After reviewing this thought I would add that the best explanation I have ever seen for the "wave thing" and ships on the horizon is contained in 'Earth Not a Globe' by Samuel Rowbotham (using the pseudonym "Parallax") which has been posted on-line.
In all sincerety, Dionysios, thanks for posting this.
I've had a look at the chapter on why ships appear to disappear hull-first over the horizon, and I am pleased to say that Rowbotham has one of the finest understandings of the mathematically demonstrable concept of perspective that I have ever come across.
Rowbotham explains the the ship-horizon issue based on the following premeses:
1.--That the larger the object the further will it require to go from the observer before it becomes invisible.
2.--The further any two bodies, or any two parts of the same body, are asunder, the further must they recede before they appear to converge to the same point.
3.--Any distinctive part of a receding body will be-come invisible before the whole or any larger part of the same body.
From these true principles he rightly concludes that a ship, receding a great distance, will appear to diminish, and that its distinct parts will become as one to a distant observer. Since the hull is just such a distinctive part, naturally the hull will itself appear to disappear.
Can a more true statement about the nature of perspective be made? I must once again praise Mr. Rowbotham's capability for demonstrating the abstract in an understable way, and also for demonstrating that he has never once in his life looked at a ship on the sea, or for that matter, the sun in the sky. His myriad diagrams all show a similar scene: an object, detailed when viewed up close but vanishing into a point as they recede into the distance, illustrate something exactly unlike the phenomena Rowbotham claims to be explaining: for who among those who claim that they have seen, through telescopes, ships recede below horizon, will admit that they seem to shrink to mere points before doing so? Who too will claim that the sun -- a disc of measurable size in the sky -- when going to its resting place in the West at the end of every day, is squeezed
uniformly into a mere speck of furiously bright light against the darkening blue sky, and then vanishes altogether?
No, indeed, perspective -- a notion elegantly, completely, and soundly elucidated by Mr. Rowbotham -- is in fact so distinct from one's view of the obvious and undeniable nature of ships and suns that one is led to conclude that Mr. Rowbotham has spent every waking minute of his life in his cellar. Possibly his internment (or interment) was broken by an occassional reptilian crawl on his belly in the thick grass lining the 3-mile wall leading out to the Poolbeg Lighthouse in Ireland --- which wall and grass must have severly limited his view of sun and sea.
To all who desire to learn the mysteries of perspective -- and nothing else at all -- from a longwinded reptile and his vague, confusing, eyestraining sketches, I heartily encourage you to read "Earth: Not a Globe" by the renouned Samuel Rowbotham.
-Erasmus