Two questions for Flat Earthers

1.) Why does the Sun dip below the horizon at sunset? On the Flat Earth model, the Sun is always above the flat plane, so the Sun should appear low on the horizon as it moves away, but never below it.

But in the spherical reality, the Sun would dip below the horizon as the Earth rotates. And that's what we see.


2.) Why does the Sun's apparent size remain constant throughout the day, if the Sun is moving & changing its distance throughout the day? Flat Earthers allege the Sun is 32 miles in diameter, and 3,000 miles above the Earth's surface, and moves above the flat plane. Those measurements are small enough and close enough to be able to have noticeable size changes in proportion to our visual angle, as the Sun moves towards us and away from us.

But in the spherical & heliocentric reality, the Sun would appear the same size regardless of what time of day it is, given that the distance remains constant throughout the day, and any minor differentiation would not be noticed at such a great distance. And that's what we see.

I'll answer your questions in reverse order.

2.) Why does the Sun's apparent size remain constant throughout the day, if its distance is changing? Flat Earthers allege the Sun is 32 miles in diameter, and 3,000 miles above the Earth's surface, and moves above the flat plane. Those measurements are small enough and close enough to be able to have noticeable size changes in proportion to our visual angle, as the Sun moves towards us and away from us.

But in the spherical & heliocentric reality, the Sun would appear the same size regardless of what time of day it is, given that the distance remains constant throughout the day, and any minor differentiation would not be noticed at such a great distance. And that's what we see.

This is a huge problem with a number of Flat Earth Theories, but not all of them. Take a look 'round the forum, there are a plethora of theories to choose from. For example, some theories argue the Sun does change size, and others ascribe it to a different conceptualization of space, but we'll get to that with your next question.

1.) Why does the Sun dip below the horizon at sunset? On the Flat Earth model, the Sun is always above the flat plane, so the Sun should appear low on the horizon as it moves away, but never below it.

But in the spherical reality, the Sun would dip below the horizon as the Earth rotates. And that's what we see.

'Spherical reality' is a slippery thing though. You could say the Earth is a sphere (or oblate spheroid if you don't want coal for Christmas, or so I've heard), but it can also be argued that the Earth is in non-Euclidean space, so light from the sun would appear to curve in the manner we see it. This can also be explained in other models through perspective tricks or atmospheric distortion.

Hopefully, those answers showed a little of all the information there is on offer in this forum, some theories are better than others, but most answer the questions you ask.

None of the flat earth models can answer this question. Not a single one. (Dual-Earth tries, but that model is completely insane on other kevels).

They will say it's refraction, (bendy light), or perspective. Both of which raise more questions than they answer.

None of the flat earth models can answer this question. Not a single one. (Dual-Earth tries, but that model is completely insane on other kevels).

They will say it's refraction, (bendy light), or perspective. Both of which raise more questions than they answer.

A: You just contradicted yourself ("None of the flat earth models can answer this question", then listing one that can)
B: I just contradicted you in my above post. Non-Euclidean Earth answers both questions just fine. The Sun isn't close to the Earth, it's exactly where science says it is, and the light behaves exactly how you would expect it to in spherical space.

I'll answer your questions in reverse order.

Quote from: December 7, 1972 on August 06, 2017, 05:03:00 AM

2.) Why does the Sun's apparent size remain constant throughout the day, if its distance is changing? Flat Earthers allege the Sun is 32 miles in diameter, and 3,000 miles above the Earth's surface, and moves above the flat plane. Those measurements are small enough and close enough to be able to have noticeable size changes in proportion to our visual angle, as the Sun moves towards us and away from us.

But in the spherical & heliocentric reality, the Sun would appear the same size regardless of what time of day it is, given that the distance remains constant throughout the day, and any minor differentiation would not be noticed at such a great distance. And that's what we see.

This is a huge problem with a number of Flat Earth Theories, but not all of them. Take a look 'round the forum, there are a plethora of theories to choose from. For example, some theories argue the Sun does change size, and others ascribe it to a different conceptualization of space, but we'll get to that with your next question.

Quote from: December 7, 1972 on August 06, 2017, 05:03:00 AM

1.) Why does the Sun dip below the horizon at sunset? On the Flat Earth model, the Sun is always above the flat plane, so the Sun should appear low on the horizon as it moves away, but never below it.

But in the spherical reality, the Sun would dip below the horizon as the Earth rotates. And that's what we see.

'Spherical reality' is a slippery thing though. You could say the Earth is a sphere (or oblate spheroid if you don't want coal for Christmas, or so I've heard), but it can also be argued that the Earth is in non-Euclidean space, so light from the sun would appear to curve in the manner we see it. This can also be explained in other models through perspective tricks or atmospheric distortion.

Hopefully, those answers showed a little of all the information there is on offer in this forum, some theories are better than others, but most answer the questions you ask.

I really think you should go read up on exactly what non-euclidian actually means!

