Self-organization

Self-organization is a process where some form of overall order or coordination arises out of the local interactions between smaller component parts of an initially disordered system. The process of self-organization can be spontaneous, and it is not necessarily controlled by any auxiliary agent outside of the system. It is often triggered by random fluctuations that are amplified by positive feedback. The resulting organization is wholly decentralized or distributed over all the components of the system. As such, the organization is typically robust and able to survive and, even, self-repair substantial damage or perturbations. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization occurs in a variety of physical, chemical, biological, robotic, social, and cognitive systems. Examples of its realization can be found in crystallization, thermal convection of fluids, chemical oscillation, animal swarming, and artificial and biological neural networks.

Overview

Self-organization is realized^[2] in the physics of non-equilibrium processes, and in chemical reactions, where it is often described as self-assembly. The concept of self-organization has proven useful in the description of biological systems,^[3] from the subcellular to the ecosystem level.^[4] Cited examples of self-organizing behaviour also appear in the literature of many other disciplines, both in the natural sciences and in the social sciences such as economics or anthropology. Self-organization has also been observed in mathematical systems such as cellular automata.^[5] Sometimes the notion of self-organization becomes conflated with that of the related concept of emergence.^[6] Properly defined, however, there may be instances of self-organization without emergence and emergence without self-organization.

Self-organization usually relies on three basic ingredients:^[7]

1. strong dynamical non-linearity, often though not necessarily involving positive and negative feedback
2. balance of exploitation and exploration
3. multiple interactions

Principles of self-organization

The cybernetician William Ross Ashby formulated the original principle of self-organization in 1947.^[8][9] It states that any deterministic dynamic system will automatically evolve towards a state of equilibrium that can be described in terms of an attractor in a basin of surrounding states. Once there, the further evolution of the system is constrained to remain in the attractor. This constraint on the system as a whole implies a form of mutual dependency or coordination between its constituent components or "subsystems". In Ashby's terms, each subsystem has adapted to the environment formed by all other subsystems.

The cybernetician Heinz von Foerster formulated the principle of "order from noise" in 1960.^[10] It notes that self-organization is facilitated by random perturbations ("noise") that let the system explore a variety of states in its state space. This increases the chance that the system would arrive into the basin of a "strong" or "deep" attractor, from which it would then quickly enter the attractor itself. The thermodynamicist Ilya Prigogine formulated a similar principle as "order through fluctuations"^[11] or "order out of chaos".^[12] It is applied in the method of simulated annealing that is used in problem solving and in machine learning.

History of the idea

The idea that the dynamics of a system can lead to an increase of the system's organization 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 his unpublished work The World.

The ancient atomists believed that a designing intelligence is unnecessary to effect natural order, arguing that given enough time and space and matter, organization is ultimately inevitable, although there is 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 Aram Vartanian, Diderot and Descartes).

The economic concept of the "invisible hand" due to Adam Smith can be understood as an attempt to describe the influence of the market as a spontaneous order on people's actions.

Beginning with the 18th century, natural scientists 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.

Sadi Carnot and Rudolf Clausius discovered the Second Law of Thermodynamics in the 19th century. It states that total entropy, sometimes understood as disorder, will always increase over time in an isolated system. This means that a system cannot spontaneously increase its order, without an external relationship that decreases order elsewhere in the system (e.g. through consuming the low-entropy energy of a battery and diffusing high-entropy heat).

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.^[8] It was taken up by the cyberneticians Heinz von Foerster, Gordon Pask, Stafford Beer, and von Foerster organized a conference on "The Principles of Self-Organization" at the University of Illinois' Allerton Park in June, 1960 which led to a series of conferences on Self-Organizing Systems.^[13] Norbert Wiener also took up the idea in the second edition of his Cybernetics: or Control and Communication in the Animal and the Machine (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.^[14] After Ilya Prigogine's 1977 Nobel Prize, the thermodynamic concept of self-organization received some attention of the public, and scientific researchers started to migrate from the cybernetic view to the thermodynamic view.^[15]

