10 July 2012, 5.30 pm
Tuesday 10th July 2012 17.30 Pugsley Lecture Theatre, Queens Building
The idea of complexity is sometimes said to be part of a new unifying framework for science, and a revolution in our understanding of systems the behaviour of which has proved difficult to predict and control thus far, such as the human brain and the world economy. However, it is important to ask whether there is such a thing as complexity science, rather than merely branches of different sciences, each of which have to deal with their own examples of complex systems. In other words: is there a single natural phenomenon called complexity, which is found in a variety of physical (including living) systems, and which can be the subject of a single scientific theory, or are the different examples of complex systems complex in ways that sometimes have nothing in common? Hence, the fundamental foundational question in the domain of the complexity sciences is: What is complexity? Assuming that there is an answer to the latter question and that `complexity' is not just an empty term, we should then ask more particularly whether there is one kind of complexity for all the sciences or whether complexity is domain-specific. In order to bring mathematical rigour to the issue we then review some standard measures of complexity from the scientific literature, and offer a taxonomy for them, before arguing that the one that best captures the qualitative notion of complexity is that of the statistical complexity. Finally, we offer our own list of necessary conditions as a characterization of complexity. These conditions are qualitative and may not be jointly sufficient for complexity. We close with some suggestions for future work.