#### StinkyOne

• 805
##### Re: The burden of proof.
« Reply #40 on: October 31, 2017, 07:02:41 PM »
I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.

Easy - send a train down the tracks. Does the train magically shrink? Does it jump the tracks? No? Well then, the tracks never ACTUALLY get any closer. If you claim they ACTUALLY get closer, you need to prove that.
I saw a video where a pilot was flying above the sun.
-Terry50

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #41 on: October 31, 2017, 07:16:15 PM »
I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.

Easy - send a train down the tracks. Does the train magically shrink? Does it jump the tracks? No? Well then, the tracks never ACTUALLY get any closer. If you claim they ACTUALLY get closer, you need to prove that.

Where did I say any of that? Perspective affects the orientation of bodies -- the determination of relative position to your own. Perspective lines cause things to shrink in their orientation. There is no argument about. Perspective lines also cause things to merge together in their orientation, which there does seem to be some objection to.

You will need to show some kind of evidence that the apparent merging is not a property of perspective and that the perspective lines actually approach each other for infinity.

#### StinkyOne

• 805
##### Re: The burden of proof.
« Reply #42 on: October 31, 2017, 07:23:21 PM »
I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.

Easy - send a train down the tracks. Does the train magically shrink? Does it jump the tracks? No? Well then, the tracks never ACTUALLY get any closer. If you claim they ACTUALLY get closer, you need to prove that.

Where did I say any of that? Perspective affects the orientation of bodies, not the position of bodies. Perspective lines cause things to shrink in their orientation. There is no argument about. Perspective lines also cause things to merge together in their orientation, which there does seem to be some objection to.

You will need to show some kind of evidence that the apparent merging is not a property of perspective and that the perspective lines actually approach each other for infinity.

Tom, you are making the claim that perspective lines merge. The onus is on you to prove your claim. I've never seen, nor have I seen a picture of, train tracks merging. You asked me to prove it was an illusion, so I did. Orientation is the relative position of objects. If orientation is changed, position has to change. Position is literally in the definition.
I saw a video where a pilot was flying above the sun.
-Terry50

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #43 on: October 31, 2017, 07:25:21 PM »
Tom, you are making the claim that perspective lines merge. The onus is on you to prove your claim. I've never seen, nor have I seen a picture of, train tracks merging. You asked me to prove it was an illusion, so I did. Orientation is the relative position of objects. If orientation is changed, position has to change. Position is literally in the definition.

The idea that perspective is changing the orientation of bodies around you is not synonymous with the change of position of the bodies.

orientation - the determination of the relative position of something or someone
position - a place where someone or something is located or has been put

Perspective changes orientation; which is your determination of relative position, not the position of a body.

#### StinkyOne

• 805
##### Re: The burden of proof.
« Reply #44 on: October 31, 2017, 07:41:32 PM »
Tom, you are making the claim that perspective lines merge. The onus is on you to prove your claim. I've never seen, nor have I seen a picture of, train tracks merging. You asked me to prove it was an illusion, so I did. Orientation is the relative position of objects. If orientation is changed, position has to change. Position is literally in the definition.

The idea that perspective is changing the orientation of bodies around you is not synonymous with the change of position of the bodies.

orientation - the determination of the relative position of something or someone
position - a place where someone or something is located or has been put

Perspective changes orientation; which is your determination of relative position, not the position of a body.

QFT

So, if the top of a railroad track is 8 inches off the ground, it will always be 8 inches off the ground, correct? No matter how far away I travel, that track is always in the same location.
I saw a video where a pilot was flying above the sun.
-Terry50

#### xenotolerance

• 307
• byeeeeeee
##### Re: The burden of proof.
« Reply #45 on: October 31, 2017, 09:03:06 PM »
hell and damn yes it is in the same location at the same height

one more time for the people in the back:

Perspective doesn't change orientation. It changes apparent orientation. Apparent as in appearing to be, visible, etc. But more accurately, perspective doesn't actually change apparent orientation: Distance from a lens does, one part of perspective. 3DGeek has repeatedly made this abundantly clear with his diagrams of pinhole cameras. And, repeating again, your eyes focus light like pinhole cameras.