Developing views

Other views of self-organization in physical systems interpret it as a strictly accumulative construction process, commonly displaying an "S" curve history of development. As discussed somewhat differently by different researchers, local complex systems for exploiting energy gradients evolve from seeds of organization, through a succession of natural starting and ending phases for inverting their directions of development. The accumulation of working processes which their exploratory parts construct as they exploit their gradient becomes the "learning", "organization" or "design" of the system as a physical artifact, such for an ecology or economy. For example, A. Bejan's books and papers describe his approach as "Constructal Theory".^[16][17][18] P. F. Henshaw's work on decoding net-energy system construction processes termed "Natural Systems Theory", uses various analytical methods to quantify and map them such as System Energy Assessment^[19] for taking true quantitative measures of whole complex energy using systems, and for anticipating their successions, such as Models Learning Change^[20] to permit adapting models to their emerging inverted designs. G. Y. Georgiev's work is utilizing the principle of least (stationary) action in Physics, to define organization of a complex system as the state of the constraints determining the total action of the elements in a system. Organization is then defined numerically as the reciprocal of the average action per one element and one edge crossing, if the system is described as a network. The elementary quantum of action, Planck's constant, is used to make the measure dimensionless and to define it as inversely proportional to the number of quanta of action expended by the elements for one edge crossing. The mechanism of self-organization is the interaction between the elements and the constraints, which leads to constraint minimization. This is consistent with the Gauss principle of least constraint. More elements minimize the constraints faster, another aspect of the mechanism, which is through quantity accumulation. As a result, the paths of the elements are straightened, which is consistent with Hertz's principle of least curvature. The state of a system with least average sum of actions of its elements is defined as its attractor. In open systems, where there is constant inflow and outflow of energy and elements, this final state is never reached, but the system always tends toward it.^[15] This method can help describe, quantify, manage, design and predict future behavior of complex systems, to achieve the highest rates of self-organization to improve their quality, which is the numerical value of their organization. It can be applied to complex systems in physics, chemistry, biology, ecology, economics, cities, network theory and others, where they are present.^[15][21][22]

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.

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.

Physics

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

• 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 transition, associated with "critical points" at which the system exhibits scale-invariant structures. 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 of Prigogine and Hermann Haken's Synergetics were developed to unify the understanding of these phenomena, which include lasers, turbulence and convective instabilities (e.g., Bénard cells) in fluid dynamics,
  • structure formation in astrophysics and cosmology (including star formation, planetary systems formation, galaxy formation)
  • self-similar expansion
  • Diffusion-limited aggregation
  • 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 tribology, friction coupled with other simultaneous effects, such as heat transfer, wear, and material diffusion. can lead to self-organized patterns at the frictional interface, ranging from stick-slip patterns to in-situ formed tribofilms and surface roughness adjustment of two materials in contact.
• 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.^[23]
• 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."^[24]

Chemistry

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. grid complexes
6. colloidal crystals
7. self-assembled monolayers
8. micelles
9. microphase separation of block copolymers
10. Langmuir-Blodgett films

Biology

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.[26]

”

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)

Computer science

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.

Algorithms

Many optimization algorithms can be considered as a self-organization system because the aim of the optimization is to find the optimal solution to a problem. If the solution is considered as a state of the iterative system, the optimal solution is essentially the selected, converged state or structure of the system, driven by the algorithm based on the system landscape.^[28][29] In fact, one can view all optimization algorithms as a self-organization system.

Networks

Self-organization is an important component for a successful ability to establish networking whenever needed. Such mechanisms are also referred to as Self-organizing networks. Intensified work in the latter half of the first decade of the 21st century was mainly due to interest from the wireless communications industry. It is driven by the plug and play paradigm, and that wireless networks need to be relatively simpler to manage than they used to be.

Only certain kinds of networks are self-organizing. The best known examples are small-world networks and scale-free networks. These emerge from bottom-up interactions, and appear to be limitless in size. In contrast, there are top-down hierarchical networks, which are not self-organizing. These are typical of organizations, and have severe size limits.

In many natural systems, self-organization results from repeated phase shifts in their underlying network of connections. Such phase shifts alter the balance between internal processes (e.g. selection and variation). They give rise to the phenomenon of dual-phase evolution.

Cloud Computing

Some scholars posit that that cloud computing systems are inherently self-organising^[30] and, while they exhibit autonomic features, are not self-managing as they do not have reducing complexity as a goal. Others argue that cloud computing represents a complex system and therefore self-organisation is an appropriate technique to address this complexity.^[31][32] The European Union, through Horizon 2020, has recently funded CloudLightning, a Research Innovation Action. This project seeks to build a next generation cloud architecture based on the principles of decentralisation, self-organisation and self-management. Self organisation is used to manage complexity effectively and tackle the challenges of providing a Services Oriented Architecture that accommodates heterogeneous resources.

Cybernetics

Norbert Wiener regarded the automatic serial identification of a black box and its subsequent reproduction as sufficient to meet the condition of self-organization.^[33] The importance of phase locking or the "attraction of frequencies", as he called it, is discussed in the 2nd edition of his "Cybernetics".^[34] K. Eric 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.^[35] Ashby used his state counting measure of variety^[36] to describe stable states and produced the "Good Regulator"^[37] theorem which requires internal models for self-organized endurance and stability (e.g. Nyquist stability criterion).

