🔬Data Science: Self-Organizing Map (Definitions)

"A clustering neural net, with topological structure among cluster units." (Laurene V Fausett, "Fundamentals of Neural Networks: Architectures, Algorithms, and Applications", 1994)

"A self organizing map is a form of Kohonen network that arranges its clusters in a (usually) two-dimensional grid so that the codebook vectors (the cluster centers) that are close to each other on the grid are also close in the k-dimensional feature space. The converse is not necessarily true, as codebook vectors that are close in feature-space might not be close on the grid. The map is similar in concept to the maps produced by descriptive techniques such as multi-dimensional scaling (MDS)." (William J Raynor Jr., "The International Dictionary of Artificial Intelligence", 1999)

"result of a nonparametric regression process that is mainly used to represent high-dimensional, nonlinearly related data items in an illustrative, often two-dimensional display, and to perform unsupervised classification and clustering." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

"a method of organizing and displaying textual information according to the frequency of occurrence of text and the relationship of text from one document to another." (William H Inmon, "Building the Data Warehouse", 2005)

"A type of unsupervised neural network used to group similar cases in a sample. SOMs are unsupervised (see supervised network) in that they do not require a known dependent variable. They are typically used for exploratory analysis and to reduce dimensionality as an aid to interpretation of complex data. SOMs are similar in purpose to Ic-means clustering and factor analysis." (David Scarborough & Mark J Somers, "Neural Networks in Organizational Research: Applying Pattern Recognition to the Analysis of Organizational Behavior", 2006)

"A method to learn to cluster input vectors according to how they are naturally grouped in the input space. In its simplest form, the map consists of a regular grid of units and the units learn to represent statistical data described by model vectors. Each map unit contains a vector used to represent the data. During the training process, the model vectors are changed gradually and then the map forms an ordered non-linear regression of the model vectors into the data space." (Atiq Islam et al, "CNS Tumor Prediction Using Gene Expression Data Part II", Encyclopedia of Artificial Intelligence, 2009)

"A neural-network method that reduces the dimensions of data while preserving the topological properties of the input data. SOM is suitable for visualizing high-dimensional data such as microarray data." (Emmanuel Udoh & Salim Bhuiyan, "C-MICRA: A Tool for Clustering Microarray Data", 2009)

"A neural network unsupervised method of vector quantization widely used in classification. Self-Organizing Maps are a much appreciated for their topology preservation property and their associated data representation system. These two additive properties come from a pre-defined organization of the network that is at the same time a support for the topology learning and its representation. (Patrick Rousset & Jean-Francois Giret, "A Longitudinal Analysis of Labour Market Data with SOM" Encyclopedia of Artificial Intelligence, 2009)

"A simulated neural network based on a grid of artificial neurons by means of prototype vectors. In an unsupervised training the prototype vectors are adapted to match input vectors in a training set. After completing this training the SOM provides a generalized K-means clustering as well as topological order of neurons." (Laurence Mukankusi et al, "Relationships between Wireless Technology Investment and Organizational Performance", 2009)

"A subtype of artificial neural network. It is trained using unsupervised learning to produce low dimensional representation of the training samples while preserving the topological properties of the input space." (Soledad Delgado et al, "Growing Self-Organizing Maps for Data Analysis", 2009)

"An unsupervised neural network providing a topology-preserving mapping from a high-dimensional input space onto a two-dimensional output space." (Thomas Lidy & Andreas Rauber, "Music Information Retrieval", 2009)

"Category of algorithms based on artificial neural networks that searches, by means of self-organization, to create a map of characteristics that represents the involved samples in a determined problem." (Paulo E Ambrósio, "Artificial Intelligence in Computer-Aided Diagnosis", 2009)

"Self-organizing maps (SOMs) are a data visualization technique which reduce the dimensions of data through the use of self-organizing neural networks." (Lluís Formiga & Francesc Alías, "GTM User Modeling for aIGA Weight Tuning in TTS Synthesis", Encyclopedia of Artificial Intelligence, 2009)

"SOFM [self-organizing feature map] is a data mining method used for unsupervised learning. The architecture consists of an input layer and an output layer. By adjusting the weights of the connections between input and output layer nodes, this method identifies clusters in the data." (Indranil Bose, "Data Mining in Tourism", 2009)

"The self-organizing map is a subtype of artificial neural networks. It is trained using unsupervised learning to produce low dimensional representation of the training samples while preserving the topological properties of the input space. The self-organizing map is a single layer feed-forward network where the output syntaxes are arranged in low dimensional (usually 2D or 3D) grid. Each input is connected to all output neurons. Attached to every neuron there is a weight vector with the same dimensionality as the input vectors. The number of input dimensions is usually a lot higher than the output grid dimension. SOMs are mainly used for dimensionality reduction rather than expansion." (Larbi Esmahi et al, "Adaptive Neuro-Fuzzy Systems", Encyclopedia of Artificial Intelligence, 2009)

"A type of neural network that uses unsupervised learning to produce two-dimensional representations of an input space." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"The Self-organizing map is a non-parametric and non-linear neural network that explores data using unsupervised learning. The SOM can produce output that maps multidimensional data onto a two-dimensional topological map. Moreover, since the SOM requires little a priori knowledge of the data, it is an extremely useful tool for exploratory analyses. Thus, the SOM is an ideal visualization tool for analyzing complex time-series data." (Peter Sarlin, "Visualizing Indicators of Debt Crises in a Lower Dimension: A Self-Organizing Maps Approach", 2012)

"SOMs or Kohonen networks have a grid topology, with unequal grid weights. The topology of the grid provides a low dimensional visualization of the data distribution." (Siddhartha Bhattacharjee et al, "Quantum Backpropagation Neural Network Approach for Modeling of Phenol Adsorption from Aqueous Solution by Orange Peel Ash", 2013)

"An unsupervised neural network widely used in exploratory data analysis and to visualize multivariate object relationships." (Manuel Martín-Merino, "Semi-Supervised Dimension Reduction Techniques to Discover Term Relationships", 2015)

"ANN used for visualizing low-dimensional views of high-dimensional data." (Pablo Escandell-Montero et al, "Artificial Neural Networks in Physical Therapy", 2015)

"Is a unsupervised learning ANN, which means that no human intervention is needed during the learning and that little needs to be known about the characteristics of the input data." (Nuno Pombo et al, "Machine Learning Approaches to Automated Medical Decision Support Systems", 2015)

"A kind of artificial neural network which attempts to mimic brain functions to provide learning and pattern recognition techniques. SOM have the ability to extract patterns from large datasets without explicitly understanding the underlying relationships. They transform nonlinear relations among high dimensional data into simple geometric connections among their image points on a low-dimensional display." (Felix Lopez-Iturriaga & Iván Pastor-Sanz, "Using Self Organizing Maps for Banking Oversight: The Case of Spanish Savings Banks", 2016)

"Neural network which simulated some cerebral functions in elaborating visual information. It is usually used to classify a large amount of data." (Gaetano B Ronsivalle & Arianna Boldi, "Artificial Intelligence Applied: Six Actual Projects in Big Organizations", 2019)

"Classification technique based on unsupervised-learning artificial neural networks allowing to group data into clusters." Julián Sierra-Pérez & Joham Alvarez-Montoya, "Strain Field Pattern Recognition for Structural Health Monitoring Applications", 2020)

"It is a type of artificial neural network (ANN) trained using unsupervised learning for dimensionality reduction by discretized representation of the input space of the training samples called as map." (Dinesh Bhatia et al, "A Novel Artificial Intelligence Technique for Analysis of Real-Time Electro-Cardiogram Signal for the Prediction of Early Cardiac Ailment Onset", 2020)

