I'm so glad that you the expert are here to teach me, the novice, about perspective.
http://www.dummies.com/how-to/content/drawing-geometric-perspective.html
The problem with this standard art school perspective, however, is that perspective lines further from the horizon do not converge at the same rate as those closer to the horizon/eye line.
Yea, because I called myself an expert, I would have known what you meant, if you said "eye
level" which is the correct term i think you were referring to, in that link there is no "eye line" either.
Still, I'm not completely sure you understand my point as you are making emphasis on the vanishing point, (just in case, the second drawing I made is not Illustrating a vanishing point either, it just shows how light reflected from objects interacts with the eye) but of course lines do converge faster closer to the horizon using the graphic i made.

On the left equidistant lines on the floor, on the right lines getting closer as the reach the horizon.
I would accept you saying that's what prevent us from seeing the whole earth if I was using a picture or a video taken at eye level, with a horizon parallel to the floor, but im not, its a video from a rocked looking down, it makes the earth horizon (which in this case would not be the same as the eye level, or camera level) go up farther from where parallel lines converge, and in a flat earth the earth horizon would be even higher (farther from eye level where parallels converge) than in a round earth, where the horizon just stops when the curvature makes the earth go down.