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Horizon views are more compatible with a Globe Earth of radius 3959 miles than a Flat Earth

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Voting Style: Open Point System: 7 Point
Started: 6/30/2018 Category: Science
Updated: 3 years ago Status: Debating Period
Viewed: 994 times Debate No: 116121
Debate Rounds (4)
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Flat Earthers often point to a variety of views of the Horizon and make several false claims that these views support their argument that the Earth is Flat. Rather than argue the general topic of Flat Earth I would like to take it point-by-point in a series of more narrow debates. If you want to debate me you can review some 350 of my arguments against the Flat Earth on my blog.

In this debate, should someone accept it, the focus is exclusively on the Horizon itself. To defeat this position you will need to demonstrate with a scientifically testable model and detailed analysis that the preponderance of Horizon views are more compatible with a Flat Earth model than a Globe Model.

I will start by explaining the Globe Model and making some observations. Response should include similar level of detailed exposition on the Flat Earth model. If you cannot mathematically explain your Flat Earth model then how can we judge your claims about what we should expect to see if the Earth is flat? Math isn't magic -- it is simply speaking accurately in a way that be tested and verified by everyone.

When you look out at the Horizon of a Globe should you expect it to curve downwards making an arc with a radius of 3959 miles as if you are seeing the entire Globe from your vantage point, very near the surface of the Earth?

This is what it seems like Flat Earthers expect to see... but this is absurd and not how spheroids actually work in reality. So let's look at the geometry of a sphere first:

Trying to explain how a Horizon works on a sphere
Your view of the vast majority of a sphere the size of the Earth is therefore blocked at the Horizon because that is where your line-of-sight hits the surface of the sphere. Standing on a beach you are seeing only about 5 miles out to the Horizon, all the way round you. The remainder of the Earth is blocked from your view by that little slice of the surface.

We are usually many radii away from the small spheres we view so we don't think about how this works, but this is all just a simple fact of how viewing a sphere up close works.

Now think about the plane in which that Horizon Circle is formed (Horizon literally comes from "Limiting Circle")... The Horizon is equal distant from the observer so it would be perpendicular to that surface, but in a plane a bit below the surface directly under the observer.

So, as shown in the bottom of the above image, the Horizon is a circle being view almost completely on edge -- so it is 100% expected that it should "look flat" from that vantage point.

This defeats 99% of Flat Earth claims that the "Horizon Looks Flat" -- because it should "Look Flat" in both models. There are, however, numerous ways to measure the Horizon and show it is not, in fact, actually flat.

#1 for an observer on a calm ocean the Horizon is roughly equidistant in every direction. This defines a CIRCLE and not a flat horizon. Your horizon curves 360° around you where a FLAT horizon would extent out infinitely in only one direction. Flat Earthers might object that this is due to some atmospheric limitation to which I would say please demonstrate this effect. The fact is that our horizon is very sharp and crisp at lower altitudes and only at great distances does it become hazy and fuzzy.

A 360 degree view clearly demonstrates that the horizon curves around us.

The 360 degree horizon viewed from high-altitude (airpano)

#2 using a sufficiently long straight-edge from a moderate altitude you can observe the expected "horizon saggita" (the arc of the horizon circle as the horizon curves around the observer). You need a wide view and high-resolution. This method can work from 800 meters and up if done carefully. The straight-edge controls for any lens distortion.

Viewing horizon sagitta using a builders level.

#3 observing the horizon drop angle as a function of radius and altitude.

Flat Earthers like to claim that the "horizon rises to eye level" but this claim doesn't hold up when you actually measure level. This is my personal image using a Theodolite app which marks level from the observer and this shows the Horizon is about 3.4° below level. This is the exact amount of Horizon drop we expect to observe on a Globe with radius 3959 miles.

There are now numerous videos using water levels showing this effect as well -- including one by a Flat Earth advocate, Jon McIntyre:

My own observation using a Theodolite to mark out level (colored reticle) at 38k feet.

Using Theodolite to mark level at 38k feet and showing the horizon well below level.

So where is the Flat Earth model that predicts this Horizon drop angle?

Where is the Flat Earth model that predicts the distance to the Horizon?

Next I would like to offer some analysis of images involving the horizon and show that the Globe model (by far) is the superior explination for these views.

