🪸On Systems Thinking: On Self-Organization (2010-)

"In the telephone system a century ago, messages dispersed across the network in a pattern that mathematicians associate with randomness. But in the last decade, the flow of bits has become statistically more similar to the patterns found in self-organized systems. For one thing, the global network exhibits self-similarity, also known as a fractal pattern. We see this kind of fractal pattern in the way the jagged outline of tree branches look similar no matter whether we look at them up close or far away. Today messages disperse through the global telecommunications system in the fractal pattern of self-organization." (Kevin Kelly, "What Technology Wants", 2010)

"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)

"Nature is capable of building complex structures by processes of self-organization; simplicity begets complexity." (Victor J Stenger, God: "The Failed Hypothesis", 2010)

"But one of the major findings of quantum theory is the recognition that the universe is an open system. Open systems are neg-entropic (-S) and exhibit a tendency toward order. This means that according to quantum theory, the universe is a self-organizing system, continuously expanding and moving toward increasing order and complexity. In this context even subatomic particles show open system behavior and self-referencing tendencies." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"A self–organizing system acts autonomously, as if the interconnecting components had a single mind. And as these components spontaneously march to the beat of their own drummer, they organize, adapt, and evolve toward a greater complexity than one would ever expect by just looking at the parts by themselves." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

"There are several reasons why reaction-diffusion systems have been a popular choice among mathematical modelers of spatio-temporal phenomena. First, their clear separation between non-spatial and spatial dynamics makes the modeling and simulation tasks really easy. Second, limiting the spatial movement to only diffusion makes it quite straightforward to expand any existing non-spatial dynamical models into spatially distributed ones. Third, the particular structure of reaction-diffusion equations provides aneasy shortcut in the stability analysis (to be discussed in the next chapter). And finally, despite the simplicity of their mathematical form, reaction-diffusion systems can show strikingly rich, complex spatio-temporal dynamics. Because of these properties, reaction-diffusion systems have been used extensively for modeling self-organization of spatial patterns." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

"Without chaos there would be no creation, no structure and no existence. After all, order is merely the repetition of patterns; chaos is the process that establishes those patterns. Without this creative self-organizing force, the universe would be devoid of biological life, the birth of stars and galaxies - everything we have come to know. (Lawrence K Samuels, "Chaos Gets a Bad Rap: Importance of Chaology to Liberty", 2015)

"Cybernetics studies the concepts of control and communication in living organisms, machines and organizations including self-organization. It focuses on how a (digital, mechanical or biological) system processes information, responds to it and changes or being changed for better functioning (including control and communication)." (Dmitry A Novikov, "Cybernetics 2.0", 2016)

🧩Out of Context: On Self-organization (Definitions)

"The phenomenon of self-organization is not limited to living matter but occurs also in certain chemical systems [...]" (Fritjof Capra, "The Turning Point: Science, Society, and the Turning Culture", 1982)

"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)

"[…] 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)

"Self-organization is seen as the process by which systems of many components tend to reach a particular state, a set of cycling states, or a small volume of their state space (attractor basins), with no external interference." (Luis M Rocha, "Syntactic Autonomy", Proceedings of the Joint Conference on the Science and Technology of Intelligent Systems, 1998)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions." (Francis Heylighen, "The science of self-organization and adaptivity", 2001)

"Self-organization is a process typically occurring within complex systems where a system is continuously fed by energy, which is transformed into a new system state or operational mode by a dissipation of energy and/or information." (Jirí Kroc & Peter M A Sloot, "Complex Systems Modeling by Cellular Automata", Encyclopedia of Artificial Intelligence, 2009)

"Self-organization is a process that increases the order of a system as a result of local interactions among low-level, simple components, without the guidance of an outside source." (Linge Bai, "Chemotaxis-based Spatial Self-organization Algorithms", 2014)

"Self-organization is a dynamical process by which a system spontaneously forms nontrivial macroscopic structures and/or behaviors over time." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

🌡️Thermodynamics II

"Everywhere […] in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called thermal equilibrium. This cannot be a consequence of known laws of change, since […] these laws are time symmetric- they permit […] time-reverse. […] The initial conditions play a decisive role in endowing the world with its sense of temporal direction. […] some prescription for initial conditions is crucial if we are to understand […]" (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Three laws governing black hole changes were thus found, but it was soon noticed that something unusual was going on. If one merely replaced the words 'surface area' by 'entropy' and 'gravitational field' by 'temperature', then the laws of black hole changes became merely statements of the laws of thermodynamics. The rule that the horizon surface areas can never decrease in physical processes becomes the second law of thermodynamics that the entropy can never decrease; the constancy of the gravitational field around the horizon is the so-called zeroth law of thermodynamics that the temperature must be the same everywhere in a state of thermal equilibrium. The rule linking allowed changes in the defining quantities of the black hole just becomes the first law of thermodynamics, which is more commonly known as the conservation of energy." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"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)

