#### Nostra

• 26
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #140 on: September 30, 2016, 05:58:01 AM »
Chemistry: Try diluting a solute by adding water to it. As long as you keep adding water, the concentration will approach zero, but will never actually reach it.

This is actually quite a relevant comparison. The angle with the horizon is related to the height:distance ratio of the object. For the angle to be zero, the ratio of height to distance has to be zero.

In both examples, you are trying to make a ratio approach zero by adding to one side. In the chemistry example, you are trying to make the ratio of solute to solvent go to zero by adding solvent. The ratio will continually get smaller, but will never actually reach zero since you aren't actually removing any solute. In the perspective example, you are trying to make the ratio of height to distance go to zero by adding distance. It will continually get smaller, but will never actually reach zero since the height isn't actually decreasing.

It could equally be argued that when you replace 100% of a chemical solution with water, the resulting concoction will be 100% water. Your example tells us nothing about what is actually occurring with perspective.

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Counter challenge: Draw a right triangle that has a non-zero height and width and one of the angles is zero. This is what you are implying is happening during sunset on a flat earth. Good luck!

The premise here is that the ancient math of the greeks is fallable, so of course their math fails on that point.

OK, so please Tom, be constructive and with your great wisdom, explain us how it is possible that something, with a finite diameter, at a finite height of a finite plan can reach a zero elevation without modifying its height.
Proud to be the 1 other!

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #141 on: September 30, 2016, 06:41:41 AM »
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Strictly speaking, correct. Since an object can never be an infinite distance away, it will never be 0 degrees with the horizon.

And where is the evidence of this phenomenon? Why should we assume that there are these pockets of infinity which prevents perspective lines from meeting?

You have repeatedly declined to show any of the real world evidence you have been asked for. Why isn't there anything to show that distances might grow exponentially near zero? If this math is so proven then an example, observation, or experiment should be readily quotable and hiding behind repeated claims of incredulity would be unnecessary.

No one claimed there is a pocket of infinity anywhere. No one claimed distances grow exponentially near zero. You are the only one making arguments based on incredulity here. I have bent over backwards to give you examples, make you drawings, explain the logic in extreme detail. I have told you exactly how you can find the evidence yourself. The only thing I haven't done is physically collected the evidence for you. Good grief.

Fine. What evidence would convince you? If I am able to correctly predict the size of an object on a picture based on its size and distance using the "ancient greek math", would that convince you? I'm not going to waste my time if you are just going to cry "fake".

Chemistry: Try diluting a solute by adding water to it. As long as you keep adding water, the concentration will approach zero, but will never actually reach it.

This is actually quite a relevant comparison. The angle with the horizon is related to the height:distance ratio of the object. For the angle to be zero, the ratio of height to distance has to be zero.

In both examples, you are trying to make a ratio approach zero by adding to one side. In the chemistry example, you are trying to make the ratio of solute to solvent go to zero by adding solvent. The ratio will continually get smaller, but will never actually reach zero since you aren't actually removing any solute. In the perspective example, you are trying to make the ratio of height to distance go to zero by adding distance. It will continually get smaller, but will never actually reach zero since the height isn't actually decreasing.

It could equally be argued that when you replace 100% of a chemical solution with water, the resulting concoction will be 100% water.

Hahahaa... what?!? Yes, and if you forcibly shoved the sun directly into the ground, decreasing its height to zero, then it would most certainly appear to touch the horizon. What's your point? You asked for an example, and I gave it. Don't throw a tantrum and toss out my solution!

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Your example tells us nothing about what is actually occurring with perspective.

It tells us exactly what is occurring with perspective. You are just too thickheaded and/or stubborn to admit it.

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Counter challenge: Draw a right triangle that has a non-zero height and width and one of the angles is zero. This is what you are implying is happening during sunset on a flat earth. Good luck!

The premise here is that the ancient math of the greeks is fallible, so of course their math fails on that point.

Ah yes. Your model requires a triangle with non-zero sides and a zero angle. Since no one has heard of such an absurd triangle, it must be those darn mathematicians' fault for not inventing such a thing! It certainly is not a problem with your model! No bias here, no sirree! Lol.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #142 on: September 30, 2016, 06:54:52 AM »
Tom, as far as I am concerned, this thread is a perfect example of something that goes on forever but never actually reaches anywhere. At least, YOU aren't going anywhere. You just keep repeating the same arguments over and over that have already been refuted numerous times. If you feel the need to make another vague argument involving infinity, don't bother. There is a very good chance I have already refuted it in this thread. Just reread the thread.

Fine. What evidence would convince you? If I am able to correctly predict the size of an object on a picture based on its size and distance using the "ancient greek math", would that convince you? I'm not going to waste my time if you are just going to cry "fake".

#### Southernhemispere

• 48
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #143 on: September 30, 2016, 03:28:51 PM »
The math you are using says that is is impossible for anything to reach the horizon. A sun would descend forever on a Flat Earth without ever reaching the horizon. The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Where has any endless approach to a point like this been reported in any scientific, everyday, or historical observation, or anywhere in the world? Please present some form of evidence that any of this is possible. Provide something, anything from reality, showing that ultra long descents would occur or that the horizon would be an infinite distance away.

The answer on a flat earth is yes, there is no way for the sun to ever approach anywhere near the horizon, assuming that the furthest point below the sun from an Antarctic base would be about 23000 kms away when the sun is over the Tropic of Capricorn on the other side of the north pole. The angle of the sun above the horizon would be 7.4 degrees. Simple trigonometry.

Why do you need to bring infinite distances into a discussion when the distances travelled by the FE sun 'orbit' is finite. Just another way to deflect the discussion as adopted in most unanswerable FE debunks.

