"I think the next [21st] century will be the century of complexity"
This course is an introduction to the core concepts of complex systems theory, an exciting new area that is offering us a fresh perspective on issues such as understanding our financial system, the environment and large social organizations. The aim of this course is to bring the often abstract and sophisticated concepts of this subject down to earth and understandable in an intuitive form. After having started with an overview to complex systems this course will focus upon five of the core concepts.
Systems: We will start with two sections on systems theory and systems thinking, this should introduce students to the bigger picture of why complex systems is seen as a new paradigm in science; what exactly this new paradigm is; why we need it and lastly how it differs from our traditional methods of scientific inquiry.
Nonlinear systems: The term nonlinear science and complex systems are often used interchangeably showing how essential the concept of nonlinearity is to this subject. In this section we draw the distinction between linear and nonlinear systems and see why it matters. The second part of this section covers the subject of chaos theory and the dynamics of nonlinear systems.
Network theory: network theory and networks in general have arisen in almost all fields of inquiry in the past few decades making it one of the most active and exciting areas of scientific study. We will explore many different types of networks, their properties and examples in the real world from social networks to logistics networks. This section will conclude by looking at graph theory, the mathematical foundations that lie behind networks.
Complex adaptive systems(CAS): CAS is increasingly being used to model a wide variety of systems from, electrical power grids to economies and cultures it represents a powerful new way of seeing the world. This section will also cover CAS’s close relative cybernetics and the basic concept of adaptation and evolution.
Self-organization: Self-organization is another of the foundational concepts within complex systems that is proving particularly relevant to the world of the 21st century as we see collaborative self-organizing groups such as Wikipedia and the Linux foundation emerge. But self-organization is more than just a social phenomenon, we explore how it is in fact ubiquitous in our world from the formation of fish schools to magnetization and traffic jams.
In conclusion a short film on complex systems Is presented to give you an idea of where the subject is today and what are the main challenges going forward.
Each subject is broken down into three lessons the first being an introduction to the topic delivered through video. This will be followed by a slide presentation that digs deeper into the main themes introduced in the first lesson, followed up with a quick(optional) quiz to get you thinking.
Complex systems are pervasive in our world from traffic jams to ant colonies they consist of multiple diverse, interconnected elements that are often capable of adaption giving rise to complex behavior as they evolve over time. Complex systems theory is an exciting new area of mathematics and science that studies these non-linear systems within a variety of domains by employing a suit of different theoretical tools from systems theory to network analysis and cybernetics. Complex systems present some of the toughest challenges in contemporary science. This video will give an introduction to what complexity is and what defines complex systems.
This lesson will dig deeper into the core concept that were introduced in the first lesson on complex systems
Systems thinking is what is called a paradigm, a paradigm is a whole way of seeing the world and the systems paradigm is one that places a greater emphasis upon seeing the relationships between parts and the system as a whole. Systems thinking is used in many areas from science to design and business and often gives us a fresh perspective with which to "think outside the box".
This lesson will dig deeper into the core concept that were introduced in the first lesson on systems thinking
Systems are sets of entities, physical or abstract, comprising a whole where each component interacts with or is related to at least one other component and they all serve a common objective. The scientific research field which is engaged in the interdisciplinary study of universal system-based properties of the world is general systems theory. This field investigates the abstract concepts and principles which are independent of the specific domain, substance, and type of system.
This lesson will dig deeper into the core concept that were introduced in the first lesson on systems theory
Many would say nonlinearity is the defining feature of complex systems. In math and science, a nonlinear system (in contrast to a linear system) is a system whose output is not directly proportional to its input due to the interconnections and interdependencies within the systems. This has been most famously capture in the term butterfly effect, where small changes in one part of a system can have disproportionately large results.
This lesson will give you a brief overview to the area of chaos theory. Chaos theory is an area of math and science that has emerged over the past few decades to study the dynamics of nonlinear systems, in particular it focuses upon deterministic systems that are sensitive to initial condition (such as the weather) which has given us the term butterfly effect.
Networks are emerging as the structure to our systems of organization in the information age, though amazingly very little was know about them until quite recently. Within just the past few decades network theory has embarked upon a scientific quest for a deeper understanding of the nature of networks. Network theory asks basic questions about the degree of connectivity within a network, the structure of networks and the properties that these various structures give rise to.
This lesson will dig deeper into some of the concepts that were introduced in the first lesson on network theory
The theory of self-organization has emerged from many different fields, with economist, sociologist and ecologist interested in the phenomena to name just a few. Counteracting our traditional assumptions about the need for centralized design and management, self organization is presenting a new way of approaching time old questions about the emergence of order and disorder and exploring new ways to design systems that are more resilient and flexible.
The definition to complexity science is still very much open to debate, for some it means the study of nonlinear systems, to others it is simply a form of interdisciplinary science. In this video we present the history of complexity science as it has emerged out of modern science and present a definition of it as the application of complexity theory to the study of the complex systems in our world such as financial networks, cities, ecosystems amongst many others