Monday, July 05, 2010

Self-organization

Self-organization

From Wikipedia, the free encyclopedia

Self-organization is the process where a structure or pattern appears in a system without a central authority or external element imposing it. This globally coherent pattern appears from the local interaction of the elements that makes up the system, thus the organization is achieved in a way that is parallel (all the elements act at the same time) and distributed (no element is a coordinator).

Contents

Overview

The most robust and unambiguous examples[1] of self-organizing systems are from the physics of non-equilibrium processes. 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.[citation needed] 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 [2]:
  1. Strong dynamical non-linearity, often though not necessarily involving Positive feedback and Negative feedback
  2. Balance of exploitation and exploration
  3. 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where he presents it hypothetically.[citation needed] Descartes further elaborated on the idea at great length in his unpublished work The World.
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 [citation needed] (For related history, see Aram Vartanian, Diderot and Descartes).
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.
Originally, the term "self-organizing" was used by Immanuel Kant in his Critique of Judgment, where he argued that teleology is a meaningful concept only if there exists such an entity whose parts or "organs" are simultaneously ends and means. Such a system of organs must be able to behave as if it has a mind of its own, that is, it is capable of governing itself.
“ In such a natural product as this every part is thought as owing its presence to the agency of all the remaining parts, and also as existing for the sake of the others and of the whole, that is as an instrument, or organ... The part must be an organ producing the other parts—each, consequently, reciprocally producing the others... Only under these conditions and upon these terms can such a product be an organized and self-organized being, and, as such, be called a physical end. ”
The term "self-organizing" was introduced to contemporary science in 1947 by the psychiatrist and engineer W. Ross Ashby[3]. It was taken up by the cyberneticians Heinz von Foerster, Gordon Pask, Stafford Beer and Norbert Wiener himself in the second edition of his "Cybernetics: or Control and Communication in the Animal and the Machine" (MIT Press 1961).
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.[4] After 1977's Ilya Prigogine Nobel Prize, the thermodynamic concept of self-organization received some attention of the public, and scientific researchers start to migrate from the cybernetic view to the thermodynamic view.

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.
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. However the tendency of hot bodies to get cold (see Thermodynamics) and by Le Chatelier's Principle- the statistical mechanics extension of Newton's Third Law- to oppose this tendency should be noted.

Self-organization in physics


Convection cells in a gravity field
There are several broad classes of physical processes that can be described as self-organization. Such examples from physics include:
  • self-organizing dynamical systems: complex systems made up of small, simple units connected to each other usually exhibit self-organization

  • 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 his colleagues 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 as a power law distribution on both the 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 criticality theory in which the parameters are not tuned, but instead are determined from within the complex system.[5]

Self-organization vs. entropy

Statistical mechanics informs us that large scale phenomena can be viewed as a large system of small interacting particles, whose processes are assumed consistent with well established mechanical laws such as entropy, i.e., equilibrium thermodynamics. However, “… following the macroscopic point of view the same physical media can be thought of as continua whose properties of evolution are given by phenomenological laws between directly measurable quantities on our scale, such as, for example, the pressure, the temperature, or the concentrations of the different components of the media. The macroscopic perspective is of interest because of its greater simplicity of formalism and because it is often the only view practicable.” Against this background, Glansdorff and Ilya Prigogine introduced a deeper view at the microscopic level, where “… the principles of thermodynamics explicitly make apparent the concept of irreversibility and along with it the concept of dissipation and temporal orientation which were ignored by classical (or quantum) dynamics, where the time appears as a simple parameter and the trajectories are entirely reversible.”[6]
As a result, processes considered part of thermodynamically open systems, such as biological processes that are constantly receiving, transforming and dissipating chemical energy (and even the earth itself which is constantly receiving and dissipating solar energy), can and do exhibit properties of self organization far from thermodynamic equilibrium.
A laser can also be characterized as a self organized system to the extent that normal states of thermal equilibrium characterized by electromagnetic energy absorption are stimulated out of equilibrium in a reverse of the absorption process. “If the matter can be forced out of thermal equilibrium to a sufficient degree, so that the upper state has a higher population than the lower state (population inversion), then more stimulated emission than absorption occurs, leading to coherent growth (amplification or gain) of the electromagnetic wave at the transition frequency.”[7]

Self-organization in chemistry


The DNA structure at left (schematic shown) will self-assemble into the structure visualized by atomic force microscopy at right. Image from Strong.[8]
Self-organization in chemistry includes:
  1. molecular self-assembly
  2. reaction-diffusion systems and oscillating chemical reactions
  3. autocatalytic networks (see: autocatalytic set)
  4. liquid crystals
  5. colloidal crystals
  6. self-assembled monolayers
  7. micelles
  8. microphase separation of block copolymers
  9. Langmuir-Blodgett films

