Sometimes I can't help myself. I just came up with a great argument which could be tried with a flat earth believer.
1 Ask them whether they acknowledge the existence of the Arctic region. (With no reference being made to a Pole, just an icy region on this earth, flat or round, which is known as the Arctic.
They will confirm that hey do. (If they do not, you are in over your head)
2: repeat this for the Antarctic
3: Ask them to confirm that they agree that this are two distinct regions.
You now have confirmation that in their worldview, they have an earth, which contains two distinct icy regions.
If the earth if flat there should be straight lines starting from each icy region, which do not traverse the other one. SO you could leave the south pole, and keep on walking in a straight ine and never encounter the North pole.
If However it is impossible, and any straight line beginning in the centre of the Antartic will end up in the center of the Arctic, than you have yourself a round earth...
This could even be verified experimentally quite quickly and relatively cheaply by them ;)
I tried this. They said that the antarctic is the "Ice wall" that keeps the sea in. Which is also apparently guarded by the US government, and we never hear about it because anyone who sees them is immediately killed. They stated that this was the reason the Titanic was sunk, despite being the wrong pole.
My favorite argument is, if there is no gravity and no electromagnetism, explain how a compass works in 500 words or less, without referencing God, the bible, or the word conspiracy.
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