The first one is the record breaking view of Pic Gaspard (3880m) and Grand Ferrand (2758m) from Pic de Finestrelles (2826m) in the Pyrénées.

The first thing to notice here is that, on a flat plane, our camera altitude (2826m) should be looking slightly down towards the peak of the Grand Ferrand and slightly upwards towards the peak of Pic Gaspard (3880m).

But what we observe in reality is that Grand Ferrand peak is a good bit higher than Pic Gaspard! The Globe model fits this perfectly as I will demonstrate in the 3D simulation of this view below the annotated photo which takes into account a small amount of refraction which is a well-supported optical phenomena.

And Flat Earthers celebrated this as their great victory -- how can we possibly see so far unless the Earth is Flat? 100% proof they said...

Fortunately we know how far apart our line-of-sight is between the two mountains in this case which tells us the angular size of this camera field of view. Using that information we can show almost exactly how tall each mountain would be at that distance if the bottom of the mountain wasn't obscured by the curvature of the Earth. That is shown in the two vertical blue lines in the upper image. [detailed analysis on my blog]

Pic Gaspard (3880m)/Grand Ferrand (2758m) from Pic de Finestrelles (2826m) in the Pyr"n"es
The 3D simulated portion is generated from Walter Bislin Horizon Tool

This view is simply vastly better explained by the Globe model than any Flat Model could ever hope to explain.

Flat Earthers can't both argue that we can see this far AND that our horizon is limited to under 3 miles on a beach with any consistency (you can argue anything with ad hoc explanations).

I'd like to add one more piece of background information here and that is a discussion on Perspective -- which Flat Earthers try to invoke without ever offering any actual explanation of it. This is relevant to our view of the Horizon because it is, in fact, Perspective that explains why the mountains SHOULD appear much larger in that image if we could see the entire mountain.

Here is how perspective actually works -- this is how 3D games work, this is how Autocad works, this is how your eye works -- and this is how we know how large those mountains SHOULD appear at these distances.

Mathematical explanation of perspective.

It follows from this that objects that truly in a straight-line would not be curved by the effects of perspective. Straight-lines remain straight because this is a strictly linear transformation.

Curvilinear or fisheye lenses are NOT a linear transformation -- they are a spherical transformation and thus are a distortion of normal perspective.

Which is why the Soundly images. such as this one, are not due to Perspective (there are now hundreds of these images taken by Soundly and many others that repeat these observations under numerous conditions using many different types of equipment from DSLR's to P900's to Telescopes to Professional Survey equipment -- and these observations match the 3D models created by Cara & Waler Bislin as well.

Soundly's P900 shot of the power lines across Lake Pontchartrain.

And if you wish to incorporate criticism of this image please note in advance:

#1 Zach's video pointed out the WRONG power lines
#2 They never demonstrate that their table is, in fact, flat
#3 a left or right bend in the towers does NOT actually produce the same effect
#4 there are now HUNDREDS of images of these power lines from DSLRs, P900s, Telescopes, and professional surveying equipment -- and posted by numerous people.

Nor are the repeated observations by Mathis of the Turning Torso building which is increasingly blocked by the Horizon with increasing distance -- again, exactly in the proportion we expect on a Globe.

Turning Torso building viewed from different distances comport with a Globe.

I look forward to someone sharing a Flat Earth model that can better account for these observations.
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Debate Round No. 4
15 comments have been posted on this debate. Showing 11 through 15 records.
Posted by Anonymous 3 years ago
Asta -- I'm looking for an intelligent challenger who can present their side of the argument cogently.
Posted by Anonymous 3 years ago
Actually, i've measured the Earth and shared the method here -- they used it as far back as the 9th century so I'm sure you can manage if you tried just a little bit.

You can measure it at many altitudes, from many locations, in many directions and you always get just about the same answer (it's oblate to 1 part in 298 which is hard to measure without professional equipment so you probably won't notice it).
Posted by Anonymous 3 years ago
Are you looking for an easy win?
Posted by Anonymous 3 years ago
I give you an A+ at being able to google the radius of the Earth.
Posted by Anonymous 3 years ago
Once you understand that in the flat earth, the sky is a projected screen, you will understand that what you're seeing at the edge is illusory and lying to you.
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