[Bobby Shafto]

"A fact of basic perspective is that the line of the horizon is always at eye level with the observer."
https://wiki.tfes.org/Horizon_always_at_Eye_Level

If this "fact of basic perspective" is true, I believe it can only be true for perspective at eye-level over a plane (flat) surface).

For perspectives from an eye-level height of a plane tangent to a curved surface, the horizon will not always be at eye-level.

This would make observations of horizon relative to eye-level a potentially good indicator of whether or not one is viewing that horizon over a flat or a curved surface.

Is there anything wrong with that line of reasoning?

[9 out of 10 doctors agree]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

[Westprog]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

[Tumeni]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

[9 out of 10 doctors agree]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

Yes. Again, the flat earthers didn't understand any of the evidence presented. They claimed that the u-tube wasn't at eye level.

[Bobby Shafto]

Define "eye-level".

I hadn't thought to ask that question, but good idea to define so that we're all on the same sheet of music.

I assumed "eye level" was a sight line at same level as the eye, parallel to the surface.



The same geometry would apply if the surface is curved, but replace the last phrase with "parallel to a tangent of the curved surface."

"The horizon is always at eye level" means (to me) that no matter the height above the surface, the horizon will appear in line of sight with no inclination or declination. It "rises" to eye level without having to angle sight line down from the horizontal.

Is that correct? (Flat earth proponents?) 

[Bobby Shafto]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

Yowza!  That's pretty much what I was thinking about doing.

But I thought I'd invite the community here to talk it through first: what am I measuring. How should I be sure to do it (and document it). And make predictions about the results or analysis of predicted results. Do all that before putting in the effort.

The wiki is making the claim and using that as the basis for a flat earth argument about horizons. I thought it might be worthwhile to test the claim.

[Tontogary]

And recently i measured, with an accurate sextant, the angle across the sky from horizon to horizon south to north, and guess what? I got over 180 degrees, proving the horizon is not at eye level.

No FEer challenged my accurate, repeatable, and conclusive observations/experiment, which pretty much qualifies as Empirical evidence and the trump card in Zetetic processes.

So I my conclusion is that the FE movement is pretty much dead.

[SiDawg]

Yeah it's a particular frustrating area. They write that they understand why the horizon rises with eye level, and they're "kind of" right, but they don't understand why it does that mathematically. They mention 3d games and turning off clipping... they're exactly right in that example! A computer game CAN mathematically calculate for infinity, and so the horizon will appear at eye level. But they don't actually seem to understand HOW this works... if they did, then they'd understand how perspective works, and if they understood that then they'd understand why the flat earth doesn't work

I've tried explaining this to them: look 2 meters in front of you, roughly 45 degrees to a parallel site line. Look 4 meters in front of you. roughly 30 degrees... etc... very simple maths to calculate that angle, and it literally never reaches "0": it would have to be 0 for it to appear on that parallel line. In mathematical terms, you can express the "limit" for the angle as 0 when the distance is infinite... but i'm pretty sure not even the FEers think they are seeing to infinity (even if they do believe the earth stretches infinitely) on account of the earth having an atmosphere n'all

So they're "kind of" right? In a way? The horizon "kind of" rises to eye level on a flat earth as well as a globe earth, in that it gets really really close, and appears level... but you have to understand the maths, you have to understand perspective, and you have to understand how the eye resolves things that are "really close to zero".

From that starting point, from an understanding of how things SHOULD appear on a flat earth, then we can quite easily show how that's not the case (and the video above is a perfect example of this, yet they dismiss it for some reason. Very frustrating). Basically their argument is "well the horizon looks like it's at eye level, so therefore the earth is flat"

[Bobby Shafto]

I confess I don't understand the horizon in a flat model. As I think I understand it, the FE "horizon" is a perceptual one (apparent) that occurs level to height of viewer (0° to the horizontal), but isn't a measurable distance. It depends on acuity (resolution) and obscuring factors in the air.



The horizon on a convex curved surface is a geometric point, calculated by height of viewer and radius of the curve, but it's always some angle below the horizontal, though appearing to be at horizontal for low values of h relative to r.



If so, then I think that if you can demonstrate that the horizon drops below horizontal eye level with increasing height, it supports a curved surface. If the horizon appears consistently at the horizontal at all values of h, it would support the flat earth claim.

Does that make sense?

