#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #120 on: September 28, 2016, 11:25:31 PM »
And I still don't understand what you mean by "if the earth is as close to the surface as math would tell".

I was refering to the following from Tom's comment:

Quote
If you assume a Flat Earth, with a flat baseline, the sun becomes a lot closer to the earth's surface.

I still don't understand that statement. How can the earth be close to its own surface?

#### andruszkow

• 563
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #121 on: September 28, 2016, 11:32:27 PM »
And I still don't understand what you mean by "if the earth is as close to the surface as math would tell".

I was refering to the following from Tom's comment:

Quote
If you assume a Flat Earth, with a flat baseline, the sun becomes a lot closer to the earth's surface.

I still don't understand that statement. How can the earth be close to its own surface?

Hah! I was so focused on the general meaning of it all, that I actually didn't see my own typo. Fixed below

Quote
But then starts all the other issues that flat earth can't explain, if the earth Sun is as close to the surface as math would tell, assuming the earth is flat. We've been telling you that a gazillion times.

Ignored by Intikam since 2016.

#### nametaken

• 87
• ͡ ͡° ͜ ʖ ͡ ͡°
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #122 on: September 29, 2016, 03:11:18 AM »
Okay I'm showing up way late to this topic, I only read most of the first page, but I already [think I] understand the misconception here. Note: I've never heard of an orthographic projection, had to google it; according to google:

a method of projection in which an object is depicted or a surface mapped using parallel lines to project its shape onto a plane.
a drawing or map made using orthographic projection.

I played Dwarf Fortress for a while, so I'm familiar with that type of design, though only from a very shrewd and limited engineer standpoint (no offense, Great Toady One).

The basic misconception I'm seeing here is.... the orthographic projection seems to be a tool for engineers to use, which doesn't typically deal with say, mile-long distances in everyday application. This is Point 1.

Now, P-Brane (the youtuber who made the video in question), is arguing that orthographic projection's are not applicable to reality on these scales, because all parallel lines converge at a specific distance, due to perspective; a detail omitted by the orthographic projection p-brane claims a 'glober' presented him with - sparking the creation of said video. This is Point 2; if all = lines converge, perspective must be taken into consideration - and by the nature of this debate, as Tom Bishop stated, it is impossible to get to a point where a orthographic projection would be possible on this scale, so we must rely on perspective, knowing that all parallel lines converge due to perspective.

Now, I'm only tentatively holding onto understanding of this at this point, so don't ask me to draw this; but seeing Point 2 (all = lines converge), that means that due to perspective, something moving parallel to a flat plane far (say a few thousand miles) overhead, would eventually reach that point of convergence, and 'disappear' beyond the horizon, before fading - though it may 'fade' somewhere thereafter - which would explain 'dusk' and 'night time' quite conveniently for a Flat Earth; the light source literally extinguished by mechanics of orthographic projection, beyond the horizon.

Now, yes, he does use 'arbitrary definitions' for lines @ 2 minutes 40 seconds; but that isn't an illustration of the argument, just an illustration of Point 2, to avoid having to make such a forum post instead.

Orthographic projections are useful for accurately portraying angles.
Perspective projections are useful for portraying what we see.

To understand the motion of the sun, both of these are needed. That is just basic geometry. The sun sometimes appears to move in straight lines, but that is just perspective. Globe science acknowledges this, that's pretty simple; the sun appears to move in straight lines, though we can be fairly sure (do to above mentioned points) that this isn't literally the case. The only way to know 'how it is really moving' is to realize that perspective isn't necessarily always 'what is really happening'.

Disclaimer: Ugh... also I am not a fan of youtube drama so I don't want to get dragged into that... lol...  if anyone sees this and claims credit for it (ie p-brane), fine take it I'm not claiming I put the ideas out there, I'm just clarifying a potential oversight I saw here. Feel free to use this as a resource if need be.
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 #123 on: September 29, 2016, 06:50:19 AM »
First of all, thanks for the nice write-up. It was very readable and your points were quite clear. I apologize in advance for the following wall of text. I tried to explain everything as clearly and precisely as possible, which means it got a little wordy.

