[Rama Set]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

And where is the Earth in your diagram? The elephants appear to be flying.

[Tom Bishop]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

[Tom Bishop]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

And where is the Earth in your diagram? The elephants appear to be flying.

The elephants are on their own perspective lines in relation to the observer, which causes them to shrink into the horizon abyss at a slightly slower pace. Go back to the high plane/low plane analogy. Multiple vanishing points, height dependant, all meeting at the horizon.

As to what their perspective lines would look like, they would look very similar to the perspective lines drawn for the dime, except with a slightly more acute angle.

As per the flat ground, the ground has its own perspective lines that are independent of even the dime, intersecting with eye level slightly to the left of it, and is unillustrated. What is seen are perspective lines of the dime.

[Rayzor]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

The reason the horizon appears to rise to eye level is that we can't perceive the curvature between ourselves and the horizon,  just as we can't perceive the curvature of the horizon in the left/right direction,   you don't perceive the horizon to be lower until you get to the altitude where the left/right curvature starts to become visible.   

So,  at low altitudes where "the horizon rises to eye level"   there will be some point where the dime can be placed to obscure anything you like,  the question that is harder to answer is where that position is,   It can't be the vanishing point,  since the dime itself would vanish,  it can't be at ground level for any reasonable distance, since the sight line to the vanishing point would be over the top of the dime.   It would have to be close and positioned about eye level to obscure the distant elephant.   No question that  distant objects can be obscured by higher objects in the foreground,  the question is does the geometry make sense.   A better diagram might help.

[markjo]

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

So, how far is it from the observer to the dime that's on the horizon and how far beyond the horizon are the elephants?

[Tom Bishop]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

The reason the horizon appears to rise to eye level is that we can't perceive the curvature between ourselves and the horizon,  just as we can't perceive the curvature of the horizon in the left/right direction,   you don't perceive the horizon to be lower until you get to the altitude where the left/right curvature starts to become visible.   

So,  at low altitudes where "the horizon rises to eye level"   there will be some point where the dime can be placed to obscure anything you like,  the question that is harder to answer is where that position is,   It can't be the vanishing point,  since the dime itself would vanish,  it can't be at ground level for any reasonable distance, since the sight line to the vanishing point would be over the top of the dime.   It would have to be close and positioned about eye level to obscure the distant elephant.   No question that  distant objects can be obscured by higher objects in the foreground,  the question is does the geometry make sense.   A better diagram might help.

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds. However, emperically, the dime is still there to block light rays and cast "shadows" behind it, as I have described, regardless if you can readily see it or not.

[Rayzor]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

The reason the horizon appears to rise to eye level is that we can't perceive the curvature between ourselves and the horizon,  just as we can't perceive the curvature of the horizon in the left/right direction,   you don't perceive the horizon to be lower until you get to the altitude where the left/right curvature starts to become visible.   

So,  at low altitudes where "the horizon rises to eye level"   there will be some point where the dime can be placed to obscure anything you like,  the question that is harder to answer is where that position is,   It can't be the vanishing point,  since the dime itself would vanish,  it can't be at ground level for any reasonable distance, since the sight line to the vanishing point would be over the top of the dime.   It would have to be close and positioned about eye level to obscure the distant elephant.   No question that  distant objects can be obscured by higher objects in the foreground,  the question is does the geometry make sense.   A better diagram might help.

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds. However, emperically, the dime is still there to block light rays and cast "shadows" behind it, as I have described, regardless if you can readily see it or not.

Ok  so everything vanishes,  and the dime can in fact obscure the elephant,  provided the elephant as close to vanishing already,   what happens when I look through a telescope,  I'm no longer limited to 1 arc second minute.   Are the elephants still hidden?
 

[Rama Set]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

On a FE the earth does not literally rise to meet your eyes. I am interested in the actual physical relationships that cause your alleged phenomena.

[Tom Bishop]

Ok  so everything vanishes,  and the dime can in fact obscure the elephant,  provided the elephant as close to vanishing already,   what happens when I look through a telescope,  I'm no longer limited to 1 arc second minute.   Are the elephants still hidden?

It depends. Looking through a telescope will change your perspective lines and create new vanishing points.

In Earth Not a Globe Rowbotham was able to look into a telescope across lakes and reverse the sinking effect. When done on the ocean the sinking effect was unable to be reversed, presumably because the disturbances on the surface whete the new vanishing point lay were still too great for the telescope to overcome.

[Rayzor]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

On a FE the earth does not literally rise to meet your eyes. I am interested in the actual physical relationships that cause your alleged phenomena.

