[inquisitive]

I suppose if there were a problem with these levels, there would be occasions when the horizon does appear to be at eye level (from elevation). Yet it never, ever does.

Anyway, I can recreate that Rowbotham observation easily enough, and better. If Tom tells me what the other one is I'll incorporate that one too.

Cheers.

Still waiting for Tom to specify equipment available today for this project.

[Max_Almond]

A block of wood is one of them. I think I can manage that. Or maybe something even better.

[AATW]

I suppose if there were a problem with these levels, there would be occasions when the horizon does appear to be at eye level (from elevation). Yet it never, ever does.

Correct. If this result was because of error then the error would cause different results. Sometimes the horizon would appear above eye level, sometimes below. But that isn’t what the experiments show. Several different ways consistently show the two results that the horizon dips below eye level and the amount of dip increases with altitude. The experiment with the tube is yet another way of demonstrating the first of those results. No lenses involved.

I look forward to the results of Tom’s experiments

[TomFoolery]

.. Even if the earth were flat the horizon would be below eye level. The horizon would be a point on the earth, you'd still be looking down at it:

I agree that we don't have a problem saying that the horizon definitely should be below eyelevel with a flat earth.

I guess what I'm struggling with is "how far down" would the horizon be?

Obviously, if we were half a mile from the outside edge, sure, it'd be down a pretty good angle.

However, if we're near the center of the earth at 600ft above sea level, looking straight out towards the edge where the sky meets the water, it's maybe what, 10,000 miles to the edge?

We would be looking down about 0.0006 degrees from true level. If there was a 600 foot high mountain at the edge, then we'd be looking straight out level.

What I'm struggling with is that even a 600 foot high mountain at 10,000 miles away is still going to be too small to see. Something 10,000 miles away will appear in the same spot whether it's at sea level or 600 feet up. That's why we say that the horizon rises to the observer's eyelevel.

Even at sealevel, it's going to be only 0.0006 degrees down, and that is such a small angle from true level, that any attempts to sight out with a water level would make the horizon to appear right at eye level for all practical purposes.

[AATW]

The problem with that maths is you're assuming that we can see all the way to the edge which is obviously not true, it's impossible to see 10,000 miles through our atmosphere. This diagram:



Is intended to show a flat earth horizon as the limit of your vision. I imagine if the earth were really flat you wouldn't get a sharp horizon line but more of a fading out of the land as it gets further away - that is what you sometimes see at altitude, the horizon is so much further away, because at altitude you can see further over the curve of the earth, so it can be harder to see a sharp horizon line because of the limits of how far we can see through the atmosphere.

The reason the horizon appears to "rise to eye level" is simply because the angle of horizon dip is so small and doesn't increase significantly until you get to heights way above what people would be at in day to day life. It is hard to perceive the dip but several different methods have consistently shown the results that horizon does dip below eye level at altitude and the amount of dip increases with altitude.

Rather than just denying this effect exists when it has been shown so clearly in several different ways it would make more sense to think about how that can be explained on a flat earth. Or if the results are really in dispute then people who dispute them should be conducting their own tests and publishing the results on here for review.

[TomFoolery]

If the water level tools and other methods showed a consistent distance above the horizon, it would be undeniable.

In ENAG Rowbotham shows at least two methods where the horizon registers at eye level or very close to it.

I think I found one in the link you provided:

"Another proof will be found in the following experiment. Select any promontory, pier, lighthouse gallery, or small island, and, at a considerable altitude, place a smooth block of wood or stone of any magnitude; let this be "levelled." If, then, the observer will place his eye close to the block, and look along its surface towards the sea, he will find that the line of sight will touch the distant horizon."

The problem with sighting down a block of wood is that it forces a bias.
In order to really sight straight down, you would have to have half of your pupil obscured by the wood. But then you can't see the target very well, so you instinctively raise your eye up a half a pupils width so your eye can see clearly over the board -- but now the centerline of your eye is half a pupils width *above* the edge of the wood, thus allowing you to see below the other edge of the wood.

You need a method that removes the bias - for example, sight through a straight tube or straw that's taped to the top of the level block of wood. That way you naturally center your pupil, and you naturally look out the center of the other end of the straw.

[TomFoolery]

The problem with that maths is you're assuming that we can see all the way to the edge which is obviously not true, it's impossible to see 10,000 miles through our atmosphere.
 
... snip ...

Is intended to show a flat earth horizon as the limit of your vision.

First, I have a problem with the phrase "Limit of your vision" in regards to distance. Your eyes don't reach out and grope the distant scenery and come back with a report.
Your vision in fact is not a thing, it's what we call the ability of the eye to record optical light rays entering through the lens.

