Jack Lewis wrote:
It could be, I really don't know. Although, it is quite true that the concave notion of the Earth will be much harder for Regner to disprove than this simple experiment. We've seen that the ships hull disappearing first is not proof positive of the Earth's convexity. From Wiki: Mostafa A. Abdelkader is a mathematician from Alexandria, Egypt, who has proposed a concave Earth theory, adjusting the laws of physics that take into account gravitation, optics, and other physical phenomena. Abdelkader has authored several scholarly papers in which he worked out a detailed mapping of the concave Earth model. See M. Abdelkader, "A Geocosmos: Mapping Outer Space Into a Hollow Earth," Six Speculations in Science & Technology, 81-89 (1983). Abstracts of two of Abdelkader's papers also appeared in Notices of the American Mathematical Society (Oct. 1981 and Feb. 1982). And Wiki again: In one chapter of his book On the Wild Side (1992), Martin Gardner discusses the hollow Earth model articulated by Abdelkader. According to Gardner, this theory posits that light rays travel in circular paths, and slow as they approach the center of the spherical star-filled cavern. 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. Martin 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 theory on the basis of Occam's Razor. In a trivial sense, one can always define 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.) Such transformations would require corresponding changes to the forms of physical laws; the consensus suggests that such theories tend towards sophistry So, we have a model of which "most mathematicians believe that an inside-out universe, with properly adjusted physical laws, is empirically irrefutable", interesting! Best Wishes, Steven.
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