only see it going counterclockwise, and Mark Bernstein could only see it going clockwise. It's still a fascinating illusion, and brains are still weird!

Update 2: Stephen Downes responded on where to focus: Focusing on the feet turns the dancer counterclockwise while focusing on the shoulders makes her appear to go clockwise. Sometimes that works for me, sometimes not. Mark Bernstein's site has two dancers turning, and sometimes, I can get them going opposite directions by focusing on the shoulders, and sometimes not. It does seem to be a matter of focusing, then. Thanks to Steve for clarifying this illusion.