According to the Ancient Greeks there were caverns under the surface which were entrances leading to the underworld, some of which were the caverns at Tainaron in Lakonia, at Trozien in Argolis, at Ephya in Thesprotia, at Herakleia in Pontos, and in Ermioni. In Thracians and Dacians legend it is said that there are underground chambers occupied by an ancient God called Zalmoxis. In Mesopotamian religion there is a story of a man who, after traveling through the darkness of a tunnel in the mountain of “Mashu”, entered a subterranean garden.
] There is an Irish myth which says tunnels in County Down, Northern Ireland lead to the land of the subterranean Tuatha de Danaan, a group of people who are believed to have introduced Druidism to Ireland, and then went back underground.
An ancient legend of the Angami Naga tribes of India claim that their ancestors emerged in ancient times from a subterranean land inside the earth. There are legends from the Taíno people that their ancestors emerged in ancient times from two caves in a mountain underground.
No energy can reach the center of the cavern, which corresponds to no point a finite distance away from Earth in the widely accepted scientific cosmology. A drill, Gardner says, would lengthen as it traveled away from the cavern and eventually pass through the “point at infinity” corresponding to the center of the Earth in the widely accepted scientific cosmology. Supposedly no experiment can distinguish between the two cosmologies.
Gardner notes that “most mathematicians believe that an inside-out universe, with properly adjusted physical laws, is empirically irrefutable”. Gardner rejects the concave hollow Earth hypothesis on the basis of Occam’s Razor.
Purportedly verifiable hypotheses of a “concave hollow Earth” need to be distinguished from a thought experiment which defines a coordinate transformation such that the interior of the Earth becomes “exterior” and the exterior becomes “interior”. (For example, in spherical coordinates, let radius r go to R²/r where R is the Earth’s radius.) The transformation entails corresponding changes to the forms of physical laws. This is not a hypothesis but an illustration of the fact that any description of the physical world can be equivalently expressed in more than one way.