Earth curvature help please (My brother-in-law is a flat earther and sent me this video about earth curvature.)

[Idun]

I was able to read all the posts on that website and I haven't joined up to Quora. You just press the "Continue Reading ˅" button at the end of the displayed part of a post to see the rest of it. (When you click the link I provided, don't touch your mouse/keyboard for a few seconds to allow it to jump to the correct post in the thread.)

Once the first video is finished playing a second one (on the same topic by the same (loony) presenter) starts up automatically and is probably followed by several others if you don't stop them playing!

Not at all. Tony Miller's post (have another look or see below) makes it clear that the distances being calculated in your video are the ones he points out are completely the wrong thing to 'measure

Yes that's because that 'horizon calculator' is measuring the same wrong thing as most 'Flat Earthers' do. (And then claim it as 'proof' of their fantasies!)


There are many factors to be taken into account (as Miller points out), not least the refraction of light in addition to the correct lines of sight. Below is an extract of the most relevant part of the Quora Post (though the remainder of it goes into much more detail); note, in particular, that the calculations carried out (using Pythagoras' Theorem) in your video are actually measuring to the height "D" as being what should be visible due to the earth's curvature, whereas, geometrically, height "B" is what should be visible (before taking any other relevant factors into account).
I suggest you have another go at reading the full article by Miller (along with some of the other posts in that thread as well); maybe draw your brother-in-law's attention to them too?
(NB: I've added the red colouring above and in the extract below for ease of comparison. )

Extract from Tony Miller's post in Quora...

"Well… Let’s see… We KNOW the rule is 8″ x miles squared, Right?​

​

8*59²/12 = 2320.7 ft or 707.3 m​

​

So this MUST be correct, right? It’s math, can’t be wrong!​

​

Well…​

​

IF you put your eye/camera lens at sea-level, so it is half-way under the dirt/water, exactly at 0 elevation, and you ignored refraction then yes — that is what you would expect.​

​

Now ask yourself, are those EVER the ACTUAL viewing conditions?​

​

No - no they are not.​

​

Since none of those assumptions are correct let’s try that again using the correct mathematics for the real-life question.​

​

In short, you are trying to measure (D) in the image below when it is clearly (B) that you should be asking about. But for some reason, Flat Earth people can never seem to grasp this difference. (B) applies whenever the observer has ANY height AT ALL — even 1 cm. And unless you’ve stuck your camera half-way under the water you aren’t at 0 elevation (you have to measure to center of the lens)."​

​

​

View attachment 37493​

Compare the horizontal (red) lines in the picture above (running from the foot of the green man to the top of the white arrow marked "D". Those are the distances being calculated in your video using Pythagoras' Theorem (at: 0:57, 3:32, 4:03, 4:53, etc.). The calculations (despite plugging in numbers that (conveniently) comply with Pythagoras' Theorem) are simply nonsensical.

It's a bit like Disraeli's comment that there are "Lies, Damned Lies and Statistics". These Flat Earth idiots are just manipulating arbitrary numbers in entirely specious attempts to substantiate their crazy theories.

It's simple common sense that the Earth is ellipsoidal. The video presenter relies heavily on data provided by Google Earth; does he not recognize that said data has been collected by satellites orbiting around this spheroidal (globe) we are on?

Doh!

Thank you Highlander for such a detailed post. I will reply in detail when I've had the chance to go through it thoroughly!

 

[Dr.Peterson]

@Dr.Peterson & @blamocur

Just out of interest, does this link (clicked in your browsers) take you to this text:-

"I think the question would have been made a lot clearer" (highlighted in purple)​

in another thread on the forum?

Yes in Chrome, No in Firefox.

 

[BigBeachBanana]

The quote from post #12 differs from the one that was linked.

Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How ...

Answer (1 of 42): Well… Let’s see… We KNOW the rule is 8″ x miles squared, Right? 8*59²/12 = 2320.7 ft or 707.3 m So this MUST be correct, right? It’s math, can’t be wrong! Well… IF you put your eye/camera lens at sea-level, so it is half-way under the dirt/water, exactly at 0 elevation, and ...

www.quora.com

 

[Dr.Peterson]

I've been trying to post a reply explaining the math on the video (which is correct), but keep being locked out of the site for an hour at a time (which happens from time to time for no apparent reason).