If so, the next step is to find agreement on how best to measure and document the horizon vs. "eye level" at different heights above the surface. I have some ideas, and I have easy access to viewpoints from sea level to 1500' with clear views to an ocean horizon, though catching a non-hazy day for a good horizon contrast is hit and miss this time of year.

I like the idea of a water level that's not cumbersome to tote on a hike, but I'd want it to be set up on a stable platform or tripod rather than handheld as in that video. Plus the camera would have to be stabilized and aligned with the leveling site.

I think about it, but would appreciate input or feedback, particularly from "horizon always at eye level" proponents.

[Westprog]

I confess I don't understand the horizon in a flat model. As I think I understand it, the FE "horizon" is a perceptual one (apparent) that occurs level to height of viewer (0° to the horizontal), but isn't a measurable distance. It depends on acuity (resolution) and obscuring factors in the air.



The horizon on a convex curved surface is a geometric point, calculated by height of viewer and radius of the curve, but it's always some angle below the horizontal, though appearing to be at horizontal for low values of h relative to r.



If so, then I think that if you can demonstrate that the horizon drops below horizontal eye level with increasing height, it supports a curved surface. If the horizon appears consistently at the horizontal at all values of h, it would support the flat earth claim.

Does that make sense?

If so, the next step is to find agreement on how best to measure and document the horizon vs. "eye level" at different heights above the surface. I have some ideas, and I have easy access to viewpoints from sea level to 1500' with clear views to an ocean horizon, though catching a non-hazy day for a good horizon contrast is hit and miss this time of year.

I like the idea of a water level that's not cumbersome to tote on a hike, but I'd want it to be set up on a stable platform or tripod rather than handheld as in that video. Plus the camera would have to be stabilized and aligned with the leveling site.

I think about it, but would appreciate input or feedback, particularly from "horizon always at eye level" proponents.

This is something that's really easy to test. I'd like to see an acknowledgement that

• "The horizon is always at eye level" is a testable proposition.
• Agreement on a test that can be readily carried out.
• Acceptance that if the test disproves the proposition, that it should no longer be put forward.

I don't expect people to reject flat Earth altogether when this test is proposed, but I would hope that the "horizon rises to eye level" idea could at least be addressed. If the FE proponents are confident that the horizon does rise to eye level then they should be demanding that such experiments take place.

I'll state my own POV up front. I'm interested in the cognitive dissonance of the FE movement, and I'm reasonably confident that the items on the above list wouldn't be accepted by any FE proponents. If I'm wrong, then a test will be devised, the experiment performed, the results accepted and the FAQ on this site amended accordingly.

It should be something performable with some kind of levelling device, a camera, and a hillside overlooking the sea.

[hexagon]

On a globe the horizon is always below your eye level, because it i physically below your eye level and perspective doesn't not change physical relations between objects. Below is always below, above is always above, left is always left and right always right with respect to the optical axis defined by your eye and the point where you are looking at. Therefor, if you are looking parallel to the tangent line of the globe where you're standing, the horizon is always below.

On a flat earth there's no horizon in that sense, because the sky would be physically always above you, the ground always below you. They would only meet at infinity at the so-called vanishing point. But because no one can look that far under the atmospheric conditions of our earth, everything would be vanishing in diffusive blur far away...   

[AATW]

This is something that's really easy to test. I'd like to see an acknowledgement that

• "The horizon is always at eye level" is a testable proposition.
• Agreement on a test that can be readily carried out.
• Acceptance that if the test disproves the proposition, that it should no longer be put forward.

I don't expect people to reject flat Earth altogether when this test is proposed, but I would hope that the "horizon rises to eye level" idea could at least be addressed. If the FE proponents are confident that the horizon does rise to eye level then they should be demanding that such experiments take place.

I'll state my own POV up front. I'm interested in the cognitive dissonance of the FE movement, and I'm reasonably confident that the items on the above list wouldn't be accepted by any FE proponents. If I'm wrong, then a test will be devised, the experiment performed, the results accepted and the FAQ on this site amended accordingly.

It should be something performable with some kind of levelling device, a camera, and a hillside overlooking the sea.