Warren McCulloch proposed "Redundancy of Potential Command"^[38] 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/H_max, where H is entropy.^[39][40] 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 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 alerting "algedonic loop" feedback: a sensitivity to both pain and pleasure produced from under-performance or over-performance relative to a standard capability.^[41]

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^[42] (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"^[43] permitted his theorem "Like concepts repel, unlike concepts attract"^[44] to state a general spin-based principle of self-organization. His edict, an exclusion principle, "There are No Doppelgangers"^[45][42] means no two concepts can be the same (all interactions occur with different perspectives making time incommensurable for actors).

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, herd behaviour, groupthink and others, abound in sociology, economics, behavioral finance and anthropology.^[46] The theory of human social self-organization is also known as spontaneous order theory.

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. Luhmann developed an evolutionary theory of Society and its subsytems, using functional analyses and systems theory.^[47]

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. The Sphere College Project seeks to apply self-organization to adult education. 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.^[15]

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".^[48] Friedrich Hayek coined the term catallaxy^[49] to describe a "self-organizing system of voluntary co-operation", in regards to the spontaneous order of the free market economy. Neo-classical economists hold that imposing central planning usually makes the self-organized economic system less efficient. On the other end of the spectrum, economists consider that market failures are so significant that self-organization produces bad results and that the state should direct production and pricing. Most 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.^[15][50]

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. 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 the book The Unity of Nature by Alan Marshall).

Psychology and education

Self-organised learning

Enabling others to "learn how to learn"^[51] is usually misconstrued as instructing them^[52] how to successfully submit to being taught. Whilst fully accepting that we can always learn from others, particularly those with more and/or different experience than ourselves; self-organised learning (SOL) repudiates any idea^[53] that this reduces to accepting that "the expert knows best" or that there is ever "the one best method." It offers an alternative definition of learning as "the construction of personally significant, relevant and viable meaning."

This more democratic 'bottom up' approach to learning is to be frequently tested experientially^[54] by the learner(s) as being more "meaningful, constructive and creatively effective for me or us."

Since human learning may be achieved by one person,^[55] or groups of learners working together;^[56] SOL is not only a more rewarding and effective way of living one's personal life; it is also applicable in any group of people living, playing and/or working together.

As many young children, pupils, students and lifelong learners eventually become ruefully aware, this ‘testing out of what I have learned’ needs to be carried out in each learner(s) whole process of living, and so it extends well beyond the confines of specific learning environments (home, school, university, etc.), and eventually beyond the reaches of the controllers of these environments (parents, teachers, employers, etc.)^[57]

SOL needs to be tested, and intermittently revised, through the ongoing personal experience^[58] of the learner(s) themselves in their ever-expanding outer and inner lives.

Whilst internal life may cease to expand, the external environment does not. If a learner allows themselves to become progressively more other-organised, they become less able to recognise and respond to varying needs for change. Unfortunately this is often the current reported experience of many during, and hence after their parenting, schooling and/or higher education.

But, this SOL way of understanding the learning process need not be restricted by either consciousness or language.^[59] Nor is it restricted to humans, since analogous directional self-organizing (learning?) processes are reported variously within the life sciences and even within the less-living sciences, for example, of physics and chemistry: (as is clearly articulated in other sections of this 'Self-organization' Section).

Since SOL is as yet only very superficially recognised within psychology and education, it is useful to place it more firmly within the human public mind-pool^[60] of achievement, knowledge, experience and understanding. SOL can also be placed within a hierarchy of scientific explanatory concepts, for example:

