chaos system sience 1273 words

Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[17]
0. it must be sensitive to initial conditions,
0. it must be topologically mixing, and
0. its periodic orbits must be dense.
[edit]
Sensitivity to initial conditions
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by ot...

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftersho...

The Systems psychology includes an illusion of homeostatic systems, although most of the living systems are in a continuous disequilibrium of various degrees.
[edit]
See also
.

In the 1880s, while studying the three-body problem, he found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point.[28][29]

He constructed a general theory of living systems by focusing on concrete systems—nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components.

At first the domains of work of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems analysis.

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

Since the beginning of chaos theory when Edward Lorenz accidentally discovered a strange attractor with his computer, computers have become an indispensable source of information.

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

Quantitatively, two trajectories in phase space with initial separation diverge

where λ is the Lyapunov exponent.

There will always be some form of corrupting noise, even if it is present as round-off or truncation error.

An easy way to visualize a chaotic attractor is to start with a point in the basin of attraction of the attractor, and then simply plot its subsequent orbit.

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

It is interesting that the most practically significant condition, that of sensitivity to initial conditions, is actually redundant in the definition, being implied by two (or for intervals, one) purely topological conditions, which are therefore of greater interest to mathematicians.

Cybernetics
Nullste. 3.3

The year before, Benoît Mandelbrot found recurring patterns at every scale in data on cotton prices.[39]

Since the beginning of chaos theory when Edward Lorenz accidentally discovered a strange attractor with his computer, computers have become an indispensable source of information.

This happens even though these systems are deterministic, meaning that their future dynamics are fully determined by their initial conditions, with no random elements involved.

Topological mixing (or topological transitivity) means that the system will evolve over time so that any given region or open set of its phase space will eventually overlap with any other given region.

In 1975 Mandelbrot published The Fractal Geometry of Nature, which became a classic of chaos theory.

Linear systems are never chaotic; for a dynamical system to display chaotic behaviour it has to be nonlinear.

Both strange attractors and Julia sets typically have a fractal structure, and a fractal dimension can be calculated for them.
[edit]
Minimum complexity of a chaotic system


Bifurcation diagram of the logistic map x → r x (1 – x).

All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[54][55]

A system from this frame of reference is composed of regularly interacting or interrelating groups of activities.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

Much of the earlier theory was developed almost entirely by mathematicians, under the name of ergodic theory.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

Arguing that a ball of twine appears to be a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be fractional.

All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[54][55]

The year before, Benoît Mandelbrot found recurring patterns at every scale in data on cotton prices.[39]

Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behaviour.

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

According to Miller's original conception as spelled out in his magnum opus Living Systems, a "living system" must contain each of 20 "critical subsystems", which are defined by their functions and visible in numerous systems, from simple cells to organisms, countries, and societies.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[40]

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

The one-dimensional logistic map defined by x → 4 x (1 – x) is one of the simplest systems with density of periodic orbits.

It is an approach in psychology, in which groups and individuals, are considered as systems in homeostasis.

The correspondence principle states that classical mechanics is a special case of quantum mechanics, the classical limit.

This sensitivity is popularly referred to as the butterfly effect.

However, the Poincaré-Bendixson theorem shows that a strange attractor can only arise in a continuous dynamical system (specified by differential equations) if it has three or more dimensions.

Currently, chaos theory continues to be a very active area of research, involving many different disciplines (mathematics, topology, physics, population biology, biology, meteorology, astrophysics, information theory, etc.).
[edit]
Distinguishing random from chaotic data
It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.'

The Lorenz attractor discussed above is generated by a system of three differential equations with a total of seven terms on the right hand side, five of which are linear terms and two of which are quadratic (and therefore nonlinear).

Systems theory first originated in biology in the 1920s out of the need to explain the interrelatedness of organisms in ecosystems.[1]

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

Organizational theory
. 4.3

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

This led to a renewed of physiology in the 1980s through the application of chaos theory, for example in the study of pathological cardiac cycles.

However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Health Informatics: Concepts of Information Technology in Health and Human Services.

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1]

The reason is, simply put, that solutions to such systems are asymptotic to a two dimensional surface and therefore solutions are well behaved.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

Aleksandr Lyapunov and Jules Henri Poincaré worked on the foundations of chaos theory without any computer at all.

Here the blue region is transformed by the dynamics first to the purple region, then to the pink and red regions, and eventually to a cloud of points scattered across the space.

Systematics - study of multi-term systems
[edit]
References
0.

The one-dimensional logistic map defined by x → 4 x (1 – x) is one of the simplest systems with density of periodic orbits.

Furthermore, the noise is amplified due to the inherent non-linearity and reveals totally new dynamical properties.

On the basis of research largely conducted in the area of education, Raven (1995) has, for example, argued that it is these sociocybernetic processes which consistently undermine well intentioned public action and are currently heading our species, at an exponentially increasing rate, toward extinction.

Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[41][42]

In fields like cybernetics, researchers like Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster examined complex systems using mathematics.

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

Some authors use the term cybernetic systems to denote a proper subset of the class of general systems, namely those systems that include feedback loops.

Some authors use the term cybernetic systems to denote a proper subset of the class of general systems, namely those systems that include feedback loops.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

Models for dynamic equilibrium in systems analysis that contrasted classical views from Talcott Parsons and George Homans were influential in integrating concepts with the general movement.

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

The one-dimensional logistic map defined by x → 4 x (1 – x) is one of the simplest systems with density of periodic orbits.

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

In fields like cybernetics, researchers like Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster examined complex systems using mathematics.

Holism
.

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

For the Primer Group at ISSS, Bánáthy defines a perspective that iterates this view:
The systems view is a world-view that is based on the discipline of SYSTEM INQUIRY.

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Worryingly, given the implications of a scale-free distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of wars.

The influential contemporary work of Peter Senge [9] provides detailed discussion of the commonplace critique of educational systems grounded in conventional assumptions about learning, including the problems with fragmented knowledge and lack of holistic learning from the "machine-age thinking" that became a "model of school separated from daily life."

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

Cybernetics is the study of feedback and derived concepts such as communication and control in living organisms, machines and organisations.

He suggests that an understanding of these systems processes will allow us to generate the kind of (non "common-sense") targeted interventions that are required for things to be otherwise - ie to halt the destruction of the planet.
[edit]
System dynamics
Main article: System dynamics
System Dynamics was founded in the late 1950s by Jay W. Forrester of the MIT Sloan School of Management with the establishment of the MIT System Dynamics Group.

Corning, P. (1983) The Synergism Hupothesis: A Theory of Progressive Evolution.

The systems approach gives primacy to the interrelationships, not to the elements of the system.

A related field of physics called quantum chaos theory investigates the relationship between chaos and quantum mechanics.

A system from this frame of reference is composed of regularly interacting or interrelating groups of activities.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in Physical Review Letters[52] describing for the first time self-organized criticality (SOC), considered to be one of the mechanisms by which complexity arises in nature.

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time.

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

Cellular automata (CA), neural networks (NN), artificial intelligence (AI), and artificial life (ALife) are related fields, but they do not try to describe general (universal) complex (singular) systems.

Subjects like complexity, self-organization, connectionism and adaptive systems had already been studied in the 1940s and 1950s.

While many of the root meanings for the idea of a "general systems theory" might have been lost in the translation and many[who?] were led to believe that the systems theorists had articulated nothing but a pseudoscience, systems theory became a nomenclature that early investigators used to describe the interdependence of relationships in organization by defining a new way of thinking about science and scientific paradigms.