The basic misconception I'm seeing here is.... the orthographic projection seems to be a tool for engineers to use, which doesn't typically deal with say, mile-long distances in everyday application. This is Point 1.

Perspective occurs at all scales (not just large scales) and orthographic projections are valid and useful at all scales (not just small scales). Orthographic projections very intentionally don't portray perspective in order to allow certain things to be accurately measured.

1. Straight lines in reality are always straight in the diagram.
2. Parallel lines in reality are always parallel in the diagram.
3. Angles parallel to the plane of projection are accurate.
4. Distances parallel to the plane of projection are proportional. Distances in the same direction are proportional.

None of these properties change with scale. If we suddenly decide to add in perspective to the diagram, at any scale, these things will stop being true, and the diagram will no longer be useful for taking measurements.

Quote
This is Point 2; if all = lines converge, perspective must be taken into consideration - and by the nature of this debate, as Tom Bishop stated, it is impossible to get to a point where a orthographic projection would be possible on this scale, so we must rely on perspective, knowing that all parallel lines converge due to perspective.

I did take perspective into consideration. Unlike Tom Bishop and the aptly named P-Brane, I have more than just a vague understanding of perspective. I know exactly how to calculate it. More on this later.

Quote
Now, I'm only tentatively holding onto understanding of this at this point, so don't ask me to draw this; but seeing Point 2 (all = lines converge), that means that due to perspective, something moving parallel to a flat plane far (say a few thousand miles) overhead, would eventually reach that point of convergence, and 'disappear' beyond the horizon, before fading - though it may 'fade' somewhere thereafter - which would explain 'dusk' and 'night time' quite conveniently for a Flat Earth; the light source literally extinguished by mechanics of orthographic projection, beyond the horizon.

This kinda-sorta makes sense if you only have a vague understanding of how perspective works. Unfortunately for Mr. Bishop and Mr. Brane, it is relatively easy to calculate exactly how far away an object is based on its height and angle with the horizon. This is where the orthographic diagram becomes useful. See this image:

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?

First: how does perspective arise?

The size of an object in a photo is proportional to the angular diameter of that object. As an object moves farther away, this angular diameter decreases, which causes the object to appear smaller. The same is true for distances between objects. This is why objects appear smaller as they get farther away. It is also why parallel lines appear to converge as they get farther away.

Look at the orthographic diagram. Notice that the 3 objects are the same size. However, the angular diameter of each object is different (4.2°, 3.0°, 2.3°). The farthest object has the smallest angular diameter. Notice that these angles are easily measurable using the orthographic diagram.

Now look at the bottom picture. Notice that the size of each object in the bottom picture corresponds to the angular diameter of the object from the orthographic diagram. We can convert these angles into sizes using the field of view of the camera. For example, if the field of view of the camera is 60°, and an object has an angular diameter of 30°, then the object will take up half the picture. (This assumes that the camera doesn't have a huge field of view or lots of optical distortion.)

We can do the exact same process for the height of each object: (skip the next two paragraphs if you already get the point)

Look at the orthographic diagram. Notice that the 3 objects are the same height. However, the angle between the object and the ground decreases as it gets farther away (20°, 14°, 11°). The farthest object has the smallest angular height. Notice that these angular heights are easily measurable using the orthographic diagram.

Now look at the bottom picture. Notice the height of each object in the bottom picture corresponds to the angular height of the object from the orthographic diagram. Once again, we can convert the angles to heights using the field of view of the camera.

Now, please notice 3 things about how we constructed the bottom image:

1. We determined the height and size of the objects from the angles in the orthographic diagram.
2. The size of the objects naturally decreases as they get farther away.
3. The objects naturally approach the horizon as they get farther away.
4. If we draw a line connecting the right edges of each object, and another line connecting the left edges of each object, those two lines will converge below the objects at the horizon. Just like perspective lines! Coincidence? I think not!

