I was just curious if anyone tried to ask ChatGPT 4 if it could prove curvature by explaining how far a 6 ft. tall person could see if they were standing on the surface of a ball with a 4K mile radius. If it gave the expected answer of approx. 3 miles, what would that imply?

Even if it understood the question and gave the correct answer, all that is doing is showing that a round Earth with a radius of ~6371 km, with a 6 archaic unit observer position would have the horizon 3 archaic units away.

This doesn't prove Earth is round.

Calculating how far away the horizon is on a round Earth doesn't prove Earth is round.

If you want to demonstrate Earth is round you need to get evidence from reality which matches the model.

If you want, I decided to ask it what the distance to the horizon was for an observer at 100 m and at 10 000 km.

For a height of 10 000 km, it told me 11 291.4 km. Given how bad that was I decided to push it to 35 000 km (approximately the height of a geostationary satellite).

For that it gave me the answer 23 094.7 km.

That applies in both directions, so if you go from one side to the other, that gives a total distance of 46 189.4 km.

Now this is a big problem.

With the radius of Earth being 6371 km, the circumference would be 40 030 km.

This means that according to Chat GPT, a geostationary satellite would be able to see more than the entire Earth. That is a geostationary satellite should be able to view a point exactly opposite on Earth, without Earth getting in the way. I would love to know how that is possible.

Perhaps it comes from the caveat it continually provided:

"assuming the ground is flat and there are no obstructions."

So even though it appeals to Earth's curvature in its calculation it says Earth needs to be flat to get this result.

I also see looking into it more, it decided to change the calculation, going from d = sqrt(2Rh), to d = sqrt(2 * R * (h + R)).

This almost looks correct if it was trying to measure from the observer directly to the horizon rather than along the surface.

But that should be d=sqrt(h*(2*R+h))=sqrt(2*r*h + h^2).

But doing that properly gives 40 877.5 km, so it clearly isn't doing that.

So I guess according to you this proves Earth isn't round? All because Chat GPT sucks at giving answers?

I also decided to go one step further, and ask it about other possibilities, i.e. "What would be the distance to the horizon for an observer height of 2 m if Earth had a radius of 1000 km".

And it told me 2 km.

Does this mean the radius of Earth is 1000 km and the distance to the horizon is 2 km?

Even if it could actually think, it would be no better than asking a person who thinks Earth is round.

It doesn't prove Earth is round. It is just dealing with hypotheticals.

If you want to demonstrate Earth is round you need evidence from reality.

As for Alpha2Omega's reply, there is nothing irrelevant or disingenuous about it.

Asking Chat GPT doesn't demonstrate Earth is round.

And if you think it is so obvious, then why are you asking such a foolish question (note the key part of it being foolish is you thinking the answer is obvious, with that obvious answer being that it wont prove Earth is round)?