| Complex systems |
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| Topics |
Systems thinking is a way of making sense of the complexity of the world by looking at it in terms of wholes and relationships rather than by splitting it down into its parts. [1] [2] It has been used as a way of exploring and developing effective action in complex contexts, [3] enabling systems change. [4] [5] Systems thinking draws on and contributes to systems theory and the system sciences. [6]
The term system is polysemic: Robert Hooke (1674) used it in multiple senses, in his System of the World, [7] : p.24 but also in the sense of the Ptolemaic system versus the Copernican system [8] : 450 of the relation of the planets to the fixed stars [9] which are cataloged in Hipparchus' and Ptolemy's Star catalog. [10] Hooke's claim was answered in magisterial detail by Newton's (1687) Philosophiæ Naturalis Principia Mathematica , Book three, The System of the World [11] : Book three (that is, the system of the world is a physical system). [7]
Newton's approach, using dynamical systems continues to this day. [8] In brief, Newton's equations (a system of equations) have methods for their solution.
By 1824 the Carnot cycle presented an engineering challenge, which was how to maintain the operating temperatures of the hot and cold working fluids of the physical plant. [12] In 1868 James Clerk Maxwell presented a framework for, and a limited solution to the problem of controlling the rotational speed of a physical plant. [13] Maxwell's solution echoed James Watt's (1784) centrifugal moderator (denoted as element Q) for maintaining (but not enforcing) the constant speed of a physical plant (that is, Q represents a moderator, but not a governor, by Maxwell's definition). [14] [lower-alpha 1]
Maxwell's approach, which linearized the equations of motion of the system, produced a tractable method of solution. [14] : 428–429 Norbert Wiener identified this approach as an influence on his studies of cybernetics [lower-alpha 2] during World War II [14] and Wiener even proposed treating some subsystems under investigation as black boxes. [18] : 242 Methods for solutions of the systems of equations then become the subject of study, as in feedback control systems, in stability theory, in constraint satisfaction problems, the unification algorithm, type inference, and so forth.
...What is a system? A system is a set of things ... interconnected in such a way that they produce their own pattern of behavior over time. ... But the system’s response to these forces is characteristic of itself, and that response is seldom simple in the real world
[a system] is "an integrated whole even though composed of diverse, interacting, specialized structures and subjunctions"
Living systems are resilient, [24] and are far from equilibrium. [19] : Ch.3 [40] Homeostasis is the analog to equilibrium, for a living system; the concept was described in 1849, and the term was coined in 1926. [41] [42]
Resilient systems are self-organizing; [24] [lower-alpha 4] [19] : Ch.3 [43]
The scope of functional controls is hierarchical, in a resilient system. [24] [19] : Ch.3
Frameworks and methodologies for systems thinking include:
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.
Systems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" when it expresses synergy or emergent behavior.
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector diverge at a rate given by
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter. A tornado may be thought of as a dissipative system. Dissipative systems stand in contrast to conservative systems.
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Separated objects attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability.
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.
Indeterminism is the idea that events are not caused, or are not caused deterministically.
Systems science, also referred to as systems research, or, simply, systems, is a transdisciplinary field that is concerned with understanding simple and complex systems in nature and society, which leads to the advancements of formal, natural, social, and applied attributions throughout engineering, technology and science, itself.
A conceptual system is a system of abstract concepts, of various kinds. The abstract concepts can range "from numbers, to emotions, and from social roles, to mental states ..". These abstract concepts are themselves grounded in multiple systems. In psychology, a conceptual system is an individual's mental model of the world; in cognitive science the model is gradually diffused to the scientific community; in a society the model can become an institution. In humans, a conceptual system may be understood as kind of a metaphor for the world. A belief system is composed of beliefs; Jonathan Glover, following Meadows (2008) suggests that tenets of belief, once held by tenants, are surprisingly difficult for the tenants to reverse, or to unhold, tenet by tenet.
A glossary of terms relating to systems theory.
Management cybernetics is concerned with the application of cybernetics to management and organizations. "Management cybernetics" was first introduced by Stafford Beer in the late 1950s and introduces the various mechanisms of self-regulation applied by and to organizational settings, as seen through a cybernetics perspective. Beer developed the theory through a combination of practical applications and a series of influential books. The practical applications involved steel production, publishing and operations research in a large variety of different industries. Some consider that the full flowering of management cybernetics is represented in Beer's books. However, learning continues.
A cyberneticist or a cybernetician is a person who applies cybernetics.
Stuart Anspach Umpleby is an American cybernetician and professor in the Department of Management and Director of the Research Program in Social and Organizational Learning in the School of Business at the George Washington University.
In physics, time is defined by its measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity and, like length, mass, and charge, is usually described as a fundamental quantity. Time can be combined mathematically with other physical quantities to derive other concepts such as motion, kinetic energy and time-dependent fields. Timekeeping is a complex of technological and scientific issues, and part of the foundation of recordkeeping.
Cybernetics is the transdisciplinary study of circular processes such as feedback systems where outputs are also inputs. It is concerned with general principles that are relevant across multiple contexts, including in ecological, technological, biological, cognitive and social systems and also in practical activities such as designing, learning, and managing.
Cybernetics: Or Control and Communication in the Animal and the Machine is a book written by Norbert Wiener and published in 1948. It is the first public usage of the term "cybernetics" to refer to self-regulating mechanisms. The book laid the theoretical foundation for servomechanisms, automatic navigation, analog computing, artificial intelligence, neuroscience, and reliable communications.
Self-organization, a process where some form of overall order arises out of the local interactions between parts of an initially disordered system, was discovered in cybernetics by William Ross Ashby in 1947. It states that any deterministic dynamic system automatically evolves towards a state of equilibrium that can be described in terms of an attractor in a basin of surrounding states. Once there, the further evolution of the system is constrained to remain in the attractor. This constraint implies a form of mutual dependency or coordination between its constituent components or subsystems. In Ashby's terms, each subsystem has adapted to the environment formed by all other subsystems.
Cybernetics in the Soviet Union had its own particular characteristics, as the study of cybernetics came into contact with the dominant scientific ideologies of the Soviet Union and the nation's economic and political reforms: from the unmitigated anti-Americanist criticism of cybernetics in the early 1950s; its legitimization after Stalin's death and up to 1961; its total saturation of Soviet academia in the 1960s; and its eventual decline through the 1970s and 1980s.
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