This is the way I interpret the effect.
If you imagine you are walking up a hill,  the horizon as you look towards the top of the hill is clearly above you,   as you crest the top of the hill the horizon clearly falls away and is lower than you.   Now consider what happens on the globe.   There is no perception that the horizon is lower than you,  and as you climb higher that doesn't really change,  so the "horizon rises to eye level"   keep going higher and as you get to 100,000 ft or more the left-right  curvature starts to become obvious and the horizon starts to look clearly lower than you.  Keep going to the ISS and the curvature is clear, and the horizon is way below you.

At least that's my interpretation.  it's our inability to detect curvature in the line between ourselves and the horizon.

[Rama Set]

Then you should be able to present a scale diagram that shows a dime standing on its edge on the ground obscuring an elephant but still has light traveling in a straight line. Would you do that for me?

This is not to scale, but it would look something like this:

The dime is at the horizon line, and therefore at eye level with the observer

So you put the dime at the vanishing point?  Why would you do that?

The plane below us rises upwards to meet the level of our eyes. Anything you see on the horizon line is at our eye level, and consequently, anything peeking up over the horizon, even imperceptibly, is above the level of our eyes.

It follows therefore, that any imperfections on the earth's surface, above that geometric plane at the horizon line, no matter how slight, would create an area for bodies to shrink and disappear behind.

On a FE the earth does not literally rise to meet your eyes. I am interested in the actual physical relationships that cause your alleged phenomena.

This is the way I interpret the effect.
If you imagine you are walking up a hill,  the horizon as you look towards the top of the hill is clearly above you,   as you crest the top of the hill the horizon clearly falls away and is lower than you.   Now consider what happens on the globe.   There is no perception that the horizon is lower than you,  and as you climb higher that doesn't really change,  so the "horizon rises to eye level"   keep going higher and as you get to 100,000 ft or more the left-right  curvature starts to become obvious and the horizon starts to look clearly lower than you.  Keep going to the ISS and the curvature is clear, and the horizon is way below you.

At least that's my interpretation.  it's our inability to detect curvature in the line between ourselves and the horizon.

But it is still just a trick of the eye. Tom needs to show the path of the light rays on a FE and how they can result in the effect he is describing. I sincerely doubt it is possible unless you start positing light that curves independently of refractive effects.

[markjo]

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds.

Oh, so then the dime isn't necessarily on the horizon or at eye level?  Thanks for clearing that up.

[Tom Bishop]

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds.

Oh, so then the dime isn't necessarily on the horizon or at eye level?  Thanks for clearing that up.

How does that follow from what you quoted?

[Tom Bishop]

But it is still just a trick of the eye. Tom needs to show the path of the light rays on a FE and how they can result in the effect he is describing. I sincerely doubt it is possible unless you start positing light that curves independently of refractive effects.

How is light curving when you hold a dime up to your eye and block out an elephant?

What I described is exactly the same, except it is perspective bringing the dime up to your eye instead of your arm, and it's happening further away.

[markjo]

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds.

Oh, so then the dime isn't necessarily on the horizon or at eye level?  Thanks for clearing that up.

How does that follow from what you quoted?

Well, on the one hand, the perspective vanishing point is always on the horizon which is always very far away.  On the other hand, small things can become too small to see (vanish) long before they reach the horizon.  The dime could reach its vanishing point at a few hundred feet while the vanishing point on the horizon is several miles away.

[Tom Bishop]

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds.

Oh, so then the dime isn't necessarily on the horizon or at eye level?  Thanks for clearing that up.

How does that follow from what you quoted?

Well, on the one hand, the perspective vanishing point is always on the horizon which is always very far away.  On the other hand, small things can become too small to see (vanish) long before they reach the horizon.

Regardless if you can see it clearly, it's still going to obscure light rays from the elephant. It is a physical obstruction.

[Rama Set]

But it is still just a trick of the eye. Tom needs to show the path of the light rays on a FE and how they can result in the effect he is describing. I sincerely doubt it is possible unless you start positing light that curves independently of refractive effects.

How is light curving when you hold a dime up to your eye and block out an elephant?

What I described is exactly the same, except it is perspective bringing the dime up to your eye instead of your arm, and it's happening further away.

I understand your position and requested you show the path of the light rays which make a plane appear to be a hill. Please let me know if you are having difficulty with understanding my request.

[markjo]

The dime vanishes at the vanishing point only in so much that you cannot easily see it, as it is beyond the resolution of the eye, which Rowbotham estimates to be at about one 60th of a degree in arc seconds.

Oh, so then the dime isn't necessarily on the horizon or at eye level?  Thanks for clearing that up.

How does that follow from what you quoted?

Well, on the one hand, the perspective vanishing point is always on the horizon which is always very far away.  On the other hand, small things can become too small to see (vanish) long before they reach the horizon.