I really think you should go read up on exactly what non-euclidian actually means!

Is there something wrong with my use of the term? If so, could you outline what that is, because I can't find any contradictions between what I said about spherical space and what the internet says.

None of the flat earth models can answer this question. Not a single one. (Dual-Earth tries, but that model is completely insane on other kevels).

They will say it's refraction, (bendy light), or perspective. Both of which raise more questions than they answer.

Wow... "Dual Earth..."? I'm new around here, so I don't know what all the theories are... but I just took a look at it and you're right, it is insane.

The fact that Flat Earthers can't agree on their own theories & be consistent is already telling. Whereas those of us who side with the spherical Earth -- and I won't call it a "theory" or even a "model" because it's a proven fact & reality -- but all of our views are consistent and are backed by the evidence/facts.

What gets me is that Flat Earthers pride themselves on how they aren't "sheep" because they "question everything", yet they never seem to question their own Flat Earth Theory when the said theory is unable to explain certain things or answer certain questions. Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative -- like saying the Sun really does changes in size (when it doesn't), or that there are optical illusions from light bending in strange directions. "Now ya see, the Sun really doesn't dip below the horizon, it's the light bending it in a way to make it look like that."

The Flat Earther who debated Stefan Molyneux was asked why people on planes can see the curvature of the Earth, and his mental gymnastic performance was to claim that the windows on airplanes were created to distort the way the horizon looks -- thereby claiming all of the numerous airplane manufacturers are in on the conspiracy to hide the Flat Earth.


If I'm not mistaken, the original "Flat Earth Theory" from thousands of years ago held the belief that the Sun moved along the "firmament" as it appears -- in an "arc" route -- emerging from behind the "edge" of the Earth in the morning, and traversing to the other side & below the edge of the Earth at night. That model was held because little was known about the world at the time -- they were unaware that the Sun did not go below any "edge" at night, and was instead illuminating other continents and oceans thousands of miles away.

Since even the most illogical Flat Earthers have to admit that there are other continents and oceans which exist, and that a section of the Earth is always illuminated by sunlight even if it's dark where you are -- they can no longer hold on to that old model of the Sun's movements. They claim that the Sun moves in a circle above the flat Earth -- but that then poses a problem, as the Sun would not dip below the horizon in such a model. It would only appear lower on the horizon. Even if one were to be generous to their model, and assume that the Sun "disappears" from sight at night, it would still "disappear" from sight above the horizon. I'm sure there are mathematical measurements that can be calculated to determine where the lowest point in the sky the Sun would appear at its furthest distance on the Flat Earth Model, but it wouldn't be below the horizon.

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

You seem incredulous that FErs will try to solve problems or consider alternatives, as though that is a negative thing. And while I do very much understand that a lot of FE content doesn't really hold up to scrutiny, offhandedly rejecting any new ideas is not how to advocate for science. Any scientist would call the spherical Earth a "model" or a "theory" because a "theorem" or "fact" cannot ever be found within the realm of science.

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

No, the "flaw" is to consistently admit errors to the Flat Earth theory but still never question the theory itself. It's like claiming you're a better chess player than someone else, and then you lose every chess game you play against that person, and at no point you consider that the opponent might be the better player. A truly objective person who "questions everything" would at least question if they really are the better player following the defeats, or just admit that the person they played is a better player.

So if a person's arguments about their theory are repeatedly debunked and defeated, a truly objective person would begin to question if their own belief is valid.

You seem incredulous that FErs will try to solve problems or consider alternatives, as though that is a negative thing.

That's the thing -- Flat Earthers don't consider the spherical Earth as any "alternative", despite overwhelming evidence, so they're not truly being objective. The only "alternatives" Flat Earthers consider is anything that will help them explain their Flat Earth beliefs.

And while I do very much understand that a lot of FE content doesn't really hold up to scrutiny, offhandedly rejecting any new ideas is not how to advocate for science. Any scientist would call the spherical Earth a "model" or a "theory" because a "theorem" or "fact" cannot ever be found within the realm of science.

Ideas can be rejected if their arguments are defeated, unproven, and/or doesn't hold up to (scientific) scrutiny.

Quote from: Here to laugh at you on August 06, 2017, 05:15:41 AM

None of the flat earth models can answer this question. Not a single one. (Dual-Earth tries, but that model is completely insane on other kevels).

They will say it's refraction, (bendy light), or perspective. Both of which raise more questions than they answer.

A: You just contradicted yourself ("None of the flat earth models can answer this question", then listing one that can)
B: I just contradicted you in my above post. Non-Euclidean Earth answers both questions just fine. The Sun isn't close to the Earth, it's exactly where science says it is, and the light behaves exactly how you would expect it to in spherical space.

Excuse me if I didn't read you correctly, but you're saying the Sun is about 93 million miles (150 million km) from Earth? Because so far, every Flat Earther I've seen has argued that the Sun is much closer -- 3,000 miles is the last I heard.

