On either the flat Earth or globe Earth models, the horizon wouldn't be a "straight line." The horizon argument is often one of the first cited by flat Earthers in my experience debating with them. "The horizon is a straight line," they say, "so the Earth must be flat." But the horizon is circular, on a flat Earth or a spherical Earth.

Say you're on a massive ocean that covers the Earth, an Earth which may or may not be spherical. You can see an equal distance in every angular direction. You may be far from the edge on a flat ocean Earth or at any point on a spherical ocean Earth. The horizon is both ahead of you and behind you, an equal distance away in every direction. That's a circle. It curves around you, irrespective to which Earth you've found yourself in. If this Earth is flat, your horizon is a circle. Its diameter is determined entirely by your height and how much the atmosphere scatters light. If this Earth is spherical, your horizon is still a circle. Its diameter is this time determined by your height, the atmosphere as mentioned previously, and the diameter of the sphere. The only discernible difference, unless you come to a visible edge, is that the spherical Earth's horizon appears lower than the flat Earth's horizon. How much lower is dependent on the atmospheric scattering of light once more and the diameter of the Earth.

Any measurements of how "low" the horizon is, taking into account instrument height, atmospheric scattering of light, and a proposed diameter of the Earth could never disprove a spherical Earth. It could certainly disprove our current understanding of gravity and even the proposed circumference of the potentially spherical Earth, but you couldn't use that measurement to disprove a globular Earth completely. I've never seen anybody do that regardless.

I'd like to see this "straight horizon" argument put to rest, unless I'm missing something critical here, in which case, I'd be delighted if you attempted to educate me :D
« Last Edit: June 20, 2019, 04:31:31 AM by JLPicard »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #1 on: June 20, 2019, 04:54:32 AM »
I would disagree with your analysis of the horizon on a flat Earth. I think you've got a good handle on the globe version.

Here is my video on the flat Earth horizon. I don't much go into the shape of it, but I do go into the dip angle.


This video is focused more on the argument that "the horizon rises to eye level," but the argument that "the horizon is straight" is closely related.

Before even discussing how to do the math to work out the exact shape of it, there is something that I'd like to challenge first. This is something that FEs often cite, but I'm not certain that it's valid. I think this needs to be established clearly before we accept it as a premise:
"If this Earth is flat, your horizon is a circle. Its diameter is determined entirely by your height and how much the atmosphere scatters light."

I have a few points related to that which I would like to dig into before I accept this:
1) I've seen haze, and I've seen crisp horizons. They don't look the same.
2) I've seen the sun passing behind a crisp horizon. The sunset is at least thousands of miles away on anyone's model, so doesn't this mean that I can see thousands of miles?

It is my conclusion based on the above that on a flat Earth there should be exceptionally clear days where we should be able to see mountains at least as far away as the sunset. (For this discussion, we can set aside the conundrum of how the Sun is there in the first place.)

What do you think?

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #2 on: June 20, 2019, 08:07:17 PM »
That is exactly what I'm been saying during the last two days... precisely https://forum.tfes.org/index.php?topic=14994.msg195235#msg195235

I've seen lots of people at Internet rubbishing texts about proving the horizon is not curved, so, wow, the earth must be flat, and other foolishness due not understanding the tridimensional real world visual basics.

Yes, without obstructions the horizon is a flat horizontal circle, the perimeter of such horizon is all around you, mostly equidistant, in the same horizontal level, just sit over the edge of how far you can see.   Any other explanation about horizon is nonsense.

People start to calculate 8 inches drop per mile, blah blah, they are just showing their ignorance.  You can not see any curvature on horizon, sorry, period.

