Some Conceptual and Measurement Aspects of Complexity, Chaos, and Randomness from Mathematical Point of View

Abstract

One of the main purposes of the mankind is to understand and explain the dynamics of real-world phenomena, i.e., modeling them, and also to build predictive models for their behaviors. The most powerful tool in modeling a deterministic dynamic is mathematics, and the most powerful tool in modeling a stochastic dynamic is statistics. Some characteristics of deterministic chaotic systems are well known, as well as of stochastic systems. Distinguishing deterministic dynamical systems from stochastic ones, based on observed data, is a difficult and yet unsolved statistical problem. Natural phenomena and human behaviors dynamics are very complex. If the existing complexity and chaos in natural dynamical systems, also inherited in their mathematical models, is not well understood, then management and control processes in such systems may result in catastrophes. This study aims to reveal and emphasize the role of mathematics in formulating the conceptual and measurement stages of complexity, chaos, and randomness.