If you believe the Sun is far, then how far are the stars? The Flat Earth model has to argue that the stars are close, otherwise how would they explain why I could see the Southern Cross constellation when I visited Australia, but can't see it in North America? That's because the curvature of the Northern & Southern hemispheres blocks the view of certain parts of the Universe.

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

You seem incredulous that FErs will try to solve problems or consider alternatives, as though that is a negative thing. And while I do very much understand that a lot of FE content doesn't really hold up to scrutiny, offhandedly rejecting any new ideas is not how to advocate for science. Any scientist would call the spherical Earth a "model" or a "theory" because a "theorem" or "fact" cannot ever be found within the realm of science.

Is Tessa or Yuri writing?

Quote from: Tessa Yuri on August 07, 2017, 02:29:49 AM

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

No, the "flaw" is to consistently admit errors to the Flat Earth theory but still never question the theory itself. It's like claiming you're a better chess player than someone else, and then you lose every chess game you play against that person, and at no point you consider that the opponent might be the better player. A truly objective person who "questions everything" would at least question if they really are the better player following the defeats, or just admit that the person they played is a better player.

So if a person's arguments about their theory are repeatedly debunked and defeated, a truly objective person would begin to question if their own belief is valid.

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

You seem incredulous that FErs will try to solve problems or consider alternatives, as though that is a negative thing.

That's the thing -- Flat Earthers don't consider the spherical Earth as any "alternative", despite overwhelming evidence, so they're not truly being objective. The only "alternatives" Flat Earthers consider is anything that will help them explain their Flat Earth beliefs.

You could say this about some of the FE community - but not all of them.

Excuse me if I didn't read you correctly, but you're saying the Sun is about 93 million miles (150 million km) from Earth? Because so far, every Flat Earther I've seen has argued that the Sun is much closer -- 3,000 miles is the last I heard.

If you believe the Sun is far, then how far are the stars? The Flat Earth model has to argue that the stars are close, otherwise how would they explain why I could see the Southern Cross constellation when I visited Australia, but can't see it in North America? That's because the curvature of the Northern & Southern hemispheres blocks the view of certain parts of the Universe.

How far are the stars in the Round Earth theory? I'd say about that far - I'm not going to pretend to have done nearly enough research to doubt the scientific community on that one. I happen to live in the Southern Hemisphere, so I too have seen the Southern Cross, and I have enough faith in everyone else on this forum to assume you cannot see it from the Northern Hemisphere. This is quite a substantial problem for many FE theories, but again, not all of them.

Is Tessa or Yuri writing?

It must cause quite a tussle if "Tessa believes in the scientific method" and "Yuri believes the Earth is a flat plane."

That is rather the point of it.

How far are the stars in the Round Earth theory? I'd say about that far - I'm not going to pretend to have done nearly enough research to doubt the scientific community on that one. I happen to live in the Southern Hemisphere, so I too have seen the Southern Cross, and I have enough faith in everyone else on this forum to assume you cannot see it from the Northern Hemisphere. This is quite a substantial problem for many FE theories, but again, not all of them.

Actually all of FET have problems with it until the introduction of magic of some sort. Why should anyone believe in stuff like aether, bendy light, non-euclidean space or, as the most recent addition "tesselation" by you, to explain a model of a solar system other than the one which works mighty fine with the calculations, repeated evidence and proven predictions that is the SHM as of now?
Do you even know how ridiculous it sounds that all of the FET can't even agree on a map of the Flat Earth so far as there are numerous theories about that alone, and so far not even one has emerged to explain a concept as basic as a sunset coherently and sufficiently?

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

You seem incredulous that FErs will try to solve problems or consider alternatives, as though that is a negative thing. And while I do very much understand that a lot of FE content doesn't really hold up to scrutiny, offhandedly rejecting any new ideas is not how to advocate for science. Any scientist would call the spherical Earth a "model" or a "theory" because a "theorem" or "fact" cannot ever be found within the realm of science.

It's true. I've seen many FEers admit there are problems with their theories.  They continue to attempt to fill in the gaps.  It's commendable.

FTers have been at out for over a century without working, testable model. Is there a point when it become apparent that you can't progress without testing the things that you do agree on?  e.g. A weather balloon and a camera to disprove the curvature.

Testing will provide data for future hypothesis.

Just a thought.

Mike

B: I just contradicted you in my above post. Non-Euclidean Earth answers both questions just fine. The Sun isn't close to the Earth, it's exactly where science says it is, and the light behaves exactly how you would expect it to in spherical space.

No, it behaves the exact opposite of what you would expect it to in spherical space.

In spherical space (depending on exactly how z changes, i.e. is it spherical as well), there would be 3 kinds of paths light can take (2 of which are limits).
One is keeping a constant altitude above the surface of this "flat" Earth, simply making a loop. This is because it is going horizontally, i.e. not changing r position and merely following the curve of space.
Another is going straight up or down as we expect it to in normal space with a round Earth. This is because it is going straight up, i.e. only changing r position.
The final one is light at an angle. In this case it will go out in a spiral, specifically a logarithmic one, where for a given change in tangential position it will move out a certain amount in r.

So no, it doesn't behave as we would expect it to in spherical space.

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

No, but they aren't admitting error.
They are still claiming they are right and Earth is flat, even without being capable of providing an explanation for a simple phenomenon.

How far are the stars in the Round Earth theory? I'd say about that far - I'm not going to pretend to have done nearly enough research to doubt the scientific community on that one. I happen to live in the Southern Hemisphere, so I too have seen the Southern Cross, and I have enough faith in everyone else on this forum to assume you cannot see it from the Northern Hemisphere. This is quite a substantial problem for many FE theories, but again, not all of them.

Far enough away to make the size of Earth quite insignificant such that the primary factor in determining the apparent angle of the star is the angular offset on Earth.

This doesn't hold on a FE.
With a FE there is a quite simple way to calculate the height, but depending on where you do it, you get completely different results.

The only FE models this isn't a problem for are ones with magic bendy light. But that then also gives you the drop due to curvature they claim can't be seen and pretty much destroys any reason for thinking Earth is flat.

Quote from: Tessa Yuri on August 06, 2017, 05:18:23 AM

B: I just contradicted you in my above post. Non-Euclidean Earth answers both questions just fine. The Sun isn't close to the Earth, it's exactly where science says it is, and the light behaves exactly how you would expect it to in spherical space.

No, it behaves the exact opposite of what you would expect it to in spherical space.

In spherical space (depending on exactly how z changes, i.e. is it spherical as well), there would be 3 kinds of paths light can take (2 of which are limits).
One is keeping a constant altitude above the surface of this "flat" Earth, simply making a loop. This is because it is going horizontally, i.e. not changing r position and merely following the curve of space.
Another is going straight up or down as we expect it to in normal space with a round Earth. This is because it is going straight up, i.e. only changing r position.
The final one is light at an angle. In this case it will go out in a spiral, specifically a logarithmic one, where for a given change in tangential position it will move out a certain amount in r.

So no, it doesn't behave as we would expect it to in spherical space.

Could you link to sources so I can read some more, I'm a little confused. I also found multiple computer programs which are used to calculate scattering of light in the upper atmosphere which rely on spherical geometric projections of the Earth - surely these couldn't work if light behaves abnormally in spherical space?

Quote from: Tessa Yuri on August 07, 2017, 02:29:49 AM

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

No, but they aren't admitting error.
They are still claiming they are right and Earth is flat, even without being capable of providing an explanation for a simple phenomenon.

Okay, I can see that.

Quote from: Tessa Yuri on August 07, 2017, 04:33:43 AM

How far are the stars in the Round Earth theory? I'd say about that far - I'm not going to pretend to have done nearly enough research to doubt the scientific community on that one. I happen to live in the Southern Hemisphere, so I too have seen the Southern Cross, and I have enough faith in everyone else on this forum to assume you cannot see it from the Northern Hemisphere. This is quite a substantial problem for many FE theories, but again, not all of them.

Far enough away to make the size of Earth quite insignificant such that the primary factor in determining the apparent angle of the star is the angular offset on Earth.

This doesn't hold on a FE.
With a FE there is a quite simple way to calculate the height, but depending on where you do it, you get completely different results.

The only FE models this isn't a problem for are ones with magic bendy light. But that then also gives you the drop due to curvature they claim can't be seen and pretty much destroys any reason for thinking Earth is flat.

Once again, in spherical space there is no difference in height.

Overall, I think there's been a misinterpretation here. I do not mean to claim that the entire universe is in spherical space, I wouldn't have the faintest how that would work, nor have I done the research to support that assertion. But each planetary object is represented by a mathematically identical Riemann manifold. Could you elaborate on your conceptualisation of my theory?

Could you link to sources so I can read some more, I'm a little confused.

I don't have any sources at the moment, but basically light follows "straight" lines through space time, where "straight" means that it follows the curvature of space time.

In flat space this is easy to visualise, just being a straight line.
In non-flat space, it is harder.
Using polar space, where coordinates are typically specified by (r,theta), where space curves in 1 of the 2 dimensions, there are many straight lines through one point (just like normal space).
In one case, where theta remains constant and thus you are travelling along a path through space which doesn't curve. As such, this "straight" line will be a straight line.
In another case, you project the light in a direction perpendicular to the first. In this case you start off purely travelling in the theta direction, with no r component at all. This is where the effect of curvature may be considered to be the greatest (for a given r anyway) and as a result the "straight" line follows the curvature of space, producing a circle. One such circle would be akin to the surface of your "flat" Earth.

For angles in between there will be a vertical component and a horizontal component. The horizontal component is still effected by the curvature of space and thus results in the "straight" line curving, producing a spiral.