"Being a particular type of ANNs, the Self Organizing Map is a simple mapping from inputs: attributes directly to outputs: clusters by the algorithm of unsupervised learning. SOM is a clustering and visualization technique in exploratory data analysis." (Yuh-Wen Chen, "Social Network Analysis: Self-Organizing Map and WINGS by Multiple-Criteria Decision Making", 2021)

🔬Data Science: Swarm Intelligence (Definitions)

"Swarm systems generate novelty for three reasons: (1) They are 'sensitive to initial conditions' - a scientific shorthand for saying that the size of the effect is not proportional to the size of the cause - so they can make a surprising mountain out of a molehill. (2) They hide countless novel possibilities in the exponential combinations of many interlinked individuals. (3) They don’t reckon individuals, so therefore individual variation and imperfection can be allowed. In swarm systems with heritability, individual variation and imperfection will lead to perpetual novelty, or what we call evolution." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Dumb parts, properly connected into a swarm, yield smart results." (Kevin Kelly, "New Rules for the New Economy", 1999)

"It is, however, fair to say that very few applications of swarm intelligence have been developed. One of the main reasons for this relative lack of success resides in the fact that swarm-intelligent systems are hard to 'program', because the paths to problem solving are not predefined but emergent in these systems and result from interactions among individuals and between individuals and their environment as much as from the behaviors of the individuals themselves. Therefore, using a swarm-intelligent system to solve a problem requires a thorough knowledge not only of what individual behaviors must be implemented but also of what interactions are needed to produce such or such global behavior." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)

"Just what valuable insights do ants, bees, and other social insects hold? Consider termites. Individually, they have meager intelligence. And they work with no supervision. Yet collectively they build mounds that are engineering marvels, able to maintain ambient temperature and comfortable levels of oxygen and carbon dioxide even as the nest grows. Indeed, for social insects teamwork is largely self-organized, coordinated primarily through the interactions of individual colony members. Together they can solve difficult problems (like choosing the shortest route to a food source from myriad possible pathways) even though each interaction might be very simple (one ant merely following the trail left by another). The collective behavior that emerges from a group of social insects has been dubbed 'swarm intelligence'." (Eric Bonabeau & Christopher Meyer, Swarm Intelligence: A Whole New Way to Think About Business, Harvard Business Review, 2001)

"[…] swarm intelligence is becoming a valuable tool for optimizing the operations of various businesses. Whether similar gains will be made in helping companies better organize themselves and develop more effective strategies remains to be seen. At the very least, though, the field provides a fresh new framework for solving such problems, and it questions the wisdom of certain assumptions regarding the need for employee supervision through command-and-control management. In the future, some companies could build their entire businesses from the ground up using the principles of swarm intelligence, integrating the approach throughout their operations, organization, and strategy. The result: the ultimate self-organizing enterprise that could adapt quickly - and instinctively - to fast-changing markets." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"Swarm Intelligence can be defined more precisely as: Any attempt to design algorithms or distributed problem-solving methods inspired by the collective behavior of the social insect colonies or other animal societies. The main properties of such systems are flexibility, robustness, decentralization and self-organization." (Ajith Abraham et al, "Swarm Intelligence in Data Mining", 2006)

"Swarm intelligence can be effective when applied to highly complicated problems with many nonlinear factors, although it is often less effective than the genetic algorithm approach discussed later in this chapter. Swarm intelligence is related to swarm optimization […]. As with swarm intelligence, there is some evidence that at least some of the time swarm optimization can produce solutions that are more robust than genetic algorithms. Robustness here is defined as a solution’s resistance to performance degradation when the underlying variables are changed." (Michael J North & Charles M Macal, "Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation", 2007)

[swarm intelligence] "Refers to a class of algorithms inspired by the collective behaviour of insect swarms, ant colonies, the flocking behaviour of some bird species, or the herding behaviour of some mammals, such that the behaviour of the whole can be considered as exhibiting a rudimentary form of 'intelligence'." (John Fulcher, "Intelligent Information Systems", 2009)

"The property of a system whereby the collective behaviors of unsophisticated agents interacting locally with their environment cause coherent functional global patterns to emerge." (M L Gavrilova, "Adaptive Algorithms for Intelligent Geometric Computing", 2009) 

[swarm intelligence] "Is a discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization. In particular, SI focuses on the collective behaviors that result from the local interactions of the individuals with each other and with their environment." (Elina Pacini et al, "Schedulers Based on Ant Colony Optimization for Parameter Sweep Experiments in Distributed Environments", 2013). 

"Swarm intelligence (SI) is a branch of computational intelligence that discusses the collective behavior emerging within self-organizing societies of agents. SI was inspired by the observation of the collective behavior in societies in nature such as the movement of birds and fish. The collective behavior of such ecosystems, and their artificial counterpart of SI, is not encoded within the set of rules that determines the movement of each isolated agent, but it emerges through the interaction of multiple agents." (Maximos A Kaliakatsos-Papakostas et al, "Intelligent Music Composition", 2013)

"Collective intelligence of societies of biological (social animals) or artificial (robots, computer agents) individuals. In artificial intelligence, it gave rise to a computational paradigm based on decentralisation, self-organisation, local interactions, and collective emergent behaviours." (D T Pham & M Castellani, "The Bees Algorithm as a Biologically Inspired Optimisation Method", 2015)

"It is the field of artificial intelligence in which the population is in the form of agents which search in a parallel fashion with multiple initialization points. The swarm intelligence-based algorithms mimic the physical and natural processes for mathematical modeling of the optimization algorithm. They have the properties of information interchange and non-centralized control structure." (Sajad A Rather & P Shanthi Bala, "Analysis of Gravitation-Based Optimization Algorithms for Clustering and Classification", 2020)

"It [swarm intelligence] is the discipline dealing with natural and artificial systems consisting of many individuals who coordinate through decentralized monitoring and self-organization." (Mehmet A Cifci, "Optimizing WSNs for CPS Using Machine Learning Techniques", 2021)

Resources:
More quotes on "Swarm Intelligence" at the-web-of-knowledge.blogspot.com.

🕸Systems Engineering: Emergence (Just the Quotes)

"[Hierarchy is] the principle according to which entities meaningfully treated as wholes are built up of smaller entities which are themselves wholes […] and so on. In hierarchy, emergent properties denote the levels." (Peter Checkland, "Systems Thinking, Systems Practice", 1981)

"[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations." (Fritjof Capra, "The web of life: a new scientific understanding of living systems", 1996)

"It may not be obvious at first, but the study of emergence and model-building go hand in hand. The essence of model-building is shearing away detail to get at essential elements. A model, by concentrating on selected aspects of the world, makes possible the prediction and planning that reveal new possibilities. That is exactly the problem we face in trying to develop a scientific understanding of emergence." (John H Holland, "Emergence" , Philosophica 59, 1997)

"When the behavior of the system depends on the behavior of the parts, the complexity of the whole must involve a description of the parts, thus it is large. The smaller the parts that must be described to describe the behavior of the whole, the larger the complexity of the entire system. […] A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be simply inferred from the behavior of its components." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)

"The phenomenon of emergence takes place at critical points of instability that arise from fluctuations in the environment, amplified by feedback loops." (Fritjof Capra, "The Hidden Connections", 2002)

"This spontaneous emergence of order at critical points of instability is one of the most important concepts of the new understanding of life. It is technically known as self-organization and is often referred to simply as ‘emergence’. It has been recognized as the dynamic origin of development, learning and evolution. In other words, creativity-the generation of new forms-is a key property of all living systems. And since emergence is an integral part of the dynamics of open systems, we reach the important conclusion that open systems develop and evolve. Life constantly reaches out into novelty." (Fritjof  Capra, "The Hidden Connections", 2002)

