Epicycles redux! The FES will be making you an honorary member directly ... Conformal geometric algebra introduces Euclidean space as the restriction of hyperbolic space to a horosphere. While the resulting algebra rather falls between two stools --- neither sufficiently simple for maximal efficiency, nor sufficiently flexible to incorporate contact geometry --- the strategy has always impressed me as engagingly improbable. WFL On Sun, Sep 15, 2019 at 5:33 PM Keith F. Lynch <kfl@keithlynch.net> wrote:
You just need to replace Einstein's physics with Mercator's.
Space repeats in the east-west direction with a period of Eratosthenes' constant, epsilon (about 40,000 kilometers).
The vacuum speed of light isn't constant, but varies with both altitude and with so-called latitude. Where c is the local speed of light, c0 is the speed of light at sea level at the equator, l is the latitude, a is the altitude, and epsilon-bar is Eratosthenes' reduced constant, (about 6366 kilometers, epsilon divided by 2 pi), I think the correct equation is c = c0 / cos(lat) exp(a/epsilon-bar).
The size of atoms, hence of objects made of atoms, are in proportion to c. So objects change in size with latitude and altitude. They change in density by the cube of this factor, so their mass remains constant. Because of the size increase, they can reach points at infinity (the so-called north pole, south pole, and center of the Earth) in finite time.
The varying c results in light curving upwards. That's what results in the illusion of a horizon, and in Earth appearing round when it's viewed from a high altitude.
Someone please double-check my math. For extra credit, figure out how to make Earth a sphere again, but wrongside out, with the stars and galaxies on the inside, and solid rock extending to infinity in all directions.
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