How to Take a Photo of the Curve of the Horizon

[Z.W. Wolf]

Reminder: What we are seeing is the edge of a circle.

Stand in any one of the three circles on a basketball court. Turn around in place. From your perspective the edge of the circle in your line of sight will be the point farthest away from you. It will therefore appear to be the top of the circle. There will always be a top of the circle as you turn through 360 degrees.

The horizon on a sphere Earth is a circle all around you. The circle is defined by where your line of sight meets the surface. That's what creates the edge of the circle. There will always be a top of the circle.

As you turn 360 degrees, the edge of the circle in your line of sight will always be the part of the circle farthest away from you, and from your perspective that will always be the top of the circle.

So what does this mean?

On a huge plane surface there wouldn't be any circle. There wouldn't be anything to define the edge of the circle. (Unless someone painted one on, like the paint on the basketball court.) Therefore the horizon on a plane Earth wouldn't be a circle and wouldn't show any curve.

 

[Mechanik]

@Chris Rippel - Your thought experiment, or a variation of it, has tricked many globers as well as flat earthers. Stated a little differently, it almost seems to be a mathematical proof that the horizon can't be curved. i.e. A) Eye level is a flat plane through the eye of the observer B) eye level out in the distance appears as a straight line, as it is part of that flat plane. C) The horizon on a spherical ocean is a constant drop below the straight eye level line. D) A line a constant distance from another line is a parallel line. Conclusion: A line, such as the horizon, that is parallel to a straight line must also be a straight line.

This is presented as a logic problem, so let's treat it as such. If A, B, C, and D are all true, then the conclusion must be true. However, the horizon on a spherical ocean is not a plane or a line parallel to a plane and the drop (as measured by the length of a line perpendicular to your eye level line or plane) is clearly not constant (i.e. equal) across your eye level flat plane. That makes C false and therefore the conclusion is also false.

A plane at eye level extends infinitely far to both left or right. For C to be true, the drop from your eye level plane to the surface of the water at the horizon must be constant (exactly 12 feet, or 12 inches, of 23 pixels, or whatever measurement you're using) across your field of view or across the field of view of the camera. It's clear from photos that placing a straight line across a photo, or across the field of vision, shows the drop is greater the farther you get from the center of your view. Therefore the drop varies from the center to right or left. The horizon on a spherical ocean is a curve and the distance of that horizon to the original plane is not constant and C is false.

We see these logic errors regularly in conspiracy theories. What seems to be a logical conclusion is reached, but one or more statements are untrue, making the conclusion false.

 

[Rory]

To try and combine all the above:

A) Eye level is a flat plane through the eye of the observer - true (could add MW's "and parallel to local down")

B) Eye level out in the distance appears as a straight line, as it is part of that flat plane - true

C) The horizon on a spherical ocean is a constant drop below the straight eye level line - true (for example, eye level always at zero degrees, and a 360 degree horizon at -0.7 degrees)

D) A line a constant distance from another line is a parallel line - kind of true (see below)

Conclusion: A line, such as the horizon, that is parallel to a straight line must also be a straight line - not true

ZWW points out that the horizon forms a circle, and I've said the horizon is akin to the curved edge of a flat coin: I think this is the key. The imaginary plane at eye level is not a circle, but rather an infinite plane. So perhaps imagine this: a large horizontal square (eye level) hovering above a much smaller flat circle, such as a coin. Every point on the circle is the same distance below the square ("a constant drop") and you could say that the edge of the circle and a similar circle traced on the plane would be parallel. But it doesn't stop the edge of the circle being curved, just as it doesn't stop "eye level in the distance" being a straight line.

An actual diagram may help that. It makes sense in my head. Though I'm sure there are better ways to visualise it.

 

[Trailblazer]

As you turn 360 degrees, the edge of the circle in your line of sight will always be the part of the circle farthest away from you, and from your perspective that will always be the top of the circle.