"Emergence is not really mysterious, although it may be complex. Emergence is brought about by the interactions between the parts of a system. The galloping horse illusion depends upon the persistence of the human retina/brain combination, for instance. Elemental gases bond in combination by sharing outer electrons, thereby altering the appearance and behavior of the combination. In every case of emergence, the source is interaction between the parts - sometimes, as with the brain, very many parts - so that the phenomenon defies simple explanation." (Derek Hitchins, "Advanced Systems Thinking, Engineering and Management", 2003)

"Emergence is the phenomenon of properties, capabilities and behaviours evident in the whole system that are not exclusively ascribable to any of its parts." (Derek Hitchins, "Advanced Systems Thinking, Engineering and Management", 2003)

"Another typical feature of theories of emergence is the layered view of nature. On this view, all things in nature belong to a certain level of existence, each according to its characteristic properties. These levels of existence constitute a hierarchy of increasing complexity that also corresponds to their order of appearance in the course of evolution." (Markus Eronen, "Emergence in the Philosophy of Mind", 2004)

"The basic concept of complexity theory is that systems show patterns of organization without organizer (autonomous or self-organization). Simple local interactions of many mutually interacting parts can lead to emergence of complex global structures. […] Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or 'punctuations' of all sizes. In the critical state, events which would otherwise be uncoupled became correlated." (Jochen Fromm, "The Emergence of Complexity", 2004)

"Complexity arises when emergent system-level phenomena are characterized by patterns in time or a given state space that have neither too much nor too little form. Neither in stasis nor changing randomly, these emergent phenomena are interesting, due to the coupling of individual and global behaviours as well as the difficulties they pose for prediction. Broad patterns of system behaviour may be predictable, but the system's specific path through a space of possible states is not." (Steve Maguire et al, "Complexity Science and Organization Studies", 2006)

"The beauty of nature insists on taking its time. Everything is prepared. Nothing is rushed. The rhythm of emergence is a gradual, slow beat; always inching its way forward, change remains faithful to itself until the new unfolds in the full confidence of true arrival. Because nothing is abrupt, the beginning of spring nearly always catches us unawares. It is there before we see it; and then we can look nowhere without seeing it. (John O'Donohue, "To Bless the Space Between Us: A Book of Blessings", 2008)

"Although the potential for chaos resides in every system, chaos, when it emerges, frequently stays within the bounds of its attractor(s): No point or pattern of points is ever repeated, but some form of patterning emerges, rather than randomness. Life scientists in different areas have noticed that life seems able to balance order and chaos at a place of balance known as the edge of chaos. Observations from both nature and artificial life suggest that the edge of chaos favors evolutionary adaptation." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"If universality is one of the observed characteristics of complex dynamical systems in many fields of study, a second characteristic that flows from the study of these systems is that of emergence. As self-organizing systems go about their daily business, they are constantly exchanging matter and energy with their environment, and this allows them to remain in a state that is far from equilibrium. That allows spontaneous behavior to give rise to new patterns." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"The notion of emergence is used in a variety of disciplines such as evolutionary biology, the philosophy of mind and sociology, as well as in computational and complexity theory. It is associated with non-reductive naturalism, which claims that a hierarchy of levels of reality exist. While the emergent level is constituted by the underlying level, it is nevertheless autonomous from the constituting level. As a naturalistic theory, it excludes non-natural explanations such as vitalistic forces or entelechy. As non-reductive naturalism, emergence theory claims that higher-level entities cannot be explained by lower-level entities." (Martin Neumann, "An Epistemological Gap in Simulation Technologies and the Science of Society", 2011)

"System theorists know that it's easy to couple simple-to-understand systems into a ‘super system’ that's capable of displaying behavioral modes that cannot be seen in any of its constituent parts. This is the process called ‘emergence’." (John L Casti, [interview with Austin Allen], 2012)

"Every system that has existed emerged somehow, from somewhere, at some point. Complexity science emphasizes the study of how systems evolve through their disorganized parts into an organized whole." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Things evolve to evolve. Evolutionary processes are the linchpin of change. These processes of discovery represent a complexity of simple systems that flux in perpetual tension as they teeter at the edge of chaos. This whirlwind of emergence is responsible for the spontaneous order and higher, organized complexity so noticeable in biological evolution - one–celled critters beefing up to become multicellular organisms." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"This spontaneous emergence of order at critical points of instability, which is often referred to simply as 'emergence', is one of the hallmarks of life. It has been recognized as the dynamic origin of development, learning, and evolution. In other words, creativity-the generation of new forms-is a key property of all living systems." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

More quotes on "Emergence" at the-web-of-knowledge.blogspot.com.

🕸Systems Engineering: Systems (Just the Quotes)

"Systems in many respects resemble machines. A machine is a little system, created to perform, as well as to connect together, in reality, those different movements and effects which the artist has occasion for.  A system is an imaginary machine invented to connect together in the fancy those different movements and effects which are already in reality performed." (Adam Smith, "The Wealth of Nations", 1776)

"A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example." (Georg C Lichtenberg, Notebook J, 1789-1793)

"A system is a whole which is composed of various parts. But it is not the same thing as an aggregate or heap. In an aggregate or heap, no essential relation exists between the units of which it is composed. In a heap of grain, or pile of stones, one may take away part without the other part being at all affected thereby. But in a system, each part has a fixed and necessary relation to the whole and to all the other parts. For this reason we may say that a building, or a peace of mechanisme, is a system. Each stone in the building, each wheel in the watch, plays a part, and is essential to the whole." (James E Creighton, "An Introductory Logic"‎, 1909)

"The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s ‘blank form of a universe’ without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition." (Lawrence J Henderson, "The Order of Nature: An Essay", 1917)

"The complexity of a system is no guarantee of its accuracy." (John P Jordan, "Cost accounting; principles and practice", 1920)

"Given a situation, a system with a Leerstelle [a gap], whether a given completion (Lueckenfuellung) does justice to the structure, is the 'right' one, is often determined by the structure of the system, the situation. There are requirements, structurally determined; there are possible in pure cases unambiguous decisions as to which completion does justice to the situation, which does not, which violates the requirements and the situation." (Max Wertheimer, "Some Problems in the Theory of Ethics", Social Research Vol. 2 (3), 1935)

"A system is difficult to define, but it is easy to recognize some of its characteristics. A system possesses boundaries which segregate it from the rest of its field: it is cohesive in the sense that it resists encroachment from without […]" (Marvin G Cline, "Fundamentals of a theory of the self: some exploratory speculations‎", 1950)

"Now a system is said to be at equilibrium when it has no further tendency to change its properties." (Walter J Moore, "Physical chemistry", 1950)

"Every part of the system is so related to every other part that any change in one aspect results in dynamic changes in all other parts of the total system." (Arthur D Hall & Robert E Fagen, "Definition of System", General Systems Vol. 1, 1956)

"Any pattern of activity in a network, regarded as consistent by some observer, is a system, Certain groups of observers, who share a common body of knowledge, and subscribe to a particular discipline, like 'physics' or 'biology' (in terms of which they pose hypotheses about the network), will pick out substantially the same systems. On the other hand, observers belonging to different groups will not agree about the activity which is a system." (Gordon Pask, "The Natural History of Networks", 1960)

"Clearly, if the state of the system is coupled to parameters of an environment and the state of the environment is made to modify parameters of the system, a learning process will occur. Such an arrangement will be called a Finite Learning Machine, since it has a definite capacity. It is, of course, an active learning mechanism which trades with its surroundings. Indeed it is the limit case of a self-organizing system which will appear in the network if the currency supply is generalized." (Gordon Pask, "The Natural History of Networks", 1960)

"Every isolated determinate dynamic system, obeying unchanging laws, will ultimately develop some sort of organisms that are adapted to their environments." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society Vol. 106 (6), 1962)

"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […]  'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"Synergy is the only word in our language that means behavior of whole systems unpredicted by the separately observed behaviors of any of the system's separate parts or any subassembly of the system's parts." (R Buckminster Fuller, "Operating Manual for Spaceship Earth", 1963)

"A system has order, flowing from point to point. If something dams that flow, order collapses. The untrained might miss that collapse until it was too late. That's why the highest function of ecology is the understanding of consequences." (Frank Herbert, "Dune", 1965)

"System theory is basically concerned with problems of relationships, of structure, and of interdependence rather than with the constant attributes of objects. In general approach it resembles field theory except that its dynamics deal with temporal as well as spatial patterns. Older formulations of system constructs dealt with the closed systems of the physical sciences, in which relatively self-contained structures could be treated successfully as if they were independent of external forces. But living systems, whether biological organisms or social organizations, are acutely dependent on their external environment and so must be conceived of as open systems." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"To find out what happens to a system when you interfere with it you have to interfere with it (not just passively observe it)." (George E P Box, "Use and Abuse of Regression", 1966)

"That a system is open means, not simply that it engages in interchanges with the environment, but that this interchange is an essential factor underlying the system's viability, its reproductive ability or continuity, and its ability to change. [...] Openness is an essential factor underlying a system's viability, continuity, and its ability to change."  (Walter F Buckley, "Sociology and modern systems theory", 1967)

"You cannot sum up the behavior of the whole from the isolated parts, and you have to take into account the relations between the various subordinate systems which are super-ordinated to them in order to understand the behavior of the parts." (Ludwig von Bertalanffy, "General System Theory", 1968)

"[…] as a model of a complex system becomes more complete, it becomes less understandable. Alternatively, as a model grows more realistic, it also becomes just as difficult to understand as the real world processes it represents." (Jay M Dutton & William H Starbuck," Computer simulation models of human behavior: A history of an intellectual technology", IEEE Transactions on Systems, 1971)

"A system in one perspective is a subsystem in another. But the systems view always treats systems as integrated wholes of their subsidiary components and never as the mechanistic aggregate of parts in isolable causal relations." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Technology can relieve the symptoms of a problem without affecting the underlying causes. Faith in technology as the ultimate solution to all problems can thus divert our attention from the most fundamental problem - the problem of growth in a finite system." (Donella A Meadows, "The Limits to Growth", 1972)

"[The] system may evolve through a whole succession of transitions leading to a hierarchy of more and more complex and organized states. Such transitions can arise in nonlinear systems that are maintained far from equilibrium: that is, beyond a certain critical threshold the steady-state regime become unstable and the system evolves into a new configuration." (Ilya Prigogine, Gregoire Micolis & Agnes Babloyantz, "Thermodynamics of Evolution", Physics Today 25 (11), 1972) 

"The system of nature, of which man is a part, tends to be self-balancing, self-adjusting, self-cleansing. Not so with technology." (Ernst F Schumacher, "Small is Beautiful", 1973)

"When a system is considered in two different states, the difference in volume or in any other property, between the two states, depends solely upon those states themselves and not upon the manner in which the system may pass from one state to the other." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974) 

"A system may be specified in either of two ways. In the first, which we shall call a state description, sets of abstract inputs, outputs and states are given, together with the action of the inputs on the states and the assignments of outputs to states. In the second, which we shall call a coordinate description, certain input, output and state variables are given, together with a system of dynamical equations describing the relations among the variables as functions of time. Modern mathematical system theory is formulated in terms of state descriptions, whereas the classical formulation is typically a coordinate description, for example a system of differential equations." (E S Bainbridge, "The Fundamental Duality of System Theory", 1975)

"Synergy means behavior of whole systems unpredicted by the behavior of their parts taken separately." (R Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"If all of the elements in a large system are loosely coupled to one another, then any one element can adjust to and modify a local a local unique contingency without affecting the whole system. These local adaptations can be swift, relatively economical, and substantial." (Karl E Weick, "Educational organizations as loosely coupled systems", 1976)

"In a loosely coupled system there is more room available for self-determination by the actors. If it is argued that a sense of efficacy is crucial for human beings. when a sense of efficacy might be greater in a loosely coupled system with autonomous units than it would be in a tightly coupled system where discretion is limited." (Karl E Weick, "Educational organizations as loosely coupled systems", 1976)

"For any system the environment is always more complex than the system itself. No system can maintain itself by means of a point-for-point correlation with its environment, i.e., can summon enough 'requisite variety' to match its environment. So each one has to reduce environmental complexity - primarily by restricting the environment itself and perceiving it in a categorically preformed way. On the other hand, the difference of system and environment is a prerequisite for the reduction of complexity because reduction can be performed only within the system, both for the system itself and its environment." (Thomas Luckmann & Niklas Luhmann, "The Differentiation of Society", 1977)

"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves at each level of system." (James G Miller, "Living Systems", 1978)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"A system is an internally organised whole where elements are so intimately connected that they operate as one in relation to external conditions and other systems. An element may be defined as the minimal unit performing a definite function in the whole. Systems may be either simple or complex. A complex system is one whose elements may also be regarded as systems or subsystems." (Alexander Spirkin, "Dialectical Materialism", 1983)

"But structure is not enough to make a system. A system consists of something more than structure: it is a structure with certain properties. When a structure is understood from the standpoint of its properties, it is understood as a system." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Any system that insulates itself from diversity in the environment tends to atrophy and lose its complexity and distinctive nature." (Gareth Morgan, "Images of Organization", 1986)

"Organization denotes those relations that must exist among the components of a system for it to be a member of a specific class. Structure denotes the components and relations that actually constitute a particular unity and make its organization real." (Humberto Maturana, "The Tree of Knowledge", 1987)

"The dynamics of any system can be explained by showing the relations between its parts and the regularities of their interactions so as to reveal its organization. For us to fully understand it, however, we need not only to see it as a unity operating in its internal dynamics, but also to see it in its circumstances, i.e., in the context to which its operation connects it. This understanding requires that we adopt a certain distance for observation, a perspective that in the case of historical systems implies a reference to their origin. This can be easy, for instance, in the case of man-made machines, for we have access to every detail of their manufacture. The situation is not that easy, however, as regards living beings: their genesis and their history are never directly visible and can be reconstructed only by fragments."  (Humberto Maturana, "The Tree of Knowledge", 1987)

"A system of variables is 'interrelated' if an action that affects or meant to affect one part of the system will also affect other parts of it. Interrelatedness guarantees that an action aimed at one variable will have side effects and long-term repercussions. A large number of variables will make it easy to overlook them." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

 "What is a system? A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment.” (William E Deming, "The New Economics for Industry, Government, Education”, 1993)

"The impossibility of constructing a complete, accurate quantitative description of a complex system forces observers to pick which aspects of the system they most wish to understand." (Thomas Levenson, "Measure for Measure: A musical history of science", 1994)

"Complex adaptive systems have the property that if you run them - by just letting the mathematical variable of 'time' go forward - they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously. [...]A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life. (J Doyne Farmer, "The Third Culture: Beyond the Scientific Revolution", 1995)

"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems. […] Self-organization provides a paradigm for behavior and cognition, as well as the structure and function of the nervous system. In contrast to a computer, which requires particular programs to produce particular results, the tendency for self-organization is intrinsic to natural systems under certain conditions." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)

"All systems evolve, although the rates of evolution may vary over time both between and within systems. The rate of evolution is a function of both the inherent stability of the system and changing environmental circumstances. But no system can be stabilized forever. For the universe as a whole, an isolated system, time’s arrow points toward greater and greater breakdown, leading to complete molecular chaos, maximum entropy, and heat death. For open systems, including the living systems that are of major interest to us and that interchange matter and energy with their external environments, time’s arrow points to evolution toward greater and greater complexity. Thus, the universe consists of islands of increasing order in a sea of decreasing order. Open systems evolve and maintain structure by exporting entropy to their external environments." (L Douglas Kiel, "Chaos Theory in the Social Sciences: Foundations and Applications", 1996)

"By irreducibly complex I mean a single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning. An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modification of a precursor, system, because any precursors to an irreducibly complex system that is missing a part is by definition nonfunctional." (Michael Behe, "Darwin’s Black Box", 1996)

"Understanding ecological interdependence means understanding relationships. It requires the shifts of perception that are characteristic of systems thinking - from the parts to the whole, from objects to relationships, from contents to patterns. […] Nourishing the community means nourishing those relationships." (Fritjof Capra, "The Web of Life: A New Scientific Understanding of Living Systems", 1996)

"The notion of system we are interested in may be described generally as a complex of elements or components directly or indirectly related in a network of interrelationships of various kinds, such that it constitutes a dynamic whole with emergent properties." (Walter F. Buckley, "Society: A Complex Adaptive System - Essays in Social Theory", 1998)

"Formulation of a mathematical model is the first step in the process of analyzing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to be modelled and to the specific information one is interested in. Thus, the aim of modelling is to produce an idealized description of reality, which is both expressible in a tractable mathematical form and sufficiently close to reality as far as the physical mechanisms of interest are concerned." (Francois Axisa, "Discrete Systems" Vol. I, 2001)

"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"One of the key insights of the systems approach has been the realization that the network is a pattern that is common to all life. Wherever we see life, we see networks." (Fritjof Capra, "The Hidden Connections: A Science for Sustainable Living", 2002)

"Technology can relieve the symptoms of a problem without affecting the underlying causes. Faith in technology as the ultimate solution to all problems can thus divert our attention from the most fundamental problem - the problem of growth in a finite system - and prevent us from taking effective action to solve it." (Donella H Meadows & Dennis L Meadows, "The Limits to Growth: The 30 Year Update", 2004)

"The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole." (Freeman Dyson, "The Scientist As Rebel", 2006)

"Humans have difficulty perceiving variables accurately […]. However, in general, they tend to have inaccurate perceptions of system states, including past, current, and future states. This is due, in part, to limited ‘mental models’ of the phenomena of interest in terms of both how things work and how to influence things. Consequently, people have difficulty determining the full implications of what is known, as well as considering future contingencies for potential systems states and the long-term value of addressing these contingencies." (William B. Rouse, "People and Organizations: Explorations of Human-Centered Design", 2007)

"Systemic problems trace back in the end to worldviews. But worldviews themselves are in flux and flow. Our most creative opportunity of all may be to reshape those worldviews themselves. New ideas can change everything." (Anthony Weston, "How to Re-Imagine the World", 2007)

"A model is a representation in that it (or its properties) is chosen to stand for some other entity (or its properties), known as the target system. A model is a tool in that it is used in the service of particular goals or purposes; typically these purposes involve answering some limited range of questions about the target system." (Wendy S Parker, "Confirmation and Adequacy-for-Purpose in Climate Modelling", Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 83, 2009)

"System theorists know that it's easy to couple simple-to-understand systems into a ‘super system’ that's capable of displaying behavioral modes that cannot be seen in any of its constituent parts. This is the process called ‘emergence’." (John L Casti, [interview with Austin Allen], 2012)

"When some systems are stuck in a dangerous impasse, randomness and only randomness can unlock them and set them free." (Nassim N Taleb, "Antifragile: Things That Gain from Disorder", 2012) 

"Complex systems defy intuitive solutions. Even a third-order, linear differential equation is unsolvable by inspection. Yet, important situations in management, economics, medicine, and social behavior usually lose reality if simplified to less than fifth-order nonlinear dynamic systems. Attempts to deal with nonlinear dynamic systems using ordinary processes of description and debate lead to internal inconsistencies. Underlying assumptions may have been left unclear and contradictory, and mental models are often logically incomplete. Resulting behavior is likely to be contrary to that implied by the assumptions being made about' underlying system structure and governing policies." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)

"Simplicity in a system tends to increase that system's efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system's inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Although cascading failures may appear random and unpredictable, they follow reproducible laws that can be quantified and even predicted using the tools of network science. First, to avoid damaging cascades, we must understand the structure of the network on which the cascade propagates. Second, we must be able to model the dynamical processes taking place on these networks, like the flow of electricity. Finally, we need to uncover how the interplay between the network structure and dynamics affects the robustness of the whole system." (Albert-László Barabási, "Network Science", 2016)

More quotes on "Systems" at the-web-of-knowledge.blogspot.com.

🕸Systems Engineering: Entropy (Just the Quotes)

"The second law of thermodynamics appears solely as a law of probability, entropy as a measure of the probability, and the increase of entropy is equivalent to a statement that more probable events follow less probable ones." (Max Planck, "A Survey of Physics", 1923)

"True equilibria can occur only in closed systems and that, in open systems, disequilibria called ‘steady states’, or ‘flow equilibria’ are the predominant and characteristic feature. According to the second law of thermodynamics a closed system must eventually attain a time-independent equilibrium state, with maximum entropy and minimum free energy. An open system may, under certain conditions, attain a time-independent state where the system remains constant as a whole and in its phases, though there is a continuous flow of component materials. This is called a steady state. Steady states are irreversible as a whole. […] A closed system in equilibrium does not need energy for its preservation, nor can energy be obtained from it. In order to perform work, a system must be in disequilibrium, tending toward equilibrium and maintaining a steady state, Therefore the character of an open system is the necessary condition for the continuous working capacity of the organism." (Ludwig on Bertalanffy, "Theoretische Biologie: Band 1: Allgemeine Theorie, Physikochemie, Aufbau und Entwicklung des Organismus", 1932)

"An isolated system or a system in a uniform environment (which for the present consideration we do best to include as a part of the system we contemplate) increases its entropy and more or less rapidly approaches the inert state of maximum entropy. We now recognize this fundamental law of physics to be just the natural tendency of things to approach the chaotic state (the same tendency that the books of a library or the piles of papers and manuscripts on a writing desk display) unless we obviate it. (The analogue of irregular heat motion, in this case, is our handling those objects now and again without troubling to put them back in their proper places.)" (Erwin Schrödinger, "What is Life?", 1944)

"Every process, event, happening - call it what you will; in a word, everything that is going on in Nature means an increase of the entropy of the part of the world where it is going on. Thus a living organism continually increases its entropy – or, as you may say, produces positive entropy – and thus tends to approach the dangerous state of maximum entropy, which is death. It can only keep aloof from it, i.e. alive, by continually drawing from its environment negative entropy – which is something very positive as we shall immediately see. What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive." (Erwin Schrödinger, "What is Life?", 1944)

"Time itself will come to an end. For entropy points the direction of time. Entropy is the measure of randomness. When all system and order in the universe have vanished, when randomness is at its maximum, and entropy cannot be increased, when there is no longer any sequence of cause and effect, in short when the universe has run down, there will be no direction to time - there will be no time." (Lincoln Barnett, "The Universe and Dr. Einstein", 1948)

"Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Clichés, for example, are less illuminating than great poems." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"[…] the characteristic tendency of entropy is to increase. As entropy increases, the universe, and all closed systems in the universe, tend naturally to deteriorate and lose their distinctiveness, to move from the least to the most probable state, from a state of organization and differentiation in which distinctions and forms exist, to a state of chaos and sameness." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"The powerful notion of entropy, which comes from a very special branch of physics […] is certainly useful in the study of communication and quite helpful when applied in the theory of language." (J Robert Oppenheimer, "The Growth of Science and the Structure of Culture", Daedalus 87 (1), 1958) 

"Entropy is a measure of the heat energy in a substance that has been lost and is no longer available for work. It is a measure of the deterioration of a system." (William B. Sill & Norman Hoss (Eds.), "Popular Science Encyclopedia of the Sciences", 1963)

"Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure 'disorder' by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the 'disorder' is less." (Richard P Feynman, "Order And Entropy" ["The Feynman Lectures on Physics"], 1964)

"The homeostatic principle does not apply literally to the functioning of all complex living systems, in that in counteracting entropy they move toward growth and expansion." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"Higher, directed forms of energy (e.g., mechanical, electric, chemical) are dissipated, that is, progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)

"To adapt to a changing environment, the system needs a variety of stable states that is large enough to react to all perturbations but not so large as to make its evolution uncontrollably chaotic. The most adequate states are selected according to their fitness, either directly by the environment, or by subsystems that have adapted to the environment at an earlier stage. Formally, the basic mechanism underlying self-organization is the (often noise-driven) variation which explores different regions in the system’s state space until it enters an attractor. This precludes further variation outside the attractor, and thus restricts the freedom of the system’s components to behave independently. This is equivalent to the increase of coherence, or decrease of statistical entropy, that defines self-organization." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972) 

"There is nothing supernatural about the process of self-organization to states of higher entropy; it is a general property of systems, regardless of their materials and origin. It does not violate the Second Law of thermodynamics since the decrease in entropy within an open system is always offset by the increase of entropy in its surroundings." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974) 

"The amount of information conveyed by the message increases as the amount of uncertainty as to what message actually will be produced becomes greater. A message which is one out of ten possible messages conveys a smaller amount of information than a message which is one out of a million possible messages. The entropy of communication theory is a measure of this uncertainty and the uncertainty, or entropy, is taken as the measure of the amount of information conveyed by a message from a source. The more we know about what message the source will produce, the less uncertainty, the less the entropy, and the less the information." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals and Noise", 1979) 

"Thus, an increase in entropy means a decrease in our ability to change thermal energy, the energy of heat, into mechanical energy. An increase of entropy means a decrease of available energy." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals and Noise", 1979)

"The third model regards mind as an information processing system. This is the model of mind subscribed to by cognitive psychologists and also to some extent by the ego psychologists. Since an acquisition of information entails maximization of negative entropy and complexity, this model of mind assumes mind to be an open system." (Thaddus E Weckowicz, "Models of Mental Illness", 1984) 

"Disorder increases with time because we measure time in the direction in which disorder increases." (Stephen W Hawking, "The Direction of Time", New Scientist 115 (1568), 1987)

"Somehow, after all, as the universe ebbs toward its final equilibrium in the featureless heat bath of maximum entropy, it manages to create interesting structures." (James Gleick, "Chaos: Making a New Science", 1987)

"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases."  (Stephen Hawking, "A Brief History of Time", 1988)

"The new information technologies can be seen to drive societies toward increasingly dynamic high-energy regions further and further from thermodynamical equilibrium, characterized by decreasing specific entropy and increasingly dense free-energy flows, accessed and processed by more and more complex social, economic, and political structures." (Ervin László, "Information Technology and Social Change: An Evolutionary Systems Analysis", Behavioral Science 37, 1992) 

"The second law of thermodynamics, which requires average entropy (or disorder) to increase, does not in any way forbid local order from arising through various mechanisms of self-organization, which can turn accidents into frozen ones producing extensive regularities. Again, such mechanisms are not restricted to complex adaptive systems." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)

"All systems evolve, although the rates of evolution may vary over time both between and within systems. The rate of evolution is a function of both the inherent stability of the system and changing environmental circumstances. But no system can be stabilized forever. For the universe as a whole, an isolated system, time’s arrow points toward greater and greater breakdown, leading to complete molecular chaos, maximum entropy, and heat death. For open systems, including the living systems that are of major interest to us and that interchange matter and energy with their external environments, time’s arrow points to evolution toward greater and greater complexity. Thus, the universe consists of islands of increasing order in a sea of decreasing order. Open systems evolve and maintain structure by exporting entropy to their external environments." (L Douglas Kiel, "Chaos Theory in the Social Sciences: Foundations and Applications", 1996)

"Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production." (Ilya Prigogine, "The End of Certainty: Time, Chaos, and the New Laws of Nature", 1996) 

"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"In a closed system, the change in entropy must always be 'positive', meaning toward death. However, in open biological or social systems, entropy can be arrested and may even be transformed into negative entropy - a process of more complete organization and enhanced ability to transform resources. Why? Because the system imports energy and resources from its environment, leading to renewal. This is why education and learning are so important, as they provide new and stimulating input (termed neg-entropy) that can transform each of us." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"Physical systems are subject to the force of entropy, which increases until eventually the entire system fails. The tendency toward maximum entropy is a movement to disorder, complete lack of resource transformation, and death." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"All systems have a tendency toward maximum entropy, disorder, and death. Importing resources from the environment is key to long-term viability; closed systems move toward this disorganization faster than open systems." (Stephen G Haines, "The Systems Thinking Approach to Strategic Planning and Management", 2000)

"Defined from a societal standpoint, information may be seen as an entity which reduces maladjustment between system and environment. In order to survive as a thermodynamic entity, all social systems are dependent upon an information flow. This explanation is derived from the parallel between entropy and information where the latter is regarded as negative entropy (negentropy). In more common terms information is a form of processed data or facts about objects, events or persons, which are meaningful for the receiver, inasmuch as an increase in knowledge reduces uncertainty." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)

"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"The acquisition of information is a flow from noise to order - a process converting entropy to redundancy. During this process, the amount of information decreases but is compensated by constant recoding. In the recoding the amount of information per unit increases by means of a new symbol which represents the total amount of the old. The maturing thus implies information condensation. Simultaneously, the redundance decreases, which render the information more difficult to interpret." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"The function of living matter is apparently to expand the organization of the universe. Here, locally decreased entropy as a result of biological order in existing life is invalidating the effects of the second law of thermodynamics, although at the expense of increased entropy in the whole system. It is the running down of the universe that made the sun and the earth possible. It is the running down of the sun that made life and us possible." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"Entropy is not about speeds or positions of particles, the way temperature and pressure and volume are, but about our lack of information." (Hans C von Baeyer," Information, The New Language of Science", 2003)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman Dyson, [Page-Barbour lecture], 2004)

"At the foundation of classical thermodynamics are the first and second laws. The first law formulates that the total energy of a system is conserved, while the second law states that the entropy of an isolated system can only increase. The second law implies that the free energy of an isolated system is successively degraded by diabatic processes over time, leading to entropy production. This eventually results in an equilibrium state of maximum entropy. In its statistical interpretation, the direction towards higher entropy can be interpreted as a transition to more probable states." (Axel Kleidon & Ralph D Lorenz, "Entropy Production by Earth System Processes" [in "Non- quilibrium Thermodynamics and the Production of Entropy"], 2005)

"However, the law of accelerating returns pertains to evolution, which is not a closed system. It takes place amid great chaos and indeed depends on the disorder in its midst, from which it draws its options for diversity. And from these options, an evolutionary process continually prunes its choices to create ever greater order."  (Ray Kurzweil, "The Singularity is Near", 2005)

