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

This paper presents a speculative sketch by a painter questioning the very foundations of number theory regarding addition and multiplication. It re-envisions the origin of numbers not as static symbols like "0" or "1," but as a dynamic, multilayered cosmic model governed by energy conservation laws, ultimately predicting a redefinition of the existence of emptiness and infinity themselves. (This approach potentially offers fundamental meaning to the limits of physics and the zero-points in Noncommutative Geometry.) Following Leibniz, this model establishes the "Monad" as the smallest 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, causing an infinite proliferation of multiplicative dimensions that 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.