Flat Out Wrong, Part 2: The Horizon

Time to have a look at some arguments flat earthers use in support of their nonsense, starting with the appearance of the horizon. Why does it look straight, if the Earth is curved? The answer should be obvious, but well... Flat earthers aren't exactly the sharpest tools in the shed, now are they? We also have a look at the Bedford Level experiments, and the methodology used by flat earthers.

[EnochTheSpaceman]

We need to argue for a spherical earth the same way flat earthers argue their points.
1)The earth is a ball because because I read a famous book that says it is, so there!
2)If the earth is flat, why doesn't it flip over on Chinese holidays?
3)If the earth is covered by a dome, where is the concession stand?
4)How many licks does it take to get to the north pole? Huh?
5)Harlem Globetrotters. BOOM!

[Valansch]

You can't prove those people wrong with math.
You probably lost them at "triangle".

[Halloweensmasher]

One time in an argument with a flat Earther I used differential calculus to prove that one of his assertions was wrong. His response was that I shouldn't use complicated math, and then he reasserted his assumption.

[D-Reaver]

"For the last fucking time, NOBODY SAID THERE'D BE MATH!"

[ShadowFalcon]

Using comprehensive math to debunk the Flat Earth hypothesis?

Isn't that kinda like using a Strv 122b tank in a paint-ball competition?

[smartsun]

i just met a flat Earther today and almost died laughing on his claims. Feel bad for the him though, more worried about his kids.

[cashflagg]

It's really depressing that anyone has to make a video saying "the Earth's not flat, y'all". We went to the fucking moon, mapped the human genome and split the atom. Why - neigh, HOW - are there still humans who think the Earth is flat?!

[LamirLakantry]

"Well I say the earth is flat."
*Watches video.
"Now dat dere din't make a lick of sense. There were math 'n' such."

[CaptIronfoundersson]

All this work by flat earthers and yet they still have not answered the most fundamental question; what IS the sex of great Atuin, the world turtle?

[lnsflare]

I mean, the fact that we have a horizon at all instead of being able to see all the way across the ocean with our bare eyes, or even the most powerful of telescopes, is indicative of the surface of the planet curving downwards out of our field of view.

[InternetLaser]

this is the first time I've received a good explanation on the trigonometry required to find the angle to the horizon, thank you

[rhetoricalquestion]

9:36 Awfully generous to say that Flat Earth passes the _'horizon looks flat'_ test, when at the same time, in the same view, it obviously fails the _'I can't see the other shore from here'_ test.

[chrisose]

At best an experiment that does not take atmospheric refraction into account would just suggest a larger diameter to the Earth, not a flat earth since regardless of refraction you will still eventually lose sight on an object over the horizon which would not happen with a flat earth.
Let's grant the flat earthers access to one of our large telescopes. If the earth is flat they should be able to use the Keck Observatory in Hawaii to see New York, London, Mount Everest or any other location on the planet.

[DavidRidlen]

Are there really 80 more Martymers on YouTube?

[kellingc]

A simple way of navigating that was ised from the 1600's and still used today - a sexton. This is a device that will not work on a flat earth, because it uses the angle a star in the sky.

[tonymcflattie]

If the earth was flat, there would be no horizon.

[Hairysteed]

If the Earth was flat, why cant you see the stars circle polaris from Australia?

[MahraiZiller]

Damn, scooped!
I was going to make a post talking about the curvature of the horizon. However, I was going to use the apothem of the horizon arc, and set a line perpendicular to this to the tangent line of the eye sight, and define the height of the "bulge" in the center of the horizon both in terms of distance and angular size.

The main point to get across is that the curvature of the horizon doesn't match the curvature of the Earth, and never will.
As you move away from the surface of the Earth, the curvature of the horizon approaches the curvature of the Earth, but it never properly reaches it (well, if we discount atmospheric refraction, anyway).
This is because of the same simple fact that you never actually see a whole hemisphere of a soccer ball.
In fact, discounting atmospheric refraction or other optical effects, you cannot see a whole hemisphere of ANY object larger than your eye.
It's simple geometry.

Draw a set of lines from the edges of a smaller circle to a larger circle, and spot where on the larger circle these lines touch the sides. You'll find that as you increase the distance between the 2 circles, the chord between the points where these lines touch the sides of the larger circle approaches the diameter of the larger circle, _but it will never reach it_.

And so, disregarding atmospheric refraction, the curvature of the horizon would never match the curvature of the Earth.
But then, this involves basic geometry, and we can't expect flat Earthers to understand that, can we?

[chrisgaming]

Do falt-earthers know what a triangle is?

[MahraiZiller]

Should have mentioned earlier: You can find the angle alpha just by finding the arccosine of r/r+h. It's exactly the same thing, and means you don't have to waste a step figuring out d.
Since everything else can be calculated without using d, and just using the trig functions of tan(a) and cos(b), it would make it a lot simpler.