Well well, this is mighty interesting. First of all I'd like to say that I find it hillarious how I explained to Tom plainly and simply (and repeatedly) that an object would not breach the horizon on an infinite plane if it was below your line of sight, but that he said it was ridiculous and that all simulations he ever ran showed otherwise, but now suddenly he supports this simulation 100%. In fact here is a quote from him:
You would like me to retort the assertion that objects would shrink infinitesimally into the horizon on a flat surface? That's just stupid. Ask any teenager if an object infinitesimally shrinks into the horizon without breaching it on his 3D simulation video game. That's all the evidence we need.
Well that's good, it's a start. Now let's see what else we have here.
However, if there is an atmosphere for the far away vanishing point to hide behind, the receding left hand prisms absolutely could appear to breach the line of the horizon.
Haha close, but no cigar. Here is the problem with that argument. Assuming that there is a specific point on this infnite plane beyond which you can no longer see anything due to the obscuring effects of the atmosphere, then we can treat the visible section of the infinite plane as a finite plane, with the hypothetical edge at the same point where visibility ceases. I think you will agree with this yes? If such is the case objects below the line of sight could technically appear to breach the horizon AT THE VERY EDGE OF THE VISIBLE PLANE - that is, if it stood on the very edge, or at this very boundary (mind you this effect would be very small and hardly noticeable, but let's go along with it anyway).
The key point is that the only objects to do this (i.e. the only waves) would be the ones
immediatelly preceeding the point where all else vanishes (i.e. our plane's hypothetical edge). If this is the point where all else vanishes, then this object would be essentially the LAST thing you could see (unless you moved forward of course). The instant any object (a boat or whatever) reached this point, it would dissapear, without the sinking effect ever taking place. A skyline would certainly not gradually sink into the horizon. Furthermore, if the atmosphere causes this obscuring effect, I should not be able to bring an object back into view by rising a few meters, as the atmosphere would continue to obscure anything beyond the point which you describe. Last but not least, given the size of this visible plane this effect would be virtually unnoticeable. I invite Ferruccio, if he wants to, to take the infinite plane and abruptly cut it off after what.. 6 or so miles, and see how it looks.
That's exactly what happens. The ship does not completely sink into the horizon. As it recedes from the viewer the ship kind of sinks into the ocean a little from the bottom up and then fades out completely.
Umm, nope, that's not at all what happens. The ship is clearly discernible until it finishes sinking into the horizon. Granted with a ship, if you're only using the naked eye and your eyesight isnt particularly good, you probably won't realize this. You'll need a good pair of binoculars. This is far more readily observable with a skyline however (a luxury Rowbotham didn't have). Furthermore, a skyline doesn't sink into the horizon a little and then dissapears, it sinks into it a lot, and continues to do so without fading out.
EDIT: I corrected a couple of minor errors.