Thursday, April 10, 2014

What is a complex system?

This week I started teaching the course 'Modelling Complex Systems'. I decided this year to make video lectures for the course. In the first one, I define complex systems. This is not an easy thing to do. There is no real recognized definition, and the wikipedia page is pretty confusing. Complex systems are systems that are, er, well, complicated (although even this obvious statement is often argued against)

My answer is simple, I just show a lot of systems which make complex looking patterns and say "complex" a lot. A similar (but more eloquent) answer is also given by Melanie Mitchell in her excellent complexity explorer course.

I do have one little twist, and that is that a complex system is one in which you can use mathematical modeling to better understand it. This leads me nicely to my second lecture: what is mathematical modeling? This question I have thought about a lot, and I think here I give a reasonably useful and general explanation of why we use mathematical models. Models are used for one of four reasons:

1, Explain data as simply as possible.
2, Link together levels of explanation.
3, To provide detailed descriptions.
4, To predict future outcomes.

Complex systems are most associated with number 2. Have a look at the video and see what you think.

I will hopefully be putting all my lectures up on a webpage in the future. One request I have now is that if anyone can suggest good articles on which the students can base mini-projects please tell me. The students on this course tend to be exceptionally good at modeling and mathematics, and highly motivated. So any 'complex systems' models that can be implemented and tested in 4 weeks would be much appreciated.


  1. This is an interesting question indeed and one that I hope to answer myself in a project I'm doing with a philosopher of science. I think one danger is to call "complex" those systems we currently don't understand, and use the word as a proxy for "interesting".

    To me the most interesting aspect is the unifying potential of complex systems theory, which for all we currently know might be superficial.

    A previous blog post of mine on the topic:

    Cheers, Philip

  2. Hi Philip, I read that earlier. How is it going? I would be interested to see what you come up with. What you write about in your article is more to do with 'measuring complexity'. I think. I will come to that in one of the lectures. Although I don't have an answer.