I do find this one particularly weird because you can think about horizon dip theoretically but then you can go and test this yourself. It can be measured.
3 different ways of doing this have been shown on here recently, they've all been rejected on spurious grounds. The real reason they've been rejected is that they don't show what the FE Dogma claims. As you say, cognitive dissonance.
Tom did outline a method of testing this which involved a camera looking across a tall building towards the horizon which actually would work in theory but there are two quite serious problems with that method
1) Buildings are, in general, not that tall and significant horizon dip can only be clearly seen at higher altitudes.
2) There is no way of accurately determining that the height of the building and the height of the camera are exactly the same.

This is where the experiment shown above wins because you can take the simple equipment with the water to any height and be sure that looking across the two tubes will be level. Tom's rejection of that was that it was hand held and therefore not that steady, but I took these stills which shows the result very clearly:



It's quite hard to argue people who literally refuse to concede a point when it is demonstrated so clearly.
For his next trick, to misquote Douglas Adams, he'll claim black is white and get killed on the next zebra crossing.

[Westprog]

It's quite hard to argue people who literally refuse to concede a point when it is demonstrated so clearly.
For his next trick, to misquote Douglas Adams, he'll claim black is white and get killed on the next zebra crossing.

This is an example of just how things work in this kind of discussion. Clearly you need some kind of objective measure of level. Since it's generally known that water flows downhill, the u-tube with a coloured liquid is a good idea. It's not totally accurate, but it doesn't need to be. The point isn't to measure the drop to the horizon - it's to demonstrate that the drop to the horizon exists.

[Bobby Shafto]

Planning this out to see if it's worth the effort. I think a set up like that water rig is the best, though I'd like to set it on a sturdy tripod, as well having the camera on a tripod level with the sight line.

I'm thinking about the following locations (all San Diego county) with elevations:

Ocean Beach
32.750551, -117.252887
H=4ft
VH=12837ft
Angle=89.98°
Expected Dip=(00.02°)

Point Loma
32.703142, -117.249516
H=400ft
VH=129369ft
Angle=89.82°
Expected Dip=(00.18°)

Black Mountain Glider Launch
32.987933, -117.122248
H=1160ft
VH=220307ft
Angle=89.70°
Expected Dip=(00.30°)

Black Mountain Summit
32.981675, -117.116565
H=1376ft
VH=239943ft
Angle=89.67°
Expected Dip=(00.33°)

That's about the most elevation I can get locally and still keep a pretty sharp contrast to the horizon. I don't gain much altitude without going further inland but then horizon gets fuzzier.

At 1376' I only calculate a dip angle below horizontal of 0.33°

I don't really care about measuring the dip. Only whether or not it is detected. But that means making sure I have an accurate level sight line. The water level rig is great because then I don't have to worry about leveling two things. I just need to level the camera.

I played around with a 4' carpenters level on a tripod, using a plumb line/square, the bubble level on both the level and the tripod, (and yes, even my iphone, for what it's worth) to try to make it level, but who knows if it's +/- a degree from 90°?

Anyway, here's the shot:


DLSR camera was not on a tripod.
I didn't get it lined up quite right. I wanted the centerline of the level to be horizontal but my camera elevation was little too high. But the perspective vanishing point is above the visible horizon. All of the photos were like this. None erred to at or below the horizon contrast point. At only 400', though, and a predicted "dip" of less than a quarter of the angular diameter of the sun, I'm not sure this is meaningful without a true level set of indices.

I'm just playing around right now. Trying to make a plan before I spend time building a leveling rig and making the hikes.

(The photo above without the annotation: http://oi65.tinypic.com/9hi0dk.jpg)

[Tom Bishop]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

https://www.youtube.com/watch?v=NqOQ_BCtqUI

Water flows down hill. How do we know that water was perfectly leveled out at the point of the line ups?

The hand held camera's slight up down motion, in line with the black line of the water in the foreground affects the scene significantly in the far background, even if it is a pixel.

Everything needs to be perfectly leveled and aligned, and this water device is insufficient.

Furthermore, on a mountain or large hill, how do you know that the true horizon hasn't disappeared into an atmospheric fog that you can't see, thousands of miles away from you, and is squished beyond imperceptibility? This is clearly what happens when you get to high altitudes like from an international flight. The horizon is very foggy. What makes you think that the same is not true at lower altitudes, but the disappearance is more squished into the horizon by perspective?

[9 out of 10 doctors agree]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

https://www.youtube.com/watch?v=NqOQ_BCtqUI

Water flows down hill. How do we know that water was perfectly leveled out at the point of the line ups?

