Perspective: focal length v. subject distance or "zooming with your feet"

Ah, talk bollocks. 😋

And what is or isn't true/relevant/meaningless is a matter of personal opinion. Glad we're back on a scientific footing...

You seem to be struggling to cope with what you see as not important being important to the op or anyone else.

A pickle barrel discussion isn't necessarily 'bollocks' (as in nonsense or bullshit). It's just a discussion to pass the time and where nothing important is at stake. A large percentage of forum discussions are like that.

Dan, from your previous posts, and I may be wrong, but you seem to struggle to see beyond your own opinion. You read everything as though you wrote it and fill in the gaps with what you think and what you would mean. I'm pointing out that a sign doesn't posses any 3D perspective and so taking photos of such with feet or zoom is really an exercise in magnification and not perspective. So taking the relationship you find between focal length and distance from subject and extrapolating that to explain 3D perspective effects of zooming with lens vs feet is necessarily very short on experimental data and very long on assumption. It is little more than an analogy, the danger of which is that you fail to explore the subject but rather try to fit it within a framework you already understand often jumping to assumption and simple parallels. But this is human nature as the desire to have everything neatly labeled and ordered often overrides our ability to question and admit doubt, or even see the cracks in our own logic...

You're proving my point. What is important to you doesn't have to be important to everyone else. It might or might not be.

If all that is important to you, all well and good.

If you use "Quote" instead or "Reply," you won't seem like you're talking to yourself!

I credit people with the ability to easily see who the reply is to.

Maybe you aren't able to?

Only if you're lazy, or think you can zoom from say 12mm-400mm with your feet in every situation

It's always nice when folks have the courtesy to use the "Quote" button, so there's no need to read every post.

Ah, the old I'm entitled to my opinion fallacy in the third person. That the statement 2 + 2 = 4 may not be important to everybody else doesn't stop it being true, but it does sidestep a rational discussion about the statement itself.

Personally I don't believe you're a troll, but you have a habit of derailing a lot of discussion usually by employing one or more argumentative fallacies. Why is not important to me but it does mean I will just ignoe the pointless remarks from yourself.

We were talking about perspective.

Turn things on their head, a useful tool to gain perspective and understanding. So the reverse of the op's example would be a distant view through a window say, the 2D on the outside and the 3d in the middle. Interestingly enough we do see an important exception where the zoom with feet/lens are actually very similar to the point of being close to identical. If we go back to my initial explanation where:

The perspective in the distance remains quite constant whether you zoom with the lens or your feet. It also contradicts the 0.12x compression factor suggested in the op when applied to distant objects.

You see! 🙂. Even you didn't need my post to be in quotes to realise I was replying to you.

I will take your opinion seriously when I see you make the same comments to other members here who do not always use quote tags.

But none of that is important to everyone. For some it is and for some it isn't.

For me none of that is important just like for some people the actual true definition of exposure is not important but for me it is.

That is incorrect as you can easily verify for yourself.

Look through the viewfinder as you turn the zoom ring on the lens. As the focal length increases, everything you see in the viewfinder appears to move closer. As the focal length decreases, everything in the viewfinder appears to get further away. That applies to mountains 5 miles away as well as to things much closer.

On the other hand, if you keep the focal length the same and move 10 yards closer to mountains that are 5 miles away, what you see in the viewfinder does not change noticeably.

I have heard many people claim that simply magnifying the image does not change the perspective. That is a serious misunderstanding of what perspective means. Whenever you drive your car you can see that the size of the image matters to your perception of distance (which is what "perspective" is all about). Look in the side mirrors to view the vehicles behind. Every driver knows that distances look greater than they should in the side mirrors. The reason is that the side mirrors give a wide-angle view by shrinking the image. Image size matters for our perception of distance in the image.

Tom, you used the same framing with your example so the same framing in my example yields virtually identical results mainly because the restriction of same framing also means same/similar focal length. But that was not the point. The point is that if you zoom 8m with your feet the distant perspective does not change, it remains constant. In your example you predict that you would need to change the landscape by ever increasing amounts as you get further away. The difference in perspective between zooming with your feet and zooming with a lens is inversely proportional to distance (affects closer subjects to a greater degree) not proportional as your analogy predicts:

Magnifying the image doesn't alter the mathematical perspective, or the way the 3D scene is rendered on the sensor, it is not a misunderstanding.

[My bold] Once again you bring human vision into the equation without making allowances for how the brain processes the information.

Perspective means the art of rendering a 3D scene on a 2D plane.

The art of looking at a 2D plane and forming a 3D understanding is a human cognitive function, not perspective. And with all human cognitive functions it is empirical and not logical or mathematical. No one is an outside observer of nature. Each of use is defined by our ecology. Ecology is necessarily relative, historical and empirical. see below

Not really, we learn, we adapt, basically we get used to it. That is what the brain allows us to do. Again you can't take the mathematical constant of how the 3D scene is rendered and apply that directly to human vision without allowing for the nature of human vision.

