What is complexity science?

Map of the internet (photo courtesy the Opte Project)

The definition of complexity science is still very much open to debate: to some, complexity science is merely the study of branches of different sciences, each with its own examples of complex systems (which are complex in ways that sometimes have nothing in common), while others argue that there is a single natural phenomenon called ‘complexity’, which is found in a variety of systems, and which can be the subject of a single scientific theory or approach.

At the Bristol Centre for Complexity Sciences we expose students to a hub of theoretical tools based in mathematics, computer science and physics which are needed to study complex systems as well as providing training in the branches of science where the most pressing open questions are amenable to these techniques such as biology, chemistry, engineering, and social sciences.

The difficulty of a complex system is that often its parts are interacting on many time and length scales. The best example of such a system is a living organism where the molecular processes inside the cell cannot be clearly separated from processes at more macroscopic levels such as the brain. Other examples of complex systems include ant colonies, insect swarms, the climate, and the economy.

Although the term "complex system" has multiple usages, some generally agreed upon properties of a complex system are:

• Multiplicity of many parts, out of whose interaction "emerges" behaviour not present in the parts alone
• Coupling to an environment with which information, energy, or other types of resources are exchanged
• Presence of both order and randomness in (spatial) structure or (temporal) behaviour
• Absence of a central control element, either internal or external
• Robustness of structure and/or behaviour against significant perturbation
• Presence of memory and feedback; enabling adaptability according to its history or feedback

The study of these systems requires a combination of methods from more than one discipline. Our PhD researchers and affiliated staff work on the development of new mathematical and computational tools for complex systems and the application of these tools and concepts to important questions in the natural and social sciences.

A conversation on complexity theory

Ants, bees and brains, with Professor Nigel Franks

This lecture was given as part of the 'Big Ideas in Science' series.

Further reading

Many books and papers have been published which discuss the definition of Complexity Sciences, and below are some recommendations for general reading if you would like to find out more:

• At Home in the Universe: The Search for the Laws of Self-Organization and Complexity by Stuart Kauffman.
• Complexity: The Emerging Science at the Edge of Order and Chaos by Mitchell Waldrop.
• Complexity; A guided Tour by Melanie Mitchell.
• What is a complex system? by James Ladyman, James Lambert and Karoline Wiesner (PDF, 283kB)

Other useful resources

• The Principia Cybernetica is a self-proclaimed organic cybernetic forum for understanding system science and complexity. It provides a very complete overview of the theoretical aspects of complexity science as well as definitions of many of the buzz words often used by complexity scientists.
• The Complex Systems Society promotes the development of all aspects of complex systems science in the countries of Europe, as well as the whole international scientific community.
• The Santa Fe Institute is a private, not-for-profit, independent research and education center, founded in 1984, where leading scientists grapple with some of the most compelling and complex problems of our time.
• The Complexity Digest is an international and interactive forum of complexity constituting a useful amalgamation of current research papers on modern complexity issues.