Points 2 and 3 are the effects of what we call perspective. Perspective naturally arises from the angles measured from the orthographic diagram! Neat!

Notice, that there is absolutely no need to overlay any arbitrarily drawn "perspective lines" onto the orthographic diagram in order to calculate the position of each object due to perspective. The perspective lines arise naturally in the bottom picture due to measurements of angles that we took from the orthographic side view diagram.

Tom Bishop's rebuttal:

So far, Tom Bishop's main argument has been to simply deny the mathematical relationship between the two pictures above. To justify this denial, he has made several... um... entertaining... arguments involving "hidden infinities" and generally denounced the usefulness of orthographic diagrams. (Even though his hero, Rowbotham, uses them quite frequently.)

However, you don't have to take my word for it. Go outside with a camera and a few objects and test the math for yourself. You will find that the mathematical relationship between the angles from the orthographic side view and the size and placement of the objects in the picture is quite accurate for any distance that you manage to test. (Use a relatively narrow field of view for more accuracy. Wide angle lens have too much optical distortion.)

Tom Bishop's other argument is that "maybe the math math suddenly stops working at super long distances that are too long to test". However, he has presented no evidence or logical reasoning that would suggest that the math suddenly stops working at a particular distance. I think we can all agree that this is a horrible argument and merely a desperate attempt to ignore evidence that contradicts his flat earth model.
« Last Edit: September 29, 2016, 07:04:06 AM by TotesNotReptilian »

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #124 on: September 29, 2016, 07:35:22 AM »
TL;DR:

It is easy to calculate the distance of an object based on its height and angle with the horizon, using an orthographic diagram or this equation:

distance = height / tan(angle)

You can deny that the math is wrong, or that orthographic diagrams are invalid all you want. However, the math works for any testable distance. Test it.

#### Woody

• 241
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #125 on: September 29, 2016, 09:19:30 AM »
TL;DR:

It is easy to calculate the distance of an object based on its height and angle with the horizon, using an orthographic diagram or this equation:

distance = height / tan(angle)

You can deny that the math is wrong, or that orthographic diagrams are invalid all you want. However, the math works for any testable distance. Test it.

What continually perplexes me is that an explanation and one that can be tested relatively easily like yours will not be accepted or tested by any true FE believer.

Similar how Tom will not do any experiments that will challenge his belief. He will stick to the safe claims of seeing stuff he should not see or shooting a laser at a target without providing any data or other information.

#### Nostra

• 26
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #126 on: September 29, 2016, 10:22:54 AM »
And (just to remind) I am still waiting for an explanation about the constancy of the angular speed of the sun, which is totally inconsistent with FE model!
Proud to be the 1 other!

#### Tom Bishop

• Zetetic Council Member
• 6472
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #127 on: September 29, 2016, 04:15:10 PM »
Tom Bishop's other argument is that "maybe the math math suddenly stops working at super long distances that are too long to test". However, he has presented no evidence or logical reasoning that would suggest that the math suddenly stops working at a particular distance. I think we can all agree that this is a horrible argument and merely a desperate attempt to ignore evidence that contradicts his flat earth model.

No, no, I'm sorry, but no.

The math you are using assumes that values near zero approach infinity. This assumption needs merit in the material world. There must be an example of this somewhere for us to accept it as reality. It is quite decieving to say that "Tom Bishop assumes the math stops working" when this part of the math has not been demonstrated anywhere.

You must show where these pockets of infinities have been seen. It is not my responsibility to "prove it wrong" any more than it is my responsibility to prove that ghosts do not exist in an argument on the existence of ghosts. This is a positive claim of something which has never been observed. It is your responsibility to show that this math is somehow right in contradiction to physical experience.

