Difference between revisions of "Self-organization"
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Revision as of 20:08, 30 April 2023
Contents
Full Title or Meme
Whenever any system spontaneously organizes itself without external assistance or design, it is a new kind of phenomenon.
Also known as: Spontaneous Order
Context
"In nature it is quite common to see systems that start disordered and featureless, but then spontaneously organize themselves to produces definite structures." [1] The first experiments focused on the power law from the natural occurrence of phenomenon like earthquakes. This evolved into Self-organization Criticality (SOC) in the work of Per Bak with sand piles.[2] and follow-on work in experimental realization.[3]How can the universe start with a few types of elementary particles at the big bang, and end up with life, history, economics, and literature? The question is screaming out to be answered bur it is seldom even asked. Why did the big bang not form a simple gas of particles, or condense into one big crystal? We see complex phenomena around us so often that we rake them for granted without looking for further explanation. In fact, until recently very little scientific effort was devoted to understanding why nature is complex.
Figure 1: "Snow Crystal.
In the beginning of Quantum Mechanics and statistical physics it was believed that a crystalline structure can be calculated by determining the minimum of the free energy. This may be true, e.g. for ionic crystals, such as sodium chloride, or metals. In this case, the Schrödinger equation for the ground state or possibly low lying states must be solved. In general, this requires the solution of a many particle problem. As the example of snow crystals shows, this picture is too narrow. It is not only necessary to calculate binding forces, but rather the whole kinetics, e.g. of dendritic growth. Besides kinetics, also symmetry, may play a decisive role, e.g. the hexagonal symmetry of the snowflake is caused by the symmetry of H2O which acts as a nucleation center. This example shows that in the formation of crystals, such as the snowflake, kinetic processes and the problem of binding forces are strongly interwoven with each other."[4]
One interpretation of the mechanisms (or principles) underlying self-organization can be traced back to Cybernetics with its many concrete examples of positive and negative feedback.[5] According to Erdi [6] behind many (if not all) self-organizing phenomena there is a balance between positive and negative feedback, or as H. Meinhardt[7] puts it, “self-enhancement balanced by an antagonistic reaction”
Societies
We see many examples of self-organization around us every day: birds in flocks, fish in schools, humans in mobs. The earliest knows societies of living organisms were the ancestors of the slime molds that continue to flourish to this day. While these organizations have no discernible Leader they have evolved to have specialized functions that can form due to Ecosystem pressures, like lack of sufficient food. In societies where the leader has special privileges over the "common" folk, we see the result of what Nietzsche called the "Will to Power". Even in this quest for power, there still existing smaller organizations of humans that are able to select a Leader on more humanitarian principles.
In Identity Ecosystems the source of the Identifier can be based on power or the common good. It is up to the Subjects of the Identifier to determine which is to prevail.
Evolution
For this page evolution is defined in Darwin's terms as survival of the fittest. As originally formulated each individual was limited to the fitness that was present at birth. With flocking individuals, the herd behavior an improve the fitness of each individual. All higher animals can learn from experience. For animals that can record what they have learned for the next generation will enable the herd to grow more fit exponentially rather than linearly.
The Hill-climbing approach to evolution describes a process where a number of small jumps in the gene alleles will make the individual more fit.
There are two ways to imagine how fitness can improve when there are many individuals with widely divergent gene alleles in an ecosystem.
- Stuart Kauffman describes the Complexity catastrophe that occurs when a long jump results in a large number of divergent alleles are present together. [8]
Light
The laser as paradigm for self-organization of the first kind: reduction of the degrees of freedom
The first in-depth theoretical treatment of a self-organizing system concerned the light-source laser (“laser” is an acronym for “light amplification by stimulated emission of radiation”. This term misses the phenomenon of self-organization. This example shows how man-made devices utilize self-organization processes. A typical example of the laser device is provided by a glass tube filled with molecules or atoms which represent the subsystems. At it end faces the glass tube carries mirrors, one of them semi-transparent. Due to the mirrors, only specific light waves can stay for a longer time in space between them (“cavity”) and can interact intensely with the light-emitting atoms (molecules). The atoms (molecules) are energetically continuous excited by an electric current that serves as control parameter. Below a critical value of the electric current, the device acts as a lamp. The atoms (molecules) emit randomly incoherent light wave tracks (which are amplified by stimulated emission). The light field amplitudes are Gaussian distributed. Above a critical value of the electric currents (the laser threshold) the properties of light change qualitatively and dramatically.
Laser light consists of a single wave with a stable amplitude on which small amplitude fluctuations and a slow phase diffusion are superimposed. The transition from the irregular light from a lamp to the highly ordered light from a laser shows the emergence of a new quality (namely coherent light). The emergent laser light wave is called the order parameter. Once established, it governs the emission acts of the individual atoms (molecules) termed enslavement. Since the (joint) action of the subsystems (atoms, molecules) generates the order parameter (the laser light wave), while the latter enslaves the individual parts (atoms, molecules), we may speak of circular Causality.
We add for the expert that in the transition region the typical phenomena of a phase transition occur (symmetry breaking, critical slowing down, critical fluctuations that were predicted and measured in great detail). In the laser phase transition a new temporal structure is formed by self-organization, i.e. by the action of the subsystem without specific interference from the outside (no wave was prescribed from the outside, only a DC current is increased). When this control parameter is further increased ultra short pulses may occur. Generally, an instability hierarchy may occur. This is, at least in general, characterized by the occurrence of an increasing number of order parameters. Under specific conditions (including high losses due to the mirrors) laser light may show deterministic chaos (see also below). The laser is an open system with an energy input (the electric current) and energy output which besides the wanted laser light comprises incoherent losses (heat).
The virtue of the laser example rests upon the fact that the laser properties can be derived from first principles: quantum theory, quantum electrodynamics, coupling to heatbaths.
References
- ↑ Stephan Wolfram, A New Kind of Science Wolfram (2002) ISBN 9781579550080
- ↑ Per Bak, How Nature Works - the science of self-organized criticality Springer (1996) ISBN 978-1-4757-5426-1
- ↑ Arka Banerjee, Self-organized criticality in sand-pile models (2012-05-11) https://guava.physics.uiuc.edu/~nigel/courses/563/Essays_2012/PDF/banerjee.pdf
- ↑ Hermann Haken, Self-organization (2008), Scholarpedia, 3(8):1401. http://www.scholarpedia.org/article/Self-organization
- ↑ Norbert Wiener, Cybernetics - or Control and Communications in the Animal and the Machine MIT (1948)
- ↑ Peter Erdi, Complexity Explained Springer text book (2007) ISBN 978-3-540-35778-0 expensive, good reviews at https://www.amazon.com/Complexity-Explained-Springer-Peter-Erdi/dp/3540357777
- ↑ H. Meinhardt Models of biological pattern formation: from elementary steps to the organization of embryonic axes, Curr. Top. Dev. Biol. 81, 1-63 (2008)
- ↑ Stuart Kauffman, The Origins of Order
Other Material
- See the wiki page on Metabiology
- See the wiki page on Emergent Behavior for on one major features of Self-organization.
