UMA Monad Theory: A Number-Theoretic Philosophy on Emptiness and Infinity

This paper is a speculative sketch by a painter questioning the foundations of number theory as it pertains to addition and multiplication. It re-envisions the origin of numbers not as static symbols like "0" or "1," but as a dynamic, multi-layered cosmic model governed by the laws of energy conservation, ultimately predicting a redefinition of the existence of emptiness and infinity itself. Following Leibniz, this model establishes the "Monad" as the fundamental unit of existence. It focuses on the problem of the singularity that arises at "0" when the additive world (parallel expansion) and the multiplicative world (dimensional generation) collide. In this collision, the infinite proliferation of multiplicative dimensions threatens cosmic equilibrium. By reinterpreting "0" not as a mere void but as a dimensional "exit," this paper argues for the necessity of the "Universal Mapping Absolute (UMA) Monad"—an absolute zero-point that integrates addition and multiplication without contradiction. (This potentiality may provide a fundamental meaning to the zero-points within Connes' Noncommutative Geometry.)