#### hexagon

• 192
##### Re: On a globe Earth the horizon should not curve
« Reply #100 on: April 18, 2018, 03:23:27 PM »
The core problem in EnaG regarding everything related to perspective, vanishing point, horizon and so on, is that the author did not understood the problem of optical resolution. He describes at some point in the book the effect, that he could no longer see the black boots of some soldiers in the distance, but he could recover them by using a telescope. Form him this is the key to the sinking ship effect. But in reality he suffered from the limited optical resolution of his eyes, at a certain distance he could simply not distinguish the boots from the dark street, while the brighter clothes of the soldiers were still visible. And of course a telescope increases the optical resolution and recovered the boots.

From the distance between the soldiers to him and his eye height he calculated an angle, which, no wonder, is roughly the angle of optical resolution. But he uses this angle now to calculate the distance to the vanishing point. And from this false conclusion everything else followed. The restoring effect of the telescope, the shift of the vanishing point depending on the height of the observer, the behavior of the so-called perspective lines, the increasing horizon and so on...

All explanations are twisted to fit to this false initial conclusion of a very simple observation.

#### HorstFue

##### Re: On a globe Earth the horizon should not curve
« Reply #101 on: April 18, 2018, 09:30:25 PM »
The core problem in EnaG regarding everything related to perspective, vanishing point, horizon and so on, is that the author did not understood the problem of optical resolution.

For me it's more like, he did not understand perspective. Especially the issue, that parallel lines from real world, would not only intersect at the vanishing point, no, they terminate in the vanishing point. Infinity from real world is in the vanishing point.
As he could not understand the reason for, that infinite long lines (real world) would terminate (in projection) at the vanishing point, he mixed in "optical resolution", to solve his problem.

Mathematically spoken, the vanishing point is a singularity, the point of a function, where you cannot give a reasonable result. In this case it's: f=1/atan(a), there's no value for a=0;
An observer looking over a flat plane would have a line of sight - the line which hits the horizon/vanishing point, that is parallel to the surface. Now building the projection of a line on the surface (easiest, that line that goes through the feet of the observer), the projection lines will hit the surface at an distance given by f=1/atan(a) (hyperbolic), where 'a' is the angle between the line of sight of the observer and the projection line. 'a' corresponds with the distances on the projected line.
As 'a' gets smaller, you find that the nearer you get to the line of sight/horizon line, the larger the distances get, that are covered by a small change of 'a' (delta a). Which ends with a huge distance of real world surface squeezed into the last little section of the projected line near the vanishing point. (s. Att.)

So there's no reason to apply eye resolution to have a vanishing point. Also the issue, when the observer is placed higher, there's no need to move the vanishing point, it's already the projection of "infinity". The angles of the perspective lines are widened and thus the distances on the projected line.
The eye resolution issue, is an independent one, does not change the vanishing point.
You could explain part of this effect, where hulls of ships are vanishing due to eye resolution, with eye resolution alone...

#### Macarios

##### Re: On a globe Earth the horizon should not curve
« Reply #102 on: April 18, 2018, 10:35:49 PM »
He describes at some point in the book the effect, that he could no longer see the black boots of some soldiers in the distance, but he could recover them by using a telescope. Form him this is the key to the sinking ship effect.

He "hides under the carpet" the fact that at the same distance he also wouldn't distinguish the hat of the same soldier, and especially his gloves.

#### HorstFue

##### Re: On a globe Earth the horizon should not curve
« Reply #103 on: April 18, 2018, 11:14:28 PM »
He describes at some point in the book the effect, that he could no longer see the black boots of some soldiers in the distance, but he could recover them by using a telescope. Form him this is the key to the sinking ship effect.
He "hides under the carpet" the fact that at the same distance he also wouldn't distinguish the hat of the same soldier, and especially his gloves.
Depends, size is not the only thing that matters. There's also contrast. High contrast objects could be "noticed", even if the viewing angle is below max. resolution. Else we would not see stars in the night sky or far away lighthouses.