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #144 on: September 30, 2016, 07:26:50 PM »
Key: (to avoid repeating myself and condense; nothing new is being stated in the KEY)
OP =  Orthographic Projection
Point 1/2 = Parrallel lines converge due to perspective.
FOV: Field of View
This is going to be long, so I'm working on explaining it in a youtube video. Funny (for me at least) I am typing this up on September 30, 2016; the day before Obama hands over the internet ICANN to international corporations and countries... so RIP internet, it was fun without censorship. Heregoes...

Totes, Great well written response, thanks; I think I get it better now, though I still take issue. The 2 images posted take into consideration perspective, with a caveat; in order to achieve the perspective of the OP 'side view' (the top image), you must be an impossible/unachievable distance away - Tom's - and partially, my - argument. Thanks for that response, your 3 recent topics here were 3 of my FE favorites prior to your posting them, as I put rather pathetically previously when I anticipated the SCP one the day before you posted it; these 3 recent topics (SCP, Perspective/Sun, Southern Hemisphere December) are really one and the same issue, just seen 'from different angles' xD lol

That said, I really don't know much about angles. My experience comes largely from simulated planes (video games), as mentioned above, I admit. From what I can tell, no new info is presented here, other than the mechanics of angles and perspective being more elaborated on. Which you do an honorable effort of, and somewhat improves my opinion of academic institutions everywhere.

SO lets get into the Meat (hopefully no hot potatoes slip in) of this post:

1. Parallel lines are parallel.
2. Parallel lines converge due to perspective; even those in a OP diagram, if drawn to 'infinity'.
3. We only see objects, at best, a few hundred miles in any direction at best from anywhere on Earth (FoV). Caveat: the sun and stars (more on this later).
4. The FE sun is ~3,000 miles above the Earth.
5. It is impossible to demonstrate perspective of 1-4 within the FoV of 3.
6. My 'few hundred' miles is quite generous. I have seen images where islands or mountains are visible over 125 miles away, but many sources cite 50-100 miles as the 'limit' of or FoV (2), (3). With Cameras/telescopes it is notably possible to see much further, ofc.
7. The image presented here has many flaws:
7a) Distance. 3,000 miles to the sun; this image covers many times that; over 12,000 miles; over half the actual equatorial distance.
7b) The perspective, viewing the sun traveling 'parallel' with the Earth, is impossible to achieve.
7c) The sun doesn't move in a straight line as depicted here on the FE model, but rotates East to West (clockwise as viewed from North Pole).
7d) The Orthographic Projection here does not accurately demonstrate the convergence of parallel lines; the top image is an impossible 'god's eye' perspective, for one; and for two, if you trace converging lines, they converge a great distance before 12,000 miles away; what the image here is depicting.
8 ) You can't understand the rest of this post without watching this (brief) youtube video.

You get the point from the video now? Okay...

At least, that is what I think Tom means about 'infinities' is that the image presented here is an impossible 'infinity' away from what we observe, looking at our observation on the FE model. Alternatively, there is also an 'infinity' in an OP as the sun gets 'further and further' away (a great point against the flat Earth, and what this topic was started to point out, and Tom and myself realize that, no one is arguing). But as stated above, we can't see anything beyond ~50-140 miles from the surface Earth (more on that later). But the mechanics here don't work, as the sun has to start coming back 'the other way' somewhere in the neighborhood of 12k-18k out on FE model (this is where I don't know the FE model well enough, but we can at least agree the sun doesn't literally travel in a straight line forever - well, you could, technically, but you'd have to create a whole other model for that).

So, lets look at the image. The common Flat Earth model shows the sun as being ~3,000 miles above the surface. This image illustrates an impossible phenomenon then (point 1 above); as Tom Bishop has already stated; no man has ever seen more than a few hundred miles in any direction; and the sun 'sets' either long before reaching, or as it reaches, that point. What Tom is saying here, is it is impossible to attain the perspective in that image, observing an observer observing the sun moving parallel to the ground, in a clockwise circle/spiral, not a straight line as depicted here. Illustration: (yes I borrowed it again sorry)

So, that image is not applicable to our observations; look at the 'ground' beneath the Red, Orange, and Yellow 'dot' or 'ball'; it is much farther than the distance from the ground to them; thus more than 3 thousand miles (even the globe states the circumference at the equator to be no more than 25,000 miles). I'll call this Point 3 for now. Keep in mind that half the circumference is roughly 12,300 miles; the limit of 'globular perspective', before the 'curve' is on 'the other side of the globe'. For FE, this represents approximately one-half the equatorial circle. The commonly agreed-upon 3,000 miles to the sun on Flat Earth is outmatched by the ground covered no matter how it is calculated; and Point 2, parallel lines converge due to perspective (assuming the sun moves parallel to the Earth in FE model). This image is WAAAAY out of proportion. The equator is only 12k miles across; this image goes way further! Up to 18k! The sun is going the other way at that point.

With that ridiculous 20k mile perspective taken into consideration, the line would be more like this:

Again that is generous at best.... as there is no way for us to know what a 20k mile line would look like, let alone 2 parallel ones, from being sandwiched between them.

Now, just as p-brane did, obviously your image is not meant to be to scale. But again, as Tom said, this 'several thousand mile perspective' is simply impossible. So, lets look at some common blueprints instead, which use principles of orthographic projection, and compare the actual buildings to the blueprints.

In this image the lines are parallel. But stand at the foot of the building to the left or right, and the roof and floor 'lines' will be 'converging', like this.

Alternatively....