Some pearls of bad auto-exposure:
https://aplanetruth.info/14-if-the-earth-is-a-curved-sphere-why-are-all-horizons-flat/

Almost, but no cigar... failed to see the light.
https://www.boredpanda.com/lake-michigan-curvature-flat-earth-gregpagel/

Is not how high you go, if you still can see the same land on your back, you still over a horizontal flat circle, the horizon.
https://steemit.com/flatearth/@barber78/flat-horizon

The only way to see "some curvature" is going very far from the object, in order to see the "horizon circle"  in front of you, as a whole, everything at once, one viewframe, then you will see the "circle", curved.  Then, obviously the same object will not be at your back, everything at once in front of you.  To do it with Earth planet, you need to go 20~30 thousand miles up in space.   Other than that, nope, your horizon will be a flat circle around you.
« Last Edit: June 20, 2019, 08:41:24 PM by spherical »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #3 on: June 20, 2019, 10:07:45 PM »
Actually, I'm going to nitpick here a bit. (Big surprise, right?)
The horizon looks perfectly flat to the naked eye... yes! You can go pretty high, and it'll still look flat... yes!
But just because it LOOKS flat, that doesn't mean it's perfectly flat. What if you had an instrument more sensitive than the naked eye? Like... a digital camera. Yup. All it takes is a digital camera. You can count pixels on the final image and BAM! It ain't flat afterall. A better way to visualize this (rather than counting raw pixels) is to compress the image... to exaggerate the curvature. (Not to CREATE the curvature, but to exaggerate any curvature that exists.)
Here's a fairly simple demonstration:
« Last Edit: June 20, 2019, 10:09:32 PM by ICanScienceThat »

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Offline Tom Bishop

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Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #4 on: June 20, 2019, 11:26:45 PM »
From the photos that author shows, which appear to be the sames ones in the video, it looks more like distortion to me:

Straight:



Then the author shows us a version with the beams tilted in comparison with the horizon. In this one we can see that there is clearly curvature on the beams:



Funny how the beams morph and curve like that.

Mick West says it himself:

Quote
>If it's the optical aberration called 'distortion' (i.e., a varying plate scale with field position) then it shouldn't vary randomly. It may vary with focal length and focus setting of the lens, but not randomly.

>>But as I noted above, it DOES vary randomly, and I suspect the cause is the image stabilization moving the sensor. This is subject to random inputs, and so is random.

Cameras are not suited for this sort of test. There is a lot of distortion in the results.

« Last Edit: June 20, 2019, 11:45:28 PM by Tom Bishop »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #5 on: June 21, 2019, 12:55:11 AM »
I would disagree Tom. That is the very point of the straight edges. Notice how straight they remain in comparison to the amazingly smooth curve of the horizon.
You've labeled them as "STRAIGHT(ISH)". Do you not see the striking contrast?

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Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #6 on: June 21, 2019, 01:10:27 AM »
I would disagree Tom. That is the very point of the straight edges. Notice how straight they remain in comparison to the amazingly smooth curve of the horizon.
You've labeled them as "STRAIGHT(ISH)". Do you not see the striking contrast?

The control in the experiment is supposed to remain straight. However, it is not straight. This is a demonstration of the presence of distortion in the camera sensor.

If you go through that Metabunk thread Mick West explains that the camera can have different amounts of distortion in different spots.

The Jeran video I posted above shows that taking a picture of a straight rectangle on a computer screen can produce distortion effects to make the straight line appear curved.
« Last Edit: June 21, 2019, 01:17:38 AM by Tom Bishop »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #7 on: June 21, 2019, 01:17:10 AM »
I would disagree Tom. That is the very point of the straight edges. Notice how straight they remain in comparison to the amazingly smooth curve of the horizon.
You've labeled them as "STRAIGHT(ISH)". Do you not see the striking contrast?

The control in the experiment is supposed to remain straight. However, it is not straight. This is a demonstration of the presence of distortion in the camera.

If you go through that Metabunk thread Mick West explains that the camera can have different amounts of distortion in different spots, and that it can manifest unpredictably.

You are not addressing the images shown. You are trying to suggest that because the lens has distortion, any photo from it cannot be used. This is not fair. Any distortion that affects the horizon affects the beam in exactly the same way. That's why the beam is there. Rory (the author of the video) goes to some lengths to take images of a grid pattern to identify what sort of distortion his camera has. He also shows how this type of test is confounded by image stabilization, and how that is not relevant to these images shown here. I have not provided links for that because it isn't important. The contrast between the beam and the horizon is undeniable.