Nitpick: the circle of the horizon, by definition, is equidistant from the observer all the way round. I assume you meant "furthest away in the direction you are looking at a given time".

 

[Z.W. Wolf]

Yes, I need to fine tune that. I'm struggling to describe how it looks.

In a simple, real world example: Standing in a circle painted on the basketball court.

Along your line of sight there will always be a "top" of the circle. It's the point that separates "curving to my left" and "curving to my right. "

But if I spin in place there's always a NEW point that looks like that. There's no problem in that simple real world example.

 

[Mick West]

In a simple, real world example: Standing in a circle painted on the basketball court.

I prefer the example of standing in the middle of a circus ring. The edge of the ring, at the bottom of the barrier, is a flar circle, and yet you can see a curve.

 

[Mad Mac]

This is a photo I took that I believe shows the curvature of the earth.

In 2018 I observed this phenomena while holding down a beer on the deck of our rental beach house. At that time I didn't say anything to anyone because I did not want to sound like a loon. In the meantime, I Googled around and found this scholarly thread on metabunk.

When we returned to Galveston this year, I used the panoramic feature on my new iPhone 8 to take this handheld picture. The railing in the foreground helps to see the curve. A lens can make a straight line appear to be curved, but I believe the railing in the foreground would have to be curved the same way and it is not.

Now I will confess that as I pivoted the camera it may have risen slightly in the middle. Position a piece of paper above the railing so that the edge rests on the corners of the railing. A tiny sliver of the gulf appears in the middle. Flip it over and position the paper so that the edge is under the corners of the railing and the gulf definitely has a bulge in it.

The picture is almost a 180 degree view, all the way northeast up the coast to Galveston and all the way southwest down the coast to the San Luis Pass. So it is not a small layout, but about 15 miles in each direction, about a 30 mile span.

But I could be wrong, I often am.

 

[Jesse3959]

I've actually thought about hiking up to a high place and tying a thick string between two trees really tight, parallel to the horizon - then hanging a few helium party balloons on it (enough to lift it if it were slack) to prove that it it's not sagging and causing an appearance of curve.
Then position the camera so the string lines up with the horizon - that way there's no argument about whether the curved horizon is from the lens or real because the string is known to be straight (or curved up from the helium balloons, but in any case not curved down..)

Why a string instead of an 8-foot straight edge? Because the string could be 50 feet long, and thus far away enough from the camera that it was in good focus along with the horizon.

I haven't had a chance to try it yet though.

 

[Rory]

The string could for sure work, but I suppose it's more difficult to verify that a string is perfectly straight than it is with a solid bar, as well as to set up. Plus the solid bar has shown to work really well - especially with the option of having one above and one below the horizon.

As far the deck shot, given the amount of visible curve from a low elevation - more than from much higher elevations, and more than the math would predict - it would appear that it's being caused by the camera. Perhaps lens, but probably more to do with the panoramic aspect of it. I would imagine that the ends of the balcony are further away than the center, so that probably has a lot to with it too. But others are much more au fait with the workings of cameras than I, so now doubt they will explain it better.

 

[Mick West]

As far the deck shot, given the amount of visible curve from a low elevation - more than from much higher elevations, and more than the math would predict - it would appear that it's being caused by the camera. Perhaps lens, but probably more to do with the panoramic aspect of it.

Yeah, it's the panorama. Look at the huge curve in the bottom rail. Unfortunately any curvature in this image is an illusion. There's about the same amount of ocean above the railing all the way across, relative to the height of the railing at that point.

 

[Jesse3959]

The string could for sure work, but I suppose it's more difficult to verify that a string is perfectly straight than it is with a solid bar, as well as to set up. Plus the solid bar has shown to work really well - especially with the option of having one above and one below the horizon.

The string won't be perfectly straight. Because of the helium balloons, it will be ever so slightly curved up in the center, favoring the flat earthers. But I like your idea of two strings, one above and the other below the horizon.

