# Help with a debate about curvature and distance calculations

#### wonderland78

##### New Member
New to this forum but I signed up because a) I'm concerned about the whole flat earth issue in that people are stubbornly asserting its validity and b) they all seem to know some version of 'science' to significant degrees and so I need to educate myself in order to, well, debate them properly.

So yeah, as I'm new, I just hoped I could post someone's argument and see if I could get some helpers with it. Hope that's ok. Here's what they assert:

"So back to perspective; the human eye can roughly see around 30 miles with the best clear conditions. At that point the eye begins to have serious trouble discerning where the actual horizon is because all the light becomes essentially pixelated and blurs together. So let's take your telescope experiment you have provided. There have been test done "with telescopes" to view ships that have clearly sailed "over the horizon but yet when zoomed in the ship clearly becomes fully visible again. Now since I told you the human eye sees roughly 30 miles (BTW that distance is in reference to something very contrastive to its background and the example given usually is a candle light seen 30 miles away in the dark) we will use that as our starting measurement. So the rough estimate for the algorithm of the curvature of the earth is about 8 inches per 1 mile and this data will vary depending on the source but we are rough estimating here. So given multiple formulas including using the Pythagoras Theorem we arrive at roughly between 450 ft. and 600 ft. of hidden mass beyond the curvature that cannot be seen by the human eye at 6 ft. from the earth' surface as I also presumed the test subject would be a little over 6 ft. tall for easy math making his eye line at roughly 6 ft. Now given that data you clearly know that most ocean bound craft ARE NOT 450-600 ft. tall then there should be NO WAY they can be viewed once they have traveled past the horizon but, alas with a telescope we can see them."
Content from External Source
and one more

So my point with that is that its all a matter of perspective and the sciences and methods used to originate the earth's curvature were not complete or substantiated on any collegiate or academic level. I believe it was Alfred Wallace (Do Not Quote that) who comprised the earliest mathematic calculations for not only claiming the earth was round but having measurements to go with it. He furthermore constructed a device that supposedly proved his theories in full but was unable to complete that task for any academic level scientist and also NOONE has been able to recreate his invention completely nor reach the same results he claimed to have reached.
Content from External Source
Thoughts?

Last edited:

#### Mick West

Staff member
They need a specific example, or at least something more specific.

Telescopes just make things bigger. If something is hidden beyond the horizon then you won't be able to see it with a telescope.

It's demonstrably false.

I zoomed in on this boat. I could see the sail with the naked eye. The bottom of the boat was still covered. Then I stood up so I could see over the horizon and the boat appeared.

#### wonderland78

##### New Member
Thanks, this is quite useful. Only a video would be more useful I guess. I hope they wouldn't then assert that if you zoomed further that the bottom would eventually be found. It's clearly behind the water.

No doubt they'll have an answer though.

#### Z.W. Wolf

##### Senior Member.
[OP copied-in full-removed to help shorten reading time]

There's so much confusion here I'm reluctant to even start but...

So back to perspective; the human eye can roughly see around 30 miles with the best clear conditions. At that point the eye begins to have serious trouble discerning where the actual horizon is because all the light becomes essentially pixelated and blurs together.
Content from External Source
Confusing perspective and resolution. See this for an introduction on resolution: https://www.metabunk.org/explainati...ther-gravitational-lending.t8592/#post-204831

There have been test done "with telescopes" to view ships that have clearly sailed "over the horizon but yet when zoomed in the ship clearly becomes fully visible again.
Content from External Source
No such thing has ever been done. It's just something FE believers keep telling each other. There are some YT videos that purport to show this, but they are just confusing resolution with "bringing something back from over the horizon." For instance they zoom in on a ship and then zoom out until the camera lens is in wide angle. The ship disappears from the video. But that's just because the image of the ship is too small - poor resolution. Then they zoom in again and it reappears. But it reappears because of better resolution.

Now since I told you the human eye sees roughly 30 miles (BTW that distance is in reference to something very contrastive to its background and the example given usually is a candle light seen 30 miles away in the dark) we will use that as our starting measurement.
Content from External Source
Once again this is a problem with resolution.