Self-organization in biology


Birds flocking, an example of self-organization in biology
Main article: Biological organisation
According to Scott Camazine.. [et al.]:
“ In biological systems self-organization is a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower-level components of the system. Moreover, the rules specifying interactions among the system's components are executed using only local information, without reference to the global pattern.[9] ”
The following is an incomplete list of the diverse phenomena which have been described as self-organizing in biology.
  1. spontaneous folding of proteins and other biomacromolecules
  2. formation of lipid bilayer membranes
  3. homeostasis (the self-maintaining nature of systems from the cell to the whole organism)
  4. pattern formation and morphogenesis, or how the living organism develops and grows. See also embryology.
  5. the coordination of human movement, e.g. seminal studies of bimanual coordination by Kelso
  6. the creation of structures by social animals, such as social insects (bees, ants, termites), and many mammals
  7. flocking behaviour (such as the formation of flocks by birds, schools of fish, etc.)
  8. the origin of life itself from self-organizing chemical systems, in the theories of hypercycles and autocatalytic networks
  9. the organization of Earth's biosphere in a way that is broadly conducive to life (according to the controversial Gaia hypothesis)

Self-organization in mathematics and computer science


Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life.[10]
As mentioned above, phenomena 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. In the field of multi-agent systems, understanding how to engineer systems that are capable of presenting self-organized behavior is a very active research area.

Self-organization in cybernetics

Wiener regarded the automatic serial identification of a black box and its subsequent reproduction as sufficient to meet the condition of self-organization.[11] The importance of phase locking or the "attraction of frequencies", as he called it, is discussed in the 2nd edition of his "Cybernetics".[12] Drexler sees self-replication as a key step in nano and universal assembly.
By contrast, the four concurrently connected galvanometers of W. Ross Ashby's Homeostat hunt, when perturbed, to converge on one of many possible stable states.[13] Ashby used his state counting measure of variety[14] to describe stable states and produced the "Good Regulator"[15] theorem which requires internal models for self-organized endurance and stability.
Warren McCulloch proposed "Redundancy of Potential Command"[16] as characteristic of the organization of the brain and human nervous system and the necessary condition for self-organization.
Heinz von Foerster proposed Redundancy, R = 1- H/Hmax , where H is entropy.[17] In essence this states that unused potential communication bandwidth is a measure of self-organization.
In the 1970s Stafford Beer considered this condition as necessary for autonomy which identifies self-organization in persisting and living systems. Using Variety analyses he applied his neurophysiologically derived recursive Viable System Model to management. It consists of five parts: the monitoring of performance[18] of the survival processes (1), their management by recursive application of regulation (2), homeostatic operational control (3) and development (4) which produce maintenance of identity (5) under environmental perturbation. Focus is prioritized by an "algedonic loop" feedback:[19] a sensitivity to both pain and pleasure.
In the 1990s Gordon Pask pointed out von Foerster's H and Hmax were not independent and interacted via countably infinite recursive concurrent spin processes[20] (he favoured the Bohm interpretation) which he called concepts (liberally defined in any medium, "productive and, incidentally reproductive"). His strict definition of concept "a procedure to bring about a relation"[21] permitted his theorem "Like concepts repel, unlike concepts attract"[22] to state a general spin based Principle of Self-organization. His edict, an exclusion principle, "There are No Doppelgangers"[23] means no two concepts can be the same (all interactions occur with different perspectives making time incommensurable for actors). This means, after sufficient duration as differences assert, all concepts will attract and coalesce as pink noise and entropy increases (and see Big Crunch, self-organized criticality). The theory is applicable to all organizationally closed or homeostatic processes that produce endurance and coherence (also in the sense of Reshcher Coherence Theory of Truth with the proviso that the sets and their members exert repulsive forces at their boundaries) through interactions: evolving, learning and adapting.
Pask's Interactions of actors "hard carapace" model is reflected in some of the ideas of emergence and coherence. It requires a knot emergence topology that produces radiation during interaction with a unit cell that has a prismatic tensegrity structure. Laughlin's contribution to emergence reflects some of these constraints.