If you have dr/dtheta be constant, then it would be a linear spiral (r=k*theta, dr/dtheta=k), but that would mean it is at different angles to vertical as you go out.
If instead you keep that angle constant it follows an exponential spiral.
That could also be stated as keeping dy/dx constant where y is the vertical component and x is the horizontal component (at that instant), where you have r=e^(k*theta), dr/dtheta=k*e^(k*theta)=k*r, r=y, theta=x/r, dr/dy=1 thus dr=dy, dtheta/dx=1/r thus dtheta=dx/r, from before dr/dtheta=k*r=dy/(dx/r)=r*dy/dx thus dy/dx=k).


Perhaps a better question would be how are you determining the curvature of space?

I also found multiple computer programs which are used to calculate scattering of light in the upper atmosphere which rely on spherical geometric projections of the Earth - surely these couldn't work if light behaves abnormally in spherical space?

They don't actually use projections of Earth, instead they treat Earth as a sphere.
Some papers can have misleading titles.

Once again, in spherical space there is no difference in height.

But there is, not without bendy light.
In normal space you can consider it as 2 contributions, one is from the light moving sideways and moving up due to the angle of projection, and the other is due to the curvature of Earth.
In spherical space, you lose that second contribution and thus get a different height.

Overall, I think there's been a misinterpretation here. I do not mean to claim that the entire universe is in spherical space, I wouldn't have the faintest how that would work

I think it would be a bigger issue the other way around.
Having only Earth in spherical space would require it to be a pocket of spherical space in normal space. How do the 2 connect? What causes it?

If it only curves in 2D, then if you get far enough away from Earth the curvature becomes insignificant. We still don't know if the universe is truly flat or the 3D surface of a very large 4D sphere.

Could you elaborate on your conceptualisation of my theory?

Basically any point can be described by 3 variables:
r, theta, phi

You can consider it as an infinite number of spherical shells where the surface of Earth is one such shell.

Quote from: Tessa Yuri on August 08, 2017, 03:03:21 AM

Could you link to sources so I can read some more, I'm a little confused.

I don't have any sources at the moment, but basically light follows "straight" lines through space time, where "straight" means that it follows the curvature of space time.

In flat space this is easy to visualise, just being a straight line.
In non-flat space, it is harder.
Using polar space, where coordinates are typically specified by (r,theta), where space curves in 1 of the 2 dimensions, there are many straight lines through one point (just like normal space).
In one case, where theta remains constant and thus you are travelling along a path through space which doesn't curve. As such, this "straight" line will be a straight line.
In another case, you project the light in a direction perpendicular to the first. In this case you start off purely travelling in the theta direction, with no r component at all. This is where the effect of curvature may be considered to be the greatest (for a given r anyway) and as a result the "straight" line follows the curvature of space, producing a circle. One such circle would be akin to the surface of your "flat" Earth.

For angles in between there will be a vertical component and a horizontal component. The horizontal component is still effected by the curvature of space and thus results in the "straight" line curving, producing a spiral.

If you have dr/dtheta be constant, then it would be a linear spiral (r=k*theta, dr/dtheta=k), but that would mean it is at different angles to vertical as you go out.
If instead you keep that angle constant it follows an exponential spiral.
That could also be stated as keeping dy/dx constant where y is the vertical component and x is the horizontal component (at that instant), where you have r=e^(k*theta), dr/dtheta=k*e^(k*theta)=k*r, r=y, theta=x/r, dr/dy=1 thus dr=dy, dtheta/dx=1/r thus dtheta=dx/r, from before dr/dtheta=k*r=dy/(dx/r)=r*dy/dx thus dy/dx=k).


Perhaps a better question would be how are you determining the curvature of space?

Quote from: Tessa Yuri on August 08, 2017, 03:03:21 AM

Overall, I think there's been a misinterpretation here. I do not mean to claim that the entire universe is in spherical space, I wouldn't have the faintest how that would work

I think it would be a bigger issue the other way around.
Having only Earth in spherical space would require it to be a pocket of spherical space in normal space. How do the 2 connect? What causes it?

If it only curves in 2D, then if you get far enough away from Earth the curvature becomes insignificant. We still don't know if the universe is truly flat or the 3D surface of a very large 4D sphere.

Wow, ok, I can see that. Yeah, that does throw a spanner in the works. If you do find a source for it, I'd love it if you could send it my way. I'll try to work through that problem myself, but I can absolutely see what you're saying.

---

QUICK NOTE: I've found some more stuff on SASKTRAN, but I think I'll hold it over until I've figured out this light stuff. I'll update you later today.

Quote from: Tessa Yuri on August 07, 2017, 02:29:49 AM

Quote from: December 7, 1972 on August 07, 2017, 02:11:39 AM

Instead, they either simply admit they "Don't know" and skip over it, or they will engage in mental gymnastics in a desperate manner to stretch the truth to fit their narrative

Is it a flaw to admit error? I was rather under the impression that it was a good idea to accept when you are wrong, but okay then...

