[Adrenoch]

I honestly don't care whether anyone believes the Earth is flat or globular, but at least get the science right.

From the wiki:

Although the sun is at all times above the earth's surface, it appears in the morning to ascend from the north-east to the noonday position, and thence to descend and disappear, or set, in the north-west. This phenomenon arises from the operation of a simple and everywhere visible law of perspective. A flock of birds, when passing over a flat or marshy country, always appears to descend is it recedes; and if the flock is extensive, the first bird appears lower or nearer to the horizon than the last, although they are at the same actual altitude above the earth immediately beneath them. When a plane flies away from an observer, without increasing or decreasing its altitude, it appears to gradually approach the horizon. In a long row of lamps, the second, supposing the observer to stand at the beginning of the series, will appear lower than the first; the third lower than the second; and so on to the end of the row; the farthest away always appearing the lowest, although each one has the same altitude; and if such a straight line of lamps could be continued far enough, the lights would at length descend, apparently, to the horizon, or to a level with the eye of the observer.

This is entirely correct. 100%. So far so good.

This explains how the sun descends into the horizon as it recedes.

Just to be clear, the preceding does not explain how the sun descends into the horizon. It describes how any given point descends into the horizon, and the Sun is made of obviously a lot of points, but the distinction is critical because it purposely gets blurred later on to suggest perspective accounts for the image of the sun setting.

Once the lower part of the Sun meets the horizon line, however, it will intersect with the vanishing point and become lost to human perception

Yes! That is correct! But here's where that distinction is blurred. If this is all due to the Sun receding, then once the lower part of the Sun meets the horizon, the upper part of the Sun must also meet the horizon. For an object to actually hit the infinite perspective point, it must be infinitely far away. Every point of that object will have converged at the perspective point, and it will be invisible. It's why objects get smaller as they get farther away. You can't have the bottom half of an object infinitely far away and the top half the same size as it was when it was overhead. Perspective doesn't work that way.

as the sun's increasingly shallow path creates a tangent beyond the resolution of the human eye. The vanishing point is created when the perspective lines are angled less than one minute of a degree. Hence, this effectively places the vanishing point a finite distance away from the observer.

Sure. Since the human eye has limits, we can't see something when it becomes extremely small. But the size of an object doesn't have anything to do with where the vanishing point of perspective is. Let's say you have two geese flying next to each other, maybe 100 feet apart. As they fly away from you, not only are they getting apparently smaller, but they're getting apparently closer together because their straight lines of flight are following those converging lines of perspective. After say half a mile, just before you lose sight of them, you can see they aren't apparently touching. So in the next second, when you have lost sight of them, did they suddenly zip together and appear to touch? Of course not because they're still following those lines of perspective. The size of an object has nothing to do with where the actual vanishing point of perspective is.

Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer, as so:



However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer as so:

Wait, who said humans can't perceive infinity? The last paragraph said humans can't perceive objects less than one minute of a degree, but whether we can perceive an object or not has nothing to do with where its perspective vanishing point is. That's not the same thing. It's a bit of a moot point because there's nothing an infinite distance away for us to look at, but at least be accurate.

This finite distance to the vanishing point

Have we established there is a finite distance to the vanishing point? We've established that humans can't perceive objects less than one minute of a degree in size. That's not the same thing. After all, a spot on an elephant may have vanished from naked-eye perception at a distance at which the elephant can still be seen. So it's not that perspective is different for the two; just that their size makes one of them imperceptible. (Of course, pull out a telescope and all of a sudden you can see them both again. Meanwhile perspective just stays the same as it always has).

is what allows ships to ascend into horizon and disappear as their hulls intersect with the vanishing point.

This does not follow from the precepts laid out before. Even in Chapter 14, this key point is laid out very poorly. In essence, it says that at a great enough distance, it's hard to tell two things apart. Makes sense. It says a white mark on an object becomes essentially indistinguishable from the ground its resting on at enough of a distance. Right again. But what happens when you pull out your telescope again? You see the white mark just fine. It's no longer indistinguishable from the ground. Likewise, if you see a distant ship with its hull apparently below the water, you should pull out your telescope. If it's on a flat plane and your telescope is strong enough, it will be distinct from the water no matter how far away it is.

Every receding star and celestial body in the night sky likewise disappears after intersecting with the vanishing point.

Absolutely right. If something, even the size of a star, moves a far enough distance away, it will effectively reach the vanishing point and disappear. It will do so by becoming smaller as all of its points "crowd" in to that vanishing point.