It's not how far we can see. It's how small we can see. Something far away looks small, yes? But can you see a single bacterium with your naked eye if it's on a table top? (The answer in one case is "yes." There's one species of bacteria that's just big enough to see: Thiomargarita namibiensis.)

There are problems with the human lens and pupil size that are too technical to get into, but another problem is: The rods and cones in the human retina have a physical size. Any image on the retina that's small enough is only going to stimulate a critically small number of them. There will be no detail. This bit about the match at 30 miles is a distorted description of being able to see a source of light on a dark night which is just bright enough to see in the darkness but which has no detail. It's a dimensionless point of light. Stars are another example. We see them, even through a telescope!, as dimensionless points of light. Whereas planets like Venus and Jupiter are just big enough to look like an object with dimensions with the naked eye. Go look!

Obviously we can see things farther away than 30 miles... if they are big enough. Do the sun and moon disappear at 30 miles?

So things "disappear" simply because the image size gets too small. There's no set mileage of course. It depends on how big it is, doesn't it?

Weather conditions and air matter too. But light itself doesn't "get all pixelated."

There's no such word as "contrastive" but contrast is also important. Think about this. You can see car headlights on a road tens of miles away... on a dark night! But could you see a car headlight that far away during the daytime? It would be too small. Poor resolution. But the car headlight at night is still shining a number of photons into your eye. You can see the light, because there are no other photons (from daylight) drowning them out. But there's no detail. It's just a point of light.

What's the smallest number of photons we need to see?

To yield colour vision, cone cells typically need a lot more light to work with than their cousins, the rods. That's why in low-light situations, colour diminishes as the monochromatic rods take over visual duties.

In ideal lab conditions and in places on the retina where rod cells are largely absent, cone cells can be activated when struck by only a handful of photons. Rod cells, though, do even better at picking up whatever ambient light is available. As experiments first conducted in the 1940s show, just one quanta of light can be enough to trigger our awareness. "People can respond to a single photon," says Brian Wandell, professor of psychology and electrical engineering at Stanford. "There is no point in being any more sensitive."

In 1941, Columbia University researchers led subjects into a darkened room and gave their eyes some time to adjust. Rod cells take several minutes to achieve full sensitivity – which is why we have trouble seeing when the lights first go out.

The researchers then flashed a blue-green light in front of the subjects’ face. At a rate better than chance, participants could detect the flash when as few as 54 photons reached their eyes.

After compensating for the loss of photons through absorption by other components in the eye, researchers found that as few as five photons activating five separate rods triggered an awareness of light by the participants.

What is the smallest and farthest we can see?

Now here’s a fact that may surprise you: There is no intrinsic limit to the smallest or farthest thing we can see. So long as an object of whatever size, distance or brevity transfers a photon to a retinal cell, we can spy it.

"All the eye cares about for vision is the amount of light that lands on the eye," says Landy. "It's just the total number of photons. So you can make [a light source] ridiculously tiny and ridiculously brief, but if it's really strong in photons, you can still see it."

Psychology textbooks, for instance, routinely state that on a clear, dark night, a candle flame can be spotted from as far away as 48 kilometres. In practice, of course, our eyes are routinely inundated by photons, so stray quanta of light from great distances get lost in the wash. "When you increase the background intensity, the amount of extra light you need to see something increases," says Landy.

The night sky, with its dark background pricked by stars, offers some startling examples of long-distance vision. Stars are huge; many we see in the night sky are millions of kilometres in diameter. Even the nearest stars, however, are more than 24 trillion miles away, and are therefore so diminished in size our eye cannot resolve them. Lo and behold, we can still see stars as intense, gleaming "point sources" of light because their photons cross the cosmic expanse and hit our retinas.
Content from External Source

So my point with that is that its all a matter of perspective and the sciences and methods used to originate the earth's curvature were not complete or substantiated on any collegiate or academic level. I believe it was Alfred Wallace (Do Not Quote that) who comprised the earliest mathematic calculations for not only claiming the earth was round but having measurements to go with it. He furthermore constructed a device that supposedly proved his theories in full but was unable to complete that task for any academic level scientist and also NOONE has been able to recreate his invention completely nor reach the same results he claimed to have reached.
Content from External Source
This is an argument from personal ignorance. The author of this quote doesn't know anything about the history of astronomy and geodesy, so he apparently concludes that it doesn't exist. We're supposed to stick to one subject per thread here, and the history of astronomy and geodesy fills books.