Now, our eye does have a limit to angular resolution - but that is different than distance, although increase in distance does reduce the angular size of an object so it can affect the eye's resolving power.

But as far as distance, there is no limit to the distance the eye can see -- if the light source in question is powerful enough to reach all the way to our eye with enough remaining light for our eye to detect the light, then by George we can see that far! That's why we can see the sun just as it slides down outside the dome, even though it's 10,000 miles away. Conversely, if the light source is too dim, we may not be able to see it 3 feet away. But that doesn't mean we can't see past 3 feet.

While we cannot see the details of things like trees or mountains or whatever at 10,000 miles away, we can often see the sun set on the ocean, getting obscured bottom side first. If you're on a ship at sea and you look out with a telescope and there's half a sun showing, I guess it's intuitive that there's the horizon, or the edge. Obviously there's no land or ocean between you and the upper visible part of the sun, and yet there's a clean horizontal cutoff line below which you do not see the sun, so obviously something is blocking it, and I guess that would be the edge.

I know that some of us here don't believe that the sun sets but that it's always a few thousand miles up somewhere nearly over the "equatorial" path, but I'm struggling with that  because that does not provide any means for it to actually set on the horizon., for anyone, anywhere on the face of the earth. And it very clearly goes down to level and vanishes bottom end first. Math just doesn't allow it to be 3,000 miles up, and 10,000 miles away, and down on the horizon.

[TomFoolery]

Theodolite? Water level? Spirit level?

I want to do an eye level test but I want it FE-approved.

Cheers.

A theodolite should be good - just make sure it's calibrated and everything. The bubble levels on them are often out of adjustment, so you must level it, turn 90, level it, then turn 90 more, and if the bubble says it's not level, then level it back to bring the bubble half way back to level. The idea is you get it so the bubble, even if off centered, reads the same all the way around. Then it's level. But if you don't know what's going on, it can be frustrating.
And the vertical zero-position can also be off, so when you sight in a vertical angle, you then write that down and rotate it 180 degrees, flip the viewfinder around, and sight it again, and average the two readings and that cancels out the vertical zero point error.
However, if both readings are the same then you don't have to worry about double-reading and averaging. But historically, surveyors always double read and averaged.
Other than that, they are very accurate compared to trying to use carpenters levels and stuff, you can literally measure the angular size of a fly across your living room with them. If the fly holds still.
You can find youtube videos on how to use them as well.
Keep the sun off the bubble levels while leveling -- if you slightly warm one end of the bubble level, the bubble goes to that end if it's level.

As far as water levels, that's about as good as it gets but there's a few gotchas to keep in mind.
If the tube is too small, capillary action can distort things - so use the same size/kind of tube, and make it at least half an inch.
The further between the end points, the better. 
Do not seal off the ends of the tube or vapor lock will prevent the water from seeking level.  You can connect them to eachother in a loop however.
You can dye the water red, but make sure it's mixed well or the water may be more dens in one end.
Make sure the water is all the same temperature, because warmer water is lighter and will rise higher in the column.
If there are bubbles in the water, wait till they stop rising. Rising bubbles will raise the water column with them. Bubbles stuck to the tube are OK.
If you use a flexible rubber tube, you can bring both ends together to check and verify that they are seeking the same level. Then move them 10 or more feet apart to check horizon.
Another possibility would be to build a "fish tank" out of plexiglass that was a couple inches wide and 4 inches deep and 48 inches long. Just prop it up and fill it with water half way!
You could even build two identical floating sight rings to look through - and again, swap ends if you suspected bias and see if the bias went to the other direction.
But a long tube is best because you can have the two vertical sections lined up and compare them to each other quite accurately by sighting past one onto the other and then onto the horizon.
If you wanted to get fancy, you could in fact put a Y in the line at one end so there was two vertical tubes on one end, so you could sight it like gun sights.

But pretty much if a large scale water level isn't good enough, nothing is going to be good enough.

[Max_Almond]

Well said.

[AATW]

First, I have a problem with the phrase "Limit of your vision" in regards to distance. Your eyes don't reach out and grope the distant scenery and come back with a report.
Your vision in fact is not a thing, it's what we call the ability of the eye to record optical light rays entering through the lens.

Limit of your vision was perhaps not the right wording. What I meant was the limit of visibility. You only get a clear, sharp horizon if visibility is greater than the distance to the edge of the globe earth - and that varies with altitude. This is why at high altitude the horizon may not be as clear, it's further to the horizon. At ground level the horizon is only a few miles so you can usually see it clearly but on a foggy say you get the same effect at ground level:



This is how I imagine the horizon would look like were the earth flat. Why would there be a sharp line? Why would the horizon be further away as your altitude increases? This makes perfect sense on a globe, altitude allows you to see further over the curve. On a flat earth though it shouldn't make any difference.

