Special Issue "Complexity and Symmetry"
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (30 April 2010)
Prof. Dr. Klaus Mainzer
Lehrstuhl für Philosophie und Wissenschaftstheorie, Direktor der Carl von Linde-Akademie, Technische Universität München, Arcisstrasse 21, D-80333 München, Germany
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
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
Symmetry 2010, 2(4), 1763-1775; doi:10.3390/sym2041763
Received: 19 September 2010; Accepted: 17 October 2010 / Published: 21 October 2010| PDF Full-text (266 KB)
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| PDF Full-text (145 KB) | Supplementary Files
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| Cited by 1 | PDF Full-text (656 KB)
Article: Engineering Life into Technology: the Application of Complexity Theory to a Potential Phase Transition in Intelligence
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| PDF Full-text (741 KB)
Last update: 5 March 2014