Showing posts with label evolution. Show all posts
Showing posts with label evolution. Show all posts

17 March 2021

❄️Systems Thinking: On Chaos (Quotes)

"Despite the disorder observed in Nature, one finds enough traces of the wisdom and power of its Author that one cannot fail to recognize Him." (Pierre L Maupertuis, "Les Loix du Mouvement et du Repos, déduites d'un Principe Métaphysique", 1746)

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The words ‘chaos’, ‘accidental’, ‘chance’, ‘unpredictable’ are conveniences behind which we hide our ignorance.” (Harlow Shapley, "Of Stars and Men", 1958) 

"One of mankind’s earliest intellectual endeavors was the attempt to gather together the seemingly overwhelming variety presented by nature into an orderly pattern. The desire to classify - to impose order on chaos and then to form patterns out of this order on which to base ideas and conclusions - remains one of our strongest urges." (Roger L Batten, 1959)

"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos. […] This is the task of natural science: to show that the wonderful is not incomprehensible, to show how it can be comprehended - but not to destroy wonder. For when we have explained the wonderful, unmasked the hidden pattern, a new wonder arises at how complexity was woven out of simplicity. The aesthetics of natural science and mathematics is at one with the aesthetics of music and painting - both inhere in the discovery of a partially concealed pattern." (Herbert A Simon, "The Sciences of the Artificial", 1968)

"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos." (Herbert A Simon, "The Sciences of the Artificial", 1969)

"One of the central problems studied by mankind is the problem of the succession of form. Whatever is the ultimate nature of reality (assuming that this expression has meaning), it is indisputable that our universe is not chaos. We perceive beings, objects, things to which we give names. These beings or things are forms or structures endowed with a degree of stability; they take up some part of space and last for some period of time. Moreover, although a given object can exist in many different guises, we never fail to recognize it [...]" (René Thom, "Structural Stability and Morphogenesis", 1972)

"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick, "Chaos", 1987)

"The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done." (Ian Stewart, "Does God Play Dice?", 1989)

"Let us tum to the question, 'What is chaos?' Certainly the typical answer, 'sensitive dependence on initial conditions', is reasonable. But to be relevant to physics, more is required: the property should be robust or preserved under perturbations of the system. A response &lat involves a mechanism and meets the criteria is: 'Chaos is the presence of a (transversal) homoclinic point'." (Steven Smale, "What is chaos?", 1990)

"Summarizing, we have indicated why homoclinic points imply chaos. The converse is less formalizable, but I believe it is basically true. However,  there is a stronger notion of chaos, which we might call full chaos, where the set of initial conditions with sensitive dependence has positive or even full measure. In this case the corresponding homoclinic point could well be associated with a chaotic attractor, such as the Lorenz attractor. " (Steven Smale, "What is chaos?", 1990)

"Never in the annals of science and engineering has there been a phenomenon so ubiquitous‚ a paradigm so universal‚ or a discipline so multidisciplinary as that of chaos. Yet chaos represents only the tip of an awesome iceberg‚ for beneath it lies a much finer structure of immense complexity‚ a geometric labyrinth of endless convolutions‚ and a surreal landscape of enchanting beauty. The bedrock which anchors these local and global bifurcation terrains is the omnipresent nonlinearity that was once wantonly linearized by the engineers and applied scientists of yore‚ thereby forfeiting their only chance to grapple with reality." (Leon O Chua, "Editorial", International Journal of Bifurcation and Chaos, Vol. l (1), 1991) 

"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)

"The term chaos is also used in a general sense to describe the body of chaos theory, the complete sequence of behaviours generated by feed-back rules, the properties of those rules and that behaviour." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"There are many possible definitions of chaos. In fact, there is no general agreement within the scientific community as to what constitutes a chaotic dynamical system." (Robert L Devaney, "A First Course in Chaotic Dynamical Systems: Theory and Experiment", 1992)

"We have found chaos, but what it means and what its relevance is to our place in the universe remains shrouded in a seemingly impenetrable cloak of mathematical uncertainty.” (Ivars Peterson, "Newton’s Clock”, 1993)

