On finding infinity and the limits of Kurt Gödel

(in process)

  1. We first introduce Gödel to circles-spheres, and base-2 notation of the Planck’s units. Gödel didn’t know there could be a mathematical progression from the Planck units in such a manner that unites space-and-time, matter-and-energy, and gravitation-and-electromagnetism. He did not know there are 202 base-notations from the Planck units to the current time. He did not ask what those units would be within the earliest notations.
  2. Gödel did not discern facets of our reality shared by the finite and the infinite.
    He did not see how the continuity, symmetry and harmony within the sphere could be axiomatic and a bridge across the finite-infinite divide.

Although special relativity pushes the absolutes out of the picture, Gödel gives Newton’s absolute time a place within General Relativity. Given Einstein’s special relations with Max Planck, it is of some interest to note that neither Einstein nor Gödel truly engaged the Planck base units. You would think it might have come up during Gödel’s time as a teacher-professor (1940-1978) at the Institute for Advanced Studies which included those long walks with Einstein.

Even with his work on numbering and base-2, Gödel did not clearly demarcate a beginning of the universe but like Einstein, waffled between steady state (Hoyle) and a big bang (Lemaître) theories.

David Hilbert.

Resources:

Publications 1929-1936, Volume 2, By Kurt Gödel, Solomon Feferman, Oxford University Press, 1990

Misner, C.W., Thorne, K.S., and Wheeler, J.A. (1973). ‘Gravitation’ (Freeman, San Francisco).

Gödel, K. (1949). ‘An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation’, Rev. Mod. Phys., Vol. 21, p. 447.

Reinhardt, M. (1973). ‘Mach’s Principle – A Critical Review’, Z. Naturforsch. Vol 28a, p. 529.

Hawking, S.W. (1969). ‘On the Rotation of the Universe’, Mon. Not. R. astr. Soc. Vol. 142, p. 529.

Collins, C.B., and Hawking, S.W. (1973). ‘The Rotation and Distortion of the Universe’, Mon. Not. R. astr.Soc. Vol 162, p. 307.

Also see: