Wish granted.

As we see, in order to see the angles indicated we must go to a SIDE VIEW scene which takes place outside of the universe.

What do you mean it "takes place outside of the universe"?? It's just a diagram. It is used to portray angles and distances. If you go outside and physically measure the angle in reality, that angle should agree exactly with the one portrayed in an orthographic view. I don't understand why you are so vehemently opposed to a simple diagram. (Actually I do know... it's because you don't want to acknowledge that the earth isn't flat.

)

In your "first person" scene we do not see any angles to measure, being impossible to draw and exist in that orientation. The positions of the objects in the first person scene are impossible to justify and calculate with just that "first person" scene alone -- making your approximations entirely arbitrary without your supporting side view image to attach with it.

It certainly wasn't arbitrary. I measured and labelled quite carefully, as you can see for yourself. It's all just simple proportions. The camera's vertical field of view is 52°. If an object has an angular diameter of 26° in the orthographic diagram, then the object will take up half the vertical room in the photo. In the above picture, the conversion is 7.7 pixels per degree. The 2.3° wide object takes up 18 pixels. No, it certainly is not arbitrary.

However, the

*real* question is: does it correspond to reality? Yes, it does, assuming negligible distortion in the camera. You can easily go test this out for yourself. Grab a camera and set up several objects. Carefully measure their distances, heights, widths, etc. Calculate their angular diameter, and angular distance from each other relative to the camera. Compare these angles to their size in the picture. Assuming the camera has a relatively narrow field of view, then I can assure you, it does.

Top is the orthographic side view. Bottom is from the perspective of the camera. Notice how the angles in the orthographic side view correspond to the dimensions and placement of the objects in the first person view. That's why the orthographic view is useful. Keep in mind, this isn't 100% accurate, sense any camera will have a bit of distortion due to the shape of the lens or sensor. As long as the camera isn't very wide angle, the distortion should be minimal.

At which point, according to your math, will the sun touch the vanishing point?

Assuming it continues to travel in a straight path? Technically, never. However, it can get arbitrarily close to the vanishing point. And our eyes can't distinguish arbitrarily small details. A commonly quoted value for the minimum angular diameter that our eyes can distinguish is 0.02°. If the sun is indeed 3000 miles high, this would correspond to a distance of 8.6 million miles. So, on a flat earth, the sun could possibly appear to touch the horizon when it travels 8.6 million miles away.

If you check your math you will find that it is impossible for the sun to ever touch the vanishing point. It will just keep slowing down and never get to the horizon. In fact, under that math, it's impossible for anything to intersect at a vanishing point.

Yes, technically. See above.

Since the vanishing point exists, the math is clearly an inaccurate representation of perspective.

Good grief, subtle shades of meaning isn't your strong point, is it? The vanishing point exists on the projection, not in 3D reality. The vanishing point is the point on the projection that objects

*approach*, as they travel an infinite distance away from you. You can calculate where the vanishing point will be on the projection using the very same math that you claim the vanishing point disproves.

Please read the following carefully, because this seems to be where you keep getting confused:

No, an object technically can never reach the vanishing point. However, the object can get arbitrarily close to the vanishing point. It can get so close to the vanishing point that we can't tell the difference with our eyes. We can predict

*exactly* how close to the vanishing point it will be using simple trigonometry like I have used. You can test this yourself with some parallel lines, a few objects, a camera, and careful measurements. Stop claiming that the math doesn't work when you can easily verify for yourself that it does work.

I agree that the sun is at 0° with the horizon when it sets. The reason the result of my math is wrong (28°) is because it started with a flawed assumption: that the earth is flat. The reason the math doesn't agree with reality is because the earth isn't flat in reality.

This is how models are tested. You make predictions assuming the model is correct. If the predictions disagree with reality, there is probably something wrong with the model. Since my prediction based on the flat earth model is wrong, there is probably something wrong with the flat earth model. Obviously.

We know that it is possible for perspective lines to intersect. Under your math it is impossible for any perspective lines to intersect. Therefore your math is wrong.

No. The lines can and do intersect at the vanishing point on the projection. However, for an object to reach the vanishing point by following the lines, they would have to travel an infinite distance, in theory. In reality, since our eyes can't tell the difference between two objects 0.00001° apart, it is possible for objects to

*appear* to reach the vanishing point. See above.

Not only does it lack the intersection of perspective lines, your math has not been demonstrated to be an accurate portrayal of large scale perspective in the real world. You bring us math created by ancient civilizations to us and expect us to just assume that it is correct for the situation. Where is the evidence that it is correct for this purpose?

Oh please, not this again.

"All our calculations agree with the round earth model. But maybe... math suddenly stops working for objects the size of the earth, and the earth is actually flat! No, I have no evidence to suggest that the math suddenly stops working except that I

*really, really, really* want the earth to be flat. Please believe me."

Good luck with that argument.

Edit:

"Warning - while you were typing a new reply has been posted. You may wish to review your post."

Rama also makes good points about the sun not changing size. Anything travelling along the "perspective lines" decreases in size as it approaches the vanishing point. Since the sun doesn't change size, as we have already thoroughly established in other threads, it clearly is not getting farther away.

And rabinoz also makes a good point, although I would really rather not get into the "ship/building is behind the horizon" argument in this thread.