Uh ooh... the parallel lines of the blueprints... converge... in reality... while the lines are drawn perfectly parallel in a schematic, you can't stop them from converging due to perspective, try as you may; esp. if you continue the line indefinitely; yes, it stays 'parallel' in reality, but it is impossible to see from any point (when continued 'indefinitely') without a 'god's eye view'; even navigating the parallel lines, from every point within it, they appear to converge. No amount of equations can defy that, though they may serve as a red herring to those unable to understand.

Additionally, maybe you can call the 'few hundred mile' FoV the 'Earth's curvature', but the higher you go, the wider the FoV gets, so there's that as well...

Anyway I'm no shill or whatever so I have no angle other than perhaps too much time on my hands. This is a very good topic, I hope I don't insult with my lack of understanding; this is just what I've posted based on how I think I understand it... I could be wrong, but it seems right to me.
The Flat Earth Society has members all around the Globe
[H]ominem unius libri timeo ~Truth is stranger.

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #145 on: September 30, 2016, 09:53:46 PM »
On top is a side view diagram of a camera and 3 round objects. On bottom is the same 3 objects as seen from the perspective of the camera. The top DOES NOT take into account perspective. The bottom DOES take into account perspective. So, how are they related?

Just realized I missed this. I'll already reconsidering my previous post. I'm still unsure how relation can be inferred from an impossible perspective, though I understand the hypothetical correlation and how it invalidates FE model. Consider me in 'Winnie the Pooh' mode right now...

As my whole argument in that wall of text relies entirely on the correlation of the two images, my argument may be invalid, I realize now. My apologies if this be the case, I'll probably have to sleep on it. Also apologies for however wrongly I may have referred to users here or my misinterpretation of framing their arguments.
« Last Edit: September 30, 2016, 09:57:19 PM by nametaken »
The Flat Earth Society has members all around the Globe
[H]ominem unius libri timeo ~Truth is stranger.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #146 on: September 30, 2016, 11:04:13 PM »
Just realized I missed this. I'll already reconsidering my previous post. I'm still unsure how relation can be inferred from an impossible perspective, though I understand the hypothetical correlation and how it invalidates FE model. Consider me in 'Winnie the Pooh' mode right now...

I saw your this post when I tried to submit this one, which means that everything below might already be out of date. I'll submit it anyway, since it might be relevant to your current thoughts on the matter. My responses get a bit repetitive, since as you guessed above, most of the issues in your post seem to stem from the same misunderstanding.

Edit: Good gravy, my post was longer than I thought. I highlighted the important points in red.

The 2 images posted take into consideration perspective, with a caveat; in order to achieve the perspective of the OP 'side view' (the top image), you must be an impossible/unachievable distance away - Tom's - and partially, my - argument.

Then both you and Tom have missed my point entirely. Human's don't have orthographic vision. Of course we can't see this view in reality. Once again, the point of an orthographic view is NOT to portray what we see. It is to accurately portray angles and distances. We can then use the measured angles to predict how it will look according to perspective.

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That said, I really don't know much about angles. My experience comes largely from simulated planes (video games), as mentioned above, I admit. From what I can tell, no new info is presented here, other than the mechanics of angles and perspective being more elaborated on. Which you do an honorable effort of, and somewhat improves my opinion of academic institutions everywhere.

Fun fact: video games use the same math that I am using to generate their perspective projections. Because the math works. And I agree, I am not presenting any new or revolutionary information. Everything I am saying is extremely well known and understood by thousands of engineers, physicists, artists, computer graphics programmers... and pretty much anyone who didn't sleep through high school math, and has bothered to think about the subject for 30 minutes. It really is not a complicated subject.

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2. Parallel lines converge due to perspective; even those in a OP diagram, if drawn to 'infinity'.

No no no no no! A thousand times no! Parallel lines are always parallel in an orthographic projection, by definition. If the parallel lines converge, then it isn't an orthographic projection.

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3. We only see objects, at best, a few hundred miles in any direction at best from anywhere on Earth (FoV). Caveat: the sun and stars (more on this later).
4. The FE sun is ~3,000 miles above the Earth.
5. It is impossible to demonstrate perspective of 1-4 within the FoV of 3.

This goes back to Tom's "maybe the math suddenly stops working at some large untestable distance" argument. Sure. Maybe it does. But the math DOES work at testable distances. And there is no evidence or logic to suggest that it suddenly might stop working at a particular distance. You might as well just appeal to magic at that point.

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7. The image presented here has many flaws:
7a) Distance. 3,000 miles to the sun; this image covers many times that; over 12,000 miles; over half the actual equatorial distance.

And yet even at that absurd distance, the object still wouldn't come close to touching the horizon according to the math. The math that is testable. The math that works.

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7b) The perspective, viewing the sun traveling 'parallel' with the Earth, is impossible to achieve.

That's not the point. Again, the point of an orthographic diagram is NOT to portray what we see. It is to allow us to accurately measure distances and angles. We can then use the measured angles to predict how it will look according to perspective.

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7c) The sun doesn't move in a straight line as depicted here on the FE model, but rotates East to West (clockwise as viewed from North Pole).

True. My diagram is somewhat simplified. If I wanted to take into account the clockwise rotation of the sun, I would draw a top-view orthographic diagram. I would then go through the same process as before, except the angles would translate to horizontal dimensions in the perspective picture, instead of vertical dimensions. The object would appear to curve off to the right as it sunk. This brings up another problem with the standard flat earth model: the sun doesn't always appear to be curving northward as it sets, like the flat earth model predicts.

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7d) The Orthographic Projection here does not accurately demonstrate the convergence of parallel lines;

Good. It isn't supposed to. If it did, it wouldn't be an orthographic projection. It allows us to predict the convergence of parallel lines in a perspective view based on the angles we measure in the orthographic diagram.