I'll just skip that and recommend this page, which explains the science instead:

Strong Refraction Simulation and Reality for 2 Oil Platforms

This is a refraction simulation of some real observations as shown in the video 9.41 Mile Earth Curvature, Platforms Habitat Hillhouse by bmlsb69. You can recall the Simulation of the Oil Platforms here.

walter.bislins.ch

The key idea is that pictures like this are not made under normal conditions, but during special weather that extends the apparent horizon beyond what it would be based only on the math.

 

[The Highlander]

Just out of interest, does this link (clicked in your browsers) take you to this text:-

"I think the question would have been made a lot clearer" (highlighted in purple)​

I takes me to your post #8 in the "Trigonometry" thread. Haven't noticed any highlighting.

Yes in Chrome, No in Firefox.

Oh, that is so very disappointing! I've been using this "technique" in the belief that it would 'send' people to specific sections of websites with key bits of text highlighted (which seemed like a really useful facility to me); it's a real pain to discover that it doesn't work reliably!

The ability to extend a link so that it (allegedly) does that is built into the latest versions of Chrome using a simple right-click but, clearly, not all other browsers are supporting this! When I click the link I get this result:-

​

However, it appears that not everyone gets the same outcome; that's major PITA!

It doesn't help, either, that some websites don't respond 'properly' to it too! And it now seems clear that Quora (for one) doesn't show up the same for everybody! The geographical variations suggested by @Dr.Peterson?

Oh well, I suppose it's good to at least know these things. It may help to avoid potential confusion.

 

[The Highlander]

I've been trying to post a reply explaining the math on the video (which is correct), but keep being locked out of the site for an hour at a time (which happens from time to time for no apparent reason).

I'll just skip that and recommend this page, which explains the science instead:

Strong Refraction Simulation and Reality for 2 Oil Platforms

This is a refraction simulation of some real observations as shown in the video 9.41 Mile Earth Curvature, Platforms Habitat Hillhouse by bmlsb69. You can recall the Simulation of the Oil Platforms here.

walter.bislins.ch

The key idea is that pictures like this are not made under normal conditions, but during special weather that extends the apparent horizon beyond what it would be based only on the math.

Thank you for that. This is exactly the kind of thing that the Tony Miller post in Quora refers to (if anyone ever gets to see it! )

 

[Idun]

I was able to read all the posts on that website and I haven't joined up to Quora. You just press the "Continue Reading ˅" button at the end of the displayed part of a post to see the rest of it. (When you click the link I provided, don't touch your mouse/keyboard for a few seconds to allow it to jump to the correct post in the thread.)

Once the first video is finished playing a second one (on the same topic by the same (loony) presenter) starts up automatically and is probably followed by several others if you don't stop them playing!

Not at all. Tony Miller's post (have another look or see below) makes it clear that the distances being calculated in your video are the ones he points out are completely the wrong thing to 'measure

Yes that's because that 'horizon calculator' is measuring the same wrong thing as most 'Flat Earthers' do. (And then claim it as 'proof' of their fantasies!)


There are many factors to be taken into account (as Miller points out), not least the refraction of light in addition to the correct lines of sight. Below is an extract of the most relevant part of the Quora Post (though the remainder of it goes into much more detail); note, in particular, that the calculations carried out (using Pythagoras' Theorem) in your video are actually measuring to the height "D" as being what should be visible due to the earth's curvature, whereas, geometrically, height "B" is what should be visible (before taking any other relevant factors into account).
I suggest you have another go at reading the full article by Miller (along with some of the other posts in that thread as well); maybe draw your brother-in-law's attention to them too?
(NB: I've added the red colouring above and in the extract below for ease of comparison. )

Extract from Tony Miller's post in Quora...

"Well… Let’s see… We KNOW the rule is 8″ x miles squared, Right?​

​

8*59²/12 = 2320.7 ft or 707.3 m​

​

So this MUST be correct, right? It’s math, can’t be wrong!​

​

Well…​

​

IF you put your eye/camera lens at sea-level, so it is half-way under the dirt/water, exactly at 0 elevation, and you ignored refraction then yes — that is what you would expect.​

​

Now ask yourself, are those EVER the ACTUAL viewing conditions?​

​

No - no they are not.​

​

Since none of those assumptions are correct let’s try that again using the correct mathematics for the real-life question.​

