Abstract
An archetypal model for the constants of nature is found from the ancient geometry of the the Cosmological Circle and is related to Plato's cosmology, with its dynamics and harmonics of time cycles. The inverse fine-structure constant and the proton-electron mass ratio are calculated, connecting fundamental mathematical constants of geometry with the latest theoretical and experimental values of these physical constants. Continuing in the tradition of George Gamow's suggestion, Since the works of Sir Arthur Eddington, it has become customary to discuss from time to time the numerical relations between various fundamental constants of nature. Although until today such discussions have not led to any practical results - that is, to any valuable road signs toward further development of the theory of the still unclear fundamental facts in physics - it may be of some interest to survey the present status of this 'clairvoyant' branch of science.
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