The contradiction of reductionism in conventional theory (which has as its subject a single part) is simply an example of changing assumptions.

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

They are complex in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience.

Systems theory as an area of study specifically developed following the World Wars from the work of Ludwig von Bertalanffy, Anatol Rapoport, Kenneth E. Boulding, William Ross Ashby, Margaret Mead, Gregory Bateson, C. West Churchman and others in the 1950s, specifically catalyzed by the cooperation in the Society for General Systems Research.

Currently, chaos theory continues to be a very active area of research, involving many different disciplines (mathematics, topology, physics, population biology, biology, meteorology, astrophysics, information theory, etc.).
[edit]
Distinguishing random from chaotic data
It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.'

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

Discrete chaotic systems, such as the logistic map, can exhibit strange attractors whatever their dimensionality.

If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, it is unclear how exponential sensitivity to initial conditions can arise in practice in classical chaos.[14]

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

There is some controversy over the existence of chaotic dynamics in plate tectonics and in economics.[10][11][12]

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

There will always be some form of corrupting noise, even if it is present as round-off or truncation error.

They are complex in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

At the same time Howard T. Odum, the radiation ecologist, recognised that the study of general systems required a language that could depict energetics and kinetics at any system scale.

Paper published in: Cybernetics and Human Knowing: a Journal of Second Order Cybernetics and Cyber-Semiotics.

Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
[edit]
Applications
Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics,[3][4][5] engineering,[6] finance,[7][8] philosophy, physics, politics, population dynamics, psychology, and robotics.[9]

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

For example, 0.3454915 → 0.9045085 → 0.3454915 is an (unstable) orbit of period 2, and similar orbits exist for periods 4, 8, 16, etc. (indeed, for all the periods specified by Sharkovskii's theorem).[23]

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behaviour.

There is some controversy over the existence of chaotic dynamics in plate tectonics and in economics.[10][11][12]

A systemic view on organizations is transdisciplinary and integrative.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

The initial conditions of three or more bodies interacting through gravitational attraction (see the n-body problem) can be arranged to produce chaotic motion.
[edit]
Chaotic dynamics


The map defined by x → 4 x (1 – x) and y → x + y if x + y < 1 (x + y – 1 otherwise) displays sensitivity to initial conditions.

The Systems psychology includes an illusion of homeostatic systems, although most of the living systems are in a continuous disequilibrium of various degrees.
[edit]
See also
.

The main catalyst for the development of chaos theory was the electronic computer.

The Cold War affected the research project for systems theory in ways that sorely disappointed many of the seminal theorists.

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

Academic programs
[edit]
Overview


Margaret Mead was an influential figure in systems theory.

In this more recent tradition, systems theory in organizational studies is considered by some as a humanistic extension of the natural sciences.
[edit]
Software and computing
In the 1960s, systems theory was adopted by the post John Von Neumann computing and information technology field and, in fact, formed the basis of structured analysis and structured design (see also Larry Constantine, Tom DeMarco and Ed Yourdon).

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Studies of the critical point beyond which a system creates turbulence was important for Chaos theory, analyzed for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence.

Linear systems are never chaotic; for a dynamical system to display chaotic behaviour it has to be nonlinear.

It is common to just refer to the largest one, i.e. to the Maximal Lyapunov exponent (MLE), because it determines the overall predictability of the system.

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

Integrating Philosophy and Theory as Knowledge, and Method and Application as action, Systems Inquiry then is knowledgeable action.[21]
[edit]
Cybernetics
Main article: Cybernetics
The term cybernetics derives from a Greek word which meant steersman, and which is the origin of English words such as "govern".

What had been beforehand excluded as measure imprecision and simple "noise" was considered by chaos theories as a full component of the studied systems.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks);

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

Recently, another field, called relativistic chaos,[15] has emerged to describe systems that follow the laws of general relativity.

In GST, he writes:
...there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and the relationships or "forces" between them.

Some authors use the term cybernetic systems to denote a proper subset of the class of general systems, namely those systems that include feedback loops.

Laszlo [5] explains that the new systems view of organized complexity went "one step beyond the Newtonian view of organized simplicity" in reducing the parts from the whole, or in understanding the whole without relation to the parts.

While many of the root meanings for the idea of a "general systems theory" might have been lost in the translation and many[who?] were led to believe that the systems theorists had articulated nothing but a pseudoscience, systems theory became a nomenclature that early investigators used to describe the interdependence of relationships in organization by defining a new way of thinking about science and scientific paradigms.

Academic programs
[edit]
Overview


Margaret Mead was an influential figure in systems theory.

The systems to organizations relies heavily upon achieving negative entropy through openness and feedback.

Both strange attractors and Julia sets typically have a fractal structure, and a fractal dimension can be calculated for them.
[edit]
Minimum complexity of a chaotic system


Bifurcation diagram of the logistic map x → r x (1 – x).

Looking to systems theory for a reductive explanation of phenomenal experience and evolutionary foundations for higher order thought Retrieved Dec.14 2007.
0.

In fields like cybernetics, researchers like Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster examined complex systems using mathematics.

Systems theory first originated in biology in the 1920s out of the need to explain the interrelatedness of organisms in ecosystems.[1]

However, the Poincaré-Bendixson theorem shows that a strange attractor can only arise in a continuous dynamical system (specified by differential equations) if it has three or more dimensions.

Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[17]
0. it must be sensitive to initial conditions,
0. it must be topologically mixing, and
0. its periodic orbits must be dense.
[edit]
Sensitivity to initial conditions
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by ot...

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

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Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation.

In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in convective Rayleigh–Benard systems.

Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[43]

Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[43]

Accordingly, the theory of complex adaptive systems bridges developments of the system theory with the ideas of 'generalized Darwinism', which suggests that Darwinian principles of evolution help explain a wide range of phenomena.[citation needed]
[edit]
Applications of system theories
[edit]
Living systems theory
Main article: Living systems theory
Living systems theory is an offshoot of von Bertalanffy's general systems theory, created by James Grier Miller, which was intended to formal...

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

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However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

Recently, another field, called relativistic chaos,[15] has emerged to describe systems that follow the laws of general relativity.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

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Thus, given a time series to test for determinism, one can:
0. pick a test state;
0. search the time series for a similar or 'nearby' state; and
0. compare their respective time evolutions.

Systems Engineering considers both the business and the technical needs of all customers, with the goal of providing a quality product that meets the user needs.[24]
[edit]
Systems psychology
Main article: Systems psychology
Systems psychology is a branch of psychology that studies human behaviour and experience in complex systems.

Young, O. R., “A Survey of General Systems Theory”, General Systems, vol. 9 (1964), pages 61–80. (overview about different trends and tendencies, with bibliography)




Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions.

This could be a single organism, any organization or society, or any electro-mechanical or informational artifact.

For the Primer Group at ISSS, Bánáthy defines a perspective that iterates this view:
The systems view is a world-view that is based on the discipline of SYSTEM INQUIRY.

^ Michael M. Behrmann (1984), Handbook of Microcomputers in Special Education.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Young, O. R., “A Survey of General Systems Theory”, General Systems, vol. 9 (1964), pages 61–80. (overview about different trends and tendencies, with bibliography)




Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions.

Lorenz's discovery, which gave its name to Lorenz attractors, proved that meteorology could not reasonably predict weather beyond a weekly period (at most).

