Wagon wheels look like they are spinning backward on television shows like Little House on the Prairie. The camera only snaps images at a certain rate. The spacing of the spokes and the rate of the rotation relative to the frequency of filming frames is such that it looks as if the wheels are spinning in the opposite direction.
I found a similar effect with my optical trackball. I have a Logitech trackball. The ball itself is red with a black speckle pattern. The optical sensors in the trackball watch the pattern of black speckles to determine which way the trackball is moving. However, if I give the trackball a good flick with my thumb, my cursor on the screen jitters in place for a few moments. Then, as friction starts to slow the ball, the cursor moves the wrong direction for an inch or two. Then, as the ball slows a bit more, the cursor jitters to a stop and then accelerates in the proper direction until it hits the edge of the screen. It jitters at the edge of the screen until the ball whirs to a full stop.
I wonder what other gadgets in my house have such aliasing "features". If I timed severe temperature increases just right, could I convince my thermostat to kick on the heat? If I move really fast will the motion detectors on my house alarm think I'm not moving? If I had anti-lock brakes, could I construct a driving situation where the system ends up slamming on the brakes or not really applying them at all? What other feedback loops do I have to play with?