No, but they aren't admitting error.
They are still claiming they are right and Earth is flat, even without being capable of providing an explanation for a simple phenomenon.

Exactly. Flat Earthers keep admitting that they can't explain or answer various holes in their theory, but still maintain that their theory is correct. Flat Earthers are the ones who are not open-minded or objective. The irony is that conspiracy theorists often pride themselves as not being "sheep", when often times they're the biggest sheep when it comes to not accepting any new information that challenges or disproves their ideas.

Like I said, a good place to start is by asking how you measure the curvature of space in the first place?
It is quite easy to just arbitrarily define Earth as flat and go from there, but that is trying to make Earth flat by defining it as flat, which is no better than defining it to be the centre of the universe and ignoring any motion.

1.) Why does the Sun dip below the horizon at sunset? On the Flat Earth model, the Sun is always above the flat plane, so the Sun should appear low on the horizon as it moves away, but never below it.

But in the spherical reality, the Sun would dip below the horizon as the Earth rotates. And that's what we see.


2.) Why does the Sun's apparent size remain constant throughout the day, if the Sun is moving & changing its distance throughout the day? Flat Earthers allege the Sun is 32 miles in diameter, and 3,000 miles above the Earth's surface, and moves above the flat plane. Those measurements are small enough and close enough to be able to have noticeable size changes in proportion to our visual angle, as the Sun moves towards us and away from us.

But in the spherical & heliocentric reality, the Sun would appear the same size regardless of what time of day it is, given that the distance remains constant throughout the day, and any minor differentiation would not be noticed at such a great distance. And that's what we see.

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

How does the sun know precisely where you are to direct the precisely correct beam of light to your location in order to maintain the illusion? How can the sun do this to every person and camera and animal on Earth, all at the same time?

Quote from: December 7, 1972 on August 06, 2017, 05:03:00 AM

1.) Why does the Sun dip below the horizon at sunset? On the Flat Earth model, the Sun is always above the flat plane, so the Sun should appear low on the horizon as it moves away, but never below it.

But in the spherical reality, the Sun would dip below the horizon as the Earth rotates. And that's what we see.


2.) Why does the Sun's apparent size remain constant throughout the day, if the Sun is moving & changing its distance throughout the day? Flat Earthers allege the Sun is 32 miles in diameter, and 3,000 miles above the Earth's surface, and moves above the flat plane. Those measurements are small enough and close enough to be able to have noticeable size changes in proportion to our visual angle, as the Sun moves towards us and away from us.

But in the spherical & heliocentric reality, the Sun would appear the same size regardless of what time of day it is, given that the distance remains constant throughout the day, and any minor differentiation would not be noticed at such a great distance. And that's what we see.

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

Nope, it definitely acts like a lantern, i.e. a point source radiating out light in all directions, just a very distant one.

Like I said, a good place to start is by asking how you measure the curvature of space in the first place?
It is quite easy to just arbitrarily define Earth as flat and go from there, but that is trying to make Earth flat by defining it as flat, which is no better than defining it to be the centre of the universe and ignoring any motion.

Okay, so I'm back! I've fallen into an old trap of mine; using the wrong terminology. When I say 'spherical space' with my big dumb typing fingers, I actually mean 'spherical geometry'. To clarify, I'm not trying to say that pockets of the universe, or the whole universe, is in spherical space, but rather each object in space has a surface which is a Euclidean representation of an arbitrarily curved Riemann manifold.

Quote from: Tessa Yuri on August 08, 2017, 03:03:21 AM

I also found multiple computer programs which are used to calculate scattering of light in the upper atmosphere which rely on spherical geometric projections of the Earth - surely these couldn't work if light behaves abnormally in spherical space?

They don't actually use projections of Earth, instead they treat Earth as a sphere.
Some papers can have misleading titles.

I did a bit more reading up, and they actually use spherical geometric models. Which is almost the same thing. From another paper regarding SASKTRAN (one of the programs):

All components of the SASKTRAN framework treat the planet and atmosphere as spherical, and all path lengths and angles are computed using a spherical geometry.

So yes, it treats the Earth as being spherical in Euclidean geometry but also uses spherical geometry for its computations.

Many, many apologies for using misleading terminology. Hope this has provided some clarification

Quote from: JackBlack on August 08, 2017, 03:14:59 PM

Like I said, a good place to start is by asking how you measure the curvature of space in the first place?
It is quite easy to just arbitrarily define Earth as flat and go from there, but that is trying to make Earth flat by defining it as flat, which is no better than defining it to be the centre of the universe and ignoring any motion.

Okay, so I'm back! I've fallen into an old trap of mine; using the wrong terminology. When I say 'spherical space' with my big dumb typing fingers, I actually mean 'spherical geometry'. To clarify, I'm not trying to say that pockets of the universe, or the whole universe, is in spherical space, but rather each object in space has a surface which is a Euclidean representation of an arbitrarily curved Riemann manifold.