"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 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)

"Thermodynamics is about those properties of systems that are true independent of their mechanism. This is why there is a fundamental asymmetry in the relationship between mechanistic descriptions of systems and thermodynamic descriptions of systems. From the mechanistic information we can deduce all the thermodynamic properties of that system. However, given only thermodynamic information we can deduce nothing about mechanism. This is in spite of the fact that thermodynamics makes it possible for us to reject classes of models such as perpetual motion machines." (Carlos Gershenson, “Design and Control of Self-organizing Systems”, 2007)

"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)

"The reactions that break down large molecules into small ones do not require an input of energy, but the reactions that build up large molecules require and input of energy. This is consistent with the laws of thermodynamics, which say that large, orderly molecules tend to break down into small, disorderly molecules." (Stanley A Rice, "Life of Earth: Portrait of a Beautiful, Middle-aged Stressed-out World", 2011)

"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)

On Synergy I

 "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)

"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)

"There is a multilayering of global networks in the key strategic activities that structure and destructure the planet. When these multilayered networks overlap in some node, when there is a node that belongs to different networks, two major consequences follow. First, economies of synergy between these different networks take place in that node: between financial markets and media businesses; or between academic research and technology development and innovation; between politics and media." (Manuel Castells, "The Rise of the Network Society", 1996)

"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)

"Systems thinking means the ability to see the synergy of the whole rather than just the separate elements of a system and to learn to reinforce or change whole system patterns. Many people have been trained to solve problems by breaking a complex system, such as an organization, into discrete parts and working to make each part perform as well as possible. However, the success of each piece does not add up to the success of the whole. to the success of the whole. In fact, sometimes changing one part to make it better actually makes the whole system function less effectively." (Richard L Daft, "The Leadership Experience", 2002)

"Self-organization can be seen as a spontaneous coordination of the interactions between the components of the system, so as to maximize their synergy. This requires the propagation and processing of information, as different components perceive different aspects of the situation, while their shared goal requires this information to be integrated. The resulting process is characterized by distributed cognition: different components participate in different ways to the overall gathering and processing of information, thus collectively solving the problems posed by any perceived deviation between the present situation and the desired situation." (Carlos Gershenson & Francis Heylighen, "How can we think the complex?", 2004)

"Synergy is the combined action that occurs when people work together to create new alternatives and solutions. In addition, the greatest opportunity for synergy occurs when people have different viewpoints, because the differences present new opportunities. The essence of synergy is to value and respect differences and take advantage of them to build on strengths and compensate for weaknesses." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

"Synergy occurs when organizational parts interact to produce a joint effect that is greater than the sum of the parts acting alone. As a result the organization may attain a special advantage with respect to cost, market power, technology, or employee." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

"In short, synergy is the consequence of the energy expended in creating order. It is locked up in the viable system created, be it an organism or a social system. It is at the level of the system. It is not discernible at the level of the system. It is not discernible at the level of the system's components. Whenever the system is dismembered to examine its components, this binding energy dissipates." (J-C Spender, "Organizational Knowledge, Collective Practice and Penrose Rents", 2009)

"Synergy is defined as the surplus gained by working together. A task which couldn’t be fulfilled by one individual, can be completed by the work of different individuals together. To maximize synergy, first, the initial task is divided into different sub-tasks. Different agents perform different tasks, which is called division of labor. An end product of one work is used for another work, which is called workflow. Finally, everything needs to be put together. We call this aggregation. This isn’t as linear as it looks. At every step in the process it can happen that a task is divided into sub tasks or aggregated with other tasks." (Evo Busseniers, "Self-organization versus hierarchical organization", [thesis] 2018)

Complex Systems VI

"In short, complex adaptive systems are characterized by perpetual novelty." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"[...] it's essentially meaningless to talk about a complex adaptive system being in equilibrium: the system can never get there. It is always unfolding, always in transition. In fact, if the system ever does reach equilibrium, it isn't just stable. It's dead." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"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 difference between complex adaptive systems and self-organizing systems is that the former have the capacity to learn from their experience, and thus to embody successful patterns into their repertoire, although there is actually quite a deep relationship between self-organizing systems and complex adaptive systems. Adaptive entities can emerge at high levels of description in simple self-organizing systems, i.e., adaptive systems are not necessarily self-organizing systems with something extra thrown in." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"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)