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

The best context to compare the different "C"-Theories about complex systems is historical, which emphasizes different tools and methodologies, from pure mathematics in the beginning to pure computer science now.

Hinrichsen, D. and Pritchard, A.J. (2005) Mathematical Systems Theory.

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

With the renewed interest in systems theory on the rise since the 1990s, Bailey (1994) notes the concept of systems in sociology dates back to Auguste Comte in the 19th century, Herbert Spencer and Vilfredo Pareto, and that sociology was readying into its centennial as the new systems theory was emerging following the World Wars.

Currently, chaos theory continues to be a very active area of research, involving many different disciplines (mathematics, topology, physics, population biology, biology, meteorology, astrophysics, information theory, etc.).
[edit]
Distinguishing random from chaotic data
It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.'

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

In GST, he writes:
...there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and the relationships or "forces" between them.

As a technical and general academic area of study it predominantly refers to the science of systems that resulted from Bertalanffy's General System Theory (GST), among others, in initiating what became a project of systems research and practice.

Quantitatively, two trajectories in phase space with initial separation diverge

where λ is the Lyapunov exponent.

The art of problem solving.

He constructed a general theory of living systems by focusing on concrete systems—nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components.

John von Neumann discovered cellular automata and self-reproducing systems, again with only pencil and paper.

Software and computing
. 4.4

^ Michael M. Behrmann (1984), Handbook of Microcomputers in Special Education.

Systems psychology "includes the domain of engineering psychology, but in addition is more concerned with societal systems and with the study of motivational, affective, cognitive and group behavior than is engineering psychology."[25]

In this respect, with the possibility of misinterpretations, von Bertalanffy [2] believed a general theory of systems "should be an important regulative device in science," to guard against superficial analogies that "are useless in science and harmful in their practical consequences."

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

New York: Springer.

The shift was from absolute and universal authoritative principles and knowledge to relative and general conceptual and perceptual knowledge [11], still in the tradition of theorists that sought to provide means in organizing human life.

Cellular automata (CA), neural networks (NN), artificial intelligence (AI), and artificial life (ALife) are related fields, but they do not try to describe general (universal) complex (singular) systems.

^ Lester R. Bittel and Muriel Albers Bittel (1978), Encyclopedia of Professional Management, McGraw-Hill, ISBN 0070054789, p.498.
0.

In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in Physical Review Letters[52] describing for the first time self-organized criticality (SOC), considered to be one of the mechanisms by which complexity arises in nature.

Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
[edit]
Applications
Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics,[3][4][5] engineering,[6] finance,[7][8] philosophy, physics, politics, population dynamics, psychology, and robotics.[9]

Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[43]

Contents [hide]
0. 1 Overview
0. 2 History
0. 3 Developments in system theories
Nullste. 3.1

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

As a technical and general academic area of study it predominantly refers to the science of systems that resulted from Bertalanffy's General System Theory (GST), among others, in initiating what became a project of systems research and practice.

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

In GST, he writes:
...there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and the relationships or "forces" between them.

Kurt Lewin was particularly influential in developing the systems perspective within organizational theory and coined the term "systems of ideology", from his frustration with behavioral psychologies that became an obstacle to sustainable work in psychology [22].

Meaning, the history of ideas that preceded were rethought not lost.

^ Lester R. Bittel and Muriel Albers Bittel (1978), Encyclopedia of Professional Management, McGraw-Hill, ISBN 0070054789, p.498.
0.

The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.

He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course.

Systems theory as an area of study specifically developed following the World Wars from the work of Ludwig von Bertalanffy, Anatol Rapoport, Kenneth E. Boulding, William Ross Ashby, Margaret Mead, Gregory Bateson, C. West Churchman and others in the 1950s, specifically catalyzed by the cooperation in the Society for General Systems Research.

Academic programs
[edit]
Overview


Margaret Mead was an influential figure in systems theory.

Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[41][42]

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks

According to Miller's original conception as spelled out in his magnum opus Living Systems, a "living system" must contain each of 20 "critical subsystems", which are defined by their functions and visible in numerous systems, from simple cells to organisms, countries, and societies.

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behaviour of certain experiments like that of the logistic map.

Von Bertalanffy traced systems concepts to the philosophy of G.W. von Leibniz and Nicholas of Cusa's coincidentia oppositorum.

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

^ Lester R. Bittel and Muriel Albers Bittel (1978), Encyclopedia of Professional Management, McGraw-Hill, ISBN 0070054789, p.498.
0.

Systems psychology "includes the domain of engineering psychology, but in addition is more concerned with societal systems and with the study of motivational, affective, cognitive and group behavior than is engineering psychology."[25]

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

"An Essay on the Relativity of Categories."

Von Bertalanffy defined system as "elements in standing relationship.
—[6]
Similar ideas are found in learning theories that developed from the same fundamental concepts, emphasizing that understanding results from knowing concepts both in part and as a whole.

At that time, he began applying what he had learned about systems during his work in electrical engineering to everyday kinds of systems.

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

With the renewed interest in systems theory on the rise since the 1990s, Bailey (1994) notes the concept of systems in sociology dates back to Auguste Comte in the 19th century, Herbert Spencer and Vilfredo Pareto, and that sociology was readying into its centennial as the new systems theory was emerging following the World Wars.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

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Lemkow, A. (1995) The Wholeness Principle: Dynamics of Unity Within Science, Religion & Society.

Others remain closer to the direct systems concepts developed by the original theorists.

Young, O. R., “A Survey of General Systems Theory”, General Systems, vol. 9 (1964), pages 61–80. (overview about different trends and tendencies, with bibliography)




Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions.

The rate of separation can be different for different orientations of the initial separation vector.

With the renewed interest in systems theory on the rise since the 1990s, Bailey (1994) notes the concept of systems in sociology dates back to Auguste Comte in the 19th century, Herbert Spencer and Vilfredo Pareto, and that sociology was readying into its centennial as the new systems theory was emerging following the World Wars.

The reason is, simply put, that solutions to such systems are asymptotic to a two dimensional surface and therefore solutions are well behaved.

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

^ (Banathy 1997: ¶ 22)
0. ^ a b 1968, General System theory: Foundations, Development, Applications, New York: George Braziller, revised edition 1976: ISBN 0-8076-0453-4
0. ^ (see Steiss 1967; Buckley, 1967)
0.

One of the most successful applications of chaos theory has been in ecology, where dynamical systems such as the Ricker model have been used to show how population growth under density dependence can lead to chaotic dynamics.

Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different (even the evolution of simple discrete systems, such as cellular automata, can heavily depend on initial conditions, and Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule 30).

Jay Forrester with his work in dynamics and management alongside numerous theorists including Edgar Schein that followed in their tradition since the Civil Rights Era have also been influential.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
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History · Positivism · Antipositivism
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The availability of cheaper, more powerful computers broadens the applicability of chaos theory.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
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In the 1880s, while studying the three-body problem, he found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point.[28][29]

Thus any real time series, even if mostly deterministic, will contain some randomness.[54]

Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
[edit]
Applications
Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics,[3][4][5] engineering,[6] finance,[7][8] philosophy, physics, politics, population dynamics, psychology, and robotics.[9]

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago

^ (Banathy 1997: ¶ 22)
0. ^ a b 1968, General System theory: Foundations, Development, Applications, New York: George Braziller, revised edition 1976: ISBN 0-8076-0453-4
0. ^ (see Steiss 1967; Buckley, 1967)
0.