#### hexagon

• 192
##### Re: On a globe Earth the horizon should not curve
« Reply #104 on: April 19, 2018, 08:06:46 AM »
Resolution without contrast is not possible. The image of a single point is given by the so-called point spread function of the optical system, which is basically a 2D Bessel function. The central peak of the Bessel function defines the size of the Airy disc.

Two points of equal brightness and color can be resolved if the centers of their Airy discs are about one diameter of the Airy disc apart. Which means there is a dip in intensity in between the centers of the Airy discs of about 50%.

Without this contrast you can't resolve anything. Of course, you also need a certain amount of intensity. That's the reason why a light source on a black background can be seen from further away than a black point on a bright background.

The consequences of this effect on the human perception are more or less described in a correct way in EnaG, but the author draws the completely wrong conclusions out of this regarding perspective and vanishing point. As mentioned above, everything else is just a consequence of this false interpretation.

It seems that at some point the author went to the see and observed that the reconstruction of an object with a telescope as it worked on the street did not work for a ship at the sea much further away and to save his false interpretation he introduced the effect of waves, which he vastly exaggerated.

In the end it is quit easy to understand EnaG and the ideas presented in that book. The bare observations are more or less correct, but because of a lack of background knowledge he draws completely wrong conclusions.

#### AllAroundTheWorld

• 3113
##### Re: On a globe Earth the horizon should not curve
« Reply #105 on: April 19, 2018, 08:38:01 AM »
For me it's more like, he did not understand perspective. Especially the issue, that parallel lines from real world, would not only intersect at the vanishing point, no, they terminate in the vanishing point. Infinity from real world is in the vanishing point.
As he could not understand the reason for, that infinite long lines (real world) would terminate (in projection) at the vanishing point, he mixed in "optical resolution", to solve his problem.
I don't know if it's that he didn't understand it or that he started with the premise of a flat earth and constructed a version of perspective that would work with that premise. It doesn't actually work of course. The idea that "waves" and "vanishing point" explains perspective is very silly. If you were at any altitude you'd be able to see over any waves so there's no way the sun could be sinking behind them. I might start a thread about sunset at altitude to see if there is any flat earth explanation.
If you are making your claim without evidence then we can discard it without evidence.

Nearly all flat earthers agree the earth is not a globe.

#### hexagon

• 192
##### Re: On a globe Earth the horizon should not curve
« Reply #106 on: April 19, 2018, 10:58:47 AM »
Hm, it's not that simple. Take for example the vanishing point. Of course, if you take the geometric definition this point is at infinity. But it this also always a practical definition? If you want to do a landscape painting or a CGI graphics where would you put the vanishing point? You would put it at a finite distance. The same if you take a photograph, let's say of a long and narrow street. Parallel lines would meet at one point at finite distance at the horizon, which is at your eye height. And so on...

The observations in EnaG are not that wrong and the models proposed are valid to describe this observations up to a certain degree. The question is more where is the limit? And from which point on you have to introduce more and more assumptions that are in contradiction to other aspects of your model.

To explain the sinking ship effect, he introduced the effect of waves. And yes, a tiny boat in a stormy sea can vanish behind waves. So far, this observation is not wrong. And of course, how strong this effect is, has something to do with distances and perspective. But it has it's limitations. You can not explain that a huge ship on calm sea is sinking behind the horizon, that simply does not work. Therefor, waves don't give you a consistent explanation for all observations in all situations. That's a problem.

And if you want to explain sunset/sunrise, you have to make even more assumptions like discontinuities in Euclidean geometry and so on.

You have to be aware of the limits of your model, if you want to be taken serious. But if you stay inside this limitations any model is fine.

#### Ballboy

• 5
##### Re: On a globe Earth the horizon should not curve
« Reply #107 on: April 20, 2018, 05:45:47 AM »

Am I being thick? Surely if you’re standing on a small island looking at the horizon all around you, you cannot tell whether you are standing on a ball or a plate. The horizon forms a sharply-defined circle all around you, 5 miles away. Because it’s 5 miles away it looks like a horizontal edge, whether it’s a large ball or a large plate.