If you throw a football some distance and keep your eye on it as it goes, it will appear to get smaller. Its size is constant. Its volume, mass, etc etc etc are unaffected by perspective. Its apparent size to you will get smaller. The inverse is true as well: If someone throws it back, it appears to get bigger as it gets closer to you. Perspective is not changing its size. Distance from pinhole + looking through that pinhole is changing its apparent size when viewed from that pinhole. That this happens is one law of perspective. Perspective doesn't DO anything. It can't; it doesn't, never has, and never will do anything, the same way that math doesn't do anything. You can use it to describe stuff, and to predict stuff. Which is awesome! Very helpful, very useful things, perspective and maths. But they don't do stuff.

So how about them parallel lines?

Quote from: Wikipedia
Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing. A one-point perspective drawing means that the drawing has a single vanishing point, usually (though not necessarily) directly opposite the viewer's eye and usually (though not necessarily) on the horizon line. All lines parallel with the viewer's line of sight recede to the horizon towards this vanishing point. This is the standard "receding railroad tracks" phenomenon. A two-point drawing would have lines parallel to two different angles. Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing.

...

A drawing has one-point perspective when it contains only one vanishing point on the horizon line. This type of perspective is typically used for images of roads, railway tracks, hallways, or buildings viewed so that the front is directly facing the viewer. Any objects that are made up of lines either directly parallel with the viewer's line of sight or directly perpendicular (the railroad slats) can be represented with one-point perspective. These parallel lines converge at the vanishing point.

One-point perspective exists when the picture plane is parallel to two axes of a rectilinear (or Cartesian) scene – a scene which is composed entirely of linear elements that intersect only at right angles. If one axis is parallel with the picture plane, then all elements are either parallel to the picture plane (either horizontally or vertically) or perpendicular to it. All elements that are parallel to the picture plane are drawn as parallel lines. All elements that are perpendicular to the picture plane converge at a single point (a vanishing point) on the horizon.

This is description. Definition, practically. It does not have to be proven, per se, because it is directly describing empirical observation. "Look at these railroad tracks! They are a constant width apart, like parallel lines. Sure do appear to converge toward that vanishing point." Tom likes to say that Euclid's ideas are hypothetical: They are not. They never were. They are empirical in nature. Specifically, Euclid defined parallel lines; he did not hypothesize them.

It is stupendously absurd that we are arguing about the worth of Euclid's definitions in a thread with the topic Burden Of Proof. Can we get back to the topic, that is, can you start ignoring the overwhelming evidence that the Earth is not flat some more?

oh yeah, that's great. thanks
« Last Edit: October 31, 2017, 09:05:44 PM by xenotolerance »

#### inquisitive

• 1093
##### Re: The burden of proof.
« Reply #46 on: October 31, 2017, 09:55:35 PM »
I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge. Under the Elucid model it should be impossible for any body to ever get to the horizon.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.
Your words, as you know, make no sense.  'seem to touch'?

#### Curious Squirrel

• 1337
##### Re: The burden of proof.
« Reply #47 on: November 01, 2017, 05:28:14 AM »
Tom,

The fundamental issue that you seem to not understand, is Euclidean geometry doesn't have anything to do with perspective. Euclidean geometry describes where something is. We can use that geometry along with a location to even determine where and when things will happen according to perspective and the angular limit of the eye. As I showed you in the other thread. But what perspective doesn't do is change the physical angle of objects.

Quote
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

This is a strawman. Euclidean geometry says nothing of the sort. It says parallel lines will never meet. Which they won't, or they wouldn't be parallel. It doesn't deal with your 'perspective lines' at all. It describes the location of something relative to another thing, and it's testably accurate at ANY distance you care to name that is physically measurable.