For example, Ilya Prigogine, of the Center for Complex Quantum Systems at the University of Texas, Austin, has studied emergent properties, suggesting that they offer analogues for living systems.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

With these ideas referring to an organized body of knowledge and "any systematically presented set of concepts, whether they are empirical, axiomatic, or philosophical", "Lehre" is associated with theory and science in the etymology of general systems, but also does not translate from the German very well; "teaching" is the "closest equivalent", but "sounds dogmatic and off the mark" [3].

Cellular automata (CA), neural networks (NN), artificial intelligence (AI), and artificial life (ALife) are related fields, but they do not try to describe general (universal) complex (singular) systems.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
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History · Positivism · Antipositivism
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An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket).

By the 1970s, General Systems Theory (GST) was the fundamental underpinning of most commercial software design techniques, and by the 1980, W. Vaughn Frick and Albert F. Case, Jr. had used GST to design the "missing link" transformation from system analysis (defining what's needed in a system) to system design (what's actually implemented) using the Yourdon/DeMarco notation.

The following year, Mitchell Feigenbaum published the noted article "Quantitative Universality for a Class of Nonlinear Transformations", where he described logistic maps.[49]

^ Michael M. Behrmann (1984), Handbook of Microcomputers in Special Education.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Gerald Weinberg. (1975).

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public so...

^ (Banathy 1997: ¶ 22)
0. ^ a b 1968, General System theory: Foundations, Development, Applications, New York: George Braziller, revised edition 1976: ISBN 0-8076-0453-4
0. ^ (see Steiss 1967; Buckley, 1967)
0.

Health Informatics: Concepts of Information Technology in Health and Human Services.

The Cold War affected the research project for systems theory in ways that sorely disappointed many of the seminal theorists.

The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.

^ (Bailey 1994: 3-8; see also Owens 2004)
0.

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

This sensitivity is popularly referred to as the butterfly effect.

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

Systems theory first originated in biology in the 1920s out of the need to explain the interrelatedness of organisms in ecosystems.[1]

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

Systems theory as an area of study specifically developed following the World Wars from the work of Ludwig von Bertalanffy, Anatol Rapoport, Kenneth E. Boulding, William Ross Ashby, Margaret Mead, Gregory Bateson, C. West Churchman and others in the 1950s, specifically catalyzed by the cooperation in the Society for General Systems Research.

Bánáthy, B (1996) Designing Social Systems in a Changing World New York Plenum
0.

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Statistical tests attempting to separate noise from the deterministic skeleton or inversely isolate the deterministic part risk failure.

Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff,[31] A. N. Kolmogorov,[32][33][34] M.L. Cartwright and J.E. Littlewood,[35] and Stephen Smale.[36]

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

In this more recent tradition, systems theory in organizational studies is considered by some as a humanistic extension of the natural sciences.
[edit]
Software and computing
In the 1960s, systems theory was adopted by the post John Von Neumann computing and information technology field and, in fact, formed the basis of structured analysis and structured design (see also Larry Constantine, Tom DeMarco and Ed Yourdon).

Studies of the critical point beyond which a system creates turbulence was important for Chaos theory, analyzed for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence.

Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model.

Snooks, G.D. (2008).

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

This attractor results from a simple three-dimensional model of the Lorenz weather system.

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

By the 1970s, General Systems Theory (GST) was the fundamental underpinning of most commercial software design techniques, and by the 1980, W. Vaughn Frick and Albert F. Case, Jr. had used GST to design the "missing link" transformation from system analysis (defining what's needed in a system) to system design (what's actually implemented) using the Yourdon/DeMarco notation.

As a transdisciplinary, interdisciplinary and multiperspectival domain, the area brings together principles and concepts from ontology, philosophy of science, physics, computer science, biology, and engineering as well as geography, sociology, political science, psychotherapy (within family systems therapy) and economics among others.

Academic programs
[edit]
Overview


Margaret Mead was an influential figure in systems theory.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

Both strange attractors and Julia sets typically have a fractal structure, and a fractal dimension can be calculated for them.
[edit]
Minimum complexity of a chaotic system


Bifurcation diagram of the logistic map x → r x (1 – x).

This could be a single organism, any organization or society, or any electro-mechanical or informational artifact.

Numerous scholars had been actively engaged in ideas before (Tectology of Alexander Bogdanov published in 1912-1917 is a remarkable example), but in 1937 von Bertalanffy presented the general theory of systems for a conference at the University of Chicago.

Systems theory first originated in biology in the 1920s out of the need to explain the interrelatedness of organisms in ecosystems.[1]

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

For example, Ilya Prigogine, of the Center for Complex Quantum Systems at the University of Texas, Austin, has studied emergent properties, suggesting that they offer analogues for living systems.

Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[43]

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

The basis of the method is the recognition that the structure of any system — the many circular, interlocking, sometimes time-delayed relationships among its components — is often just as important in determining its behavior as the individual components themselves.

By the 1970s, General Systems Theory (GST) was the fundamental underpinning of most commercial software design techniques, and by the 1980, W. Vaughn Frick and Albert F. Case, Jr. had used GST to design the "missing link" transformation from system analysis (defining what's needed in a system) to system design (what's actually implemented) using the Yourdon/DeMarco notation.

Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand.

The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 was printed as 0.506.

Yet his advisor did not agree with his conclusions at the time, and did not allow him to report his findings until 1970.[47][48]

The influential contemporary work of Peter Senge [9] provides detailed discussion of the commonplace critique of educational systems grounded in conventional assumptions about learning, including the problems with fragmented knowledge and lack of holistic learning from the "machine-age thinking" that became a "model of school separated from daily life."

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

Laszlo [5] explains that the new systems view of organized complexity went "one step beyond the Newtonian view of organized simplicity" in reducing the parts from the whole, or in understanding the whole without relation to the parts.

Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[40]

This sensitivity is popularly referred to as the butterfly effect.

The initial conditions of three or more bodies interacting through gravitational attraction (see the n-body problem) can be arranged to produce chaotic motion.
[edit]
Chaotic dynamics


The map defined by x → 4 x (1 – x) and y → x + y if x + y < 1 (x + y – 1 otherwise) displays sensitivity to initial conditions.

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

Cybernetics as the theory of control mechanisms in technology and nature is founded on the concepts of information and feedback, but as part of a general theory of systems;" then reiterates: "the model is of wide application but should not be identified with 'systems theory' in general", and that "warning is necessary against its incautious expansion to fields for which its concepts are not made." (17-23).

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

By the 1970s, General Systems Theory (GST) was the fundamental underpinning of most commercial software design techniques, and by the 1980, W. Vaughn Frick and Albert F. Case, Jr. had used GST to design the "missing link" transformation from system analysis (defining what's needed in a system) to system design (what's actually implemented) using the Yourdon/DeMarco notation.

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

Accordingly, the theory of complex adaptive systems bridges developments of the system theory with the ideas of 'generalized Darwinism', which suggests that Darwinian principles of evolution help explain a wide range of phenomena.[citation needed]
[edit]
Applications of system theories
[edit]
Living systems theory
Main article: Living systems theory
Living systems theory is an offshoot of von Bertalanffy's general systems theory, created by James Grier Miller, which was intended to fo...

Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[17]
0. it must be sensitive to initial conditions,
0. it must be topologically mixing, and
0. its periodic orbits must be dense.
[edit]
Sensitivity to initial conditions
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by ot...