But we've been here before.

from above From Beau Lotto's TED talk of 2009.

I think you'd both better agree on any possible definitions of perspective before your discussion can be fruitful. Is it really only applicable to renderings on a 2D plane? Can we not experience perspective with our own eyes? We experience something when absolute or relative object distances are changed. If that's not perspective at work, what is it?

See above:

These are not my definitions, and yes it is only applicable to renderings on a 2D plane. This is basic human vision, the rendering of the 3D world on the 2D surface of the retina. There is a very interesting paragraph in the article linked, and again not my words but of Beau Lotto:

So, illusions are often used, especially in art, in the words of a more contemporary artist, “to demonstrate the fragility of our senses.” Okay, this is complete rubbish. The senses aren’t fragile. And if they were, we wouldn’t be here. Instead, color tells us something completely different, that the brain didn’t actually evolve to see the world the way it is. We can’t. Instead, the brain evolved to see the world the way it was useful to see in the past. And how we see is by continually redefining normality.

Ok so here's the rub, and why you can't explain how we see or experience perspective with the maths of geometry:

Light passes through the lens and hits the retina producing pulses in the rods and cones. And that is all they are, pulses of energy generated by the rods and cones on a 2D plane. There is no other data attached. The idea that we can rebuild a 3D understanding through Euclidean Geometry or "ray tracing" would first necessitate that we have an instant and clear knowledge that the signal was generated by a light ray traveling through 3D space towards the eye, and we would also have to have prior knowledge of Euclidean Geometry genetically imprinted. Think about it, how does a 5 year old navigate the world? It raises absurd questions like, why Euclidean Geometry and not QED? If you're not good at maths do you see a different world? (Though this may explain Abstract Impressionism...) And also why do we see a world where shape and colour are consistent when our understanding of the absolute data and the geometry predict the opposite?

There is another aspect to this which becomes move visible if you turn things on their head. If the perspective you see can be described in terms of absolute maths then it must also necessarily be as constant and inflexible as the maths. You would not learn or evolve as your framework of understanding must remain within the static confines of the maths. How could we create art and also understand it if this were the case?

The research is there, it has been done. It may not be complete and I may not fully understand it. It is more than a bit of a mind f*** to get your head around some of the concepts, it's taken me years to readjust my thinking to the point that it begins to make sense. Believe me, I know that it's easier to try and fit it within a framework you already understand and that makes sense to you, but what do you learn? Nothing that you don't already know.

I think finding a mutual definition that's kind to either of our pre-defined viewpoints is a barrier to understanding. Mathematical perspective and the way we construct an understanding of 3D space from 2D information are two separate things. It's the way it must be to explain all observed data.

Sure, I saw the above, and I had a feeling you would extend it to the human retina as a 2D plane. However, I have three dictionaries in the house, which all include the same additional definition seen here:

www.merriam-webster.com/dictionary/perspective

'the appearance to the eye of objects in respect to their relative distance and positions'

If you write your own dictionary, you might prefer to leave it out.

But for now, I'm not even sure in what way you and TomAxford actually disagree. Can that be concisely stated?

I'm sorry if I'm still not making myself clear here, I thought I was. From your own link:

3: the appearance to the eye of objects in respect to their relative distance and positions

4a: the technique or process of representing on a plane or curved surface the spatial relation of objects as they might appear to the eye
specifically : representation in a drawing or painting of parallel lines as converging in order to give the illusion of depth and distance

b: a picture in perspective

None of that contradicts the science and none of that is actually the science. Looking in dictionaries for the meaning of words does not constitute understanding perspective. Niether does it contradict the definition I gave, which is also there twice, in both 3 and 4a.

I am quite clear here and everywhere before:

You can describe how the shape of a cube is projected on a 2D surface. And perspective is always a projection on a 2D surface because perspective is also defined as the distortion caused by viewing from a unique point in space. A cube is defined by equal sides and all 90 degree angles, which is it's 3D shape. It's perspective is NEVER all equal sides and every angle at 90 degrees.

As per your definitions above.

I'm sorry you can't see this, as I said, I though I was being quite plain. But so far we have Tom whose op suggests that when zooming with your feet you have to move the scenery proportionally with distance when to the eye it's clear that it's inversely proportional. This was derived by taking pictures of 2D signs, we formulate about 3D rendering by considering a case void of 3D information.

Then Dan wanders off into his argumentative fallacies, "whats important to you..."

The you come along and quote dictionaries at me as though it provides the missing insight into understanding perspective.

2a: the interrelation in which a subject or its parts are mentally viewed
places the issues in proper perspective

Aye, sure does. I can't be bothered with this anymore. Soz but I'm off as well.