Synergetics — Fundamental Attributes of the Theory of Self-Organization and Its Meaning for Economics

The current article will focus on the fundamental idea of synergetics. It addresses the question of how to explain self-organization in a complex system. For this purpose synergetic will be explained with the use of the classic physical example, the laser light. Although the synergetic theory was developed in the field of physics, it is an interdisciplinary approach enabling the general examination of self-organization of complex systems, especially in economic contexts. The so-called swarm intelligence contributes as a bright example from another context. Furthermore, exemplifying for economic application a simple national economy will be interpreted from the synergetic perspective. From an economic perspective, finally the conclusion includes a critical reflection of the approach.


Introduction
The proposition that order cannot be regarded as a result of planning is supported by Nobel Prize Winner von Hayek, who postulated a constructivist error [1] in this context 1 .Following von Hayek, such an order cannot be adequately researched with commonly used mechanistic models2 because they are based on lineal 3 cause-andeffect chains that are too predictable.
Exogenous perturbances or random variables have traditionally been used to model the complex developments that are encountered in real life.Eventually, irregular and rapid developments are examined by methods that seem to be applicable only to linear conditions, lineal conditions or steady operations.For a long time, economic science was dominated by the mechanistic worldview, which relied, for instance, on models whose trajectories 4 (with an equilibrium tendency) are predictable and become tangible after partial analysis [3].
The economic reality is often more difficult and complex than, for example, that linear models might suggest [4].For instance, self-organized processes that are far from being in equilibrium cannot be explained with a linear model.Nijkamp and Poot justifiably postulate a significant discrepancy between existing dynamic economics phenomena and the linear statistical methods available to us by which they are to be examined [5].
Addressing non-linear, complex systems can play a central role when searching for an expansion of the "economic toolbox".These systems enable us to depict a broad range of economic behavior patterns and explanatory models.Complexity can be described, analyzed and understood, for example, in situations where traditional static methods completely fail in analyzing complexity 5 .
Besides catastrophe theory or thermodynamics as well as fractal geometry and chaos theory, the theory of selforganization (i.e.synergetics), on which we will lay our focus, shall be particularly noted in this context.Although these approaches differ significantly from one another, they primarily concern questions regarding the emergence and analysis of complex order patterns; thus, they justifiably belong to a branch of a conceptual superstructure that we call the "science of complexity" 6 .As we will apply it in economics, we will call it "econoplexity" 7 .
First, this article will elaborate on the basic idea of synergetics and address the question of how to explain self-organization in a complex system.For this purpose, synergetics-from the field of physics-will be explained with the use of laser light (the classic example).The so-called swarm intelligence of birds is a vivid example from another context.Second, for economic applications, a simple national economy will be interpreted from the synergetic perspective, and we will highlight the "slaving principle" as a characterizing feature of synergetics.Finally, the conclusion includes a critical appraisal of this paper's approach from an economic perspective.

Explaining Self-Organization Phenomena
Synergetics is an interdisciplinary approach that enables examination of the self-organization of complex systems 8 .In this context, one can also discuss the emergence of a new attribute through interactions of distinct parts 9 , although the newly created quality of the emerging structure cannot be reduced to its original parts 10 .
The physician Hermann Haken founded this theory in 1969.He was the first to show that laser light can be explained only by self-organization phenomena 11 .
Definition: Synergetics describes the self-organized establishment of order within systems through the behavior of their components.This term refers to systems characterized by openness, dynamic behavior, and complexity [9].