The reason I'm interested in a string for this is because many cameras will not focus sharply at infinity and at 4 feet away at the same time. With a string, the straight edge can be much farther from the camera and still fill the horizontal field of view.

There are also some unexpected conditions relating to the effective aperture of the camera lens when especially close to an object. By moving the straight edge out these effects are reduced.

As to knowing that a straight edge is straight, I think for many people, doubters may say "Well your red stick wasn't straight." But everyone knows that a taut line has to be nearly straight - and it's buoyancy determines the direction of the curve.

(I'm not personally doubting your red ruler, but rather pointing out that a taut line is inherently straight (to the degree it is straight) while a stick can be any shape you like. It does not have an inherent straightness. A taut line does - and it is a function of it's buoyancy and tension and length.)

 

[Rory]

As to knowing that a straight edge is straight, I think for many people, doubters may say "Well your red stick wasn't straight."

That's true, and though I included ways to show that the red bars were straight - rotating them; showing along their length; and measuring the distance between them - it was always more a demonstration of what 'doubters' could do for themselves. But as far as I'm aware, no globe denier has yet repeated the observation.

 

[AmberRobot]

I would think that an ideally executed panorama would by definition not show curvature is the horizon.

 

[Mick West]

I would think that an ideally executed panorama would by definition not show curvature is the horizon.

What definition are you using?

 

[AmberRobot]

What definition are you using?

I envision an "ideal" execution of a panoramic photograph would have very little horizontal field of view that sweeps across a large angle. That would minimize distortions, rather that stitching together multiple wide angle photographs.

if you expected curvature to show in a panoramic photograph what would you expect to happen in a 360 degree panorama?

 

[Jesse3959]

So we really would have to look at the method used to form the panorama.

The normal way we take a panorama is with a smart phone or an equally smart camera - it takes multiple photos as we rotate the camera then it tries its best to distort and stitch them together into a seamless scene. But the shape of the horizon is completely up to how the software distorts the pictures to make them all stitch. It's really completely useless for measuring the curve of the horizon without a known-straight reference bar in the field of view.

For a panorama to actually measure the curve, you would need a camera that records a single vertical column of pixels at a time, and the camera would be on a swivel which would allow it to turn and take in the next vertical column of pixels, one column at a time, eventually taking in the whole desired scenery.

If the swivel were perfectly level, no curve would be seen. The horizon would be a straight line, so many degrees down from level.

However, if the swivel axis were tilted slightly down so that it was exactly at right angles to the horizon in one direction, then it would produce a panorama which correctly showed the curve of the horizon.

This fellow built himself one using the guts of an old flatbed scanner: https://hackaday.com/2009/12/29/panoramic-scanner-camera/

 

[AmberRobot]

However, if the swivel axis were tilted slightly down so that it was exactly at right angles to the horizon in one direction, then it would produce a panorama which correctly showed the curve of the horizon.

yes. If it were tilted down and spun in a plane it would be tilted up at 180.

 

[Jesse3959]

yes. If it were tilted down and spun in a plane it would be tilted up at 180.

So I guess in summary, all a panorama proves is that the horizon is a circle. And that if you are at some altitude and you point a tube at the horizon in one direction, it will be pointing above the horizon in the other direction.

(And obviously the earth has to be essentially spherical for the horizon to be close enough that there's a distinct boundary, because if the edge was the horizon then we couldn't see it at all unless we were at the edge of the disk..)

 

[AmberRobot]

So I guess in summary, all a panorama proves is that the horizon is a circle. And that if you are at some altitude and you point a tube at the horizon in one direction, it will be pointing above the horizon in the other direction.

I saw a YouTube video in which a guy did exactly that. He was on a hill that had a view of water in both directions and set up a tube and pointed it at the horizon looking one way and showed that it was above the horizon looking the other way.