Quote
If they do touch at some distance, then your diagram will look a whole lot different.

Your parallel lines will never touch though. They will seem to touch because of the angular limit of the eye, and we can predict accurately where this occurs as I showed you. But once again, Euclidean geometry is dealing with the physical location of something, and there it is correct that two parallel lines will never meet. There is nothing here about 'perspective lines' as you keep saying.

Quote
The fundamental premise of this continuous universe model needs empirical evidence behind it -- things to suggest that is how it is in the real world.

What continuous universe? What are you even talking about, as it has nothing to do with the subject of simple geometry. For the third time I say it, in the hopes that repetition will somehow help you get it. Euclidean geometry in and of itself doesn't deal with where things appear to be. It deals with where they physically are. We can use it's properties and the properties of the eye to accurately predict where, say two railroad tracks will no longer be distinguishable as two separate objects, but that's not part of what it tells us on it's own.

Once again, if you wish to say the sun appears to be at 0 degrees, when the math says it's at 20 degrees then you must present one of the following:
A) Proof that the math no longer works accurately beyond 'X' Miles/KM.
B) Proof that the math doesn't work in the real world, contrary to the proofs done upon it since Euclids time.
C) Evidence that the sun is somehow 'special' and immune to this mathematical law.

I think the burden of proof is on you, good sir. You are claiming that they will eventually touch. Have you ever seen this or have evidence.

Railroad tracks will seem to touch at the horizon, and the fact that things are able touch the horizon at all demonstrates that the perspective lines appear to merge. Under the Elucid model it should be impossible for any body to ever get to the horizon.

Empirical observation vs. ancient mathematical hypothesis. You need to show that it is all an illusion. Go.
BTW, this is another strawman, just in case you didn't get that above. Perspective lines have no part in Euclidean geometry. Parallel lines will never meet. They will appear to 'meet' at the point which our eyes can no longer distinguish the angular distance between them. Roughly 0.02 degrees. Now clearly things can get in the way, but you need to explain how a sun that should still be 20 degrees above the horizon, is appearing at 0 degrees.

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #48 on: November 01, 2017, 05:45:36 AM »
Quote from: xenotolerance
Tom likes to say that Euclid's ideas are hypothetical: They are not.

Where is the real world evidence for these infinitely-approaching perspective lines, then?

Tom,

The fundamental issue that you seem to not understand, is Euclidean geometry doesn't have anything to do with perspective. Euclidean geometry describes where something is. We can use that geometry along with a location to even determine where and when things will happen according to perspective and the angular limit of the eye. As I showed you in the other thread. But what perspective doesn't do is change the physical angle of objects.

Perspective changes the orientation angle of railroad tracks below your feet and brings them up to the level of your eye. It has caused the railroad tracks to be at the level of your eye when the railroad tracks are only a couple of inches from the ground: A clear example of change of orientation.

Quote from: Curious Squirrel
Quote
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

This is a strawman. Euclidean geometry says nothing of the sort. It says parallel lines will never meet. Which they won't, or they wouldn't be parallel. It doesn't deal with your 'perspective lines' at all. It describes the location of something relative to another thing, and it's testably accurate at ANY distance you care to name that is physically measurable.

We see that railroad tracks meet at the horizon. What kind of real world evidence do you have to suggest otherwise?

Quote
Your parallel lines will never touch though. They will seem to touch because of the angular limit of the eye

Do you have any evidence for that? The railroad tracks also meet in a wide angle lens, or even with lens-less cameras.

Quote
Once again, if you wish to say the sun appears to be at 0 degrees, when the math says it's at 20 degrees then you must present one of the following:
A) Proof that the math no longer works accurately beyond 'X' Miles/KM.
B) Proof that the math doesn't work in the real world, contrary to the proofs done upon it since Euclids time.
C) Evidence that the sun is somehow 'special' and immune to this mathematical law.

