Self-organization

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Self-organization is a process in which the internal organization of a system, normally an open system, increases in complexity without being guided or managed by an outside source. Self-organizing systems typically (though not always) display emergent properties.

Overview[]

CA rule30s — Cellular automaton here running Stephen Wolfram's "rule 30", a mathematical construct displaying self-organization

The most robust and unambiguous examples of self-organizing systems are from physics, where the concept was first noted. Self-organization is also relevant in chemistry, where it has often been taken as being synonymous with self-assembly. The concept of self-organization is central to the description of biological systems, from the subcellular to the ecosystem level. There are also cited examples of "self-organizing" behaviour found in the literature of many other disciplines, both in the natural sciences and the social sciences such as economics or anthropology. Self-organization has also been observed in mathematical systems such as cellular automata.

Sometimes the notion of self-organization is conflated with that of the related concept of emergence. Properly defined, however, there may be instances of self-organization without emergence and emergence without self-organization, and it is clear from the literature that the phenomena are not the same. The link between emergence and self-organization remains an active research question.

Self-organization usually relies on four basic ingredients:

Positive feedback
Negative feedback
Balance of exploitation and exploration
Multiple interactions

History of the idea[]

The idea that the dynamics of a system can tend by themselves to increase the inherent order of a system has a long history. One of the earliest statements of this idea was by the philosopher Descartes, in the fifth part of his Discourse on Method, where he presents it hypothetically. Descartes further elaborated on the idea at great length in a book called Le Monde that was never published.

The ancient atomists (among others) believed that a designing intelligence was unnecessary, arguing that given enough time and space and matter, organization was ultimately inevitable, although there would be no preferred tendency for this to happen. What Descartes introduced was the idea that the ordinary laws of nature tend to produce organization (For related history, see Avram Vartanian, From Descartes to Diderot).

Beginning with the 18th century naturalists a movement arose that sought to understand the "universal laws of form" in order to explain the observed forms of living organisms. Because of its association with Lamarckism, their ideas fell into disrepute until the early 20th century, when pioneers such as D'Arcy Wentworth Thompson revived them. The modern understanding is that there are indeed universal laws (arising from fundamental physics and chemistry) that govern growth and form in biological systems.

The term "self-organizing" seems to have been first introduced in 1947 by the psychiatrist and engineer W. Ross Ashby. Self-organization as a word and concept was used by those associated with general systems theory in the 1960s, but did not become commonplace in the scientific literature until its adoption by physicists and researchers in the field of complex systems in the 1970s and 1980s.

(As an indication of the increasing importance of this concept, when queried with the keyword self-organ*, Dissertation Abstracts finds nothing before 1954, and only four entries before 1970. There were 17 in the years 1971--1980; 126 in 1981--1990; and 593 in 1991--2000.)

Examples[]

The following list summarizes and classifies the instances of self-organization found in different disciplines. As the list grows, it becomes increasingly difficult to determine whether these phenomena are all fundamentally the same process, or the same label applied to several different processes. Self-organization, despite its intuitive simplicity as a concept, has proven notoriously difficult to define and pin down formally or mathematically, and it is entirely possible that any precise definition might not include all the phenomena to which the label has been applied.

It should also be noted that, the farther a phenomenon is removed from physics, the more controversial the idea of self-organization as understood by physicists becomes. Also, even when self-organization is clearly present, attempts at explaining it through physics or statistics are usually criticized as reductionistic. See holism, reductionism, emergence.

Similarly, when ideas about self-organization originate in, say, biology or social science, the farther one tries to take the concept into chemistry, physics or mathematics, the more resistance is encountered, usually on the grounds that it implies direction in fundamental physical processes. See teleology.

Self-organization in physics[]

There are several broad classes of physical processes that can be described as self-organization. Such examples from physics include:

In equilibrium thermodynamics: It is sometimes debated whether static systems deserve the label of "self-organizing".
- structural (order-disorder, first-order) phase transitions, and spontaneous symmetry breaking such as
  - spontaneous magnetization, crystallization (see crystal growth, and liquid crystal) in the classical domain and
  - the laser, superconductivity and Bose-Einstein condensation, in the quantum domain (but with macroscopic manifestations).
- second-order phase transitions, associated with "critical points" at which the system exhibits scale-invariant structures (see fractal). Examples of these include:
  - critical opalescence of fluids at the critical point
  - percolation in random media

structure formation in thermodynamic systems away from equilibrium. The theory of dissipative structures was developed to unify the understanding of these phenomena, which include
- turbulence and convection (e.g., Bénard cells) in fluid dynamics,
- structure formation in astrophysics and cosmology (including star formation, galaxy formation)
- self-similar expansion
- percolation
- reaction-diffusion systems, such as Belousov-Zhabotinsky reaction.

