A discussion on TFES forum

[brimstoneSalad]

Here, I edited this to provide the diagram so you don't fuck up:

obvious1.jpg

Now you do the math.

It's about 30% smaller. If you get a number very far off from that, then try again.

[teo123]

So, if the image plane is usually curved, why is it almost always drawn like a straight plane?
Sorry if I was insulting, I assumed you were joking, or haven't spent literary a few seconds of thinking before posting something, as I often do.

[brimstoneSalad]

So, if the image plane is usually curved, why is it almost always drawn like a straight plane?

It isn't. Diagrams of eyes show it how it is. Cameras have straight planes, which adds some additional distortion that has to be corrected.

That is, they used to anyway: http://www.geek.com/chips/sonys-curved- ... s-1598720/

Sorry if I was insulting, I assumed you were joking, or haven't spent literary a few seconds of thinking before posting something, as I often do.

Then stop doing that.
I told you before and I'm telling you again: just assume I am right, and that I know more than you do about this stuff even if (and especially if) it sounds strange. Instead of doubting what I say, or claiming I'm wrong, try to understand it.

Even if I told you there was a tiny wizard in your eye who manually caught each photon and squished it to make it smaller before delivering it to the rods and cones toward the edge of your view, you should have just accepted it for the time being and tried to understand how it works. You don't understand enough about any of this to contradict anything I say, so you need to just assume I'm right if you want me to teach you, otherwise you're on your own because I don't have time for this disrespect. I'm taking time out of my day to educate you.

[teo123]

It isn't. Diagrams of eyes show it how it is.

But the image plane IS usually depicted as a straight plane, at least when we are talking about the perspective.
https://en.wikipedia.org/wiki/Perspective_(graphical)#Overview
http://www.webexhibits.org/sciartperspective/tylerperspective.html
I think that this has something to do with our perception. From the diagram you've shown me, it's obvious that the area of the retina an object is projected is proportional only to the visual angle and to the total area of the retina. So, if you read your math notebook from 20cm distance, and that notebook is 20x30cm large (A4), the grid should appear atan(0.5/20)/(atan(10/20)-atan(9.5/20))=1.432/(26.565-25.408)=1.24 (each field in the grid being 0.5x0.5 cm) times larger at the center than at the edges. We don't notice that difference, right?

Cameras have straight planes, which adds some additional distortion that has to be corrected.

I don't really understand how can the Petzval field curvature make the objects appear smaller as they go the end of a scene (if that's what you are saying). The light ray that goes both through the center of the lens and though the point being projected still gets to the focal plane, even if the image isn't actually there. Or maybe the projections in the space project orthogonally on the focal plane? That would make the objects appear smaller, but that doesn't appear to be the way the light works. Let's move it into some different context: if you move a projector away from a plane, the image doesn't only become blurred, it becomes enlarged. Is this a false analogy?

Then stop doing that.
I told you before and I'm telling you again: just assume I am right, and that I know more than you do about this stuff even if (and especially if) it sounds strange. Instead of doubting what I say, or claiming I'm wrong, try to understand it.
Even if I told you there was a tiny wizard in your eye who manually caught each photon and squished it to make it smaller before delivering it to the rods and cones toward the edge of your view, you should have just accepted it for the time being and tried to understand how it works. You don't understand enough about any of this to contradict anything I say, so you need to just assume I'm right if you want me to teach you, otherwise you're on your own because I don't have time for this disrespect. I'm taking time out of my day to educate you.

And would you trust a doctor who tells you to start smoking? If not, why should you trust a mathematician (or whatever are you in real life) who appears to imply that homothety stops making similar shaped once the distances get too big? Now I know that's not what you were saying, but if I didn't try to contradict your arguments, I would start believing nonsense.

[brimstoneSalad]

It isn't. Diagrams of eyes show it how it is.

But the image plane IS usually depicted as a straight plane, at least when we are talking about the perspective.
https://en.wikipedia.org/wiki/Perspecti ... )#Overview

You're reading an artistic explanation, that's the problem.
Yes, that's how artists draw paintings. A painting is not your eye.