I'm pretty sure we are talking about the same thing here, unless you are just saying that you can map the surface of Earth to a sphere, which would just mean Earth is a sphere in normal space.

In order for Earth to be flat, space itself needs to curve. If this happens with all objects like the sun and moon, you would need to have pockets of curved space joined to normal space, and an associated explanation for why.

I did a bit more reading up, and they actually use spherical geometric models. Which is almost the same thing. From another paper regarding SASKTRAN (one of the programs):

Quote

All components of the SASKTRAN framework treat the planet and atmosphere as spherical, and all path lengths and angles are computed using a spherical geometry.

So yes, it treats the Earth as being spherical in Euclidean geometry but also uses spherical geometry for its computations.

The issue is that a simple reading of that statement directly contradicts itself.
If Earth is spherical in Euclidean geometry, then using spherical geometry centred on Earth wouldn't produce the correct results.
Looking at the paper, they appear to use spherical geometry when analysing a point that light scatters, having the spherical geometry centred there and analysing spherical shells centred on that point.

So they are treating Earth as a sphere.

Quote from: TheMelkur on August 08, 2017, 05:07:14 PM

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

How does the sun know precisely where you are to direct the precisely correct beam of light to your location in order to maintain the illusion? How can the sun do this to every person and camera and animal on Earth, all at the same time?

It's only the direction light travels in, it doesn't need to know where you are, light travels in directed lines like lasers whether you're there to observe or not. I don't believe the Sun is one object radiating light, rather it is the cosmic background radiation of the universe, but because of the dome around us we only see one circular Sun at a time. When you move, different lines of light hit your eyes.

Quote from: Tessa Yuri on August 08, 2017, 05:48:12 PM

Quote from: TheMelkur on August 08, 2017, 05:07:14 PM

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

How does the sun know precisely where you are to direct the precisely correct beam of light to your location in order to maintain the illusion? How can the sun do this to every person and camera and animal on Earth, all at the same time?

It's only the direction light travels in, it doesn't need to know where you are, light travels in directed lines like lasers whether you're there to observe or not. I don't believe the Sun is one object radiating light, rather it is the cosmic background radiation of the universe, but because of the dome around us we only see one circular Sun at a time. When you move, different lines of light hit your eyes.

And how does this dome only let in a beam? Why does the beam change?
Why does it change smoothly, including with you walking around to different spots?
Do you have any evidence at all for this?

If Earth is spherical in Euclidean geometry, then using spherical geometry centred on Earth wouldn't produce the correct results.

The coordinate system of spherical geometry would allow for more accurate and more useful results, wouldn't it? If the Earth was being mapped in Euclidean space, then the coordinates would be almost unmanageable.

In order for Earth to be flat, space itself needs to curve. If this happens with all objects like the sun and moon, you would need to have pockets of curved space joined to normal space, and an associated explanation for why.

Normal physics has pockets of curved space 'joined' to normal space, so I don't see why I have to provide an alternate explanation. Could you elaborate?

---

Quote from: Tessa Yuri on August 08, 2017, 05:48:12 PM

Quote from: TheMelkur on August 08, 2017, 05:07:14 PM

The light from the Sun appears to be directional, more like a laser light than a lantern. The light you see is not the exact same as the light someone a few meters to your left would see. It isn't exactly an illusion, but you can treat it as such.

How does the sun know precisely where you are to direct the precisely correct beam of light to your location in order to maintain the illusion? How can the sun do this to every person and camera and animal on Earth, all at the same time?

It's only the direction light travels in, it doesn't need to know where you are, light travels in directed lines like lasers whether you're there to observe or not. I don't believe the Sun is one object radiating light, rather it is the cosmic background radiation of the universe, but because of the dome around us we only see one circular Sun at a time. When you move, different lines of light hit your eyes.

So many questions...

• How does the sun move across the sky during the day?
• Where is the sun at night?
• Why is background radiation being concentrated into a series of lasers?
• Is there a scientific precedent for such a thing?
• Bananas emit small amounts of radiation, far greater than cosmic background, so why is my fruit bowl not erupting in a lightshow right now?
• During sunset, why does some of the sun slip off the bottom of the dome?
• How is a series of lasers which are emitted radially different to how a lantern operates?
• Why are these lasers organised into 'sets' (if the size of the sun remains constant, but more than one beam of light is hitting my eyes, them most or all beams must be showing a part of the same image, which you claim changes as we move.)
• Why do different lines of light all show the same image?
• What process causes this?
• Why are eclipses only visible from certain locations, when in all other circumstances you claim the sun appears the same from all positions?
• What does a laser-background-radiation-on-the-dome-sun do that isn't done by a normal sun (i.e. how can we scientifically verify your claims)?