"Complex systems seem to have this property, with large periods of apparent stasis marked by sudden and catastrophic failures. These processes may not literally be random, but they are so irreducibly complex (right down to the last grain of sand) that it just won’t be possible to predict them beyond a certain level. […] And yet complex processes produce order and beauty when you zoom out and look at them from enough distance." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)

"We forget - or we willfully ignore - that our models are simplifications of the world. We figure that if we make a mistake, it will be at the margin. In complex systems, however, mistakes are not measured in degrees but in whole orders of magnitude." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)

"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)

Complex Systems V

"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)

"[a complex system is] a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution." (Melanie Mitchell, "Complexity: A Guided Tour", 2009)

"A typical complex system consists of a vast number of identical copies of several generic processes, which are operating and interacting only locally or with a limited number of not necessary close neighbours. There is no global leader or controller associated to such systems and the resulting behaviour is usually very complex." (Jirí Kroc & Peter M A Sloot, "Complex Systems Modeling by Cellular Automata", Encyclopedia of Artificial Intelligence, 2009)

On Automata I

"Ninety-nine [students] out of a hundred are automata, careful to walk in prescribed paths, careful to follow the prescribed custom. This is not an accident but the result of substantial education, which, scientifically defined, is the subsumption of the individual." (William T Harris, "The Philosophy of Education", 1889)

"We are automata entirely controlled by the forces of the medium being tossed about like corks on the surface of the water, but mistaking the resultant of the impulses from the outside for free will. The movements and other actions we perform are always life preservative and tho seemingly quite independent from one another, we are connected by invisible links." (Nikola Tesla, "My Inventions", 1919)

"Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method." (Norbert Wiener, "Cybernetics", 1948)

"Automata have begun to invade certain parts of mathematics too, particularly but not exclusively mathematical physics or applied mathematics. The natural systems (e.g., central nervous system) are of enormous complexity and it is clearly necessary first to subdivide what they represent into several parts that to a certain extent are independent, elementary units. The problem then consists of understanding how these elements are organized as a whole. It is the latter problem which is likely to attract those who have the background and tastes of the mathematician or a logician. With this attitude, he will be inclined to forget the origins and then, after the process of axiomatization is complete, concentrate on the mathematical aspects." (John Von Neumann, "The General and Logical Theory of Automata", 1951)

"A world of automata – of creatures that worked like machines – would hardly be worth creating." (Clive S Lewis, "Mere Christianity", 1952)

"Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions. They consist of a lattice of sites, each with a finite set of possible values. The value of the sites evolve synchronously in discrete time steps according to identical rules. The value of a particular site is determined by the previous values of a neighbourhood of sites around it." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Cellular automata may be considered as discrete dynamical systems. In almost all cases, cellular automaton evolution is irreversible. Trajectories in the configuration space for cellular automata therefore merge with time, and after many time steps, trajectories starting from almost all initial states become concentrated onto 'attractors'. These attractors typically contain only a very small fraction of possible states. Evolution to attractors from arbitrary initial states allows for 'self-organizing' behaviour, in which structure may evolve at large times from structureless initial states. The nature of the attractors determines the form and extent of such structures." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Finite Nature is a hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities. [...] We take the position that Finite Nature implies that the basic substrate of physics operates in a manner similar to the workings of certain specialized computers called cellular automata." (Edward Fredkin, "A New Cosmogony", PhysComp ’92: Proceedings of the Workshop on Physics and Computation, 1993)

On Nonlinearity V (Chaos I)

"When one combines the new insights gained from studying far-from-equilibrium states and nonlinear processes, along with these complicated feedback systems, a whole new approach is opened that makes it possible to relate the so-called hard sciences to the softer sciences of life - and perhaps even to social processes as well. […] It is these panoramic vistas that are opened to us by Order Out of Chaos." (Ilya Prigogine, "Order Out of Chaos: Man's New Dialogue with Nature", 1984)

