Here's a fun experiment you can perform to test your coordination and, if you're like a lot of people, experience the precise moment when your brain and muscles go off to la-la land.
First, stand up and extend your arms directly out in front of you. Rotate your right arm clockwise (CW) and your left arm counterclockwise (CCW) at the same rate. Maintain the rotation, and by pushing your elbows outward, begin to draw your forearms toward your chest until your fingers are pointing at each other. This should not be particularly challenging. Return your arms to the starting position and repeat the process, only this time have your right arm moving CCW and the left CW. Again, if you're like most folks, this shouldn't be a great challenge. So far so good, right?
OK, finally, return to the starting position and rotate both arms either CW or CCW. Chances are, when you get to around 45 degree of elbow angle, all hell will break loose! One of your arms will probably reverse direction. I don't know why this is, but it has happened with virtually everyone I know who has tried it. I also know that with a little practice, you can learn to do this. You have to start slowly, but it will come eventually. I practiced this motion for a couple minutes a few times each day and within a few days I could do it passably well. In another week, it felt pretty normal.
Here's a cheesy 10 fps AVI that I made with my digital point-and-shoot camera to illustrate: Arm Circles.