We don't notice that difference, right?

You wouldn't tend to notice it, no. Also, your eyes only resolve an area very close to the center (around the blind spot) with detail. They track around to take in the whole image.
Nobody looks at things without moving their eyes around, particularly with such a wide angle (as in wide angle photography). You'd only really see a small part of the image at a time.

What we're dealing with is a tilted camera, though:

http://cache3.asset-cache.net/gc/101659 ... sAt9%2FOao

You'll see in those images that the horizon isn't in the center, or they're wide angle shots.
We're looking up at the sky.
(In a wide angle shot, you can look up at the sky AND down at the ground in the same photo, it's special)

I don't really understand how can the Petzval field curvature make the objects appear smaller as they go the end of a scene (if that's what you are saying).

All I'm saying is shown in the diagram.

The light ray that goes both through the center of the lens and though the point being projected still gets to the focal plane, even if the image isn't actually there.

I don't know what you're talking about. Draw a diagram and do math.

Or maybe the projections in the space project orthogonally on the focal plane? That would make the objects appear smaller, but that doesn't appear to be the way the light works. Let's move it into some different context: if you move a projector away from a plane, the image doesn't only become blurred, it becomes enlarged. Is this a false analogy?

Again, I don't know what you're talking about.
A projector has a lens that spreads the light at an angle.

And would you trust a doctor who tells you to start smoking?

You shouldn't, you should trust scientific consensus on that. It's very clear: Smoking is bad for you.

And you should trust scientific consensus on the distance of the sun, which is also very clear, and the shape of the Earth, and rockets, and planes.
None of these things are complicated claims: just believe them if you don't understand them.

If not, why should you trust a mathematician (or whatever are you in real life) who appears to imply that homothety stops making similar shaped once the distances get too big?

You should trust scientific consensus on these matters. Go to the most authoritative source. E.g. ADA for nutrition information, WHO, NASA, etc.
Hundreds of scientists are less likely to misunderstand something than one.

Now I know that's not what you were saying, but if I didn't try to contradict your arguments, I would start believing nonsense.

That would be fine as long as the moment somebody else credible came along and said something different, you changed your belief to match that.
Your belief should never be committed, but tentative.
When somebody else seems to contradicts me who is credible, then believe them, because you probably misunderstood me (e.g. they probably aren't actually contradicting me, but contradicting your misconception).

[teo123]

So, would the real image (where the light rays intersect) be projected on the focal plane in the point A (which is the closest to the real image, but that would make the objects appear smaller as they go to the edge of the image), or in the point B?

[brimstoneSalad]

I don't know what that diagram is supposed to represent or what you're asking. What you said doesn't make sense. It doesn't look like it has anything to do with an eye.

So, would the real image (where the light rays intersect)

Light rays "intersecting" has nothing to do with it. All that does is invert the image.

be projected on the focal plane in the point A

Images are not projected onto a point. That wouldn't be an image, it would be an incoherent point of overlapping photons burning through whatever it's touching: it's how children kill ants with a magnifying glass.

[teo123]

I don't know what that diagram is supposed to represent or what you're asking. What you said doesn't make sense. It doesn't look like it has anything to do with an eye.

That's the diagram of Petzval's field curvature from Wikipedia.

That wouldn't be an image, it would be an incoherent point of overlapping photons burning through whatever it's touching: it's how children kill ants with a magnifying glass.

Doesn't seem to make sense. The focus isn't exactly on the film, so even less light is getting to the point on the film where it should get. If the film would get burned, it would be at the center, where it's perfectly focused. Would a plane get burned if you move it farther away from a projector? The diagram is more than likely an exaggeration. I was reading about photography on the Internet a lot, and I thought you might help me to understand how the abberations work (do they just make things blured, or can they also change the apparent shapes and sizes). OK, it's not that important.