Colorado: University of Colorado Press.
0.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

Living systems theory
. 4.2

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

For example, consider the simple dynamical system produced by repeatedly doubling an initial value.

Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model.

This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points will eventually become widely separated.

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

Integrating Philosophy and Theory as Knowledge, and Method and Application as action, Systems Inquiry then is knowledgeable action.[21]
[edit]
Cybernetics
Main article: Cybernetics
The term cybernetics derives from a Greek word which meant steersman, and which is the origin of English words such as "govern".

For example, an irrational rotation of the circle is topologically transitive, but does not have dense periodic orbits, and hence does not have sensitive dependence on initial conditions.[22]

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1]

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

It is interesting that the most practically significant condition, that of sensitivity to initial conditions, is actually redundant in the definition, being implied by two (or for intervals, one) purely topological conditions, which are therefore of greater interest to mathematicians.

Rethinking the Fifth Discipline: Learning within the unknowable."

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

The preface explains that the original concept of a general system theory was "Allgemeine Systemtheorie (or Lehre)", pointing out the fact that "Theorie" (or "Lehre") just as "Wissenschaft" (translated Scholarship), "has a much broader meaning in German than the closest English words ‘theory’ and ‘science'" [3].

New Jersey: Prentice-Hall.
0.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Niklas Luhmann (1996),"Social Systems",Stanford University Press, Palo Alto, CA
0.

Jay Forrester with his work in dynamics and management alongside numerous theorists including Edgar Schein that followed in their tradition since the Civil Rights Era have also been influential.

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

The natural philosophy of the new developments in the sciences.

These "applied" investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.

Accordingly, the theory of complex adaptive systems bridges developments of the system theory with the ideas of 'generalized Darwinism', which suggests that Darwinian principles of evolution help explain a wide range of phenomena.[citation needed]
[edit]
Applications of system theories
[edit]
Living systems theory
Main article: Living systems theory
Living systems theory is an offshoot of von Bertalanffy's general systems theory, created by James Grier Miller, which was intended to fo...

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

Then in 1986 the New York Academy of Sciences co-organized with the National Institute of Mental Health and the Office of Naval Research the first important conference on Chaos in biology and medicine.

The terms "systems theory" and "cybernetics" have been widely used as synonyms.

Second, all systems, whether electrical, biological, or social, have common patterns, behaviors, and properties that can be understood and used to develop greater insight into the behavior of complex phenomena and to move closer toward a unity of science.

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket).

The Lyapunov exponent characterises the extent of the sensitivity to initial conditions.

While many of the root meanings for the idea of a "general systems theory" might have been lost in the translation and many[who?] were led to believe that the systems theorists had articulated nothing but a pseudoscience, systems theory became a nomenclature that early investigators used to describe the interdependence of relationships in organization by defining a new way of thinking about science and scientific paradigms.

For example, Ilya Prigogine, of the Center for Complex Quantum Systems at the University of Texas, Austin, has studied emergent properties, suggesting that they offer analogues for living systems.

While many of the root meanings for the idea of a "general systems theory" might have been lost in the translation and many[who?] were led to believe that the systems theorists had articulated nothing but a pseudoscience, systems theory became a nomenclature that early investigators used to describe the interdependence of relationships in organization by defining a new way of thinking about science and scientific paradigms.

Accordingly, the theory of complex adaptive systems bridges developments of the system theory with the ideas of 'generalized Darwinism', which suggests that Darwinian principles of evolution help explain a wide range of phenomena.[citation needed]
[edit]
Applications of system theories
[edit]
Living systems theory
Main article: Living systems theory
Living systems theory is an offshoot of von Bertalanffy's general systems theory, created by James Grier Miller, which was intended to fo...

Béla H. Bánáthy, who argued - along with the founders of the systems society - that "the benefit of humankind" is the purpose of science, has made significant and far-reaching contributions to the area of systems theory.

However, the approach of the complex adaptive systems does not take account in adoption of information which enables people to use it.[citation needed]
CAS ideas and models are essentially evolutionary.

This led to a renewed of physiology in the 1980s through the application of chaos theory, for example in the study of pathological cardiac cycles.

However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

First, all phenomena can be viewed as a web of relationships among elements, or a system.

Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand.

He constructed a general theory of living systems by focusing on concrete systems—nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components.

Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood.[citation needed] Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

The basis of the method is the recognition that the structure of any system — the many circular, interlocking, sometimes time-delayed relationships among its components — is often just as important in determining its behavior as the individual components themselves.

Slightly revising the original model a dozen years later, he distinguished eight "nested" hierarchical levels in such complex structures.

Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[40]

Its focus is how anything (digital, mechanical or biological) processes information, reacts to information, and changes or can be changed to better accomplish the first two tasks.

Alluding to Thomas Kuhn's concept of a paradigm shift exposed in The Structure of Scientific Revolutions (1962), many "chaologists" (as some self-nominated themselves) claimed that this new theory was an example of such as shift, a thesis upheld by J. Gleick.

However, as a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers (that is, vacuum tubes) and noticed, on Nov. 27, 1961, what he called "randomly transitional phenomena".

Niklas Luhmann (1996),"Social Systems",Stanford University Press, Palo Alto, CA
0.

^ Lawrence S. Bale (1995).

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

Béla H. Bánáthy, who argued - along with the founders of the systems society - that "the benefit of humankind" is the purpose of science, has made significant and far-reaching contributions to the area of systems theory.

In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature.[30]

Some authors use the term cybernetic systems to denote a proper subset of the class of general systems, namely those systems that include feedback loops.

According to Miller's original conception as spelled out in his magnum opus Living Systems, a "living system" must contain each of 20 "critical subsystems", which are defined by their functions and visible in numerous systems, from simple cells to organisms, countries, and societies.

If anything it appears that although the two probably mutually influenced each other, cybernetics had the greater influence.

Differentiated from Western rationalist traditions of philosophy, C. West Churchman often identified with the I Ching as a systems approach sharing a frame of reference similar to pre-Socratic philosophy and Heraclitus [13].

What had been beforehand excluded as measure imprecision and simple "noise" was considered by chaos theories as a full component of the studied systems.

Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[40]

On the basis of research largely conducted in the area of education, Raven (1995) has, for example, argued that it is these sociocybernetic processes which consistently undermine well intentioned public action and are currently heading our species, at an exponentially increasing rate, toward extinction.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

There will always be some form of corrupting noise, even if it is present as round-off or truncation error.

Chaos was observed by a number of experimenters before it was recognized; e.g., in 1927 by van der Pol[44] and in 1958 by R.L. Ives.[45][46]

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

At first the domains of work of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems analysis.

For example, 0.3454915 → 0.9045085 → 0.3454915 is an (unstable) orbit of period 2, and similar orbits exist for periods 4, 8, 16, etc. (indeed, for all the periods specified by Sharkovskii's theorem).[23]

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Cognizant of advances in science that questioned classical assumptions in the organizational sciences, Bertalanffy's idea to develop a theory of systems began as early as the interwar period, publishing "An Outline for General Systems Theory" in the British Journal for the Philosophy of Science, Vol 1, No. 2, by 1950.

The theorists sought holistic methods by developing systems concepts that could be integrated with different areas.

His desire was to use the word "system" to describe those principles which are common to systems in general.

Integrating Philosophy and Theory as Knowledge, and Method and Application as action, Systems Inquiry then is knowledgeable action.[21]
[edit]
Cybernetics
Main article: Cybernetics
The term cybernetics derives from a Greek word which meant steersman, and which is the origin of English words such as "govern".

