21 December 2020

Knowledge Representation: On Cognitive Maps (Quotes)

"[...] we believe that in the course of learning something like a field map of the environment gets established in the rat's brain [...] and it is this tentative map, indicating routes and paths and environmental relationships, which finally determines what responses, if any, the animal will finally release." (Edward C Tolman, "Cognitive maps in rats and men", Psychological Review 55(4), 1948)

"[…] learning consists not in stimulus-response connections but in the building up in the nervous system of sets which function like cognitive maps […] such cognitive maps may be usefully characterized as varying from a narrow strip variety to a broader comprehensive variety." (Edward C Tolman, "Cognitive maps in rats and men", Psychological Review 55(4), 1948)

"The cognitive map is a construct that has been proposed to explain how individuals know their environment. It assumes that people store information about their environment in a simplified form and in relation to other information they already have. It further assumes that this information is coded in a structure which people carry around in their heads, and that this structure corresponds, at least to a reasonable degree, to the environment it represents. It is as if an individual carried a map or model of the environment in his head." (Stephen Kaplan, "Cognitive maps, human needs and the designed environment", Environmental design research vol. 1, 1973)

"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)

"A cognitive map is a specific way of representing a person's assertions about some limited domain, such as a policy problem. It is designed to capture the structure of the person's causal assertions and to generate the consequences that follow front this structure. […]  a person might use his cognitive map to derive explanations of the past, make predictions for the future, and choose policies in the present." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"The cognitive mapping approach promises to be more helpful to the decision maker for two reasons. First, since the advice can be expressed in terms of the person's own cognitive map, it can be solidly based in his own experience, using his own concepts, his own causal beliefs. and his own values. Equally important, when the cognitive map approach offers advice, it takes explicit account of the finite capacities of people and the way in which they simplify their images when dealing with a complex policy issue. Thus, with the cognitive mapping approach, a better understanding of how decisions are made can lead to the making of better decisions." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"Briefly, a cognitive map would consist of two major systems, a place system and a misplace system. The first is a memory system which contains information about places in the organism's environment, their spatial relations, and the existence of specific objects in specific places. The second, misplace, system signals changes in a particular place, involving either the presence of a new object or the absence of an old one. The place system permits an animal to locate itself in a familiar environment without reference to any specific sensory input, to go from one place to another independent of particular inputs (cues) or outputs (responses), and to link together conceptually parts of an environment which have never been experienced at the same time. The misplace system is primarily responsible for exploration, a species-typical behaviour which functions to build maps of new environments and to incorporate new information into existing maps." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"The cognitive map is not a picture or image which 'looks like' what it represents; rather, it is an information structure from which map-like images can be reconstructed and from which behaviour dependent upon place information can be generated." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"We would agree that organisms do not 'see' absolute space; cognitive maps are not pictures of the universe, they are schemata from which any portion of space can be constructed. The fact that we cannot perceive unified space does not mean we cannot conceive it; the latter potentiality derives from the possession of a structure which can be used to construct spaces that stretch endlessly in all dimensions." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"[...] cognitive maps can be seen as a picture or visual aid in comprehending the mappers' understanding of particular, and selective, elements of the thoughts (rather than thinking) of an individual, group or organization. They may also be seen as a representation that is amenable to analysis by both the mapper and others." (Colin Eden, "One the nature of cognitive maps", Journal of Management Studies 29 (3), 1992)

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

"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems."  (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

[cognitive map:] "A mental representation of a portion of the physical environment and the relative locations of points within it." (Andrew M Colman, "A Dictionary of Psychology" 3rd Ed, 2008)

[cognitive map:] "A mental model (or map) of the external environment which may be constructed following exploratory behaviour." (Michael Allaby, "A Dictionary of Zoology" 3rd Ed., 2009)