Again, I don't care what people believe, but if you're going to have any hope of the scientific world taking you even somewhat seriously, then you can't promote erroneous ideas. At the very least get the science right.

[QED]

I honestly don't care whether anyone believes the Earth is flat or globular, but at least get the science right.

From the wiki:

Although the sun is at all times above the earth's surface, it appears in the morning to ascend from the north-east to the noonday position, and thence to descend and disappear, or set, in the north-west. This phenomenon arises from the operation of a simple and everywhere visible law of perspective. A flock of birds, when passing over a flat or marshy country, always appears to descend is it recedes; and if the flock is extensive, the first bird appears lower or nearer to the horizon than the last, although they are at the same actual altitude above the earth immediately beneath them. When a plane flies away from an observer, without increasing or decreasing its altitude, it appears to gradually approach the horizon. In a long row of lamps, the second, supposing the observer to stand at the beginning of the series, will appear lower than the first; the third lower than the second; and so on to the end of the row; the farthest away always appearing the lowest, although each one has the same altitude; and if such a straight line of lamps could be continued far enough, the lights would at length descend, apparently, to the horizon, or to a level with the eye of the observer.

This is entirely correct. 100%. So far so good.

This explains how the sun descends into the horizon as it recedes.

Just to be clear, the preceding does not explain how the sun descends into the horizon. It describes how any given point descends into the horizon, and the Sun is made of obviously a lot of points, but the distinction is critical because it purposely gets blurred later on to suggest perspective accounts for the image of the sun setting.

Once the lower part of the Sun meets the horizon line, however, it will intersect with the vanishing point and become lost to human perception

Yes! That is correct! But here's where that distinction is blurred. If this is all due to the Sun receding, then once the lower part of the Sun meets the horizon, the upper part of the Sun must also meet the horizon. For an object to actually hit the infinite perspective point, it must be infinitely far away. Every point of that object will have converged at the perspective point, and it will be invisible. It's why objects get smaller as they get farther away. You can't have the bottom half of an object infinitely far away and the top half the same size as it was when it was overhead. Perspective doesn't work that way.

as the sun's increasingly shallow path creates a tangent beyond the resolution of the human eye. The vanishing point is created when the perspective lines are angled less than one minute of a degree. Hence, this effectively places the vanishing point a finite distance away from the observer.

Sure. Since the human eye has limits, we can't see something when it becomes extremely small. But the size of an object doesn't have anything to do with where the vanishing point of perspective is. Let's say you have two geese flying next to each other, maybe 100 feet apart. As they fly away from you, not only are they getting apparently smaller, but they're getting apparently closer together because their straight lines of flight are following those converging lines of perspective. After say half a mile, just before you lose sight of them, you can see they aren't apparently touching. So in the next second, when you have lost sight of them, did they suddenly zip together and appear to touch? Of course not because they're still following those lines of perspective. The size of an object has nothing to do with where the actual vanishing point of perspective is.

Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer, as so:



However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer as so:

Wait, who said humans can't perceive infinity? The last paragraph said humans can't perceive objects less than one minute of a degree, but whether we can perceive an object or not has nothing to do with where its perspective vanishing point is. That's not the same thing. It's a bit of a moot point because there's nothing an infinite distance away for us to look at, but at least be accurate.

This finite distance to the vanishing point

Have we established there is a finite distance to the vanishing point? We've established that humans can't perceive objects less than one minute of a degree in size. That's not the same thing. After all, a spot on an elephant may have vanished from naked-eye perception at a distance at which the elephant can still be seen. So it's not that perspective is different for the two; just that their size makes one of them imperceptible. (Of course, pull out a telescope and all of a sudden you can see them both again. Meanwhile perspective just stays the same as it always has).

is what allows ships to ascend into horizon and disappear as their hulls intersect with the vanishing point.

This does not follow from the precepts laid out before. Even in Chapter 14, this key point is laid out very poorly. In essence, it says that at a great enough distance, it's hard to tell two things apart. Makes sense. It says a white mark on an object becomes essentially indistinguishable from the ground its resting on at enough of a distance. Right again. But what happens when you pull out your telescope again? You see the white mark just fine. It's no longer indistinguishable from the ground. Likewise, if you see a distant ship with its hull apparently below the water, you should pull out your telescope. If it's on a flat plane and your telescope is strong enough, it will be distinct from the water no matter how far away it is.

Every receding star and celestial body in the night sky likewise disappears after intersecting with the vanishing point.

