Surfaces and Superposition: Field Notes on Some Geometrical Excavations

Buildings appear to rest on the Earth's surface, yet the surface has actually been permeated by the building's foundations. If blueprints of the foundation are unavailable, excavation would be needed to discover what actually supports a specific building. Geometry and topology have easily observable concepts resting on the surface of theoretical underpinnings that have not been completely discovered, unearthed or understood. Geometrical and topological principles of superposition provide insight into probing the connections between accessible superstructures and their hideen underpinnings. This book develops and applies these insights, from physics to mathematics to philosophy. This text examines the dimensionality of surfaces, how superpositions can make stable frameworks and gives a quasi-Leibnizian account of the relative "spaces" that are defined by these frameworks.