What you have is MATH. What I have is empirical observation. Your math only works under the model it is intended for. If the assumptions of the underlying model changes, or is wrong, the math does not work.

2 + 2 = 4 relies on the underlying model, and is not a universal truth. Under some models 2 + 2 does not equal 4. See Two Plus Two Equals Four, But Not Always.

All math relies on the underlying model for it to have truth. You need to prove that your underlying model for perspective lines is valid. That is your claim. You are the claimant. I am the skeptic. I am not going to prove a negative. You need to prove your positive. My position on this subject is backed by empirical observation, while yours relies on ancient hypothetical models. So get proving already. Demonstrate that your perspective model is founded in the real world.

Quote
BTW, this is another strawman, just in case you didn't get that above. Perspective lines have no part in Euclidean geometry. Parallel lines will never meet. They will appear to 'meet' at the point which our eyes can no longer distinguish the angular distance between them. Roughly 0.02 degrees. Now clearly things can get in the way, but you need to explain how a sun that should still be 20 degrees above the horizon, is appearing at 0 degrees.

Wrong. You need to explain why we need to assume that perspective lines will never meet when this has never been observed.
« Last Edit: November 01, 2017, 06:14:14 AM by Tom Bishop »

#### inquisitive

• 1093
##### Re: The burden of proof.
« Reply #49 on: November 01, 2017, 09:10:30 AM »
Quote from: xenotolerance
Tom likes to say that Euclid's ideas are hypothetical: They are not.

Where is the real world evidence for these infinitely-approaching perspective lines, then?

Tom,

The fundamental issue that you seem to not understand, is Euclidean geometry doesn't have anything to do with perspective. Euclidean geometry describes where something is. We can use that geometry along with a location to even determine where and when things will happen according to perspective and the angular limit of the eye. As I showed you in the other thread. But what perspective doesn't do is change the physical angle of objects.

Perspective changes the orientation angle of railroad tracks below your feet and brings them up to the level of your eye. It has caused the railroad tracks to be at the level of your eye when the railroad tracks are only a couple of inches from the ground: A clear example of change of orientation.

Quote from: Curious Squirrel
Quote
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

This is a strawman. Euclidean geometry says nothing of the sort. It says parallel lines will never meet. Which they won't, or they wouldn't be parallel. It doesn't deal with your 'perspective lines' at all. It describes the location of something relative to another thing, and it's testably accurate at ANY distance you care to name that is physically measurable.

We see that railroad tracks meet at the horizon. What kind of real world evidence do you have to suggest otherwise?

Quote
Your parallel lines will never touch though. They will seem to touch because of the angular limit of the eye

Do you have any evidence for that? The railroad tracks also meet in a wide angle lens, or even with lens-less cameras.

Quote
Once again, if you wish to say the sun appears to be at 0 degrees, when the math says it's at 20 degrees then you must present one of the following:
A) Proof that the math no longer works accurately beyond 'X' Miles/KM.
B) Proof that the math doesn't work in the real world, contrary to the proofs done upon it since Euclids time.
C) Evidence that the sun is somehow 'special' and immune to this mathematical law.

What you have is MATH. What I have is empirical observation. Your math only works under the model it is intended for. If the assumptions of the underlying model changes, or is wrong, the math does not work.

2 + 2 = 4 relies on the underlying model, and is not a universal truth. Under some models 2 + 2 does not equal 4. See Two Plus Two Equals Four, But Not Always.

All math relies on the underlying model for it to have truth. You need to prove that your underlying model for perspective lines is valid. That is your claim. You are the claimant. I am the skeptic. I am not going to prove a negative. You need to prove your positive. My position on this subject is backed by empirical observation, while yours relies on ancient hypothetical models. So get proving already. Demonstrate that your perspective model is founded in the real world.

