How to argue about perspective (I'm looking at you, Tom)

I already posted this is another thread, but it deserves its own I think. In addition to the FAQ we really need a FPBA (Frequently Posted Bullshit Arguments) so that we can refer people to it.

I honestly cannot believe that this perspective argument is still coming up. "Basic laws of perspective" they say, "obvious empirical evidence" they say. Even if the FEers are correct about the whole "sinking into the ground" thing, it cannot be due to perspective. Perspective is nothing more than the appearance of objects becoming smaller as they move further away. All of the "laws" of perspective that people love to reference so much are simply due to trivial trigonometry. I'm even going to demonstrate with a picture.



Diagram 1: Here the object's actual distance from our center of vision is y. Its apparent distance is theta. Even as y remains constant, as x approaches infinity, theta approaches 0. That is, the object appears closer to the center of our vision as it moves further away even though it is physically not moving closer. This is because theta = arctan(y/x) and arctan(0) = 0.

Diagram 2: Here the object's distance from the observer is x, it's actual height is y, and it's apparent height is theta. Yet again, as the object moves further away y remains constant, x approaches infinity, and consequently theta approaches 0. To simplify the math, let's just assume that the object is vertically centered in our vision (this only affects the coefficients). We can split the triangle in half along the horizontal and thus get theta/2 = arctan(y/2x) and yet again arctan(0) = 0. So as the object moves further away, it appears to be smaller even though its actual height is not changing.

See? All that there is is relative position and trigonometry. Now whenever you crazy FEers bring up "perspective" you have to argue it with only those two things: relative position and trigonometry. Use math, use pictures, do NOT cite Samuel "Rowboatman" Rowbotham.

You will receive no coherent reply. I've tried this:
http://theflatearthsociety.org/forum/index.php?topic=18286.0

You have a much better diagram though.

Perspective is not only the shrinking of objects as they recede, but the gradual descent of receding bodies into the surface of the earth.

Although an airplane might be at all times the same altitude above the earth's surface, on approach it may appear to ascend to overhead, and thence to descend and disappear, or set, into the horizon as it recedes. This phenomenon arises from the operation of a simple and everywhere visible law of perspective. A flock of birds, when passing over a flat or marshy country, always appears to descend is it recedes; and if the flock is extensive, the first bird appears lower or nearer to the horizon than the last, although they are at the same actual altitude above the earth immediately beneath them. When a hot air baloon flies away from an observer, without increasing or decreasing its altitude, it appears to gradually approach the horizon. In a long row of lamps, the second--supposing the observer to stand at the beginning of the series---will appear lower than the first; the third lower than the second; and so on to the end of the row; the farthest away always appearing the lowest, although each one has the same altitude; and if such a straight line of lamps could be continued far enough, the lights would at length descend, apparently, to the horizon, or to a level with the eye of the observer. This explains how overhead bodies descend into the horizon as they recede.

Once the lower part of the plane meets the horizon line, however, it will intersect with the vanishing point and become lost to human perception as the plane's increasingly shallow path creates a tangent of perspective lines beyond the resolution of the human eye. The vanishing point is created when the perspective lines are angled less than one minute of a degree. Hence, this effectively places the vanishing point a finite distance away from the observer.

Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer, as so:



However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer as so:



This finite distance to the vanishing point is what allows ships to ascend into horizon and disappear as their hulls intersect with the vanishing point. Every receding star and celestial body in the night sky likewise disappears after intersecting with the vanishing point.

For more information please read Chapter 14 of Earth Not a Globe

Like ﮎingulaЯiτy said

You will receive no coherent reply. I've tried this:
http://theflatearthsociety.org/forum/index.php?topic=18286.0

You have a much better diagram though.

so once again Tom copies and pastes the exact same totally untrue quotation from the mechanical pig. he has no idea what any of it means!