"Algorithmic complexity theory and nonlinear dynamics together establish the fact that determinism reigns only over a quite finite domain; outside this small haven of order lies a largely uncharted, vast wasteland of chaos." (Joseph Ford, "Progress in Chaotic Dynamics: Essays in Honor of Joseph Ford's 60th Birthday", 1988)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In the everyday world of human affairs, no one is surprised to learn that a tiny event over here can have an enormous effect over there. For want of a nail, the shoe was lost, et cetera. But when the physicists started paying serious attention to nonlinear systems in their own domain, they began to realize just how profound a principle this really was. […] Tiny perturbations won't always remain tiny. Under the right circumstances, the slightest uncertainty can grow until the system's future becomes utterly unpredictable - or, in a word, chaotic." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"There is a new science of complexity which says that the link between cause and effect is increasingly difficult to trace; that change (planned or otherwise) unfolds in non-linear ways; that paradoxes and contradictions abound; and that creative solutions arise out of diversity, uncertainty and chaos." (Andy P Hargreaves & Michael Fullan, "What’s Worth Fighting for Out There?", 1998)

"Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

"Complexity theory can be defined broadly as the study of how order, structure, pattern, and novelty arise from extremely complicated, apparently chaotic systems and conversely, how complex behavior and structure emerges from simple underlying rules. As such, it includes those other areas of study that are collectively known as chaos theory, and nonlinear dynamical theory." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"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)

"Even more important is the way complex systems seem to strike a balance between the need for order and the imperative for change. Complex systems tend to locate themselves at a place we call 'the edge of chaos'. We imagine the edge of chaos as a place where there is enough innovation to keep a living system vibrant, and enough stability to keep it from collapsing into anarchy. It is a zone of conflict and upheaval, where the old and new are constantly at war. Finding the balance point must be a delicate matter - if a living system drifts too close, it risks falling over into incoherence and dissolution; but if the system moves too far away from the edge, it becomes rigid, frozen, totalitarian. Both conditions lead to extinction. […] Only at the edge of chaos can complex systems flourish. This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity." (Stephen H Buhner, "Plant Intelligence and the Imaginal Realm: Beyond the Doors of Perception into the Dreaming of Earth", 2014)

"To remedy chaotic situations requires a chaotic approach, one that is non-linear, constantly morphing, and continually sharpening its competitive edge with recurring feedback loops that build upon past experiences and lessons learned. Improvement cannot be sustained without reflection. Chaos arises from myriad sources that stem from two origins: internal chaos rising within you, and external chaos being imposed upon you by the environment. The result of this push/pull effect is the disequilibrium [...]." (Jeff Boss, "Navigating Chaos: How to Find Certainty in Uncertain Situations", 2015)

On Nonlinearity II

"Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property - to the extent that such systems can be described by mathematics at all - is a nonlinear equation: one whose graph is curvy." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"Today the network of relationships linking the human race to itself and to the rest of the biosphere is so complex that all aspects affect all others to an extraordinary degree. Someone should be studying the whole system, however crudely that has to be done, because no gluing together of partial studies of a complex nonlinear system can give a good idea of the behaviour of the whole." (Murray Gell-Mann, 1997)

"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)

"The mental models people use to guide their decisions are dynamically deficient. […] people generally adopt an event-based, open-loop view of causality, ignore feedback processes, fail to appreciate time delays between action and response and in the reporting of information, do not understand stocks and flows and are insensitive to nonlinearities that may alter the strengths of different feedback loops as a system evolves." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Most physical processes in the real world are nonlinear. It is our abstraction of the real world that leads us to the use of linear systems in modeling these processes. These linear systems are simple, understandable, and, in many situations, provide acceptable simulations of the actual processes. Unfortunately, only the simplest of linear processes and only a very small fraction of the nonlinear having verifiable solutions can be modeled with linear systems theory. The bulk of the physical processes that we must address are, unfortunately, too complex to reduce to algorithmic form - linear or nonlinear. Most observable processes have only a small amount of information available with which to develop an algorithmic understanding. The vast majority of information that we have on most processes tends to be nonnumeric and nonalgorithmic. Most of the information is fuzzy and linguistic in form." (Timothy J Ross & W Jerry Parkinson, "Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Systems", 2002)

"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 [...]. 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)

"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

"A network of many simple processors ('units' or 'neurons') that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in various applications such as robotics, speech recognition, signal processing, medical diagnosis, or power systems." (Adnan Khashman et al, "Voltage Instability Detection Using Neural Networks", 2009)

"Linearity is a reductionist’s dream, and nonlinearity can sometimes be a reductionist’s nightmare. Understanding the distinction between linearity and nonlinearity is very important and worthwhile." (Melanie Mitchell, "Complexity: A Guided Tour", 2009)

On Randomness V (Systems I)

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?” (Deborah J Bennett, "Randomness", 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)

