Let's assume that if (like real life) what you're seeing is continuously changing, and noisy, your brain can pick out the sparse signal from the data very effectively. It can supersample (as we talked about above), and derive twice the data from it. In fact, the signal has to be noisy for the best results - we know that from a phenomenon known as Stochastic Resonance.

What' more, if we accept that an oscillation of 83.68Hz allows us to perceive double the resolution, what happens if you show someone pictures that vary (like a movie, or a videogame) at less than half the rate of the oscillation?

We’re no longer receiving a signal that changes fast enough to allow the super-sampling operation to happen. So we’re throwing away a lot of perceived-motion data, and a lot of detail as well.

If it’s updating higher than half the rate of oscillation? As the eye wobbles around, it’ll sample more details, and can use that information to build up a better picture of the world. Even better if we’ve got a bit of film-grain noise in there (preferably via temporal anti-aliasing) to fill in the gaps.

It just so happens that half of 83.68Hz is about 41Hz. So if you’re going to have high-resolution pulled properly out of an image, that image needs to be noisy (like film-grain) and update at > 41Hz. Like, say, The Hobbit. Or any twitch-shooter.

Less than that? Say, 24fps? Or 30fps for a game? You’re below the limit. Your eye will sample the same image twice, and won’t be able to pull out any extra spatial information from the oscillation. Everything will appear a little dreamier, and lower resolution. (Or at least, you’ll be limited to the resolution of the media that is displaying the image, rather than some theoretical stochastic limit).

Some readers of this article have suggested that this is all an artifact of motion-blur – double the frame rate, half the motion-blur, and you naturally get twice the sharpness.

It may play a part – though I’m not sure it plays a large one – The Hobbit, the shutter was set to 1/64th of a second. For regular movies? The shutter exposes for 1/48th of a second. That’s not halving; half the motion blur of 24 fps film would require an exposure time of 1/96th of a second. So I suspect that motion blur isn’t the whole story here.