The issue with curvature

Whenever you venture into the fairytale world of the flat-earther you hear the oft-made lament 'but where is the curvature?'. But of course, the question is rather childish as it seems to infer a vertical curvature which of course would require extreme altitude to see - and not really be vertical anyhow. But the truth is that the curvature is easily visible and literally at sea level.

Go out in a boat (or plane for that matter) away from land and take a look in all directions. What you will of course see it a horizon CURVING its way around you in a perfect CIRCLE and circles are just 360 degree curves. Get in a balloon no higher than the local geography and you will see the exact same thing - a distinct circular horizon where you are in the exact middle. In fact, being able to do this at any point on earth is yet another proof of a sphere as an equidistant horizon is impossible anywhere on the FE other than at the north pole. 

I am sure that FEers have countless ludicrous objections to this, but from my position, curvature is easily visible at any point on the earth and many of them at sea level.

Does anyone else feel the same as me that the 'where is the curvature?' argument is largely based on a chronic misunderstanding of what a curve actually is on a massive object?

Whenever you venture into the fairytale world of the flat-earther you hear the oft-made lament 'but where is the curvature?'. But of course, the question is rather childish as it seems to infer a vertical curvature which of course would require extreme altitude to see - and not really be vertical anyhow. But the truth is that the curvature is easily visible and literally at sea level.

Go out in a boat (or plane for that matter) away from land and take a look in all directions. What you will of course see it a horizon CURVING its way around you in a perfect CIRCLE and circles are just 360 degree curves. Get in a balloon no higher than the local geography and you will see the exact same thing - a distinct circular horizon where you are in the exact middle. In fact, being able to do this at any point on earth is yet another proof of a sphere as an equidistant horizon is impossible anywhere on the FE other than at the north pole. 

I am sure that FEers have countless ludicrous objections to this, but from my position, curvature is easily visible at any point on the earth and many of them at sea level.

Does anyone else feel the same as me that the 'where is the curvature?' argument is largely based on a chronic misunderstanding of what a curve actually is on a massive object?

No.

But there certainly is a misunderstanding here, though.

Whenever you venture into the fairytale world of the flat-earther you hear the oft-made lament 'but where is the curvature?'. But of course, the question is rather childish as it seems to infer a vertical curvature which of course would require extreme altitude to see - and not really be vertical anyhow. But the truth is that the curvature is easily visible and literally at sea level.

To use some "Navy Words" (LOL). 
One proof of the curvature is noting the difference of how far the man sitting down or standing up in the "Liberty Boat" down next to the level of the sea can see to the horizon compared with the distance the man on the Main Deck, Bridge, Highest Deck or Crow's Nest on the ship can see to the horizon.
(See: Table in "Navy Manual For Lookouts" for reference.)
A range of  from  about 2 to 10 miles, according to the height of the observer.

I would like to see some "flat earth figures" in regard to the distances to the horizon....If it is visible through "the thickness of the
atmoplane." ?

Wow, you were in the Navy?

Why are pictures of the horizon always taken from so far away?

Why are pictures of the horizon always taken from so far away?

If the cameraman were to take closer pictures of the horizon, he would spin around the Globe like a madman trying to catch it. Even if he would have a telescope like-camera to zoom in, the horizon line would remain the same and not reveal anything past it due to the curvature of the earth.

If the cameraman were to take closer pictures of the horizon, he would spin around the Globe like a madman trying to catch it.

That sounds reasonable.

Whenever you venture into the fairytale world of the flat-earther you hear the oft-made lament 'but where is the curvature?'. But of course, the question is rather childish as it seems to infer a vertical curvature which of course would require extreme altitude to see - and not really be vertical anyhow. But the truth is that the curvature is easily visible and literally at sea level.

Go out in a boat (or plane for that matter) away from land and take a look in all directions. What you will of course see it a horizon CURVING its way around you in a perfect CIRCLE and circles are just 360 degree curves. Get in a balloon no higher than the local geography and you will see the exact same thing - a distinct circular horizon where you are in the exact middle. In fact, being able to do this at any point on earth is yet another proof of a sphere as an equidistant horizon is impossible anywhere on the FE other than at the north pole. 

I am sure that FEers have countless ludicrous objections to this, but from my position, curvature is easily visible at any point on the earth and many of them at sea level.

Does anyone else feel the same as me that the 'where is the curvature?' argument is largely based on a chronic misunderstanding of what a curve actually is on a massive object?

