Here's a fun thing I just discovered.

If you bounce the tip of your tongue against the roof of your mouth (kind of like rolling an R) while forcing air out, it vibrates your skull a little bit. Try it. Go faster. Make that t-t-t-t-t-t faster and faster until it starts sounding like a buzz. Now, look at an LED alarm clock.

Far Out! My guess is, those lights that make up the numbers on your alarm clock are flicking on and off all the time! As your 'ttttt' vibration approaches the frequency of the clock, you start seeing the lights turn on in different parts of your visual field. Your brain doesn't know what's going on, and stitches it into a cohesive image of the little bars sliding up and down. The rest of the world is lit up 100% of the time, so it just looks a little blurry.

I bet you can infer which parts of the clock display are on different cycles by their apparent motion, too.