"The voyage of discovery into our own solar system has taken us from clockwork precision into chaos and complexity. This still unfinished journey has not been easy, characterized as it is by twists, turns, and surprises that mirror the intricacies of the human mind at work on a profound puzzle. Much remains a mystery. We have found chaos, but what it means and what its relevance is to our place in the universe remains shrouded in a seemingly impenetrable cloak of mathematical uncertainty." (Ivars Peterson, "Newton’s Clock", 1993)

"Chaos has three fundamental characteristics. They are (a) irregular periodicity, (b) sensitivity to initial conditions, and (c) a lack of predictability. These characteristics interact within any one chaotic setting to produce highly complex nonlinear variable trajectories."(Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"In its essence, chaos is an irregular oscillatory process. Because chaos is a subset of the more general classification of oscillatory dynamics, it is useful before venturing into chaos to review briefly the extent to which regular oscillatory processes influence human behavior." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"In addition to dimensionality requirements, chaos can occur only in nonlinear situations. In multidimensional settings, this means that at least one term in one equation must be nonlinear while also involving several of the variables. With all linear models, solutions can be expressed as combinations of regular and linear periodic processes, but nonlinearities in a model allow for instabilities in such periodic solutions within certain value ranges for some of the parameters." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"The dimensionality and nonlinearity requirements of chaos do not guarantee its appearance. At best, these conditions allow it to occur, and even then under limited conditions relating to particular parameter values. But this does not imply that chaos is rare in the real world. Indeed, discoveries are being made constantly of either the clearly identifiable or arguably persuasive appearance of chaos. Most of these discoveries are being made with regard to physical systems, but the lack of similar discoveries involving human behavior is almost certainly due to the still developing nature of nonlinear analyses in the social sciences rather than the absence of chaos in the human setting."  (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"Chaos appears in both dissipative and conservative systems, but there is a difference in its structure in the two types of systems. Conservative systems have no attractors. Initial conditions can give rise to periodic, quasiperiodic, or chaotic motion, but the chaotic motion, unlike that associated with dissipative systems, is not self-similar. In other words, if you magnify it, it does not give smaller copies of itself. A system that does exhibit self-similarity is called fractal. [...] The chaotic orbits in conservative systems are not fractal; they visit all regions of certain small sections of the phase space, and completely avoid other regions. If you magnify a region of the space, it is not self-similar." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Most of us use the word 'chaos' rather loosely to represent anything that occurs randomly, so it is natural to think that the motion described by the erratic pendulum above is completely random. Not so. The scientific definition of chaos is different from the one you may be used to in that it has an element of determinism in it. This might seem strange, as determinism and chaos are opposites of one another, but oddly enough they are also compatible." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Nonlinearity is important because it can lead to chaos. That's not to say that we get chaos all the time with nonlinear equations; in practice it only occurs under certain conditions." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What chaos implies is not catastrophes, but rather our inability to make long-range predictions [...]" (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What is chaos? Everyone has an impression of what the word means, but scientifically chaos is more than random behavior, lack of control, or complete disorder. [...] Scientifically, chaos is defined as extreme sensitivity to initial conditions. If a system is chaotic, when you change the initial state of the system by a tiny amount you change its future significantly." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"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)

"An apparent paradox is that chaos is deterministic, generated by fixed rules which do not themselves involve any elements of change. We even speak of deterministic chaos. In principle, the future is completely determined by the past; but in practice small uncertainties, much like minute errors of measurement which enter into calculations, are amplified, with the effect that even though the behavior is predictable in the short term, it is unpredictable over the long term." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science" 2nd Ed., 2004)

"Chaos theory, too, is occasionally in danger of being overtaxed by being associated with everything that can be even superficially related to the concept of chaos. Unfortunately, a sometimes extravagant popularization through the media is also contributing to this danger; but at the same time this popularization is also an important opportunity to free areas of mathematics from their intellectual ghetto and to show that mathematics is as alive and important as ever." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science" 2nd Ed., 2004)

