Special Issue "Complexity and Symmetry"


A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 May 2015

Special Issue Editor

Guest Editor
Prof. Dr. Klaus Mainzer
Lehrstuhl für Philosophie und Wissenschaftstheorie, Direktor der Carl von Linde-Akademie, Technische Universität München, Arcisstrasse 21, D-80333 München, Germany
Website: http://www.mcts.tum.de/en/cvl-a/philwiss/mitarbeiter/klaus-mainzer/
E-Mail: mainzer@cvl-a.tum.de
Phone: +49 (0)89 2 89 2 53 60
Fax: +49 (0)89 2 89 2 53 62
Interests: philosophy of science; symmetry and complexity

Special Issue Information

Dear Colleagues,

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
Guest Editor

Published Papers (4 papers)

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Displaying article 1-4
p. 1763-1775
by  and
Symmetry 2010, 2(4), 1763-1775; doi:10.3390/sym2041763
Received: 19 September 2010; Accepted: 17 October 2010 / Published: 21 October 2010
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(This article belongs to the Special Issue Complexity and Symmetry)
p. 1250-1269
Symmetry 2010, 2(3), 1250-1269; doi:10.3390/sym2031250
Received: 9 March 2010; in revised form: 25 May 2010 / Accepted: 23 June 2010 / Published: 25 June 2010
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(This article belongs to the Special Issue Complexity and Symmetry)
p. 1135-1155
by , , ,  and
Symmetry 2010, 2(2), 1135-1155; doi:10.3390/sym2021135
Received: 12 May 2010; in revised form: 9 June 2010 / Accepted: 10 June 2010 / Published: 14 June 2010
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(This article belongs to the Special Issue Complexity and Symmetry)
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p. 150-183
Symmetry 2010, 2(1), 150-183; doi:10.3390/sym2010150
Received: 30 December 2009; in revised form: 7 February 2010 / Accepted: 19 February 2010 / Published: 23 February 2010
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Planned Papers

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
Eduardo Alonso*, Nicos Karcanias and Ali G. Hessami
Systems and Control Research Centre, School of Mathematics, Computer Science and Engineering, City University London, London EC1V 0HB, UK
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.

Last update: 9 October 2014

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