Synergetics

The synergetic is the study of the interaction of elements of any kind, which within a complex dynamic system with each other in interaction occur (eg. Molecules, cells or human). It researches general principles and laws of interaction (also called synergy ) that occur universally in physics , chemistry , biology , psychology and sociology and provides a uniform mathematical description of these phenomena. The spontaneous formation of synergetic structures is called self-organization .

Synergetics emerged in the 1970s from the statistical physics of non-equilibrium systems ( Hermann Haken ) and accordingly initially treated purely physical systems, the best-known of which is the laser as a central example of collective behavior. With this exemplary system of self-organization far from thermodynamic equilibrium , the essential principles such as the principle of order parameters, the principle of enslavement and the connection with the theory of phase transitions could be developed.

The principle of the order parameters states that the behavior, i.e. the dynamics, of the system parts of a complex overall system is determined by a few order parameters. Compared to the complexity when considering a single system, this results in considerable information compression. For to describe the behavior of the overall system, it is sufficient to set up a few equations that describe the overall system, depending on the order parameter space.

Due to the fundamental similarity of all systems, which are composed of many constituents regardless of the specific interaction, the methods developed could be extended to many other areas. In chemistry, the best-known example is the Belousov-Zhabotinsky reaction , in which spatial and temporal patterns can be observed.

Further examples are:

chemotactic activity of the slime mold

Predator-prey systems

public opinion formation

Synergetics were represented by their broad applicability in interdisciplinary partial areas on a keyword reduced, no more than a community action means that over the sum of the powers of the individual goes. However, synergetics is more a mathematically precisely formulated theory than a philosophical or epistemological position.

Synergetics according to hook

Laser theory

Hermann Haken developed a laser theory in the 1960s, which is understood as a theory of complex systems, in particular as a theory of self-organization - i.e. the development of system states without external constraint (self-organized), which moreover cannot be precisely predicted . One goal of this theory is to calculate the temporal course of the atomic states and to be able to predict the future behavior of the laser medium atoms with the highest possible probability.

In general, individual states of systems are often described using differential equations. By relating the respective equation of state to its time derivative , with complete knowledge of the current state, theoretically every possible future state can be calculated. In complex systems such as that of light and medium, however, the equations are often coupled, ie the interactions of the atoms are “translated” into mathematical formulas through the mutual dependence of the variables in the equations. The differential equations for such complex systems cannot be solved with the methods of fundamental physical theories because, in contrast to statistical physics, they have mostly developed solutions for relatively simple systems with few components.

Especially with laser systems, the decisive phase transition (change of state) of light with a superposition of numerous wavelengths in laser light is the so-called laser threshold : If this is exceeded, the atoms of the laser begin to oscillate in unison and emit light of only approximately one wavelength . The almost common mode of the atomic oscillations in the laser light enables a first simplification of the calculation of the differential equations, since the light waves do not have many different wavelengths but approximately one. As a result, only three variables are required to solve the differential equations to describe the possible system states at a certain point in time:

${\ displaystyle b _ {\ lambda}}$ describes the time-dependent amplitudes of the possible electromagnetic oscillation states, also called modes ( denotes the index of the modes, i.e. ) ${\ displaystyle \ lambda}$ ${\ displaystyle b_ {1}, b_ {2}, b_ {3}, \ dotsc}$

{\ displaystyle d _ {\ mu}}

expresses the atomic inversion, i.e. the difference in the occupation numbers of the energy levels in which the laser-active atoms can be located ( is the index for the individual atoms, i.e. )

{\ displaystyle \ mu}

{\ displaystyle d_ {1}, d_ {2}, d_ {3}, \ dotsc}

{\ displaystyle \ alpha _ {\ mu}}

describes the dipole moments of the individual atoms.