"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)

"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"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)

"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)

"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)

"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini, "Chaos: From Simple Models to Complex Systems", 2010)

"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)

On Emergence III

"The principle that whole entities exhibit properties which are meaningful only when attributed to the whole, not to its parts - e.g. the smell of ammonia. Every model of human activity system exhibits properties as a whole entity which derive from it component activities and their structure, but cannot be reduced to them." (Peter Checkland, "Systems Thinking, Systems Practice", 1981)

"[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)

"At the other far extreme, we find many systems ordered as a patchwork of parallel operations, very much as in the neural network of a brain or in a colony of ants. Action in these systems proceeds in a messy cascade of interdependent events. Instead of the discrete ticks of cause and effect that run a clock, a thousand clock springs try to simultaneously run a parallel system. Since there is no chain of command, the particular action of any single spring diffuses into the whole, making it easier for the sum of the whole to overwhelm the parts of the whole. What emerges from the collective is not a series of critical individual actions but a multitude of simultaneous actions whose collective pattern is far more important. This is the swarm model." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Clearly, complex adaptive systems have a tendency to give rise to other complex adaptive systems. […] The appearance of more and more complex forms is not a phenomenon restricted to the evolution of complex adaptive systems, although for those systems the possibility arises of a selective advantage being associated under certain circumstances with increased complexity." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)

"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. The amount of information necessary to describe the behavior of such a system is a measure of its complexity." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"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)

"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)

"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)

🪸On Systems Thinking: On Self-Organization (2000-2009)

"I propose a new concept based on an interpretation of ecosystems: sympoietic systems. These are complex, self-organizing but collectively producing, boundaryless systems. A subsequent distinction between sympoietic and autopoietic systems is discussed. This distinction arises from defining a difference between three key system characteristics: 1) autopoietic systems have self-defined boundaries, sympoietic systems do not; 2) autopoietic systems are self-produced, sympoietic systems are collectively produced; and, 3) autopoietic systems are organizationally closed, sympoietic systems are organizationally ajar." (Beth Dempster, "Sympoietic and Autopoietic Systems: A New Distinction for Self-Organizing Systems". 2000)

"Perhaps the greatest puzzle in self-organisation is the question of emergent properties. That is, how do features that characterise a system as a whole emerge from the interplay of the parts that go to makeup the system? […] The issue of self-organisation remains as great a challenge today as it ever has been. Though there remains much yet to learn about self-organisation, we can at least identify some of the processes involved." (David G Green, "Self-organisation in complex systems", 2000)

"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)

"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)

"In principle, a self-organising system cannot be constructed, since its organisation and behaviour cannot be prescribed and created by an external source. It emerges autonomously in certain conditions (which cannot be prescribed either). The task of the researcher is to investigate in what kind of systems and under what kind of conditions self-organisation emerges." (Rein Vihalemm, "Chemistry as an Interesting Subject for the Philosophy of Science", 2001)

"Self-organization [is] the appearance of structure or pattern without an external agent imposing it." (Francis Heylighen, "The science of Self-organization and Adaptivity", 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)
"This is a general characteristic of self-organizing systems: they are robust or resilient. This means that they are relatively insensitive to perturbations or errors, and have a strong capacity to restore themselves, unlike most human designed systems." (Francis Heylighen, "The Science of Self-Organization and Adaptivity", 2001)

"Through self-organization, the behavior of the group emerges from the collective interactions of all the individuals. In fact, a major recurring theme in swarm intelligence (and of complexity science in general) is that even if individuals follow simple rules, the resulting group behavior can be surprisingly complex - and remarkably effective. And, to a large extent, flexibility and robustness result from self-organization." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 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)

"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)

"A self-organizing system not only regulates or adapts its behavior, it creates its own organization. In that respect it differs fundamentally from our present systems, which are created by their designer. We define organization as structure with function. Structure means that the components of a system are arranged in a particular order. It requires both connections, that integrate the parts into a whole, and separations that differentiate subsystems, so as to avoid interference. Function means that this structure fulfils a purpose." (Francis Heylighen & Carlos Gershenson, "The Meaning of Self-organization in Computing", IEEE Intelligent Systems, 2003)

"Self-organization can be seen as a spontaneous coordination of the interactions between the components of the system, so as to maximize their synergy. This requires the propagation and processing of information, as different components perceive different aspects of the situation, while their shared goal requires this information to be integrated. The resulting process is characterized by distributed cognition: different components participate in different ways to the overall gathering and processing of information, thus collectively solving the problems posed by any perceived deviation between the present situation and the desired situation." (Carlos Gershenson & Francis Heylighen, "How can we think the complex?", 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)

