A discussion on TFES forum

[teo123]

I don't know now. Anything I read about perspective seems to confirm my beliefs. I couldn't find anything about the "perspective bowing effect" you are talking about.
I know that things get smaller as they go away from you in the direction you are looking at. So do parallel lines appear to converge if they go away from you in the direction you are looking at. But things don't get smaller as they go to the left, relative to the direction you are looking at, or to the right, relative to the direction you are looking at. For example, a bird that's flying high in the sky is going to be the same apparent size as if it were on the point on the ground exactly below, right?

All the blue squares have an equal apparent size, and so do all the red squares, and neither the purple, nor the yellow lines appear to converge, right?
Right before I asked this question on this forum, I assumed that the solution is that the sunrays on the photos aren't exactly vertical, but appear vertical because of the clouds, and that the sunrays are actually vertical if and only if the sun is exactly in zenith. Could this be the correct answer?

[brimstoneSalad]

I don't know now. Anything I read about perspective seems to confirm my beliefs. I couldn't find anything about the "perspective bowing effect" you are talking about.

It wouldn't be very obvious in a single view without a wide angle lens.
Look left: smaller at a distance. Look right: smaller at a distance. Center (next to you) is the largest.

http://c8.alamy.com/comp/BR79KA/a-base- ... BR79KA.jpg
Left: far away. Right: far away. Center: close.
It's not rocket science.

But things don't get smaller as they go to the left, relative to the direction you are looking at, or to the right, relative to the direction you are looking at.

Of course they do. Center is the closest. Both left and right are farther away.

For example, a bird that's flying high in the sky is going to be the same apparent size as if it were on the point on the ground exactly below, right?

No, the bird in the sky is smaller if you're on the ground. Draw the triangle between you, the bird on the ground, and the bird in the sky. The hypotenuse is longer than the side. The distance to the flying bird is largest, so that bird will appear smaller.
Perspective depends on total distance, not ground distance (that would be absurd).

All the blue squares have an equal apparent size, and so do all the red squares, and neither the purple, nor the yellow lines appear to converge, right?

The purple and yellow lines converge, but not all the way: they aren't long enough in view.
The effect is small so you probably wouldn't notice it looking straight at this.

Right before I asked this question on this forum, I assumed that the solution is that the sunrays on the photos aren't exactly vertical, but appear vertical because of the clouds, and that the sunrays are actually vertical if and only if the sun is exactly in zenith. Could this be the correct answer?

This could also contribute to the effect: it's very unlikely they were perfectly vertical. But even if they were vertical, perspective distortion should create a similar effect. We can't analyze any of this without knowing the camera position, the lens, the height of the clouds, the distance to the clouds and the sun on the water, etc. It's silly to try, because none of this would be rigorous.

[teo123]

It wouldn't be very obvious in a single view without a wide angle lens.
Look left: smaller at a distance. Look right: smaller at a distance. Center (next to you) is the largest.

And it can be entirely explained by this diagram of barrel distortion, right?

And if we used some lens with the pincushion distortion, center would appear smaller than the sides, right?
And human eye creates none of those distortions, right?

No, the bird in the sky is smaller if you're on the ground. Draw the triangle between you, the bird on the ground, and the bird in the sky. The hypotenuse is longer than the side. The distance to the flying bird is largest, so that bird will appear smaller.
Perspective depends on total distance, not ground distance (that would be absurd).

Why would that be absurd? I simply don't understand what you are talking about. If you are looking towards the horizon, the distance in the direction you are looking at is called ground distance. And the projection of the bird on the image plane has to be the same size because of the triangle similarity.

The purple and yellow lines converge, but not all the way: they aren't long enough in view.
The effect is small so you probably wouldn't notice it looking straight at this.

What are you talking about? They go from one end of the visual field to another, and therefore they have maximal possible visual angle.

This could also contribute to the effect: it's very unlikely they were perfectly vertical. But even if they were vertical, perspective distortion should create a similar effect. We can't analyze any of this without knowing the camera position, the lens, the height of the clouds, the distance to the clouds and the sun on the water, etc. It's silly to try, because none of this would be rigorous.

That's the only argument I can use when I discuss with Flat Earthers, right? Using the argument that the perspective would create the same effect even if they were perfectly vertical would be intellectually dishonest, since I don't even understand it, right?

[brimstoneSalad]

And it can be entirely explained by this diagram of barrel distortion, right?

Not the perspective. Barrel distortion may exaggerate it slightly.