Absolutely right. If something, even the size of a star, moves a far enough distance away, it will effectively reach the vanishing point and disappear. It will do so by becoming smaller as all of its points "crowd" in to that vanishing point.

Again, I don't care what people believe, but if you're going to have any hope of the scientific world taking you even somewhat seriously, then you can't promote erroneous ideas. At the very least get the science right.

The description you have boldly provided only holds in Minkowski space. In general, your arguments will fail. So technically, you haven’t got the science right either. Which is a bit ironic.

[Adrenoch]

The description you have boldly provided only holds in Minkowski space. In general, your arguments will fail. So technically, you haven’t got the science right either. Which is a bit ironic.

Wow! I'm going to need you to explain that one to me. Given that we're talking about distances on on the order of kilometers and nothing approaching relativistic speeds, I can't see how Minkowski space comes into play. But I'm very excited to hear what you have to say.

[QED]

The description you have boldly provided only holds in Minkowski space. In general, your arguments will fail. So technically, you haven’t got the science right either. Which is a bit ironic.

Wow! I'm going to need you to explain that one to me. Given that we're talking about distances on on the order of kilometers and nothing approaching relativistic speeds, I can't see how Minkowski space comes into play. But I'm very excited to hear what you have to say.

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

[Adrenoch]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

[QED]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

Dude, please re-read my previous reply, and then read again what you just wrote. Parallel lines at the equator will meet at the poles. Look at a globe. That is the whole point of longitude lines.

Dramatic is subjective. The curvature of a spherical surface is 2/R^2, which can be derived from Einstein’s field equations. It’s dramatic enough for our purposes here.

[Adrenoch]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

Dude, please re-read my previous reply, and then read again what you just wrote. Parallel lines at the equator will meet at the poles. Look at a globe. That is the whole point of longitude lines.

Dramatic is subjective. The curvature of a spherical surface is 2/R^2, which can be derived from Einstein’s field equations. It’s dramatic enough for our purposes here.

You said "parallel lines in curved spacetime won't stay parallel." I agreed with you.

Lines on a globe have nothing to do with lines of perspective unless that globe is warping spacetime enough to bend it into a similar sphere. The Earth has absolutely nowhere near enough mass to do anything like that.

What other connection are you trying to draw between lines of perspective and lines on a globe?

[QED]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

Dude, please re-read my previous reply, and then read again what you just wrote. Parallel lines at the equator will meet at the poles. Look at a globe. That is the whole point of longitude lines.

Dramatic is subjective. The curvature of a spherical surface is 2/R^2, which can be derived from Einstein’s field equations. It’s dramatic enough for our purposes here.

You said "parallel lines in curved spacetime won't stay parallel." I agreed with you.

Lines on a globe have nothing to do with lines of perspective unless that globe is warping spacetime enough to bend it into a similar sphere. The Earth has absolutely nowhere near enough mass to do anything like that.

What other connection are you trying to draw between lines of perspective and lines on a globe?

The correct one. The surface of the Earth is a curved surface. Two parallel lines, which begin on the equator, will meet at the poles. That’s it. If you and your pal begin at the equator and walk parallel to each other, then you will meet at the poles.

I frankly do not understand why you think this doesn’t apply to perspective.

[some_engineer]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

Dude, please re-read my previous reply, and then read again what you just wrote. Parallel lines at the equator will meet at the poles. Look at a globe. That is the whole point of longitude lines.

Dramatic is subjective. The curvature of a spherical surface is 2/R^2, which can be derived from Einstein’s field equations. It’s dramatic enough for our purposes here.

You said "parallel lines in curved spacetime won't stay parallel." I agreed with you.

Lines on a globe have nothing to do with lines of perspective unless that globe is warping spacetime enough to bend it into a similar sphere. The Earth has absolutely nowhere near enough mass to do anything like that.

What other connection are you trying to draw between lines of perspective and lines on a globe?

The correct one. The surface of the Earth is a curved surface. Two parallel lines, which begin on the equator, will meet at the poles. That’s it. If you and your pal begin at the equator and walk parallel to each other, then you will meet at the poles.

I frankly do not understand why you think this doesn’t apply to perspective.

Because the earth isn't a black hole and we don't life on its event horizon hence light won't be following its curvature people walking on it will.

[QED]

Irrelevant. Objects/events across the surface will, and the light from them will come to our eyes and tell us there is curvature.

You don’t have to live on a black hole to get curvature. You’ve been watching too much Star Trek.

[stack]

Well, nothing has to be relativistic here. Minkowski space is, basically, 4-dimensional Euclidean space. It’s flat! So parallel lines will appear to converge.

