The mathematical basis of standards

Abstract

Standards are fundamental to any rigorous form of communications and are used in every civilization. Given that mathematics provides a rigorous way to understand very basic phenomena, this paper explores the mathematical basis of standards. Five successions of standards are identified from pre-history to the present and mathematical models of each are presented. These mathematical models more rigorously define the standards successions proposed. The impact of these standard successions on existing standardization issues is examined. he ubiquity of technical standards in all human societies argues for a rigorous understanding - why are standards necessary? At SIIT 2001, Krechmer (2001) proposed to answer this question using set theory and information theory. The current paper builds on that paper. It develops a philosophical basis for technical standards, models the mathematical relationship between standards and entropy, and identifies five successions of standards. The term "standard" often refers to published documents or the output of specific standardization committees. This is an application view of standards. This paper focuses on a conceptual view of standards. A standard is defined as: A codification for a society of the constraints used for one or more comparisons between implementations. This definition is taken from Krechmer, 2005 which discusses prior definitions of standards and the rational behind this definition. Standardization is the term used to refer to the application of creating, implementing or using a standard. This paper concludes by using the new conceptual models of standards to better comprehend the impact of standardization on society and technology.