 

[Rory]

That'd be by Australian debunker 'Critical Think'. I can't find his original video (within thirty seconds), but here's Wolfie6020's version of it:


Source: https://www.youtube.com/watch?v=uXhBewZ1EOs

 

[Priyadi]

My attempt at this. Taken from the third floor of the Hotel Santika Premiere Belitung:

The situation at the balcony. There are glass railings that I used as a reference:

The shot. Exposure is f/22, 1/160s, ISO 3200. Taken using Canon EOS R with EF 16-35 f/4 lens, at the widest setting. I aligned the horizon with the glass railing and focused on the horizon.

Vertically stretched:

I was surprised at how easy this was, considering this was taken less than 30 m (100 ft) above sea level and I was without any preparation. I brought the correct lens by chance & had only about 10 minutes before the fog came in.

 

[Mick West]

Vertically stretched:

I was surprised at how easy this was, considering this was taken less than 30 m (100 ft) above sea level and I was without any preparation. I brought the correct lens by chance & had only about 10 minutes before the fog came in.

I'm not sure about this one. You are not really high enough, and the tops of the glass panels don't form a continuous verifiably straight line. So it's hard to tell what role lens distortion has.

Did you try correcting with the lens profile in Photoshop? If you email me the original photo I can give that a go. mick@mickwest.com

 

[Priyadi]

I'm not sure about this one. You are not really high enough, and the tops of the glass panels don't form a continuous verifiably straight line. So it's hard to tell what role lens distortion has.

Did you try correcting with the lens profile in Photoshop? If you email me the original photo I can give that a go. mick@mickwest.com

I had "lens aberration correction - lens distortion correction" enabled in-camera, so the camera will correct barrel distortions. doing it again in PS will only 'correct' it for the second time and reintroduce the distortions. unfortunately, I did not take raw version of the pictures.

the pictures are here: https://priyadi.smugmug.com/Other/Flat-Earth-Debunking/Belitung-Pictures/n-jrggHN/i-344WLzt

 

[Priyadi]

As a follow up to my attempt above, I have managed to get a simulated view of the scene using Walter Bislin's curvature app. The problem is that the observation is very close to the surface, and by default, the resolution of the output is too small to show the curvature. Here's a crude way I did to get a higher resolution simulation:

• Go to Walter's curvature app
• Input the height of the observation (25 m) and the focal length of my camera (16 mm)
• Maximize the browser window across my triple monitor setup (6400 px of horizontal pixels)
• Increase the zoom of the browser window to 500%

With these steps, the app gave me a simulated view with a resolution of 4530x3020.

Here is my photo & the result of Walter's simulation, vertically stretched together, side by side:

 

[DavidB66]

At #72 above I posted a link to a photo taken from a hillside above the Bonneville Salt Flats, showing clear curvature along a very long straight road. Now a YouTuber going by the name Don't Stop Motion has gone one better by taking a video from much the same viewpoint. The resulting video is here: The Curvature of the Earth - Bonneville Salt Flats (from West Wendover) - YouTube
By zooming in and out the video gives a better idea than the still photo of the distances involved. I tried identifying surface features on Google Earth to estimate the distance of the horizon, but didn't have much luck. Overall, the view of curvature is strikingly similar to Soundly's footage from Lake Ponchartrain, except that this time it is taken over land. As I stressed in earlier comments, it is essential to be sure that the road is straight and that the relevant surface is very level. Google Earth seems to confirm this to within a few feet over a 20-mile stretch.

 

[JMartJr]

The problem with this simple analogy is of course that Flat Earthers will then say "So you mean the Earth is flat like a coin?" and we're back where we started! I'm trying to think of a common object that is shaped like a very flat circular dome, like the section of the Earth's surface above the horizon...