About the Laser
Because synergetics suggests an initial structure when examining systems, it differentiates between macro-and micro-level phenomena [11].
The actual system is located at the micro level; it is characterized by a high number of elements and, as a rule, has a variety of degrees of freedom.In the case of the laser (e.g., a gas discharge lamp), on a microscopic level, countless atoms or molecules are continually stimulated with electricity.The electricity functions as an external parameter or control parameter [11].
Below the critical value, the experimental assembly operates as a standard lamp: the atoms and molecules emit random, incoherent and chaotic light waves, which include internal variables called modes [11].
The properties of light dramatically change in a self-organizational manner when the laser reaches a point above the critical amperage.This specific value is called the "laser threshold", which is also known as the phase transition or bifurcation in more general terms.At this level, self-organization only involves the reduction of degrees of freedom, and above this threshold, "efficiency is largely increased" [11].The system becomes unstable through changes in the control parameters.Thus, a high number of variables that remain stable can eventually be expressed by only a single internal variable that becomes unstable.This variable, which corresponds to the emergent laser light wave, is referred to as the order parameter and determines the emission activities of all other atoms and molecules such that concentrated laser light is produced by having all atoms pulsate in full harmony.In this regard, Haken speaks of "slaving": the unstable mode enslaves the stable mode [11].
Within the process of self-organization, only a few elements that influence the enslavement of the system crystallize out of an entire range of elements.Thus, this slaving principle creates a new structure.These few parameters, namely, the order parameters, can be observed on a macroscopic level.Hence, the patterns or order structures of the system become apparent at this level.Whereas the initial system has a homogenous structure, broken symmetry can be observed in the emerging end system 12 .
The theory of laser light is certainly only a theory of physics.This general theory can help to describe and explain self-organization processes in fields such as biology, medicine, sociology, psychology, and economics.
The theory of self-organization is a powerful alternative to the typical, traditional mechanistic view that can still be found in economics to some extent [7].
Figure 1 illustrates the concept of synergetics.
A prerequisite for the self-organization process is that the system must be an open system because a system can only be self-organizing if power is added externally, as illustrated by the example of lasers.Similarly, a pendulum can swing permanently only if energy is consistently added to it.This added energy does not determine the particular behavior of the system or the movement (see, for example, the movement of a pendulum), but without energy the movement and the dynamics of the system would come to an end.
In short, only open systems can create self-organized evolutionary structures, as all other systems die of heat Figure 1.The synergetic concept [13].
exhaustion [14].One can also speak about control parameters in this context, although they can at most symbolize unspecific control by the environment [15].Ultimately, such parameters do not determine the order structure, but they enable it because they exert influence on the microscopic level by controlling the energy supply.Because of the mutual interactions, however, there is interplay between the order parameters and the control parameters.The patterns created can be destabilized if the control parameters are changed, and this change leads to new order parameters.Which possible behavior could ultimately become an order parameter cannot be foreseen because the slightest change in the initial conditions can lead to completely different order parameters.This concept is known as the "butterfly effect" and can be formulated as follows: an insignificant flap of a butterfly's wings in Hong Kong could eventually create a tornado in New York.

Swarm Intelligence-Bird Migration
The migration of birds toward their winter quarters is a suitable example for applying the idea of synergetics.
Self-organization implies the reduction of the degrees of freedom on the micro level.Thus, each bird could theoretically choose an individual flight route, but this occurrence is not observed in nature.Instead, migratory birds create flocks using a process of self-organization.Among the abundance of parameters that could influence the system of the flock of birds, the parameters that do influence the self-organization of the system become apparent.These few parameters are called order parameters and can be observed on a macro level.In the case of a flock of birds, this parameter could be the birds' wing shape or the size of the birds.The distance between the birds and their response behavior as well as the energetic effect of the slipstream derived from such parameters.Hence, a formation of the system's components (i.e., the birds in this case) is developed on the macro level.The overall pattern of the flock makes the order structure (i.e., the pattern of the system) visible.The described flock intelligence is a simple form of self-organization based on three rules that each bird follows [16]: • Staying together: Attempt to move toward the center of the flock.
• Separation: Move outward as soon as someone becomes too close.
• Alignment: Move just as your direct neighbor does.Thus, the group acts without any central control because every bird is autarkic and the flock operates dynamically in a self-organized (synergetic) manner.Furthermore, flocks are flexible and show a high degree of adaptation to different conditions (e.g., mountains, houses, seas).Moreover, flocks are also quite robust when individual birds stray.As a result, the order of a flock is not dependent on any single bird [17].

Subsystems and Overall Systems in Synergetics
The two systems S 1 and S 2 will be examined by means of an example.Suppose that system S 1 is a national economy without governmental activities, whereas system S 2 represents the government.The states of the systems can then be characterized by a variety of modes.Thus, whereas system S 1 can be described by the balance of payments, the unemployment rate, the level of prices, interest rates, gross domestic product, and other features, system S 2 can be described by features that include its institutions, jurisdiction, national expenditures, inland revenues, subsidies, and transfer payments.
Furthermore, it is expected that system S 2 can influence system S 1 through certain forces: indirect taxes could be raised in system S 2 to eliminate, for example, financial difficulties.This tax increase would evoke a change in the status of system S 1 .For example, the tax increase could have an unwanted crowding-out effect in S 1 .If S 2 does not intervene in S 1 by changing its parameters and if the tax increase is nullified, then S 1 will return to its initial state.Thus, the economic fluctuation triggered by the government in this example would be revoked.In the language of synergetics, system S 2 organized system S 1 .
Again, it must be emphasized that synergetics is tailored to self-organization.Hence, it is wise to interpret all the forces that influence system S 1 as part of the overall system [12].For this reason, the overall system S = S 1 S 2 , i.e., the system of the national economy with governmental activities will be considered.Thus, S is self-organizing such that the influence of sub-system S 2 on sub-system S 1 represents internal forces 13 .