Self-organization in human society


Social self-organization in international drug routes
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 (sociodynamics), herd behaviour, groupthink and others, abound in sociology, economics, behavioral finance and anthropology.[24]
In social theory the concept of self-referentiality has been introduced as a sociological application of self-organization theory by Niklas Luhmann (1984). For Luhmann the elements of a social system are self-producing communications, i.e. a communication produces further communications and hence a social system can reproduce itself as long as there is dynamic communication. For Luhmann human beings are sensors in the environment of the system.{p410 Social System 1995} Luhmann developed an evolutionary theory of Society and its subsytems, using functional analyses and systems theory. {Social Systems 1995}.
Self-organization in human and computer networks can give rise to a decentralized, distributed, self-healing system, protecting the security of the actors in the network by limiting the scope of knowledge of the entire system held by each individual actor. The Underground Railroad is a good example of this sort of network. The networks that arise from drug trafficking exhibit similar self-organizing properties. Parallel examples exist in the world of privacy-preserving computer networks such as Tor. In each case, the network as a whole exhibits distinctive synergistic behavior through the combination of the behaviors of individual actors in the network. Usually the growth of such networks is fueled by an ideology or sociological force that is adhered to or shared by all participants in the network.[original research?][citation needed]

In economics

In economics, a market economy is sometimes said to be self-organizing. Paul Krugman has written on the role that market self-organization plays in the business cycle in his book "The Self Organizing Economy"[25]. Friedrich Hayek coined the term catallaxy to describe a "self-organizing system of voluntary co-operation," in regard to capitalism. Most modern economists hold that imposing central planning usually makes the self-organized economic system less efficient. By contrast, some socialist economists consider that market failures are so significant that self-organization produces bad results and that the state should direct production and pricing. Many economists adopt an intermediate position and recommend a mixture of market economy and command economy characteristics (sometimes called a mixed economy). When applied to economics, the concept of self-organization can quickly become ideologically-imbued (as explained in chapter 5 of A. Marshall, The Unity of Nature, Imperial College Press, 2002).

In collective intelligence


Visualization of links between pages on a wiki. This is an example of collective intelligence through collaborative editing.
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. Marvin Minsky's "Society of Mind" and the no-central editor in charge policy of the open sourced internet encyclopedia, called Wikipedia, 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. (The connections between self-organisation and Gaia theory and the environmental movement are explored in A. Marshall, 2002, The Unity of Nature, Imperial College Press: London).

Self-organization in linguistics

Self-organization refers to a property by which complex systems spontaneously generate organized structures"[26].[Full citation needed] It is the spontaneous formation of well organized structures, patterns, or behaviors, from random initial conditions. It is the process of macroscopic outcomes emerging from local interactions of components of the system, but the global organizational properties are not to be found at the local level. The systems used to study this phenomenon are referred to as dynamical systems: state-determined systems. They possess a large number of elements or variables, and thus very large state spaces.
Traditional framework of good science is Reductionism, in the sense that sub-parts are studied individually to understand the bigger part. However, many natural systems cannot simply be explained by a reductionist study of their parts. Self-organization is not studying the whole structure by breaking it down to smaller sub-parts which are then studied individually. The emphasis of the “self-organization” is, rather, the process of how a super macro global structure evolves from local interactions.
"The self that gets organized should not be just the language ability but the cluster of competencies through which it emerges. These probably include a variety of cognitive, social, affective, and motor skills."[27][Full citation needed] The human brains, and thus the phenomena of sensation and thought, are also under the strong influence of features of spontaneous organization in their structure. Indeed, the brain, composed of billions of neurons dynamically interacting among themselves and with the outside world, is the prototype of a complex system. A good example of self organization in linguistics is the evolution of Nicaraguan Sign Language. Examples of linguistic questions in the light of self organization are: e.g. the decentralized generation of lexical and semantic conventions in populations of agents.[28][Full citation needed][29][Full citation needed];the formation of conventionalized syntactic structures[30];[Full citation needed] the conditions under which combinatoriality, the property of systematic reuse, can be selected[31];[Full citation needed] shared inventories of vowels or syllables in groups of agents, with features of structural regularities greatly resembling those of human languages[32][Full citation needed][33][Full citation needed]

Methodology

In many complex systems in nature, there are global phenomena that are the irreducible result of local interactions between components whose individual study would not allow us to see the global properties of the whole combined system. Thus, a growing number of researchers think that many properties of language are not directly encoded by any of the components involved, but are the self-organized outcomes of the interactions of the components.
Building mathematical models in the context of research into language origins and the evolution of languages is enjoying growing popularity in the scientific community, because it is a crucial tool for studying the phenomena of language in relation to the complex interactions of its components. These systems are put to two main types of use: 1) they serve to evaluate the internal coherence of verbally expressed theories already proposed by clarifying all their hypotheses and verifying that they do indeed lead to the proposed conclusions ; 2) they serve to explore and generate new theories, which themselves often appear when one simply tries to build an artificial system reproducing the verbal behavior of humans.
Therefore, constructing operational models to test hypothesis in linguistics is gaining popularity these days. An operational model is one which defines the set of its assumptions explicitly and above all shows how to calculate their consequences, that is, to prove that they lead to a certain set of conclusions.

[edit] In the emergence of language

The emergence of language in the human species has been described in a game-theoretic framework based on a model of senders and receivers of information (Clark 2009[34], following Skyrms 2004[35]).[Full citation needed] The evolution of certain properties of language such as inference follow from this sort of framework (with the parameters stating that information transmitted can be partial or redundant, and the underlying assumption that the sender and receiver each want to take the action in his/her best interest) [36].[Full citation needed] Likewise, models have shown that compositionality, a central component of human language, emerges dynamically during linguistic evolution, and need not be introduced by biological evolution (Kirby 2000)[37].[Full citation needed] Tomasello (1999)[38][Full citation needed] argues that through one evolutionary step, the ability to sustain culture, the groundwork for the evolution of human language was laid. The ability to ratchet cultural advances cumulatively allowed for the complex development of human cognition unseen in other animals.

[edit] In language acquisition

Within a species' ontogeny, the acquisition of language has also been shown to self-organize. Through the ability to see others as intentional agents (theory of mind), and actions such as 'joint attention,' human children have the scaffolding they need to learn the language of those around them (Tomasello 1999)[39].[Full citation needed]

In articulatory phonology

Articulatory phonology takes the approach that speech production consists of a coordinated series of gestures, called 'constellations,' which are themselves dynamical systems. In this theory, linguistic contrast comes from the distinction between such gestural units, which can be described on a low-dimensional level in the abstract. However, these structures are necessarily context-dependent in real-time production. Thus the context-dependence emerges naturally from the dynamical systems themselves. This statement is controversial, however, as it suggests a universal phonetics which is not evident across languages[40]. Cross-linguistic patterns show that what can be treated as the same gestural units produce different contextualised patterns in different languages[41]. Articulatory Phonology fails to attend to the acoustic output of the gestures themselves (meaning that many typological patterns remain unexplained)[42]. Freedom among listeners in the weighting of perceptual cues in the acoustic signal has a more fundamental role to play in the emergence of structure[43]. The realization of the perceptual contrasts by means of articulatory movements means that articulatory considerations do play a role[44], but these are purely secondary.

In diachrony and synchrony

Several mathematical models of language change rely on self-organizing or dynamical systems. Abrams and Strogatz (2003)[45][Full citation needed] produced a model of language change that focused on “language death” - the process by which a speech community merges into the surrounding speech communities. Nakamura et al. (2008)[46][Full citation needed] proposed a variant of this model that incorporates spatial dynamics into language contact transactions in order to describe the emergence of creoles. Both of these models proceed from the assumption that language change, like any self-organizing system, is a large-scale act or entity (in this case the creation or death of a language, or changes in its boundaries) that emerges from many actions on a micro-level. The microlevel in this example is the everyday production and comprehension of language by speakers in areas of language contact.

