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

It really isn't, though, if perspective isn't all that important to the "success" of your photo. Just like saying to use a wider aperture in lower light isn't stupid if DOF isn't all that important to the "success" of the photo.

HAND.

Excellent !!

I once had that as my signature line elsewhere ...

The problem with this thread is semantics. The thread is about magnification rather than perspective. It also only applies to one point perspective.

I'm hoping my previous comment was deleted because of the comment at the start. If so it was a fair cop, and hopefully this one will stand.

Briefly:

Do it with a machine. If we did and were careful too look only at the retinal image and not at our perception we would find that our machine would see exactly the same image at all distances. That is it's mathematical truth, the relationships do not change. If we give our machine the correct height, width and depth (if we have memory of all then allow our machine to as well) then the only correct answer it will ever come up with is that we are looking at a magnified image of the correct perspective of a distant object.

So why don't we as humans instinctively understand the absolute mathematical truth in the image? It's a more logical and simpler deduction that what actually happens.

If we keep blindly assuming that what we see is absolute then we keep treating what we see as the retinal image. We therefore automatically try to apply the maths to describe what we see rather than how the real world should look.

It's pretty much fact that human cognitive function prevents us from seeing our retinal image. We see a composite derived form memory, from scanning the scene as we actively move through it, modifying the data to remove or clarify paradox, plus other cognitive functions. It is not and can't be condensed to ray tracing or linear geometry.

You proof says that the height of the object and the angle is subtends is a mathematical function of the image, in geometry yes. But so is the relationship between height and depth in the image, why don't we compare those as the machine does? In your proof you choose the maths that describes what you see, you subconsciously try to fit what we see to the mathematical model rather that how the world should actually look.

The proof is really in front of you. We misinterpret the distance of the object, we don't see the relationship between height and depth correctly. You're applying linear geometry to predict why we don't see the linear geometry in the image correctly.

If you do the maths we (and our machine) know that perspective renders all distant objects as foreshortened.

What do we see when we view our t-c image?

If human cognitive function prevents us from seeing our retinal image then we would have no memory of context for this foreshortened (or compressed) view. So we assume that it's height is representative of the distance as the most likely explanation for the image. Because our vision is there to make sense of the world not nonsense the way we misinterpret the rest of the information can most definitely be related to the model of linear geometry. But not exactly because we are still over the line and are talking about cognitive function and not retinal image.

That we decide to interpret the height of the object in the image as representative of it's distance from us the viewer is a choice, human cognitive function. It is not a function of the maths of the image, if it were then so is the relationship between height and depth. We choose to hold one as true and modify the other. YOur theory also fails to explain how we can adapt and learn to interpret images correctly

If we view the image at the centre of perspective then we make no error in assuming the distance and so process the data much the same way as we do in the real world, they will look very similar.

If we are prevented from seeing the world of linear geometry by our cognitive function then it must also always fail to describe how you see.

Ciao

You're attempting to speak on everyone else's behalf by saying "we" when in fact you are posting just your opinion. Attempting to speak on everyone's behalf is just plain dumb.

Not everyone's eyes interact with their brain in exactly the same way.

What Tom posted in his op is consistent with my observations.

But that doesn't prove that the world that our cognitive function presents us with is an exact match to linear geometry.

I can only speak for myself and my research into the history of art and perspective. Correct perspective is visible in graeco/roman art, but per object. There is no unified linear perspective. That came with the Renaissance and was: Linear; separation of planes; atmospheric; and classical colour theory. If we only stick with linear perspective we find that although limited in viewpoint it was absolutely derived by rigorous and correct maths (barring the visits from the Inquisition). But what is left out of these discussions is that even before Leonardo it was widely understood that it always looked slightly odd, or different to the way we see the actual 3D world. It was well understood that it depended a lot on viewing distance to the point that the practical understanding was that when viewing images people never really saw linear perspective correctly, it always looked slightly distorted.