The Mathematical Trick: The "Slaving Principle"
However, a problem arises when describing self-organizing systems: as a rule, complex systems of this type can be described only with a large number of variables and, hence, only by a comprehensive system of equations.For this reason, a mathematical technique is used: the stable variable is described directly by unstable order parameters.Generally, many stable variables and several unstable variables appear.Therefore, S 1 follows the path of S 2 instantaneously.As a result, we say that system S 2 has enslaved S 1 (through the slaving principle).Both the number of degrees of freedom and the complexity can be reduced through this procedure.As a result, a new condition is established and can be expressed by relatively few order parameters.
The term "slaving principle" is used in a completely value-free manner in synergetics; it is not a compulsory measure triggered by relevant actors 14 .
Using a particular equation-system 15 , Haken compared the results derived from a computer calculation with the calculated results on the basis of the slaving principle.The outcome reveals that for a certain period, a precise level of conformity can be shown; however, a sudden discrepancy occurs that "remains for the rest of the time" [12].In this manner, Haken showed that if the slaving principle fails and if the former stable solution is destabilized by changing the control parameters, then irregular, chaotic movements appear.Thus, chaos in a system is closely linked to the failure of the slaving principle 16 .
Examining systems from a synergetic perspective as described above requires a new perspective indicating that it is generally impossible to completely control a complex system such as the economy of a nation; because even minor interventions result in unpredictable consequences (the butterfly effect).The failure of the anticyclical fiscal policy of the federal government of Germany in the 1970s or the even more extreme failure of the command economy in the Eastern European states constitute empirical evidence of such behavior.Basically, every type of governmental interference in the economic processes of a market (regardless of the motive) can lead to failure if the intent is to provide more parameters than necessary for the functioning of the system 17 .
Von Hayek noted that "enabling an extensive division of labor and continuously adapting the economic action to millions of facts and incidents" [1] is the great achievement of the market.

Discussion
According to Haken, all internal variables can be expressed by order parameters (see Ch. 2).Hence, all stable modes would be eliminated, and only the unstable modes (i.e., the order parameters) would thus be relevant.Thus, modes are presumed.New system properties are created through enslavement.But the question of how those characteristics develop at the point of phase transition (i.e., the point at which the condition of the system changes) and in what relation the old condition stands to the new condition has not yet been resolved.In synergetics, the old structure is not depicted in the new structure, and hence, topological variation is lacking.
According to the synergetics-model, there is no finished construction plan on the micro level of a system; there is merely an initial point for the evolution of a figure.Its formation energy is added from outside by means of a control parameter, which serves as a "creatio ex nihilo" through feedback and gradually surfaces as a dynamic structure on the macro level by means of order parameters.The exciting aspect of the synergetic interpretation of national economies is that complex systems can be generated only in a self-organizational manner (see Ch. 3).

Conclusions
Synergetics is a theory of self-organization that lacks a global stability criterion.Despite this critique, synergetics is generally an adequate approach that can be used to sufficiently describe and analyze self-organizing systems, such as economic systems that are based on free market principles.Moreover, it has been proven by Haken that at the threshold, "when self-organization takes place, the efficiency jumps dramatically" [11].
For these reasons and the mentioned butterfly effect, it is generally impossible to control a complex system such as the economy of a nation because even minor interventions can have unpredictable consequences in the long term.
The presented insight from the field of synergetics (e.g., with regard to the market system) do not necessarily lead to incompatibility between "social justice" and "freedom", as one could easily presume.Nonetheless, these observations can be used to visualize and apply the market economy's self-organizational forces of freedom, which are consistently diminished by excessive governmental interference to the detriment of all citizens.
The study of complex systems does not come to an end by means of synergetics.On the contrary, this article provides only an initial introduction to the topic.Nevertheless, there is still a lot of room for research in order to better understand and judge complex systems and to recognize valid options for intervention.