Complexity Theory Overview

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In this video, we will be giving an overview to the area of complexity theory by looking at the major theoretical frameworks that are considered to form part of it and contribute to the study of complex systems. For full courses see:

Transcription excerpt:
Complexity theory is a set of theoretical frameworks used for modeling and analyzing complex systems within a variety of domains. Complexity has proven to be a fundamental feature to our world that is not amenable to our traditional methods of modern science, and thus as researchers have encountered it within many different areas from computer science to ecology to engineering they have had to develop new sets of models and methods for approaching it. Out of these different frameworks has emerged a core set of commonalities that over the past few decades has come to be recognized as a generic framework for studying complex systems in the abstract. Complexity theory encompasses a very broad and very diverse set of models and methods, as yet there is no proper formulation to structure and give definition to this framework, thus we will present it as a composite of four main areas that encompasses the different major perspective on complex systems and how to best interpret them.

Firstly systems theory; Systems theory is in many ways the mother of complexity theory, before there was complexity theory, systems theory was dealing with the ideas of complexity, self-organization, adaptation and so on, almost all interpretations to complexity depend upon the concept of a system. In the same way that modern science can be formalized within the formal language of mathematics, all of complex systems science can be formalized within the language of systems theory but, systems theory is a very abstract and powerful formal language and it is typically too abstract for most people and thus is understood and used relatively little. Cybernetics is another closely related area of systems theory, it was also part in forming the foundation to complexity theory, cybernetics during the mid to late 20th century studied control systems and provided a lot of the theoretical background to modern computing, and thus we can see how the interplay between computing and complexity science goes all the way back to its origins as the two have developed hand-in-hand. A lot of systems theory is associated with and has come out of the whole area of computation. The areas of computer science and its counter part information theory have continued to be one of the few major contributors to complexity theory in many different ways, though systems theory is about much more than just computers it is a fully fledged formal language.

Next nonlinear systems and chaos theory; Nonlinearity is an inherent feature and major theme that crosses all areas of complex systems. A lot of nonlinear systems theory has its origins in quite dense and obscure mathematics and physics. Out of the study of certain types of equations, weather patterns, fluid dynamics and particular chemical reactions has emerged some very counter intuitive phenomena in the form of the butterfly effect and chaos. Chaos theory, which is the study of nonlinear dynamical systems, was one of the first major challenges to the Newtonian paradigm that was except into the mainstream body of scientific knowledge. Our modern scientific framework is based upon linear systems theory and this places significant constrains upon it, linear systems theory is dependent upon the concept of a system having an equilibrium, although linear systems theory often works as an approximation, the fact is that many of the phenomena we are interested in describing are nonlinear and process of change such as regime shifts within ecosystems and society, happen far-from-equilibrium they are governed by the dynamics of feedback loops and not linear equations. Trying to model complex systems by using traditional linear systems theory is like trying to put a screw into a piece of wood with a hammer, we are simply using the wrong tool because it is the only one we have. Thus the areas of nonlinear systems and their dynamics is another major part to the framework of complexity theory that has come largely from physics, mathematics and the study of far-from-equilibrium processes in chemistry.