Special Issue "Complexity and Symmetry"

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.cvl-a.tum.de/mainzer1.html
E-Mail:
Interests: philosophy of science; symmetry and complexity

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.

Literature:
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

Please visit the Instructions for Authors page before submitting a manuscript. For the first couple of issues, to be published in 2010, the Article Processing Charges (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections.

Title: Complexity and Instability: Prospects of Late-Modern Physics. On a Structure Scientific Revolution
Author: Jan Cornelius Schmidt
Affiliation: Darmstadt University of Applied Sciences, Haardtring 100, D -64295 Darmstadt, Germany; E-Mail: jan.schmidt@h-da.de
Abstract: to be added

Type of Paper: Article
Title: An Application of Symmetry Approach to Finance — Gauge Symmetry in Finance
Author: Shipeng Zhou
Affiliation: Business School, University of Shanghai for Science and Technology, 516 Jungong Rd., Shanghai, China; E-mail: Shipengzhou@yahoo.com.cn
Abstract: The paper will present an application of symmetry approach to finance which is based on our research. This symmetry approach comes from the gauge field theory in physics. We revise the model of financial derivative pricing in a market of multiple assets in a gauge symmetry view, and find a kind of gauge symmetry in the equation of financial derivative pricing under local transformations such as a numeraire changing or a generalized discounting in finance. We show that the pricing function of financial derivatives can be naturally represented as a smooth section on a specified fiber bundle. Using this representation on the fiber bundle, we prove that the pricing equation must be rewritten as a partial differential equation in covariant differential form in order to keep this symmetry. And this covariant form leads to a connection on the fiber bundle. The gauge field which is determined by this connection provides a new insight to the research on the financial derivative pricing. In the paper we give the related preliminary concepts and deduce our main results, at the same time the paper shows a technique of time coordinate treatment for obtaining a unified covariant differential operator as well.
Keywords: Financial derivative pricing; gauge symmetry; fiber bundle; covariant differential; connection

Type of Paper: Article
Title: Will Science and Consciousness ever meat? Complexity, Symmetry and Qualia
Author: Roger Vergauwen
Affiliation: Catholic University of Leuven, Institute of Philosophy, Centre for Logic and Analytical Philosophy, Kardinaal Mercierplein 2, 3000 Leuven, Belgium; E-mail: Roger.Vergauwen@hiw.kuleuven.be
Abstract: A lot of the discussion in contemporary Philosophy of Mind has turned around the nature of consciousness. More specifically, the nature of phenomenal states or qualia (also called ‘raw feels’ or ‘what it is like to be’) has been an important focus of interest. Proponents of Mind-Body Type-Identity theories have e.g. claimed that mental states can in some sense be reduced to neurophysiological states of the brain while others have denied that such a reduction is altogether impossible and that therefore there remains an explanatory gap.
There is also an important and growing body of research suggesting that Mind (and consciousness) can be modelled along the lines of non linear complex dynamical system, an approach which seeks too avoid certain metaphysical implications of the first kind of approaches whether reductive or non-reductive and aims to show that cognitive activity and consciousness are neither different from nor just identical with brain-activity and are also not epiphenomena. In this paper I investigate the nature and status of the aforementioned approaches. In a first part the kind of explanation offered in dynamical models is specified and the importance and effectiveness of the mathematics involved is discussed in the background of the ‘reality’ of the existence of qualitative states or qualia and in relation to the residual functionalism these models seem to exhibit . In a second part physicalism, property dualism and epiphenomenalism are contrasted and compared to this approach and it is shown how Donald Davidson’s Anomalous Monism as a Token-Identity theory of the mental may be seen as an alternative approach wherein qualia may be ascribed a kind of causal efficacy but not incompatible with a dynamical systems approach. Finally, the embodiment of the mental is investigated in relation to the hypothesis according to which different phases in the case of living brain tissue are the various qualia whereas symmetry breaking within phase gives the values for a quale and whether the resulting theory can still properly be called a computable one.

Type of Paper: Article
Title: Dimensional Reduction and Aggregation of Variables in Nonlinear Dynamical Systems
Author: Martin Nilsson Jacobi; E-mail: mjacobi@chalmers.se
Abstract: We show how spectral methods developed for lumping of states in Markov chains can be used for dimensional reduction in continuous systems through implicit manifold foliations. We explore the relation between this method and the quotient manifold projections defined by Lie group symmetries. Furthermore, we extend the analysis to include aggregation of variables in nonlinear dynamical systems.

Type of Paper: Article
Title: Complexity Change and Spatial Symmetry Breaking: Phase Transition in World Trade Network
Authors: F. Ruzzenenti 1, R. Basosi 1, 2
Affiliation: 1 Center for the Study of Complex Systems, University of Siena, Italy; 2 Department of Chemistry, University of Siena, Italy; E-mail: ruzzenenti@unisi.it
Abstract: The aim of this article is to outline the role of space symmetry breaking in complexity change and to advance a plausible thermodynamic explanation to the underlying evolutionary pattern. It will be described how a change of the symmetry of the structure can be seen as a change in the space symmetry of some interacting particles, embedded in a network. As an example, it will be shown how allometric scaling in living networks display an optimal transport network, conditional to spatial constrains and it will also be shown how network topology can be linked to spatial symmetry. The underlying evolutionary pattern is then analyzed. This evolutionary pattern here advocated, relies on the hypothesis that thermodynamic evolutionary systems are characterized by an ever-growing influx of energy driven into the system by self-catalytic processes that must find their way through the constraints of the system. The system initially disposes of the energy by expanding, in extent and in the number of components, up to saturation due to inner or outer constraints. The two counteractive forces, constraints and growing energy flux, expose the system to new gradients. Every new (spatial) gradient applied on the system exerts a symmetry breaking in the components’ space. By exploring a new gradient, the system imposes further restrictions on its components and increases its overall degree of freedom. The counteractive effects of reduction/increase of degree of freedom concern two different hierarchical levels and occur at two different space and time scales. A case study will be presented concerning the evolution of the world-wide productive structure in the last five decades. The analysis will focus on factors’ trade network aiming at detecting phase transitions in the world trade web. The phase transition in the world trade web was generated, according to our hypothesis, by a space’s symmetry breaking of the productive network, driven by a dramatic energy efficiency improvement in transport means, occurred during the late 1970s.