All the attention is being put to this concept of 'perspective lines'. But it's really just a side-effect, an optical illusion, of what's really going on: the field of view (or visual field) getting wider with distance. When Tom says things like 'The Ancient Greek depiction of perspective has perspective lines which approach each other for infinity', he refers to the field of view gradually getting wider...the further you go, the wider it gets..forever.
But what he's actually arguing is that the field of view has a distance at which it suddenly gets infinitely wide, giving everything at that distance an infinitely small viewing angle. But only vertically, because objects only disappear from the bottom (and supposedly the ground from the top), not from the sides. Or, the horizon would be a single point where ever we would look, right? I wonder what keeps that phenomenon only working at a perfect 90 degree angle from the ground. What should happen if I tilt my head?