Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #120 on: May 14, 2018, 02:10:25 PM »
It strikes me that the more interconnected tubes there are, the more chances that an unfriendly Team Hoaxer will assert;

"The water's flowing too slowly"
"The tubes are restricting the water flow"

and such ...  so;

Take a clear plastic lid or tray...place on a reasonably flat surface, and fill with coloured water. The water will find its own level, and give a long edge to sight along. No issues/concerns over water flow.

I'm going to go with something like this.

hexagon

• 192
Re: The Horizon is Always at Eye Level
« Reply #121 on: May 14, 2018, 04:33:31 PM »
This is all very nice and demonstrates very well how perspective works in the real world, but I guess that will not impress any EnaG believer. If you look it up, they construct "perspective lines" in a very different way. First they place the vanishing point, which is given by a right-angled triangle, where the hypotenuse is the direct line between your eyes and the vanishing point. One cathetus is down from your eyes to sea level, the other one going from there to the vanishing point. The angle at the vanishing point is fixed, therefore the vanishing point is moving away if you go higher.

Everything behind this vanishing point you can't see, everything in front adopts in size so that it fits into the triangle. The angle is defined by the optical resolution of your eyes. Therefore, if you take a telescope, the angle changes and the vanishing point is moving further away, which leads to the recovery effect.

That's a kind of far-field perspective, where the Euclidean geometry is no longer valid. You demonstrate near-field perspective, which goes along with Euclidean geometry. To disprove this concept, you would need a device that goes from you to the horizon. But that's not possible. And something like railway tracks does not help, because that's give you no conclusive result. Because they are to narrow and apparently melt into a single point at the horizon and if you climb up, the horizon will indeed move away while the tracks apparently still melt into one point at the horizon.

It's a debate you can not win, because for every proof you show, they will demand another one that will set the level for you even higher...

I see that someone here has actually read Earth Not a Globe.
Well, I have too -- both editions. Can't say I understand the flat earth explanation for horizon, but for this effort, all that matters is whether or not the horizon is level with the eye, regardless of why or why not.

But you have to understand it, if you want to understand why they don't believe in your argumentation or your experiments. It does't help that you climb mountains with your apparatus and make nice pictures and draw some lines to show something they do not deny. To convince them, you have to show that all the lines you draw are representing the real behavior up to what they call the vanishing point. Good luck with that...

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #122 on: May 14, 2018, 05:44:03 PM »
But you have to understand it, if you want to understand why they don't believe in your argumentation or your experiments…
I don't think I do. The objective is to simply verify or refute the claim that "the horizon is always at eye-level."

I would love to understand the explanation for why that would be so on a flat surface earth, but it's not necessary that I do in order to test the claim.

Now, if I demonstrate that the horizon is NOT always at eye-level, any dispute will have to come from test set up or the method with which I attempt to observe it. But such issues have nothing to do with understanding why the horizon is always at eye-level.

If it can be shown that the horizon drops below level as elevation increases, then that doesn't mean it'll refute a flat earth. It will just refute the horizon claim. Flat earth proponents will have to theorize another explanation for why the horizon appears as it does.

On a convex curved surface, the horizon will drop from level.
How it appears on a flat surface? I'm interested, but that's not my concern in this effort. I just want to see if it drops or not.

If there are problems with setup or method, I've invited feedback numerous times. I feel confident I'm being more careful, meticulous and guarded against obtaining a preferred outcome than was Samuel Rowbotham, but if there's a technique or method he used to verify the horizon was always at eye-level that I am missing, I encourage anyone to speak up and allow me the opportunity to include it.

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #123 on: May 14, 2018, 08:10:06 PM »
Preliminary look: today, from 100' bluff. Marine layer ceiling but clear horizon.

Photos are 1600x900 resolution, so don't want to inline them. Should open as links a new tab:

1. Original photo
2. With lines of perspective

(Did not use plumb bob due to wind)

Tontogary

• 431
Re: The Horizon is Always at Eye Level
« Reply #124 on: May 14, 2018, 10:53:12 PM »
Preliminary look: today, from 100' bluff. Marine layer ceiling but clear horizon.

