[Regicide]

I think we are all missing the point here. All debate is being focused on one screenshot, and whether the observed curve (surely we can at least agree that there appears to be a curve) is a product of optics or an observation of a round earth. But I didn't post a screenshot. I posted a link to an unedited 2 1/2 hour-long video from the ground to the apogee to the ground again. If you look at the video right after the garlic bread breaks through the clouds, at about 3.1 km, you can see that the horizon essentially appears flat. Take a screenshot and kick up the contrast for a better view.

Then if you look again at 15 km, a subtle curve is visible.

Finally, at the highest point, you can clearly see a curve.

How could a camera artifact account for a changing curve? Just interested .

Additionally, I don't think anyone has made any claims to the diameter of the earth:

...claiming that the Earth is round but 5 times smaller than in RET, or demonstrating your excellent knowledge of geometry as you did above, you're guaranteed to blow me away.

Also, just wanted to point out this:

EDIT: I note that I've been referring to these curves as "arcs" which may be a bit hasty - they could be arcs, but they might not be depending on the specific situation. I'll leave the phrasing as-is since it doesn't particularly affect any of the underlying reasoning, but it's only fair that I highlight that inaccuracy.

Word choice does not necessarily affect an argument. I used the term "fairly straight" because if I had used the word "perfectly straight" I would have been lying. It's not perfectly straight, there's a slight distortion. However, it's much closer to straight than the screenshots from 35 km.

Looking forward to your response

[Pete Svarrior]

Please fix your image links. People shouldn't have to reverse-engineer your post just to be able to figure out what point you're making.

Take a screenshot and kick up the contrast for a better view.

We cannot know what that line actually is. It's most likely not the horizon, which is why you needed to "kick up" the contrast.

Then if you look again at 15 km, a subtle curve is visible.

Ah, yes, interesting - once the horizon appears slightly above the middle of the frame, it starts to look like it's curving a little. I wonder why that might be. I wonder why it follows the formula for barrel distortion to the tee, and why adjusting for it makes it disappear. Truly mind-boggling, that one.

Finally, at the highest point, you can clearly see a curve.

Your red line doesn't even attempt to align with the horizon here - I'm not sure if that's you being incompetent or just trying to lie. Hilariously enough, the curve here is lesser than that in your 15km screenshot. I wonder if that might have something to do with the fact that the horizon is closer to the middle of the frame.

EDIT: For the absolute avoidance of doubt, here's your screenshot with the actual horizon traced correctly:



Now, let's take my purple shape and superimpose it on your supposedly "less curved" horizon at 15km:



Blimey! Who'da thunk it. When you do things correctly, you get consistent results.

How could a camera artifact account for a changing curve? Just interested .

Let's start with the basics - this isn't "a camera effect". It's basic optics. "How does optics affect what we see?" is a question I sincerely consider beneath anyone here.

Additionally, I don't think anyone has made any claims to the diameter of the earth

Yes, you would think that. However, claims have consequences. If you simultaneously claim that:

• The Earth is round
• Your video is not subject to barrel distortion
• It was not taken with a wide-angle lens
• You can see a curvature at altitudes as low as 15km with the naked eye

Then only one option remains geometrically feasible - the Earth must be tiny. Of course, the alternative is that one of the claims above is false - I strongly suggest you consider that possibility.

[Longtitube]

The ratio between the "line" and "dip" have nothing to do with the eccentricity of these two arcs. I can keep pointing out that you're wrong and explaining why you're wrong, but in the end of the day you won't accept it, because you're not interested in being correct - you just want to confirm your preconceptions.

But hey, let's keep on keeping on. Let's illustrate the issue with my previous example:

The span of the white frame is 590 pixels, and the "dip" (sagitta) of the first arc is 14 pixels.

The second arc has a span of 195 pixels and a sagitta of 1.5 pixels.

You assert that I can make these comparable through a simple ratio. Let's do that.

1.5*590/195 = 4.53

As you can see, by your logic, I should expect that the arc towards the bottom of the image is much less curved than the one closer to the middle. However, even a cursory visual comparison will reveal that not to be the case. In reality, when measured correctly, the sagitta of the second arc is 23 pixels.