"A system described as self-organizing is one in which elements interact in order to achieve dynamically a global function or behavior." (Carlos Gershenson, "A general methodology for designing self-organizing systems", 2006)

"In engineering, a self-organizing system would be one in which elements are designed to dynamically and autonomously solve a problem or perform a function at the system level. In other words, the engineer will not build a system to perform a function explicitly, but elements will be engineered in such a way that their behaviour and interactions will lead to the system function. Thus, the elements need to divide, but also to integrate, the problem." (Carlos Gershenson, “Design and Control of Self-organizing Systems”, 2007)

"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)

"To state that the Web is different from other modern technologies is an obvious and gross oversimplification. The Web is not just different, it is different in a very specific way, and its highly connected, self-organizing complexity sets it apart from all other man-made systems. But many do not understand the very basics of complexity, let alone how these might be applicable to a modern technology or its association with a concept such as life. So it is indeed appropriate to visit this supposed black art in order to give an insight into the very nature of complexity and explain just why our current understandings are so applicable to the Web at a number of levels." (Philip Tetlow, "The Web’s Awake: An Introduction to the Field of Web Science and the Concept of Web Life", 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)

"Like resilience, self-organizazion is often sacrificed for purposes of short-term productivity and stability." (Donella H Meadows, “Thinking in Systems: A Primer”, 2008)

"In that sense, a self-organizing system is intrinsically adaptive: it maintains its basic organization in spite of continuing changes in its environment. As noted, perturbations may even make the system more robust, by helping it to discover a more stable organization." (Francis Heylighen, "Complexity and Self-Organization", 2008)

"Like resilience, self-organizazion is often sacrificed for purposes of short-term productivity and stability." (Donella H Meadows, “Thinking in Systems: A Primer”, 2008)"

" […] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"Democracy is a highly robust, but at the same time very fragile, complex system, which requires constant change to maintain its self-organized state. Democracy is by definition not in equilibrium. The random graph pattern may pose a system of boring and very low-complexity equilibrium. If all of us ever find ourselves with plenty of resources, that will be THE END of our history." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)

"Practically every complex system can be imagined as a network. Atoms form a network making macromolecules. Proteins form a network making cells. Cells form a network making organs and bodies. We form a network making our societies, and so on. Most of these networks are a result of self-organization. In fact, self-organization seems to be an inherent property of matter in our Universe. The resulting networks have a lot of common features, from their topology to their dynamism." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)

"Self-organizing networks suffer various types of random damage. Therefore, if the network remained static, it would soon become dysfunctional. Some networks have developed highly specific screening systems which recognize and repair random damage. On the one hand, this process requires energy, which arrives in the form of perturbations or noise. On the other hand, noise-triggered network restructuring will repeat a few steps of the original self-organization and therefore constitutes a much cheaper way of providing a continuous repair function, with the additional advantage that it is always adaptive with respect to the actual environment of the network." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)

🪸On Systems Thinking: On Self-Organization (1990-1999)

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"The cybernetics phase of cognitive science produced an amazing array of concrete results, in addition to its long-term (often underground) influence: the use of mathematical logic to understand the operation of the nervous system; the invention of information processing machines (as digital computers), thus laying the basis for artificial intelligence; the establishment of the metadiscipline of system theory, which has had an imprint in many branches of science, such as engineering (systems analysis, control theory), biology (regulatory physiology, ecology), social sciences (family therapy, structural anthropology, management, urban studies), and economics (game theory); information theory as a statistical theory of signal and communication channels; the first examples of self-organizing systems. This list is impressive: we tend to consider many of these notions and tools an integrative part of our life […]" (Francisco Varela, "The Embodied Mind", 1991)

"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)

"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)

“[…] 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)

"Distributed control means that the outcomes of a complex adaptive system emerge from a process of self-organization rather than being designed and controlled externally or by a centralized body." (Brenda Zimmerman et al, "A complexity science primer", 1998)

"In our analysis of complex systems (like the brain and language) we must avoid the trap of trying to find master keys. Because of the mechanisms by which complex systems structure themselves, single principles provide inadequate descriptions. We should rather be sensitive to complex and self-organizing interactions and appreciate the play of patterns that perpetually transforms the system itself as well as the environment in which it operates." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)