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes. What I find laughable is people who claim to have seen the "curvature" first hand (from an airplane window for example). In that case I always ask: "did you see the curvature from the left hand or right hand side of the plane and also were you flying level at the time?" If the penny still hasn't dropped I would ask where exactly then does the horizon curve back upwards so that it may complete a full circle allowing the right hand and left hand "curvature" to meet up again. You see on a ball earth the horizon must necessarily fall away downwards at altitude and if you do, at extreme altitude, see the horizon (and imagined curvature) at eye level, the opposite window cannot possibly show the same scenery, but instead should be showing a view of space. Obviously you cannot be flying level and will have to be banking for this to happen. So you see, curvature is but an illusion.

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

Why do you think the horizon is always at eye level from high altitude? It isn't.

Are you suggesting that the horizon is the rim of a circular flat disk that is the earth? As you travel a few miles in one direction does the horizon get closer in the direction you're traveling and further away in the opposite direction, or does it appear that you're always at or above the center of the disk?

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

Sure, but then you’d be claiming to be literally seeing to the ends of the earth.

If this field of view encompass everything up to the ice wall (or whatever), it’s a case for a flat earth disc.

If you can only see a relatively small proportion of the surface before the horizon curves away, it’s a round earth.

Also no matter where you are, the curvature of the earth looks the same in all directions.  If it were a disc, you’d expect the closest edge to be different from the furthest.

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

No, what he described is the curvature.
You are right, the curve should curve around you. That means it goes around, remaining at the same angle of dip. It doesn't curve downwards like the FEers pretend.

And yes, the higher you go, the further down the horizon gets. But you need to get very high for the horizon to be noticeably not at eye level. Otherwise you need to use instruments to actually measure it. If you do, you find that the horizon is not at eye level, even when on the ground it is slightly below.

I would ask where exactly then does the horizon curve back upwards so that it may complete a full circle

So you still don't understand how it works?
They are now looking partially down, and the horizon is still a circle.

if you do, at extreme altitude, see the horizon (and imagined curvature) at eye level

Who cares about this hypothetical scenario which doesn't exist?
The horizon isn't at eye level, it is below it.

the opposite window cannot possibly show the same scenery, but instead should be showing a view of space.

I know this might be hard to understand, but the windows on planes don't just show a sliver. Instead you have a large vertical FOV.
You can see quite a bit below the plane and above the plane.
This allows both sides to be looking partially down and seeing the curve.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

Why do you think the horizon is always at eye level from high altitude? It isn't.

Are you suggesting that the horizon is the rim of a circular flat disk that is the earth? As you travel a few miles in one direction does the horizon get closer in the direction you're traveling and further away in the opposite direction, or does it appear that you're always at or above the center of the disk?

I can answer your question with the reverse question: how do you know the horizon is not at eye level at extreme altitude? Even at 120 000 ft this phenomenon has been observed. Granted, I have not personally witnessed this, but then in all probability, neither have you! My point though was against those who claim to have seen the curvature from an ordinary passenger plane, as that can be verified by anyone as opposed to extreme altitude situations which can not. I have been in passenger jets frequently and the horizon undoubtedly remains at eye level.

No, I am not suggesting the horizon is the edge of a circular earth obviously. The flat earth is clearly at least as large as the round earth (far larger actually since all of it can be observed at once), so the horizon is simply the edge of your vision limited by perspective. The higher you go, the more of the earth below can be seen and yes, you always appear to be at the center of an apparently infinite disk.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

Sure, but then you’d be claiming to be literally seeing to the ends of the earth.

If this field of view encompass everything up to the ice wall (or whatever), it’s a case for a flat earth disc.

If you can only see a relatively small proportion of the surface before the horizon curves away, it’s a round earth.

Also no matter where you are, the curvature of the earth looks the same in all directions.  If it were a disc, you’d expect the closest edge to be different from the furthest.

See above reply. My usage of the analogy with the plate was perhaps a little clumsy I admit. I did say it was a huge plate though! Hie hie.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

No, what he described is the curvature.
You are right, the curve should curve around you. That means it goes around, remaining at the same angle of dip. It doesn't curve downwards like the FEers pretend.

