I was under the impression that 24 FPS was the threshold. I guess some human eyes are more sensitive than others.
The human eye responds differently to color (via the cones) and light levels[Black and while] (via the rods).
Not getting into it too much:
The rods have a limit higher "FPS" than the cones. Your eye focuses in the center, with the outlining visual field blurred. This is in contrast to say a picture, which generally can have the entire thing in focus at once. light coming in around the outermost diameter of the eye (Peripheral vision) will tend to only hit rods, because most of the cones are in the most center. Cones are also responsible for defining shape / sharpness. This is why you can see certain fluorescent lights flicker when its just coming in the corner of your eye, but when you look right at the light it goes solid.
Around 24 FPS is the minimum to construct the illusion of fluid motion. even if we say your eye "sees" at precisely 24 fps, displaying some to an eye at 24fps would probably still look off. The two systems most likely wouldn't be synced, and the eye could sample at a time when the display isnt 100% ready because its transitioning.
Phisicaly, a human eye samples at around 30-35 hertz. But this when observing more or less static things( so in essence a display of infinitesimally large FPS / infinitesimally small transitions).
When you start making the fps smaller, the transition get larger - with more likelihood of them being sampled by the eye. If you are only caring about sharp things in color, the eye at 24hz (42ms) is an alright compromised minimum. so you want a display of at least an order of magnitude larger = 240FPS (4.2ms)minimum.That's why monitors usually have a minium "response time" of 5ms. Doubling 240 takes it down another 1/10th of as much chance to see the transition, so at 480 (2ms) are you unlikely to notice the FPS not being infinitesimally large. That is why high end monitors clam at least a 2ms response time.
My eyes are one of the 5 tools I'm literally using all the time. It pays to know how your tools work, so you know what you can and cannot do / measure with them. Everyone that has the time should spend some reading on how their eyes (and other
senses tools) perform and operation.
But don't take my word* for it, Go read about it at the library!

* My apologies if anything isnt 100% accurate above. Its very late, I should be in bed, and I didnt brush up before typing this