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if you trace converging lines, they converge a great distance before 12,000 miles away; what the image here is depicting.

Oh really? And how did you calculate this? I assume you are referring to the vanishing point. If so, I can assure you that you are misunderstanding what the vanishing point is.

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At least, that is what I think Tom means about 'infinities' is that the image presented here is an impossible 'infinity' away from what we observe, looking at our observation on the FE model. Alternatively, there is also an 'infinity' in an OP as the sun gets 'further and further' away (a great point against the flat Earth, and what this topic was started to point out, and Tom and myself realize that, no one is arguing). But as stated above, we can't see anything beyond ~50-140 miles from the surface Earth (more on that later). But the mechanics here don't work, as the sun has to start coming back 'the other way' somewhere in the neighborhood of 12k-18k out on FE model (this is where I don't know the FE model well enough, but we can at least agree the sun doesn't literally travel in a straight line forever - well, you could, technically, but you'd have to create a whole other model for that).

If you are going to make an argument about infinity, you will need to be much more specific than this. "the image presented here is an impossible 'infinity' away" does not really make sense. I understand what you are trying to say, but your argument just is not relevant. Once again, orthographic projections are not SUPPOSED to show what we are able to see. They are supposed to allow us to accurately measure distances and angles. You know... that thing that you did when you took the height of the object as 3000 miles, turned it sideways, and then counted out "3, 6, 9, 12, 18" to determine the horizontal width of the diagram? That's exactly what an orthographic diagram is useful for. Good job!

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no man has ever seen more than a few hundred miles in any direction; and the sun 'sets' either long before reaching, or as it reaches, that point. What Tom is saying here, is it is impossible to attain the perspective in that image, observing an observer observing the sun moving parallel to the ground, in a clockwise circle/spiral, not a straight line as depicted here. Illustration: (yes I borrowed it again sorry)

(Obligatory: orthographic diagrams aren't supposed to portray what we observe.... blah blah blah, etc etc)

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So, that image is not applicable to our observations; look at the 'ground' beneath the Red, Orange, and Yellow 'dot' or 'ball'; it is much farther than the distance from the ground to them; thus more than 3 thousand miles (even the globe states the circumference at the equator to be no more than 25,000 miles). I'll call this Point 3 for now.

You are correct. According to the standard flat earth model, the sun would get no farther away from us than the yellow ball. Therefore, the MINIMUM angle it would make with the horizon is 20 degrees. Since we can observe the sun going much lower than that every single day, this proves that the earth isn't flat. How is this not blatantly obvious?

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This image is WAAAAY out of proportion. The equator is only 12k miles across; this image goes way further! Up to 18k! The sun is going the other way at that point.

Fine. Remove the orange and red balls. Congratulations, now it is in proportion!

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With that ridiculous 20k mile perspective taken into consideration, the line would be more like this:

No, it would not. That is no longer an orthographic projection. Also, how on earth did you calculate the slant of that line? Everything having to do with perspective in the bottom image was very carefully calculated. I did not place anything arbitrarily.

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Now, just as p-brane did, obviously your image is not meant to be to scale.

My image was not intended to exactly represent the dimensions of a flat earth. I never said it was. If you remove the red and orange objects, then the distances are a good approximation of a flat earth.

The difference between my image and p-brane's, is that the bottom image that I drew was carefully calculated according to the math I have been describing. Nothing about it was arbitrary. The perspective effect portrayed in the bottom image arose naturally from the math. On the otherhand, the perspective lines that p-brane (and you) drew are completely arbitrary. They are nothing more than a vague guess based on a vague/poor understanding of how perspective works.

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But again, as Tom said, this 'several thousand mile perspective' is simply impossible. So, lets look at some common blueprints instead, which use principles of orthographic projection, and compare the actual buildings to the blueprints.

In this image the lines are parallel. But stand at the foot of the building to the left or right, and the roof and floor 'lines' will be 'converging', like this.

Yes. The first image is an orthographic projection. The second image is a perspective projection (a picture from a camera). One shows perspective. One doesn't. What's your point? If you give me the orthographic projection, I can predict how it will look in the perspective projection, using the math that I have described. That's how we know the math works.

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Alternatively....

Uh ooh... the parallel lines of the blueprints... converge... in reality...

Of course they do. I have never claimed otherwise. That's not an orthographic projection. It's a perspective projection.

Here is the irony: that image is not a picture from a camera (obviously). It was generated based on a 3D mapping of points by software that uses... wait for it... THE SAME MATH THAT I HAVE BEEN USING. The fact that you agree that it is a good representation of what we would see in reality is evidence that THE MATH WORKS.

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while the lines are drawn perfectly parallel in a schematic, you can't stop them from converging due to perspective, try as you may

No kidding. I have never claimed otherwise.

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Yes, it stays 'parallel' in reality, but it is impossible to see from any point (when continued 'indefinitely') without a 'god's eye view'; even navigating the parallel lines, from every point within it, they appear to converge. No amount of equations can defy that...

The "equations" don't defy that parallel lines converge. They PREDICT it. I am not trying to defy that parallel lines converge. I am saying that I can PREDICT exactly how, when, and where those parallel lines converge using math. Perspective is not some mysterious, poorly understood phenomenon. It is easy to predict, easy to calculate, and the math involved is easy to test.

Using the same math, I can also predict the angular diameters of objects that we see based on their size and distance from us. I can also predict the angular distance between two objects based on their distance from us and distance between each other. I can also predict the angle between the sun and the horizon on a flat earth based on the sun's distance and height. The fact that all of these predictions turn out to be correct except the one based on a flat earth is evidence that the earth isn't flat.

