# A Maxwell Universe – PART II — A. THE POINT-MASS PATH Part II traces the evolution of different understandings of space, from early relational notions to the space-as-container picture most people now assume. It is not a complete historical account, but a selection of ideas that shaped how space, matter, and structure came to be described. The history can be seen as a sequence of serendipitous developments—sometimes mutually incompatible—that together produced an increasingly accurate description of experience. From ancient thinkers, through Descartes and Newton, to modern theories, each step preserved convenient assumptions while extending their domain of applicability. Yet if the experiences that led to the abstraction of Maxwell’s equations had appeared earlier, before the point-mass and point-charge intuitions had taken root, we might think of matter very differently. We would see it as a stable electromagnetic configuration with inertia, not as a distinct substance called “mass.” Charge, too, would not be an intrinsic primitive but an emergent property of structured energy flow. Objects would be extended rather than punctual. Many assume that Maxwell’s equations, being continuous and classical, cannot produce discrete (“quantum”) effects. But discreteness does not require a non-classical theory. It can arise from topology. Consider a standing electromagnetic wave on the surface of a torus in a source-free Maxwell universe. Such a configuration admits two winding numbers $(m,n)$: the poloidal and toroidal cycles of the Poynting flow. These integers count how many times energy wraps around each independent loop of the torus. A $(1,1)$ mode wraps once around each hole; a $(2,1)$ mode wraps twice around one hole and once around the other. A standing wave is obtained from opposing counter-circulating flows. In a source-free universe, $$ \nabla \cdot \mathbf{E} = 0, \qquad \nabla \cdot \mathbf{B} = 0, $$ and therefore the Gaussian flux of $\mathbf{E}$ or $\mathbf{B}$ across any closed surface is zero. Even so, nothing prevents non-zero *tangential* flow along the toroidal surface. This flow is proportional to the total energy $E(m,n)$ of the standing wave. For a shell at radius $r$ surrounding the configuration, the magnitude of the tangential flow scales as $$ \propto \frac{E(m,n)}{\text{surface area at radius } r} \propto \frac{E(m,n)}{r^2}. $$ Thus, a radial $1/r^2$ decay profile—indistinguishable from that of an electric charge—is recovered without postulating any source. The “charge” is not a fundamental entity but the measurement of diluted tangential flow from a topologically quantized electromagnetic configuration. As later chapters will show, this mechanism allows us to recover the full structure of electromagnetism *with* sources, but with the sources now understood as emergent rather than fundamental.