Thank you, Jimmy.

I live in hope that at least one FEer might indulge me by engaging in this thought experiment. As has been commented elsewhere (by you, I think), if we were only a few micrometers tall (actually around 17 if you assume a human is 2m for arguments sake and ease of calculation) and were standing on a beach ball, our senses would tell us that we were standing on an enormous colourful plastic plain, stretching on for miles and miles - flat as the proverbial pancake; no curve in sight.

I know I'm not exactly the kind of FEer you're looking for, because I'm honestly investigating these claims. Already getting myself into quite a bind trying to disprove gravity, I think it's an experiment out of my league, and I'm really needing some help from fellow flat earther's my self:

https://forum.tfes.org/index.php?topic=13661.msg183727#msg183727But mathematically speaking, if we were on a 8k mile diameter ball.. well I guess mathematically speaking it would look similar to a flat one.

There would be subtle differences, however.

For example, on a flat earth, the horizon would essentially rise to eyelevel for observer elevations up to a few miles because perspective: If the observer goes up a mile, the horizon goes down a mile compared to the observer. But since the distance where the sky meets the water is so far away, the change in angle is so small that the eye cannot resolve it - so the horizon still appears to be at eye level. (By that I mean a water level would still show the horizon to be level with the eye.)

On a ball of the NASA size, the apparent angle of the horizon would go down slightly as the observer went up.

Basically, on a ball earth, if you were 1 mile above sea level, the horizon would be 89 miles away, and the curve would dip down 1 mile in those 89 miles.

So compared to local level, you would be seeing the horizon at 89 miles away and 2 miles below your eyelevel (Remember, you're up one mile, and the earth has curved down a mile, so that's two miles above the horizon.)

arctan(2/89)=1.3 degrees -- so we would see the horizon 1.3 degrees down.

If your water level was 4 foot long, the horizon would be an inch below level at the far end of your level, if you were at 5280 feet elevation. Absurd!

Also, if you were 1 mile up, looking at the horizon, you could observe a very slight curve, but you would need to hold up a straight edge or a super tight string as a straight edge.

The math is as follows:

First, the horizon is 89 miles away, and forms a circle around you.

Let's say your eyes clearly see a 90 degree field of view. Some people are a little more than that, but let's keep it simple.

So your eye is seeing part of a circle, that's 89 miles away and 70 miles long, and 2 miles below you.

You could approximate this if you drew a 90 section of a 35" radius circle on a flat board then held your eye 1" above the center of it and looked out at the curve.

So it would be a very slight curve, but I suspect you would be able to see it if you held up a straight edge.

Another thing that would be different is the angular height of distant mountains.

A mountain that is 75 miles away would appear 3750 feet lower then actual height on a curved earth. At 100 miles away, it would appear 6700 feet lower than the actual height..

According to round earth math, if you were 1 mile up and looking at a mountain that was 2 miles high but 100 miles away, it would actually be below eyelevel even though it's twice as tall!

We could easily check this either with a surveyor's theodolite or a water level.

So if the earth really were a 8000 mile diameter ball, distant mountains would appear lower than they are the further you are from them we go, the horizon would be below eye level if the observer was a mile up or more, and a very slight curve could be seen on the horizon if the observer was at least a mile up.

Of course all of these things are absurd, we know that the horizon rises to eyelevel, and we know that we can see mountains in the distance that would be hidden by the curve, and we know that we don't see a curve on the horizon, but I'm just telling you what the round earth math says!