Quote
BTW, this is another strawman, just in case you didn't get that above. Perspective lines have no part in Euclidean geometry. Parallel lines will never meet. They will appear to 'meet' at the point which our eyes can no longer distinguish the angular distance between them. Roughly 0.02 degrees. Now clearly things can get in the way, but you need to explain how a sun that should still be 20 degrees above the horizon, is appearing at 0 degrees.

Wrong. You need to explain why we need to assume that perspective lines will never meet when this has never been observed.
Your understanding of the word perspective is very strsnge. There is no such thing as a perspective model.

##### Re: The burden of proof.
« Reply #50 on: November 01, 2017, 09:46:22 AM »
You will need to show some kind of evidence that the apparent merging is not a property of perspective and that the perspective lines actually approach each other for infinity.

Tom this reads like you are suggesting that unless someone proves that the railway tracks continue to "appear to converge" for infinity you are not going to accept any further debate on this. Are you suggesting that someone needs to physically follow a pair of railway tracks for infinity to ensure that they do not ever actually meet?

##### Re: The burden of proof.
« Reply #51 on: November 01, 2017, 09:50:18 AM »
Wrong. You need to explain why we need to assume that perspective lines will never meet when this has never been observed.

It is observed every day Tom. Train tracks always appear to meet in the distance and yet they never do, we know they never do and we can see that they always appear to. This does not need any further proof, it is a very safe assumption to hold as it is one we see bear out every day.

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #52 on: November 01, 2017, 02:34:49 PM »
You will need to show some kind of evidence that the apparent merging is not a property of perspective and that the perspective lines actually approach each other for infinity.

Tom this reads like you are suggesting that unless someone proves that the railway tracks continue to "appear to converge" for infinity you are not going to accept any further debate on this. Are you suggesting that someone needs to physically follow a pair of railway tracks for infinity to ensure that they do not ever actually meet?

You will need a real world demonstration that your model for perspective is accurate.

Wrong. You need to explain why we need to assume that perspective lines will never meet when this has never been observed.

It is observed every day Tom. Train tracks always appear to meet in the distance and yet they never do, we know they never do and we can see that they always appear to. This does not need any further proof, it is a very safe assumption to hold as it is one we see bear out every day.

The idea that perspective is changing the orientation of bodies around you is not synonymous with the change of position of the bodies.

orientation - the determination of the relative position of something or someone
position - a place where someone or something is located or has been put

Perspective changes orientation; which is your determination of relative position, not the position of a body.

#### Jura-Glenlivet

• 1537
• Life is meaningless & everything dies.
##### Re: The burden of proof.
« Reply #53 on: November 01, 2017, 02:37:05 PM »

This Tom, is London Road rail station in Leicester, as we can see the tracks seem to converge before they even leave the station, however they do not, how do I know this? I have travelled both ways, to London and Nottingham. Don’t take my word for this check trainline for times and more importantly see if you can find complaints from people buying a ticket for any of the destinations, who only got as far as the end of the platform. From the many plainly ridiculous things you have ever said, your need for proof on something as fundamental as this leads me to the conclusions that either you are a troll, or you have dementia.

Just to be clear, you are all terrific, but everything you say is exactly what a moron would say.

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #54 on: November 01, 2017, 02:39:54 PM »

This Tom, is London Road rail station in Leicester, as we can see the tracks seem to converge before they even leave the station, however they do not

Perspective changes your determination of relative position. See my above quote:

The idea that perspective is changing the orientation of bodies around you is not synonymous with the change of position of the bodies.

orientation - the determination of the relative position of something or someone
position - a place where someone or something is located or has been put

Perspective changes orientation; which is your determination of relative position, not the position of a body.

##### Re: The burden of proof.
« Reply #55 on: November 01, 2017, 03:54:59 PM »
You will need a real world demonstration that your model for perspective is accurate.

