Mathematical modeling and analysis of system behavior are at the core of the development of high-tech system. Modern engineering sciences, to include naval engineering, call for more sophisticated mathematical and statistical methods in order to efficiently understand and resolve the increasing complexity of the tasks at hand. There is a need of a deeper understanding of the mathematical tools most needed to proper support naval research. Indeed, invariably, in the press to “get on with it,” highly complex issues are addressed by engineers using existing tools and knowledge to produce approximate methods and results that have not been rigorously substantiated and are thus subject to unintended consequences, most importantly, breakage/failure in unpredictable circumstances. Nowhere is this situation more chaotic than in the field of information extraction, signal and image processing, acoustics, and nonlinear vibration analysis where a “witches’ brew” of inadequately posed concepts, questionable/unrecognized assumptions, approximations of convenience, and heuristically defined metrics combined to yield what could be reasonably described as bordering on “technological sorcery.”