The starting point of the laser theory according to Haken is the observation that different process speeds exist, i.e. that the variables change at different time intervals: changes the slowest, changes a little faster, changes the fastest when a change occurs. On the basis of this difference, a hierarchy is established in which everyone is at the top. ${\ displaystyle b _ {\ lambda}}$ ${\ displaystyle d _ {\ mu}}$ ${\ displaystyle \ alpha _ {\ mu}}$ ${\ displaystyle b _ {\ lambda}}$

In the vocabulary of synergetics, a single one (e.g. ) wins the competition and sets the pace of the vibrations. That makes it the so-called order parameter. The former enslaves the others, that is, he determines them. It is a basic principle of synergetics according to Haken that the state and the temporal course of a system can be aptly described by slowly changing variables, because faster changing variables are understood in such a way that they are “oriented” to the slower ones. ${\ displaystyle b}$ ${\ displaystyle b_ {239}}$

As a result, the uniform basic mode , which is created by breaking symmetry in the system of laser light and medium, can be calculated solely by the clock . This simplifies the differential equations so that they can be solved. From a physical point of view, the atoms in a laser immediately follow the specifications of the clock-setting order parameter according to the method of adiabatic approximation in the sense of synergetics according to Haken . ${\ displaystyle b}$

Criticism of the postulated causality

According to Achim Stephan , the synergetic approach according to Haken connects an empirically well-tested and mathematically soundly formulated, descriptive thesis to a causal theoretical thesis without further justification . With the concept of order parameters and the principle of enslavement, the most diverse processes can be described mathematically correctly and with a high degree of probability calculated in advance, however, in this case, Haken would make a fallacy of the type post hoc, ergo propter hoc (Latin for `` afterwards ''): Although the later behavior of the overall system can be predicted well from the order parameters, one cannot necessarily conclude from this that the parameters determine the cause of the system behavior. The application of the causal theory thesis is particularly problematic in social systems . B. "enslave" the working atmosphere not the behavior of an employee or the "[...] working atmosphere does nothing."

In addition, it is unclear how Haken's talk of circular causality between an order parameter representative of the overall system and the (other) system components can be understood: Either as causal interactions within the level of the system components or as causal interactions between the level of the system components and the level of the overall system . In the latter case, it would be a special variant of downward causality, since the same individual component (order parameter), to which the behavior of the overall system is causally traced back in the sense of synergetics according to Haken , at the same time has a causal effect on the individual components again from the level of the overall system would.

literature

Hermann Haken : Synergetics . Springer-Verlag, Berlin / Heidelberg / New York 1982, ISBN 3-540-11050-X .
R. Graham, A. Wunderlin (Eds.): Lasers and Synergetics . Springer-Verlag, Berlin / Heidelberg / New York 1987, ISBN 3-540-17940-2 .
A. Korotayev , A. Malkov, D. Khaltourina: Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow 2006, ISBN 5-484-00414-4 . (Table of contents and review online)
AS Mikhailov: Foundations of Synergetics I. Distributed active systems. Springer Verlag, Berlin, 1990, ISBN 3-540-52775-3 . (2nd rev. Ed. 1994)
AS Mikhailov, A. Yu. Loskutov: Foundations of Synergetics II. Chaos and Noise. (= Springer Series in Synergetics. Volume 52). 2nd revised and enlarged edition. Springer, Berlin / Heidelberg 1996, ISBN 3-540-61066-9 .
Norbert Niemeier: Organizational change from the point of view of synergetics. Deutscher Universitätsverlag, Wiesbaden 2000, ISBN 3-8244-0524-5 .

Individual evidence

↑ ^a ^b Meinard Kuhlmann: Theories of Complex Systems: Non-fundamental and yet indispensable? In: Andreas Bartels, Manfred Stöckler (Ed.): Theory of Science. mentis Verlag, Paderborn 2009, pp. 310–314 (a) and pp. 324–326 (b)
↑ Achim Stephan : Emergence: From unpredictability to self-organization. Dresden University Press, Dresden / Munich 1999, p. 237.