The 'hollow earth theory', a staple of archaic science fiction, suggests that worlds beyond our comprehension, filled with strange and mystical sights, exist inside the hollow centre of the planet. Such ideas are clearly nonsense, but they led to some interesting historical anecdotes.
The idea of a hollow earth in the Jules Verne sense, with humans living on the outside surface, is unsupported by the laws of physics - literally, as a hollow structure the size of a planet would instantly collapse under the force of gravity. But in the late eighteenth century a refinement of the theory was suggested by an eccentric American, Cyrus Teed, who postulated that humans lived on the inside surface of a hollow spherical space containing the entirety of the known universe. Such a model, where light travels in curves towards the centre of the space, would be experimentally indistinguishable from the convex model (assuming all physical laws were adjusted to act opposite to the normal fashion). The idea of the 'inside-out universe' became popular as a thought experiment, and was widely written about in the twentieth century; it seemed to gain particular credence in Germany, and it is known that Hitler was familiar with the concept. Unsubstantiated stories have emerged of Nazi expeditions sent to spy on the British fleet by pointing infrared cameras at the sky...
The concave hollow earth hypothesis never received any real support. As Martin Gardner says (in the book 'On the Wild Side', 1992), it can be discounted via the principle of Occam's Razor - the simplest solution to a problem being the most likely to be true. Its original proponent, Cyrus Teed, attempted to turn the radical idea into a religion - Koreshanity - after shocking himself with electricity during an experiment, having a vision that he was humanity's messiah. His supporters became quite numerous at the turn of the last century, but their sect is now extinct. Teed himself died in 1908, from the complications of a fight between Fort Myers men and his followers. He was buried on the Southern end of Estero Island, but shortly afterwards a hurricane washed his coffin out to sea.
-TJT
Read more about the evolution of various hollow earth hypotheses: http://www.wired.com/2014/07/fantastically-wrong-hollow-earth/ Image from the collections of the Koreshan State Historic Site - a depiction of Teed's concave earth model.