We have one. We are showing it to you with the railway tracks. They are in the real world, they appear to converge due to perspective but by getting onto the train and following them we can be sure that this is only due to perspective as they do not converge in reality. When looking ahead the tracks in the distance still appear to converge in the distance and yet sure enough the train passes the point where they appeared to meet and they have not met. This continues the entire journey. How can this not be considered a real world model?

#### 3DGeek

• 1024
• Path of photon from sun location to eye at sunset?
##### Re: The burden of proof.
« Reply #56 on: November 01, 2017, 04:20:35 PM »
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

May I suggest you go back and actually READ my post?   The pinhole camera demonstrates the geometry - from that we can use similar triangles to turn this into algebra - and then we can try sticking some numbers in there to try to get Hsubject to be zero.   When you do that - the ONLY way to get the sun onto the flat earth horizon is to have Dsubject to be infinity.   This is another way of saying "parallel lines appear to touch at an infinite distance from the eye".  (They don't literally touch no matter how far away you are.)   This is PROOF that the vanishing point is at infinity.
Quote
If they do touch at some distance, then your diagram will look a whole lot different. The fundamental premise of this continuous universe model needs empirical evidence behind it -- things to suggest that is how it is in the real world. It is only backed by math which assumes a hypothetical model, and this is wholly insufficient.
But they don't touch at any finite distance...and they don't literally touch in the real world at all...only in images that are focussed.

There is nothing of the "continuous universe" in here - it's simple grade-school geometry and algebra.

But if you're now denying that mathematics can address the real world - then you have truly entered a world where only magic applies.  Perhaps this is a good place for you to exist - beyond the realms of reality where logic and reason cannot assail you.

Most of us would call that "insanity"...but if that's your choice, then maybe we shouldn't be listening to your ravings any longer.

Hey Tom:  What path do the photons take from the physical location of the sun to my eye at sunset?

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #57 on: November 01, 2017, 04:53:49 PM »
We have one. We are showing it to you with the railway tracks. They are in the real world, they appear to converge due to perspective but by getting onto the train and following them we can be sure that this is only due to perspective as they do not converge in reality.

Perspective affects orientation, not position. Perspective changes the orientation of railroad tracks to appear at the level of the eye, and it has oriented them to converge.

Quote
When looking ahead the tracks in the distance still appear to converge in the distance and yet sure enough the train passes the point where they appeared to meet and they have not met. This continues the entire journey. How can this not be considered a real world model?

Perspective is how the world shows itself to us, and is dependant on the observer. From the train's perspective those tracks are not meeting, and so it is able to travel across them easily.

#### Tom Bishop

• Zetetic Council Member
• 10735
• Flat Earth Believer
##### Re: The burden of proof.
« Reply #58 on: November 01, 2017, 04:54:13 PM »
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

May I suggest you go back and actually READ my post?   The pinhole camera demonstrates the geometry - from that we can use similar triangles to turn this into algebra - and then we can try sticking some numbers in there to try to get Hsubject to be zero.   When you do that - the ONLY way to get the sun onto the flat earth horizon is to have Dsubject to be infinity.   This is another way of saying "parallel lines appear to touch at an infinite distance from the eye".  (They don't literally touch no matter how far away you are.)   This is PROOF that the vanishing point is at infinity.
Quote
If they do touch at some distance, then your diagram will look a whole lot different. The fundamental premise of this continuous universe model needs empirical evidence behind it -- things to suggest that is how it is in the real world. It is only backed by math which assumes a hypothetical model, and this is wholly insufficient.
But they don't touch at any finite distance...and they don't literally touch in the real world at all...only in images that are focussed.

There is nothing of the "continuous universe" in here - it's simple grade-school geometry and algebra.

But if you're now denying that mathematics can address the real world - then you have truly entered a world where only magic applies.  Perhaps this is a good place for you to exist - beyond the realms of reality where logic and reason cannot assail you.

Most of us would call that "insanity"...but if that's your choice, then maybe we shouldn't be listening to your ravings any longer.