Photos are 1600x900 resolution, so don't want to inline them. Should open as links a new tab:

1. Original photo
2. With lines of perspective

(Did not use plumb bob due to wind)

Comment. It looks very good to me! I can clearly see, even between the levels on the left the horizon is below the level. This is at 100 feet, then it will be more so and clearer at higher elevations.

Maybe a picture taken with the horizon lined up with one of the water surfaces in the tubes might help coinvince some of the effect of moving the camera up or drown, as there might be some questions of whether the camera is lined up with the water levels. I know it wont make a difference, but will likely head off some comments about it.

Also, if you haven't heard of bronies before, that reflects poorly on your understanding of the world that surrounds you. It's practically impossible not to know about them.

Tom Bishop

• Zetetic Council Member
• 10712
• Flat Earth Believer
Re: The Horizon is Always at Eye Level
« Reply #125 on: May 14, 2018, 11:18:12 PM »

1. In Arctic conditions conditions people have reported seeing objects hundreds of miles away. What makes you think that you are actually looking at the real horizon at this particular time?

2. The camera does not appear to be perfectly center level alignment with the center string and the water line. The distance from the top of the picture to the string is 419 pixels and the distance from the bottom of the picture to the string is 485 pixels. This means the center of camera lens is below at the level of the water, looking up at it.

If you wanted to make sure that three points in space are in perfect alignment with each other would you look at those points from below the points, above those points, or anywhere other than in the same line of those three points?

3. The water itself does not appear to be perfectly level: https://i.imgur.com/FlPL33D.png
« Last Edit: May 14, 2018, 11:22:54 PM by Tom Bishop »

Curious Squirrel

• 1337
Re: The Horizon is Always at Eye Level
« Reply #126 on: May 14, 2018, 11:21:53 PM »

1. In Arctic conditions people have reported seeing objects hundreds of miles away. What makes you think that you are actually looking at the real horizon?

2. The camera does not appear to be perfectly center level alignment with the center string and the water line. The distance from the top of the picture to the string is 419 pixels and the distance from the bottom of the picture to the string is 485 pixels. This means the center of camera lens is below at the level of the water, looking up at it.

If you wanted to make sure three points in space are in perfect alignment with each other would you look at those points from below the points, above those points, or anywhere other than in the same line of those three points?

3. The water itself does not appear to be perfectly level: https://i.imgur.com/FlPL33D.png
Per #1, please define 'real horizon' in this circumstance. I see nothing else in the image one could define as a horizion in my mind.

Per #2, did you note the crate itself is not even on both sides of the string? This will change the center of the image in relation to the crate.

Tom Bishop

• Zetetic Council Member
• 10712
• Flat Earth Believer
Re: The Horizon is Always at Eye Level
« Reply #127 on: May 14, 2018, 11:23:45 PM »

1. In Arctic conditions people have reported seeing objects hundreds of miles away. What makes you think that you are actually looking at the real horizon?

2. The camera does not appear to be perfectly center level alignment with the center string and the water line. The distance from the top of the picture to the string is 419 pixels and the distance from the bottom of the picture to the string is 485 pixels. This means the center of camera lens is below at the level of the water device, looking up at it.

If you wanted to make sure three points in space are in perfect alignment with each other would you look at those points from below the points, above those points, or anywhere other than in the same line of those three points?

3. The water itself does not appear to be perfectly level: https://i.imgur.com/FlPL33D.png
Per #1, please define 'real horizon' in this circumstance. I see nothing else in the image one could define as a horizion in my mind.

Per #2, did you note the crate itself is not even on both sides of the string? This will change the center of the image in relation to the crate.

1. The horizon is at times, to varying degrees, hidden behind atmosphere. How can you tell whether this enlargement of the scene is showing the true horizon or a very distant fog?

2. We have three points in space. We want to see if they are in perfect alignment. Why would you look at those points from any other position than in a straight line alignment with those three points?
« Last Edit: May 14, 2018, 11:36:56 PM by Tom Bishop »

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #128 on: May 14, 2018, 11:29:29 PM »

1. In Arctic conditions people have reported seeing objects hundreds of miles away. What makes you think that you are actually looking at the real horizon?

2. The camera does not appear to be perfectly center level alignment with the center string and the water line. The distance from the top of the picture to the string is 419 pixels and the distance from the bottom of the picture to the string is 485 pixels. This means the center of camera lens is below at the level of the water, looking up at it.