And if we used some lens with the pincushion distortion, center would appear smaller than the sides, right?

Depends on how severe the distortion was. You'd have to have the distortion stronger than the perspective. A near-by object on the side would appear massive, though.

And human eye creates none of those distortions, right?

The brain typically corrects for any distortions the eye makes, so you see only perspective. Eyes are weird, though.

And the projection of the bird on the image plane has to be the same size because of the triangle similarity.

Use a shorter or taller person in the image or use a bird that's closer to the ground or higher up.

Obviously if you are half as tall as the bird is flying (which would be absurdly tall, by the way, since when you see a bird in the sky it's usually over the trees) then they will appear the same size.
You are certainly NOT half as tall as the clouds. You would have to be standing on a very high mountain or in a plane (which I already explained in a prior post).

That's the only argument I can use when I discuss with Flat Earthers, right? Using the argument that the perspective would create the same effect even if they were perfectly vertical would be intellectually dishonest, since I don't even understand it, right?

If you only understand that argument, then you can use that argument, but I don't think it will be very compelling to them.

[teo123]

Use a shorter or taller person in the image or use a bird that's closer to the ground or higher up.

Obviously if you are half as tall as the bird is flying (which would be absurdly tall, by the way, since when you see a bird in the sky it's usually over the trees) then they will appear the same size.
You are certainly NOT half as tall as the clouds. You would have to be standing on a very high mountain or in a plane (which I already explained in a prior post).

But it isn't.

And if that with the triangle similarities isn't obvious from that diagram, let me try to make it even more obvious.

Obviously, the sizes of the projections are going to be directly proportional to the sizes of the objects, and not dependent on whether the object is left, relative to the eye, or right, relative to the eye, or in the center, relative to the eye, as long as their distances from the eye, in the direction the eye is looking at (the height of the triangle), regardless of the total distance, is equal.
When I claimed that the sunset is caused by the waves, you said I was insulting for denying the most basic common sense. How is what you are now doing different?
OK, it may be that I am just greatly misinterpreting what you are saying, so, please, be more clear.

[brimstoneSalad]

But it isn't.

Yes, it is. Stop being an idiot. The hypotenuse is obviously longer than the side. The bird in the sky is farther away from the ant than the bird on the ground. Stop trying to contradict that fact.

Farther away = visually smaller. In ANY direction.

Even if you use the angle, the two lines you've drawn to the bird in the sky obviously have a tighter angle between them, meaning the projection inside the eye (at a set distance) is smaller.

And if that with the triangle similarities isn't obvious from that diagram, let me try to make it even more obvious.

It is obvious from the diagram you just drew that what I said is correct. If it isn't visually obvious to you, then do the fucking math.
Instead, you've drawn another convoluted diagram with no math whatsoever: it's clearly not useful to you.

When I claimed that the sunset is caused by the waves, you said I was insulting for denying the most basic common sense. How is what you are now doing different?

Because you're a moron. "Why" is something you're going to have to figure out on your own, because you're pissing me off by continuing to argue for your position (again without attempting to do the math) when your assumption should be that it is wrong, and your effort here should be to humbly try to understand why that is rather than challenging me. You're doing again what I have repeatedly tried to teach you not to do.

This basically sumarizes this thread: http://www.nbc.com/saturday-night-live/ ... val/n12792

[teo123]

Even if you use the angle, the two lines you've drawn to the bird in the sky obviously have a tighter angle between them, meaning the projection inside the eye (at a set distance) is smaller.

Yes, of course, but the distance between the eye and the image plane isn't constant, rather it grows with the angle (not the visual angle, but the angle between the horizontal line and the line that connects the eye with the object). For example, the projection the ant sees of the bird in the sky is farther away than the projection of the bird on the ground. The differences in visual angles and the distances between the eye and the projections, in this case, cancel each other out.

If it isn't visually obvious to you, then do the fucking math.

If I do the math showing that homothety doesn't create similar shapes (see the second diagram), that means that my math is, as usually, wrong.

[brimstoneSalad]

rather it grows with the angle (not the visual angle, but the angle between the horizontal line and the line that connects the eye with the object).

No. Not even close.

The angle is based on the difference in two lines: From the top of the object, and from the bottom of the object, each to the eye. An arbitrary horizontal line factoring into this has no place (sometimes, in some illustrations, the object will happen to retreat from the eye along a horizontal path and the bottom will stay fixed to that line, but it's nothing special about the horizontal, that's just where the bottom happened to be in that illustration).
Where the hell are you getting this nonsense? Is this some fucked up flat-earther logic?