"Self-organization is seen as the process by which systems of many components tend to reach a particular state, a set of cycling states, or a small volume of their state space (attractor basins), with no external interference." (Luis M Rocha, "Syntactic Autonomy", Proceedings of the Joint Conference on the Science and Technology of Intelligent Systems, 1998) 

"The concept ‘complexity’ is not univocal either. Firstly, it is useful to distinguish between the notions ‘complex’ and ‘complicated’. If a system- despite the fact that it may consist of a huge number of components - can be given a complete description in terms of its individual constituents, such a system is merely complicated. […] In a complex system, on the other hand, the interaction among constituents of the system, and the interaction between the system and its environment, are of such a nature that the system as a whole cannot be fully understood simply by analysing its components. Moreover, these relationships are not fixed, but shift and change, often as a result of self-organisation. This can result in novel features, usually referred to in terms of emergent properties." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"The internal structure of a connectionist network develops through a process of self-organisation, whereas rule-based systems have to search through pre-programmed options that define the structure largely in an a priori fashion. In this sense, learning is an implicit characteristic of neural networks. In rule-based systems, learning can only take place through explicitly formulated procedures." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

🪸On Systems Thinking: On Self-Organization (1970-1989)

"In self-organizing systems, on the other hand, ‘control’ of the organization is typically distributed over the whole of the system. All parts contribute evenly to the resulting arrangement." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"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)

"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)

"[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)

"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)

"The phenomenon of self-organization is not limited to living matter but occurs also in certain chemical systems […] [Ilya] Prigogine has called these systems 'dissipative structures' to express the fact that they maintain and develop structure by breaking down other structures in the process of metabolism, thus creating entropy­ disorder - which is subsequently dissipated in the form of degraded waste products. Dissipative chemical structures display the dynamics of self-organization in its simplest form, exhibiting most of the phenomena characteristic of life self-renewal, adaptation, evolution, and even primitive forms of 'mental' processes." (Fritjof Capra, "The Turning Point: Science, Society, and the Turning Culture", 1982)

"Effect spreads its 'tentacles' not only forwards (as a new cause giving rise to a new effect) but also backwards, to the cause which gave rise to it, thus modifying, exhausting or intensifying its force. This interaction of cause and effect is known as the principle of feedback. It operates everywhere, particularly in all self-organising systems where perception, storing, processing and use of information take place, as for example, in the organism, in a cybernetic device, and in society. The stability, control and progress of a system are inconceivable without feedback." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Cellular automata may be considered as discrete dynamical systems. In almost all cases, cellular automaton evolution is irreversible. Trajectories in the configuration space for cellular automata therefore merge with time, and after many time steps, trajectories starting from almost all initial states become concentrated onto 'attractors'. These attractors typically contain only a very small fraction of possible states. Evolution to attractors from arbitrary initial states allows for 'self-organizing' behaviour, in which structure may evolve at large times from structureless initial states. The nature of the attractors determines the form and extent of such structures." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica D (10), 1984)

"Every system of whatever size must maintain its own structure and must deal with a dynamic environment, i.e., the system must strike a proper balance between stability and change. The cybernetic mechanisms for stability (i.e., homeostasis, negative feedback, autopoiesis, equifinality) and change (i.e., positive feedback, algedonodes, self-organization) are found in all viable systems." (Barry Clemson, "Cybernetics: A New Management Tool", 1984)

"The concept of entropy relates to the tendency of things to move toward greater disorder, or disorganization. […] The second law of thermodynamics expresses precisely the same concept. This states that heat dissipates from a central source and the energy becomes degraded, although total energy remains constant (the first law of thermodynamics). Entropy suggests that organisms, organizations, societies, machines, and so on, will rapidly deteriorate into disorder and "death." The reason they do not is because animate things can self-organize and inanimate things may be serviced by man. These are negentropic activities which require energy. Energy, however, can be made available only by further degradation. Ultimately, therefore, entropy wins the day and the attempts to create order can seem rather a daunting task in the entropic scheme of things. Holding back entropy, however, is another of the challenging tasks for the systems scientist." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

Francis Heylighen - Collected Quotes

"In self-organizing systems, on the other hand, ‘control’ of the organization is typically distributed over the whole of the system. All parts contribute evenly to the resulting arrangement." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium. 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)

"[Systems science] does not aim to find the one true representation for a given type of systems (e. g. physical, chemical or biological systems), but to formulate general principles about how different representations of different systems can be constructed so as to be effective in problem-solving." (Francis Heylighen, "Classical and non-classical representations in physics" I, Cybernetics and Systems 21, 1990)