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Additionally, maybe you can call the 'few hundred mile' FoV the 'Earth's curvature', but the higher you go, the wider the FoV gets, so there's that as well...

FoV doesn't get wider. FoV generally refers to the angle of your vision, not the distance. But yeah, the distance you can see DOES increase as you get higher... because the earth is round... I don't think you thought that argument through very well.

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Anyway I'm no shill or whatever so I have no angle other than perhaps too much time on my hands. This is a very good topic, I hope I don't insult with my lack of understanding; this is just what I've posted based on how I think I understand it... I could be wrong, but it seems right to me.

Cheers.
« Last Edit: September 30, 2016, 11:20:39 PM by TotesNotReptilian »

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #147 on: October 01, 2016, 02:26:59 AM »
Lol great post, I caught my error before you posted though. I thought you were trying to pull a fast one, but then I realized I was wrong. That is my fault for jumping the gun. I got some really good chuckles reading your post, though spot on. I deserved it.

Most of the 'arguments' I elaborated on, weren't presentations so much as me representing what's already been posted here my own way. I didn't mean to come off as arguing the infinities! Or the difference between parallel and perspective (though I thought it was being passed off that there wasn't a difference, is all; I realize my mistake).

Everything I am saying is extremely well known and understood by [...] pretty much anyone who didn't sleep through high school math, and has bothered to think about the subject for 30 minutes. It really is not a complicated subject.

Yes, and you provided an excellent crash course herein.

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2. Parallel lines converge due to perspective; even those in a OP diagram, if drawn to 'infinity'.

No no no no no! A thousand times no! Parallel lines are always parallel in an orthographic projection, by definition. If the parallel lines converge, then it isn't an orthographic projection.

On a life-sized, really big, OP projection, they would converge that's why I stated 'due to perspective' and 'if drawn to infinity'. IE, the highway is a physical representation of it's OP. A orthographic projection of that scale would appear to converge, is all I meant; or, alternatively, if you traced the lines of an orthographic projection into the horizon, they would converge (ie god's eye view). That's all I meant here; I can see how that offends good taste - I did it deliberately to offend, thinking the "God's Eye View" was to assume that parallel lines don't converge (20,000 mile lines). I knew 20,000 mile lines would converge. I thought you were trying to say that they wouldn't.

And yet even at that absurd distance (3,000+ miles), the object still wouldn't come close to touching the horizon according to the math. The math that is testable. The math that works.

Yes, here is where the FE model begins to mathematically come undone, as best I have ever been able to tell. I only brought it up in relation, and to provide context for, the idea of Field of View; my only argument here is not about 'spooky mathematics', but rather that, how the sun disappears at the 50-mile mark, when it is supposed to be 12,000+ miles away. Not a typical Flat Earther question, I think.

This brings up another problem with the standard flat earth model: the sun doesn't always appear to be curving northward as it sets, like the flat earth model predicts.

Yup.

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if you trace converging lines, they converge a great distance before 12,000 miles away; what the image here is depicting.

Oh really? And how did you calculate this? I assume you are referring to the vanishing point. If so, I can assure you that you are misunderstanding what the vanishing point is.

Most demonstrably shaky part of my argument (other than using 3D generated blueprints). Touche, I regretted typing that part and even omitted it several times in my rough drafts. I don't even know how to calculate the 'convergence point', even utilizing what you provided.

If you are going to make an argument about infinity, you will need to be much more specific than this.

I wasn't making this argument, but offering my speculation about the "infinities' I kept seeing repeated again and again in this thread, since they don't make sense to me. Also why I posted the Toy Story clip. Was meant to be considered tongue in cheek, though I do like the idea of a completed Flat Earth model, these topics make it seem rather bleak (to me, at least). Perhaps it's due to my (lack of) education   I have been skimming Gleason and Parallax's books, but I'm no closer to comprehension than I was when I first decided to pick this topic up (FE).

According to the standard flat earth model, the sun would get no farther away from us than the yellow ball. Therefore, the MINIMUM angle it would make with the horizon is 20 degrees. Since we can observe the sun going much lower than that every single day, this proves that the earth isn't flat. How is this not blatantly obvious?

Honestly, I thought I was most clever in the construction of this paragraph, glad someone pointed it out already. I knew I slid a silent 'checkmate' in there but wasn't sure if it would be noticed. Point 3 has been bothering me for a while now; it seems the sun shouldn't set on a flat earth with these dimensions. Although I admit p-brane did pull me in a bit with his 'perspective' as a solution to why it 'sets' on FE. This is one of my biggest problems with the [dimensions of the] FE model.

Also, how on earth did you calculate the slant of that line? Everything having to do with perspective in the bottom image was very carefully calculated. I did not place anything arbitrarily.

Short answer: MS Paint Magic. Long answer: No calculations were done. Shame on me on this one. My second major blunder in that post. I knew p-brane had his arbitrary position, and the top image was arbitrary as well, so I put an arbitrary line to demonstrate the 'convergence' of the two 20,000 mile lines on the top image. I felt this wasn't too much of a step, but yes I should have calculated I suppose.

My image was not intended to exactly represent the dimensions of a flat earth. I never said it was. If you remove the red and orange objects, then the distances are a good approximation of a flat earth.

Yes, you did say that in your first response to me. I missed it. That's my fault. I wouldn't have posted my previous post if I realized this. I thought about deleting it, but realized I was probably being responded to already (as I correctly guessed). So I'll let my stupidity stand, I figured, and I double-posted instead to point this out. I thought there was shady logic being passed off as math, then realized I was wrong. I owe an apology there, so sorry. My bad.

