Reality is a Mathematical Model

In this work a base algebra is constructed consistent with Euclidean space commonly described with the Cartesian coordinate system. Remarkably, smooth functions in this space satisfy Maxwell's equations of the electromagnetic field. A geometric variation with scalar-only field is consistent with the gravitational field. A doublet-modification yields a set of linear equations with massive field carrying constituents, consistent with the 4-vector Klein-Gordon equation and Maxwell's equations when the mass constituents vanish. Thus, this constructive algebra forms and fashions both the space known to exist, and the rules by which the existents within it are obedient. Further characteristics of the field are determined; and then the construction is extended into higher dimensions. Disgarding the old concept of separate notions of space as something to exist in, and devise increasingly complex and undisprovable laws of physics as how things happen in an increasingly complex and undisprovable notion of space - and wondering why each; a simple single unified approach combining algebra and analysis has delivered preferred geometries for space and laws of physics. Thus, not a 'Theory of Everything', or a 'theory of theories', or a 'promising theory'; but a rigorous mathematical construction consistent with manifested reality. Furthermore, a door has been opened to space and physics of higher dimensionality.