But the Renaissance was the era of science and so artists spent a lot of time trying to get around this by both modifying the mathematical model, or deriving more empirical ways of defining it (the movement of hand and eye) such as lengths of string through a fixed hole.

If we want to look at the history of perspective in art then we need to look at all of it, these discussions tend to be selective.

Tom has often said that he is only discussing the retinal image. In this context there is no problem with semantics. But “if” the assumption is that because the angle subtended on our retina pre cognitive function is the relevant data for the conclusions we must arrive at through cognitive function… Then we must be making one hell of an assumption about how the brain collects processes the data. What if that explanation isn’t even close?

The height of a known object subtends an angle and so if you magnify it and it subtends a different angle then this affects our interpretation of height and that defines how we must interpret the relative distances… Why do we only consider one dimension when there is a lot of other information that is relevant to the correct mathematical perspective in the image?

Are you sure that wouldn’t require us to program the machine to follow that logic?

”If” t-c can only be explained by including an element of cognitive function that explains why we make an error of judgement, (why we disregard some information in favor of other), then are we also aware that explanation we are pursuing specifically excludes that possibility? Just sayin’.

I am only talking about one issue, that we keep trying to explain the latter, interpretation, which includes cognative function, through an understanding of geometry. We keep mixing the two, we keep using visul example as ptroof of geometric fact without allowing for the nature of cognitive function. We use the eye to see a valid point and do bot consider whether we've introduced part of the error we try to explain with the maths.

The proven truth is it is not just the geometry, cognative function actively alters the data. This is key, this is what your outlook and the conclusions you seek prohibit. Even you can't see beyond the geometry as a complete and full explanation. That is what is wrong here.

Didn't I say that very thing a page ago? The part I have a problem with is Tom's conclusion that t-c is a mathematical truth in the image explained by the image geometry, and so is predicted by the image geometry:

And doesn't answer my main objection (though a bit of a keyboard mash):

I don't know enough about the maths of colour theory, but I'm pretty sure we don't use the physics of light without taking into account cognitive function. Linear geometry explains the mapping of a 3D scene perfectly, and our perception well enough to be used as a solid example. But we have to recognise the limits.

Say you are a stone age man (I know your not because like me you don't have enough hair) standing in a field, spear in right hand, scratching ass with left, when a tiger jumps out of the hedgerow. What do you do, reassign the task of your left hand or have a discussion with yourself about phenomenology? It may sound daft, but consider if Darwin is correct then which course of action is most likely to promote your survival long enough to be discussing this on an internet forum 6000 years later; developing absolute vision or being able to trust that vision is absolute and act instinctively on it? Optical illusion shows us that it's the latter, the brain actively works to present a consistent understanding over an absolute one. And it's this that holds the key to why we make the initial (wrong) assumption about distance in t-c images. It isn't a mathematical function of the image. And so even the Adams fallacy falls flat (he was just trying to give an easy visual key) because the assumptions of the maths are flawed when we don't consider that perhaps the reason we don't see some images correctly is highlighting the slight differences between cognitive function and linear geometry rather than trying to make them confirm the maths.

I think it's still a very valid point. I do understand yours and within the points outlined above pretty much agree. Nice talkin'.

Andrew, I suggest you start a new thread to give your explanation of telephoto compression in detail.

I think you have said that you agree with the science and mathematics of perspective. My own ideas are based entirely on the science and mathematics of perspective established over the past 500 years or so. I have added nothing to the accepted theory of perspective. Yet you strongly disagree with almost anything I say about perspective. I'm puzzled.

I think it is time you started your own thread to give your view of telephoto compression and related topics in perspective. How do you explain telephoto compression? It would be much more constructive than simply attacking my threads on the subject in a purely destructive and often highly offensive manner.

Please forgive me David, but I don't understand why you feel compelled to continue reading and contributing to a thread that you find "unedifying"? There are plenty of threads that I do not like for one reason or another, but I do not read them (beyond the title and sometimes the first post or two) and I certainly do not contribute to them.