Very good, Pete, I always enjoy the chance to learn something new, and found a handy sagittal calculator should anyone like to check the following figures. https://www.liutaiomottola.com/formulae/sag.htm

The arc of 715 pixels has a measured sagitta (couldn't remember the term - thank you) of 3 pixels – this corresponds to an arc radius of 21302 pixels. The same arc extended to a width of 1117 pixels would generate a sagitta of 7.3 pixels, so yes, a simple proportional calculation is wrong. So near the bottom edge of the screenshot we have an equivalent full-width distortion of 7.3 pixels and barrel distortion of a straight horizon line much nearer the middle of the image would show distortion of rather less than that.

You also entirely ignored the many issues with your "23 pixels" estimate - the line you're using as your reference point does not touch the horizon on either edge of the frame (or, indeed, at all). When adjusted appropriately, the correct sagitta is more akin to 10 pixels.

Fair point about the red line in the screenshot, so I had my own try at it. I do hope the (black) line is distinct enough this time:–



Oh dear, "akin to 10 pixels"? Did you try measuring it yourself? My point still stands – if the tray seam (assumed by both of us to be straight) has distortion equivalent to 7.3 pixels across the entire frame, an assumed straight horizon close to the middle should show much less distortion, not more than twice as much. I attach very slight importance to your claim – if these words mean anything.

The lens was an 18-135mm zoom

Do you realise how extremely wide this range is, and how useless that statement is as a result? An 18mm focal would be bordering on a fisheye lens, which this obviously isn't. A 135mm focal wouldn't capture anything remotely close to this wide an area. Before you can perform your experiment, you need to know the actual focal of the lens at the time of filming, not what the particular device is capable of.

Dear me, I should have made abundantly clear the 18-135mm zoom lens is the one that took the test image of the grid, not the view from tens of kilometers above Earth. I do apologise for the misunderstanding, the intention was to demonstrate barrel distortion in a known, measured case and yes, I do understand how wide this range is.

But do you know the film or sensor size of the camera that this zoom lens was attached to? Was it perhaps a phone? Or a 35mm camera? Perhaps a micro 4/3 DSLR, an APS-C digital camera, a medium format or even an 8"x10" field camera? I'll spare you, it was fixed to an APS-C digital camera and 18mm is a typical wideangle focal length on an APS-C camera, with a 76 degree angle of view across the diagonal. Nowhere near fisheye with this camera format and I do hope this helps you.

..claiming that the Earth is round but 5 times smaller than in RET...

Eh? You must be confusing me with someone else.

Oi now, governor. There is absolutely no need to get personal, innit.

Praise be, the man has a sense of humour! Until next time, mate.

[Pete Svarrior]

The same arc extended to a width of 1117 pixels would generate a sagitta of 7.3 pixels

It'll be a bit more complicated than that - to get any number for direct comparisons, we'll first need to establish which barrel distortion formula to use. This is one of the reasons why I'm advocating for a visual solution, rather than a numerical one.

Oh dear, "akin to 10 pixels"? Did you try measuring it yourself?

I did, but I neglected to illustrate it at the time. 16 pixels is definitely pushing it. Of course, the challenge here will be agreeing on how to distinctly identify the horizon as a line where the image is (understandably) out of focus at that distance. The way I see it, your top line seems rather arbitrary - it doesn't seem to follow any arc at all, and your bottom line appears to only intersect the horizon on the right hand side. I'll draw something more appropriate later today, when I have access to software that doesn't suck.

Dear me, I should have made abundantly clear the 18-135mm zoom lens is the one that took the test image of the grid, not the view from tens of kilometers above Earth.

That still makes no sense - the lens had a single focal length at the time the photograph was taken. The range of possible lengths is irrelevant.

I'll spare you, it was fixed to an APS-C digital camera and 18mm is a typical wideangle focal length on an APS-C camera, with a 76 degree angle of view across the diagonal. Nowhere near fisheye with this camera format and I do hope this helps you.

I should be clear: I already have a good enough idea of the equipment used. That's what enables me to speak with a decent amount of confidence here, and why I recommended giving Lightroom a shot.

[Longtitube]

It'll be a bit more complicated than that - to get any number for direct comparisons, we'll first need to establish which barrel distortion formula to use. This is one of the reasons why I'm advocating for a visual solution, rather than a numerical one.

Which barrel distortion formula? Can't you handle the algebra for arcs? It's given on the page for that sagittal calculator; any O-level schoolboy should be able to do the calculations.

I should be clear: I already have a good enough idea of the equipment used. That's what enables me to speak with a decent amount of confidence here...

