If you want to understand how the real world works and the nature and limitaions of the models we build that support that understanding it is essential to know about the concept of non-linearity.
Nonlinearity and complexity.
My view is that complexity arises from non-linearity, feedback and emergence. It is useful to look at the sceinec of complexity to identify if the people who work in this area agree or not with my view and, if they disagree, why?
Unfortunatly there is a lot of fog around complexity science, partly because, when talking to people who claim to be working in the field, you are likely to come away with many different perspectives and definitions.
The first question to be asked is: Do these people who claim to be working on complex systems actually understand complexity or just their little area, which may in fact not be related to complexity? The authors of this paper What is a Complex System? try to understand complexity by talking to researchers in complexity. They don't seem to come to a real conslusion.
My view is that there needs to be a definition of scope. What is the full range of systems that exhibit complexity? Secondly, there needs to be an analysis of these systems in oreder to understand the underlying principles and mechanisms that both characterise complex systems and explain why they are complex.
I don't think that the scope has been defined properly. For example, I often use the Three Body Problem as a system that exhibits complex behaviour. When I then look at definitions of complexity I ask teh question: Is the Three Body Problem included or not. If not, them I question the veracity of the definition.
State of the Art of Non-Linearity
A submission for UKSim - The Elephant in the Model
Links and Resources
Bernard Robertson-Dunn 2014