If you wanted to make sure that three points in space are in perfect alignment with each other would you look at those points from below the points, above those points, or anywhere other than in the same line of those three points?

3. The water itself does not appear to be perfectly level: https://i.imgur.com/FlPL33D.png
Thanks. Allow me to address each point separately.

#1. How can I tell if the horizon is real? How did Rowbotham tell when he did Experiment #15?

Some days, from that spot, I can see San Clementi island clearly. Today, I couldn't at all. Too much haze.

If the haze is obscuring the horizon, and it's actually higher than what I'm seeing today (which I do think it could be, though I don't anticipate it will rise to the level line), how will I know I have enough clarity to see the true horizon? Will improved clarity extend the horizon so that its appears higher or does it just refine the resolution at the point where the perspective lines meet?

My lines of perspective matched the level line. Are you saying that the actual horizon, and an uber-clear day will reach that line, and if they don't, then I must not be seeing the real horizon? If so, I need some way to know that. Maybe being able to see San Clemente island is enough? Because in 20 years living in coastal San Diego, I've never seen the horizon above the island nor have I ever seen the base.

That might be a good criterion to add to the requisite conditions. But I appreciate more insight on the matter, from a flat earth point of view about what I'm looking for in "true horizon."

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #129 on: May 14, 2018, 11:39:44 PM »
2. The camera does not appear to be perfectly center level alignment with the center string and the water line. The distance from the top of the picture to the string is 419 pixels and the distance from the bottom of the picture to the string is 485 pixels. This means the center of camera lens is below at the level of the water, looking up at it.

Laterally, you're right. It's very difficult without a tranverse adjustment to set up precisely on center line along the y-axis. A plumb bob giving me a vertical line makes it easier, but I still have to adjust by moving the camera tripod rather than having a slide I can just adjust on the tripod.

But lateral centering isn't a problem. It won't change the horizon leveling observation. In fact, I may take the earlier suggestion to align the camera sight line purposely oblique so that the water tube levels overlap. The perspective lines should still converge, however they'll be at a level vanishing point that is leftward as well.

Vertically is another issue entirely. Leveling the camera in the center of the grid isn't critical. However, leveling the camera so that's it's level with the horizontal sight line is. That sightline doesn't have to be centered. In fact, I chose it to be elevated slightly, to the point at the top of that middle row of wire squares. It's easier to align the water level along one of the wires rather than to gauge it as halfway between two, which is where center would be. So, I filled the water to a level where it was just below the wire, since my sightline string won't slide all the way up. I did the best I could in the time allotted to make the water level and sighting line match. It's not centered, yes. But it's above center by the same amount. And the perspective lines confirm this, assuming that I got the cage straight.

So center-ness shouldn't be an issue. The issue is making sure the sighting guideline is parallel to the water levels. I could set them at the extreme top or extreme bottom. It wouldn't matter, as long as the whole cage is square.

But, a good critique is to look at how closely I do get the water level with the sight line, whether they are on the apparatus.

Tom Bishop

• Zetetic Council Member
• 10712
• Flat Earth Believer
Re: The Horizon is Always at Eye Level
« Reply #130 on: May 14, 2018, 11:53:17 PM »
So center-ness shouldn't be an issue. The issue is making sure the sighting guideline is parallel to the water levels. I could set them at the extreme top or extreme bottom. It wouldn't matter, as long as the whole cage is square.

But, a good critique is to look at how closely I do get the water level with the sight line, whether they are on the apparatus.

Of course the center of the viewing apparatus being centered with the string and the water level of the device is an issue. Move the center of the viewing apparatus vertically 2 feet above or below the string and water level of the water device. Consider what would happen. Is the centering of the viewing apparatus an issue now?
« Last Edit: May 14, 2018, 11:57:21 PM by Tom Bishop »

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #131 on: May 14, 2018, 11:54:50 PM »

3. The water itself does not appear to be perfectly level: https://i.imgur.com/FlPL33D.png
I'm sure what you mean is that the camera is not level with the water, because we must assume the water is level no matter what. Unless I've got a blockage or vacuum that is restricting flow, the water will be level. That's the premise for using a water level. I can't make the water not level unless I plug the top of the tubes or trap some air into the tubing. The water will be level.

