If the earth is flat and surrounded by a wall of ice as your model states:
How did these explorers walk from one side of Antarctica to the other?
Key:
The lines each represent an expedition by an explorer or group of explorers. These guys are (for the most part) not agents of the government and would have no reason to cover anything up, which begs the question:
Where's the ice wall? Wouldn't they have hit it before reaching the other side of the planet?