To me, that makes the whole discussion of horizon curve, and the somewhat related "horizon always rises to eye level" flat Earth claim, extremely odd. The horizon does indeed curve, and does not rise to eye level, as is demonstrably true in this thread and others ad nauseum. It seems this would be expected whether the Earth was flat or the globe that it actually is -- the difference, if any, would be in the degree of horizon curve or drop below eye level as you ascend. It hurts my head that flat apologists insist that a bit of evidence that works as well with their theory as with the correct one, mus be wrong, when if their claims are true it would argue against their hypothesis as well as against the globe model.

Coins are flat, balls are round, you get horizon curve either way. And the horizon drops as you ascend, either way.

 

[Mendel]

The horizon does indeed curve, and does not rise to eye level, as is demonstrably true in this thread and others ad nauseum. It seems this would be expected whether the Earth was flat or the globe that it actually is -- the difference, if any, would be in the degree of horizon curve or drop below eye level as you ascend.

The problem is that the horizon is not where the edge of the Earth is -- you can't see all the way to Antarctica or beyond, you can't even see Europe from America. So that curved horizon can't be the edge of the Earth, it must be caused by something else, but there's no good explanation for it. It can't be caused by some limit on how you can see, because you can see things beyond the horizon if they're big enough (like wind farms or big ships).

 

[Rory]

The horizon does indeed curve. It seems this would be expected whether the Earth was flat or the globe that it actually is

If the Earth was flat there wouldn't be a horizon, there'd be nothing to cause it.

 

[Mendel]

If the Earth was flat there wouldn't be a horizon, there'd be nothing to cause it.

That depends on how you define "horizon". Flat Earth would have a line where the ground meets the sky. But the sun couldn't set on it while lighting other parts of Earth.

 

[Rory]

Flat Earth would have a line where the ground meets the sky.

I always find it hard to imagine how things would appear if we actually lived on a plane. Wouldn't the point where, for example, sea meets sky be rather indistinguishable on a flat plane, as though fading into a mist due to atmostpheric conditions, etc?

 

[FatPhil]

If the Earth was flat there wouldn't be a horizon, there'd be nothing to cause it.

If the earth were flat *and infinite in extent in all directions* there wouldn't be a visible horizon. There would be a theoretical horizon, but being at infinite distance would be attenuated to non-visibility (not to mention it would get in the way of the sun ducking below it).

However, none of the "circled by antarctica" flat earth models show something infinite in extent, so your argument does not address their currently favoured model.

I will confess that I generally find flat earth arguments to be so idiotic they're not even worth paying attention to - they've all been debunked a myriad times - but if we are going to waste time debunking them, we should do so with precision.

 

[Mendel]

If the earth were flat *and infinite in extent in all directions* there wouldn't be a visible horizon. There would be a theoretical horizon, but being at infinite distance would be attenuated to non-visibility (not to mention it would get in the way of the sun ducking below it).

Is a far mountain not there when it's hidden by haze? We know where it is, right?
The horizon on "infinite flat world" is clearly, precisely, sharply defined. It is exactly at the eye height of the observer. And with the naked eye, it'll be indistinguishable from the horizon on the globe.

 

[FatPhil]

Is a far mountain not there when it's hidden by haze? We know where it is, right?

I mentioned no mountain. What mountain are you talking about? What promped this question, it doesn't seem a response to what I posted. How far is this mountain? The only farness that is relevant to my argument refarging planes is farther than any finite farness - i.e. at infinity. A mountain at infinity that's never been observed - if we can talk about such a concept at all, then no we don't know where it is. Your asking the question seems to imply that objects at infinity can (a) exist; and (b) be seen. I'm a mathematician, I reject even the former until you precisely define the topology which permits "at infinity" to have an unambiguous meaning. Why have you deviated the discussion down this tangent, it seems pointless?