Then please don't describe a lens as "bordering on fisheye" when it is anything but. A fisheye lens has a field of view of 180 degrees, more than twice that of an 18mm on APS-C.

I look forward to your own arbitrary arc drawing, since you had little difficulty with Regicide's screen captures:–

EDIT: For the absolute avoidance of doubt, here's your screenshot with the actual horizon traced correctly:

[Pete Svarrior]

Which barrel distortion formula?

That depends on the specifics of the lens.

Can't you handle the algebra for arcs? It's given on the page for that sagittal calculator; any O-level schoolboy should be able to do the calculations.

I can "handle" it, just like I could "handle" your last proposed proportion. What I question is whether you chose to apply the right calculation. As I pointed out yesterday, these curves may or may not be arcs.

A fisheye lens has a field of view of 180 degrees, more than twice that of an 18mm on APS-C.

Again with the silly comparisons. Firstly, fish eye lenses start at 100° FOV. Secondly, the lens you propose this is is only a tiny bit away from a fish eye in terms of focal lengths.

You really try to force ratios where they don't belong. It does not inspire confidence.

I look forward to your own arbitrary arc drawing, since you had little difficulty with Regicide's screen captures

As I said, as soon as I have access to software that doesn't suck, I'll provide an appropriate illustration, like I did yesterday. I'm not sure why you'd complain about me not being at my desk right now, instead of just waiting a while.

[Longtitube]

fish eye lenses start at 100° FOV. Secondly, the lens you propose this is is only a tiny bit away from a fish eye in terms of focal lengths.

You really try to force ratios where they don't belong. It does not inspire confidence.

Really? Name an APS-C fisheye lens with a 100° field of view: not a rectilinear wideangle, a curvilinear lens. Then demonstrate how the video we're all discussing is shot using a fisheye lens.

[Pete Svarrior]

Righto, here's where I'm getting 10px from:



It's difficult to see what's going on with the naked eye, but this curve follows through pixels which received the same amount of light at the time of shooting, thus likely representing a "true" horizon. It's a bit more intuitive when viewed at higher contrast:



Of course, the horizon is extremely blurry, so you may want to argue that we should follow one of the other well-defined lines that become visible at higher contrast. Using the second layer gives us a result that looks a bit more intuitive at low contrast.





That gives us a sagitta of 11px. So, yeah, "more akin to 10px" seems to pretty much get us there, but if you prefer I'll stick to "10-11px"

Really? Name an APS-C fisheye lens with a 100° field of view: not a rectilinear wideangle, a curvilinear lens.

Why would I do that?

EDIT: I'm still unsure what this achieves, but: Tokina AT-X 107 DX Fisheye @ 17mm f: https://tokinalens.com/product/at_x_107_dx_fisheye/

Then demonstrate how the video we're all discussing is shot using a fisheye lens.

Why would I demonstrate something that I patently don't believe, and which I actively argue against? The video being shot at a narrow angle only helps my case.

[Pete Svarrior]

Oh, while we're at it, let's verify your "3px" estimate for the tray. I'm not sure why I chose not to question it before, but...



In a truly shocking turn of events, it's actually 7px.

You might be starting to see where this is going.

[Pete Svarrior]

Since you refused to solve the problem visually, I will. Let's find out if Tiny Round Earth* holds any water.

First, let's ensure that we're only looking at arcs of identical** spans. I am discarding the sides of the image that we can't compare to the tray.



Now, let's trace the horizon.





Turns out the actual sagitta is 4-4.5px for an equivalent** span. A visual comparison also makes it plainly obvious that it is the tray that appears more curved. So, yes, the curvature of the horizon is much less pronounced than that of the tray. Tiny Round Earth* is not consistent with this observation.

You see the tray seam as "straight" because you expect it to be, and you see the horizon as "curved" because you really want it to be. However, at this altitude, and with such a narrow field of view, seeing any significant curvature should not be possible, and, unsurprisingly, is not possible.

Combine this with my rebuttal of Regicide's point: he was at the liberty to choose his own screenshots from multiple altitudes, and he ended up showing that the curvature decreases with altitude. This would not be consistent with the geometry of a sphere... unless we account for the optical effect you're so opposed to.

As always: when you follow a consistent and correct methodology, you get consistent results. Turns out that, despite your protestations, Tiny Round Earth* cannot be proved with this footage.