#### Woody

• 241
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #128 on: September 29, 2016, 04:41:42 PM »
If we take a line and define a segment then we are no longer assuming infinity.

When we select how accurate a calculation needs to be using something like Pi or 1/3 we are no longer using an infinite number.

The math has been constantly proven to work in real world applications.

#### andruszkow

• 563
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #129 on: September 29, 2016, 05:28:18 PM »
Tom Bishop's other argument is that "maybe the math math suddenly stops working at super long distances that are too long to test". However, he has presented no evidence or logical reasoning that would suggest that the math suddenly stops working at a particular distance. I think we can all agree that this is a horrible argument and merely a desperate attempt to ignore evidence that contradicts his flat earth model.

No, no, I'm sorry, but no.

The math you are using assumes that values near zero approach infinity. This assumption needs merit in the material world. There must be an example of this somewhere for us to accept it as reality. It is quite decieving to say that "Tom Bishop assumes the math stops working" when this part of the math has not been demonstrated anywhere.

You must show where these pockets of infinities have been seen. It is not my responsibility to "prove it wrong" any more than it is my responsibility to prove that ghosts do not exist in an argument on the existence of ghosts. This is a positive claim of something which has never been observed. It is your responsibility to show that this math is somehow right in contradiction to physical experience.
But that's what they have been doing all along. The only reason to refute it, is if you assume that Pi = 4 and that proven math has been wrong from day 1. With this, I'm referring specifically to your claims about math and the ancient Greeks for instance.

In that regard, yes, it's still up to you to prove where math is wrong, using real world examples, just as the RE'ers in this and many other threads has shown you how math and real world examples are 1:1.
Ignored by Intikam since 2016.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #130 on: September 29, 2016, 06:03:04 PM »
Tom Bishop's other argument is that "maybe the math math suddenly stops working at super long distances that are too long to test". However, he has presented no evidence or logical reasoning that would suggest that the math suddenly stops working at a particular distance. I think we can all agree that this is a horrible argument and merely a desperate attempt to ignore evidence that contradicts his flat earth model.

No, no, I'm sorry, but no.

The math you are using assumes that values near zero approach infinity.

For the... *counts on fingers... takes off shoes... counts on toes* ...12th time?

1. Your logic is vague and lazy. What "value near zero approaches infinity"? Distance to the object? Size of the object on the projection? Distance from the vanishing point on the projection? Be specific.
2. Your statement is absurd. Near zero. Approaches infinity. Do you not see the contradiction here? The "math" certainly makes no such assumptions.

The math assumes that there is a 1 to 1 relationship between the ratio of sides of a right triangle and the angle of a right triangle. It assumes euclidean geometry. For the math to be applicable and accurate, we assume that light travels in a straight line.

Given 2 objects moving in straight lines parallel to each other away from the observer, the math predicts that the objects will appear closer to the vanishing point. The math predicts that for any arbitrary finite (NOT infinite) distance away, the objects will appear a non-zero distance away from the vanishing point on the projection. This non-zero distance can also become arbitrarily small, thus indistinguishable from zero since our eyes and cameras don't have perfect resolution.

Please notice that nowhere did I say the math predicts or assumers (there is a difference) that any object actually reaches an infinite distance away from the observer. Nor does any other value actually reach infinity.

How many more times do I have to refute this ridiculous argument before you stop bringing it up? 20 times? 100 times? Would a language other than English make it more clear? I am quite proficient in Pig Latin.

Quote
It is quite decieving to say that "Tom Bishop assumes the math stops working" when this part of the math has not been demonstrated anywhere.

First of all, these are two unrelated arguments. Second of all, it is an argument (the red part) you have made implicitly in this thread, and quite explicitly in other threads. If you want to disavow this argument, that is perfectly fine by me. However, I'll bet anyone five I-told-you-so's that you will go back to this argument eventually.

Quote
You must show where these pockets of infinities have been seen.