The difference between my image and p-brane's, is that the bottom image that I drew was carefully calculated according to the math I have been describing. Nothing about it was arbitrary

Again. Sincerest apologies. See above. You did a great job. I pooped on it. I'm ashamed.

The perspective effect portrayed in the bottom image arose naturally from the math. On the otherhand, the perspective lines that p-brane (and you) drew are completely arbitrary. They are nothing more than a vague guess based on a vague/poor understanding of how perspective works.

Again, above. I thought the top image was trying to convey something else, so I made something up to counter it. That's my own oversight at work there. I see now.

-------

Okay Everything bellow here is just a repeat of the points already corrected, I think. Like I said I'm not going to retract it, though I now see how it was wrong. I underestimated your presentation, didn't read it enough times, thought I saw a representation of what I thought was a deliberate lie, and went to work. I realize that now. Also, my math is terribly vague estimates. I thought about it, and the sun should be 'turning around' before the 12k miles point, I'm fairly certain. Though the fact you didn't bother addressing that speaks louder than I can say anyway. Thanks for the effort, and sorry for the potential aneurysm. I honestly got a great chuckle out of this, realizing how simple my misunderstand was. Still, I can't get it to add up without 'spooky mathematics', as you say, for FE. I feel really bad, but at the same time, this was very cathartic. I laughed pretty good, hope you will too.
The Flat Earth Society has members all around the Globe
[H]ominem unius libri timeo ~Truth is stranger.

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #148 on: October 01, 2016, 04:35:29 AM »
Okay, now that I got the apologies out of the way, I think p-brane makes some good points. I totally misconstrued your argument, thus mine was approaching the wrong way... Here is what I meant to say, had I not thought someone was saying parallel lines never converge due to perspective:

Now, again, I don't understand the math of the angles represented in the diagrams he is 'debunking'. But his point at 4:50 seems solid, right?

I mean, airplanes do seem to travel slower near the horizon, but they do emerge - and pass over - as it were. The higher the object, the more downward elevating is the angle. That's simple high school geometry. The sun should travel slower, 'but muh vanishing point'. Obviously the sun makes it there (it is night time in contiguous America right now), and p-brane seems to demonstrate how it can get there on a Flat Earth; perspective.

Which is what that video is about; showing how theoretical math predictions about where parallel line locations will be has nothing to do with where they actually are.

I don't know the angular math but I can see what he is saying. The vanishing point is the same for all parallel lines, no matter how high up you draw them; all parallel lines converge on the exact same location. Like so:

Again I find myself thinking that mathematical geometry is just a red herring for uninquisitive and under-educated minds. Which I guess I am. Claiming the sun is exempt from this rule because maths still sounds funny to me. I think he made good points, and I don't see how explaining how angles and perspective works changes the fact that all parallel lines converge in the same spot. Though I imagine I'll shortly be pulling my foot out of my mouth again; in which case I would apologize ahead of time, but I know you wouldn't have made this topic if you didn't already consider the nature of the vanishing point, and are already anticipating this type of response. I'm sure I'm just missing something. I swear it's like I can feel it coming already.
The Flat Earth Society has members all around the Globe
[H]ominem unius libri timeo ~Truth is stranger.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #149 on: October 01, 2016, 09:42:49 PM »
Lol great post, I caught my error before you posted though. I thought you were trying to pull a fast one, but then I realized I was wrong. That is my fault for jumping the gun. I got some really good chuckles reading your post, though spot on. I deserved it.

No worries. I apologize if the tone of my post was a bit snippy. In my defense, I have been arguing in circles with Tom for awhile now.

Quote
Quote
2. Parallel lines converge due to perspective; even those in a OP diagram, if drawn to 'infinity'.

No no no no no! A thousand times no! Parallel lines are always parallel in an orthographic projection, by definition. If the parallel lines converge, then it isn't an orthographic projection.

On a life-sized, really big, OP projection, they would converge

Oh... I see what you are saying. Lol, yes, since you view everything through the perspective projection created by your own eyes, then even the parallel lines on an orthographic projection will appear to converge. This doesn't change the actual angles measured in the orthographic diagram though. This has more to do with the size or closeness of the physical piece of paper that you draw the diagram on, and nothing to do with the scale of the object being portrayed by the diagram. If you are having problems with perspective while viewing your orthographic diagram, I suggest that you not use a sheet of paper the size of a football field. -_-

Quote
If you are going to make an argument about infinity, you will need to be much more specific than this.

I wasn't making this argument, but offering my speculation about the "infinities' I kept seeing repeated again and again in this thread, since they don't make sense to me.

Here's the thing. All these arguments about infinity are vague, and basically amount to "the idea of infinity is somehow related to this concept, therefore everything involved with this concept is impossible and wrong".

The problem is, we can relate just about ANY concept to infinity if you are vague enough. How many times can an inch be subdivided? An infinite amount of times? Does this mean it's impossible for anything to be an inch long? No, of course not.

Mathematicians deal with infinity all the time, despite the apparent impossibility of any value actually reaching infinity. They do this by being precise with their assumptions and meanings. For example, we can say "as x approaches infinity, 1/x approaches zero". Note that we are not saying that x REACHES infinity. Nor are we saying that 1/x REACHES zero. This is a common topic in introductions to calculus.

If you want some food for thought, I recommend this Vsauce video on the size of numbers. Or this one on Zeno's Paradox. Of course, these videos, as awesome as they are, will not give you much more than just a vague understanding of the topics. If you want a working knowledge, you will have to study hard! I recommend starting with courses titled "number theory" or "set theory". Preferably with the word "introduction" in their title. (This post took a long time to make because I got distracted by the Vsauce channel. RIP my Saturday.)