* - Remember, if you were correct here, the Earth would have to be round and much smaller than advertised. Regardless of FET vs RET, we can safely discard the "tiny" factor.
** - There is some room for inaccuracy here since our reference lines are at slightly different angles. Unfortunately, that's the experimental setup we were given. However, even with generous margins of error, there is no room for alternative conclusions.

[Longtitube]

Righto, here's where I'm getting 10px from:

You pointed out inaccuracies in my version and Regicide's attempts to measure the horizon sagitta, so I expect you to apply the same standards to your own . Your purple straight line is not aligned with the left of the horizon. I measured from where the white area becomes pale blue at either side: yours goes from the middle of the pale blue at left to close to the transition at right. The "increased contrast" version I have been unable to reproduce by merely increasing contrast in my own bitmap editor, but if you can give me a link to the Bad Acid plug-in used I'd be obliged: I have an unrelated use for it in mind. For the purposes of this discussion it's useless and your result of 11 pixels invalid. Indeed, you're on shaky "Photoshopped" grounds there, see the wiki FAQ.

Oh, while we're at it, let's verify your "3px" estimate for the tray. I'm not sure why I chose not to question it before, but...



In a truly shocking turn of events, it's actually 7px.

Well, let's have a closer look again. My measurement was across a width of 715 pixels and I was very interested to see yours being across 776 pixels. Big deal, you may say, but I was very careful to avoid the curved area at either end of that seam, something you haven't done. At the left side especially, your measurement clearly strays into that curved area to the benefit of an increase in sagittal measurement. Tut, tut. I'm not saying you are being disingenuous, but both these measurements are sloppily done, so both are invalid.

Finally, you mention Tiny Round Earth, a term I'm unfamiliar with. I don't know whose tiny round head is supposed to have mentioned the subject, but it wasn't me, and I couldn't find it on the forums or the wiki. Could we have an explanation? With calculations for the result you claim?

[Pete Svarrior]

Your purple straight line is not aligned with the left of the horizon

It is, and I showed you my methodology for why/how. If you dispute the methodology, it's on you to illustrate your objection. I used Photoshop, and reproduced the results in Corel. I'm not interested in your inability to adjust contrast in an image - honestly, if you can't perform such simple tasks, you probably shouldn't be getting involved in discussions that exceed your capabilities.

This, by the way, is why I keep suggesting that you use Lightroom. It's clear that all you can do is eyeball lines in MS Paint. You have an idiot-proof solution available to you. Use it.

Big deal, you may say

I may, and, indeed, if this is the best argument you have to offer, then I'll have to conclude you're no longer arguing in good faith - after all, if you had a sincere argument, you would have immediately followed up with a reasoned substsntiation. As a consequence, we're done here - I will not waste my time with someone who tries to lie his way through an inconvenient discussion.

I wish you the best of luck in arguing that the entirety of the Earth is roughly the size of the USA. In the meantime, the solution to your problem is plainly visible to all. You failed to analyse the images at every step of the process, starting with your inability to accurately trace the horizon, meausre heights, or even correctly apply proportions. There is nothing one can do to help a person who does not want to be helped.

If you wish to return to good-faith arguing, I will reconsider, but until then, this thread is now dead. Your failure has been illustrated, and you were not interested in rising up to the challenge. Fine by me.

(Of course, you may wish to defend your position by repeating the analysis over whatever width you find appropriate. Spoiler alert: you will not succeed at defending your Tiny Round Earth delusion.)

your measurement clearly strays into that curved area to the benefit of an increase in sagittal measurement. Tut, tut. I'm not saying you are being disingenuous, but both these measurements are sloppily done, so both are invalid.

I don't respesct liars, and you just showed yourself to be one.

If you're going to make a claim like this, substantiate it. Specifically, show the section of the image in which I "clearly stray into that curved area". Spoiler alert: you won't be able to, because I started my measurement at the very pixel the "curved area" ends. The quality of your work has been consistently atrocious. That's the crux here, really. Re-read through your failures. Note how you haven't been able to get a single technical detail correctly. Every measurement was wrong, every attempt at defining a proportion was wrong. You even challenged me to identify an example of one of the most abundant lenses out there. You know very little, and it's pretty obvious. And all that to defend a hypothesis that directly contradicts your worldview.