"The second law of thermodynamics states that in an isolated system, entropy can only increase, not decrease. Such systems evolve to their state of maximum entropy, or thermodynamic equilibrium. Therefore, physical self-organizing systems cannot be isolated: they require a constant input of matter or energy with low entropy, getting rid of the internally generated entropy through the output of heat ('dissipation'). This allows them to produce ‘dissipative structures’ which maintain far from thermodynamic equilibrium. Life is a clear example of order far from thermodynamic equilibrium." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"We have to be aware that even in mathematical and physical models of self-organizing systems, it is the observer who ascribes properties, aspects, states, and probabilities; and therefore entropy or order to the system. But organization is more than low entropy: it is structure that has a function or purpose." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"Heat is the energy of random chaotic motion, and entropy is the amount of hidden microscopic information." (Leonard Susskind, "The Black Hole War", 2008)

"Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system - which is a measure of the system’s disorder, or ‘randomness’ - is greater (or at least not smaller) at later times than it was at earlier times." (Roger Penrose, "Cycles of Time: An Extraordinary New View of the Universe", 2010) 

"The laws of thermodynamics tell us something quite different. Economic activity is merely borrowing low-entropy energy inputs from the environment and transforming them into temporary products and services of value. In the transformation process, often more energy is expended and lost to the environment than is embedded in the particular good or service being produced." (Jeremy Rifkin, "The Third Industrial Revolution", 2011)

"In a physical system, information is the opposite of entropy, as it involves uncommon and highly correlated configurations that are difficult to arrive at." (César A Hidalgo, "Why Information Grows: The Evolution of Order, from Atoms to Economies", 2015)

"The passage of time and the action of entropy bring about ever-greater complexity - a branching, blossoming tree of possibilities. Blossoming disorder (things getting worse), now unfolding within the constraints of the physics of our universe, creates novel opportunities for spontaneous ordered complexity to arise." (D J MacLennan, "Frozen to Life", 2015)

"Information theory leads to the quantification of the information content of the source, as denoted by entropy, the characterization of the information-bearing capacity of the communication channel, as related to its noise characteristics, and consequently the establishment of the relationship between the information content of the source and the capacity of the channel. In short, information theory provides a quantitative measure of the information contained in message signals and help determine the capacity of a communication system to transfer this information from source to sink over a noisy channel in a reliable fashion." (Ali Grami, "Information Theory", 2016)

"The Second Law of Thermodynamics states that in an isolated system (one that is not taking in energy), entropy never decreases. (The First Law is that energy is conserved; the Third, that a temperature of absolute zero is unreachable.) Closed systems inexorably become less structured, less organized, less able to accomplish interesting and useful outcomes, until they slide into an equilibrium of gray, tepid, homogeneous monotony and stay there." (Steven Pinker, "The Second Law of Thermodynamics", 2017)

"In information theory this notion, introduced by Claude Shannon, is used to express unpredictability of information content. For instance, if a data set containing n items was divided into k groups each comprising n i items, then the entropy of such a partition is H = p 1 log( p 1 ) + … + p k log( p k ), where p i = n i / n . In case of two alternative partitions, the mutual information is a measure of the mutual dependence between these partitions." (Slawomir T Wierzchon, "Ensemble Clustering Data Mining and Databases", 2018) [where i is used as index]

"Entropy is a measure of amount of uncertainty or disorder present in the system within the possible probability distribution. The entropy and amount of unpredictability are directly proportional to each other." ("G Suseela & Y Asnath V Phamila, "Security Framework for Smart Visual Sensor Networks", 2019)

"In the physics [entropy is the] rate of system´s messiness or disorder in a physical system. In the social systems theory - social entropy is a sociological theory that evaluates social behaviors using a method based on the second law of thermodynamics." (Justína Mikulášková et al, "Spiral Management: New Concept of the Social Systems Management", 2020)

More quotes on "Entropy" at the-web-of-knowledge.blogspot.com.

🕸Systems Engineering: Complex Systems (Just the Quotes)

"The complexity of a system is no guarantee of its accuracy." (John P Jordan, "Cost accounting; principles and practice", 1920)

"[…] to the scientific mind the living and the non-living form one continuous series of systems of differing degrees of complexity […], while to the philosophic mind the whole universe, itself perhaps an organism, is composed of a vast number of interlacing organisms of all sizes." (James G Needham, "Developments in Philosophy of Biology", Quarterly Review of Biology Vol. 3 (1), 1928)

"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12 (4), 1945)

"[Disorganized complexity] is a problem in which the number of variables is very large, and one in which each of the many variables has a behavior which is individually erratic, or perhaps totally unknown. However, in spite of this helter-skelter, or unknown, behavior of all the individual variables, the system as a whole possesses certain orderly and analyzable average properties. [...] [Organized complexity is] not problems of disorganized complexity, to which statistical methods hold the key. They are all problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole. They are all, in the language here proposed, problems of organized complexity." (Warren Weaver, "Science and Complexity", American Scientist Vol. 36, 1948)

"Cybernetics is likely to reveal a great number of interesting and suggestive parallelisms between machine and brain and society. And it can provide the common language by which discoveries in one branch can readily be made use of in the others. [...] [There are] two peculiar scientific virtues of cybernetics that are worth explicit mention. One is that it offers a single vocabulary and a single set of concepts suitable for representing the most diverse types of system. [...] The second peculiar virtue of cybernetics is that it offers a method for the scientific treatment of the system in which complexity is outstanding and too important to be ignored. Such systems are, as we well know, only too common in the biological world!" (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society, Vol. 106 (6), 1962)

"A more viable model, one much more faithful to the kind of system that society is more and more recognized to be, is in process of developing out of, or is in keeping with, the modern systems perspective (which we use loosely here to refer to general systems research, cybernetics, information and communication theory, and related fields). Society, or the sociocultural system, is not, then, principally an equilibrium system or a homeostatic system, but what we shall simply refer to as a complex adaptive system." (Walter F Buckley, "Society as a complex adaptive system", 1968)

"[…] as a model of a complex system becomes more complete, it becomes less understandable. Alternatively, as a model grows more realistic, it also becomes just as difficult to understand as the real world processes it represents." (Jay M Dutton & William H Starbuck," Computer simulation models of human behavior: A history of an intellectual technology", IEEE Transactions on Systems, 1971)

"Any system that insulates itself from diversity in the environment tends to atrophy and lose its complexity and distinctive nature." (Gareth Morgan, "Images of Organization", 1986)

"Because the individual parts of a complex adaptive system are continually revising their ('conditioned') rules for interaction, each part is embedded in perpetually novel surroundings (the changing behavior of the other parts). As a result, the aggregate behavior of the system is usually far from optimal, if indeed optimality can even be defined for the system as a whole. For this reason, standard theories in physics, economics, and elsewhere, are of little help because they concentrate on optimal end-points, whereas complex adaptive systems 'never get there'. They continue to evolve, and they steadily exhibit new forms of emergent behavior." (John H Holland, "Complex Adaptive Systems", Daedalus Vol. 121 (1), 1992)

"The impossibility of constructing a complete, accurate quantitative description of a complex system forces observers to pick which aspects of the system they most wish to understand." (Thomas Levenson, "Measure for Measure: A musical history of science", 1994)

"Artificial complex systems will be deliberately infused with organic principles simply to keep them going." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Complex adaptive systems have the property that if you run them - by just letting the mathematical variable of 'time' go forward - they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously. [...] A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life. (J Doyne Farmer, "The Third Culture: Beyond the Scientific Revolution", 1995)

"Complexity must be grown from simple systems that already work." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Even though these complex systems differ in detail, the question of coherence under change is the central enigma for each." (John H Holland," Hidden Order: How Adaptation Builds Complexity", 1995)