Last edited by a moderator:

#### Trailblazer

##### Moderator
Staff member
No such thing has ever been done. It's just something FE believers keep telling each other. There are some YT videos that purport to show this, but they are just confusing resolution with "bringing something back from over the horizon." For instance they zoom in on a ship and then zoom out until the camera lens is in wide angle. The ship disappears from the video. But that's just because the image of the ship is too small - poor resolution. Then they zoom in again and it reappears. But it reappears because of better resolution.
Yes, I had this video shown to me as an example of "zooming in bringing a ship back into view":

The boat disappears when zoomed out!

Even thought it is clearly way in front of the horizon:

#### Mick West

Staff member
Even thought it is clearly way in front of the horizon:

Not only that, it's clearly in front of the horizon and the same shape (i.e. the bottom is not missing) through the entire zoom back right up until it's smaller than the resolution of the camera.

Even of the very last frame it's perceptible in the video, the wake of the boat is below the horizon:

"Zooming in to look over the horizon" has always been an odd claim since Rowbotham made it in the 1860s. It flew back then because hardly anyone had access to a telescope. But now lots of people have cameras like the P900 - or at least can examine videos like this - and can see that it's false.

Of course the challenge here is that the FE believer fundamentally misunderstands what they are seeing, and are highly resistant to explanation. Perhaps some kind of socratic dialog while looking at this video might help:

(invented example dialog follows)

Globe: If the earth is flat, then why do ships sink below the horizon?
Flat: It's the Law of Perspective, if you zoom in on it the ship will reappear
Globe: Do you have an example?
Flat: yes, look at this video: Nikon P900 fishing boat that merges with horizon becomes visible under zoom
Globe: So where is that boat behind the horizon
Flat: 20 seconds in, you can see it's vanished
Globe: But you can see the wake of the boat. Doesn't that mean you can see the bottom of the boat
Flat: Maybe, but it's merging with the horizon
Globe: Isn't the claim that the bottom will vanish first? At 19 seconds in I can still make out the wake, but not the boat.

Flat: It become visible as you zoom in!
Globe: It looks like it's just getting bigger, and look, even at 18 seconds it's in front of the horizon. This isn't a boat going over the horizon at all:

Flat: But you can't see it, then you zoom in and see it.
Globe: Can you give an example where the boat is actually hidden by the horizon?
Flat: Can you?
Globe: Here. This video shows two similar sized boat, but this time they are actually "hull down" - the bottom portion is hidden by the horizon.

Here's no zoom where you can see the sails.

A little bit of zoom:

Flat: So zooming in will reveal the hull
Globe: No, if you zoom in the same amount is hidden

Flat: That's just waves
Globe: Look at the building behind the boats at the start of the video. They are obscured by the horizon too. If it's just waves, why do we never see the bottom of the building or the beach?
Flat: Perspective
..... etc .....

Last edited:

#### Mick West

Staff member
Hi mr.Mick.......what do you think of this explanation for why boats/cities disappear bottom up.
Can you summarize the explanation?

#### OTACHI

##### New Member
Can you summarize the explanation?

Here's the description:

" Using a P-900 at 83x zoom, Wide Awake filmed a boat until it literally disappeared into the distant horizon. The boat simply decreased in size due to the extreme distance and was covered up by the much closer waves located at the horizon line, i.e., where the horizon rises up to eye level. This has nothing to do with curvature but is a natural result of perspective and the angle of the observer. I hope that I explained the issue well enough."
Content from External Source

#### Mick West

Staff member
So in that explanation there are nearby waves that are higher than eye level which block the boats.

The problem there is that the ocean horizon is measurable slightly below eye level. For waves to block your view of the boat they would have to be higher above sea level than your eyes/camera.

#### OTACHI

##### New Member
Well obviously in flat earth the ocean horizon is always at eye level.

#### Mick West

Staff member
And that's especially problematic with larger more distant object viewed from higher up.

Even at six feet it's quite apparent that there's no waves more than a few feet high, and nothing nearby is blocking my view.