See also

References

  1. ^ Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley-Interscience, London. ISBN 0471302805
  2. ^ Eric. Bonabeau, Marco Dorigo, and Guy Theraulaz (1999). Swarm intelligence: from natural to artificial systems. pp.9-11.
  3. ^ Ashby, W.R., (1947): Principles of the Self-Organizing Dynamic System, In: Journal of General Psychology 1947. volume 37, pages 125--128
  4. ^ 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.
  5. ^ Self-organized theory in quantum gravity
  6. ^ “Thermodynamics, Nonequilibrium,” Glansdorff, P. & Prigogine, I. The Encyclopedia of Physics, Second Edition, edited by Lerner, R. and Trigg, G., VCH Publishers, 1991. Pp. 1256-1262.
  7. ^ “Lasers,” Zeiger, H.J. and Kelley, P.L. The Encyclopedia of Physics, Second Edition, edited by Lerner, R. and Trigg, G., VCH Publishers, 1991. Pp. 614-619.
  8. ^ M. Strong (2004). "Protein Nanomachines". PLoS Biol. 2 (3): e73-e74. doi:10.1371/journal.pbio.0020073. 
  9. ^ Camazine, Deneubourg, Franks, Sneyd, Theraulaz, Bonabeau, Self-Organization in Biological Systems, Princeton University Press, 2003. ISBN 0-691-11624-5 --ISBN 0-691-01211-3 (pbk.) p. 8
  10. ^ Daniel Dennett (1995), Darwin's Dangerous Idea, Penguin Books, London, ISBN 978-0-14-016734-4, ISBN 0-14-016734-X
  11. ^ The mathematics of self-organising systems. Recent developments in information and decision processes, Macmillan, N. Y., 1962.
  12. ^ Cybernetics, or control and communication in the animal and the machine, The MIT Press, Cambridge, Mass. and Wiley, N.Y., 1948. 2nd Edition 1962 "Chapter X "Brain Waves and Self-Organizing Systems"pp 201-202.
  13. ^ "Design for a Brain" Chapter 5 Chapman & Hall (1952) and "An Introduction to Cybernetics" Chapman & Hall (1956)
  14. ^ "An Introduction to Cybernetics" Part Two Chapman & Hall (1956)
  15. ^ Conant and Ashby Int. J. Systems Sci., 1970, vol 1, No 2, pp89-97 and in "Mechanisms of Intelligence" ed Roger Conant Intersystems Publications (1981)
  16. ^ "Embodiments of Mind MIT Press (1965)"
  17. ^ "A Predictive Model for Self-Organizing Systems", Part I: Cybernetica 3, pp. 258–300; Part II: Cybernetica 4, pp. 20–55, 1961 with Gordon Pask.
  18. ^ "Brain of the Firm" Alan Lane (1972) see also Viable System Model also in "Beyond Dispute " Wiley Stafford Beer 1994 "Redundancy of Potential Command" pp157-158.
  19. ^ see "Brain.." and "Beyond Dispute"
  20. ^ * 1996, Heinz von Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories, Systems Research (1996) 13, 3, pp. 349-362
  21. ^ "Conversation, Cognition and Learning" Elesevier (1976) see Glossary.
  22. ^ "On Gordon Pask" Nick Green in "Gordon Pask remembered and celebrated: Part I" Kybernetes 30, 5/6, 2001 p 676 (a.k.a. Pask's self-described "Last Theorem")
  23. ^ proof para. 188 Pask (1992) and postulates 15-18 in Pask (1996)
  24. ^ cmol.nbi.dk Interactive models
  25. ^ "The Self Organizing Economy". 1996. http://www.amazon.com/Self-Organizing-Economy-Paul-R-Krugman/dp/1557866996
  26. ^ de Boer, B, 1998
  27. ^ Wimsatt, p. 232, Cycles of Contingency
  28. ^ Steels, 1997
  29. ^ Kaplan, 2001
  30. ^ Batali, 1998
  31. ^ Kirby, 1998
  32. ^ de Boer, 2001
  33. ^ Oudeyer, 2001
  34. ^ Clark 2009
  35. ^ Skyrms 2004
  36. ^ (Skyrms 2004)
  37. ^ Kirby 2000
  38. ^ Tomasello (1999)
  39. ^ Tomasello 1999
  40. ^ Sole, M-J. (1992). "Phonetic and phonological processes: nasalization." Language & Speech 35: 29-43
  41. ^ Ladefoged, Peter (2003). "Commentary: some thoughts on syllables - an old-fashioned interlude." In Local, John, Richard Ogden & Ros Temple (eds.). Papers in laboratory Phonology VICambridge University Press: 269-276.
  42. ^ see papers in Phonetica 49, 1992, special issue on Articulatory Phonology
  43. ^ Ohala, John J. (1996) "Speech perception is hearing sounds, not tongues." Journal of the Acoustical Society of America 99: 1718-1725.
  44. ^ Lindblom, B. (1999). "Emergent phonology.", doi=10.1.1.10.9538
  45. ^ Abrams and Strogatz (2003)
  46. ^ Nakamura et al. (2008)

