The concave earth theory — also called the Cellular Cosmogony — proposes that we do not live on the outer surface of a solid or hollow sphere but on the inner surface of a hollow sphere. In this model, the earth is a shell and humanity inhabits the concave interior: looking up, we see the sun, moon and stars not at astronomical distances but in the central void of the sphere; the sky is not an infinite expanse but the air of a closed interior space. The ground curves up and away from us in all directions — if we could see far enough, we would see the ground above our heads. This is among the mathematically most interesting alternative cosmologies because, under certain optical transformations, the observable predictions of the concave earth model and the standard globe model are mathematically equivalent — making it, in principle, impossible to distinguish one from the other by observation alone.
Cyrus Reed Teed (1839–1908) — who took the name Koresh — was the most systematic proponent of the concave earth model in the modern era. An American physician and alchemist, Teed claimed to have received a direct divine revelation in 1869 during which the nature of the universe was disclosed to him: the universe is a hollow sphere 8,000 miles in diameter; the earth's surface is the inner shell; the sun, moon and planets are smaller spheres rotating in the central space; the stars are luminous cells of energy in the central region.
Teed founded the Koreshan Unity, a communal religious organisation that at its peak in the 1890s had several thousand members. The community established a settlement in Estero, Florida in 1894 — where the community attempted to verify the concave earth experimentally. Their most significant experiment was the Rectilineator Experiment (1897): a geodetic survey using a series of perfectly straight, carefully levelled metal sections extending 4.25 miles along the Gulf Coast beach. Standard globe earth geometry predicts the ocean surface would curve downward away from a straight horizontal line; the Koreshan measurements appeared to show the surface curving upward — consistent with the concave earth model. The experiment has been discussed in geodesy literature and its methodology disputed.
The mathematical equivalence problem: in 1901, the mathematician and physicist Heinrich Schlichting demonstrated that through a specific geometric transformation (an inversion), any observation made in a convex world (standard globe earth) can be exactly replicated by an equivalent observation in a concave world. The two models are mathematically equivalent — the same equations describe both, with only the perspective inverted. This is not a rhetorical point but a genuine mathematical result: there is no observation that can, in principle, distinguish between the two models. This is one reason serious physicists find the concave earth model philosophically interesting even when they do not endorse it — it raises genuine questions about the relationship between mathematical models and physical reality, and about what it means for a theory to be "true" when it is observationally indistinguishable from an alternative.
If we lived on the inner surface of a concave sphere, what would we observe? Several things would be different from what we observe in the globe model — and these differences are where the concave earth model can be tested:
In the concave model, the horizon would not be explained by the earth's curvature (which in the concave model curves upward, not downward) but by atmospheric optics — the progressive scattering and absorption of light over distance that eventually obscures objects regardless of their position. Ships would not disappear hull-first over the horizon but would fade progressively into atmospheric haze. The maximum visible distance would be determined by atmospheric transparency rather than curvature. Stars would not be at incomprehensible distances but would be relatively local features of the central void. The behaviour of the midnight sun at the poles, the path of the sun across the sky and the appearance of lunar eclipses would all need to be explained by the geometry of the concave model rather than by standard astronomy.
Koreshan proponents argued that all observable celestial and geographical phenomena are consistent with the concave model when correctly interpreted. Mainstream astronomy disagrees, citing stellar parallax, the independently verified distances of astronomical objects and the behaviour of spacecraft and satellites as observations that the concave model cannot accommodate without becoming unfalsifiable.