Feel free to restrict the image as much as you'd like and repeat the measurements. Here's a shocker: it won't suddenly make your Tiny Round Earth delusion true. No matter how far you run, you will not find a subsection in which your sloppy allegations work.

Have a fantastic day, TRE'er.

[Longtitube]

I'll let the above images stand and let other readers judge for themselves.

[Pete Svarrior]

I'll let the above images stand and let other readers judge for themselves.

Very well, if you ran out of couter-arguments, all I can do is rest my case and, once more, wish you a fantabulous day.

In the meantime, if anyone else wants to question my methodology or claim that the Earth is round and very small, you know where to find me. Longiboy's mantle is there for you to pick up!

[RhesusVX]

In the meantime, if anyone else wants to question my methodology or claim that the Earth is round and very small, you know where to find me. Longiboy's mantle is there for you to pick up!

Not claiming anything, but an interesting debate for sure, with some logic and reasoning presented on both sides.  I've read it all, looked at all of the images presented, and will try to keep things very simple because that's normally where the answers lie.  Based on what I see, and accounting for the fact that there are no hard edges in the video to accurately draw against:

1. Near the start of the climb (roughly 1m into the video) the horizon looks straight regardless of position or orientation (conforms to agreed flat Earth theory)
2. Near the end of the climb (roughly 1h 50m into the video) the horizon looks curved regardless of position or orientation (conforms to agreed globe Earth theory)

If we consider that the same camera was used throughout the entire video, with no cuts, it's fair to say that any distortion in any part of the image would manifest itself equally regardless of altitude.  Given that there are enough images in that video where the horizon is in the middle of the screen, and it looks straight near the ground, the only rational explanation for the horizon being curved when viewed high up is that it is indeed curved.

What causes that curve?  Interesting question...and we already determined that it's not the camera.  So...

a. If you stand on the surface of a large enough sphere and look out to the horizon, it looks flat from that perspective.  If you rise high enough above the surface of that sphere, you would see a curved horizon, I think we can all agree on that one, surely?  That's just common sense and observation that you can do at home with a large beach ball and a tiny camera.  Get high enough and you'd see the full sphere.
b. If you stand on the surface of a large enough flat disc and look out to the horizon, it would also look flat from that perspective.  However, what sort of horizon would you expect to see if you were to rise high enough?  A flat one?  Well no, you'd see the curved edge of the disc. Get high enough and you'd see the full disc.

Both models predict a curved horizon at high altitude, so why are flat Earth supporters going out of their way to claim that the horizon viewed high up is in fact straight?  That in itself shows a level of rejection of logical reasoning and observable fact.  Surely you'd be agreeing that yes, it is curved, and instead disagreeing on what that horizon actually represents (the edge of the Earth if it's a flat disc, or the Earth's surface curving away if it's a globe).

[Longtitube]

Interesting observations, unfortunately this thread was hardly a shining example of methodical, precise demonstration of the case for either side.

Pete claims "very obvious" barrel distortion, but I wonder if he has thought this one through. There is very mild distortion (tray seam line dips down a little in middle) consistent with barrel distortion at the bottom edge of the camera view, the sort that most photographers would tolerate. This distortion would be reversed at the top of the camera view (straight line would rise up a little in middle) and be of a similar amount.

However, nobody has demonstrated distortion across the middle of the camera view, where the horizon is shown in the screen capture displayed in the OP. Barrel distortion would not distort the view there, perhaps Pete is thinking of a bottle bottom lens?  http://cameramaker.se/Coke_Lens.htm

My original point was to do with how barrel distortion would affect the video image and drawing lines/boosting contrast & saturation to extreme levels didn't help much. I kept thinking there must be a better, more obvious way for anyone to assess the video or screenshots from it, and I think I may have one. I'm using screenshots and anyone can do this with MS Paint: use Photoshop if you prefer, or Paint.NET, Gimp, PhotoPaint, whatever.

Starting with a plain orthogonal grid, all straight lines:-




Apply an amount of barrel distortion to the grid, such as would be experienced with a fairly wide-angle rectilinear lens and the grid distorts like this:–





But when we get on to real images from the video, how might we simply check how straight or curved the horizon line is? The barrel-distorted grid is pretty obvious, but how about this image from the video, just 8km above the ground?