And yes, the higher you go, the further down the horizon gets. But you need to get very high for the horizon to be noticeably not at eye level. Otherwise you need to use instruments to actually measure it. If you do, you find that the horizon is not at eye level, even when on the ground it is slightly below.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

I would ask where exactly then does the horizon curve back upwards so that it may complete a full circle

So you still don't understand how it works?
They are now looking partially down, and the horizon is still a circle.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

if you do, at extreme altitude, see the horizon (and imagined curvature) at eye level

Who cares about this hypothetical scenario which doesn't exist?
The horizon isn't at eye level, it is below it.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

the opposite window cannot possibly show the same scenery, but instead should be showing a view of space.

I know this might be hard to understand, but the windows on planes don't just show a sliver. Instead you have a large vertical FOV.
You can see quite a bit below the plane and above the plane.
This allows both sides to be looking partially down and seeing the curve.

My point is not to say that you can NOT see the supposed curvature. Quite the opposite; even on a flat earth the horizon must appear to curve around you, so what I am saying is that appearances are not all they seem an no conclusion can be drawn from that sort of observation, either for or against FE.

Just for clarity, let me modify my first post to say that "you see what appears to be the rim of the plate". My apologies.

I can answer your question with the reverse question: how do you know the horizon is not at eye level at extreme altitude? Even at 120 000 ft this phenomenon has been observed.

The FEers are the one claiming it does. As such the burden is on them.
Also, there is no evidence that that phenomenon has ever been observed and is actually impossible to show as it requires infinite precision.
The best you can actually show is that it is within some range.
For the numerous reports, these people are merely using their eyes, with no actual reference and just deeming it to be at eye level.
That allows a massive error range.
Meanwhile, with appropriate instruments (i.e. a theolodite) the horizon can, and in every occurrence where one was used where the horizon wasn't above the person (i.e. from an object with a greater elevation), HAS been observed to be below eye level.
Theodolites can and have easily measured an angle of dip to the horizon.
With modern smart-phones, you can measure this dip from the top of tall buildings.

This has been discussed previously on these fora.
For example, this one here:


So no, the horizon does not rise to eye level. Not even when you are fairly close to the ground. So why would it magically do so at a higher altitude?

Rather than just assert it rises to eye level because you can't tell with your eyes if it does or not, plenty of people have actually measured it and found it not to.

I have been in passenger jets frequently and the horizon undoubtedly remains at eye level.

And what tool did you use to measure that?
Did it just look like it was at eye level? Or were you able to actually quantity it by using a measuring device, like this:

Of course, this suffers from relying upon the apparent direction of down, as would most measuring tools.
In order to actually confirm it you need to measure horizons opposite each other at the same time, and use the difference between them to compensate for the bank of the plane, or use a fully inertial system which keeps its orientation in 3D space.

the horizon is simply the edge of your vision limited by perspective.

Except perspective doesn't just magically limit your vision.
If perspective was going to cause the horizon, it would be the edge of Earth, or infinitely far away.
But the limited visibility through the atmosphere stops it way before that, meaning you would just get a blur.

If it was perspective, objects wouldn't disappear from the bottom up. If you got higher it would be harder to see the bottom as you would then be further away.

If perspective did magically make the horizon magically nearer than infinitely far away then you would be able to use a telescope to make it get further and further away, while in reality, it remains in the same location and you can just see it more clearly.

So no, what we see is fundamentally different to what we would expect for a FE.

My point is not to say that you can NOT see the supposed curvature.

And my point is that you are completely wrong.
For a FE you shouldn't see the horizon at all, unless you removed the atmosphere. If you did, it would then be infinitely far away, rather than relatively close with the distance depending upon your elevation. The fact that the horizon is close, where no one claims the edge of the FE is, shows that it is curvature, as the horizon is an edge. The fact that it moves around as you move around, is evidence of curvature as it is an edge. The fact that it gets further away as you go higher shows it is an edge that you are looking over as you get higher.
What shape do you know of that has edges everywhere? A sphere or shapes similar to them.

Here is a video of a simple apparatus you can make yourself.
2 tubes, connected at the top and bottom, the top to allow air pressure to equalise, and the bottom to allow the water level to equalise, sealed to prevent leaks:


The water between the 2 tubes will remain level. Look along the water level and see if the horizon is there as you get higher.
Spoilers: IT DOESN'T!

Quote from: Alpha2Omega on August 16, 2018, 07:21:29 AM

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

Why do you think the horizon is always at eye level from high altitude? It isn't.

Are you suggesting that the horizon is the rim of a circular flat disk that is the earth? As you travel a few miles in one direction does the horizon get closer in the direction you're traveling and further away in the opposite direction, or does it appear that you're always at or above the center of the disk?