Further reading

  • W. Ross Ashby (1947), "Principles of the Self-Organizing Dynamic System", Journal of General Psychology Vol 37, pp. 125–128.
  • W. Ross Ashby (1966), Design for a Brain, Chapman & Hall, 2nd edition.
  • Per Bak (1996), How Nature Works: The Science of Self-Organized Criticality, Copernicus Books.
  • Philip Ball (1999), The Self-Made Tapestry: Pattern Formation in Nature, Oxford University Press.
  • Stafford Beer, Self-organization as autonomy: Brain of the Firm 2nd edition Wiley 1981 and Beyond Dispute Wiley 1994.
  • A. Bejan (2000), Shape and Structure, from Engineering to Nature , Cambridge University Press, Cambridge, UK, 324 pp.
  • Mark Buchanan (2002), Nexus: Small Worlds and the Groundbreaking Theory of Networks W. W. Norton & Company.
  • Scott Camazine, Jean-Louis Deneubourg, Nigel R. Franks, James Sneyd, Guy Theraulaz, & Eric Bonabeau (2001) Self-Organization in Biological Systems, Princeton Univ Press.
  • Falko Dressler (2007), Self-Organization in Sensor and Actor Networks, Wiley & Sons.
  • Manfred Eigen and Peter Schuster (1979), The Hypercycle: A principle of natural self-organization, Springer.
  • Myrna Estep (2003), A Theory of Immediate Awareness: Self-Organization and Adaptation in Natural Intelligence, Kluwer Academic Publishers.
  • Myrna L. Estep (2006), Self-Organizing Natural Intelligence: Issues of Knowing, Meaning, and Complexity, Springer-Verlag.
  • J. Doyne Farmer et al. (editors) (1986), "Evolution, Games, and Learning: Models for Adaptation in Machines and Nature", in: Physica D, Vol 22.
  • Heinz von Foerster and George W. Zopf, Jr. (eds.) (1962), Principles of Self-Organization (Sponsored by Information Systems Branch, U.S. Office of Naval Research.
  • "Aeshchines" (false identity made in reference to the classical Greek orator Aeschines) (2007). "The Open Source Manifesto" the self organization of economic and geopolitical structure through the Open Source movement permanent link at Sourceforge.net
  • Carlos Gershenson and Francis Heylighen (2003). "When Can we Call a System Self-organizing?" In Banzhaf, W, T. Christaller, P. Dittrich, J. T. Kim, and J. Ziegler, Advances in Artificial Life, 7th European Conference, ECAL 2003, Dortmund, Germany, pp. 606–614. LNAI 2801. Springer.
  • Hermann Haken (1983) Synergetics: An Introduction. Nonequilibrium Phase Transition and Self-Organization in Physics, Chemistry, and Biology, Third Revised and Enlarged Edition, Springer-Verlag.
  • F.A. Hayek Law, Legislation and Liberty, RKP, UK.
  • Francis Heylighen (2001): "The Science of Self-organization and Adaptivity".
  • Henrik Jeldtoft Jensen (1998), Self-Organized Criticality: Emergent Complex Behaviour in Physical and Biological Systems, Cambridge Lecture Notes in Physics 10, Cambridge University Press.
  • Steven Berlin Johnson (2001), Emergence: The Connected Lives of Ants, Brains, Cities and Software.
  • Stuart Kauffman (1995), At Home in the Universe, Oxford University Press.
  • Stuart Kauffman (1993), Origins of Order: Self-Organization and Selection in Evolution Oxford University Press.
  • J. A. Scott Kelso (1995), Dynamic Patterns: The self-organization of brain and behavior, The MIT Press, Cambridge, MA.
  • J. A. Scott Kelso & David A Engstrom (2006), "The Complementary Nature", The MIT Press, Cambridge, MA.
  • Alex Kentsis (2004), Self-organization of biological systems: Protein folding and supramolecular assembly, Ph.D. Thesis, New York University.
  • E.V.Krishnamurthy(2009)," Multiset of Agents in a Network for Simulation of Complex Systems", in "Recent advances in Nonlinear Dynamics and synchronization, ,(NDS-1) -Theory and applications, Springer Verlag, New York,2009. Eds. K.Kyamakya et al.
  • Paul Krugman (1996), The Self-Organizing Economy, Cambridge, Mass., and Oxford: Blackwell Publishers.
  • Niklas Luhmann (1995) Social Systems. Stanford, CA: Stanford University Press.
  • Elizabeth McMillan (2004) "Complexity, Organizations and Change".
  • Marshall, A (2002) The Unity of Nature, Imperial College Press: London (esp. chapter 5)
  • Müller, J.-A., Lemke, F. (2000), Self-Organizing Data Mining.
  • Gregoire Nicolis and Ilya Prigogine (1977) Self-Organization in Non-Equilibrium Systems, Wiley.
  • Heinz Pagels (1988), The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity, Simon & Schuster.
  • Gordon Pask (1961), The cybernetics of evolutionary processes and of self organizing systems, 3rd. International Congress on Cybernetics, Namur, Association Internationale de Cybernetique.
  • Gordon Pask (1993) Interactions of Actors (IA), Theory and Some Applications, Download incomplete 90 page manuscript.
  • Gordon Pask (1996) Heinz von Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories, Systems Research (1996) 13, 3, pp. 349–362
  • Christian Prehofer ea. (2005), "Self-Organization in Communication Networks: Principles and Design Paradigms", in: IEEE Communications Magazine, July 2005.
  • Mitchell Resnick (1994), Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds, Complex Adaptive Systems series, MIT Press.
  • Lee Smolin (1997), The Life of the Cosmos Oxford University Press.
  • Ricard V. Solé and Brian C. Goodwin (2001), Signs of Life: How Complexity Pervades Biology, Basic Books.
  • Ricard V. Solé and Jordi Bascompte (2006), Selforganization in Complex Ecosystems, Princeton U. Press
  • Steven Strogatz (2004), Sync: The Emerging Science of Spontaneous Order, Theia.
  • D'Arcy Thompson (1917), On Growth and Form, Cambridge University Press, 1992 Dover Publications edition.
  • Norbert Wiener (1962), The mathematics of self-organising systems. Recent developments in information and decision processes, Macmillan, N. Y. and Chapter X in Cybernetics, or control and communication in the animal and the machine, The MIT Press, 2nd Edition 1962
  • Tom De Wolf, Tom Holvoet (2005), 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.
  • Tsekeris, Charalambos and Konstantinos Koskinas (2010) "A Weak Reflection on Unpredictability and Social Theory", tripleC – Cognition, Communication, Co-operation: Open Access Journal for a Global Sustainable Information Society, 8, 1, pp. 36-42.
  • K. Yee (2003), "Ownership and Trade from Evolutionary Games," International Review of Law and Economics, 23.2, 183-197.
  • Louise B. Young (2002), The Unfinished Universe
  • Mikhail Prokopenko (ed.) (2008), Advances in Applied Self-organizing Systems, Springer.