​

In short, you are trying to measure (D) in the image below when it is clearly (B) that you should be asking about. But for some reason, Flat Earth people can never seem to grasp this difference. (B) applies whenever the observer has ANY height AT ALL — even 1 cm. And unless you’ve stuck your camera half-way under the water you aren’t at 0 elevation (you have to measure to center of the lens)."​

​

​

View attachment 37493​

Compare the horizontal (red) lines in the picture above (running from the foot of the green man to the top of the white arrow marked "D". Those are the distances being calculated in your video using Pythagoras' Theorem (at: 0:57, 3:32, 4:03, 4:53, etc.). The calculations (despite plugging in numbers that (conveniently) comply with Pythagoras' Theorem) are simply nonsensical.

It's a bit like Disraeli's comment that there are "Lies, Damned Lies and Statistics". These Flat Earth idiots are just manipulating arbitrary numbers in entirely specious attempts to substantiate their crazy theories.

It's simple common sense that the Earth is ellipsoidal. The video presenter relies heavily on data provided by Google Earth; does he not recognize that said data has been collected by satellites orbiting around this spheroidal (globe) we are on?

Doh!

Sorry- I didn't realise that my embedded video link would continue on a playlist like that! Not my intention and I haven't watched any of those.

I got the Andrew Wyld Quora's post too (who's using same horizon distance calculator as the video). Funnily though the url had Tony Miller's name in it.

I was able to get Tony's post in a different browser.

in particular, that the calculations carried out (using Pythagoras' Theorem) in your video are actually measuring to the height "D" as being what should be visible due to the earth's curvature, whereas, geometrically, height "B" is what should be visible (before taking any other relevant factors into account).

They seemed to have been using this calculator for how much of the platforms should be obscured https://dizzib.github.io/earth/curve-calc/?d0=30&h0=10&unit=imperial

Yes that's because that 'horizon calculator' is measuring the same wrong thing as most 'Flat Earthers' do. (And then claim it as 'proof' of their fantasies!)

I still get a "distance to horizon" at 4.5km (for my height) https://www.scientificamerican.com/article/how-far-away-is-the-horizon/ Which still doesn't match with how far I can see when standing at the waters edge (at my local beach as I described).

 

[Idun]

I've been trying to post a reply explaining the math on the video (which is correct), but keep being locked out of the site for an hour at a time (which happens from time to time for no apparent reason).

I'll just skip that and recommend this page, which explains the science instead:

Strong Refraction Simulation and Reality for 2 Oil Platforms

This is a refraction simulation of some real observations as shown in the video 9.41 Mile Earth Curvature, Platforms Habitat Hillhouse by bmlsb69. You can recall the Simulation of the Oil Platforms here.

walter.bislins.ch

The key idea is that pictures like this are not made under normal conditions, but during special weather that extends the apparent horizon beyond what it would be based only on the math.

Thank you for confirming that the math at least is being used correctly. I really appreciate that you and Highlander have given me the time of day on this.

In a nutshell - the explanation is that they are partial or full mirages?

Can I ask something else then, which I mentioned earlier? This was when I stood at the beach; a city is visible on my left, and on my right is the tip of an island. I can see further from left to right than that, but the distance between those two points is 68 kilometers. The curvature across 68 kilometers (i.e. my horizon left to right) should be 360 meters, but it's completely flat? How can the horizon not be curved at all?

 

[Dr.Peterson]

I still get a "distance to horizon" at 4.5km (for my height) https://www.scientificamerican.com/article/how-far-away-is-the-horizon/ Which still doesn't match with how far I can see when standing at the waters edge (at my local beach as I described).

That link also says this:

A bigger issue is that our atmosphere acts like a lens, refracting light that passes through it, and this effect is biggest at the horizon, where light must move through the most air to reach your eyes. This allows you to see objects beyond the physical horizon because their light gets refracted downward. In a vacuum, that light would pass over your head, but our planet’s air instead bends it into your eye. This gets complicated quickly, but in the end the 3.58 multiplicative factor becomes 3.86—so your perceived horizon is approximately 8 percent farther away than it would be without air.​

(Rather than "physical horizon", I'd rather say "nominal horizon"; light refraction is physical!)

I get a horizon distance of 4.88 km for you.

Even so, this is talking about normal conditions, you may be seeing under different conditions. And it is easy to be fooled into thinking you are seeing the beach.

In a nutshell - the explanation is that they are partial or full mirages?