1. Cause and Effect (requires "other things being equal")
2. Cybernetics^[43] (incorporates item 1 in this list) with greater complexity, providing internal feedback and feed-forward controls: but still implying a sealed boundary. (i.e. other things being equal)
3. Systems Theory^[61] (incorporates item 2 in this list, and opens the boundaries)
4. Self-organized System (incorporates item 3 in this list) and attributes this property to the interaction, patterning and coordination among the sub-systems of the system in question; in response to flow across its boundaries
5. Self-Organised Learning (SOL)^[62] (incorporates item 4 in this list) but also requires that the parts each systematically respond, change and develop in the light of their experience, whilst self-organizing in the developing experiential interest of the whole).
   SOL not only involves self-organization of the first order, i.e. what is mostly experienced as learning from experience without much conscious awareness of the process. At a second level of SOL consciousness enables us, (possibly uniquely among living beings) to reflect upon and thus self-organise the very process of self-organisation itself, (See 'Cybernetic algorithm' figure). It also enables organisations small and large to self-organise themselves, (see 'System algorithm' figure).
   Once this approach to human learning is acknowledged, then we can re-set science into its place within the total human mind-pool. A mind-pool of human know-how and feel-how as an ever expanding and hopefully self-organizing resource.
6. Learning Conversation (incorporates item 5 in this list) and yet is at the same time its major tool. The Learning Conversation is a two-way process between SOLers, even within one person (conversing with oneself). Whilst not necessarily requiring language i.e. dialogue; it does require that the each participant really attempts to represent their meaning to the other(s), and that they all attempt to create personally significant, relevant and viable meaning in themselves in response to the others representations. So art, drama, music, computer programs, maths problems, ???, etc., can all create different, if limited, forms of Learning Conversation which really only become fully functional when at least two humans really attempt to fully communicate, and effectively share their understanding. That is achieve shared meaning in an event that approximates to what Maslow called a creative encounter^[63]
7. Conversational Science^[64] (will require item 6 in this list, the main method of SOL) among all seekers after significant, relevant and viable shared meaning. Science and many other human activities still need major paradigm shifts if we are to achieve Self-Organised Living. It also requires equal stakeholder-ship for each converser. Thus SOL can be seen as necessary but not sufficient for science to contribute positively to the benefit of the society, within which it may have only spasmodically been conversing successfully (SOL wise). Until, perhaps, both science and society as a whole will become Self-Organised Learners (SOLers) continually learning from their own shared experience and using what they learn in the shared interest of all concerned.

Traffic flow

The self-organizing behavior of drivers in traffic flow determines almost all traffic spatiotemporal phenomena observed in real traffic data, such as traffic breakdown at a highway bottleneck, highway capacity, the emergence of moving traffic jams, etc. Self-organization in traffic flow is an extremely complex spatiotemporal dynamic process. For this reason, only in 1996–2002 did spatiotemporal self-organization effects in traffic become understood in real measured traffic data and explained by Boris Kerner's three-phase traffic theory.

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.

As it were, the construction of operational models to test proposed hypotheses in linguistics is gaining much contemporary attention. 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.

In the emergence of language

Investigators have examined the emergence of language in the human species in a game-theoretic framework^[65] based on a model of senders and receivers of information. 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 their own best interest). 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. Tomasello (1999) argues that one evolutionary step, the ability to sustain culture, laid the groundwork for the evolution of human language.^[66] The ability to ratchet cultural advances cumulatively allowed for the complex development of human cognition not seen in other animals.

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.

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.^[67] Cross-linguistic patterns show that what can be treated as the same gestural units produce different contextualised patterns in different languages.^[68] Articulatory Phonology fails to attend to the acoustic output of the gestures themselves (meaning that many typological patterns remain unexplained).^[69] 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.^[70] The realization of the perceptual contrasts by means of articulatory movements means that articulatory considerations do play a role,^[71] 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) 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) 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.

Criticism

Heinz Pagels, in a balanced, but ultimately negative 1985 book review of Ilya Prigogine and Isabelle Stengers' Order Out of Chaos in Physics Today, appeals to authority:^[72]

“

Most scientists would agree with the critical view expressed in Problems of Biological Physics (Springer Verlag, 1981) by the biophysicist L. A. Blumenfeld, when he wrote: "The meaningful macroscopic ordering of biological structure does not arise due to the increase of certain parameters or a system above their critical values. These structures are built according to program-like complicated architectural structures, the meaningful information created during many billions of years of chemical and biological evolution being used." Life is a consequence of microscopic, not macroscopic, organization.

”

“

In short, they [Prigogine and Stengers] maintain that time irreversibility is not derived from a time-independent microworld, but is itself fundamental. The virtue of their idea is that it resolves what they perceive as a "clash of doctrines" about the nature of time in physics. Most physicists would agree that there is neither empirical evidence to support their view, nor is there a mathematical necessity for it. There is no "clash of doctrines." Only Prigogine and a few colleagues hold to these speculations which, in spite of their efforts, continue to live in the twilight zone of scientific credibility.

”

In theology, Thomas Aquinas (1225–1274) in his Summa Theologica assumes a teleological created universe in rejecting the idea that something can be a self-sufficient cause of its own organization:^[73]

“

Since nature works for a determinate end under the direction of a higher agent, whatever is done by nature must needs be traced back to God, as to its first cause. So also whatever is done voluntarily must also be traced back to some higher cause other than human reason or will, since these can change or fail; for all things that are changeable and capable of defect must be traced back to an immovable and self-necessary first principle, as was shown in the body of the Article.

”

("The body of the Article" consists of the quinque viae.)

See also

References

Further reading

External links

Dissertations and theses on self-organization