I'm confused about your thoughts on sunset, if the sun is really disappearing below the edge of the earth (I believe this is what some ancient civilisations believed) then surely it would be night everywhere. A reasonable belief in the ancient world where there was no quick long distance communication or transport, but now we know that when it's dark in London, England it's light in Sydney, Australia

You are correct though that a sun 3,000 miles above the plane of the earth would not set, there would be nothing to stop you seeing it at all times.

[TomFoolery]

First, I have a problem with the phrase "Limit of your vision" in regards to distance. Your eyes don't reach out and grope the distant scenery and come back with a report.
Your vision in fact is not a thing, it's what we call the ability of the eye to record optical light rays entering through the lens.

Limit of your vision was perhaps not the right wording. What I meant was the limit of visibility. You only get a clear, sharp horizon if visibility is greater than the distance to the edge of the globe earth - and that varies with altitude. This is why at high altitude the horizon may not be as clear, it's further to the horizon. At ground level the horizon is only a few miles so you can usually see it clearly but on a foggy say you get the same effect at ground level:



This is how I imagine the horizon would look like were the earth flat. Why would there be a sharp line? Why would the horizon be further away as your altitude increases? This makes perfect sense on a globe, altitude allows you to see further over the curve. On a flat earth though it shouldn't make any difference.

I'm confused about your thoughts on sunset, if the sun is really disappearing below the edge of the earth (I believe this is what some ancient civilisations believed) then surely it would be night everywhere. A reasonable belief in the ancient world where there was no quick long distance communication or transport, but now we know that when it's dark in London, England it's light in Sydney, Australia

You are correct though that a sun 3,000 miles above the plane of the earth would not set, there would be nothing to stop you seeing it at all times.

Ahh, ok, "Limit of visibility" -- I can definitely go with that.
There's definitely days when clouds, fog, smoke, or smog obscure our view of the sun when it is low on the horizon. Heh, there's even days when they obscure it when it's straight over head!

But hey, there are also days we can see bright lights from a long ways away. That's what I'm concerned with. The fact that some days are cloudy doesn't mean we can't talk about the clear days! Our vision may be obscured way shorter than 10,000 miles on some days, but on others we can see stuff very far away.

But yeah, we do have some issues to work through with the sun.

On one hand, when it sets on a clear evening, we get the effect where the sun vanishes bottom first like this:
so in that case, we do have a clear horizon line and we're obviously seeing something from a long ways away.
We can't hardly say that the sun is just going down to ground level 3000 miles away because then it'd be sitting in someone's back yard. It has to be farther. And yet it doesn't get much smaller when it sets so I'm not sure how to work that out.

In fact, a lot of people would swear that the sun and the moon look bigger when they are on the horizon, which is exactly the opposite of what we would expect because they should be farther then, not closer.
My belief on that though is that they actually have essentially the same angular size but that it's just an optical illusion that make them look bigger on the horizon because the brain compares them to the trees and stuff in front of them. One day I'll get out and take two photos on the same day at rise/set and straight up.

As I said, some things to work through there.

As to the horizon, granted it cannot always be seen, but on those days and situations where we can see a clear horizon line, then on a flat earth the horizon line should definitely rise to eyelevel. You should be able to look out and see the line at whatever your eyelevel is, even using a level to make sure you're looking straight out.
In actuality, if you're above sea level, the horizon would not be exactly straight out, but it's so close to straight out that your eye does not have the resolving power to discern that  few millionths of a degree.

Conversely, that's why it would be so easy for the globists -- if they could -- just go up a few hundred feet and sight to the horizon and measure the down tilt to confirm their beloved 8 inches per mile squared.

[Max_Almond]

A lot of people swear that the sun and the moon look bigger when they are on the horizon, which is exactly the opposite of what we would expect because they should be farther then, not closer.

My belief on that though is that they actually have essentially the same angular size but that it's just an optical illusion that make them look bigger on the horizon because the brain compares them to the trees and stuff in front of them. One day I'll get out and take two photos on the same day at rise/set and straight up.

No need for belief there, sir: the sun's angular size throughout the day has been measured many times, such as this:

Conversely, that's why it would be so easy for the globists - if they could - to just go up a few hundred feet and sight to the horizon and measure the down tilt to confirm their beloved 8 inches per mile squared.