My mention of attentuation was to *stop* pointless deviations down this path - nothing exists "at infinity" even on an infinite plane, so it's silly to talk about such things as if they're real. Hence my couching in terms of "theoretical horizon" - it's not a horizon - the parallel planes never meet. So there's nothing to see - anything that you can see has something visible behind it, so nothing is "the" horizon. Hiding the concept of existence (which apparently you seem to have not addressed) behind the practical nature of something not even being visible in a world with particles in it (which is part of the model both sides of the argument hold) was intended to protect you from the mathematical pedantry which makes your wording look sloppy.

The horizon on "infinite flat world" is clearly, precisely, sharply defined. It is exactly at the eye height of the observer. And with the naked eye, it'll be indistinguishable from the horizon on the globe.

Do not agree at all.
The horizon on an infinite flat world is a virtual circle at infinity in the plane of the observer's eye line parallel to the surface.
The horizon on a globe is a circle parallel and below the observer's eye line.
In the former, the horizons in opposite directions are antiparallel; in the latter they are not, being rays down a cone they are at an angle of less than 180 degrees.
I don't even understand why you've proposed this falsity, as you seem to be aware of these facts, they've even been stated upthread.

 

[Mendel]

@FatPhil

I mention the mountain hidden by haze because your argument seems to be that the horizon isn't there if it's hidden.

The horizon is not a physical place. It's something an observer sees; it depends on the position of the observer and where they're looking. I am describing the horizon as "the line where sky and ground/sea meet". The line does not exist, but ground and sky do.

So if you have an observer, you can say for that observer with certainty where that line is because you can tell whether they are looking at the sky or not. You can do the same thing for the "infinite plane world" in the absence of atmosphere; in fact, you can do it more easily because any sight line tilted down will hit ground; any sight line not tilted down will hit sky. So that's where the horizon is in that world.

In an infinite plane world with an atmosphere, it's just slightly more difficult because of refraction and because haze makes it harder to see objects in the distance (IR photography may come in handy). Are you arguing that adding an atmosphere to a world makes the horizon go away? like adding fog would make the mountain go away?

 

[Rory]

If the Earth was flat there wouldn't be a horizon, there'd be nothing to cause it.

None of the "circled by antarctica" flat earth models show something infinite in extent, so your argument does not address their currently favoured model.

I guess to be more precise, if the Earth was a flat plane (infinite or otherwise) there wouldn't be a horizon - although, as you point out, if you were within visual range of "the edge" there'd be something different.

Whatever a person imagines to be at the edge, though, I don't think one could call it a horizon.

 

[FatPhil]

The horizon is not a physical place. It's something an observer sees; .... The line does not exist, but ground and sky do.

OK, that's nicely abstract, I can salute that as it's run up the flagpole.

From previous posts, in the context of a sphere model, I had inferred a more concrete horizon which exists as points on the sphere's surface. Referring to the "distance to the horizon", as people commonly do, reinforces the reification of those as real points that do exist on the surface, as you can't have the distance to something that doesn't exist. Most of the time, in a real world context, I believe most people think this way, that the horizon is real points in the distance over ---> there.

Of course, the infinite plane case has a horizon with none of these properties, and the above fails. The definition of the virtual horizon as, for example, an angle (in our plane case, 0 degrees) below the viewing plane, such that above is sky and below is ground, makes the most sense (that angle being a function of azimuthal angle as you turn around your own upright axis, but in our plane case constant). (This declension definition has the property of working if you're standing on silly things like an infinite cylinder, where it varies from 0 to down to 0 to down again as you turn.)

The real/abstract thing is where the confusion lies. For the actual world we live in, I don't think the completely natural assumption that it is real points on the earth will be anything apart from the default people think of when they hear the word horizon. Thank you for clarifying that you understand the distinction.

 

[FatPhil]

I guess to be more precise, if the Earth was a flat plane (infinite or otherwise) there wouldn't be a horizon - although, as you point out, if you were within visual range of "the edge" there'd be something different.

Whatever a person imagines to be at the edge, though, I don't think one could call it a horizon.

