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

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.