Studies of the critical point beyond which a system creates turbulence was important for Chaos theory, analyzed for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence.

The Lorenz attractor discussed above is generated by a system of three differential equations with a total of seven terms on the right hand side, five of which are linear terms and two of which are quadratic (and therefore nonlinear).

Other discrete dynamical systems have a repelling structure called a Julia set which forms at the boundary between basins of attraction of fixed points – Julia sets can be thought of as strange repellers.

Accordingly, the theory of complex adaptive systems bridges developments of the system theory with the ideas of 'generalized Darwinism', which suggests that Darwinian principles of evolution help explain a wide range of phenomena.[citation needed]
[edit]
Applications of system theories
[edit]
Living systems theory
Main article: Living systems theory
Living systems theory is an offshoot of von Bertalanffy's general systems theory, created by James Grier Miller, which was intended to fo...

Between 1929-1951, Robert Maynard Hutchins at the University of Chicago had undertaken efforts to encourage innovation and interdisciplinary research in the social sciences, aided by the Ford Foundation with the interdisciplinary Division of the Social Sciences established in 1931[14].

One of the weaknesses of System dynamics is the fact that it does not pay attention much to dynamic causation in interelated entities.
[edit]
Systems engineering
Main article: Systems Engineering
Systems Engineering is an interdisciplinary approach and means for enabling the realization and deployment of successful systems.

Subjects like complexity, self-organization, connectionism and adaptive systems had already been studied in the 1940s and 1950s.

For example, Ilya Prigogine, of the Center for Complex Quantum Systems at the University of Texas, Austin, has studied emergent properties, suggesting that they offer analogues for living systems.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

By the 1970s, General Systems Theory (GST) was the fundamental underpinning of most commercial software design techniques, and by the 1980, W. Vaughn Frick and Albert F. Case, Jr. had used GST to design the "missing link" transformation from system analysis (defining what's needed in a system) to system design (what's actually implemented) using the Yourdon/DeMarco notation.

Studies of the critical point beyond which a system creates turbulence was important for Chaos theory, analyzed for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence.

Chaos theory is also currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions.[13]

Von Bertalanffy defined system as "elements in standing relationship.
—[6]
Similar ideas are found in learning theories that developed from the same fundamental concepts, emphasizing that understanding results from knowing concepts both in part and as a whole.

If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, it is unclear how exponential sensitivity to initial conditions can arise in practice in classical chaos.[14]

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket).

Von Bertalanffy opened up something much broader and of much greater significance than a single theory (which, as we now know, can always be falsified and has usually an ephemeral existence): he created a new paradigm for the development of theories.

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1]

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

New Jersey: Englewood Cliffs.
0.

For the Primer Group at ISSS, Bánáthy defines a perspective that iterates this view:
The systems view is a world-view that is based on the discipline of SYSTEM INQUIRY.

The influential contemporary work of Peter Senge [9] provides detailed discussion of the commonplace critique of educational systems grounded in conventional assumptions about learning, including the problems with fragmented knowledge and lack of holistic learning from the "machine-age thinking" that became a "model of school separated from daily life."

The theorists sought holistic methods by developing systems concepts that could be integrated with different areas.

Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[41][42]

Determining the exact date of the founding of the field of system dynamics is difficult and involves a certain degree of arbitrariness.

In the most general sense, system means a configuration of parts connected and joined together by a web of relationships.

All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[54][55]

^ Karl Ludwig von Bertalanffy: ... aber vom Menschen wissen wir nichts, (English title: Robots, Men and Minds), translated by Dr. Hans-Joachim Flechtner. page 115.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

Chaos was observed by a number of experimenters before it was recognized; e.g., in 1927 by van der Pol[44] and in 1958 by R.L. Ives.[45][46]

^ Hull 1970
0.

Encyclopedia of Systems and Cybernetics, Introducing the 2nd Volume [1] and further links to the ENCYCLOPEDIA, K G Saur, Munich [2] see also [3] * Kahn, Herman. (1956).

Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[17]
0. it must be sensitive to initial conditions,
0. it must be topologically mixing, and
0. its periodic orbits must be dense.
[edit]
Sensitivity to initial conditions
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other poi...

These "applied" investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.

To criticize it as such is to shoot at straw men.

In his work with the Primer Group, Béla H. Bánáthy generalized the domains into four integratable domains of systemic inquiry:
Domain Description
Philosophy the ontology, epistemology, and axiology of systems;
Theory a set of interrelated concepts and principles applying to all systems
Methodology the set of models, strategies, methods, and tools that instrumentalize systems theory and philosophy
Application the application and interaction of the domains
These operate in a recursive r...

In the system studied, "Hadamard's billiards," Hadamard was able to show that all trajectories are unstable in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.

If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, it is unclear how exponential sensitivity to initial conditions can arise in practice in classical chaos.[14]

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

Statistical self-similarity and fractional dimension," showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[43]

One of the early thinkers in the field was Alexander Bogdanov, who developed his Tectology, a theory widely considered a precursor of von Bertalanffy's GST, aiming to model and design human organizations (see Mattessich 1978, Capra 1996).

Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[41][42]

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

Here two series of x and y values diverge markedly over time from a tiny initial difference.

The systems to organizations relies heavily upon achieving negative entropy through openness and feedback.

In this more recent tradition, systems theory in organizational studies is considered by some as a humanistic extension of the natural sciences.
[edit]
Software and computing
In the 1960s, systems theory was adopted by the post John Von Neumann computing and information technology field and, in fact, formed the basis of structured analysis and structured design (see also Larry Constantine, Tom DeMarco and Ed Yourdon).

New York: Avon.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public so...

In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in convective Rayleigh–Benard systems.

Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model.

New York: Laurel.
0.

Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood.[citation needed] Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

One complication is that as the dimension increases the search for a nearby state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension) to find a suitably close candidate.

Where assumptions in Western science from Greek thought with Plato and Aristotle to Newton's Principia have historically influenced all areas from the hard to social sciences (see David Easton's seminal development of the "political system" as an analytical construct), the original theorists explored the implications of twentieth century advances in terms of systems.

Von Bertalanffy defined system as "elements in standing relationship.
—[6]
Similar ideas are found in learning theories that developed from the same fundamental concepts, emphasizing that understanding results from knowing concepts both in part and as a whole.

Systems psychology
0. 5 See also
0. 6 References
0. 7 Further reading
0. 8 External links
０. 8.1

He constructed a general theory of living systems by focusing on concrete systems—nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components.

Mattessich, R. (1978) Instrumental Reasoning and Systems Methodology: An Epistemology of the Applied and Social Sciences.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

^ Michael M. Behrmann (1984), Handbook of Microcomputers in Special Education.

Quantitatively, two trajectories in phase space with initial separation diverge

where λ is the Lyapunov exponent.

In this more recent tradition, systems theory in organizational studies is considered by some as a humanistic extension of the natural sciences.
[edit]
Software and computing
In the 1960s, systems theory was adopted by the post John Von Neumann computing and information technology field and, in fact, formed the basis of structured analysis and structured design (see also Larry Constantine, Tom DeMarco and Ed Yourdon).

In fact, Bertalanffy’s organismic psychology paralleled the learning theory of Jean Piaget. [7] Interdisciplinary perspectives are critical in breaking away from industrial age models and thinking where history is history and math is math segregated from the arts and music separate from the sciences and never the twain shall meet [8].

Since the beginning of chaos theory when Edward Lorenz accidentally discovered a strange attractor with his computer, computers have become an indispensable source of information.

Young, O. R., “A Survey of General Systems Theory”, General Systems, vol. 9 (1964), pages 61–80. (overview about different trends and tendencies, with bibliography)




Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions.

While the Poincaré–Bendixson theorem means that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behaviour.[citation needed]
[edit]
History


Fractal fern created using chaos game.

Systems psychology
0. 5 See also
0. 6 References
0. 7 Further reading
0. 8 External links
０. 8.1

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

In recent years, systems thinking has been developed to provide techniques for studying systems in holistic ways to supplement traditional reductionistic methods.

Von Bertalanffy's objective was to bring together under one heading the organismic science that he had observed in his work as a biologist.

The main catalyst for the development of chaos theory was the electronic computer.

He constructed a general theory of living systems by focusing on concrete systems—nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components.

What had been beforehand excluded as measure imprecision and simple "noise" was considered by chaos theories as a full component of the studied systems.

In December 1977 the New York Academy of Sciences organized the first symposium on Chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw (a physicist, part of the Eudaemons group with J. Doyne Farmer and Norman Packard who tried to find a mathematical method to beat roulette, and then created with them the Dynamical Systems Collective in Santa Cruz, California), and the meteorologist Edward Lorenz.

The terms "systems theory" and "cybernetics" have been widely used as synonyms.

He suggests that an understanding of these systems processes will allow us to generate the kind of (non "common-sense") targeted interventions that are required for things to be otherwise - ie to halt the destruction of the planet.
[edit]
System dynamics
Main article: System dynamics
System Dynamics was founded in the late 1950s by Jay W. Forrester of the MIT Sloan School of Management with the establishment of the MIT System Dynamics Group.

New Jersey: Englewood Cliffs.
0.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

The preface explains that the original concept of a general system theory was "Allgemeine Systemtheorie (or Lehre)", pointing out the fact that "Theorie" (or "Lehre") just as "Wissenschaft" (translated Scholarship), "has a much broader meaning in German than the closest English words ‘theory’ and ‘science'" [3].

College Hill Press.

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

An example is the properties of these letters which when considered together can give rise to meaning which does not exist in the letters by themselves.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Niklas Luhmann (1996),"Social Systems",Stanford University Press, Palo Alto, CA
0.

Important names in contemporary systems science include Russell Ackoff, Béla H. Bánáthy, Anthony Stafford Beer, Peter Checkland, Robert L. Flood, Fritjof Capra, Michael C. Jackson, and Werner Ulrich, among others.

According to Miller's original conception as spelled out in his magnum opus Living Systems, a "living system" must contain each of 20 "critical subsystems", which are defined by their functions and visible in numerous systems, from simple cells to organisms, countries, and societies.

While many of the root meanings for the idea of a "general systems theory" might have been lost in the translation and many[who?] were led to believe that the systems theorists had articulated nothing but a pseudoscience, systems theory became a nomenclature that early investigators used to describe the interdependence of relationships in organization by defining a new way of thinking about science and scientific paradigms.

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1]

Living systems theory
. 4.2

Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations.

This is at difference to conventional models that center on individuals, structures, departments and units separate in part from the whole instead of recognizing the interdependence between groups of individuals, structures and processes that enable an organization to function.

The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because it was not only one of the first, but it is also one of the most complex and as such gives rise to a very interesting pattern which looks like the wings of a butterfly.

Sensitivity to initial conditions is popularly known as the "butterfly effect," so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

Since the end of the Cold War, there has been a renewed interest in systems theory with efforts to strengthen an ethical view.
[edit]
Developments in system theories
[edit]
General systems research and systems inquiry
Many early systems theorists aimed at finding a general systems theory that could explain all systems in all fields of science.

All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[54][55]

One of the weaknesses of System dynamics is the fact that it does not pay attention much to dynamic causation in interelated entities.
[edit]
Systems engineering
Main article: Systems Engineering
Systems Engineering is an interdisciplinary approach and means for enabling the realization and deployment of successful systems.

^ Karl Ludwig von Bertalanffy: ... aber vom Menschen wissen wir nichts, (English title: Robots, Men and Minds), translated by Dr. Hans-Joachim Flechtner. page 115.

As a technical and general academic area of study it predominantly refers to the science of systems that resulted from Bertalanffy's General System Theory (GST), among others, in initiating what became a project of systems research and practice.

Sensitivity to initial conditions is popularly known as the "butterfly effect," so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicag...

Each level is "nested" in the sense that each higher level contains the next lower level in a nested fashion.
[edit]
Organizational theory


Kurt Lewin attended the Macy conferences and is commonly identified as the founder of the movement to study groups scientifically.

Studies of the critical point beyond which a system creates turbulence was important for Chaos theory, analyzed for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence.

With the renewed interest in systems theory on the rise since the 1990s, Bailey (1994) notes the concept of systems in sociology dates back to Auguste Comte in the 19th century, Herbert Spencer and Vilfredo Pareto, and that sociology was readying into its centennial as the new systems theory was emerging following the World Wars.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

The term complex adaptive systems was coined at the interdisciplinary Santa Fe Institute (SFI), by John H. Holland, Murray Gell-Mann and others.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Sensitivity to initial conditions is popularly known as the "butterfly effect," so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

Von Bertalanffy's objective was to bring together under one heading the organismic science that he had observed in his work as a biologist.

Contents [hide]
0. 1 Overview
0. 2 History
0. 3 Developments in system theories
Nullste. 3.1

This again is incorrect.

Von Bertalanffy's objective was to bring together under one heading the organismic science that he had observed in his work as a biologist.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftersho...

According to Jackson (2000), von Bertalanffy promoted an embryonic form of general system theory (GST) as early as the 1920s and 1930s but it was not until the early 1950s it became more widely known in scientific circles.

Chaos was observed by a number of experimenters before it was recognized; e.g., in 1927 by van der Pol[44] and in 1958 by R.L. Ives.[45][46]

To explore the current inroads of systems theory into sociology (primarily in the form of complexity science) see sociology and complexity science.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftersho...

Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand.

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1]

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

There, Bernardo Huberman presented a mathematical model of the eye tracking disorder among schizophrenics.[51]

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

The art of problem solving.

In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in convective Rayleigh–Benard systems.

Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
[edit]
Applications
Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics,[3][4][5] engineering,[6] finance,[7][8] philosophy, physics, politics, population dynamics, psychology, and robotics.[9]

Alluding to Thomas Kuhn's concept of a paradigm shift exposed in The Structure of Scientific Revolutions (1962), many "chaologists" (as some self-nominated themselves) claimed that this new theory was an example of such as shift, a thesis upheld by J. Gleick.

These principles were incorporated into computer-aided software engineering tools delivered by Nastec Corporation, Transform Logic, Inc., KnowledgeWare (see Fran Tarkenton and James Martin), Texas Instruments, Arthur Andersen and ultimately IBM Corporation.
[edit]
Sociology and Sociocybernetics

Sociology

Portal
General aspects
History · Positivism · Antipositivism
Functionalism · Conflict theory
Social theory · Critical theory
Structure & agency · Socialization
Research · Public sociology...

It is in this way that systems theorists attempted to provide alternatives and an evolved ideation from orthodox theories with individuals such as Max Weber, Emile Durkheim in sociology and Frederick Winslow Taylor in scientific management, which were grounded in classical assumptions [10].