Not exactly a mirage, but similar.

Can I ask something else then, which I mentioned earlier? This was when I stood at the beach; a city is visible on my left, and on my right is the tip of an island. I can see further from left to right than that, but the distance between those two points is 68 kilometers. The curvature across 68 kilometers (i.e. my horizon left to right) should be 360 meters, but it's completely flat? How can the horizon not be curved at all?

Why would you expect to see a bulge, when everything you see is at the same height?

The horizon is not like an arc in a vertical plane, but a circle in a horizontal plane whose center you are standing on. And the curvature calculation is about curvature in a line away from you, not across your field of view.

At any rate, the mere existence of a horizon argues against a flat earth. There's plenty of evidence against the flat earth idea, which was recognized millennia ago.

 

[The Highlander]

Sorry- I didn't realise that my embedded video link would continue on a playlist like that! Not my intention and I haven't watched any of those.

I got the Andrew Wyld Quora's post too (who's using same horizon distance calculator as the video). Funnily though the url had Tony Miller's name in it.

I was able to get Tony's post in a different browser.



They seemed to have been using this calculator for how much of the platforms should be obscured https://dizzib.github.io/earth/curve-calc/?d0=30&h0=10&unit=imperial



I still get a "distance to horizon" at 4.5km (for my height) https://www.scientificamerican.com/article/how-far-away-is-the-horizon/ Which still doesn't match with how far I can see when standing at the waters edge (at my local beach as I described).

Well, whatever 'results' you are getting, on whatever websites you visit, I do hope none of them entice you to lend any credence to the lunacy of our brother-in-law and his cronies!

As I trust we have confirmed for you, the Mathematical techniques some of the mused are perfectly sound but they are being (ab)used incorrectly to support specious outcomes.

You might compare it to the computing adage that, given a perfectly good program or routine, if you put rubbish in then you get rubbish out!

At the end of the day, the fact of the matter is that...

This is reality         while... This is Fantasy
 

 

[The Highlander]

Can I ask something else then, which I mentioned earlier? This was when I stood at the beach; a city is visible on my left, and on my right is the tip of an island. I can see further from left to right than that, but the distance between those two points is 68 kilometers. The curvature across 68 kilometers (i.e. my horizon left to right) should be 360 meters, but it's completely flat? How can the horizon not be curved at all?

The horizon is always "flat"; hence the term 'horizontal'.

Here's an even better explanation...

The horizon is not like an arc in a vertical plane, but a circle in a horizontal plane whose center you are standing on. And the curvature calculation is about curvature in a line away from you, not across your field of view.-

Think about holding a hula-hoop around your head at eye-level; all you see in front of you is a straight line (even if you turn your head from side to side).

 

[BigBeachBanana]

It doesn't help, either, that some websites don't respond 'properly' to it too! And it now seems clear that Quora (for one) doesn't show up the same for everybody! The geographical variations suggested by @Dr.Peterson?

Did you see post #23? You're linking the wrong Quora thread.

You're linking the thread "How can you see 100 miles out to sea if the earth is round?"
But you're quoting from "Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How can it be seen?"

 

[Dr.Peterson]

Did you see post #23? You're linking the wrong Quora thread.

You're linking the thread "How can you see 100 miles out to sea if the earth is round?"
But you're quoting from "Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How can it be seen?"

The thing that bothers me whenever I look at Quora is that they mix in answers to other (related or unrelated) questions. (I see one about Harry and William!) I wonder if they do that somewhat randomly, so that this Miller answer was included from the 100 mile page, but we don't all see it the same. Or maybe TH followed a link to it and forgot it was not the same page.

 

[The Highlander]

Did you see post #23? You're linking the wrong Quora thread.

You're linking the thread "How can you see 100 miles out to sea if the earth is round?"
But you're quoting from "Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How can it be seen?"

You're absolutely right, my original link was, indeed, to the "How can you see 100 miles out to sea if the earth is round?" thread.

I don't know how I managed to jump to the "Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How can it be seen?" thread when I copied the extract but it's the same post (by Tony Miller) that appears in both of those threads, so I'm not sure it really matters very much.
(Especially since it would seem that different people using different browsers in different regions appear to see quite different things when visiting Quora websites. )

But thank you for pointing out the discrepancy.