"By irreducibly complex I mean a single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning. An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modification of a precursor, system, because any precursors to an irreducibly complex system that is missing a part is by definition nonfunctional." (Michael Behe, "Darwin’s Black Box", 1996)

"A dictionary definition of the word ‘complex’ is: ‘consisting of interconnected or interwoven parts’ […] Loosely speaking, the complexity of a system is the amount of information needed in order to describe it. The complexity depends on the level of detail required in the description. A more formal definition can be understood in a simple way. If we have a system that could have many possible states, but we would like to specify which state it is actually in, then the number of binary digits (bits) we need to specify this particular state is related to the number of states that are possible." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"When the behavior of the system depends on the behavior of the parts, the complexity of the whole must involve a description of the parts, thus it is large. The smaller the parts that must be described to describe the behavior of the whole, the larger the complexity of the entire system. […] A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be simply inferred from the behavior of its components." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled." (Paul Cilliers," Complexity and Postmodernism", 1998)

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder."  (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"With the growing interest in complex adaptive systems, artificial life, swarms and simulated societies, the concept of 'collective intelligence' is coming more and more to the fore. The basic idea is that a group of individuals (e. g. people, insects, robots, or software agents) can be smart in a way that none of its members is. Complex, apparently intelligent behavior may emerge from the synergy created by simple interactions between individuals that follow simple rules." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"Bounded rationality simultaneously constrains the complexity of our cognitive maps and our ability to use them to anticipate the system dynamics. Mental models in which the world is seen as a sequence of events and in which feedback, nonlinearity, time delays, and multiple consequences are lacking lead to poor performance when these elements of dynamic complexity are present. Dysfunction in complex systems can arise from the misperception of the feedback structure of the environment. But rich mental models that capture these sources of complexity cannot be used reliably to understand the dynamics. Dysfunction in complex systems can arise from faulty mental simulation-the misperception of feedback dynamics. These two different bounds on rationality must both be overcome for effective learning to occur. Perfect mental models without a simulation capability yield little insight; a calculus for reliable inferences about dynamics yields systematically erroneous results when applied to simplistic models." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Much of the art of system dynamics modeling is discovering and representing the feedback processes, which, along with stock and flow structures, time delays, and nonlinearities, determine the dynamics of a system. […] the most complex behaviors usually arise from the interactions (feedbacks) among the components of the system, not from the complexity of the components themselves." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"To avoid policy resistance and find high leverage policies requires us to expand the boundaries of our mental models so that we become aware of and understand the implications of the feedbacks created by the decisions we make. That is, we must learn about the structure and dynamics of the increasingly complex systems in which we are embedded." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000) 

"Falling between order and chaos, the moment of complexity is the point at which self-organizing systems emerge to create new patterns of coherence and structures of behaviour." (Mark C Taylor, "The Moment of Complexity: Emerging Network Culture", 2001)

"[…] most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"A sudden change in the evolutive dynamics of a system (a ‘surprise’) can emerge, apparently violating a symmetrical law that was formulated by making a reduction on some (or many) finite sequences of numerical data. This is the crucial point. As we have said on a number of occasions, complexity emerges as a breakdown of symmetry (a system that, by evolving with continuity, suddenly passes from one attractor to another) in laws which, expressed in mathematical form, are symmetrical. Nonetheless, this breakdown happens. It is the surprise, the paradox, a sort of butterfly effect that can highlight small differences between numbers that are very close to one another in the continuum of real numbers; differences that may evade the experimental interpretation of data, but that may increasingly amplify in the system’s dynamics." (Cristoforo S Bertuglia & Franco Vaio, "Nonlinearity, Chaos, and Complexity: The Dynamics of Natural and Social Systems", 2003) 

"Complexity is the characteristic property of complicated systems we don’t understand immediately. It is the amount of difficulties we face while trying to understand it. In this sense, complexity resides largely in the eye of the beholder - someone who is familiar with s.th. often sees less complexity than someone who is less familiar with it. [...] A complex system is created by evolutionary processes. There are multiple pathways by which a system can evolve. Many complex systems are similar, but each instance of a system is unique." (Jochen Fromm, The Emergence of Complexity, 2004)

"In complexity thinking the darkness principle is covered by the concept of incompressibility [...] The concept of incompressibility suggests that the best representation of a complex system is the system itself and that any representation other than the system itself will necessarily misrepresent certain aspects of the original system." (Kurt Richardson, "Systems theory and complexity: Part 1", Emergence: Complexity & Organization Vol.6 (3), 2004)

"The basic concept of complexity theory is that systems show patterns of organization without organizer (autonomous or self-organization). Simple local interactions of many mutually interacting parts can lead to emergence of complex global structures. […] Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or 'punctuations' of all sizes. In the critical state, events which would otherwise be uncoupled became correlated." (Jochen Fromm, "The Emergence of Complexity", 2004)

"Complexity arises when emergent system-level phenomena are characterized by patterns in time or a given state space that have neither too much nor too little form. Neither in stasis nor changing randomly, these emergent phenomena are interesting, due to the coupling of individual and global behaviours as well as the difficulties they pose for prediction. Broad patterns of system behaviour may be predictable, but the system's specific path through a space of possible states is not." (Steve Maguire et al, "Complexity Science and Organization Studies", 2006)

"Thus, nonlinearity can be understood as the effect of a causal loop, where effects or outputs are fed back into the causes or inputs of the process. Complex systems are characterized by networks of such causal loops. In a complex, the interdependencies are such that a component A will affect a component B, but B will in general also affect A, directly or indirectly.  A single feedback loop can be positive or negative. A positive feedback will amplify any variation in A, making it grow exponentially. The result is that the tiniest, microscopic difference between initial states can grow into macroscopically observable distinctions." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"The butterfly effect demonstrates that complex dynamical systems are highly responsive and interconnected webs of feedback loops. It reminds us that we live in a highly interconnected world. Thus our actions within an organization can lead to a range of unpredicted responses and unexpected outcomes. This seriously calls into doubt the wisdom of believing that a major organizational change intervention will necessarily achieve its pre-planned and highly desired outcomes. Small changes in the social, technological, political, ecological or economic conditions can have major implications over time for organizations, communities, societies and even nations." (Elizabeth McMillan, "Complexity, Management and the Dynamics of Change: Challenges for practice", 2008)

"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system. This property of a non-linear system such as the weather is known as the butterfly effect where it is purported that a butterfly flapping its wings in Japan can give rise to a tornado in Kansas. This unpredictable behaviour of nonlinear dynamical systems, i.e. its extreme sensitivity to initial conditions, seems to be random and is therefore referred to as chaos. This chaotic and seemingly random behaviour occurs for non-linear deterministic system in which effects can be linked to causes but cannot be predicted ahead of time." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)

"If an emerging system is born complex, there is neither leeway to abandon it when it fails, nor the means to join another, successful one. Such a system would be caught in an immovable grip, congested at the top, and prevented, by a set of confusing but locked–in precepts, from changing." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013) 

"Simplicity in a system tends to increase that system’s efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system’s inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences." (Lawrence K Samuels,"Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"One of the remarkable features of these complex systems created by replicator dynamics is that infinitesimal differences in starting positions create vastly different patterns. This sensitive dependence on initial conditions is often called the butterfly-effect aspect of complex systems - small changes in the replicator dynamics or in the starting point can lead to enormous differences in outcome, and they change one’s view of how robust the current reality is. If it is complex, one small change could have led to a reality that is quite different." (David Colander & Roland Kupers, "Complexity and the art of public policy : solving society’s problems from the bottom up", 2014)

"The problem of complexity is at the heart of mankind's inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", 2014)

More quotes on "Complex Systems" at the-web-of-knowledge.blogspot.com.