Now, am I getting the camera level? Or, am I able to see the water level edge well enough to make a level sighting? Those are good questions, and it's why I don't like the idea of this water level experiment being done with a handheld contraption or a handheld camera, or even by itself with everything stable. Particularly at the low elevations, you can have enough sighting error that one minute you see a dip and the next you don't, all depending on how you align the eye/camera with the levels.

But the cage helps prevent that. If the cage is leveled independently (using spirit level/plumb bob), then the lines of perspective should merge on the water level line. If they don't, it means the cage is tilted OR the water level is not sighted correctly. If they converge, you have more confidence than in either case alone that you're square and level.

Don't confuse perpendicular in the image with "level." The camera may have a slight roll tilt, but the water will be level. I drew a straight yellow line along the center of the dark band of water and the top of each water level. It runs parallel to the sighting line.

I think it's pretty close; certainly not enough off to account for the observed difference between the line and the apparent horizon.

Thanks for the feedback. I think the real question I have in reply, though, is your first issue raised. All this attempt at precision is fine and good, but it means nothing if the true horizon is different from what I am seeing. Can the true horizon actually be equal to or higher than the gap seen here at 100' MSL?

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #132 on: May 15, 2018, 12:02:18 AM »

Of course the center of the viewing apparatus being centered with the string and the water level of the device is an issue. Move the center of the viewing apparatus to 1 foot above or below the string and water level of the water device. Consider what would happen. Is centering an issue now?

If I do that an leave the camera where it is? Sure. Then I'm relying solely on the lines of perspective to give me my horizon vanishing point.

But if I move the camera down to level with the water, both are "off center" relative to the cube, but the lines of perspective should still converge on that line. That's how perspective works.

Or, I could leave the camera where it is and instead of trying to sight parallel along the water levels, I use equivalent points on the tubing to draw a perspective line and see if it converges with the rest of the cage. That's harder though, and more prone to error since I'd be having to make a judgment call where those points on the tubes are.

What I'll do is provide a demonstration, showing how different water levels, camera levels and sight lines affect the results. It would be ultra ideal if I could get everything perfectly centered because it makes it easier to evaluate. But the point of combining water leveling with perspective lines of a squared cage is to reduce potential for single point error.

Tom Bishop

• Zetetic Council Member
• 10712
• Flat Earth Believer
Re: The Horizon is Always at Eye Level
« Reply #133 on: May 15, 2018, 12:17:40 AM »

Of course the center of the viewing apparatus being centered with the string and the water level of the device is an issue. Move the center of the viewing apparatus to 1 foot above or below the string and water level of the water device. Consider what would happen. Is centering an issue now?

If I do that an leave the camera where it is? Sure. Then I'm relying solely on the lines of perspective to give me my horizon vanishing point.

But if I move the camera down to level with the water, both are "off center" relative to the cube, but the lines of perspective should still converge on that line. That's how perspective works.

Or, I could leave the camera where it is and instead of trying to sight parallel along the water levels, I use equivalent points on the tubing to draw a perspective line and see if it converges with the rest of the cage. That's harder though, and more prone to error since I'd be having to make a judgment call where those points on the tubes are.

What I'll do is provide a demonstration, showing how different water levels, camera levels and sight lines affect the results. It would be ultra ideal if I could get everything perfectly centered because it makes it easier to evaluate. But the point of combining water leveling with perspective lines of a squared cage is to reduce potential for single point error.

Consider this:

We have four jelly beans. One is on the floor at your feet, the other is on the floor 20 feet ahead of you, one is on the floor 100 feet ahead from you, and the other is on the floor ahead of you on the distant horizon (assuming that we can see it). Where would we need to place our eyeball to see whether all three jellybeans line up?

Clearly, our eye would need to be exactly center with the line of jelly beans. If we look at the scene from any other angle or position we cannot say whether they all line up or not. At any other position they would appear in different positions relative to each other.

« Last Edit: May 15, 2018, 12:24:56 AM by Tom Bishop »

Tontogary

• 431
Re: The Horizon is Always at Eye Level
« Reply #134 on: May 15, 2018, 12:23:33 AM »

1. In Arctic conditions conditions people have reported seeing objects hundreds of miles away. What makes you think that you are actually looking at the real horizon at this particular time?