In fact we can see the surface of the ocean for several miles out.

The wave theory is even more impossible when you look at the 40 foot view.

#### Mick West

Staff member
Well obviously in flat earth the ocean horizon is always at eye level.
Why can you see it then? Notice in my pics above the horizon is a sharp line when viewed from a few feet up. It's also in front of the island, and not behind it. So what are we seeing? What is the the horizon in the above three photos of Catalina Island (or the boat pictures)

#### Henk001

##### Senior Member.
Another example. Two photographs of a windfarm in the North sea with windmills at a distance between 36 and 45 km. First made while standing on the beach. Second while standing on a 24m high dune. Also Notice the buoy, that shows that you can see further away when your standpoint is higher.

Same distance, same zoom.

#### OTACHI

##### New Member
Hmm,you're right,thanks Mick.

#### deirdre

##### Senior Member.
Here's the description:
if that were the case then the boat wouldn't unshrink if you increase your viewing height.

#### Henk001

##### Senior Member.
Same windfarm different standpoint. 55 km away standing on a 28 m high dune.

Center part cropped contrast enhanced

#### Trailblazer

##### Moderator
Staff member
And that's especially problematic with larger more distant object viewed from higher up.

Even at six feet it's quite apparent that there's no waves more than a few feet high, and nothing nearby is blocking my view.

In fact we can see the surface of the ocean for several miles out.

The wave theory is even more impossible when you look at the 40 foot view.
Yes, big things like islands are a much better example than boats, because they are large enough to be clearly visible with the naked eye even at a distance where a significant portion of them is hidden over the horizon. And nobody can argue that an island several hundred feet high is being obscured by "nearby waves".

#### Trailblazer

##### Moderator
Staff member
This is a really good photo. To me, at least, the three-dimensional "hump" of the ocean, with the wind turbines behind the "summit", is very visually apparent.

#### JL Born

##### New Member
New to this forum but I signed up because a) I'm concerned about the whole flat earth issue in that people are stubbornly asserting its validity and b) they all seem to know some version of 'science' to significant degrees and so I need to educate myself in order to, well, debate them properly.

So yeah, as I'm new, I just hoped I could post someone's argument and see if I could get some helpers with it. Hope that's ok. Here's what they assert:

"So back to perspective; the human eye can roughly see around 30 miles with the best clear conditions. At that point the eye begins to have serious trouble discerning where the actual horizon is because all the light becomes essentially pixelated and blurs together. So let's take your telescope experiment you have provided. There have been test done "with telescopes" to view ships that have clearly sailed "over the horizon but yet when zoomed in the ship clearly becomes fully visible again. Now since I told you the human eye sees roughly 30 miles (BTW that distance is in reference to something very contrastive to its background and the example given usually is a candle light seen 30 miles away in the dark) we will use that as our starting measurement. So the rough estimate for the algorithm of the curvature of the earth is about 8 inches per 1 mile and this data will vary depending on the source but we are rough estimating here. So given multiple formulas including using the Pythagoras Theorem we arrive at roughly between 450 ft. and 600 ft. of hidden mass beyond the curvature that cannot be seen by the human eye at 6 ft. from the earth' surface as I also presumed the test subject would be a little over 6 ft. tall for easy math making his eye line at roughly 6 ft. Now given that data you clearly know that most ocean bound craft ARE NOT 450-600 ft. tall then there should be NO WAY they can be viewed once they have traveled past the horizon but, alas with a telescope we can see them."
Content from External Source
and one more

So my point with that is that its all a matter of perspective and the sciences and methods used to originate the earth's curvature were not complete or substantiated on any collegiate or academic level. I believe it was Alfred Wallace (Do Not Quote that) who comprised the earliest mathematic calculations for not only claiming the earth was round but having measurements to go with it. He furthermore constructed a device that supposedly proved his theories in full but was unable to complete that task for any academic level scientist and also NOONE has been able to recreate his invention completely nor reach the same results he claimed to have reached.
Content from External Source
Thoughts?
I have a flat earth friend and sometimes it is super hard to explain stuff, so for this example, if we can only see 30 miles, why can we see stars? I know light travels, but how far can our eyes really see with no atmospheric turbulence?