"There is no reason to believe that cognitive maps are like iconic maps except, rather than being inscribed in the dirt, or on a rock, or imprinted on paper, they are somehow inscribed in neural tissue. They seem to be more like lists of significant places intertwined with bearings and headings between one place and another. The vital significance of these places is part and parcel of the map; the “map” is not a neutral spatial substrate to which vital significance is later attached. The space of cognitive maps is not merely about physical position; it is about needs and satisfiers, vantage points and opportunities for action." (William Benzon, "Maps, Iconic and Abstract", 2011)

[Cognitive Map:] "A representation of the conceptualization that the subject constructs of the system in which he evolves. The set of cognitive representations that emerge make it possible to understand his actions, the links between the factors structuring the cognitive patterns dictating his behaviors." (Henda E Karray & Souhaila Kammoun, "Strategic Orientation of the Managers of a Tunisian Family Group Before and After the Revolution", 2020)

20 December 2020

Systems Thinking: Nonlinearity vs. Linearity (Quotes)

"Any organism must be treated as-a-whole; in other words, that an organism is not an algebraic sum, a linear function of its elements, but always more than that. It is seemingly little realized, at present, that this simple and innocent-looking statement involves a full structural revision of our language […]" (Alfred Korzybski, "Science and Sanity", 1933)

"Beauty had been born, not, as we so often conceive it nowadays, as an ideal of humanity, but as measure, as the reduction of the chaos of appearances to the precision of linear symbols. Symmetry, balance, harmonic division, mated and mensurated intervals - such were its abstract characteristics." (Herbert E Read, "Icon and Idea", 1955)

"Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions. (Edward N Lorenz, "Deterministic Nonperiodic Flow", Journal of the Atmospheric Science 20, 1963)

"Up until now most economists have concerned themselves with linear systems, not because of any belief that the facts were so simple, but rather because of the mathematical difficulties involved in nonlinear systems [... Linear systems are] mathematically simple, and exact solutions are known. But a high price is paid for this simplicity in terms of special assumptions which must be made." (Paul A Samuelson, "Foundations of Economic Analysis", 1966)

"We've seen that even in the simplest situations nonlinearities can interfere with a linear approach to aggregates. That point holds in general: nonlinear interactions almost always make the behavior of the aggregate more complicated than would be predicted by summing or averaging." (Lewis Mumford, "The Myth of the Machine" Vol 1, 1967)

"The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by non‐linear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive‐feedback loops describing growth processes as well as negative, goal‐seeking loops." (Jay F Forrester, "Urban Dynamics", 1969)

"In complex systems cause and effect are often not closely related in either time or space. The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by nonlinear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive-feedback loops describing growth processes as well as negative, goal-seeking loops. In the complex system the cause of a difficulty may lie far back in time from the symptoms, or in a completely different and remote part of the system. In fact, causes are usually found, not in prior events, but in the structure and policies of the system." (Jay Wright Forrester, "Urban dynamics", 1969)

"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)

"[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)

"I would therefore urge that people be introduced to [the logistic equation] early in their mathematical education. This equation can be studied phenomenologically by iterating it on a calculator, or even by hand. Its study does not involve as much conceptual sophistication as does elementary calculus. Such study would greatly enrich the student’s intuition about nonlinear systems. Not only in research but also in the everyday world of politics and economics, we would all be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties." (Robert M May, "Simple Mathematical Models with Very Complicated Dynamics", Nature Vol. 261 (5560), 1976)

"A nonlinear relationship causes the feedback loop of which it is a part to vary in strength, depending on the state of the system. Linked nonlinear feedback loops thus form patterns of shifting loop dominance- under some conditions one part of the system is very active, and under other conditions another set of relationships takes control and shifts the entire system behavior. A model composed of several feedback loops linked nonlinearly can produce a wide variety of complex behavior patterns." (Jørgen Randers, "Elements of the System Dynamics Method", 1980)

"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)

