What are complex systems? They are systems which have so many parts and variables that traditional scientific models fail to describe them. They are found across the physical, biological, and social sciences. The salient features that distinguish complex systems are:
- Many small parts that interact to create large-scale behavior. These "parts" may be molecules, cells, people, animals, air particles, or grains of sand.
- A sufficient number of parts so that even if the individual interactions between them were perfectly understod (as they are in some physics situations), it would still be computationally impossible to precisely predict the large-scale behavior.
- Despite the impossibility of exact predictions, these systems still exhibit characteristic behaviors which make them amenable to mathematical analysis. These behaviors may include self-similarity (intermediate-scale behavior mimics large-scale behavior, e.g. local governments resemble national governments) and tradeoffs or fluctuations between large-scale cooperation and individual or small-scale action.
So why study these systems? First of all, we study them because they shape our world. I think it's no exaggeration to say that the future of humanity depends on our understanding of how complex systems work (for example, responding to global warming will require a deep understanding of the many systems that interact to create greenhouse gases, and how these systems can be changed.)
The second reason we study these systems is that it has not already been done. Broadly speaking, the problems of simple systems in science have already been solved. Given two particles, molecules, or cells; a physicist, chemist, or biologist could pretty much tell you how they will interact. Small-scale interactions are well-understood in all areas of the physical sciences (the social sciences are a different matter, but we can discuss this later.) On the other hand, complex systems are not only poorly understood, they have historically been ignored in many areas of science. The reason for this is that exact predictions are the stock and trade of physical science. To scientifically tackle problems where exact prediction is impossible requires a paradigm shift. Scientists must learn to ask different kinds of questions and expect different kinds of answers. This paradigm shift started sometime in the 80's (more on complex systems history in further posts) and it is still occuring today. Because the field is so young, many fundamental questions are still open. This makes it a great field for the scientifically adventurous.
The third argument for complex systems study is that it is fascinating. Inherently interdisciplinary, complex systems research brings together scholars from across the hard and soft sciences. Because the focus is on big-picture questions, an open mind can be just as valuable an asset as libraries of technical knowledge. The culture of complex systems research is such that no questions are off limits, and investigating problems outside of your field of expertise is encouraged rather than shunned. So you get to work on fascinating problems, and no one tells you not to!
That's my summary of what I do and why. Future posts will focus more on specific systems or conceptual issues. In the meantime, please comment!