I you are in a curved spacetime, then parallel lines will not stay parallel, hence they may not appear to converge in the distance.

Just think of the surface of a globe (I know I know). The lines of longitude are parallel at the equator but meet at the poles. This is because a globe’s surface has curvature.

Make sense?

Ah, I didn't see what angle you were going for there. You're absolutely right that in curved spacetime parallel lines would not stay parallel.

That said, the amount of curvature for Earth's mass/size is infinitesimally small. I don't have the calculations with me, but I'd wager that across a whole flat Earth disk there wouldn't be enough curvature to make two parallel lines starting five feet apart actually converge by the other end of the disk, let alone to account for something the size of the Sun. So unless there's something to suggest such a dramatic curvature, I don't think you can suggest perspective on Earth works any differently than it would in perfectly flat space.

Dude, please re-read my previous reply, and then read again what you just wrote. Parallel lines at the equator will meet at the poles. Look at a globe. That is the whole point of longitude lines.

Dramatic is subjective. The curvature of a spherical surface is 2/R^2, which can be derived from Einstein’s field equations. It’s dramatic enough for our purposes here.

You said "parallel lines in curved spacetime won't stay parallel." I agreed with you.

Lines on a globe have nothing to do with lines of perspective unless that globe is warping spacetime enough to bend it into a similar sphere. The Earth has absolutely nowhere near enough mass to do anything like that.

What other connection are you trying to draw between lines of perspective and lines on a globe?

The correct one. The surface of the Earth is a curved surface. Two parallel lines, which begin on the equator, will meet at the poles. That’s it. If you and your pal begin at the equator and walk parallel to each other, then you will meet at the poles.

I frankly do not understand why you think this doesn’t apply to perspective.

I may have missed something (happens a lot) or am just not getting it (common) why would two parallel lines, which begin on the equator, meet at the poles? Why would they follow longitudinal lines? In the example image, the cricket ball, red line its equator, you and I head upward in a parallel manner following the stitching, we never meet at its pole.

[QED]

Because, if you head due north, then you should hit the North Pole, right? No matter where you start on the equator.

With your cricket ball. If we traveled along the stitches, we would not be traveling due north for long. We mighty start off that way, but would have to correct our headings to maintain the parallel status. If instead we begin side by side, and set a parallel trajectory, then close our eyes and follow that trajectory, we will run into each other.

Same thing in a curved spacetime. Two parallel rays will meet. Of course, they could force themselves to stay a set distance apart. But then they would not be parallel throughout their trajectory.

The confusion with the cricket ball arises because you are viewing a 2D curved surface in 3 dimensions. In 3D it looks parallel, but it’s not in 2D.

This is a great example you’ve found.

[stack]

Because, if you head due north, then you should hit the North Pole, right? No matter where you start on the equator.

With your cricket ball. If we traveled along the stitches, we would not be traveling due north for long. We mighty start off that way, but would have to correct our headings to maintain the parallel status. If instead we begin side by side, and set a parallel trajectory, then close our eyes and follow that trajectory, we will run into each other.

Same thing in a curved spacetime. Two parallel rays will meet. Of course, they could force themselves to stay a set distance apart. But then they would not be parallel throughout their trajectory.

The confusion with the cricket ball arises because you are viewing a 2D curved surface in 3 dimensions. In 3D it looks parallel, but it’s not in 2D.

This is a great example you’ve found.

I guess where I'm confused is that we're not walking due north, we are walking parallel to one another. Our cardinal direction has nothing to do with it. So If we remove the notion of each walking due North, for instance, and just concentrate on walking a straight line next to each other, why would we bump into each other on a 2d plane but not on a sphere?  Lastly, how does this walking in parallel lines translate to perspective via eyeballs?

[QED]

Because, if you head due north, then you should hit the North Pole, right? No matter where you start on the equator.

With your cricket ball. If we traveled along the stitches, we would not be traveling due north for long. We mighty start off that way, but would have to correct our headings to maintain the parallel status. If instead we begin side by side, and set a parallel trajectory, then close our eyes and follow that trajectory, we will run into each other.

Same thing in a curved spacetime. Two parallel rays will meet. Of course, they could force themselves to stay a set distance apart. But then they would not be parallel throughout their trajectory.

The confusion with the cricket ball arises because you are viewing a 2D curved surface in 3 dimensions. In 3D it looks parallel, but it’s not in 2D.

This is a great example you’ve found.