It's very easy, open the image in a bitmap editor and scale the width down without altering the image height. I'm scaling the image down to 33% of its original width, leaving the image height unchanged. The dialog box shows the settings for MS Paint Resize (Ctrl-W):–


     


The cloud line looks pretty straight to me. If the barrel-distorted grid gets the same treatment, it shows the distortion quite clearly:–





This works when the horizon is not level too, like the following grid which has been rotated about 12 degrees:–





The red lines are straight, but scaling the image doesn't alter them being straight:–





The vertical distortion of the lines is still obvious. What we want to see is what the horizon looks like when the balloon gets up to 35km or so when it burst. Here the horizon is above the middle of the frame:–





The horizon looks curved, so let's compare it to the barrel-distorted grid and scale both images to 33% on width:–





The horizon is clearly curved and a good match for the barrel-distorted grid at the same area of the image. Yep, could be barrel distortion! But before lighting the cigars and pouring the brandy, let's check how the images compare if the horizon is in the middle of the frame (or below that). Middle first:–







Oh. Not straight. Possible barrel distortion? A straight horizon should be showing straight in the middle of the frame - note the grid lines are curved up just above the horizon area and curved down just below it. So not a convincing case for barrel distortion here.

Finally with the horizon below the middle of frame:–







That's all wrong for barrel distortion, the horizon is curving the opposite way to the grid, a grid which replicates the effect of barrel distortion.

So, the case for dismissing this footage as hopelessly compromised by barrel distortion fails. How you interpret the clear evidence for a curved horizon is up to you, but this video clearly shows the horizon at a height of 35.7km (117,126ft) is curved.

[Pete Svarrior]

Longitube, I'm afraid I already provided you with both correct calculations and methodology for this. You were unable to address them, and now you're just ignoring them, sneaking in new distortions of optics instead - like pretending that rotating your subject is equivalent to rotating your lens, a complete contradiction. At this point it's hard not to suspect that these "errors" are deliberate.

This time you didn't even bother drawing the sagittae - you just hope that people will take your word for it. Apparently, correctly identifying the lines you want to be evaluating "didn't help much" - yeah, I'm sure it didn't help your argument. How many times are we going to have to do this before you address the critical issues with your argument?

I was willing to originally assume horrendous incompetence on your part, but it would take a fool not to see your actions for what they are. This "I don't like to do things correctly, so let's do things simply instead (and sneak in some whoopsies to make my argument look correct)" schtick is transparent, and frankly a display of disrespect towards the work I've put towards explaining things to you.

When you mangle your methodology, you get mangled results. You seem to really want that. If you're not going to argue honestly, please don't argue at all.

[Tim Alphabeaver]

Yet another post that shows why low-quality pictures are not a good source of evidence, oh joy!

[RhesusVX]

Longitube, I'm afraid I already provided you with both correct calculations and methodology for this.

This doesn't need any calculations, and it's convenient that some things get ignored to suit narrative.  I posit the following which is in relation to this, and am questioning why you are doing your best to show that the horizon from space would be/is flat? 

a. If you stand on the surface of a large enough sphere and look out to the horizon, it looks flat from that perspective.  If you rise high enough above the surface of that sphere, you would see a curved horizon, I think we can all agree on that one, surely?  That's just common sense and observation that you can do at home with a large beach ball and a tiny camera.  Get high enough and you'd see the full sphere.
b. If you stand on the surface of a large enough flat disc and look out to the horizon, it would also look flat from that perspective.  However, what sort of horizon would you expect to see if you were to rise high enough?  A flat one?  Well no, you'd see the curved edge of the disc. Get high enough and you'd see the full disc.

Both models predict a curved horizon at high altitude, so why are flat Earth supporters going out of their way to claim that the horizon viewed high up is in fact straight?  Perhaps you turn to the EA theory to say that the light is curved upwards the further it travels and so that compensates for the curvature of the edge of the disk, making it look straight?  Fair enough.

RET has a proven, scientific model for showing that light travels in a straight line.
FET only has a theory that light curves upwards, and the further it travels the more it curves.  There is no proven, scientific model for this.

[Pete Svarrior]

I posit the following which is in relation to this, and am questioning why you are doing your best to show that the horizon from space would be/is flat? 

I'm not. Assuming FET, the horizon would not appear flat from space. The argument here is not whether the horizon appears curved - I'm simply criticising Longitube's crusade against proper analysis of evidence. Perhaps instead of projecting your insecurities onto me, you should familiarise yourself with the ideas you're trying to dispute, ideally prior to disputing them?