Synergetics (Haken)

Synergetics is the study of interaction of elements of any kind that occur within a complex dynamic system interact with each other (eg, molecules, cells, or human ). She explores universal 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 synergistic structures is referred to as self-organization.

Synergetics evolved in the 1970s from the statistical physics of nonequilibrium systems ( Hermann Haken ) and treated accordingly at first purely physical systems, the most famous of the laser. In this exemplary system of self-organization far from the thermodynamic equilibrium, the essential principles such as the principle of order parameter, the Versklavungsprinzip and the connection with the theory of phase transitions could be developed.

The principle of the order parameter indicates that the behavior, ie the dynamics of the system components of a complex system as a whole by a few order parameters is determined. This is compared to the complexity of viewing a single system a significant information compression instead. Because the behavioral description of the complete system, it is sufficient, depending on the order parameter space to set up a few equations that describe the overall system.

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

Other examples are:

• Bénard and Taylor instability
• Cloud pattern
• Brain waves (EEG )
• Chemotactic activity of the slime mold
• Predator-prey systems
• Formation of public opinion

Synergetics has been reduced by their wide applicability in interdisciplinary areas partly on a keyword that does not mean more than a community action that goes beyond the sum of the powers of the individual. However, Synergetics is more of an exact mathematical theory formulated as a philosophical or epistemological position.

Synergetics by hook

Laser theory

Work Albert Einstein stimulated emission led to the consideration that the light amplification is possible, which is limited by mutually stimulated emission of photons. 1960 for the first time laser light generated in the form of a ruby laser, since then numerous other media were harnessed. Hermann Haken developed a short time later a laser theory, which is seen as a theory of complex systems, in particular as a theory of self- organization - the development of system states without external constraint ( self-organized ), which also can not be accurately predicted.

The decisive phase transition (change of state ) of light with a superposition of many wavelengths in laser light, the laser threshold: If those were exceeded, the atoms of the laser begin to vibrate in unison and emit light of only approximately one wavelength. Compared with numerous light wavelengths, eg the light of an incandescent lamp, laser light is spatially coherent to a high degree.

Individual system states are usually described by differential equations. Due to the placement in relation to the respective equation of state with its time derivative can, in full knowledge of the current state, by substituting variables of each possible future state can be calculated. In complex systems such as the system of light and medium, the equations are often coupled, ie the interactions of the atoms are "translated " by the mutual dependence of the variables in the equations in mathematical formulas. The approximate common atomic oscillations in the laser light makes it possible in this case a first simplification of the calculation, since the light waves do not have many different wavelengths, but also approximately one. This will be for the resolution of the differential equations describing the possible states at any given time requires only three variables:

• Bλ describes the time-dependent amplitude of the possible electromagnetic vibrational states, called modes ( λ denotes the index of the modes, that b1, b2, b3, ...)
• Dμ expresses the atomic inversion from, ie the difference of the occupation numbers of the energy levels in which the laser-active atoms can be located ( μ is the index for the individual atoms, ie, d1, d2, d3 ... )
• αμ describes the dipole moments of the individual atoms.

With the methods of fundamental physical theories the complex systems of differential equations can not be solved, because they have as opposed to statistical physics mostly developed solutions for relatively simple systems with few components. Hook approach of laser theory, which he later generalized to Synergetics, allows the resolution of extremely many and coupled differential equations, which is shown in simplified form here:

Starting point of the laser theory hook is the finding that different process speeds exist, therefore changing the variables in different time intervals: bλ varies slowest, slightly slower changes dμ, fastest, a change in αμ on. On the basis of this difference, a hierarchy is established, is highest in the bλ. It is seen as a so-called order parameter, " enslaved " the other two variables which, therefore align all other variables in the order parameter and determined in their variations of this. It is a fundamental principle of Synergetics by hooks that you can describe by slowly changing variables of the state and its temporal development of a system, because faster changing variables to be construed that they are " geared " to the slow. In the calculation applies bλ thus constant over time, the " enslaving " bλ determined by the hook state and the numerical value of dμ and αμ.

In the vocabulary of Synergetics wins a single b (eg B239 ) competition between order parameters and sets the pace of the oscillations, so that the uniform fundamental mode, which forms by means of symmetry breaking in the system of laser light and medium will be calculated solely by the clocking b can. Through this so-called Einmodenfall in combination with the assumption of a prominent, the system state determining the order parameter, the differential equations simplify such a way that they can be solved. Physically follow the atoms in a laser so in the sense of synergetics by hook instantly to the specifications of clock-generating order parameter by the method of adiabatic approximation.

Criticism of the postulated causal

According to Achim Stephan synergetics approach closes after hook without further justification of an empirically well- tested and formulated mathematically sound, descriptive thesis on a theoretical causal thesis. Although it is possible with the view of Ordnungsparamtern and the Versklavungsprinzip describe a variety of processes mathematically correct and predict with high probability, but commit hook in this case a fallacy of the kind of post hoc ergo propter hoc (Latin for, after that, therefore because of this '): Although the subsequent behavior of the overall system can be well predicted from the order parameters, one can not necessarily conclude that the parameters specify the system behavior cause thereof. In particular, in social systems, the application of causal theoretical argument is problematic, for example, " Enslave " the working climate is not the behavior of an employee or the " [ ... ] working environment does not do anything. "

In addition is unclear how the hook talk of circular causality between a representative of the overall system order parameter and the ( rest of ) system components can be understood either as causal interactions within the plane of the system components or as causal interactions between the level of system components and the level of the overall system. In the latter case, it would be a special variant of downward causation, since the same single-component, at the same time act ( order parameter ), to which in the sense of synergetics after hook the behavior of the overall system is attributed causally from the level of the overall system back to the individual constituents causally would.