I can answer your question with the reverse question: how do you know the horizon is not at eye level at extreme altitude? Even at 120 000 ft this phenomenon has been observed. Granted, I have not personally witnessed this, but then in all probability, neither have you! My point though was against those who claim to have seen the curvature from an ordinary passenger plane, as that can be verified by anyone as opposed to extreme altitude situations which can not. I have been in passenger jets frequently and the horizon undoubtedly remains at eye level.

No, I am not suggesting the horizon is the edge of a circular earth obviously. The flat earth is clearly at least as large as the round earth (far larger actually since all of it can be observed at once), so the horizon is simply the edge of your vision limited by perspective. The higher you go, the more of the earth below can be seen and yes, you always appear to be at the center of an apparently infinite disk.

How do we know?  Because anyone can test it themselves.


and it looks like JackBlack beat me to it.

Just for clarity, let me modify my first post to say that "you see what appears to be the rim of the plate". My apologies.

In the following earlier post, you seem to accept that curvature can be seen, though I'm not sure what altitude you would claim would be needed for that.

My point is not to say that you can NOT see the supposed curvature. Quite the opposite; even on a flat earth the horizon must appear to curve around you, so what I am saying is that appearances are not all they seem and no conclusion can be drawn from that sort of observation, either for or against FE.

And the in

High Altitude Photographs
Most pictures of the earth taken by amateur balloonists at very high altitudes are not doctored. Flat Earth Theory holds that there is elliptical curvature from the edge of space, over 50 miles in altitude. Any photograph showing a curved elliptical horizon from very high altitudes poses no affront to FE.

Curvature results from the fact that at the edge of the atmosphere we are looking down at the illuminated circular area of the sun's light. The observer is looking down at a circle. A circle is always curved in two dimensions. When looking down at the circular area of the sun's light upon the earth we see elliptical curvature.

There are no details given of that photo in "the Wiki" but I suspect that it might be from a balloon flight, so I'll guess it was taken from 121,000 ft (a common upper limit).
"The Wiki" claims "over 50 miles in altitude" but no amateur balloon has flown to that altitude. The "professional record" is much less

During 2002 an ultra-thin-film balloon named BU60-1 made of polyethylene film 3.4 µm thick with a volume of 60,000 m³ was launched from Sanriku Balloon Center at Ofunato City, Iwate in Japan at 6:35 on May 23, 2002. The balloon ascended at a speed of 260 m per minute and successfully reached the altitude of 53.0 km (173,900 ft), breaking the previous world record set during 1972.

The big problem, however, with your explanation and that in "the Wiki" is that on the Globe, from say 121,000 ft, is that the horizon is about 427 miles (687 km) away
but, depending on the location of the balloon flight, the edge of the lit region could be about 3100 miles (5000 km) away.

There is no way that any curvature could be observed on a circular edge 3100 miles away when viewed from only 23 miles (37 km km) altitude.
Now the observed curvature from balloons is still slight but is quite observable and that photo in "the Wiki" shows a curve.

To put it bluntly, I do not accept this flat earth explanation for observed "left to right" curvature on the horizon.

I will admit I am not as deep into this question as some experts- both "round" and "flat" earth.

But it seems rather elementary when you consider that the earth is a sphere and there is a curvature.
And you can see that you are in the middle of a circle if you are on a ship in the middle of the ocean..
The diameter of that circle is limited by the horizon.
And that is limited by the height you are above the level of the sea.
It all seems very simple if you have ever observed this for yourself .
And has been observed by anyone who has ever been to sea - civilian or military.

If the earth was flat, you should be able to see the North Pole from the stern of a ship in the middle of the ocean and the "ice wall"
from the bow if you had a powerful enough telescope and were able to see through "the thickness of the atmoplane." There is also the question of where the horizon would be if the earth was flat.I have yet to read of the flat earth explanation. It would seem that if the earth was flat , you could see an infinite distance in all directions if - again - if it wasn't for "the thickness of the atmoplane The diameter of that circle you were in would also be infinite for the same reason..

Wow, you were in the Navy?

What's so "wow"about that ?
Lots of people have been in the Navy and/or have been to sea ?
Or were you just being sarcastic for the sake of being sarcastic ?

Some "flat earthers" seem to be completely "at sea" on some subjects or issues such as this. 
LOL
I try to limit my posts to things I can back up with facts and figures.

