The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.

The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?

I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.

I can stand at a certain point in my garden and measure the angular height of a tree at the other end of the garden. If I stand closer to the tree, the angle gets larger, further away and the angle gets smaller. What if anything I can deduce about the shape of the earth from this I really don't know and I don't know what additional test I could make to my tree measurement to determine the shape of the earth either.

If the tree was 323 light-years tall, then you could determine the shape by plotting the angles easily enough, just like we do with the North Star.

For a normal sized tree, if you get far enough away from it then the angle is going to behave differently if you are on a plane or a sphere. It will get lower faster on a sphere and eventually vanish. On a flat plane the angle will change rapidly when close, but far away it will slow down until it hardly changes at all.

Either way, if you plot the angle and distance measurements, they are only going to fit one shape.

The tree is quite tall, it's a Scots pine. I'm trying to imagine it 323 light-years tall, that would be something to behold!

Just to take a step back here and explain the thinking behind my original post, I've been trying to separate measuring the angle from measuring distances, because the minute we introduce distance, we get into shape and then bendy light/refraction, general relativity, non-euclidean geometries, interactive scale maps and all that stuff which goes around and around and gets nowhere with no agreement at all. The discussions become polarised.

Since you can measure an angle and/or measure a span of time, without measuring any distances at all, I'm saying let's just do that. We end up with two angles, a latitude and a longitude. We know that these are useful for navigation on the earth, because they've been used for centuries (especially latitude which goes back much much further).

9th century Arab sailors were using a kamal to determine latitude for navigation even before compasses were available.

What I want to know from flat earthers then is why they think measuring latitude with a kamal back in the 9th century can be dismissed as irrelevant because it's based on a spherical earth. It isn't, it's just measuring an angle, why can't you measure an angle on a flat earth?

I'd have liked to include longitude as well, but because that's more complicated and wasn't reliably used until the 17th C, then I'm happy to leave that out of the discussion too.

Honestly I'm just trying to backtrack to find some common ground we can all agree on. Haven't really got anywhere so far though.