#### Mick West

Staff member
I have a flat earth friend and sometimes it is super hard to explain stuff, so for this example, if we can only see 30 miles, why can we see stars? I know light travels, but how far can our eyes really see with no atmospheric turbulence?
The example was a candle, visible from 30 miles away in ideal condition. The limit is because a candle is small and dim. If you have something bigger and/or brighter, then you can see it from a longer distance.

While interstellar distances are really large (one light year is about 6 trillion miles) stars are also really large. Our sun is a pretty dim star, and it puts out 3.75×10^28 lumens, with is about 3x10^27 (3,000,000,000,000,000,000,000,000,000) as much as a candle. There are also lots of much bigger stars - and some of the things you see in the sky are actually galaxies made up of billions of stars.

So there's no real limit, if the light source is big enough.

#### Whitebeard

##### Senior Member.
The example was a candle, visible from 30 miles away in ideal condition. The limit is because a candle is small and dim.
Early off shore lighthouse such as the Eddystone and Bell Rock lighthouses were powered by candles. Older on shore lighthouses traditionally used coal or wood fired braziers, but could consume over 800 tons of combustibles per uear, fine when your on land, but when your in a slender tower, x number of miles out to sea and often isolated for months on end this was not practical. So when Henry Winstanley was commissioned to build the first Eddystone Lighthouse in 1698 he experimented with a number of light sources and discovered that ordinary tallow candles, in a bank of up to 12 (increased to 24 for the second and third lighthouses 1709 & 1759 - the original building having been destroyed in a storm in 1703) magnified by a large mirror and a simple lens was more than adequate to be seen upto 20 nautical miles away, with the added advantage of being easier to store, transport and handle than oil for oil lamps. In fact it wasn't until the 1850's that oil fired lamps began to replace candles as the standard means of lighthouse illumination.

(Source - The Lighthouses of Trinity House - by Richard Woodman and Jane Wilson, 2002, (ISBN: 9781904050001) )

#### Trailblazer

##### Moderator
Staff member
I have a flat earth friend and sometimes it is super hard to explain stuff, so for this example, if we can only see 30 miles, why can we see stars? I know light travels, but how far can our eyes really see with no atmospheric turbulence?
And you can see things much further than 30 miles away, no candles in darkness required. I've posted this photo before, but this mountain was perfectly well visible with the naked eye (otherwise I wouldn't have known to take the photo!).

Almost 85 miles from the camera location in Tongariro National Park to the summit of Mt Taranaki, in New Zealand. The increasing haziness caused by the atmosphere shows up well on the successive ridges, but you can still see.

#### Chris Berry

##### New Member
@Henk001

Can you confirm that in your wind turbine images the only thing that changed was the height to 24m? The focal length (zoom) and distance were identical?

#### Qulaey

##### New Member
@Chris Berry Still that wouldn't make a difference tho, no matter how much you zoom you cant bring anything back to the horizon if its below.

#### Chris Berry

##### New Member
@Chris Berry Still that wouldn't make a difference tho, no matter how much you zoom you cant bring anything back to the horizon if its below.

HI, that's not my concern. My concern is the drastic change in angular size of the turbines. If he used the same zoom and distance and only a changed the height, wouldn't the angular size be virtually the same that far away but only adding 80 feet? If you calculate the hypotenuse (distance to object), there is no change simply by adding 80 feet.

Why is that happening?

#### Rory

##### Senior Member.
Hi, that's not my concern. My concern is the drastic change in angular size of the turbines. If he used the same zoom and distance and only a changed the height, wouldn't the angular size be virtually the same?

The angular size is "virtually the same" - but he's zoomed in on it.

Perhaps the easiest way to think of it is to imagine yourself taking a photo of a person say twenty feet away. Now zoom in on them. Same person. Same distance. Same calculable angular size. But they will appear larger in the photo because of the zoom.

Last edited:

#### Chris Berry

##### New Member
The angular size is "virtually the same" - but he's zoomed in on it.

Perhaps the easiest way to think of it is to imagine yourself taking a photo of a person say twenty feet away. Now zoom in on them. Same person. Same distance. Same calculable angular size. But they will appear larger in the photo because of the zoom.