"A collective mental map functions first of all as a shared memory. Various discoveries by members of the collective are registered and stored in this memory, so that the information will remain available for as long as necessary. The storage capacity of this memory is in general much larger than the capacities of the memories of the individual participants. This is because the shared memory can potentially be inscribed over the whole of the physical surroundings, instead of being limited to a single, spatially localized nervous system. Thus, a collective mental map differs from cultural knowledge, such as the knowledge of a language or a religion, which is shared among different individuals in a cultural group but is limited by the amount of knowledge a single individual can bear in mind." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"The three basic mechanisms of averaging, feedback and division of labor give us a first idea of a how a CMM [Collective Mental Map] can be developed in the most efficient way, that is, how a given number of individuals can achieve a maximum of collective problem-solving competence. A collective mental map is developed basically by superposing a number of individual mental maps. There must be sufficient diversity among these individual maps to cover an as large as possible domain, yet sufficient redundancy so that the overlap between maps is large enough to make the resulting graph fully connected, and so that each preference in the map is the superposition of a number of individual preferences that is large enough to cancel out individual fluctuations. The best way to quickly expand and improve the map and fill in gaps is to use a positive feedback that encourages individuals to use high preference paths discovered by others, yet is not so strong that it discourages the exploration of new paths." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 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)

"Science, and physics in particular, has developed out of the Newtonian paradigm of mechanics. In this world view, every phenomenon we observe can be reduced to a collection of atoms or particles, whose movement is governed by the deterministic laws of nature. Everything that exists now has already existed in some different arrangement in the past, and will continue to exist so in the future. In such a philosophy, there seems to be no place for novelty or creativity." (Francis Heylighen, "The science of self-organization and adaptivity", 2001)

"This is a general characteristic of self-organizing systems: they are robust or resilient. This means that they are relatively insensitive to perturbations or errors, and have a strong capacity to restore themselves, unlike most human designed systems." (Francis Heylighen, "The Science of Self-Organization and Adaptivity", 2001)

"[…] self-organization [is] the appearance of structure or pattern without an external agent imposing it." (Francis Heylighen, "The science of self-organization and adaptivity", 2001)

"In that sense, a self-organizing system is intrinsically adaptive: it maintains its basic organization in spite of continuing changes in its environment. As noted, perturbations may even make the system more robust, by helping it to discover a more stable organization." (Francis Heylighen, "Complexity and Self-Organization", 2008)

On Feedback (1990-1999)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback - increasing returns - makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the ‘best’ one."  (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)

"There must be, however, cybernetic or homeostatic mechanisms for preventing the overall variables of the social system from going beyond a certain range. There must, for instance, be machinery for controlling the total numbers of the population; there must be machinery for controlling conflict processes and for preventing perverse social dynamic processes of escalation and inflation. One of the major problems of social science is how to devise institutions which will combine this overall homeostatic control with individual freedom and mobility." (Kenneth Boulding, "Economics of the coming spaceship Earth", 1994)

"An essential element of dynamics systems is a positive feedback that self-enhances the initial deviation from the mean. The avalanche is proverbial. Cities grow since they attract more people, and in the universe, a local accumulation of dust may attract more dust, eventually leading to the birth of a star. Earlier or later, self-enhancing processes evoke an antagonistic reaction. A collapsing stock market stimulates the purchase of shares at a low price, thereby stabilizing the market. The increasing noise, dirt, crime and traffic jams may discourage people from moving into a big city." (Hans Meinhardt, "The Algorithmic Beauty of Sea Shells", 1995)

“[…] 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)

"Something of the previous state, however, survives every change. This is called in the language of cybernetics (which took it form the language of machines) feedback, the advantages of learning from experience and of having developed reflexes." (Guy Davenport, "The Geography of the Imagination: Forty Essays", 1997)

"Cybernetics is the science of effective organization, of control and communication in animals and machines. It is the art of steersmanship, of regulation and stability. The concern here is with function, not construction, in providing regular and reproducible behaviour in the presence of disturbances. Here the emphasis is on families of solutions, ways of arranging matters that can apply to all forms of systems, whatever the material or design employed. [...] This science concerns the effects of inputs on outputs, but in the sense that the output state is desired to be constant or predictable – we wish the system to maintain an equilibrium state. It is applicable mostly to complex systems and to coupled systems, and uses the concepts of feedback and transformations (mappings from input to output) to effect the desired invariance or stability in the result." (Chris Lucas, "Cybernetics and Stochastic Systems", 1999)