And you should trust scientific consensus on the distance of the sun, which is also very clear, and the shape of the Earth, and rockets, and planes.None of these things are complicated claims: just believe them if you don't understand them.

And what if I can't believe them? I can't just choose to believe something, a belief is a result of becoming convinced. To someone with such misconceptions about perspective, physics and logic, the arguments Flat Earthers and other conspiracy theorists make are very convincing.
And, back when I was a Flat Earther, I posted this:
" Hey, even if I happen to be wrong, I will say that I made the wrong conclusion form the wrong facts that, in our school, they presented to us as science. That they made no sense, and that I thought they would make sense if the Earth was flat. And I will explain to them in details what I am talking about, and they will have a lot fewer misconceptions about the world around them than what I, and probably you, do. "
http://www.theflatearthsociety.org/forum/index.php?topic=58309.msg1756140#msg1756140
So, do you think that I am right to blame the education system for all of this?

[teo123]

I mean, look, the way of thinking I was using is valued in school. When you solve some mathematics, physics, geometry or chemistry task, you often use your intuition, that, as I see now, isn't reliable. You also use your understanding of the laws of nature, which isn't very reliable either. If you don't just accept what you don't understand (or even just pretend not to) and you ask questions about it, which you say isn't good either, you get a better mark. What are your thoughts on that things?

[brimstoneSalad]

That's the diagram of Petzval's field curvature from Wikipedia.

It seems you've misunderstood the diagram. The distortion occurs due to the difference between the two planes (curved and flat).

That has nothing to do with focus, but on the spread of the light (yes, a change in shape and size of the image).

The intersection of the lines showing the image edges is the focal point for the light coming from that image, it's irrelevant to the illustration, and only means the image has flipped upside down after that point.
The points of intersection between the lines delineating the top and bottom of the object with the straight and curved projection planes are only to show how large the object appears and where on those planes.

Doesn't seem to make sense.

Not everything will make sense to you. The extent of scientific knowledge is more than you will ever understand, and you need to come to terms with that and learn to trust scientists who do understand it when you can not.

It's as if you were blind, and those with eyes told you there was a hole in the ground here or there. Or that the grass is green. Or that there's a sun and moon. You have no choice but to believe them if you want to function and know something about the world, since it would be very difficult for you to confirm those things yourself.

And what if I can't believe them?

Then you have a problem. Paranoia is dangerous, you need to learn to trust others, and have a little faith in things that are credible (which is very different from having faith in religion).

I can't just choose to believe something, a belief is a result of becoming convinced.

You can become convinced that science is a credible method for learning about reality (in contrast to religion), that scientists are experts in their respective fields, and they they are overwhelmingly probably right and not lying. Thus, if you are convinced of those things, you should be convinced that what they say (as a consensus) is true.

You can not be convinced of the exact function of everything on Earth; you don't have the time or brain cells to spare for it. You need to be convinced of the credibility of the scientific institution.

So, do you think that I am right to blame the education system for all of this?

They didn't tell you the Earth was flat. So no. You should have trusted the scientific consensus, whether you could understand it or not.

Their failing may have been in not teaching you why you should trust science, and that it would be impossible for you to understand all science. I'm getting pretty close to a very basic understanding of all science (far from specialization), and I've had many more years of study than you have, but there are STILL gaps in my knowledge. I could learn ten times more than what I have and still have more.

When I don't understand something, I just trust the experts who have spent their lives studying it, because there's NOT some grand conspiracy to deceive me, and they're more likely right after decades of study and research than my best guess is.

If you don't just accept what you don't understand (or even just pretend not to) and you ask questions about it, which you say isn't good either, you get a better mark. What are your thoughts on that things?

What got you better marks is working harder to understand it a little better than your peers; which didn't mean you understood it at all really.

You need accept what you don't understand. However, that doesn't mean you should give up trying to understand it. However, in trying to understand it, I suggest you choose a field to focus on: if you try to learn everything, you'll be very busy and you'll never learn enough of any one thing to be of use.