Three Key Questions about Complex Systems

Jonathan D. H. Smith

Department of Mathematics

Iowa State University

Ames, IA 50011, U.S.A.

This paper is not for reproduction without permission of the author.


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.

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