The hand held camera's slight up down motion, in line with the black line of the water in the foreground affects the scene significantly in the far background, even if it is a pixel.

Everything needs to be perfectly leveled and aligned, and this water device is insufficient.

Furthermore, on a mountain or large hill, how do you know that the true horizon hasn't disappeared into an atmospheric fog that you can't see, thousands of miles away from you, and is squished beyond imperceptibility? This is clearly what happens when you get to high altitudes like from an international flight. The horizon is very foggy. What makes you think that the same is not true at lower altitudes, but the disappearance is more squished into the horizon by perspective?

Tell me, why does the distance to a horizon over water increase with altitude then?

[Tontogary]

Define "eye-level".

And also, we've discussed this at length before and the flat earthers didn't understand any of the evidence presented.

Wasn't there an experiment performed a short while ago that soundly disproved this, using a u-tube filled with coloured water?

https://www.youtube.com/watch?v=NqOQ_BCtqUI

Water flows down hill. How do we know that water was perfectly leveled out at the point of the line ups?

The hand held camera's slight up down motion, in line with the black line of the water in the foreground affects the scene significantly in the far background, even if it is a pixel.

Everything needs to be perfectly leveled and aligned, and this water device is insufficient.

Furthermore, on a mountain or large hill, how do you know that the true horizon hasn't disappeared into an atmospheric fog that you can't see, thousands of miles away from you, and is squished beyond imperceptibility? This is clearly what happens when you get to high altitudes like from an international flight. The horizon is very foggy. What makes you think that the same is not true at lower altitudes, but the disappearance is more squished into the horizon by perspective?

In have dealt with this question and proved through measurements with a sextant (accurate and calibrated) that the arc of the sky is more than 180 degrees, by pretty much the same amount as is expected for the hieght of the observer.
What dont you understand about that Tom?
If the sky, from clear, sharp horizon, to the south, across the sky to a clear sharp horizon on the north is more than 180 degrees, then the bit below you is less, therefore the horizon is NOT rising to meet you.

I cannot really explain much clearer, and a young teenage child would likely understand that.

[SiDawg]

Water flows down hill. How do we know that water was perfectly leveled out at the point of the line ups?

That's the beauty of the two tubes... yes if you angle them "downhill" there will be a slight delay as liquid from one moves to the other, but given the size of the pipes, that's almost instantaneous. That's like saying the water in a bucket isn't level when you tip it... if you tip it quickly it might 'wobble' but it very quickly finds level.

The hand held camera's slight up down motion, in line with the black line of the water in the foreground affects the scene significantly in the far background, even if it is a pixel.

Everything needs to be perfectly leveled and aligned, and this water device is insufficient.

I agree it's a rough demonstration: but for some frames, he's actually misaligned so that the far tube water line is ABOVE the near level: so if the horizon is appearing below both, then that's even GREATER proof... if they were all level and on a flat earth (horizon and both tubes), then the horizon would've appeared ABOVE the second tube line.

Furthermore, on a mountain or large hill, how do you know that the true horizon hasn't disappeared into an atmospheric fog that you can't see, thousands of miles away from you, and is squished beyond imperceptibility? This is clearly what happens when you get to high altitudes like from an international flight. The horizon is very foggy. What makes you think that the same is not true at lower altitudes, but the disappearance is more squished into the horizon by perspective?

That's a fair call. I wish this guy had've run the experiment in a colder/clearer climate. The final distance especially shows huge atmospheric effects. The important thing to remember is that the world IS a globe, it is not flat, and you're looking for ways to justify your confirmation bias

[Westprog]

I wish this guy had've run the experiment in a colder/clearer climate. The final distance especially shows huge atmospheric effects. The important thing to remember is that the world IS a globe, it is not flat, and you're looking for ways to justify your confirmation bias

An important point is that because the horizon as seen from a height is much further away, it's likely to be fuzzier, because there's more atmosphere in the way. Note that this effect only happens on a round Earth, because on a flat Earth, the horizon is an effect of... well, I'm not clear exactly what it's an effect of. If the flat Earth horizon is due to atmospheric distortion, then it should always be fuzzy. If it's due to "perspective" then who knows?

It should also be noted that even though the horizon is fuzzy, it's still perfectly possible to see that it is below eye level.