"Natural laws, and for that matter determinism, do not exclude the possibility of chaos. In other words, determinism and predictability are not equivalent. And what is an even more surprising rinding of recent chaos theory has been the discovery that these effects are observable in many systems which are much simpler than the weather. [...] Moreover, chaos and order (i.e., the causality principle) can be observed in juxtaposition within the same system. There may be a linear progression of errors characterizing a deterministic system which is governed by the causality principle, while (in the same system) there can also be an exponential progression of errors (i.e., the butterfly effect) indicating that the causality principle breaks down." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science" 2nd Ed., 2004)

"Chaos is not pure disorder, it carries within itself the indistinctness between the potentialities of order, of disorder, and of organization from which a cosmos will be born, which is an ordered universe." (Edgar Morin, "Restricted Complexity, General Complexity" [in (Carlos Gershenson et al [Eds.], "Worldviews, Science and Us: Philosophy and Complexity", 2007)])

"Chaos has three primary features: unpredictability, boundedness, and sensitivity to initial conditions. Unpredictability means that a sequence of numbers that is generated from a chaotic function does not repeat. This principle is perhaps a matter of degree, because some of the numbers could look as though they are recurring only because they are rounded to a convenient number of decimal points. [...] Boundedness means that, for all the unpredictability of motion, all points remain within certain boundaries. The principle of sensitivity to initial conditions means that two points that start off as arbitrarily close together become exponentially farther away from each other as the iteration process proceeds. This is a clear case of small differences producing a huge effect." (Stephen J Guastello & Larry S Liebovitch, "Introduction to Nonlinear Dynamics and Complexity" [in "Chaos and Complexity in Psychology"], 2009)

"[...] 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)

"Entropy is the crisp scientific name for waste, chaos, and disorder. As far as we know, the sole law of physics with no known exceptions anywhere in the universe is this: All creation is headed to the basement. Everything in the universe is steadily sliding down the slope toward the supreme equality of wasted heat and maximum entropy." (Kevin Kelly, "What Technology Wants", 2010)

"Chaos provides order. Chaotic agitation and motion are needed to create overall, repetitive order. This ‘order through fluctuations’ keeps dynamic markets stable and evolutionary processes robust. In essence, chaos is a phase transition that gives spontaneous energy the means to achieve repetitive and structural order." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Order is not universal. In fact, many chaologists and physicists posit that universal laws are more flexible than first realized, and less rigid - operating in spurts, jumps, and leaps, instead of like clockwork. Chaos prevails over rules and systems because it has the freedom of infinite complexity over the known, unknown, and the unknowable." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

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

"Chaos can be understood as a dynamical process in which microscopic information hidden in the details of a system’s state is dug out and expanded to a macroscopically visible scale (stretching), while the macroscopic information visible in the current system’s state is continuously discarded (folding)." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

01 March 2020

❄️Systems Thinking: On Emergence (Quotes)

"The component parts of a vegetable or animal substance do not lose their mechanical and chemical properties as separate agents, when, by a peculiar mode of juxtaposition, they, as an aggregate whole, acquire physiological or vital properties in addition. Those bodies continue, as before, to obey mechanical and chemical laws, in so far as the operation of those laws is not counteracted by the new laws which govern them as organized beings. […] Though there are laws which, like those of chemistry and physiology, owe their existence to a breach of the principle of Composition of Causes, it does not follow that these peculiar, or, as they might be termed, heteropathic laws, are not capable of composition with one another." (John S Mill, "A System of Logic: Ratioconative and Inductive", 1843) [the heteropathic laws is synonymous with emergence]

"The higher quality emerges from the lower level of existence and has its roots therein, but it emerges therefrom, and it does not belong to that lower level, but constitutes its possessor a new order of existent with its special laws of behaviour. The existence of emergent qualities thus described is something to be noted, as some would say, under the compulsion of brute empirical fact, or, as I should prefer to say in less harsh terms, to be accepted with the ‘natural piety’ of the investigator. It admits no explanation." (Samuel Alexander, "Space, Time and Deity", 1922)

