UMA Monad Theory: A Sketch of the Zeros in Noncommutative Geometry

This paper is a speculative sketch by a painter, attempting to redefine the ''zero point'' in addition and multiplication. By reconceptualizing the origin of numbers not as static symbols like ''0'' or ''1,'' but as a multi-layered universe model where the law of conservation of energy functions dynamically, this approach has the potential to provide fundamental meaning to the existence of the zero point in Connes' noncommutative geometry. Following Leibniz, this model posits the ''Monad'' as the minimum unit of existence, focusing on the problem of the singularity that occurs when the additive world (parallel expansion) and the multiplicative world (dimensional generation) collide at ''0,'' where the infinite proliferation of multiplicative dimensions threatens the equilibrium of the universe. By reinterpreting ''0'' not merely as an absence but as a dimensional ''exit,'' this paper argues for the necessity of an absolute zero point---the ''Universal Mapping Absolute (UMA) Monad''---which integrates addition and multiplication without contradiction. The purpose of this paper is to present these intuitive ideas as a preliminary stage prior to rigorous mathematical proof.