In think the clue is in your question! i.e. In arctic conditions. Is California in the Artic tom?

Those artic conditions may be due not abnormal refraction, and if so it affects object that are over the (RE) horizon, but of course such a thing does not occur on FE, only perspective happens, and the vanishing point.

Glad you brought it up tom, so now you can explain how artic conditions affect the vanishing point, and perspective! Particularly when you say the vanishing point is defined as when an object is less than 1 minute of arc.

Also, if you haven't heard of bronies before, that reflects poorly on your understanding of the world that surrounds you. It's practically impossible not to know about them.

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #135 on: May 15, 2018, 01:55:53 AM »
Same as yours, given that scenario.

But I'm not looking for a point. I'm looking for a line.
And I'm not depending on alignment of points, solely. I'm also using perspective lines.

In your jellybean example. I don't have to be aligned with the jellybeans to find the horizon LINE. I can be off to the side, and if the line they do make is parallel to the plane of the ground, then I know the plane of my eyeline is in the same plane as the jellybeans.

But it's more than that. Because if I'm using multiple lines of perspectives, i.e. other alignments of jellybeans, then I don't have to be inline with any of them. I just see where all of those lines are converging; and not to a point but to a plane.

That's what I consider to be the strength of this method: I'm using both a leveling plane and perspective lines, hoping that each will back the other up. It takes some precision, no doubt. But I'm not trying to measure "dip." I'm just trying to detect whether it exists or not.

I can (and will, time permitting) demonstrate in a controlled environment how changing different parameters of the setup effect the observation. Things like aligning the sight line away from the cube center, both vertically and horizontally. Changing the location of the camera. Changing orientation of the camera (pitch, roll & yaw). Changing orientation of the cube (pitch & roll).

I concede it's very hard, using those 1 1/4" vinyl tubes to ensure  a level sighting. Not that the water won't be level (because it will be, a priori); but because the camera height is hard to match. It's difficult even if I move the camera well off center laterally so that the tubes line up. Which is why I like the idea of using a basin of some sort to provide a liquid surface unaffected by glass or plastic optical effects. I may not ditch the tubes, since they're already there. Might as well keep them. But adding an "infinity pool" of a sort would remove the deficiency those present.

I do still hope to resolve the question about how we can know we're seeing the true horizon. I could see this island today, at a distance of nearly 20 miles:

...but I couldn't see San Clemente Island 60-some miles on the bearing I took today's picture ¹.

At 100', the globe earth calculation of visual horizon is about 12 1/4 miles with no refraction. With refraction? Maybe 14 miles.
I don't know how to calculate a distance to the horizon if assuming a flat earth, but how far away should the vanishing line be from a height of 100'? More than 20 miles? Even if I could have seen San Clemente 60 miles away, I wouldn't be seeing it's shore. I'd only be seeing its higher elevation. But there'd be a clear line of horizon. If I'm able to see the Islas Coronado but not San Clemente, does that mean I should consider it a no-go for observation?

You need to tell me because I don't know.

¹ 66 miles, for the record. (Had to check)
« Last Edit: May 15, 2018, 02:19:45 AM by Bobby Shafto »

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #136 on: May 15, 2018, 02:30:09 AM »
Per #2, did you note the crate itself is not even on both sides of the string? This will change the center of the image in relation to the crate.
I want to be sure I understand this comment.

Do you mean "not even on both sides of the string" in that the crate is warped? Or not level?

Or do you just mean offset to the right on the tripod? It is balanced on its center of gravity, which is left of center due to the water-filled tubing. The camera, however, is (supposed to be) aligned on the crate, and not the forward tripod.

My argument is that even if it's not center aligned, that shouldn't impact observations of any horizontal planes. I could have the camera looking downline from the outside left edge of the cube and it would work, which is probably what I'd have to do if I want to get the water tubes inline with each other.

If you mean something else, let me know. I may be missing something important.

