Persistence of Vision
Persistence of vision is the name we give to the phenomenon that allows us to perceive the optical illusion of motion created by film (and, in fact, all media that involves seeing motion). There is no way for any camera to actually capture motion. All that can be captured is a series of still images that, when played back create the optical illusion of motion.
Exactly what is going on when this happens is still not very well understood. Most of the "folk" explanations for the phenomena is demonstrably wrong. Here are two examples.
The first explanation that people offered was that 1/20 of a second was the time it took for the neurons carrying the image from the retina to the brain to "cycle;" that is to discharge and return to their resting state. Because the frames per second (fps) rate exceeded that, the neurons couldn't entirely recover and thus the illusion of motion was created. This is simply technically incorrect. A common modern number given for the number of times a neuron can fire in a second is 200. That means that for persistence of motion to be created by over-running the firing speed of neurons, film would have to move about 10 times faster than it does.
The second is that the refresh rate of the brain is about 60 fps...that is that for whatever reason, human brains tend to capture the visible world kind of-like a movie and at about that rate (people who accept this sometimes argue that other animals have higher rates. For example, dogs are so great at catching balls or frisbees because their refresh rate is faster. Because of this, if a human could see like a dog, things would appear to move in slow motion (what it's like for the dog, we can't know)). But, again, the science behind this seems unreliable. For example, we know that we can see things that happen very fast (for example, a bolt of lightning takes about 30 millionths of a second but are easily seen). With training, at least some people can recognize images that they see for as little as one 200th of a second. It's hard to reconcile this with a 60 fps refresh rate.
BTW, modern movies run at 24 fps. However, film shown at that speed without modification usually appears a little jerky. To get rid of this problem, projectors usually show each frame 2-3 times to simulate a refresh speed of 50-70 fps. In other words, a projector shows a frame of film, then shows the same frame again (and sometimes a third time) before advancing to the next frame of film. As long as the film is moving through the projector at 24 fps, this does not affect the speed of what you're seeing.
In the end, how fast we can see something and the degree to which it merges with other things to create the illusion of motion seems to depend on the exact characteristics of the thing being seen and the conditions under which it is seen.
One thing it is worth remembering is that you don't see with your eyes. You see with your brain. That is to say that although your eyes (and optic nerve etc.) transmit impulses to your brain, the actual act of seeing...sensing of shapes, motion, whatever else...happens in your brain.
Here's another cool persistence of vision example: