[TotesNotReptilian]

What do you mean it "takes place outside of the universe"?? It's just a diagram. It is used to portray angles and distances. If you go outside and physically measure the angle in reality, that angle should agree exactly with the one portrayed in an orthographic view. I don't understand why you are so vehemently opposed to a simple diagram. (Actually I do know... it's because you don't want to acknowledge that the earth isn't flat.)

The first person view scene you presented doesn't make any sense without the accompanying side view scene. It can't. In the first person scene the angles you represented don't even exist from that view. You are in an entirely different dimension when you switch between the two scenes.

The angles from the side view are translated to the first person view via the field of view of the camera. Seriously, stop complaining about this, and just go test it. It is easy to test.

No, an object technically can never reach the vanishing point.

Where is the evidence of this? We see that they do. What kind of evidence is there that they do not?

It's common sense. Of course an object can never reach the vanishing point, because the vanishing point is at infinity. An object can never travel an infinite distance away from you. How on earth could it?

However, the object can get arbitrarily close to the vanishing point. It can get so close to the vanishing point that we can't tell the difference with our eyes. We can predict exactly how close to the vanishing point it will be using simple trigonometry like I have used. You can test this yourself with some parallel lines, a few objects, a camera, and careful measurements. Stop claiming that the math doesn't work when you can easily verify for yourself that it does work.

Surely if this math is so tested and true for this purpose, you can provide evidence justifying it.

It's rather difficult to justify anything with you, when you seem to be in denial of basic geometry, number theory, calculus and algebra. I'm not going to personally teach you several years worth of math in order to justify something that you could just walk outside and test with several objects and a camera. Just go test it for yourself. It is trivially easy. Here, I'll give you the exact hypothesis to test:

Assuming our naked eyes can't distinguish anything less than 0.02°, an object will appear to touch another object when the ratio of distance between the objects to distance from our eyes is approximately 1:3000.

So, if they are 1 mm away from each other, they will appear to touch when they are 3 meters away from your eyes. Go test it. Stop begging me to prove it for you.

You are telling us that the Ancient Greeks calculated infinite distances and we should take that as an unquestionable truth. This has not been demonstrated. This type of math is founded on a shaky premise which exists only in imagination.

What on earth do you mean by "calculated infinite distances"? Of course you don't have to accept any of this as unquestionable truth. It helps to have at least a basic understanding of the subject before you declare it to be useless though.

It is well known that the math and physics of the Ancient Greeks don't really work.

By whom? You? You are the only person I have ever heard espouse this opinion. I think you are exaggerating here.

For example, they also predict the concept of line and point graphs, which are infinitely indivisible, and that space and time can be represented on them to explain physical actions. We are taught this in school and are encouraged to use their methods. For some simple high level things it may seem to work. But this math it is also makes it impossible to walk through a door, or for a rabbit to overcome a tortoise in a  race. See: Zeno's Paradox

Lol. No, Zeno's paradox does not prevent us from reaching a destination according to basic geometry. It's mostly just a philosophical thought experiment. Calculus deals with infinities and infinitesimals quite easily.

Any continuous mathematical model like this which predicts infinities should be looked at with scrutiny and demands justification.

Trigonometry does not predict infinity. It assumes continuity. There is a difference. However, you don't have to assume that space is continuous in order for trigonometry to be useful. Just round your answers to the nearest discreet value of space. Problem solved. I assume that's what you are arguing for, right? That space is somehow quantized? If space is in fact quantized, there is no reason to suspect that it would effect the answers significantly for the scale that we are working on (thousands of miles).

[Tom Bishop]

Come on, common sense? Is that how this math is justified? "It is this way because of common sense" may have worked in Ancient Greece, but today we require, you know, actual evidence.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

[Rama Set]

Come on, common sense? Is that how this math is justified? "It is this way because of common sense" may have worked in Ancient Greece, but today we require, you know, actual evidence.

Oh irony.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

Have you even looked in to this?  I thought that was the zetetic way?  Anyway, what follows is a link to proofs and texts for projective geometry.  The field that was given birth by the exploration of perspective drawing in the renaissance:

http://www-history.mcs.st-and.ac.uk/~john/MT4521/Lectures/L20.html
https://www-m10.ma.tum.de/foswiki/pub/Lehre/WS0809/.../ch1.pdf
www.math.uchicago.edu/~may/VIGRE/VIGRE2008/REUPapers/Dean.pdf
www.math.rug.nl/~piter/KR/Hartshorne.pdf
https://opus4.kobv.de/opus4-zib/frontdoor/deliver/index/docId/101/.../SC-93-05.pdf
www.mit.edu/~alexrem/ProjectiveGeometry.pdf

Indeed as you look over this (you probably won't), you will be astonished to find that projective geometry has advanced substantially since the renaissance, when perspective drawing was first explored formally and gave birth to projective geometry.  Now do you have anything other than arguments from personal credulity?  Can you actually attack the substance of perspective diagrams or orthographic diagrams?  Better yet, can you explain how the FE model utterly fails to explain the sun passing behind the horizon from the bottom up without ever changing apparent size?  And even better than that, can you do it in a meaningful way, like real physics and mathematics can?

[rabinoz]

Come on, common sense? Is that how this math is justified? "It is this way because of common sense" may have worked in Ancient Greece, but today we require, you know, actual evidence.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

There are no "mathematical infinities" involved.

The sun is a  (supposedly) 3,000 miles high, quite a finite height.
At the time of sunset the distance to the sun at that time depends entirely on the season and the location of the observer, but a 10,000 mile horizontal distance is a resonable value.

Like it or not this puts the sun at about 17° above the horizon and that calculation is what perspective is - you can't then "bring" the sun down further.

You still seem to labour under the misapprehension that the horizon is always the "vanishing point". It is not and there is no justification, theoretical or otherwise for claiming that.

And on top of this there is this critical point that you will never admit. It is quite provable that on a given day the angular size is the same

from everywhere on earth from where the sun can be seen.

Claiming that this can be explained away by "due to a known magnification effect caused by the intense rays of light passing through the strata of the atmolayer" is simply a meaningless statement!

There might be glare around the sun, which in clear conditions can be removed with a filter, but there simply is no "known magnification effect caused by the intense rays of light passing through the strata of the atmolayer". Glare around a bright can hardly be called "magnification"!

There is simply no validity in that. These simply observations show that it cannot explain what we see.

• When suitable filters are used to remove the glare, we certainly do see the sun size remain the same size - always around 0.52° (it varies a little with the season.
  
  
• When a filter is used and enough magnification to observe the sunspots the pattern is the same from all over the earth, quite unaffected by location.

[TotesNotReptilian]

Come on, common sense? Is that how this math is justified?

No. Everything in mathematics is justified with tediously rigorous proofs, even stuff that appears to be common sense. I appealed to common sense because you really shouldn't need a rigorous proof to realize this is true. It is not a complicated issue. If you really want the proofs, you can probably find it in the papers Rama provided. Or, as I have said numerous times, you can just go outside with a camera, a measuring tape, a protractor, and several objects and test it yourself.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

Mountains of research has been provided. Thanks Rama.

Time to face the music Tom. You are waaaay beyond grasping at straws here.

[cel]

It appears that FEs Tom, etal and GEs Rabinoz, etal have all exerted efforts and tried to prove their respective claims, but all in vain... sorry, i just could not see that both parties can ever prove anything on what really is the truth about the shape or form of earth. I suggest raise or bring this topic to the next level as I always suggested. Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position. You both GEs and FEs here appears to go around a circle like in merry go round.

What we, truth seekers, observe is that FEs keep on proving their claims just like seeing the number "6" from their position, while the GEs also keep on proving their claims just like seeing the same number "6" as number "9" from their position at the opposite side. From your arguments and explanations, it's a fact that  all of you have seen distant objects, e.g. sun, bldgs, moon, etc., all by and through the LP/VP, NO ONE with eyes can escape this law. So whether you have a GE mindset or FE mindset, you all have more or less similar observation when it comes to seeing objects at a distance on this enormously HUGE earth as you are only a virus size compared to it.

For GEs even though you have a spherical or global shape in mind, you cannot really prove curvature with unaided eyes because you can only see flatness just like what the flat minded FEs see or wanted to see. Both of you are actually seeing flatness in general with unaided eyes, plus the fact that objects seen are governed by LP/VP, hence, a very limited view. For GEs, you should both consider curvature and LP/VP in explaining why objects disappear from horizon, while FEs are expected to consider only LP/VP. But with the huge earth surface appearing to be flat for both withtheir unaided eyes, they'll just end up at nothing worth their efforts. It's a pity... The truth is out there people, but we have to change strategy, and use tools like high powered telescope or camera to significantly extend this LP/VP much farther for us to find the absolute truth. Better think out of the box in resolving this issue.. Wake up...

[andruszkow]

It appears that FEs Tom, etal and GEs Rabinoz, etal have all exerted efforts and tried to prove their respective claims, but all in vain... sorry, i just could not see that both parties can ever prove anything on what really is the truth about the shape or form of earth. I suggest raise or bring this topic to the next level as I always suggested. Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position. You both GEs and FEs here appears to go around a circle like in merry go round.

What we, truth seekers, observe is that FEs keep on proving their claims just like seeing the number "6" from their position, while the GEs also keep on proving their claims just like seeing the same number "6" as number "9" from their position at the opposite side. From your arguments and explanations, it's a fact that  all of you have seen distant objects, e.g. sun, bldgs, moon, etc., all by and through the LP/VP, NO ONE with eyes can escape this law. So whether you have a GE mindset or FE mindset, you all have more or less similar observation when it comes to seeing objects at a distance on this enormously HUGE earth as you are only a virus size compared to it.

For GEs even though you have a spherical or global shape in mind, you cannot really prove curvature with unaided eyes because you can only see flatness just like what the flat minded FEs see or wanted to see. Both of you are actually seeing flatness in general with unaided eyes, plus the fact that objects seen are governed by LP/VP, hence, a very limited view. For GEs, you should both consider curvature and LP/VP in explaining why objects disappear from horizon, while FEs are expected to consider only LP/VP. But with the huge earth surface appearing to be flat for both withtheir unaided eyes, they'll just end up at nothing worth their efforts. It's a pity... The truth is out there people, but we have to change strategy, and use tools like high powered telescope or camera to significantly extend this LP/VP much farther for us to find the absolute truth. Better think out of the box in resolving this issue.. Wake up...

There's nothing to prove. This whole notion and community builds on the assumption that every single person that actually witnessed earth's curvature are liars, including, but not limited to, the Apollo project participants (Read: thousands of people).

When that's said and done, it relies on Rowbotham, even though his fan boys on this board misquote him constantly. Even with statements that contradicts what Rowbotham stated.

I took a photo of earth's curvature from 24.218 meters of altitude. That's a "lie" as well. So you see, this is only a debate because:

1. Someone's hardcore trolling
2. Lack of intellect
3. People refusing to admit they're wrong for whatever reason. Broken marriages, mental issues, whatever.

There's nothing to prove. Just facts. Reproducible results and facts. Flat earth religion has none of those.

[TotesNotReptilian]

It appears that FEs Tom, etal and GEs Rabinoz, etal have all exerted efforts and tried to prove their respective claims, but all in vain... blah blah blah same post as all your other posts blah blah REers and FEers are 69'ing each other blah

All I have ever seen you do is declare that our arguments are not good enough. Perhaps contribute to the actual discussion? This thread is about how angles relate to perspective when viewing the sun at sunset. Be specific. No more blanket declarations. And no, I'm not going to buy you an expensive telescope.

Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position.

Yes, I am aware. If you had read this thread, you would know that I was very specific about how perspective and the vanishing point effects how we see angles. That's the whole point of this thread, in case you didn't notice.

[cel]

All I have ever seen you do is declare that our arguments are not good enough. Perhaps contribute to the actual discussion? This thread is about how angles relate to perspective when viewing the sun at sunset. Be specific. No more blanket declarations. And no, I'm not going to buy you an expensive telescope.

Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position.

Yes, I am aware. If you had read this thread, you would know that I was very specific about how perspective and the vanishing point effects how we see angles. That's the whole point of this thread, in case you didn't notice.

I think you missed my point. All I want to convey to you both GEs and FEs is that you've got good enough arguments and/or proofs supporting your claims, your shortcoming is that you missed to see that you're both seeing or observing the same object or thing with differing mindsets which blinded or shielded you both from the real thing or truth out there (FE or GE?; moving or stationary sun or moon, etc.). What I want people in this thread to understand is that both your arguments or explanations are quite good enough to support each other's claims or proposition, but you missed or don't want to see the "forest". Haven't you wondered why is this so? It's simple. Each of your biased mindsets prevent you from seeing things with open mind. Try seeing what truth seekers see that the number "6" can well be seen also as "9" depending on where the vantage point of the observer or reader is. No one should argue against this, for it is the truth. This is the kind of mindset we want you both to have inorder to arrive at what's really the truth about the earth in relation to the sun, moon or its shape...

Ok, you know what I think where you are right now in your debate re LP/VP (law of perspective/vanishing point), angles etc., you're both arguing for something you observed within only the limits of LP/VP governing human eyes' capacity. You've not even gone beyond such limitation towards what it is really like without the LP/VP limitation. To have this limitation expanded, i think you view things with aided eyes. Also, sun's angles, perspective (setting or rising) can be analyzed well with empirical data taken real time frm all over the world. I think if you have those kind of data, no one dares debunking them as they're what people see in real time. What we can do is to understand and explain the results, whether or not they're inconsistent with our pre-conceived beliefs, mindsets or biases. Be a truth seeker...

[andruszkow]

All I have ever seen you do is declare that our arguments are not good enough. Perhaps contribute to the actual discussion? This thread is about how angles relate to perspective when viewing the sun at sunset. Be specific. No more blanket declarations. And no, I'm not going to buy you an expensive telescope.

Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position.

Yes, I am aware. If you had read this thread, you would know that I was very specific about how perspective and the vanishing point effects how we see angles. That's the whole point of this thread, in case you didn't notice.

I think you missed my point. All I want to convey to you both GEs and FEs is that you've got good enough arguments and/or proofs supporting your claims, your shortcoming is that you missed to see that you're both seeing or observing the same object or thing with differing mindsets which blinded or shielded you both from the real thing or truth out there (FE or GE?; moving or stationary sun or moon, etc.). What I want people in this thread to understand is that both your arguments or explanations are quite good enough to support each other's claims or proposition, but you missed or don't want to see the "forest". Haven't you wondered why is this so? It's simple. Each of your biased mindsets prevent you from seeing things with open mind. Try seeing what truth seekers see that the number "6" can well be seen also as "9" depending on where the vantage point of the observer or reader is. No one should argue against this, for it is the truth. This is the kind of mindset we want you both to have inorder to arrive at what's really the truth about the earth in relation to the sun, moon or its shape...

Ok, you know what I think where you are right now in your debate re LP/VP (law of perspective/vanishing point), angles etc., you're both arguing for something you observed within only the limits of LP/VP governing human eyes' capacity. You've not even gone beyond such limitation towards what it is really like without the LP/VP limitation. To have this limitation expanded, i think you view things with aided eyes. Also, sun's angles, perspective (setting or rising) can be analyzed well with empirical data taken real time frm all over the world. I think if you have those kind of data, no one dares debunking them as they're what people see in real time. What we can do is to understand and explain the results, whether or not they're inconsistent with our pre-conceived beliefs, mindsets or biases. Be a truth seeker...

You still don't get it.

Science is explaining these things with proven math and geometry, test, tests, and more tests. While new findings might be the target of some bias in the scientific community, the shape of the earth isn't. The shape of the earth is as unbiased a fact as they'll ever come.

You seem to miss the point of why some of the more eloquent and obviously educated "GE'ers" participate in debates on this site. To me, as a "GE'er", it's quite clear:

We want to make sure, that the next person who joins the board to ask questions about their newly found belief, aren't misinformed. That the social presence of TFES doesn't lead young people to believe what TFES is actually claiming. To me, that's just as dangerous as religious indoctrination.

[inquisitive]

Why this discussion about the setting sun? It will be rising at the same time for someone else hence the proof of a round earth.

[cel]

All I have ever seen you do is declare that our arguments are not good enough. Perhaps contribute to the actual discussion? This thread is about how angles relate to perspective when viewing the sun at sunset. Be specific. No more blanket declarations. And no, I'm not going to buy you an expensive telescope.

Each one of you should recognize and be aware that the law on perspective and vanishing point (LP/VP) is inherent in or governs our unaided eyes in seeing or viewing objects at a distance, whether or not the objects are moving towards or away from our position.

Yes, I am aware. If you had read this thread, you would know that I was very specific about how perspective and the vanishing point effects how we see angles. That's the whole point of this thread, in case you didn't notice.

I think you missed my point. All I want to convey to you both GEs and FEs is that you've got good enough arguments and/or proofs supporting your claims, your shortcoming is that you missed to see that you're both seeing or observing the same object or thing with differing mindsets which blinded or shielded you both from the real thing or truth out there (FE or GE?; moving or stationary sun or moon, etc.). What I want people in this thread to understand is that both your arguments or explanations are quite good enough to support each other's claims or proposition, but you missed or don't want to see the "forest". Haven't you wondered why is this so? It's simple. Each of your biased mindsets prevent you from seeing things with open mind. Try seeing what truth seekers see that the number "6" can well be seen also as "9" depending on where the vantage point of the observer or reader is. No one should argue against this, for it is the truth. This is the kind of mindset we want you both to have inorder to arrive at what's really the truth about the earth in relation to the sun, moon or its shape...

Ok, you know what I think where you are right now in your debate re LP/VP (law of perspective/vanishing point), angles etc., you're both arguing for something you observed within only the limits of LP/VP governing human eyes' capacity. You've not even gone beyond such limitation towards what it is really like without the LP/VP limitation. To have this limitation expanded, i think you view things with aided eyes. Also, sun's angles, perspective (setting or rising) can be analyzed well with empirical data taken real time frm all over the world. I think if you have those kind of data, no one dares debunking them as they're what people see in real time. What we can do is to understand and explain the results, whether or not they're inconsistent with our pre-conceived beliefs, mindsets or biases. Be a truth seeker...

You still don't get it.

Science is explaining these things with proven math and geometry, test, tests, and more tests. While new findings might be the target of some bias in the scientific community, the shape of the earth isn't. The shape of the earth is as unbiased a fact as they'll ever come.

You seem to miss the point of why some of the more eloquent and obviously educated "GE'ers" participate in debates on this site. To me, as a "GE'er", it's quite clear:

We want to make sure, that the next person who joins the board to ask questions about their newly found belief, aren't misinformed. That the social presence of TFES doesn't lead young people to believe what TFES is actually claiming. To me, that's just as dangerous as religious indoctrination.

What you've just said is also exactly what your FE opponents have been saying. You both are using science, scientific explanation, empirical data, tests, etc..... About your intention, it's noble, but let me tell you this, the more you engage into debate and defend your claims like the way you do here or perhaps in other venues as well (in not so clear, flawless and empirically convincing manner), the more people become more curious. This is a fact. The FEs will thank you for that. You can never control people from being curious. All has access to internet, youtube, facebook, this one, etc... It's impossible to control this now.

All you have to do, i think, if you really want to stop these FEs from further exposing their claims/proofs is to really show an irrefutable proof of at least one of your claims such as presenting real time unedited video showing that at, say, 100+ mi away (all other given data should be confirmed true), you cannot anymore see a tower, bldg, etc... by using high-powered telescopic camera. If you can show this with precision, you'll really be the "global man" for GEs and people around, and they, even FEs, will believe. How can this be refuted? Be a truth seeker then... be challenged...

[Rama Set]

This ISS has a live feed. Case closed.

[Nostra]

What you've just said is also exactly what your FE opponents have been saying. You both are using science, scientific explanation, empirical data, tests, etc.....

I'll come back on this, but please stop saying that FE "opponents" have provided anything using "science", "scientific explanation" and "empirical data". All that have been presented is either really bad science, profound misanderstanding of basic maths or a complete joke. If you were a real "truth seeker", instead of trying to explain that both side have good argument, you should analyze in depth all arguments and check there validity.

Some basic maths have been provided in another thread. This is clearly a proof that the earth is not flat. There's no debate! Anyone can check the maths, it's only basic trigonometry, and anyone can observe that the sun is not accelerating in the sky up to noon and deccelerating afterwards. Therefore the Earth is not flat.

And finally, let me remind you that only one counterexample is necessary to prove that an affirmation is wrong and that tens have been presented to FE believers. If you really think that the arguments advanced by FE are legitimate, it means that you are denying the laws governing our world (beginning with very simple maths as geometry).

So please, instead of trying to explain that everyone have good arguments (according to you) in every single thread. Could you please try to be more constructive and try by yourself some calculation or providing some "scientific explanation"  (either to explain how the world is in FE or GE), so that we would have something concrete and scientific to discuss? First excercie could be to reproduce the topic about the elevation and the speed of the sun and confirm ("or not") the results? Just do that and you will be convincs that the earth is a sphere. Don't bother to ask question if you have, I would be glad to help you (if needed of course!)

[TotesNotReptilian]

...Try seeing what truth seekers see that the number "6" can well be seen also as "9" depending on where the vantage point of the observer or reader is. No one should argue against this, for it is the truth. This is the kind of mindset we want you both to have inorder to arrive at what's really the truth about the earth in relation to the sun, moon or its shape...

All you have to do, i think, if you really want to stop these FEs from further exposing their claims/proofs is to really show an irrefutable proof of at least one of your claims such as presenting real time unedited video showing that at, say, 100+ mi away...

This ISS has a live feed. Case closed.

Wish granted

you cannot anymore see a tower, bldg, etc... by using high-powered telescopic camera. If you can show this with precision, you'll really be the "global man" for GEs and people around, and they, even FEs, will believe. How can this be refuted? Be a truth seeker then... be challenged...

Wish granted

You have one wish left. Make it count.

[Tom Bishop]

Come on, common sense? Is that how this math is justified? "It is this way because of common sense" may have worked in Ancient Greece, but today we require, you know, actual evidence.

Oh irony.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

Have you even looked in to this?  I thought that was the zetetic way?  Anyway, what follows is a link to proofs and texts for projective geometry.  The field that was given birth by the exploration of perspective drawing in the renaissance:

http://www-history.mcs.st-and.ac.uk/~john/MT4521/Lectures/L20.html
https://www-m10.ma.tum.de/foswiki/pub/Lehre/WS0809/.../ch1.pdf
www.math.uchicago.edu/~may/VIGRE/VIGRE2008/REUPapers/Dean.pdf
www.math.rug.nl/~piter/KR/Hartshorne.pdf
https://opus4.kobv.de/opus4-zib/frontdoor/deliver/index/docId/101/.../SC-93-05.pdf
www.mit.edu/~alexrem/ProjectiveGeometry.pdf

Indeed as you look over this (you probably won't), you will be astonished to find that projective geometry has advanced substantially since the renaissance, when perspective drawing was first explored formally and gave birth to projective geometry.  Now do you have anything other than arguments from personal credulity?  Can you actually attack the substance of perspective diagrams or orthographic diagrams?  Better yet, can you explain how the FE model utterly fails to explain the sun passing behind the horizon from the bottom up without ever changing apparent size?  And even better than that, can you do it in a meaningful way, like real physics and mathematics can?

Regarding those links, a mathematical proof is not the same thing as a real world evidence of application. A mathematical proof validates an equation or concept against that mathematical framework, not the real world.

[Tom Bishop]

Come on, common sense? Is that how this math is justified?

No. Everything in mathematics is justified with tediously rigorous proofs, even stuff that appears to be common sense. I appealed to common sense because you really shouldn't need a rigorous proof to realize this is true. It is not a complicated issue. If you really want the proofs, you can probably find it in the papers Rama provided. Or, as I have said numerous times, you can just go outside with a camera, a measuring tape, a protractor, and several objects and test it yourself.

This math on perspective should be backed up by mountains of research. As if mathematical infinities are mere common sense and translate perfectly to the real world. That is ridiculous.

Mountains of research has been provided. Thanks Rama.

Time to face the music Tom. You are waaaay beyond grasping at straws here.

Again, a mathematical proof doesn't have anything to do with reality.

[rabinoz]

Come on, common sense? Is that how this math is justified?

Again, a mathematical proof doesn't have anything to do with reality.

So, what do we base things on "common sense", though you seem to have ruled that out,
Or "a mathematical proof" that "doesn't have anything to do with reality"?

You don't seem to have left much.

So, what do you base you ideas of perspective on? Whatever you need to prop up the Flat Earth it seems.

[Tom Bishop]

Apparently you and several people are completely uneducated as to what a mathematical proof actually is. I do not wish to continue this discussion.

[rabinoz]

Apparently you and several people are completely uneducated as to what a mathematical proof actually is. I do not wish to continue this discussion.

I guess you wouldn't.
It is no point with your weird ideas on perspective and inability to accept that we can use simple mathematics to calculate "vanishing points", which you just assume are always on the horizon.