Well yet again you ignore me, Tom. I asked for math and you gave me bullshit. But I'll even translate your (read: Rowbotham's) argument into math for you (I'm so nice)!

On an infinite, perfectly flat plane (which the Earth arguably isn't) we can illustrate the phenomenon of objects above us descending to the horizon as such: the physical vertical distance between the object and the eye-level of the observer is y (constant, here), the horizontal distance between observer and object is x and the apparent height of the object would be theta, a function of x and y. theta = arctan(y/x). As x increases, y/x approaches 0, and arctan(0) = 0 so the object will appear to be at the eye-level of the observer once its distance exceeds the resolution of the human eye. That all makes perfect sense, I agree with Rowboatman.

Rhobottom sort of fudges the next bit though.

In a long row of lamps, the second--supposing the observer to stand at the beginning of the series---will appear lower than the first; the third lower than the second; and so on to the end of the row; the farthest away always appearing the lowest, although each one has the same altitude; and if such a straight line of lamps could be continued far enough, the lights would at length descend, apparently, to the horizon, or to a level with the eye of the observer. This explains how overhead bodies descend into the horizon as they recede.

True, the top of each successive lamp will have a smaller apparent height than the previous one. However, Robot-ham never actually addresses how the tops of the lamps descending causes the bottom to appear to sink into the ground. Yet again, I shall translate into mathematics.

Here we have a block with two colored sections. Roughbawtham claims that as this object moves further away, it will become smaller while sinking into the ground. X is the horizontal distance to the object, Y is the vertical distance to the top of the object from the eye-level of the observer, alpha is the apparent distance to the top of the green section, and beta is the apparent height to the top of the blue section. Y is split into y1 and y2 which label the blue/green sections respectively. Now, the claim is that the green section will "sink into the ground" due to perspective; i.e. the apparent height of the green section will be 0. Well y2 is constant, so that means that eventually X will be large enough that alpha will be approximately 0 according to the human eye (alpha = arctan(y2/x)). However, if X is large enough that arctan(y2/x) = 0 approximately, then unless y1 is very large arctan(y/x) = arctan((y1 + y2)/x) = beta = 0 approximately as well! However, that does not accurately reflect the reality observed in images such as:
(thanks, cpt_bthimes)
In this case, we're seeing the top of the ship on the horizon while the apparent height of the hull of the ship is approximately 0. However, unless this is some kind of skyscraper ship the actual height of the top of the ship isn't too much different from that of the hull! Say, for example, that the ship here is perfectly sunken in half. That is, half of the ship has sunk below the horizon due to Roabofthnam's perspective laws while half of it has yet to do so. So we have y1 = y2 and X is large enough that arctan(y2/x) = 0 approximately but arctan((2*y2)/x) = arctan(y/x) = beta does not approximately equal zero!? That just isn't possible. Especially since from the picture it is clear that x is very, very large in relation to y (the ship's height).

In non-mathematical speak, what this all means is that as objects move further away from an observer all parts of the object appear to merge with the vanishing point equally. That is, even though certain parts of the object will be closer to the vanishing point than others, they will appear to approach that point more slowly so that the entire object will merge with the vanishing point simulatenously. NOT from the bottom up as Rwotohabm claims. This is all due to the simple properties of limits at infinity with regard to fractions.

Like ﮎingulaЯiτy said

Quote from: ﮎingulaЯiτy on December 24, 2007, 01:28:27 PM

You will receive no coherent reply. I've tried this:
http://theflatearthsociety.org/forum/index.php?topic=18286.0

You have a much better diagram though.

Is that link still valid? It won't load on my PC.

According to my counterpart, TB, perspective causes receding bodies to descend into the Earth. Well, that's what happened to Titanic, right? Make sure no one watches you as you leave in your car, it'll get compacted into the ground.

jimztar, the link works for me. And Tom, where are you!?

Upside Down and all jumbled up.

Perspective causes things to be crushed into the surface of the earth by perspective as they recede