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #137 on: May 15, 2018, 03:06:45 AM »
Maybe a picture taken with the horizon lined up with one of the water surfaces in the tubes might help coinvince some of the effect of moving the camera up or drown, as there might be some questions of whether the camera is lined up with the water levels. I know it wont make a difference, but will likely head off some comments about it.
Maybe. Anytime I have to move the camera tripod, it takes time to realign, refocus, find the best exposure settings, look at all my index points to make sure I'm capturing what needs to be captured/documented.

I think what you're suggesting I can do in a "lab" setting, creating a demonstration of what happens with different arrangements of camera positions & heights, cube orientation, water levels, etc. Trying to explain is harder than just showing.

But I do want to invite nitpicking. If Tom or someone objects to not being horizontally or vertically centered, I need to know why and either account for it or defend why not.

I thought about even trying to "cheat" and try to bias the set up to make it look like the horizon doesn't dip, and what it would take to make that happen.  I don't know if that's possible. Something (levels, water, perspective lines) will give it away.

One thing that bothers me is that my shelving unit is starting to warp. The panels seem to be bending outward from where I carry it or how it rests on a plank or stool and not on a wide/flat platform. I've tried to be careful to pick it up from the edges and not the center of the panels, but with time, the panels will bend. Not to mention the grid wires aren't perfectly machined either. They're pretty consistently distanced at the weld points, but you can plainly see the wires aren't true along their lengths. Since I'm using "off the shelf" materials for this homemade device, I can't expect to have perfectly machined everything. I believe I'm offsetting that by plotting from weld-to-weld, but who knows? I might be letting my choices bias me toward choosing lines that converge the way I want them to.

And to remind everyone, this was more like a dry run. The conditions weren't ideal. Too much wind. I would like less haze. And I was pressed for time. (And there are always people who are curious and want to ask what I'm doing. I'm polite, but it is distracting and slows me down. Tom's objection to the true horizon is legit, I think. Maybe. I'm pretty confident I'm seeing the horizon today if globe calculations are right. The horizon from 100' is closer than Islas Coronados, which I could see.

But if FE has a different method for determining if what one is seeing is the horizon, I don't know what that is.

Bobby Shafto

• 1390
Re: The Horizon is Always at Eye Level
« Reply #138 on: May 15, 2018, 03:21:52 AM »
But if FE has a different method for determining if what one is seeing is the horizon, I don't know what that is.
This is the sunset last night (I didn't take the photo) looking from Ocean Beach (San Diego) under the pier. Sunset was on the 293° azimuth, which means San Clemente Island is somewhere slightly left of this sunset line. But it's too hazy to see it. Nevertheless, the setting sun is bright enough to penetrate the haze (and offer an interesting color glow), making the horizon line is very clear.

Wouldn't that be a true horizon?

Tontogary

• 431
Re: The Horizon is Always at Eye Level
« Reply #139 on: May 15, 2018, 03:25:08 AM »
I think you will run into a road block on what is a true horizon.

In GE we can know that there is a horizon, and calculate its distance, but on a FE it is completely subjective, as the ground, sea whatever rises up until it gets fuzzy, and disappears into .......... well something!

If you cannot see some land or islands, it will be proof that you cannot possibly be seeing the true horizon as it will be obscured, However if you CAN see some land on the horizon, then it will be used as proof that you could have seen further, and again used as proof that you were not seeing the horizon. This is one of those arguments you cannot possibly win.

I know what a sharp horizon looks like, i need it to take astronomical position fixes, and can pretty much tell if i am seeing a good horizon. Plus the truth is in the actual position. If i take multiple star sights, and get a good, tight, position with little “cocked hat” then i am pretty certain that my measurements are accurate, and i have a good horizon. Where i cannot see a clear horizon my sights will be inaccurate, and my subsequent position lines be inaccurate, causing a larger area of uncertainty.

Over the years you learn what is a good horizon and what is not. It’s called experience, and not something easy to explain.

However even if i get a less than perfect horizon, and i think it is good enough for sights, the margin of error on the sights is between 0 to 5 minutes of arc, which is certainly much less than the dip of the horizon at our normal height of 34 meters (about 110 feet) which gives a dip of the horizon of 10 minutes of arc.
« Last Edit: May 15, 2018, 03:43:24 AM by Tontogary »

Also, if you haven't heard of bronies before, that reflects poorly on your understanding of the world that surrounds you. It's practically impossible not to know about them.