There are lots more people than those I mentioned  who have never been in the Navy and/or have never been to sea.
They may have always  lived in "the flatlands" all their lives and never been more than a few miles from their home.
I had a shipmate in the Navy whose parents had immigrated from Sicily, opened a shop in lower Manhattan , and had never been more than a few blocks from where they lived.
They could care less about whether the earth was round or flat and had no concept of this thing called "the horizon."

There are probably lots of people on this website who could honestly say that they truly believed that the earth was flat because it looked that way to them. And they had never even given it a thought. All because it didn't affect  them a bit and they hadn't had the opportunities and experiences that those "other people" have had.

My apology for getting on the soapbox and getting so wordy.
I had the misfortune to minor in English and  Journalism and write a lot of stuff for the school papers.
Old habits die hard . LOL

Quote from: JackBlack on August 16, 2018, 03:37:39 PM

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

What you are describing above is no curvature. If you were floating above a huge round (and flat) tray, you would also see the rim of the tray "curve" around you and interestingly, the higher you go, the more acute the seeming curvature would be and the more you would need to look at a downwards angle rather than the always-at-eye-level horizon actually observed even at very high altitudes.

No, what he described is the curvature.
You are right, the curve should curve around you. That means it goes around, remaining at the same angle of dip. It doesn't curve downwards like the FEers pretend.

And yes, the higher you go, the further down the horizon gets. But you need to get very high for the horizon to be noticeably not at eye level. Otherwise you need to use instruments to actually measure it. If you do, you find that the horizon is not at eye level, even when on the ground it is slightly below.*

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

I would ask where exactly then does the horizon curve back upwards so that it may complete a full circle

So you still don't understand how it works?
They are now looking partially down, and the horizon is still a circle.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

if you do, at extreme altitude, see the horizon (and imagined curvature) at eye level

Who cares about this hypothetical scenario which doesn't exist?
The horizon isn't at eye level, it is below it.

Quote from: MagicFlame007 on August 16, 2018, 06:17:09 AM

the opposite window cannot possibly show the same scenery, but instead should be showing a view of space.

I know this might be hard to understand, but the windows on planes don't just show a sliver. Instead you have a large vertical FOV.
You can see quite a bit below the plane and above the plane.
This allows both sides to be looking partially down and seeing the curve.

My point is not to say that you can NOT see the supposed curvature. Quite the opposite; even on a flat earth the horizon must appear to curve around you, so what I am saying is that appearances are not all they seem an no conclusion can be drawn from that sort of observation, either for or against FE.

But the questions. I am asking again for the sake of emphasis.
(1) Where is the horizon if the earth was flat ?
(2) How far away from an observer  or what is the radius and  diameter of the circle  from the observer to the horizon if the earth was flat ?
(3) How would you estimate the distance you can see to the horizon if the earth was flat ?

Why are pictures of the horizon always taken from so far away?

How "far away" do you mean ?
"Pictures of the horizon" are best taken at sea on a calm, clear day, for purposes of illustration.
As has been pointed out so many times  , the horizon is only about 2 or 3 miles "away" if you are at sea level.
And only 10 or 12 miles "away" if you are about 100 feet above sea level.
But to the eye, I suppose  even  those distances can look "far away" to you ?
Been there
Done that.
LOL

Quote from: Bullwinkle on July 26, 2018, 04:51:02 PM

Why are pictures of the horizon always taken from so far away?

How "far away" do you mean ?

Miles.

Quote from: Googleotomy on August 17, 2018, 02:57:25 PM

Quote from: Bullwinkle on July 26, 2018, 04:51:02 PM

Why are pictures of the horizon always taken from so far away?

How "far away" do you mean ?

Miles.

Point taken. Even if you were on the ocean or on a flat, level piece of ground , I would guess something only 2 or 3 miles away might look like it was "far away."
But still..........Where's the horizon if the earth was flat ?

The simple fact is that, the higher you (as the observer) go the more of the Earth is visible to the  horizon.  To a swimmer in the ocean, whose head is just inches above the water, the horizon is about 3 miles.  Standing up at the shoreline, the horizon is about 7 miles.  From the top of the Empire State Building, about 250 miles.  The distance to the horizon is calculated by a mathematical formula (not very challenging) that necessarily is based on the size of the Earth as a sphere.  If we were on another planet (of a different size than Earth) the formula would be slightly different (and predictable from the size of that planet).

This phenomenon and the formula would not work at all unless the Earth is round and of a specified size.