The image above in post #106 ( https://www.metabunk.org/threads/how-to-take-a-photo-of-the-curve-of-the-horizon.8859/post-243657 ) implies that the people who like have that model use the edge as their horizon. It works from a nomenclature perspective, even if from no other. Wrongthink has a tendency to weirdify language. ( ;-) )

 

[Mendel]

The real/abstract thing is where the confusion lies. For the actual world we live in, I don't think the completely natural assumption that it is real points on the earth will be anything apart from the default people think of when they hear the word horizon. Thank you for clarifying that you understand the distinction.

I'm pretty sure I didn't understand that second sentence.

You can look at this picture and know where the horizon is, even if you don't know the distance.
If we lived on Flat Earth, on a world surrounded by ocean, the horizon would look just the same (though we could debate the sun and the clouds). I believe the "natural" assumption is to look at this picture and think "that's the horizon" without knowing how distant it is.

It's true that on the globe, the horizon line coincides with a line that is "the furthest points you can see", which is also quite hard to pin down exactly because of refraction (and haze, and sometimes inferior mirage), which is why I'm using the terms "geometric horizon" and "apparent horizon" when discussing this. On the infinite plane, you can geometrically see everything, so there is no geometric horizon on the surface; and on the finite Flat Earth, it coincides with the edge of the Earth (and we'd typically imagine those points at sea level).

Larry Niven's Ringworld has two horizons -- or none, if you don't recognize the edge of the world as horizon, and instead look for the "edge" of an infinite tube.

 

[Rory]

The image above in post #106 ( https://www.metabunk.org/threads/how-to-take-a-photo-of-the-curve-of-the-horizon.8859/post-243657 ) implies that the people who like have that model use the edge as their horizon. It works from a nomenclature perspective, even if from no other. Wrongthink has a tendency to weirdify language. ( ;-) )

I would say I don't think anyone thinks of the edge as the horizon, or at least no one I've come across - especially because flat earthers don't believe anyone can get close to the edge. They all believe in horizons though - but getting them to think about what would cause a horizon on their hypothetical flat plane hasn't been easy, in my experience (last I heard it was mumblings about "visual limits" and "diffraction").

That image was posted by a non-flat earther to demonstrate that we always look down to the horizon whether on a ball or on a plane, so I don't think it quite relates to discussions on the horizon or "the edge".

 

[FatPhil]

Yeah, it's the panorama. Look at the huge curve in the bottom rail. Unfortunately any curvature in this image is an illusion. There's about the same amount of ocean above the railing all the way across, relative to the height of the railing at that point.

One minor frustration is that this situation could possibly have been an interesting opportunity to demonstrate the curvature of the earth. I wonder what the horizon would have looked like if the level at which the photo had been taken was lowered by about 15cm, with the bottom of the railing above the horizon, but put centre-of-frame, thus the reference straight line. Were the earth flat, then, like the bottom of the railing, the horizon would be concave up in the photo as everything converges to the two vanishing points. However, if as you look left and right of centre it had started to fall away from the top rail, that would have been clear proof that the curvature was great enough to not just counter, but perhaps *beat* the cylindrical distortion of the panorama, at least in part of the frame. Maybe more altitude would have been required, who knows. If someone has such an opportunity again, it might be a fun one to try. (The output of my wondering is 'perhaps even w shaped', as the distortion could eventually win, but it would be setup dependent.)

I've found a wildlife viewing tower on a (alas low and flat) peninsula near me, and feel inspired to try to reproduce the 'tube and spirit-level' experiment with nothing but a long stick (maybe with some twist-ties to make 'sights'), in such a minimalistic fashion that literally anyone who can get their hands on a stick (and a peninsula, but the spirit level's not needed) can reproduce it. If I can contrive it, I will even try to do away with the stick, and make it a zero-equipment experiment. I'm not expecting clear weather to reliably have a clearly visible horizon for months, so not even I am holding my breath.