 

[The Highlander]

The thing that bothers me whenever I look at Quora is that they mix in answers to other (related or unrelated) questions. (I see one about Harry and William!) I wonder if they do that somewhat randomly, so that this Miller answer was included from the 100 mile page, but we don't all see it the same. Or maybe TH followed a link to it and forgot it was not the same page.

I like the new moniker: "TH".

 

[Dr.Peterson]

I don't know how I managed to jump to the "Chicago is 59 miles from the opposite shore of Lake Michigan. Given the earth’s curvature, it should be 2320 feet below the horizon. How can it be seen?" thread when I copied the extract but it's the same post (by Tony Miller) that appears in both of those threads, so I'm not sure it really matters very much.
(Especially since it would seem that different people using different browsers in different regions appear to see quite different things when visiting Quora websites. )

... except that Tony Miller doesn't appear in both for me.

I'm wondering if they just treat answers to related questions similarly to ads, and let them vary from person to person, whereas answers in their own threads are fixed?

In any case, I avoid Quora.

I like the new moniker: "TH".

I was lazy.

 

[The Highlander]

... except that Tony Miller doesn't appear in both for me.

I'm wondering if they just treat answers to related questions similarly to ads, and let them vary from person to person, whereas answers in their own threads are fixed?

In any case, I avoid Quora.

Tony Miller has his own page on Quora it seems (though he too, is very unhappy with the site!).

The Quora website just won't let me create a link directly to the post in question () but, if I have counted correctly, it's the 19th post on his list, however, if you quickly scroll down (just past the picture of a Coke can) you should find the post in question there. (Surely?)

If you're at all still interested in seeing it, then the link to his own page is (I hope, lol): Tony Miller.

PS: You may need to click "(more)", to the right just above the picture, for it to display properly.

 

[BigBeachBanana]

The thing that bothers me whenever I look at Quora is that they mix in answers to other (related or unrelated) questions. (I see one about Harry and William!) I wonder if they do that somewhat randomly, so that this Miller answer was included from the 100 mile page, but we don't all see it the same. Or maybe TH followed a link to it and forgot it was not the same page.

Quora likes to put "promoted/related/sponsored" questions in the middle of another thread as an attempt at clickbaiting (Similar to the YouTube suggestion). Except that it's confusing. Since these are recommendations based on personal usage, these suggestion posts are different for everyone.

When reading Quora, you need to look at the top left tags.

 

[Idun]

Why would you expect to see a bulge, when everything you see is at the same height?

The horizon is not like an arc in a vertical plane, but a circle in a horizontal plane whose center you are standing on. And the curvature calculation is about curvature in a line away from you, not across your field of view.

I would expect to see a bulge because it's a relatively small sphere. When I'm standing on a sphere, I'm at the highest point, and the surface falls down/away from me in every direction (i.e. it's not all at the same height).

The circle on a horizontal plane (hula hoop at eye level was a great visualisation) would only make sense on a sphere so big that the human eye couldn't see far enough to capture any of its curvature.

The example where there's a distance of 68km from the city on my left to the island tip on my right; results in 360 meters of curvature. If there's that much curvature between those two points infront of me - why would it look flat between them?




The horizon should be only 4.5km away from me, but I can see the ground/ocean traveling up/away toward the horizon much further than that, every time I'm at the beach or in a relatively flat area.

Is the only explanation for this really that - anything I can see past that distance is all some kind of unwarped, detailed, perfect mirage, consistent in 'continuation of image' with what I see closer to me?

 

[Dr.Peterson]

The circle on a horizontal plane (hula hoop at eye level was a great visualisation) would only make sense on a sphere so big that the human eye couldn't see far enough to capture any of its curvature.

But that's exactly what the earth is! If it weren't, would you be tempted to think it's flat?? We are, in fact, very small compared to the earth.

On the other hand, the fact that there is a horizon at all (and that ships do disappear over it) supports the roundness of the earth.

Empirical evidence for the spherical shape of Earth - Wikipedia

en.wikipedia.org

How Do We Know the Earth Is Round?

Like the other planets, the Earth is a sphere.

askanearthspacescientist.asu.edu

10 ways you can tell the Earth is round

Next time a flat-earth conspiracy theorist confronts you, you'll be prepared. Here are 10 ways to prove that the Earth is round.

www.popsci.com

To believe in a flat earth, you need not just one picture that seems to imply it isn't, but a refutation of all that evidence.