"This, however, is very speculative; the point of interest for our present enquiry is that physical reality is built up, apparently, from a few fundamental types of units whose properties determine many of the properties of the most complicated phenomena, and this seems to afford a sufficient explanation of the emergence of analogies between mechanisms and similarities of relation-structure among these combinations without the necessity of any theory of objective universals." (Kenneth Craik, "The Nature of Explanation", 1943)

"The moment of truth, the sudden emergence of a new insight, is an act of intuition. Such intuitions give the appearance of miraculous flushes, or short-circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links. (Arthur Koestler, "The Act of Creation", 1964)

"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)

"Curiously, the unexpected complexity that has been discovered in nature has not led to a slowdown in the progress of science, but on the contrary to the emergence of new conceptual structures that now appear as essential to our understanding of the physical world - the world that includes us. (Isabelle Stengers, "Order Out of Chaos", 1984)

"Catastrophes are often stimulated by the failure to feel the emergence of a domain, and so what cannot be felt in the imagination is experienced as embodied sensation in the catastrophe. (William I Thompson, "Gaia, a Way of Knowing: Political Implications of the New Biology", 1987)

"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)

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

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

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

"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)

"The central proposition in [realistic thinking] is that human actions and interactions are processes, not systems, and the coherent patterning of those processes becomes what it becomes because of their intrinsic capacity, the intrinsic capacity of interaction and relationship, to form coherence. That emergent form is radically unpredictable, but it emerges in a controlled or patterned way because of the characteristic of relationship itself, creation and destruction in conditions at the edge of chaos." (Ralph D Stacey et al, "Complexity and Management: Fad or Radical Challenge to Systems Thinking?", 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)

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

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

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

"In particular, complexity examines how components of a system can through their dynamic interaction 'spontaneously' develop collective properties or patterns, such as colour, that do not seem implicit, or at least not implicit in the same way, within individual components.  Complexity investigates emergent properties, certain regularities of behaviour that somehow transcend the ingredients that make them up. Complexity argues against reductionism, against reducing the whole to the parts. And in so doing it transforms scientific understanding of far-from-equilibrium structures, of irreversible times and of non-Euclidean mobile spaces. It emphasizes how positive feedback loops can exacerbate initial stresses in the system and render it unable to absorb shocks to re-establish the original equilibrium. Positive feedback occurs when a change tendency is reinforced rather than dampened clown. Very strong interactions occur between the parts of such systems, with the absence of a central hierarchical structure that unambiguously' governs' and produces outcomes. These outcomes are to be seen as both uncertain and irreversible." (John Urry, "Global Complexity", 2003)

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

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

"Emergence refers to the relationship between the details of a system and the larger view. Emergence does not emphasize the primary importance of the details or of the larger view; it is concerned with the relationship between the two. Specifically, emergence seeks to discover: Which details are important for the larger view, and which are not? How do collective properties arise from the properties of parts? How does behavior at a larger scale of the system arise from the detailed structure, behavior and relationships on a finer scale?" (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004) 

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

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

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

[emergence:] "The process of complex pattern formation from simpler rules; emergent properties are neither properties had by any parts of the system taken in isolation nor a resultant of a mere summation of properties of parts of the system." (Ani Calinescu & Janet Efstathiou, "Measures of Network Structure", Encyclopedia of Networked and Virtual Organizations, 2008) 

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

"Emergence is defined as the occurrence of new processes operating at a higher level of abstraction then is the level at which the local rules operate." (Jirí Kroc & Peter M A Sloot, "Complex Systems Modeling by Cellular Automata", Encyclopedia of Artificial Intelligence, 2009)

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

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

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

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

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

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

"Emergence is a nontrivial relationship between the properties of a system at microscopic and macroscopic scales. Macroscopic properties are called emergent when it is hard to explain them simply from microscopic properties." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

[emergence:] "A feature in a complex system that is generated through the dynamic interactions between the parts of a system at one level, and is realized at the next level of organization without intentionality or causality." (A Faye Bres, "Integral Post-Analysis of Design-Based Research of an Organizational Learning Process for Strategic Renewal of Environmental Management", Integral Theory and Transdisciplinary Action Research in Education, 2019)
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