This book presents a new, comprehensive, and effective approach to the challenges of measurement, coding, and control. For the first time, the definitions of scale, unit of measurement, standard, and the mathematical interpretations of interdisciplinary theories of measurement, coding, and control are grounded in fundamental constructs of analysis—specifically, Cartan filters, the orientations (generalized sequences) of Moore and Smith, as well as methods from set theory, topology, and functional analysis. The results obtained are applicable in the development of scales and the creation of standards across a wide range of classical and non-classical fields in modern metrology and control theory, as well as in mathematical and technical physics. This work is intended for a broad audience of specialists and researchers utilizing modern information technologies in the natural, technical, biological, and social sciences, as well as for graduate students and university undergraduates.