[Max_Almond]

As for Tom being confused as to why something can be "accurate enough for purpose", it's occurred to me that perhaps it's a simple and even forgiveable misunderstanding.

Maybe this will help clear it up. Here's a photo of a water level showing the dip to the horizon from 1500 feet:



And here's the same water level with the camera raised so that the water in the far bottle is level with the horizon:



I think maybe he was confused because he was thinking that a millimetre here or there would make a significant difference. Whereas in reality it's much more clearcut than that, and not possible to receive ambiguous results.

Hope that helps.

[TomFoolery]

I think that's an admirable pursuit, to try to bring credibility to the flat earth side of things. I've generally reached a stage where I don't mind people believing something incorrect - but I do like it if they at least try to use the correct calculations.

I actually think most flat earthers do believe there is mathematics to describe a sphere, but just that many of them don't know how to apply it properly, or which equation they should use for which measurement.

That's probably why I describe "8 inches per mile squared" as, for all intents and purposes, as far as the flat earth discussion is concerned, "useless".

I mean, when would you actually use that?

"8 inches per mile squared" can be used for any situation where you can use C^2=A^2+B^2 if exact accuracy doesn't matter and it's a sight distance under 1000 miles.
It's simpler as it removes a bunch of constants and still gives surprising accuracy.

By way of comparison, the dip at 1000 miles according to C^2=A^2+B^2 and 8 inches per mile squared is as follows:

656,525ft for C^2=A^2+B^2, and
666,667ft for 8"/mi^2

That is an error of only 1.5%. And that's at a thousand miles which of course is usually too far to clearly see objects unless they are super bright.

For more reasonable distances, like 100 miles:
6667.287ft for P's T, and
6666.667ft for 8"/mi^2

The error there is less than 0.01%!

So for near distances, like a hundred miles, it's very accurate -- its error is much less than other errors like leveling errors or atmospheric refraction etc.

So yeah, a simple easy accurate shortcut can be real handy when a glober and I are standing on a hill looking at another hill 100 miles away, and we're talking about whether the far hill appears where it should appear, or if it's about 6700 feet too low or not.

It's important to be able to keep things simple so nobody gets lost in the math. Right?

[Max_Almond]

I guess. I've always thought of the dip to the horizon being measured as an angle rather than in feet, but I suppose 8 inches per mile squared could occasionally have some practical purposes. Like if you and I were stood in the location of one of my recent shots of the Spanish coast:



We could say: those mountains are about 80 miles away, and 80 squared is 6400, multiplied by 8 inches is...gee whizz, let's just convert it to feet: multiply by two - 12800 - and divide by three - 4270ish and...

How high are the mountains again?

The one on the left's about 4600 feet. The one on the right's 5100 feet.

And how high are we?

About 600 feet.

So with a drop of 4300ish, the peaks of those mountains should be right at our eye level, if the earth's a globe, and massively above it - like 80-90% of them - if the earth is flat.

Whaddya know: it can be quite useful.

[TomFoolery]

I guess. I've always thought of the dip to the horizon being measured as an angle rather than in feet, but I suppose 8 inches per mile squared could occasionally have some practical purposes. Like if you and I were stood in the location of one of my recent shots of the Spanish coast:



We could say: those mountains are about 80 miles away, and 80 squared is 6400, multiplied by 8 inches is...gee whizz, let's just convert it to feet: multiply by two - 12800 - and divide by three - 4270ish and...

How high are the mountains again?

The one on the left's about 4600 feet. The one on the right's 5100 feet.

And how high are we?

About 600 feet.

So with a drop of 4300ish, the peaks of those mountains should be right at our eye level, if the earth's a globe, and massively above it - like 80-90% of them - if the earth is flat.

Whaddya know: it can be quite useful.

That is a lovely sunset.

I guess about the only thing I have to say in response is that NASA is fake and perspective.
I do feel that I've won the argument though because that's two reasons, and globers only have one kind of duct tape - gravity.

[ChrisTP]

And all those photos from space of the earth from private companies and different national space agencies.

EDIT: regarding perspective, obviously theres nothing fake about that. It is simply objects in the distance taking up less of your cone shaped vision. So the less of your vision they take up, the smaller they appear. There is no bendy tricky illusion of perspective, that's just how our eyes work. Perspective doesn't bend the horizon down.

[Max_Almond]

That is a lovely sunset.

I guess about the only thing I have to say in response is that NASA is fake and perspective.

My hope is that before I die I will have found two more solid proofs to support my shaky and insubstantial belief, and then I can rest at peace in my soul - assuming we Pythagorean Satanist Freemasons have one.

[TomFoolery]

As to 8 inches per mile confusing people, if you look at the kind of people that get confused when they see 8 inches per mile squared, just imagine what mental consternation they would suffer if you told them C^2=A^2+B^2! It would turn their brains to CABbage^2!

That's what's different about us is we don't mind a little math and we don't mind facing the challenging issues!

Keep this sort of trash to CN.

I've finally figured out that CN means Complete Nonsense, but I'm still completely mystified about what the trash is.
The other guy had said that the formula of 8 inches per mile squared confused people. I simply replied that the real formula, (known as the Pythagorean Theorem, which is the mathematical formula C squared equals A squared plus B squared,) would really confuse people. The cabbage squared was just a little mathematical humor.

Did you mistake the mathematical expression "c^2=a^2+b^2" and think it was bleeped out bad language?

Or was it my indication that we are different because we don't mind a little math and we don't mind a good challenge?