Lorenz tracked this down to the computer printout.

As a technical and general academic area of study it predominantly refers to the science of systems that resulted from Bertalanffy's General System Theory (GST), among others, in initiating what became a project of systems research and practice.

In most cases the whole has properties that cannot be known from analysis of the constituent elements in isolation.

Models for dynamic equilibrium in systems analysis that contrasted classical views from Talcott Parsons and George Homans were influential in integrating concepts with the general movement.

He also states it is clear to Gorelik (1975) that the "conceptual part" of general system theory (GST) had first been put in place by Bogdanov.

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Classical science had not been overthrown, but questions arose over core assumptions that historically influenced organized systems, within both social and technical sciences.[citation needed]
[edit]
History
TIMELINE
0. 1820-1903 Herbert Spencer
0. 1848-1923 Vilfredo Pareto
0. 1858-1917 Emile Durkheim
0. 1882-1950 Nicolai Hartmann
0. 1922 Alexander Bogdanov publishes Tectology in Russian (German translation 1928, English 1980)
0. 1929-1951 Robert Maynard Hutchins, University of Chicago
0. 19...

Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different (even the evolution of simple discrete systems, such as cellular automata, can heavily depend on initial conditions, and Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule 30).

In fields like cybernetics, researchers like Norbert Wiener, William Ross Ashby, John von Neumann and Heinz von Foerster examined complex systems using mathematics.

Indeed, it has extremely simple behaviour: all points except 0 tend to infinity.
[edit]
Density of periodic orbits
Density of periodic orbits means that every point in the space is approached arbitrarily closely by periodic orbits.

Toronto: Lexington Books.
0.

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

At the same time Howard T. Odum, the radiation ecologist, recognised that the study of general systems required a language that could depict energetics and kinetics at any system scale.

The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.

The preface explains that the original concept of a general system theory was "Allgemeine Systemtheorie (or Lehre)", pointing out the fact that "Theorie" (or "Lehre") just as "Wissenschaft" (translated Scholarship), "has a much broader meaning in German than the closest English words ‘theory’ and ‘science'" [3].

With these ideas referring to an organized body of knowledge and "any systematically presented set of concepts, whether they are empirical, axiomatic, or philosophical", "Lehre" is associated with theory and science in the etymology of general systems, but also does not translate from the German very well; "teaching" is the "closest equivalent", but "sounds dogmatic and off the mark" [3].

In other words, it transcends the perspectives of individual disciplines, integrating them on the basis of a common "code", or more exactly, on the basis of the formal apparatus provided by systems theory.

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftershocks); s...

If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory there is no problem choosing the dimension too large – the method will work.

The year before, Benoît Mandelbrot found recurring patterns at every scale in data on cotton prices.[39]

An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket).

With the modern foundations for a general theory of systems following the World Wars, Ervin Laszlo, in the preface for Bertalanffy's book Perspectives on General System Theory, maintains that the translation of "general system theory" from German into English has "wrought a certain amount of havoc" [3].

Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behaviour such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law[53] describing the frequency of aftersho...

Von Bertalanffy defined system as "elements in standing relationship.
—[6]
Similar ideas are found in learning theories that developed from the same fundamental concepts, emphasizing that understanding results from knowing concepts both in part and as a whole.

Second, all systems, whether electrical, biological, or social, have common patterns, behaviors, and properties that can be understood and used to develop greater insight into the behavior of complex phenomena and to move closer toward a unity of science.

Its focus is how anything (digital, mechanical or biological) processes information, reacts to information, and changes or can be changed to better accomplish the first two tasks.

Contemporary ideas from systems theory have grown with diversified areas, exemplified by the work of Béla H. Bánáthy, ecological systems with Howard T. Odum, Eugene Odum and Fritjof Capra, organizational theory and management with individuals such as Peter Senge, interdisciplinary study with areas like Human Resource Development from the work of Richard A. Swanson, and insights from educators such as Debora Hammond.

The first discoverer of chaos was Henri Poincaré.

The influential contemporary work of Peter Senge [9] provides detailed discussion of the commonplace critique of educational systems grounded in conventional assumptions about learning, including the problems with fragmented knowledge and lack of holistic learning from the "machine-age thinking" that became a "model of school separated from daily life."

In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature.[30]

Here two series of x and y values diverge markedly over time from a tiny initial difference.

Slightly revising the original model a dozen years later, he distinguished eight "nested" hierarchical levels in such complex structures.

n systems science, systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result.

In this respect, with the possibility of misinterpretations, von Bertalanffy [2] believed a general theory of systems "should be an important regulative device in science," to guard against superficial analogies that "are useless in science and harmful in their practical consequences."

Mechanistic thinking was particularly critiqued, especially the industrial-age mechanistic metaphor of the mind from interpretations of Newtonian mechanics by Enlightenment philosophers and later psychologists that laid the foundations of modern organizational theory and management by the late 19th century [12].

If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory there is no problem choosing the dimension too large – the method will work.

Subjects like complexity, self-organization, connectionism and adaptive systems had already been studied in the 1940s and 1950s.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices.

Since the end of the Cold War, there has been a renewed interest in systems theory with efforts to strengthen an ethical view.
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Developments in system theories
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General systems research and systems inquiry
Many early systems theorists aimed at finding a general systems theory that could explain all systems in all fields of science.

Systems theory thus serves as a bridge for interdisciplinary dialogue between autonomous areas of study as well as within the area of systems science itself.

Techniques of System Analysis, Rand Corporation* Laszlo, E. (1995).

The preface explains that the original concept of a general system theory was "Allgemeine Systemtheorie (or Lehre)", pointing out the fact that "Theorie" (or "Lehre") just as "Wissenschaft" (translated Scholarship), "has a much broader meaning in German than the closest English words ‘theory’ and ‘science'" [3].

Jay Forrester with his work in dynamics and management alongside numerous theorists including Edgar Schein that followed in their tradition since the Civil Rights Era have also been influential.

John von Neumann discovered cellular automata and self-reproducing systems, again with only pencil and paper.

For example, an irrational rotation of the circle is topologically transitive, but does not have dense periodic orbits, and hence does not have sensitive dependence on initial conditions.[22]

Odum developed a general systems, or Universal language, based on the circuit language of electronics to fulfill this role, known as the Energy Systems Language.

Important names in contemporary systems science include Russell Ackoff, Béla H. Bánáthy, Anthony Stafford Beer, Peter Checkland, Robert L. Flood, Fritjof Capra, Michael C. Jackson, and Werner Ulrich, among others.

In most cases the whole has properties that cannot be known from analysis of the constituent elements in isolation.

Cellular automata (CA), neural networks (NN), artificial intelligence (AI), and artificial life (ALife) are related fields, but they do not try to describe general (universal) complex (singular) systems.

For example, in noting the influence in organizational psychology as the field evolved from "an individually oriented industrial psychology to a systems and developmentally oriented organizational psychology," it was recognized that organizations are complex social systems; reducing the parts from the whole reduces the overall effectiveness of organizations [4].

Systems theoretical approaches were later appropriated in other fields, such as in the structural functionalist sociology of Talcott Parsons and Niklas Luhmann.

In Living Systems Miller provides a detailed look at a number of systems in order of increasing size, and identifies his subsystems in each.

In the most general sense, system means a configuration of parts connected and joined together by a web of relationships.