But his point at 4:50 seems solid, right?

Sort of. The fact that "they all visually go to the same place" is exactly what is predicted by the math. Notice that in the bottom perspective drawing that I made, the 3 objects are approaching a point on the horizon. They are following perspective lines.

1. 5:17 "These are true perspective lines, these are parallel lines, but the observer, which is this little guy down here, this what these parallel lines would look like."

Absolutely not. The "little guy down here" is not the observer. The camera is the observer. That little guy down there was arbitrarily placed in that scene. He is trying to combine the orthographic diagram (which shows distances between objects, including the observer) and the perspective projection (which shows how things appear, from the observers point of view). Everything he tries to calculate from this combined diagram will be wrong.

I mean, airplanes do seem to travel slower near the horizon, but they do emerge - and pass over - as it were. The higher the object, the more downward elevating is the angle. That's simple high school geometry. The sun should travel slower, 'but muh vanishing point'. Obviously the sun makes it there (it is night time in contiguous America right now), and p-brane seems to demonstrate how it can get there on a Flat Earth; perspective.

Which is what that video is about; showing how theoretical math predictions about where parallel line locations will be has nothing to do with where they actually are.

I don't know the angular math but I can see what he is saying. The vanishing point is the same for all parallel lines, no matter how high up you draw them; all parallel lines converge on the exact same location. Like so:

Ok, instead of telling you how each statement is wrong or right, let me give you this challenge:

Using that diagram, how long would it take for an object to REACH the vanishing point by following the two bottom parallel lines?

Quote
Again I find myself thinking that mathematical geometry is just a red herring for uninquisitive and under-educated minds. Which I guess I am.

Well, you certainly aren't uninquisitive. But I disagree. Geometry is a fantastic subject for everyone to understand, not just mathematicians. In fact, I am of the opinion that the method of creating geometric proofs that most people learn in highschool is the single most important subject for promoting good problem solving skills and logical reasoning.

Quote
I know you wouldn't have made this topic if you didn't already consider the nature of the vanishing point, and are already anticipating this type of response. I'm sure I'm just missing something. I swear it's like I can feel it coming already.

Good guess...

(Edit: Removed Jack Nicholson picture. His smile creeps me out.)

Just do the challenge from above, then we can get back to this.
« Last Edit: October 02, 2016, 04:38:42 AM by TotesNotReptilian »

#### markjo

• Purgatory
• 4117
• Zetetic Council runner-up
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #150 on: October 02, 2016, 03:42:52 AM »
The math you are using says that is is impossible for anything to reach the horizon. A sun would descend forever on a Flat Earth without ever reaching the horizon. The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Where has any endless approach to a point like this been reported in any scientific, everyday, or historical observation, or anywhere in the world? Please present some form of evidence that any of this is possible. Provide something, anything from reality, showing that ultra long descents would occur or that the horizon would be an infinite distance away.
Tom, if the math doesn't fit your model, then maybe it's time to start considering the possibility that your model just might be wrong.
Abandon hope all ye who press enter here.

Science is what happens when preconception meets verification.

If you can't demonstrate it, then you shouldn't believe it.

#### Tom Bishop

• Zetetic Council Member
• 6734
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #151 on: October 02, 2016, 03:01:41 PM »
The math you are using says that is is impossible for anything to reach the horizon. A sun would descend forever on a Flat Earth without ever reaching the horizon. The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Where has any endless approach to a point like this been reported in any scientific, everyday, or historical observation, or anywhere in the world? Please present some form of evidence that any of this is possible. Provide something, anything from reality, showing that ultra long descents would occur or that the horizon would be an infinite distance away.
Tom, if the math doesn't fit your model, then maybe it's time to start considering the possibility that your model just might be wrong.

Many people have seen a flat earth. No one has seen that aspect of the math that causes perspective lines to perpetually approach each other for infinity. The ball is in your court for this highly theoretical concept, I am afraid.
"The biggest problem in astronomy is that when we look at something in the sky, we don’t know how far away it is" — Pauline Barmby, Ph.D., Professor of Astronomy

#### inquisitive

• 1062
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #152 on: October 02, 2016, 05:34:06 PM »
The math you are using says that is is impossible for anything to reach the horizon. A sun would descend forever on a Flat Earth without ever reaching the horizon. The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Where has any endless approach to a point like this been reported in any scientific, everyday, or historical observation, or anywhere in the world? Please present some form of evidence that any of this is possible. Provide something, anything from reality, showing that ultra long descents would occur or that the horizon would be an infinite distance away.
Tom, if the math doesn't fit your model, then maybe it's time to start considering the possibility that your model just might be wrong.

Many people have seen a flat earth. No one has seen that aspect of the math that causes perspective lines to perpetually approach each other for infinity. The ball is in your court for this highly theoretical concept, I am afraid.
You will have to explain how these many people decided they have seen a flat earth, beyond 'it looks flat'.  Ask how they explain the path of the sun as seen from many locations.

You need to understand the definition of perspective.

How's the dish measurements going?

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #153 on: October 02, 2016, 05:53:05 PM »
Many people have seen a flat earth. No one has seen that aspect of the math that causes perspective lines to perpetually approach each other for infinity.

Still have your fingers firmly implanted in your ears, repeating the same refuted argument I see... Whatever. Just answer the question:

Fine. What evidence would convince you? If I am able to correctly predict the size of an object on a picture based on its size and distance using the "ancient greek math", would that convince you? I'm not going to waste my time if you are just going to cry "fake".

Quote
The ball is in your court

Still? We must be playing make-it-take-it.

Quote
for this highly theoretical concept, I am afraid.

Ah yes. Highly theoretical highschool geometry.