The differences in visual angles and the distances between the eye and the projections, in this case, cancel each other out.

That's not true, and your underlying assumptions about how all of this works are inherently false. There are so many obvious implications to such a claim that are absurd. If you hold a pencil out an equal distance from your face with your arm, and you move it in an arc over your head (keeping the same distance) does it appear to grow larger?

Do the fucking math and it will become obvious while you're doing it that none of your assumptions hold.

If I do the math showing that homothety doesn't create similar shapes (see the second diagram), that means that my math is, as usually, wrong.

If you do some math of any kind, it will at least help you identify your errors.

[teo123]

If you hold a pencil out an equal distance from your face with your arm, and you move it in an arc over your head (keeping the same distance) does it appear to grow larger?

I don't know now. No, and I guess it is because your eyes follow it, so the image plane doesn't stay the same, for the same reason as the horizon seems to raise with you as you go up. I've tried to do that experiment while I was focused on another non-moving pencil in my other hand exactly in front of my eyes, but not close to them, and, yes, that moving pencil I wasn't focused on appeared to grow larger. The difference was barely perceptible, and it could be only because I expected it.

Do the fucking math and it will become obvious while you're doing it that none of your assumptions hold.

OK, let me try. Let's not deal with the third dimension, to make things simpler. Let's assume that the ant, looking towards the horizon, is at A(0,0), that the bottom part of the bird on the ground is at B(10,0), that the top part of the bird on the ground is at C(10,10), that the bottom part of the bird in the sky is at D(10,100) and that the top part of the bird in the sky is at E(10,110), and that the image plane is the line x=1 (because, again, we are not dealing with the third dimension).
The light ray between A and B is y=0, so the projection of B on the image plane is (where the light ray and the image plane intersect) B'=(1,0). The light ray between C and A is y=x, so C'=(1,1). The light ray between D and A is y=10*x, so D'=(1,10). The light ray between E and A is y=11*x, so E'=(1,11).
So, the size of the projection of the bird on the ground is the distance between B' and C', which is 1. The size of the projection of the bird in the sky is the distance between D' and E', which is also 1. Are their projections equal? Yes, they are. It just affirmed my beliefs.

[brimstoneSalad]

I don't know now. No, and I guess it is because your eyes follow it, so the image plane doesn't stay the same, for the same reason as the horizon seems to raise with you as you go up.

No, it's because if it's at the same distance from you, it doesn't get larger based on perspective just because it's higher up. That's ridiculous.

What you are describing is a pincushion distortion.

The difference was barely perceptible, and it could be only because I expected it.

At least you recognize that. If you move off center from a lens, there are also optical distortions (different levels of zoom).
If you wanted to do this properly, you'd have to use a camera and account for that.
The whole idea is based on a misunderstanding of perspective, though.

OK, let me try. Let's not deal with the third dimension, to make things simpler. Let's assume that the ant, looking towards the horizon, is at A(0,0), that the bottom part of the bird on the ground is at B(10,0), that the top part of the bird on the ground is at C(10,10), that the bottom part of the bird in the sky is at D(10,100) and that the top part of the bird in the sky is at E(10,110), and that the image plane is the line x=1 (because, again, we are not dealing with the third dimension).

The ant's lens (assuming it has a human-like eye, which it doesn't) is at that position. It doesn't matter what way the ant is looking unless you assume some kind of distortion from the lens. That's not something you want to deal with to just understand basic perspective.

The image plane is not at x=1. It is a curved surface behind the eye where the image falls after passing through the lens (assume a pinhole camera).




As such, all of this is complete nonsense:

The light ray between A and B is y=0, so the projection of B on the image plane is (where the light ray and the image plane intersect) B'=(1,0). The light ray between C and A is y=x, so C'=(1,1). The light ray between D and A is y=10*x, so D'=(1,10). The light ray between E and A is y=11*x, so E'=(1,11).

Do it again. Draw a correct diagram, and calculate the projections on the back of the eye. Also, if you don't want to move the eye, then keep both birds within the range of human view by moving them both father away along X, or lowering the higher bird and making the birds smaller.

Are their projections equal? Yes, they are. It just affirmed my beliefs.

It should not have. If you were wise, and less arrogant, it should have affirmed that you do not understand something very fundamental to perspective and projection.