self-organizing dynamical systems: complex systems made up of small, simple units connected to each other usually exhibit self-organization.
- Self-organized criticality (SOC)
In spin foam system and loop quantum gravity that was proposed by Lee Smolin. The main idea is that the evolution of space in time should be robust in general. Any fine-tuning of cosmological parameters weaken the independency of the fundamental theory. Philosophically, it can be assumed that in the early time, there has not been any agent to tune the cosmological parameters. Smolin and chis olleagues in a series of works show that based on the loop quantization of spacetime, in the very early time a simple evolutionary model similar to the sand pile model, behaves a power law distribution on the both size and area of avalanche.
- Although, this model, which is restricted only on the frozen spin networks, exhibits a non-stationary expansion of the universe. However, it is the first serious attempt toward the final ambitious goal of determining the cosmic expansion and inflation based on a self-organized critialy theory in which the parameters are not tuenned, instead they are determined from within the complex system; http://arxiv.org/abs/hep-th/0412307.

Self-organization vs. entropy[]

The idea of self-organization challenges an earlier paradigm of ever-decreasing order which was based on a philosophical generalization from the second law of thermodynamics in statistical thermodynamics where entropy is envisioned as a measure of the statistical "disorder" at a microstate level. However, at the microscopic or local level, the two need not be in contradiction: it is possible for a system to reduce its entropy by transferring it to its environment.

In open systems, it is the flow of matter and energy through the system that allows the system to self-organize, and to exchange entropy with the environment. This is the basis of the theory of dissipative structures. Ilya Prigogine noted that self-organization can only occur far away from thermodynamic equilibrium.

It would appear that, since isolated systems cannot decrease their entropy, only open systems can exhibit self-organization. However, such a system can gain macroscopic order while increasing its overall entropy. Specifically, a few of the system's macroscopic degrees of freedom can become more ordered at the expense of microscopic disorder.

In many cases of biological self-assembly, for instance metabolism, the increasing organization of large molecules is more than compensated for by the increasing entropy of small molecules, especially water. At the level of a whole organism and over longer time scales, though, biological systems are open systems feeding from the environment and dumping waste into it.

Self-organization in chemistry[]

Self-organization in chemistry includes:

self-assembly
reaction-diffusion systems and oscillating chemical reactions
autocatalytic networks (see: autocatalytic set)

Self-organization in biology[]

The following is an incomplete list of the diverse phenomena which have been described as "self-organizing" in biology.

spontaneous folding of proteins and other biomacromolecules,
formation of lipid bilayer membranes,
homeostasis (the self-maintaining nature of systems from the cell to the whole organism)
morphogenesis, or how the living organism develops and grows. See also embryology.
the coordination of human movement, e.g. seminal studies of bimanual coordination by Kelso
the creation of structures by social animals, such as social insects (bees, ants, termites), and many mammals
flocking behaviour (such as the formation of flocks by birds, schools of fish, etc.)
The origin of life itself from self-organizing chemical systems, in the theories of hypercycles and autocatalytic networks.

Self-organization in mathematics and computer science[]

As mentioned above, phenomenon from mathematics and computer science such as cellular automata, random graphs, and some instances of evolutionary computation and artificial life exhibit features of self-organization. In swarm robotics, self-organization is used to produce emergent behavior.

In particular the theory of random graphs has been used as a justification for self-organization as a general principle of complex systems.

Self-organization in human society[]

The self-organizing behaviour of social animals and the self-organization of simple mathematical structures both suggest that self-organization should be expected in human society.

Tell-tale signs of self-organization are usually statistical properties shared with self-organizing physical systems (see Zipf's law, power law, Pareto principle).

Examples such as Critical Mass (bicycle), herd behaviour, groupthink and others, abound in sociology, economics, behavioral finance and anthropology.

In economics, the theoretical free market is self-organizing. Economists dispute the extent to which the benefits of self-organization occur in real societies. Friedrich Hayek coined the term catallaxy to describe a "self-organizing system of voluntary co-operation," in regard to capitalism. By contrast, some socialist economists consider that market failures are so significant that self-organization produces bad results. Most economists adopt an intermediate position that, in many cases, economic decentralisation is valuable.

In collective intelligence[]

Non-thermodynamic concepts of entropy and self-organization have been explored by many theorists. Cliff Joslyn and colleagues and their so-called "global brain" projects, and Marvin Minsky's "Society of Mind" idea, are examples of applications of these principles - see collective intelligence.

Donella Meadows, who codified twelve leverage points that a self-organizing system could exploit to organize itself, was one of a school of theorists who saw human creativity as part of a general process of adapting human lifeways to the planet and taking humans out of conflict with natural processes. See Gaia philosophy, deep ecology, ecology movement and Green movement for similar self-organizing ideals.