#### markjo

• Purgatory
• 4117
• Zetetic Council runner-up
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #154 on: October 02, 2016, 06:03:21 PM »
The math you are using says that is is impossible for anything to reach the horizon. A sun would descend forever on a Flat Earth without ever reaching the horizon. The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Where has any endless approach to a point like this been reported in any scientific, everyday, or historical observation, or anywhere in the world? Please present some form of evidence that any of this is possible. Provide something, anything from reality, showing that ultra long descents would occur or that the horizon would be an infinite distance away.
Tom, if the math doesn't fit your model, then maybe it's time to start considering the possibility that your model just might be wrong.

Many people have seen a flat earth. No one has seen that aspect of the math that causes perspective lines to perpetually approach each other for infinity. The ball is in your court for this highly theoretical concept, I am afraid.
Tom, you are the one who is claiming that sunsets on a flat earth are the results of perspective.  Doesn't it stand to reason that you should be the one show the math that supports your claim?  You do realize that perspective does indeed have a mathematical foundation to it, don't you?
https://www.math.utah.edu/~treiberg/Perspect/Perspect.htm
Abandon hope all ye who press enter here.

Science is what happens when preconception meets verification.

If you can't demonstrate it, then you shouldn't believe it.

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #155 on: October 03, 2016, 01:46:12 AM »
If you are having problems with perspective while viewing your orthographic diagram, I suggest that you not use a sheet of paper the size of a football field. -_-

Can't help it, I'm a final solution kind of individual. I got tired of running out of toilet paper.

I get it with the infinities, I think now, and why they are running infinitely through this topic...

The fact that "they all visually go to the same place" is exactly what is predicted by the math. Notice that in the bottom perspective drawing that I made, the 3 objects are approaching a point on the horizon. They are following perspective lines.

1. 5:17 "These are true perspective lines, these are parallel lines, but the observer, which is this little guy down here, this what these parallel lines would look like."

Absolutely not. The "little guy down here" is not the observer. The camera is the observer.

I get this. It's kind of like back to the first image in this thread, we are looking at someone else's perspective, the 'tilted' middle piece.

However, when we are 'that little guy down there', with our face pressed against that wall, the lines still converge... but oh shi- I think I see where this is going.

Ok, instead of telling you how each statement is wrong or right, let me give you this challenge:

Using that diagram, how long would it take for an object to REACH the vanishing point by following the two bottom parallel lines?

Ugh. From wikipedia: When the image plane is parallel to two world-coordinate axes, lines parallel to the axis which is cut by this image plane will meet at infinity i.e. at the vanishing point.

That image makes my brain hurt.
The Flat Earth Society has members all around the Globe
[H]ominem unius libri timeo ~Truth is stranger.

#### Rama Set

• 5871
• Round and round...
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #156 on: October 03, 2016, 02:56:43 PM »
@totesnotreptilian-Correct me if I am wrong but isn't it incorrect to say that "the math says perspective lines meet at inifinity"?  Instead, isn't it more accurate to say that the mathematically, the only place parallel lines could meet under Eulcid's axioms is at inifinity?   So it is more about excluding the lines intersecting in real space, rather than saying they actually do meet at inifinity?

Hope this makes sense.
You don't get races of anything ... accept people.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #157 on: October 03, 2016, 10:26:29 PM »
Ok, instead of telling you how each statement is wrong or right, let me give you this challenge:
Using that diagram, how long would it take for an object to REACH the vanishing point by following the two bottom parallel lines?
Ugh. From wikipedia: When the image plane is parallel to two world-coordinate axes, lines parallel to the axis which is cut by this image plane will meet at infinity i.e. at the vanishing point.

Well, yes. My point is that you don't have to take wikipedia's or my word for it. You can come to the same conclusion from that diagram.

@totesnotreptilian-Correct me if I am wrong but isn't it incorrect to say that "the math says perspective lines meet at inifinity"?  Instead, isn't it more accurate to say that the mathematically, the only place parallel lines could meet under Eulcid's axioms is at inifinity?   So it is more about excluding the lines intersecting in real space, rather than saying they actually do meet at inifinity?

Hope this makes sense.

I wouldn't say the first wording is completely incorrect. But yeah, your wording is much more clear and precise.

#### Tom Bishop

• Zetetic Council Member
• 6734
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #158 on: October 04, 2016, 12:05:24 AM »
You will have to explain how these many people decided they have seen a flat earth, beyond 'it looks flat'.  Ask how they explain the path of the sun as seen from many locations.

What observations would those be? Surely you can reference a paper on the subject rather than make up observations.

Quote
How's the dish measurements going?

« Last Edit: October 04, 2016, 12:08:20 AM by Tom Bishop »
"The biggest problem in astronomy is that when we look at something in the sky, we don’t know how far away it is" — Pauline Barmby, Ph.D., Professor of Astronomy

#### Tom Bishop

• Zetetic Council Member
• 6734
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #159 on: October 04, 2016, 12:09:12 AM »
Still have your fingers firmly implanted in your ears, repeating the same refuted argument I see... Whatever. Just answer the question:

Fine. What evidence would convince you? If I am able to correctly predict the size of an object on a picture based on its size and distance using the "ancient greek math", would that convince you? I'm not going to waste my time if you are just going to cry "fake".

I don't know. Would that prove that the perspective lines perpetually approach each other for infinity?

Quote from: TotesNotReptilian
Ah yes. Highly theoretical highschool geometry.

The same geometry fantasy which says that perfect circles exist when they, in fact, do not.
"The biggest problem in astronomy is that when we look at something in the sky, we don’t know how far away it is" — Pauline Barmby, Ph.D., Professor of Astronomy