[edit] External links

Dissertations and Theses on Self-organization
Retrieved from "http://en.wikipedia.org/wiki/Self-organization"
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Sunday, June 27, 2010

Virasoro algebra

Black hole thermodynamics

From Wikipedia, the free encyclopedia

In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.

 It is important that ones is able to see the progression from abstraction to a interpretation of foundational approach.

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Andy Strominger:
This was a field theory that lived on a circle, which means it has one spatial dimension and one time dimension. We derived the fact that the quantum states of the black hole could be represented as the quantum states of this one-plus-one dimensional quantum field theory, and then we counted the states of this theory and found they exactly agreed with the Bekenstein-Hawking entropy.See:Quantum Microstates: Gas Molecules in the Presence of a Gravitational Field

See:Microscopic Origin of the Bekenstein-Hawking Entropy

Of course I am interested the mathematical framework as it might be compared to some phenomenological approach that gives substance to any theoretical thought.

For example, Tommaso Dorigo is a representative of the type of people who may affect the general distribution of "subjects" that may grow at CERN or the Fermilab in the next decade or two. And he just published a quote by Sherlock Holmes - no kidding - whose main point is that it is a "capital mistake" to work on any theory before the data are observed.See:Quantum gravity: minority report

I think you were a little harsh on Tommaso Dorigo  Lubos because he is really helping us to understand the scientific process at Cern. But you are right about theory in my mind, before the phenomenological approach can be seen. The mind need to play creatively in the abstract notions before it can be seen in it's correlations in reality.

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Virasoro algebra

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Group theory
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Group theory
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In mathematics, the Virasoro algebra (named after the physicist Miguel Angel Virasoro) is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in string theory.

Contents

Definition

The Virasoro algebra is spanned by elements
Li for i\in\mathbf{Z}
and c with
Ln + L − n
and c being real elements. Here the central element c is the central charge. The algebra satisfies
[c,Ln] = 0
and
[L_m,L_n]=(m-n)L_{m+n}+\frac{c}{12}(m^3-m)\delta_{m+n}.
The factor of 1/12 is merely a matter of convention.
The Virasoro algebra is a central extension of the (complex) Witt algebra of complex polynomial vector fields on the circle. The Lie algebra of real polynomial vector fields on the circle is a dense subalgebra of the Lie algebra of diffeomorphisms of the circle.
The Virasoro algebra is obeyed by the stress tensor in string theory, since it comprises the generators of the conformal group of the worldsheet, obeys the commutation relations of (two copies of) the Virasoro algebra. This is because the conformal group decomposes into separate diffeomorphisms of the forward and back lightcones. Diffeomorphism invariance of the worldsheet implies additionally that the stress tensor vanishes. This is known as the Virasoro constraint, and in the quantum theory, cannot be applied to all the states in the theory, but rather only on the physical states (confer Gupta-Bleuler quantization).