The one way to find out whether it’s a ball or a plate is to step onto on a chair or go up a hill. If the plate stays the same size then you are on a 10 mile diameter plate.

But if the horizon recedes with elevation, what other conclusion can there be but that this plate must be domed or ball-shaped?

I must be lacking in my logical facilities not to be able to conceive of any other explanation - can someone help me understand how that can point to the earth being flat?

Oh and I read earlier someone saying the horizon rises to eye level. What does this mean? That the earth is actually concave? Or that when you look directly down at the horizon from a height then, well, you are looking directly at it so it meets your eye level? Or that it physically moves? Surely anything you look at meets your eye level, whether you have to look up at it or down at it? I just can’t grasp these concepts.

#### hexagon

• 192
##### Re: On a globe Earth the horizon should not curve
« Reply #108 on: April 20, 2018, 07:27:37 AM »
Our visual perception is the result of a one-point projection of a 3D environment onto a 2D plane. In the same way as photography works.

If you look on a picture with lots of virtual lines going straight away from parallel to the optical axis of the camera, you will notice that all this line below the optical axis (which is at the center of your image) will point upwards, all lines below will point downwards, all lines left will point right and all lines right will point left.

And all lines close to the optical axis will finally seem to meet at one point, the so-called vanishing point. Mathematically this point lies in infinite distance from the observer, but that's not what you observe. Lines too far away from the optical axis will not meet at the vanishing point. But all of this lines and their symmetric counterparts below and above the optical axis will meet on one horizontal line. That's the horizon of your image.

If you are sea level this image horizon and the horizon of the earth with the sky are practically identical. You can't resolve the difference. If you climb up, your perception will be more or less the same. Both, the horizon of your image and the real horizon will seem to go up with you. But, with the help of some reference tools or carefully analyzing your picture, you will notice that the real horizon is falling more and more below the image horizon (which is defined by your eye level). And it will become more apparent the higher you climb up.

The real horizon would only stay at eye level if it would be located at infinity, but it's not. And all horizontal in a one-point projection stay below optical axis. But nevertheless, horizontal lines further away appear higher than horizontal lines close to you in a picture. And because the real horizon is already quite far away from you, he appears quite close to the image horizon. And if you climb up the real horizon is even pushed away from you, so in the projection the real horizon also seems to go up. But not as fast as the image horizon.

#### Tumeni

• 1868
##### Re: On a globe Earth the horizon should not curve
« Reply #109 on: April 20, 2018, 08:46:45 AM »
Surely if you’re standing on a small island looking at the horizon all around you, you cannot tell whether you are standing on a ball or a plate. The horizon forms a sharply-defined circle all around you, 5 miles away. Because it’s 5 miles away it looks like a horizontal edge, whether it’s a large ball or a large plate.

The one way to find out whether it’s a ball or a plate is to step onto on a chair or go up a hill. If the plate stays the same size then you are on a 10 mile diameter plate.

To aid visualisation of this, I would add that this 'plate' is, in geometric terminology, a Spherical Cap;

https://en.wikipedia.org/wiki/Spherical_cap

The observer is at the top of height line h, or above it, on a continuation of that line. The higher you go above height line h, the larger the cap will be.  Simple trig tells us how much can be seen from a given height.
« Last Edit: April 20, 2018, 02:20:06 PM by Tumeni »
=============================
Not Flat. Happy to prove this, if you ask me.
=============================

Nearly all flat earthers agree the earth is not a globe.

Nearly?

#### robinofloxley

• 169
##### Re: On a globe Earth the horizon should not curve
« Reply #110 on: April 20, 2018, 01:52:57 PM »

Am I being thick? Surely if you’re standing on a small island looking at the horizon all around you, you cannot tell whether you are standing on a ball or a plate. The horizon forms a sharply-defined circle all around you, 5 miles away. Because it’s 5 miles away it looks like a horizontal edge, whether it’s a large ball or a large plate.

