Special Issue "Complexity and Symmetry"
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (31 May 2015)
Prof. Dr. Klaus Mainzer
Symmetry and complexity determine the spirit of 21st century science. The expansion of the universe, the evolution of life and the globalization of human economies and societies lead from symmetry and simplicity to complexity and diversity. The emergence of new order and structure means symmetry breaking and transition from unstable to stable states of balance. It is explained by physical, chemical, biological, and social self-organization, according to the laws of complex dynamical systems. Atomic and molecular clusters, stars and clouds, organisms and brains, economies and societies, information, computation and communication networks (e.g., WWW) are only examples of complex dynamical systems. Thus, symmetry and complexity are the basic principles of a common systems science in the 21st century, overcoming traditional boundaries between natural, cognitive, and social sciences, mathematics, humanities and philosophy.
Symmetry also means unity. In physical science unified theories are explained by mathematical symmetries and invariance of fundamental laws. Are they only theoretical tools used in order to reduce the diversity of observations and measurements to some useful schemes of research or do they represent fundamental structures of reality? This has been a basic question of philosophy since Antiquity. Empirical results of modern science confirm that symmetries are not only mathematical imaginations of our mind. They dominated the universe long before mankind came into existence: in the beginning there was a dynamical symmetry expanding to the complex diversity of broken symmetries. Phase transitions involve the emergence of new phenomena on hierarchical levels of atoms, molecules, life, and mankind. They have not been determined from the beginning, but depend on changing conditions that happen more or less randomly. It is a challenge of systems science to explore their fascinating symmetry and complexity.
1. Mainzer, K. Thinking in Complexity. The Computational Dynamics of Matter, Mind, and Mankind, 5th Ed.; Springer Verlag: Berlin - Heidelberg - New York, 2007.
2. Mainzer, K. Symmetry and Complexity. The Spirit and Beauty of Nonlinear Science; World Scientific Series on Nonlinear Science Series A: Singapore, 2005.
3. Mainzer, K. Symmetry and complexity in dynamical systems. European Review , 2005, 13, Supplement 2, 29-48.
4. Mainzer, K. Complexity. European Review , 2009, 17(2), 219-452.
Prof. Dr. Klaus Mainzer
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Title: Partial Symmetries and Groupoids: Emergence in Systems of Systems
Authors: Eduardo Alonso*, Nicos Karcanias and Ali G. Hessami
Affiliation: Systems and Control Research Centre, School of Mathematics, Computer Science and Engineering, City University London, London EC1V 0HB, UK
Abstract: Systems of Systems, complex collections of autonomous sub-systems, are ubiquitous. Examples include cyber-physical, biological, and sociological systems such as the Internet, energy grids, traffic networks, the brain, eco-systems, supply chain management, and inter-court law relationships. Despite the increasing attention that such systems have recently attracted we are still missing a formal framework that characterises them rigorously. In this paper we propose an abstract model of Systems of Systems based on the notion of partial symmetry formalized in groupoids and n-categories. In so doing we characterise two defining characteristics of Systems of Systems, namely, emergence and their hierarchical nature.
Title: Relation of Origins of Primitive Chaos
Author: Yoshihito Ogasawara
Affiliation: School of Fundamental Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
Abstract: A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [J. Phys. Soc. Jpn. 2014, 83, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.