[Max_Almond]

I just noticed something in pictures like this one:



The clouds are also below eye level.

This does a number of things, but mainly what I want to point out is that it falsifies the claim that the horizon would rise to eye level if we could actually see it: obviously the sea level horizon can't appear higher than clouds for a guy 600 feet above it.

[ChrisTP]

To be fair though round or flat, clouds will converge with the land or sea at the vanishing point anyway.

[Max_Almond]

Vanishing point is always at eye level, [added for clarity] for an observer looking straight ahead/perpendicular to down. Clouds might converge there, but they can't be below it.

[ChrisTP]

Vanishing point is always at eye level. Clouds might converge there, but they can't be below it.

Thats a strange thing to say... The vanishing point doesn’t physically exist, it’s simply a point at which the distance of things is so far that your eyes cannot make it out anymore. So if you see train tracks in the corner of your eyes whiling looking up and to the side it’ll still have a point at which the railway converges to, it won’t be your eye level, it would be anywhere within your vision.

[AATW]

Vanishing point is always at eye level. Clouds might converge there, but they can't be below it.

thats a strange thing to say... the vanishing point doesn’t physically exist, it’s simple a point at which the distance of things is so far that your eyes cannot make it out anymore. The if you see train tracks in the corner of your eyes whiling looking up and to the side it’ll still have a point at which the railway converges to, it won’t be your eye level, it would be anywhere within your vision.

The FE understanding of "vanishing point" is particularly bizarre. As you say, the vanishing point doesn't actually exist, it's a concept from art, not physics.
If you're looking up at these buildings then you can draw perspective lines and "vanishing points"



That doesn't mean that if the sun went over these buildings it would "set", you'd still see it.

[TomFoolery]

I guess. I've always thought of the dip to the horizon being measured as an angle rather than in feet, but I suppose 8 inches per mile squared could occasionally have some practical purposes. Like if you and I were stood in the location of one of my recent shots of the Spanish coast:



We could say: those mountains are about 80 miles away, and 80 squared is 6400, multiplied by 8 inches is...gee whizz, let's just convert it to feet: multiply by two - 12800 - and divide by three - 4270ish and...

How high are the mountains again?

The one on the left's about 4600 feet. The one on the right's 5100 feet.

And how high are we?

About 600 feet.

So with a drop of 4300ish, the peaks of those mountains should be right at our eye level, if the earth's a globe, and massively above it - like 80-90% of them - if the earth is flat.

Whaddya know: it can be quite useful.

I can't figure out how you faked that. The bottles are so big that the surface tension, while visible around the edge, is easily ruled out.
The water in the bottles obviously are level with eachother, and parallel with the horizon.
If you'd pinched off the tube between the bottles to lock a level then raise one up, it would have shown because the water in the two bottles wouldn't be level compared to each other. Same if you'd put salt in one bottle, while it would make one higher, it wouldn't tip the water in them.

How did you fake that?

I'm going to have to try that one when the weather warms up and the snow clears from some of the roads. I'll figure out what you did there one way or another 

[Max_Almond]

How did you fake that?

In this case, the simplest answer is also the correct one: I didn't.

[TomFoolery]

How did you fake that?

In this case, the simplest answer is also the correct one: I didn't.

Fair enough, but we'll see if I get a chance to try that when the snow clears 

[TomFoolery]

How did you fake that?

In this case, the simplest answer is also the correct one: I didn't.

The snow is starting to diminish some, and I went to walmart today and purchased food coloring so I can be in style when I prove that the horizon rises to the eyelevel of the observer!

[Max_Almond]

Good luck!

Are you near the coast? Can you find some elevation?

[TomFoolery]

Good luck!

Are you near the coast? Can you find some elevation?

Well my friend, you were right.

I did a water level test at 50ft elevation, and at around 2240ft elevation.
Even at 50ft the horizon appeared a little below the horizon.
At 2250 ft elevation, entire snow-capped mountain ranges were below the horizon.
I had to tredge through melting snow and mud to get up to the 2250 ft high site, but I took my water level tube, a theodolite, and a tripod. Oh and a DSLR camera.

I've seen it with my own eyes.

Maybe the real horizon was at eyelevel but obscured by the fog.
I guess I need to find a place where I can see the sun set so I know if it's the horizon I'm seeing or just a fading limit of vision.

[Tom Bishop]

Try using a control to determine if the water levels actually line up.



A three container water level device was created, and surprise surprise, the water levels did not align and the device was unable to be calibrated.

[TomFoolery]

Try using a control to determine if the water levels actually line up.



A three container water level device was created, and surprise surprise, the water levels did not align and the device was unable to be calibrated.

That's very interesting, Thanks! I'll have to try that!

So water doesn't seek it's own level?

Or perhaps the center one was slightly warmer? Or maybe it was surface tension? or clinging to the side of the tube?
I did notice the center one was the higher one, maybe the earth is curved.

I also noticed a strong relatively steady breeze creating turbulence around the microphone. Perhaps the tops of the tubes were at different angles and the center one had less pressure due to the wind?

I think I'll have to make mine to have large diameter chambers so as to reduce the affect of surface tension/sticking/capillary and have the tops all connected together so the water is free to seek level but the wind can't influence it.

Perhaps it was perspective that caused the center one to look higher.

I did have to chuckle - the guy asks people to leave comments at the end of the video - but then he has comments disabled.

I would love to see what his 3 pronger would do at let's say 100ft AMSL -- and see how the error compared to the horizon dip.