It is easy to do that, and has been done many times also - a few examples of which are in this thread.

I don't think "8 inches per mile squared" is any globist's 'beloved equation', though - that's more of a flat earth thing. In reality, it's not useful for very much, apart from confusing people.

[TomFoolery]

A lot of people swear that the sun and the moon look bigger when they are on the horizon, which is exactly the opposite of what we would expect because they should be farther then, not closer.

My belief on that though is that they actually have essentially the same angular size but that it's just an optical illusion that make them look bigger on the horizon because the brain compares them to the trees and stuff in front of them. One day I'll get out and take two photos on the same day at rise/set and straight up.

No need for belief there, sir: the sun's angular size throughout the day has been measured many times, such as this:

It is easy to do that, and has been done many times also - a few examples of which are in this thread.

I don't think "8 inches per mile squared" is any globist's 'beloved equation', though - that's more of a flat earth thing. In reality, it's not useful for very much, apart from confusing people.

OK thanks for the pictures, but what's that dark spot? did the ISS take a dump last time it transited? Just sayin'.

Now, regarding 8 inches per mile squared, if you'll be so kind as to pardon my British, 8 inches per mile squared is bloody  useful.
Equally useful is it's inverse function miles_to_horizon=sqrt(observer_height_inches/8)
I checked it against the Pythagorean Theorem (which is the correct way to do the calculations on a sphere) and 8 inches per mile squared  was within a percent out to like a thousand miles range as I recall. I was surprised as anything but yeah it's not a bad approximation really, and it's super handy to remember and do quick calculations with.

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!

[Pete Svarrior]

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.

[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.

My sincere apologies good sir, I will do my best to keep that kind of trash to CN, but as I am new here could you enlighten me as to which part was the trash, and what is CN?
I didn't mean any trash by the fact that so many NASA supporters get confused about 8 inches per mile squared.

Thank you very much!

[Max_Almond]

To clarify, eight inches per mile squared calculates the drop below a hypothetical horizontal plane measured from a hypothetical observer's feet. The reason I say it's not very useful is because, in general, we want to measure the predicted hidden amount of things. And the reason I say it confuses people is because flat earth believers often use it when what they really want is the predicted hidden amount.

In a nutshell, I'm not saying it's inaccurate, I'm just saying there's rarely a reason to apply it.

[TomFoolery]

To clarify, eight inches per mile squared calculates the drop below a hypothetical horizontal plane measured from a hypothetical observer's feet. The reason I say it's not very useful is because, in general, we want to measure the predicted hidden amount of things. And the reason I say it confuses people is because flat earth believers often use it when what they really want is the predicted hidden amount.

In a nutshell, I'm not saying it's inaccurate, I'm just saying there's rarely a reason to apply it.

OK gotcha. That's why I find it so useful, since it's the same math we use on a soccer ball.
We use the inverse formula to get the distance to the obsever's horizon, then the 8 inches per mile squared to get drop beyond the horizon. Or so they say.

[Max_Almond]

I'm really not sure who uses that, other than confused flat earthers. Or who says its used to calculate "drop beyond horizon".

It's used to calculate the "drop", full stop, whether beyond, before, or at the horizon - which is almost never a useful thing to know.

Distance to the horizon is calculated by sqrt((r+h)*(r+h)-r^2)

Also not sure who uses the same kind of math as "8 inches per mile" on a football.

Can you clarify please?

[TomFoolery]

I'm really not sure who uses that, other than confused flat earthers. Or who says its used to calculate "drop beyond horizon".

It's used to calculate the "drop", full stop, whether beyond, before, or at the horizon - which is almost never a useful thing to know.

Distance to the horizon is calculated by sqrt((r+h)*(r+h)-r^2)

Also not sure who uses the same kind of math as "8 inches per mile" on a football.

Can you clarify please?

By "same math as used on a soccer ball," I meant the Pythagorean theorem which just happens to be readily approximated by 8 inches per mile squared, at least for the first thousand miles on a sphere 4k miles in radius.

The reason I mentioned the soccer ball is because I'm trying to help bring credibility to the cause, and many flat earthers seem to cringe at the idea that there is math to describe the curve of a sphere. But no, we as flat earthers can fully accept and understand the math of a sphere without accepting that the earth is one.

This is important because when a ball earther is visiting with a flat earther and finds the flat earther doesn't even understand the math for a sphere, it doesn't help things.

And sqrt(h/8) takes the observer height and gives you distance to your horizon. It's just the inverse of 8 inches per mile squared, and it's a handy way to estimate the distance to your horizon given a specific altitude in inches.

[Max_Almond]

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?