Hi, the poster @Henk001 says, in the post, it was the same zoom. So, until I find out he is wrong, I'm asking the question. Apparently he's been gone for a while and may never see this.

Also, if you do a comparison, the top image is about 2.2x larger than the bottom. So the angular size is quite a bit different.

#### Mick West

Staff member
Another example. Two photographs of a windfarm in the North sea with windmills at a distance between 36 and 45 km. First made while standing on the beach. Second while standing on a 24m high dune. Also Notice the buoy, that shows that you can see further away when your standpoint is higher.

Same distance, same zoom.

If he used the same zoom and distance and only a changed the height, wouldn't the angular size be virtually the same that far away but only adding 80 feet? If you calculate the hypotenuse (distance to object), there is no change simply by adding 80 feet.

Hi, the poster @Henk001 says, in the post, it was the same zoom. So, until I find out he is wrong, I'm asking the question. Apparently he's been gone for a while and may never see this.

Also, if you do a comparison, the top image is about 2.2x larger than the bottom. So the angular size is quite a bit different.

@Chris Berry, I agree that the comparison is not very good. For a start the bouy is a different size in each photo, also it appears to be a totally different set of windmills. The distance to each windmill is going to be proportional to how dim is appears, as well as its size. The high photo has none of the large clear windmills, just two that are medium clear.

So I suspect the photographer had to walk along the beach a ways to take the photo. If we resize the low photo so the buoy matches then the one windmill that has similar dimness is a rough match for size.

So not the best illustration if you want to compare the exact same scene. However, it does show all the windmills hidden by the horizon from a low viewpoint, and then having their vanes visible from a higher viewpoint.

Last edited:

#### derwoodii

##### Senior Member.
this might help

this is shorter cut version there is a longer 17 minute one as well

Eratosthenes was a Greek scientist who discovered the circumference of the Earth back in 240 B.C by mesuring the length of sun cast shadows from distance location at the same time..

#### Arc

##### New Member
Same windfarm different standpoint. 55 km away standing on a 28 m high dune.

Center part cropped contrast enhanced

Beautiful photos, we can actually estimate earth's radius r with great precision by the data you provided (i assume GPS data was used): take points A, B and C in a straight line from the dune's observer (A) to windfarm (C) such that the line is tangent to the surface of earth at point B, use d1 to denote distance AB and d2 to denote distance BC such that d = AC = d1+d2 = 55 000 m, a = 28 m is the height of the dune, and h is the height of the turbine, which by their shape we can say have like h ~ 200 m (standard blade size of 80 m and about 40 m from blade tip to sea level, if you have more info on that we can improve calculation).

Consider half of the turbines to be visible, while the other half is below point B, and thus hidden from Dune's observer. Take the center of the earth at point O, then we construct two right triangles, back to back, OBA, with sides r, d1, r+a (hypotenuse) and OBC with sides r, d2 and r+h/2 (hypotenuse), where h/2 is used because we consider the lower half of the turbine to be hidden.

Then we have two square sum rules: r^2 + d1^2 = (r+a)^2 and r^2 + d2^2 = (r+h/2)^2, of which we know a, h and d1+d2, and the unknown is r. First, combine both expressions to eliminate r and obtain d1. Atfer some manipulations you get a second degree equation on d1: (2a-h)*d1^2 + (-4ad)*d1 + (2ad^2 - ah^2/2 + ha^2)= 0, take the negative root (the other gives a negative distance) and you get d1 = 19 032 m (which means that, when you climbed 28 m in the dune, you literally gained 19 km of extra horizon view), then d2 = 35 967 m from d = d1 + d2, and solve the second square sum rule for the radius: r = d2^2/h - h/4, which gives us r = 6 468 km.

Compared to the real earth radius, which is 6 371 km, this gives us a difference of 97 km, and thus a relative error of 1,5%. All this using only the data provided, h = 200 m, a = 28 m and d = 55 km, and the half-turbine visibility condition.

And you didn't even had to measure the distance between Alexandria and Syene by foot!

Cheers,
Fabio

Last edited:

Replies
20
Views
5K
Replies
34
Views
3K
Replies
9
Views
2K
Replies
57
Views
5K