Regardless if you can see it clearly, it's still going to obscure light rays from the elephant. It is a physical obstruction.

How can the dime obstruct your view of the elephant if the dime is too small to see and below your eye level?

[Tom Bishop]

But it is still just a trick of the eye. Tom needs to show the path of the light rays on a FE and how they can result in the effect he is describing. I sincerely doubt it is possible unless you start positing light that curves independently of refractive effects.

How is light curving when you hold a dime up to your eye and block out an elephant?

What I described is exactly the same, except it is perspective bringing the dime up to your eye instead of your arm, and it's happening further away.

I understand your position and requested you show the path of the light rays which make a plane appear to be a hill. Please let me know if you are having difficulty with understanding my request.

Imagine a light diagram of someone holding out a dime with their hand to obscure an elephant. Where does the light go and how does a small thing obscure a large thing?That is basically what would be drawn.

How can the dime obstruct your view of the elephant if the dime is too small to see and below your eye level?

For the first point, the dime may be too small to see, but it is still going to block light rays. Consider a tower on the horizon. Although the bricks which make up the tower are too small to see, they are still each undeniably blocking the light of the things behind it.

For the second point, perspective places things at the horizon on your eye level.

Consider: Imagine we are on a very large dirt plane. We are 5 feet 10 inches tall. We look directly 90 degrees ahead at the horizon and see a dirt line. How can we see dirt at our eye level if we know that the dirt is 5 feet 10 inches below us?

From Chapter 5 of The Perspective Handbook by Joseph D'Amelio we read:

Anyone who has ever been to the seaside will have seen a horizon (as long as it wasn't foggy). This is the line you see far away, out to sea. It's the line where the water stops and the sky starts. There are horizon lines everywhere, but usually you don't see them because something like a hill or a tree or a house is in the way.

You always see the horizon line at your eye level. In fact, if you change your eye level (by standing up, or sitting down) the horizon line changes too, and follows your eye level. Your eye level always follows you around everywhere because it's your eye level. If you sit on the floor the horizon is at your eye level. If you stand up, it's at your eye level. If you stand on top of a very tall building, or look out of the window of an aeroplane, the horizon is still at your eye level.

It's only everything else that appears to change in relation to your eye level. The fact is, that everything looks the way it does from your point of view because you see it in relation to yourself. So if you are sitting looking out of the window of an airliner everything is going to look shorter than you because at this moment you are taller (or higher) than everything else.

In an editorial from the London Journal, July 18, 1857, one journalist describes the following from a hot-air balloon ascent:

The chief peculiarity of the view from a balloon at a considerable elevation was the altitude of the horizon, which remained practically on a level with the eye at an elevation of two miles, causing the surface of the earth to appear concave instead of convex, and to recede during the rapid ascent, whilst the horizon and the balloon seemed to be stationary.

During the rapid ascent in the balloon the author saw new and distant lands reveal themselves from the stationary horizon. His perspective lines were constantly changing, revealing additional lands, while the horizon line remained stationary at eye level.

It could be argued that this should not have happened if the earth were a globe. The horizon should have been seen to drop rather than remain stationary.

If you believe that the horizon is below eye level, that will need to be demonstrated, as experience in nature suggests otherwise.

[markjo]

How can the dime obstruct your view of the elephant if the dime is too small to see and below your eye level?

For the first point, the dime may be too small to see, but it is still going to block light rays. Consider a tower on the horizon. Although the bricks which make up the tower are too small to see, they are still each undeniably blocking the light of the things behind it.

Yes, but we're talking about a dime blocking an elephant.  Let's please stick with one bad example at a time.

For the second point, perspective places things at the horizon on your eye level.

Consider: Imagine we are on a very large dirt plane. We are 5 feet 10 inches tall. We look directly 90 degrees ahead at the horizon and see a dirt line. How can we see dirt at our eye level if we know that the dirt is 5 feet 10 inches below us?

The horizon and eye level can be quite subjective.  For example, I live in a river valley with hills all around me.  I have to raise my eye level well above horizontal to see the horizon at the top of a near by hill.

During the rapid ascent in the balloon the author saw new and distant lands reveal themselves from the stationary horizon. His perspective lines were constantly changing, revealing additional lands, while the horizon line remained stationary at eye level.

It could be argued that this should not have happened if the earth were a globe. The horizon should have been seen to drop rather than remain stationary.

Only if you don't understand how your eye is drawn to the horizon (whether it be above or below horizontal) rather than the other way around.

If you believe that the horizon is below eye level, that will need to be demonstrated, as experience in nature suggests otherwise.

Take a bubble level to the beach some time and use it to see if the horizon is exactly horizontal.  Or try a theodolite app for your phone.
http://downloads.tomsguide.com/Theodolite-Droid,0301-55333.html