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

Sort of. And being a former builder/bricklayer I have to confess that I may, perhaps, be a very slow learner... We are all individual and so all have a unique view because we all view from a sightly different position, both philosophically and directly in what we see with our eyes. And what you learn, how you are taught (to classify, order and label) even how you understand physics does affect how your brain processes the information and forms the image you "see".

But in reality similar social/political groups have a similar shared environment and so true variance within that environment is very small, we all have roughly the same skills and the difference between beginner and expert is really just practice. You have to separate shared experience by a long distance before you see any significant change. However, if you start to encourage people only to glance rather than look, then we don't see correctly or completely. We then fill in the gaps from the only place we know, our own experience and memory. And if we are encouraged to do this emotively rather than rationally (something you see quite frequently on social media these days) then that perception, provided largely by our own memory and containing that bias, becomes physical proven fact supported by the evidence. Never underestimate the power of the human brain to ignore what it doesn't wish to see.

Perspective drawings are, or should be, mathematically correct. And any modern draughtsman will know that pure linear perspective always looks slightly odd. The reason is if human cognitive function prevents you seeing the world of pure mathematical perspective then that 2D representation is one you never see, it will look different (slightly) to the real world "as you perceive it". Because they are technical in nature they include lots of geometry and so it is more obvious that a photo of a landscape. But artists have known this since the Renaissance, that true linear perspective doesn't represent what we see and have been working their way around it since before Leonardo. BTW, it's quite easy to show that you never see perspective in a photo correctly either, and see the second paragraph above, it applies.

If I look out of the window and don't see the real world, what exactly do I see?

From that response:

With colour the composition of the light reflected from objects depends on the composition of light hitting the object. The scientific reality of the world is that colour constantly changes. Yet this is not the world you see. You see one where your understanding of colour remains remarkably consistent. There are many processes that evolution has promoted to do this, I showed you proof that it also actively changes data so it matches experience.

With perspective the mathematical model dictates that shape and relative distance must be in constant motion as you move through 3D space. Yet this is not the world you see. You see one where your understanding of shape and relative distance remains remarkable consistent. There are many processes that evolution has promoted to do this, I showed you proof that it also actively changes data so it matches experience.

Seeing depth in a 2D image is entirely a human cognitive process. Sorry but it isn't a mathematical function of the image, it exists only in how we process the data. The image projected on the retina of a 2D image is a facsimile, that is mathematical and geometrically a fact. There is no 3D information attached, only what we work out with our brains. That calculation only happens in the brain, if you discuss depth perception you are discussing that function and not perspective. That what we see in a 2D image relates to the maths of how it is rendered is only because we are very good at it. But it is not visual proof of scientific fact. See my previous response.

From your own definition, your bold:

The reality of geometry is that if you view from a single point in 3D space (the only thing we can physically do) then perspective effects distort what we see in a way that changes as we move through the space. It shows a far more confusing and unstable landscape than we see. In reality the image that our brains construct is far more representative of the real static nature of 3D space, a view that's made impossible for us to see because we can only ever view it from a single point in space, and so our view is always distorted by perspective (the way the 3D world is projected on the retina). We can do this because of human cognitive process.

But it also means that what you see is not directly representative of mathematical perspective. It is also true to say: Seeing depth in the real 3D world is entirely a human cognitive process.

Andrew, I think what you are saying here is so bloody obvious that I hadn't realised that you could be making such a fuss over something so obvious. Everyone with reasonable scientific understanding knows that when we look at anything our eyes are recording photons that hit our retinas, this is converted into electrical and chemical signals that get transmitted to our brain and go through very complex processing to interpret those signals, etc, etc.

So what? This does not mean that we are not looking at the real world! Of course there are situations in which we may be unable to interpret what we see or interpret it incorrectly. This does not negate the usefulness of having a mathematical model of perspective that works when we are able to correctly interpret what we see.

Your lack of understanding of how science works is seriously clouding your ability to talk rationally about these things. It is possible to discuss perspective without having to consider how the eye works, how the brain works, how depth perception works and all the other things that may be involved when we look at a photograph or when we look at a real scene. Science always works by the abstraction and separation of ideas so that we can consider one thing at a time. Real situations are always much more complicated than the idealised models that scientists consider. But those idealised models are an essential part of the scientific process.

I give up Tom, you cannot see past your need to have a mathematical model, and to defien what you see by the metrics you understand.

So what is more likely?

The human eye is a perfectly calibrated piece of scientific equipment and we can trust the data as an accurate representation of scientific reality.

The human eye is the product of evolution and it's sole purpose is to give us the best chance of survival. You are looking at the real world but do you see it correctly.

Darwin was a scientist as well.

Absolutely, but it is not possible to talk about how the eye works, how the brain works, how depth perception works and all the other things that may be involved when we look at a photograph or when we look at a real scene without considering human cognitive function. And you continually do and relate that directly the the geometry of perspective. You are a walking contradiction of your own definitions and conclusions and yet you still don't see it.

Ciao

Finished your popcorn yet?

Finished it about 5 posts ago and just made some more 😊

The Matrix.

Laugh if you want, but if you can't understand that that act of looking involves collecting and interpreting data through an interface, and you don't wish to accept that that interface involves human cognitive function. Or if you think you refusal to question the nature of this and rather assume that what you see must match a mathematical model, because talking maths makes you a scientist, then you carry on. But I'm not the one photographing purely 2D data (mathmatically described as a facimile) because:

Joke away... 😂

You are entitled to your opinions just like everyone else.

