The Ansel Adams Fallacy: "True perspective depends only on the camera-to-subject distance"

How about a diagram, and some maths to back it up?

First of all, it wasn't a trick. I simply asked you to explain "what you think observation would show in the following situation." I didn't force you to describe it in terms of pure maths or anything else. I was curious about how you would describe it. It seems that you don't want to describe it at all, except in very vague generalisations, e.g.

Nothing precise there, no mathematical formulas, almost nothing of any practical value to anyone.

I like to give people the benefit of the doubt and give them every opportunity to explain themselves more fully and in more detail if I cannot understand what they say. You have been given every opportunity, but you simply repeat the same vague statements time and again and refuse to go into any more detail, yet you have the temerity to criticise the theory of perspective that has been understood for centuries and claim that it is not possible to explain what we see in a photograph in terms of mathematics.

You claim that you agree with the statements about perspective in the Manual of Photography, but you then proceed to describe perspective in your own fanciful ways that contradict the traditional understanding of perspective.

I guess that you will continue to talk the same old nonsense and continue to claim that what you say is sound science and that I (or anyone else disagreeing with you) am the one talking nonsense. The Donald Trump technique?

Much preferred to the Fauci's "I am the science" technique you are using all the time.

Either I am not a good mathematician, or your statement is wrong (or both).

@TomAxford Your theories on perspective contradict the traditional view of perspective, they contradict the maths of image geometry, they contradict what is clear by simple observation and they contradict current scientific theory.

You don't even seem to understand the maths of pure geometry to the point that you can't see the world it predicts, or how it differs from the world we see through human eyes. It's not hard to do this, any halfway competent mathematical can do it.

Instead you take an effect where we see distortion in the fixed perspective of a 2D image when we view it through human eyes and insist that it can be explained through pure geometry alone, even though pure geometry predicts something quite different.

You haven't even worked it out that "telephoto compression" and "wide angle distortion" are the true geometries of the respective images. Instead you take the one point when you view an image and don't see that perspective and use that as the point that you see perspective as described by pure geometry.

I've been trying all through this to prompt you to question your base assumptions and question that you are not looking at this whole thing back to front. But no, TomAxford alone has absolute vision and so what he sees is the absolute truth and this relates directly to pure geometry.

Even though that viewpoint even contradicts pure geometry, and everything else noted above.

It's a nonsense question.

FACT: We do not see the world of pure geometry through human eyes. The camera sees it, and we can glimpse it in images but only if we view them from a position outside the centre of perspective. That is the correct way around. And it's pointless discussing anything until you are able to see just a little way beyond your own opinion, even if it's just the true nature of the world that pure geometry predicts.

No need to "shout", Tom.

I made no mention of the absolute size of the image. My comment referred only to the relative angular size of the two persons.

I'm very sorry, I was not intending to shout, simply trying to be unambiguous and to the point.

I agree that you referred only to the relative size, but you then deduced that there was no difference between the two cases (I assume that is what you meant by "ergo, no difference").

That deduction implied to me that you had assumed that the absolute size was unimportant. Why did you not mention the absolute angular size when it is the main thing that varies when the viewing distance changes?

No one - they are independent concepts. That's the whole point if you had actually read what I wrote.

You're doing the same thing - bringing up an unrelated point (that viewing condition can change human perception of an image) to argue something entirely separate, namely that viewing condition changes perspective, which it doesn't. Only the relative position between the camera and the scene can change perspective.

Yep, I should have said "no difference between the relative angular size of the two persons in the image in case (1) and case (2) irrespective of the absolute physical size of the viewed image" ... thereby trying to avoid misunderstanding by your good self. Pardon my lack of clarity , folks.

I did not feel that it was a factor in the context of my post.