Horizons are not physical edges on Earth’s surface.

They certainly act like it in every way, just being a very smooth edge, just like a ball.

When there is a physical edge on a surface, that is not a horizon, which is only a visual phenomenon called perspective and vanishing point.

No it isn't.

The vanishing point is infinitely far away. The horizon is not.

On Earth, we observe the ground appearing at a higher and higher angle of elevation until it reaches the horizon which is below 0 degrees and stops.

Then, by observing objects above the ground (but still below us), we can tell this ground, if we could see it, would be going to a lower angle of elevation.

You’re already aware that when the surface appears to rise upward in the distance, it is not a physical rise of the surface, right?

I am aware that it is a physical angle to the surface.

Why do you think it is an endless effect on a flat surface, while a physical edge that cuts off the surface with a line across the surface on a curved surface?

Simple geoemtry as already explained.

If you are a height h above a surface which is perfectly flat, then a point on that surface a distance of d away from the point directly below you will appear at an angle of:

a = atan(h/d) BELOW you.

This is simple geometry.

It can't stop rising.

Conversely, a round surface will be different, as that h will vary with distance.

If we take a simple approximation for a round Earth, then you will have an additional drop of d^2/2R. This gives us:

a = atan((h+d^2/2R)/d) = atan(h/d+d/2R)

Now we have 2 competing effects. The h/d term from before, as well as the d/2R term.

At small values of d, i.e. d/2R<<h/d, the h/d term dominates, and the angle gets closer to 0. But at large distances, the d/2R term dominates and the angle gets further away from 0.

This means for a curved surface, the ground will have the angle of elevation appear to increase, getting closer to 0, until it reaches the horizon, and starts going back down.

Again, simple images demonstrate this

This is what we would expect for a RE:

The surface "appears to rise" until it reaches the peak at the horizon, and then goes back down with Earth blocking the view to more distant objects (but not if they are tall enough).

This is what we would expect for a FE:

The angle of elevation continues to increase, so the ground continues to "appear to rise", never stopping, never producing a horizon, and never blocking the view.

This is what you need:

Pure magic.

If you want to claim otherwise, you need to tell us what magic stops perspective from working after some distance so it stops appearing to rise, and what magic blocks the view.

Perspective doesn’t just make the surface appear to rise unless cut off by a real edge on a curved surface.

That is exactly what perspective does.

It will make a flat surface below you appear to rise until you reach the edge.

There is no way for it to magically stop.

That is what you have been fleeing from this entire time.

Curved surfaces don’t appear to rise unless they’re almost a flat surface, which is what it really is.

Pure BS.

Curved surfaces DO appear to rise. The question is how much will the appear to rise and for what distance?

If it didn't, then all you would ever see of a ball is a tiny point.

Because as soon as you move away from that point, it "appears to rise".

You can even test this yourself with a simple basketball.

Go put your head above it.

If you straight down (i.e. directly at an angle of elevation of -90 degrees) you will see the ball.

If your delusional BS was true, that is the ONLY spot you would ever see the ball.

But if you increase your angle of elevation, you will see more of the ball.

i.e. the surface of the ball is "appearing to rise".

This continues until you hit the horizon on the ball.

The closer you are to the ball, and the larger the ball, the greater the final angle of elevation. For a sufficent large ball with a sufficiently small height above it, the angle to the horizon will be ~0.

We can all see that the surface is flat, while appearing to rise due to perspective.

No, we can't.

The fact there is the horizon shows it is curved.

You have NOTHING to support your idea of it being flat.

We don’t know what a curved surface of three miles long would really look like

Sure we do. Look at Earth.

But this is you basically just saying you have absolutely no idea if Earth is round or flat.

You don't even know what to look for for such a round surface of Earth, so you just ignore that and blindly assert it must be flat.

The only way you’ll understand what a flat surface looks like, which has a horizon on it, is if you first accept a flat surface is really flat.

So the only way I will understand is if I entirely ignore reality?

No thanks.

I will stick to reality.

Simulations of surfaces is quite trivial.

Imagine a microscopic sized person on a big flat table.

As they are above the table, they would see the entire table (assuming that table is actually flat).

This is because there is nothing blocking the view.

Even more important, if there is another object on that table top somewhere, he would be able to see it, without any of it hidden.

Compare this to a microscopic sized person on a big round ball.

They would see the ball appear to rise up, until almost reaching 0 degreees, before producing a horizon.

If they were to observe an object moving away from them, they would see it reach that horizon and appear to sink.

The round surface matches what is seen on Earth. The flat surface does not.

But horizons appear at all sorts of distances away

Horizons, other than those from things like mountains, appear at a distance away depending upon your altitude.

But it keeps rising up, when the surface curves more and more than at 3 miles out. It would not rise up with more and more of a curve downward with more distance out.

As above, a = atan(h/d+d/2R)

We can easily find the point where it should stop appearing to rise and instead appear to go down.

We do this by finding the point where the change is 0.

As h/d+d/2R is always positive, and atan(x) is an increasing function when x>0, we can simplify and just find when the change in h/d+d/2R is 0.

To do this, we differentiate and set it to 0.

-h/d^2 +1/2R = 0

1/2R = h/d^2

d^2/2R=h

d^2=2Rh

d=sqrt(2Rh).

And we see that as you increase in elevation, the horizon gets further away.

This also matches simple observations of balls.

If your eye right up close, you can see a small portion of it. As you get further away, you see more of it, i.e. the horizon is more distant.

Even a child could understand this.

So why are you still playing dumb?

Even you have implied to understand it, at least if you understand that going higher is equivalent to having a smaller ball as you can just scale the entire system.

Again, what magic produces the horizon in your fantasy?