References[]

Non-technical[]

In alphabetical order

Per Bak, How Nature Works: The Science of Self-Organized Criticality, Copernicus Books, 1996, ISBN 0387947914, ISBN 038798738X.
Philip Ball, The Self-Made Tapestry: Pattern Formation in Nature, Oxford University Press, 1999 ISBN 038798738X.
Mark Buchanan Nexus: Small Worlds and the Groundbreaking Theory of Networks W. W. Norton & Company; 2002 ISBN 0393324427
John Holland, Emergence: From Chaos to Order Addison-Wesley, 1997 ISBN 0201149435, ISBN 0738201421
Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities and Software, 2001, ISBN 068486875X ISBN 0684868768
Stuart Kauffman, At Home in the Universe, Oxford University Press, 1995, ISBN 0195095995, ISBN 0195111303
J. A. Scott Kelso & David A Engstrom, "The Complementary Nature", The MIT Press, Cambridge, MA 2006, ISBN 0262112914
Heinz Pagels, The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity, Simon & Schuster, 1988 ISBN 0671627082
Mitchel Resnick, Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds, Complex Adaptive Systems series, MIT Press, 1994, ISBN 0262181622, ISBN 0262680939
Lee Smolin, The Life of the Cosmos Oxford University Press, 1997, ISBN 019510837X, ISBN 0195126645
Steven Strogatz, Sync: The Emerging Science of Spontaneous Order, Theia, 2004, ISBN 0786887214

Technical works[]

In chronological order

D'Arcy Thompson, On Growth and Form, Cambridge University Press, 1917 (1992 Dover Publications edition, ISBN 0486671356)
W. Ross Ashby, "Principles of the Self-Organizing Dynamic System", Journal of General Psychology (1947), volume 37, pages 125--128
Heinz Von Foerster and George W. Zopf, Jr. (eds.), Principles of Self-Organization (Sponsored by Information Systems Branch, U.S. Office of Naval Research), 1962
W. Ross Ashby, Design for a Brain, Chapman & Hall, 2nd edition, 1966 ISBN 0-412-20090-2
Gregoire Nicolis and Ilya Prigogine Self-Organization in Non-Equilibrium Systems, 1977, Wiley, ISBN 0471024015
Manfred Eigen and Peter Schuster The Hypercycle: A principle of natural self-organization, 1979, Springer ISBN 0387092935
Hermann Haken Synergetics: An Introduction. Nonequilibrium Phase Transition and Self-Organization in Physics, Chemistry, and Biology, Third Revised and Enlarged Edition, 1983, Springer-Verlag ISBN 0387123563
J. Doyne Farmer et al. (editors), Evolution, Games, and Learning: Models for Adaptation in Machines and Nature. Physica D 22 (1986).
Stuart Kauffman, Origins of Order: Self-Organization and Selection in Evolution Oxford University Press, 1993, ISBN 0195079515.
J. A. Scott Kelso "Dynamic Patterns: The self-organization of brain and behavior", 1995, Paperback Edition, 1997, The MIT Press, Cambridge, MA. ISBN 0-262-11200-0
Paul Krugman, The Self-Organizing Economy, Cambridge, Mass., and Oxford: Blackwell Publishers, 1996, ISBN 1557866988, ISBN 1557866996
Henrik Jeldtoft Jensen, Self-Organized Criticality: Emergent Complex Behaviour in Physical and Biological Systems, Cambridge Lecture Notes in Physics 10, Cambridge University Press, 1998, ISBN 0521483719
Scott Camazine, Jean-Louis Deneubourg, Nigel R. Franks, James Sneyd, Guy Theraulaz, Eric Bonabeau (editors) Self-Organization in Biological Systems, 2001, Princeton Univ Press, ISBN 0691012113
K. Yee, "Ownership and Trade from Evolutionary Games," International Review of Law and Economics, 23.2, 183-197 (2003) PDF file.
Alex Kentsis, Self-organization of biological systems: Protein folding and supramolecular assembly, Ph.D. Thesis, New York University, 2004, (UMI ProQuest), ISBN 0496680981
Tom De Wolf, Tom Holvoet, Emergence Versus Self-Organisation: Different Concepts but Promising When Combined, In Engineering Self Organising Systems: Methodologies and Applications, Lecture Notes in Computer Science, volume 3464, pp 1-15, 2005, (download here)
Christian Prehofer, Christian Bettstetter, Self-Organization in Communication Networks: Principles and Design Paradigms, IEEE Communications Magazine, July 2005.
A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK, 2000m 324 p. ISBN 0521793882

External links[]

PDF file on self-organized common law with references
An entry on self-organization at the Principia Cybernetica site
The Science of Self-organization and Adaptivity, a review paper by Francis Heylighen
The Self-Organizing Systems (SOS) FAQ by Chris Lucas, from the [news://comp.theory.self-org-sys USENET newsgroup comp.theory.self-org.sys]
David Griffeath, Primordial Soup Kitchen (graphics, papers)
nlin.AO, nonlinear preprint archive, (electronic preprints in adaptation and self-organizing systems)
Computational Mechanics Group at the Santa Fe Institute
Cosma Shalizi's notebook on self-organization from 2003-06-20, used under the GFDL with permission from author.
Connectivism:SelfOrganization

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