Three Key Questions about Complex Systems

The paper considers three questions that arise in the study of complex systems: • What constitutes a hierarchical level? • How do phase transitions arise? • What is the relationship between invariance and information? Answering these questions appears to be a prerequisite for essential progress in the field. In the course of studying complex systems, certain concepts feature prominently. Among these are the notions of hierarchical level, phase transition, and information. Unfortunately, considerable uncertainty still surrounds these concepts. In an attempt to reduce this uncertainty, the current paper intends to consider three key questions involving each of the concepts in turn. The questions are designed to provoke a discussion that may lead to some clarification of the concepts. 6 WHAT CONSTITUTES A HIERARCHICAL LEVEL? In discussions of complex systems, the concept of a hierarchical level is a theme that recurs constantly. Indeed, the presence of a hierarchy of levels is often used to characterize a system as being complex. Nevertheless, there are many different notions of hierarchical level, some more and some less well defined. What are the connections between them? Which roles can be played by each? These questions have been asked many times throughout the history of systems science. An early survey of possible answers was given by (Wilson 1969). Salthe initiated a classification of hierarchies with his distinction between specification and scalar hierarchies. For Salthe, this is the distinction between “levels of generality” (Salthe 1985: 166) and “matters of scale” (Salthe 1985: 47). However, it turns out that each of these classes is actually more ramified than is apparent from Salthe’s discussion. While retaining