You cannot throw out this result based on lens distortion. Lens distortion can be measured and accounted for. As has been done here.

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #8 on: June 21, 2019, 03:42:37 PM »
It seems you guys don't grasp it, do yah?

There is no horizontal curvature on the circled horizon around you, and I am talking about oblate spherical planet.
If it exist, so it would accumulate and go very deep down on your back view, right?
The problem on any optical device is the lens, only expensive lens can give you a very good orthoscopy image.
You need to read https://clickitupanotch.com/lens-distortion/

There is no horizon curvature, except if you go very very high in a way where you have the whole object in front of you, nothing on your back.  In case of Earth planet, "very high" means more than 20 thousands miles up.

Apparently this thread is being diverted to discuss camera pixels accuracy, trying to ignore the original post.
« Last Edit: June 21, 2019, 04:12:36 PM by spherical »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #9 on: June 21, 2019, 05:13:10 PM »
It seems you guys don't grasp it, do yah?

There is no horizontal curvature on the circled horizon around you, and I am talking about oblate spherical planet.
If it exist, so it would accumulate and go very deep down on your back view, right?
The problem on any optical device is the lens, only expensive lens can give you a very good orthoscopy image.
You need to read https://clickitupanotch.com/lens-distortion/

There is no horizon curvature, except if you go very very high in a way where you have the whole object in front of you, nothing on your back.  In case of Earth planet, "very high" means more than 20 thousands miles up.

Apparently this thread is being diverted to discuss camera pixels accuracy, trying to ignore the original post.
I believe you are mistaken. Yes there IS a horizon curve. I just posted a video showing you that it's there. I also explained how any amount of lens distortion affects the straight-edge in exactly the same way as the horizon. You can then compare the curve of the straight-edge to the curve of the horizon to see what the true curve of the horizon is. It's curved, and if you'd care to do the math, it matches amazingly well.

Am I misunderstanding you here? Let me try to lay out some logical flow in case we're not communicating effectively.

1) Imagine that the horizon is a circle equally distant in all directions.
2) That circle is level. It is perpendicular to the direction of the pull of gravity.
3) You are in the center of that circle.
4) That circle is below eye-level very slightly.
Right? We're all on the same page so far?
5) Let's take that "below eye-level" to the extreme and explore what that would cause. Use the hula hoop visualization. Stand in the middle of a hula hoop and take a photo of the front of it. The front of the hoop is dead center in your frame. To the right, the hula hoop exits the frame lower than that. To the left, the hula hoop exits the frame lower as well. You're looking down on a circle, so of course it looks curved.
6) Now slowly raise that hula hoop up towards eye level. At what point does that curve finally become a straight line?
7) It's a straight line when it's at eye level, and it's a curve on the floor. How does it go from one to the other?
8) There won't be any discontinuity. It's going to smoothly transition becoming less and less curved as you raise it until it finally hits perfectly straight at exactly eye level.

Right?

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #10 on: June 21, 2019, 06:17:53 PM »
Yes, it all depends on how high you are compared to the diameter of the horizon circle.   

The problem with the hola-loop is the diameter is so small (and fixed) compared to you, and its diameter never change according to you moving it up and down.  In the oblate spherical planet, such diameter changes according to your altitude, to a certain point. 

Think with me:  If you are floating on the open high sea, you can not see very far, your horizon is limited by the 8"/mile, and most of all, the waves and turbulence in the water, but imagine you stand at 30 ft high, and can see far because you can see over the waves and turbulence.  Even so, your horizon view distance is limited by the 8"/mile, maybe not considering waves of moisture affecting refraction of light, you will be able to see 3 to 4 miles, so that is the radius of your hola-loop.  If you fly up to 300 ft, your hola-loop horizon radius will increase, keep the flat horizon line straight. Fly up to 10km high, hola-loop becomes bigger, still flat horizon.   The only altitude your hola-loop stop increasing radius, is when the horizon increase can not keep up with your height, the curvature escaped in an bigger angle than your distance (altitude) can not see it, and that is when you start to see the curvature of the horizon as you stated, yes, it happens, I agree with you, but only in altitude proportional to the diameter of the hola-loop.   In case of the Earth, the diameter is big, you need to be far away for that to happen.  See, I agree with you, it is just a matter of proportions.