It seems to me you are just cherry-picking bits from the op that suit the agenda you are pushing.

What Tom describes in the op is consistent with my observations in the real world. YMMV.

Those are certainly some ifs to think about. Here's another one: If reality is only a simulation, as has been hypothesized, then humans are not necessarily “real” beings, but instead predetermined, coded constructs within the simulation. In that case, ourselves, perspective and all other aspects of our universe are just algorithms running in the simulation - not much more than mathematical models at all.

Well, this thread looks like it's run it's course, so I'll go along with this diversion. First of all, what is "real", if anything at all, is a whole can of worms, in and of itself. Secondly, simply because something can be described mathematically does not mean it is predetermined. As I'm sure we're all aware, probabilistic events are not predetermined, yet are described by quite a bit of mathematics. While some may say that there are no probabilistic events, that, instead, we use probability and statistics as an approximation for phenomena too complicated to be worked out exactly, Quantum Field Theory posits that "reality" is inherently random. Yet, despite this inherent randomness, we can make very precise predictions about any number of things.

Then leave out predetermined. I'm not sure why I had it there in the first place. The terms code and algorithms can allow for non-predetermined events - for example, if they include a random number generator.

OK, sure. But it still doesn't make a difference. First of all, you have to define what is "real". For example, in modern physics, an electron is a point particle. It has zero size. Yet it has angular momentum. That doesn't make any [classical] sense. A point "particle" isn't a particle at all. A particle would have to have some size. And yet, even given that a particle would necessary have size, it would also necessarily be made of something. But an electron isn't made of anything (again, per modern physical theories). It just is.

So, what's "real"? Why can't information be as "real" as something physical. And now that I bring it up, what does it even mean to be physical? I guess it's like the whole God thing -- rather than say God created the Universe, it's easier to say that the Universe just suddenly came into being on it's own or has always existed. After all, if God created the Universe, where did God come from? You're just adding an extra unnecessary step by introducing God into the equation.

Thus, it's probably best to simply think of "reality" as information, and that information is, so far, best described by mathematics. The question then is two-fold: why is the information described by the particular mathematics we have found (or, at least, very nearly described by this mathematics) and why are the initial conditions (need not be "initial", but conditions at any particular state of the Universe) for the solutions what they were? If you like, you can define God as The Equations of "Reality" and the Initial Conditions. 😁

Since we have a hard time with that word, I also put it in quotes and said not necessarily. It's open.

Actually, I think people who hypothesize about reality being a simulation eventually decide that it doesn't matter much unless we can identify a difference.

Really going off topic now...

I think it was classical physics that described an electron as a point particle (or as I remember it, a point charge) and the incongruity of that in the physical world was one of many things that led to modern physics.

It's unfortunate that the word "particle" has been used to describe any sub-atomic entity. A particle, to me at least, describes something that has form in the physical world. As soon as we delve into the sub-atomic realm, entities, from electrons, protons, neutrons and beyond, are foundational constituents of the physical world. It is hard to even find the right words because our minds are typically so pre-programmed to think in terms of 3D space, time and object - what our senses present to us - and language has evolved to describe our experience in the physical world. How to describe / conceptualize something that exists beyond the framework of the descriptive mechanism?

I think you still may be missing the point.

You can use geometry to define exactly how an image is formed on the sensor or the retina. If a person is 170cm tall and standing 200m away he subtends a specific angle on the sensor, then with the assumption the second person is 170cm tall then we can assume how much further he is away by comparing angles. But you have to measure the angles on the photo, the actual physical data.

That mathematical relationship is not true if you run it through the human cognitive function because you are no longer looking at absolute data.

The only world you can ever see or experience is the image generated by the brain based on the data from the eye. It depends not only on how the human eye has biologically evolved but how we've learnt to decipher this data through purely empirical means. I don't know why we find it so difficult to understand that the human visual system doesn't present you with absolute data. As you walk into a room your understanding of your favorite armchair is knowledge and memory of a deep and happy relationship. It is built form walking all around and compiling the data from all views, it is built from your knowledge of doing the same with other chairs. From all that data you have a deeper understanding of its true 3D shape, one that's a lot freer from the distortion when viewed from a singular point in space as perspective demands. Look again at Beau Lotto's optical illusion. We are not seeing absolute data that's being interpreted, we are seeing modified visual data that clarifies our interpretation.

And yet we are still treating vision on the basis that everything is a single still photo and that the geometry that defines that is the absolute data we see.

You can only ever see the world through the layer of human cognitive function, you can only view photos through that same layer. When you view a photo against the real 3D world you are not comparing retinal images. You are not able to see your retinal image.

We cannot keep making the blind assumption that what we perceive (we see) is absolute data as defined by linear geometry, or jumping from that retinal image to the processed construct of the brain and not allow for that extra process.

Yet Tom keeps doing this. If you apply the wrong mathematical model then your conclusions will be flawed. And Tom's conclusions about how we process information in both the real world and in photos is flawed because he keeps trying to relate both to linear geometry.

In some cases we probably could justifiably make that assumption because not everyone's eyes and brain interact in exactly the same way in every situation.

And in some cases Tom's conclusions are totally valid because not everyone's eyes and brain interact in exactly the same way in every situation.

You are assuming a generalisation about how everyone perceives/sees in exactly the same way in every situation which in itself is a flawed generalisation because not everyone's eyes and brain interact in exactly the same way in every situation.