What is a complex system?
What do we mean when we say a particular system is "complex"? We main have some intuition that it means there are many degrees of freedom and/or that it is hard to understand. "Complexity" is sometimes used as a buzzword, just like "emergence." There are many research institutes that claim to be studying "complex systems" and there is something called "complexity theory". Complexity seems to mean different things to different people. I am particularly interested in understanding the relationship between emergence and complexity. To do this we first need to be more precise about what we mean by both terms. A concrete question is the following. Consider a system that exhibits emergent properties. Often that will be associated with a hierarchy of scales. For example: atoms, molecules, proteins, DNA, genes, cells, organs, people. The corresponding hierarchy of research fields is physics, chemistry, biochemistry, genetics, cell biology, phys