This book presents a novel and unorthodox approach to the wave theory, attempting to explain complex physical phenomena and derive fundamental laws of physics using natural numbers. The book is an elaboration and expansion of work presented in "What is a Photon? (Wunderman, 2000) and "Planck's Constant and Pi" (Wunderman, 2004) which introduced a new interpretation for the space between integers of the natural number counting system. Mechanisms of wave propagation provide the essence of this theory. In addition, foundations emerge from the natural numbers themselves. The thesis makes a distinction between indeterminism and lack of causality in de facto physical processes. This work utilizes an uncommon method to describe how a wave-front surface area grows. The theory can infer a slightly altered interpretation of how space progresses as a square law when advancing away from an origin. Section I and Section II present an overview of the analysis method. The analysis in this treatise derives circumstances for viably transmitted cyclic modes and the consequence of their existence. Section I addresses the motion of objects like spontaneous emission photons that propagate at the highest rate, light-speed C. Section II covers the relative motion of slower rest mass objects. This treatise does not analyze relative motion in the presence of fields like gravity that could act on the moving object. This thesis purports that our interpretation of relative motion, what we call inertial velocity, is best expressed quite differently than has traditionally been done. This thesis hopes to show that the speed of light should numerically be absolute unity, based exclusively on the mechanism by which area accrues on the information-transferring-wave-front generated by events on a moving object. This thesis hopes to demonstrate that a more general type wave description better satisfies portrayal of a photon's "frequency". The harmonic exponential function "e" is therefore purported to be an inappropriate mathematical function for physically representing propagating waves, photon frequencies, electromagnetic-radiation, and affiliated cyclic phenomena. An appropriate function must involve a reaction that temporally follows an initiating cause and presents a response that includes effects of Planck's constant and indeterminism associated therewith. This theory presents such a function and the waves generated are called unified waves.