Representation theory

A lowest weight representation of the Virasoro algebra is a representation generated by a vector v that is killed by Li for i ≥1 , and is an eigenvector of L0 and c. The letters h and c are usually used for the eigenvalues of L0 and c on v. (The same letter c is used for both the element c of the Virasoro algebra and its eigenvalue.) For every pair of complex numbers h and c there is a unique irreducible lowest weight representation with these eigenvalues.
A lowest weight representation is called unitary if it has a positive definite inner product such that the adjoint of Ln is L−n. The irreducible lowest weight representation with eigenvalues h and c is unitary if and only if either c≥1 and h≥0, or c is one of the values
c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots
for m = 2, 3, 4, .... and h is one of the values
h = h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}
for r = 1, 2, 3, ..., m−1 and s= 1, 2, 3, ..., r. Daniel Friedan, Zongan Qiu, and Stephen Shenker (1984) showed that these conditions are necessary, and Peter Goddard, Adrian Kent and David Olive (1986) used the coset construction or GKO construction (identifying unitary representations of the Virasoro algebra within tensor products of unitary representations of affine Kac-Moody algebras) to show that they are sufficient. The unitary irreducible lowest weight representations with c < 1 are called the discrete series representations of the Virasoro algebra. These are special cases of the representations with m = q/(p−q), 0<r<q, 0< s<p for p and q coprime integers and r and s integers, called the minimal models and first studied in Belavin et al. (1984).
The first few discrete series representations are given by:
  • m = 2: c = 0, h = 0. The trivial representation.
  • m = 3: c = 1/2, h = 0, 1/16, 1/2. These 3 representations are related to the Ising model
  • m = 4: c = 7/10. h = 0, 3/80, 1/10, 7/16, 3/5, 3/2. These 6 representations are related to the tri critical Ising model.
  • m = 5: c = 4/5. There are 10 representations, which are related to the 3-state Potts model.
  • m = 6: c = 6/7. There are 15 representations, which are related to the tri critical 3-state Potts model.
The lowest weight representations that are not irreducible can be read off from the Kac determinant formula, which states that the determinant of the invariant inner product on the degree h+N piece of the lowest weight module with eigenvalues c and h is given by
A_N\prod_{1\le r,s\le N}(h-h_{r,s}(c))^{p(N-rs)}
which was stated by V. Kac (1978), (see also Kac and Raina 1987) and whose first published proof was given by Feigin and Fuks (1984). (The function p(N) is the partition function, and AN is some constant.) The reducible highest weight representations are the representations with h and c given in terms of m, c, and h by the formulas above, except that m is not restricted to be an integer ≥ 2 and may be any number other than 0 and 1, and r and s may be any positive integers. This result was used by Feigin and Fuks to find the characters of all irreducible lowest weight representations.

Generalizations

There are two supersymmetric N=1 extensions of the Virasoro algebra, called the Neveu-Schwarz algebra and the Ramond algebra. Their theory is similar to that of the Virasoro algebra.
The Virasoro algebra is a central extension of the Lie algebra of meromorphic vector fields on a genus 0 Riemann surface that are holomorphic except at two fixed points. I.V. Krichever and S.P. Novikov (1987) found a central extension of the Lie algebra of meromorphic vector fields on a higher genus compact Riemann surface that are holomorphic except at two fixed points, and M. Schlichenmaier (1993) extended this to the case of more than two points.

History

The Witt algebra (the Virasoro algebra without the central extension) was discovered by E. Cartan (1909). Its analogues over finite fields were studied by E. Witt in about the 1930s. The central extension of the Witt algebra that gives the Virasoro algebra was first found (in characteristic p>0) by R. E. Block (1966, page 381) and independently rediscovered (in characteristic 0) by I. M. Gelfand and D. B. Fuks (1968). Virasoro (1970) wrote down some operators generating the Virasoso algebra while studying dual resonance models, though he did not find the central extension. The central extension giving the Virasoro algebra was rediscovered in physics shortly after by J. H. Weis, according to Brower and Thorn (1971, footnote on page 167).

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Wednesday, June 23, 2010

Stephen Hawking At PI Institute



Waterloo, Ontario, Canada, June 20, 2010 - In a public address before a packed audience at Perimeter Institute for Theoretical Physics (PI), Prof. Stephen Hawking, PI Distinguished Research Chair, recounted his research, life and times, saying that it has been a glorious period to contribute to our picture of the universe. Prof. Hawking is conducting private research activities at PI this summer, in what is expected to be the first of many visits.  

See: Stephen Hawking on Perimeter Institute and Special Places & Times for Scientific Progress

About TVO

TVO is Ontario's public educational media organization and a trusted source of interactive educational content that informs, inspires and stimulates curiosity and thought. TVO's vision is to empower people to be engaged citizens through educational media. The TVO signal can be found across Canada on Bell TV channel 265 or Shaw Direct channel 353. You will also find TVO on channel 2 via cable or over-the-air in most areas of Ontario.


Prof. Hawking's lecture will air on TVO on:
     - Sunday, June 20 at 8:00 pm and
       12:30 am EDT
     - Saturday, June 26 at 6:00 pm EDT
     - Sunday, June 27 at 5:00 pm EDT
     - Tuesday, July 6 at 10:00 pm EDT
TVO is viewable across Canada on Bell TV channel 265, Shaw Direct channel 353, and channel 2 in most areas of Ontario. 
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