Math does not prove the nature of perspective lines. That math is only valid if certain assumptions made about that underlying model are true.You are using math under a model which assumes that the perspective lines are continuous.

See my post about how 2 + 2 does not always equal 4:

Quote from: Tom Bishop
What you have is MATH. What I have is empirical observation. Your math only works under the model it is intended for. If the assumptions of the underlying model changes, or is wrong, the math does not work.

2 + 2 = 4 relies on the underlying model, and is not a universal truth. Under some models 2 + 2 does not equal 4. See Two Plus Two Equals Four, But Not Always.

All math relies on the underlying model for it to have truth. You need to prove that your underlying model for perspective lines is valid. That is your claim. You are the claimant. I am the skeptic. I am not going to prove a negative. You need to prove your positive. My position on this subject is backed by empirical observation, while yours relies on ancient hypothetical models. So get proving already. Demonstrate that your perspective model is founded in the real world.

#### Curious Squirrel

• 1337
##### Re: The burden of proof.
« Reply #59 on: November 01, 2017, 05:17:53 PM »
Quote from: xenotolerance
Tom likes to say that Euclid's ideas are hypothetical: They are not.

Where is the real world evidence for these infinitely-approaching perspective lines, then?
'Perspective lines' is an art phrase Tom. They appear to approach until the resolving power of whatever you're using can no longer tell the difference. Which I showed you in the other thread we can predict when/where that happens using math. I even provided the proof using your favorite railroad track example.

Tom,

The fundamental issue that you seem to not understand, is Euclidean geometry doesn't have anything to do with perspective. Euclidean geometry describes where something is. We can use that geometry along with a location to even determine where and when things will happen according to perspective and the angular limit of the eye. As I showed you in the other thread. But what perspective doesn't do is change the physical angle of objects.

Perspective changes the orientation angle of railroad tracks below your feet and brings them up to the level of your eye. It has caused the railroad tracks to be at the level of your eye when the railroad tracks are only a couple of inches from the ground: A clear example of change of orientation.
Still hasn't changed the actual location of those objects has it? So I'm not sure what you could possibly be arguing for here.

Quote from: Curious Squirrel
Quote
And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

This is a strawman. Euclidean geometry says nothing of the sort. It says parallel lines will never meet. Which they won't, or they wouldn't be parallel. It doesn't deal with your 'perspective lines' at all. It describes the location of something relative to another thing, and it's testably accurate at ANY distance you care to name that is physically measurable.

We see that railroad tracks meet at the horizon. What kind of real world evidence do you have to suggest otherwise?
I've already shown you how the math bares out that railroad tracks will 'appear' to meet roughly at the horizon. So you're attacking something I'm not claiming here at all.

Quote
Your parallel lines will never touch though. They will seem to touch because of the angular limit of the eye

Do you have any evidence for that? The railroad tracks also meet in a wide angle lens, or even with lens-less cameras.
Yes, and they will do so for the same reason with a camera as for an eye. Geometry can tell us when the angle reaches the point that the device can no longer distinguish between the two of them. As I showed you before.

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Once again, if you wish to say the sun appears to be at 0 degrees, when the math says it's at 20 degrees then you must present one of the following:
A) Proof that the math no longer works accurately beyond 'X' Miles/KM.
B) Proof that the math doesn't work in the real world, contrary to the proofs done upon it since Euclids time.
C) Evidence that the sun is somehow 'special' and immune to this mathematical law.

What you have is MATH. What I have is empirical observation. Your math only works under the model it is intended for. If the assumptions of the underlying model changes, or is wrong, the math does not work.

2 + 2 = 4 relies on the underlying model, and is not a universal truth. Under some models 2 + 2 does not equal 4. See Two Plus Two Equals Four, But Not Always.