No, I don't. I'm not sure how you expect anyone to show that something is infinite. However, I will give you a more apt analogy, for funsies:

Spread your arms in front of you, making a 90 degree angle between your arms. What is the maximum width of an object that will fit inside the visual field between your arms? Go.

#### markjo

• Purgatory
• 3778
• Zetetic Council runner-up
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #131 on: September 29, 2016, 07:22:57 PM »
Tom, correct me if I'm wrong, but are you essentially saying that the mathematical foundations of visual perspective that are used in highly detailed and accurate systems, like flight simulators, are unproven?
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.

#### Woody

• 241
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #132 on: September 30, 2016, 01:49:48 AM »
Tom, correct me if I'm wrong, but are you essentially saying that the mathematical foundations of visual perspective that are used in highly detailed and accurate systems, like flight simulators, are unproven?

His argument is at some certain unspecified distance and reason the math fails to work.  From what I can gather from his post the math fails at around 12 miles where most sailors on lookout duty would see the horizon and again around 3,000 miles the altitude of the Sun.

#### Tom Bishop

• Zetetic Council Member
• 6472
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #133 on: September 30, 2016, 03:39:59 AM »
You sure seem defensive over math that is so proven. Just show us where these approaches to infinity or ultra long decents have been found in realty, and we can just see that the math is undeniable, OKAY?

#### markjo

• Purgatory
• 3778
• Zetetic Council runner-up
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #134 on: September 30, 2016, 04:03:08 AM »
You sure seem defensive over math that is so proven. Just show us where these approaches to infinity or ultra long decents have been found in realty, and we can just see that the math is undeniable, OKAY?
Tom, are you suggesting that the sun is infinitely far away?
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.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #135 on: September 30, 2016, 04:06:09 AM »
You sure seem defensive over math that is so proven. Just show us where these approaches to infinity or ultra long decents have been found in realty, and we can just see that the math is undeniable, OKAY?

Who are you talking to? No one claimed anything approaches infinity. And what the heck are "ultra long decents"?

#### Tom Bishop

• Zetetic Council Member
• 6472
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #136 on: September 30, 2016, 04:20:22 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.

#### TotesNotReptilian

• 802
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #137 on: September 30, 2016, 05:13:52 AM »
The math you are using says that is is impossible for anything to reach the horizon.

Assuming it is traveling in a straight line parallel to a flat earth, sure.

Quote
A sun would descend forever on a Flat Earth without ever reaching the horizon.

No it wouldn't. After noon, it would start sinking and turning northwards (because it is circling the north pole). By 6 pm it would be about 28 degrees above the horizon. It would reach a minimum of 20 degrees above the horizon around midnight and would be due north. After that, it would start rising again. (Edit: your bi-polar model would be slightly different of course, since it sometimes circles the south pole instead.)

Quote
The math says that touching the horizon is impossible, as 0 degrees is defined as infinity.

Strictly speaking, correct. Since an object can never be an infinite distance away, it will never be 0 degrees with the horizon. Please notice: it CAN get arbitrarily close to the horizon, if it is a very long distance away relative to its height. It can be so close to the horizon that we cannot tell the difference with our eyes, because our eyes aren't perfect.

We have covered this already. Stop bringing up the same refuted arguments over and over.

Quote
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. <-- I did not claim the horizon is an infinite distance away. Your strawman arguments are getting tiring. Almost every single post contains one.

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.

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!
« Last Edit: September 30, 2016, 05:17:51 AM by TotesNotReptilian »

#### Tom Bishop

• Zetetic Council Member
• 6472
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #138 on: September 30, 2016, 05:31:21 AM »
Quote
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.

#### Tom Bishop

• Zetetic Council Member
• 6472
• Flat Earth Believer
##### Re: Angles, Perspective, and the Setting Sun.
« Reply #139 on: September 30, 2016, 05:54:47 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.

Quote
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.
« Last Edit: September 30, 2016, 06:03:20 AM by Tom Bishop »