I guess where I'm confused is that we're not walking due north, we are walking parallel to one another. Our cardinal direction has nothing to do with it. So If we remove the notion of each walking due North, for instance, and just concentrate on walking a straight line next to each other, why would we bump into each other on a 2d plane but not on a sphere?  Lastly, how does this walking in parallel lines translate to perspective via eyeballs?

We would bump into each other on a sphere, that’s what I’m saying. We walk in a straight line, but the geometry we are walking through curves. Look, draw two straight lines on a globe, now peel the surface off and lay it out flat. The lines are not straight anymore. Vice Versa: start with a sheet of paper, then curve it over a globe.

This is one way you can identify curved geometries. Another example: the sides of a cylinder are not a curved surface. To verify this just draw two straight lines and curve it into a soup can label. They still straight yo!

If you take the surface of your cricket ball, peel it off, and flatten it out, you will see that those lines are not parallel on the 2D surface, they only appear as such when viewed from a 3D perspective.

What does this have to do with eyeballs? Light from objects hit them, and we form an image. If our line of sight is through a curved geometry, then it is not easy to interpret what is happening.

This should be obvious by now, since absolutely no one is talking about it correctly. I’m trying to guide things in the right direction by asking loaded/leading questions, but emotions cloud the conversations and entrenchment occurs. Sooner or later, some folks are just going to have to study the shit formally. I can’t perform miracles.

Hope this helps.

[stack]

Because, if you head due north, then you should hit the North Pole, right? No matter where you start on the equator.

With your cricket ball. If we traveled along the stitches, we would not be traveling due north for long. We mighty start off that way, but would have to correct our headings to maintain the parallel status. If instead we begin side by side, and set a parallel trajectory, then close our eyes and follow that trajectory, we will run into each other.

Same thing in a curved spacetime. Two parallel rays will meet. Of course, they could force themselves to stay a set distance apart. But then they would not be parallel throughout their trajectory.

The confusion with the cricket ball arises because you are viewing a 2D curved surface in 3 dimensions. In 3D it looks parallel, but it’s not in 2D.

This is a great example you’ve found.

I guess where I'm confused is that we're not walking due north, we are walking parallel to one another. Our cardinal direction has nothing to do with it. So If we remove the notion of each walking due North, for instance, and just concentrate on walking a straight line next to each other, why would we bump into each other on a 2d plane but not on a sphere?  Lastly, how does this walking in parallel lines translate to perspective via eyeballs?

We would bump into each other on a sphere, that’s what I’m saying. We walk in a straight line, but the geometry we are walking through curves. Look, draw two straight lines on a globe, now peel the surface off and lay it out flat. The lines are not straight anymore. Vice Versa: start with a sheet of paper, then curve it over a globe.

This is one way you can identify curved geometries. Another example: the sides of a cylinder are not a curved surface. To verify this just draw two straight lines and curve it into a soup can label. They still straight yo!

If you take the surface of your cricket ball, peel it off, and flatten it out, you will see that those lines are not parallel on the 2D surface, they only appear as such when viewed from a 3D perspective.

What does this have to do with eyeballs? Light from objects hit them, and we form an image. If our line of sight is through a curved geometry, then it is not easy to interpret what is happening.

This should be obvious by now, since absolutely no one is talking about it correctly. I’m trying to guide things in the right direction by asking loaded/leading questions, but emotions cloud the conversations and entrenchment occurs. Sooner or later, some folks are just going to have to study the shit formally. I can’t perform miracles.

Hope this helps.

It does help and thanks for walking me through it. I get the whole "peel the globe, flatten it out" thing. Much like flat maps possess some distortion because they are projections from a globe (3d curved) to a plane (2d flat). So totally makes sense. However, we're not necessarily talking about a conversion between a 3d space to a 2d space or vice versa. We're talking about two separate and distinct spaces, globe versus plane, not anything inbetween.

So taken separately, on a 2d plane an object receding into the distance would not bottom-up disappear into the vanishing point, it would just continue to get uniformly smaller until the entire object is a pinpoint and then it's gone. But we don't see that. Especially daily, with the sun.

I think that's the point of 'getting the science right'. The wiki 'science' doesn't get it right even if the earth was flat.

[some_engineer]

Irrelevant. Objects/events across the surface will, and the light from them will come to our eyes and tell us there is curvature.

You don’t have to live on a black hole to get curvature. You’ve been watching too much Star Trek.

I won't dispute that but from what I understand the person I was responding to was claiming that the light traveling would follow the curve of the earth but I might have misunderstood that.