I don't have a graphic generator software here, tonight I will post some nice drawing about mending 4 "pictures" of 90° aperture to make a panoramic view of 360°, even with small degrees of curvature down on the edges, the final image becomes what you do not see in real life. It will be a dented horizon, you don't see it when turning your head on open seas, not real.

There is a visual misconception about what is up/down, front/back on our world observation.
If you see a hola-loop in the ground, and you are standing up one meter outside it, you could state that in a 2D representation the farther side of the loop is high, the closer side is down, it appears like that in a photo, right?  But your intelligence tells you the hola-loop is flat on the ground, so it is leveled horizontally, no up, no down, just a visual interpretation of the 2D observation.   You can even swear that loop forms a curvature, yes, but horizontal one, over the ground.

Now, imagine 100 hola-loops each one with an increasing diameter as a function of sine(), if you pile up those loops you will have one half of a ball (hemisphere), number those loops from 1 to 100, being 1 the small on top, the largest (100) touching the floor.  Now, if the diameter of the #100 is 10 thousand times bigger than you, and you are over the #1, maybe you could see the #1 and #2, being the horizon.  If you go higher vertically, start to see the #3, #4 and so on, perhaps very high you could see #50, much higher, #70, astonishing higher, perhaps #99 or even #100.   What curvature would you see, even when seeing the #100?  The curvature of the loop, you can not see the curvature made by the sequence #1 to #100, you can not, you are on vertical top, you only see concentric circles.  Of course, 3D image can show you the #100 is further down than #1, but you still "not seeing any curvature", only the curve (circle) of each loop in the pile.  Well, the curvature of each loop is a nice proof of the hemisphere being curved, but that is horizontally curved, not vertically.   To see it vertically, you need to move yourself down and out of the top, go horizontally far, at height of loop #50, then maybe you will see the hemisphere sideways, curved vertically.

We are talking the same thing, just a matter of proportions and what curvature you are trying to show, the horizon circle curvature or the vertical curvature made from you to distance?  That is the one people try to prove showing boats disappearing below the horizon.  You can not capture that curvature horizontally in front of you with a photo picture.
 

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #11 on: June 21, 2019, 07:11:01 PM »
spherical, I'd like to clarify. I think we are saying the same thing, but language is getting in the way.

The horizon is a circle that is flat and level. That is, if we were to draw the thing and then go up in a spaceship to look at what we drew, we'd see we had drawn a flat, level circle. Every spot on a perfect horizon is at exactly the same actual height relative to the observer.

When the observer views that level circle, it is projected onto an image plane - be it an eyeball or a camera frame. In the image we make in this way, the flat, level circle forms a curve.

Are we on the same page here?

If I may say this simply, the horizon on a sphere should BE a circle. The horizon on a sphere should LOOK LIKE a curve. The higher the observer, the more curved it LOOKS.

Right?

Edit: I came up with another way to describe it that may help...
The horizon is a circle.
That circle is parallel with your local "level".
If you look at the horizon, you are NOT looking "level".
Therefore, the horizon (if you look at it) is a circle that is TILTED compared to your view direction.
The higher you are, the more you need to TILT to look at it, and the more TILTED that circle looks.
« Last Edit: June 21, 2019, 07:40:08 PM by ICanScienceThat »

Re: The horizon isn't a straight line. Stop saying it's a line.
« Reply #12 on: June 21, 2019, 08:03:27 PM »
Therefore, the horizon (if you look at it) is a circle that is TILTED compared to your view direction.
The higher you are, the more you need to TILT to look at it, and the more TILTED that circle looks.

Correct, the same example of the hola-loop on the ground, you may say there is a up and down on the 2D image, because it is tilted.
Yes, if you go high enough you will see the circle curvature, and the vertical curvature, and there is a height where it starts to show that, really small and then it grows.  We are in the same page.