Quote from: JackBlack on August 09, 2017, 03:03:00 PM

If Earth is spherical in Euclidean geometry, then using spherical geometry centred on Earth wouldn't produce the correct results.

The coordinate system of spherical geometry would allow for more accurate and more useful results, wouldn't it? If the Earth was being mapped in Euclidean space, then the coordinates would be almost unmanageable.

That depends upon what origin you use and how you calculate it all.

Consider a simple case of a beam of light passing through the atmosphere (a single beam), without scattering, in Euclidean space that is described as a simple vector <x,y,z>, where in some cases due to the exact reference used (like the example in the paper), it would simplify down to x=k*t, y=y0, z=0.
And that describes the path of the beam.

For spherical geometry it is no where near that simple.
If the light ray passes through the origin, then it is simple, where you have r=k*t, theta=theta0, phi=phi0.
But otherwise it gets horribly complicated as theta, phi and r all change as a complex (in the sense of not simple, no i needed) function of t.
Something like (for the above case):
r=sqrt(k^2*t^2+y0^2)
phi=0,
theta=atan(k*t/y0).

If you tried a simple approach like the above, where just one vector changes you have the light circling Earth which it simply doesn't do, or just heading straight towards or away from Earth.

For a more complicated case you have (you can remove one of the 0s and change the others for an equivalent result):
x=x0+kx*t
y=y0+ky*t
z=z0+kz*t

Now for the spherical coordinates you have:
r=sqrt((x0+kx*t)^2+(y0+ky*t)^2+(z0+kz*t)^2)
theta=atan((x0+kx*t)/(y0+ky*t))
phi=atan((z+kz*t)/sqrt((x0+kx*t)^2+(y0+ky*t)^2)

I think, I may have made some errors.

Quote from: JackBlack on August 09, 2017, 03:03:00 PM

In order for Earth to be flat, space itself needs to curve. If this happens with all objects like the sun and moon, you would need to have pockets of curved space joined to normal space, and an associated explanation for why.

Normal physics has pockets of curved space 'joined' to normal space, so I don't see why I have to provide an alternate explanation. Could you elaborate?

But that is curved in a different way.
Normal physics has curved space time where the time axis can be tilted towards a dense object. It is more akin to fabric with some regions stretched out/pulled down.

So looking at lines/planes through space, where some just bend towards the object.
This allows a smooth transition where the lines curve less and less.

You have it quite different.
You have entirely different space embedded in normal space, where your space somehow loops around and connects back on itself.
There is no way to have a gradual change (at least not one I can think of). The best you get is getting far enough away from the centre of the space such that the curvature is insignificant.

Here is an image to help illustrate what I mean:


Can you think of a way to smoothly transition that curved space to the Euclidean space around it, noting that there is no preferred orientation, so you can't do it differently on the diagonals to the sides?

So many questions...

• How does the sun move across the sky during the day?
• Where is the sun at night?
• Why is background radiation being concentrated into a series of lasers?
• Is there a scientific precedent for such a thing?
• Bananas emit small amounts of radiation, far greater than cosmic background, so why is my fruit bowl not erupting in a lightshow right now?
• During sunset, why does some of the sun slip off the bottom of the dome?
• How is a series of lasers which are emitted radially different to how a lantern operates?
• Why are these lasers organised into 'sets' (if the size of the sun remains constant, but more than one beam of light is hitting my eyes, them most or all beams must be showing a part of the same image, which you claim changes as we move.)
• Why do different lines of light all show the same image?
• What process causes this?
• Why are eclipses only visible from certain locations, when in all other circumstances you claim the sun appears the same from all positions?
• What does a laser-background-radiation-on-the-dome-sun do that isn't done by a normal sun (i.e. how can we scientifically verify your claims)?

1. The Sun is not a star moving across the sky, we are inside a multi-layered dome, one layer opaque rock and the other clear crystal or ice. The movement of the rock, and the holes in it, give the appearance of a moving Sun.
2. See above. At night you don't see any holes larger than the stars.
3. The background radiation is outside the dome. When it passes through to us it is directed by the dome.
4. Everyone knows about directed light and lasers.
5. The cosmic background radiation inside the dome is far less than the radiation outside. I expect this is down to the core of the Earth, inside the north pole, emanating cold like many things emanate heat.
6. This is once more due to the fact what we observe is a hole, rather than a light source.
7. Lasers that point directly at one source are only visible at that one location. When you move, you have to be looking at a different laser, while with a lantern the same part of it can be seen from many locations.
8. Nearby locations on the dome are near enough to parallel, so the lasers reaching you are parallel. You can only see one at a time.
9. They just show the holes, and the image is not always the same depending on the time of day and where you are.
10. It's just light.
11. The Sun you see in one position is not the same as the Sun viewed elsewhere.
12. It would be easy to verify if you wanted to go to Antarctica and walk to the dome. Otherwise the intensity of the Sun's heat should demonstrate it is more directed than a lantern.