ABSTRACT
Complexity is a multifarious concept; different researchers focus on different aspects. The situation for emergence is very similar to that for complexity in that there is no agreed-upon universal definition of emergence. The Hamiltonian framework provides a useful formal way for understanding the basis for many of the nonseparable phenomena of complexity. The concept of hierarchy is of central importance in complex systems. For noncomplex systems, there is a distinguishable ordering of scales of structure due to the hierarchy of physical forces and dynamical time scales. The various cases of nonseparability in the form of strong nonlinearity, constraints and feedback loops acting across spatial scales and the “holism” exhibited by such complex systems have proved fruitful for understanding more about how emergence works in complex phenomena. The interplay between parts and wholes in complex systems and their environments mediated by positive and negative feedback loops typically leads to the self-organization observed in such systems.
