- Synergetics (Fuller), a school of thought on thinking and geometry developed by Buckminster Fuller.
Synergetics is the empirical study of systems in transformation, with an emphasis on total system behavior unpredicted by the behavior of any isolated components, including humanity’s role as both participant and observer.
Since systems are identifiable at every scale from the quantum level to the cosmic, and humanity both articulates the behavior of these systems and is composed of these systems, synergetics is a very broad discipline, and embraces a broad range of scientific and philosophical studies including tetrahedral and close-packed-sphere geometries,thermodynamics, chemistry, psychology, biochemistry, economics, philosophy and theology. Despite a few mainstream endorsements such as articles by Arthur Loeb and the naming of a molecule “buckminsterfullerene,” synergetics remains an iconoclastic subject ignored by most traditional curricula and academic departments.
Buckminster Fuller (1895-1983) coined the term and attempted to define its scope in his two volume work Synergetics. His oeuvre inspired many researchers to tackle branches of synergetics. Three examples: Haken explored self-organizing structures of open systems far from thermodynamic equilibrium, Amy Edmondson explored tetrahedral and icosahedral geometry, and Stafford Beer tackled geodesics in the context of social dynamics. Many other researchers toil today on aspects of Synergetics, though many deliberately distance themselves from Fuller’s broad all-encompassing definition, given its problematic attempt to differentiate and relate all aspects of reality including the ideal and the physically realized, the container and the contained, the one and the many, the observer and the observed, the human microcosm and the universal macrocosm.
- Synergetics (Haken), a school of thought on thermodynamics and other systems phenomena developed by Hermann Haken.
Synergetics is an interdisciplinary science explaining the formation and self-organization of patterns and structures in open systems far from thermodynamic equilibrium. It is founded by Hermann Haken, inspired by the laser theory. Haken’s interpretation of the laser principles as self-organization of non-equilibrium systems paved the way at the end of the 1960s to the development of synergetics, of which Haken is recognized as the founder. One of his successful popular books is Erfolgsgeheimnis der Natur, translated into English as The Science of Structure: Synergetics.
Self-organization requires a ‘macroscopic’ system, consisting of many nonlinearly interacting subsystems. Depending on the external control parameters (environment, energy-fluxes) self-organization takes place.
Order Parameter Concept
Essential in synergetics is the order-parameter concept which was originally introduced in the Ginzburg-Landau theory in order to describe phase-transitions in thermodynamics. The order parameter concept is generalized by Haken to the “enslaving-principle” saying that the dynamics of fast-relaxing (stable) modes is completely determined by the ‘slow’ dynamics of as a rule only a few ‘order-parameters’ (unstable modes). The order parameters can be interpreted as the amplitudes of the unstable modes determining the macroscopic pattern.
As a consequence, self-organization means an enormous reduction of degrees of freedom (entropy) of the system which macroscopically reveals an increase of ‘order’ (pattern-formation). This far-reaching macroscopic order is independent of the details of the microscopic interactions of the subsystems. This supposedly explains the self-organization of patterns in so many different systems in physics, chemistry and biology.
Adapted from Wikipedia.
Scaling: In physics we are most often concerned with connecting problems at different length scales. For example, we start from atomic forces and use these to predict the properties of solids. We need some method for describing how to extrapolate effects over many orders of magnitude of different lengths to form connections among different theories. The word for this kind of extrapolation is scaling.
Universality: As one traverses the different length scales, one only retains a few characteristics of the original problem. Thus many different microscopic problems have the same macroscopic manifestation, depending mostly upon the symmetry of the original problem. Thus the Ising model, magnet and liquid-gas phase transition all have the same behaviour near critical point.
Universality Classes: Problems then fall into few different categories depending upon the nature of their solution. These categories are called “universality classes”. Scientists now use this phrase to describe many different kinds of things beyond phase transitions. One of these days I expect to hear a description of different kinds of pop music as different universality classes.
Renormalization: The renormalization method ties all this together. Wilson described the effect of many renormalizations in which the length scale was changed again and again, as the motion of the interactions toward a “fixed point”, a state of constant and unchanging interaction.
New Calculational Paradigm: Previously one started with a “problem” i.e. a description of the interactions among the particles in the system. The job of the theorist was mostly to calculate an “answer”, that is a detailed description of the behaviour of the particles.
In the new era, one does renormalization calculations in which one starts with one problems (i.e. set of interactions) and constructs another equivalent problem on another length scale. A partial but often sufficient description of the behaviour is encoded in the relation between different scales.
Old era: One said that quantum electrodynamics was characterized by an interaction strength called α, having the value 1/137.036.
New Era: One says that at smaller distance scale, α gets larger and eventually this electromagnetic interaction gets very strong. In informal language, one says that interaction strength runs.
The practice of physics has changed and moved away from the mode of calculation of Newton, Boltzmann, Einstein, and Dirac, going from solving problems to discussing the relationship among such problems. In addition to the aforementioned people who pushed in this direction, all the workers in the fields determine the subject’s content.
– Leo P. Kadanoff
Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity – Lewis Fry Richardson
Kolmogorov length scale >> Turbulence
Theories of the known, which are described by different physical ideas may be equivalent in all their predictions and are hence scientifically indistinguishable. However, they are not psychologically identical when trying to move from that base into the unknown. For different views suggest different kinds of modifications which might be made and hence are not equivalent in the hypotheses one generates from them in ones attempt to understand what is not yet understood.