The one way to find out whether it’s a ball or a plate is to step onto on a chair or go up a hill. If the plate stays the same size then you are on a 10 mile diameter plate.

But if the horizon recedes with elevation, what other conclusion can there be but that this plate must be domed or ball-shaped?

I must be lacking in my logical facilities not to be able to conceive of any other explanation - can someone help me understand how that can point to the earth being flat?

Oh and I read earlier someone saying the horizon rises to eye level. What does this mean? That the earth is actually concave? Or that when you look directly down at the horizon from a height then, well, you are looking directly at it so it meets your eye level? Or that it physically moves? Surely anything you look at meets your eye level, whether you have to look up at it or down at it? I just can’t grasp these concepts.

Agree with all of that. I'd also add that since you are standing in the exact centre of a 5 mile radius circle, if you decided to move a mile or so away, the circle would apparently move with you. A bit like one of those old Victorian era dresses that move around the floor with you. That rules out the simple plate idea, but is precisely what you'd expect to see on a sphere. A very simple explanation for what you see. You don't need to complicate this explanation with atmospheric effects, refraction, perspective, lens distortions. As an explanation it works just fine on its own.

#### Ballboy

• 5
##### Re: On a globe Earth the horizon should not curve
« Reply #111 on: April 20, 2018, 05:28:26 PM »
Exactly. I mean it’s odd that those old seafaring dudes thought the earth was flat for so long; after all they used crows’ nests to see further, they must have seen the masts of other ships over the horizon, they must have chased the edge only to see it recede as they approached, they must have seen the tops of mountains lit up by the low sun as it rose or set. At some point all the evidence mounted up and they changed their world view. The earth was a ball, the sun was at the centre, etc.

Why are some people keen on going back to the time before that was made clear?

#### HorstFue

##### Re: On a globe Earth the horizon should not curve
« Reply #112 on: April 20, 2018, 07:46:59 PM »
And all lines close to the optical axis will finally seem to meet at one point, the so-called vanishing point. Mathematically this point lies in infinite distance from the observer, but that's not what you observe. Lines too far away from the optical axis will not meet at the vanishing point. But all of this lines and their symmetric counterparts below and above the optical axis will meet on one horizontal line. That's the horizon of your image.
All parallel lines (unless parallel to the image plane) will meet in one vanishing point, if these lines are long enough. Remember: Infinity is in the vanishing point.
The horizon in your image is the projection of the "optical plane", that goes though observers eye or camera and is parallel to the surface. At "infinity" this plane and the surface converge as described for the lines above. The result is the (projective!) horizon line.

If you are sea level this image horizon and the horizon of the earth with the sky are practically identical. You can't resolve the difference. If you climb up, your perception will be more or less the same. Both, the horizon of your image and the real horizon will seem to go up with you. But, with the help of some reference tools or carefully analyzing your picture, you will notice that the real horizon is falling more and more below the image horizon (which is defined by your eye level). And it will become more apparent the higher you climb up.

The real horizon would only stay at eye level if it would be located at infinity, but it's not. And all horizontal in a one-point projection stay below optical axis. But nevertheless, horizontal lines further away appear higher than horizontal lines close to you in a picture. And because the real horizon is already quite far away from you, he appears quite close to the image horizon. And if you climb up the real horizon is even pushed away from you, so in the projection the real horizon also seems to go up. But not as fast as the image horizon.
Yes, I agree.
Trying to describe it a bit different: Assuming an infinite plane or surface, this surface will meet the "optical plane" as described above at the projective horizon. By definition, the "optical plane" includes the observers point, eye or camera, so this horizon is always at "eye level".
But on a sphere, the surface of the sphere will "bend" away/down from the assumed infinite plane and define a new real horizon due to the curvature, at a finite distance, below the assumed infinite plane. So projective horizon and horizon built by curvature are not identical. But - I agree again - these two horizon lines are close together, so that without a reference and a precise measure no one would notice it.
« Last Edit: April 20, 2018, 08:44:15 PM by HorstFue »