Derivation of Quaternary-Based Mathematical Operators to Manage Innovation in Complex Adaptive Systems

Organizations ranging from the Internet, to economies, to large global corporations, to rapidly changing technological ecosystems can be thought of as Complex Adaptive Systems (CAS). When viewed from the bottom-up, as is commonly the case, CAS is often characterized by distributed control, connectivity, co-evolution, emergence, and unpredictability. When viewed from the top-down, a view unique to the mathematical framework further developed in this paper, characteristics such as an implicit order, qualified determinism, and directional integrity emerge. There are advantages and a different management system required when CAS is viewed from the top-down. This paper will derive a series of mathematical operators representative of the quaternary basis of any CAS that can be used in the management of innovation of such CAS and suggest an application employing a series of operators to innovate in a representative rapidly evolving technological environment.