All math relies on the underlying model for it to have truth. You need to prove that your underlying model for perspective lines is valid. That is your claim. You are the claimant. I am the skeptic. I am not going to prove a negative. You need to prove your positive. My position on this subject is backed by empirical observation, while yours relies on ancient hypothetical models. So get proving already. Demonstrate that your perspective model is founded in the real world.
The math bears out the real world observations, every time the distance is measurable. I showed you that with the railroad tracks, that the math predicted they will appear to meet to the eye, at the point they are observed to do so. You're the one claiming it doesn't. Give me an example, and I can test the math against it to show you it works once again if you wish.

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BTW, this is another strawman, just in case you didn't get that above. Perspective lines have no part in Euclidean geometry. Parallel lines will never meet. They will appear to 'meet' at the point which our eyes can no longer distinguish the angular distance between them. Roughly 0.02 degrees. Now clearly things can get in the way, but you need to explain how a sun that should still be 20 degrees above the horizon, is appearing at 0 degrees.

Wrong. You need to explain why we need to assume that perspective lines will never meet when this has never been observed.
I've never, ever said 'perspective lines' will never meet. I've said parallel lines will never physically meet (true) but they can appear to meet due to perspective. Note how perspective lines are never mentioned. Stop strawmanning. What you are saying here is utter nonsense, because it claims that two parallel lines will physically meet at the point observed. Which you and I both know doesn't happen (we both do, don't we?) so stop conflating your imaginary 'perspective lines' with parallel lines. They are not the same meaning.

Once again, geometry can tell us where something is physically located, in relation to another thing. That's all it does. We then need to bring in focal length, and angular limit, and other things to determine if that object can be properly seen. The math is backed up every time it's used in reality. If you have an example where it doesn't, present it. But at the moment you have a sun 20 degrees above the horizontal.

Thought experiment on this. If I took an object, set it 20 feet away from you and 10 feet up, could you still see it? How about 200 feet away and 100 feet up? Where does this stop working? Why? How do you know? Because what you are presently claiming is at some point that distance ration will produce an object appearing to touch the ground. Prove it.

And where is the evidence that the perspective lines will approach each other forever and never touch, as hypothesized by Euclid?

May I suggest you go back and actually READ my post?   The pinhole camera demonstrates the geometry - from that we can use similar triangles to turn this into algebra - and then we can try sticking some numbers in there to try to get Hsubject to be zero.   When you do that - the ONLY way to get the sun onto the flat earth horizon is to have Dsubject to be infinity.   This is another way of saying "parallel lines appear to touch at an infinite distance from the eye".  (They don't literally touch no matter how far away you are.)   This is PROOF that the vanishing point is at infinity.
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If they do touch at some distance, then your diagram will look a whole lot different. The fundamental premise of this continuous universe model needs empirical evidence behind it -- things to suggest that is how it is in the real world. It is only backed by math which assumes a hypothetical model, and this is wholly insufficient.
But they don't touch at any finite distance...and they don't literally touch in the real world at all...only in images that are focussed.

There is nothing of the "continuous universe" in here - it's simple grade-school geometry and algebra.

But if you're now denying that mathematics can address the real world - then you have truly entered a world where only magic applies.  Perhaps this is a good place for you to exist - beyond the realms of reality where logic and reason cannot assail you.

Most of us would call that "insanity"...but if that's your choice, then maybe we shouldn't be listening to your ravings any longer.

Math does not prove the nature of perspective lines. That math is only valid if certain assumptions made about that underlying model are true.You are using math under a model which assumes that the perspective lines are continuous.
Yes, the model assumes the lines will never physically touch in the real world. And if we have infinite resolving power, we would see that. We don't, so we must take the limits of the human eye into account. These match up with real world observations EVERY TIME. As I showed you with the railroad tracks. So please, show an example that the math (taking into account the resolution limits of the lens in use) does NOT match what is seen. I dare you. (Reminder: Neither the sun nor the moon, nor anything that goes through the sky can be used as an example, for doing so is you begging the question. NOTHING that relies on the Earth being flat to be a proof is admissible.)