"Linear relationships are easy to think about: the more the merrier. Linear equations are solvable, which makes them suitable for textbooks. Linear systems have an important modular virtue: you can take them apart and put them together again - the pieces add up. Nonlinear systems generally cannot be solved and cannot be added together. [...] Nonlinearity means that the act of playing the game has a way of changing the rules. [...] That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems." (James Gleick, "Chaos: Making a New Science", 1987)

"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)

"It is sometimes said that the great discovery of the nineteenth century was that the equations of nature were linear, and the great discovery of the twentieth century is that they are not." (Thomas W Körner, "Fourier Analysis", 1988)

"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)

"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)

"Just as few concrete physical systems are strictly deterministic in their behavior, so very few are strictly linear. The great importance of linearity lies in a combination of two circumstances. First, many tangible phenomena behave approximately linearly over restricted periods of time or restricted ranges of the variables, so that useful linear mathematical models can simulate their behavior. A pendulum swinging through a small angle is a nearly linear system. Second, linear equations can be handled by a wide variety of techniques that do not work with nonlinear equations." (Edward N Lorenz, "The Essence of Chaos", 1993)

"Scientists try to make things simple. That is in good part why we are stuck with bivalence. Scientists' first instinct is to fit a linear model to a nonlinear world. This creates another mismatch problem, the math modeler's dilemma: linear math, nonlinear world." (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"An artificial neural network is an information-processing system that has certain performance characteristics in common with biological neural networks. Artificial neural networks have been developed as generalizations of mathematical models of human cognition or neural biology, based on the assumptions that: 1. Information processing occurs at many simple elements called neurons. 2. Signals are passed between neurons over connection links. 3. Each connection link has an associated weight, which, in a typical neural net, multiplies the signal transmitted. 4. Each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals) to determine its output signal." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"Symmetry breaking in psychology is governed by the nonlinear causality of complex systems (the 'butterfly effect'), which roughly means that a small cause can have a big effect. Tiny details of initial individual perspectives, but also cognitive prejudices, may 'enslave' the other modes and lead to one dominant view." (Klaus Mainzer, "Thinking in Complexity", 1994)

"[…] nonlinear interactions almost always make the behavior of the aggregate more complicated than would be predicted by summing or averaging."  (John H Holland," Hidden Order: How Adaptation Builds Complexity", 1995)

"When it comes to modeling processes that are manifestly governed by nonlinear relationships among the system components, we can appeal to the same general idea. Calculus tells us that we should expect most systems to be 'locally' flat; that is, locally linear. So a conservative modeler would try to extend the word 'local' to hold for the region of interest and would take this extension seriously until it was shown to be no longer valid." (John L Casti, "Five Golden Rules", 1995)

"When we examine the modeling literature, its most striking aspect is the predominance of 'flat' linear models. Why is this the case? After all, from a singularity theory viewpoint these linear objects are mathematical rarities. On mathematical grounds we should certainly not expect to see them put forth as credible representations of reality. Yet they are. And the reason is simple: linearity is a neutral assumption that leads to mathematically tractable models. So unless there is good reason to do otherwise, why not use a linear model?"  (John L Casti, "Five Golden Rules", 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)

"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)

"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)

"Bounded rationality simultaneously constrains the complexity of our cognitive maps and our ability to use them to anticipate the system dynamics. Mental models in which the world is seen as a sequence of events and in which feedback, nonlinearity, time delays, and multiple consequences are lacking lead to poor performance when these elements of dynamic complexity are present." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems."  (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

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

"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 systems, particularly those complex ones, are extremely difficult to model by an accurate and precise mathematical formula or equation due to the complexity of the system structure, nonlinearity, uncertainty, randomness, etc. Therefore, approximate modeling is often necessary and practical in real-world applications. Intuitively, approximate modeling is always possible. However, the key questions are what kind of approximation is good, where the sense of 'goodness' has to be first defined, of course, and how to formulate such a good approximation in modeling a system such that it is mathematically rigorous and can produce satisfactory results in both theory and applications." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"In a linear system a tiny push produces a small effect, so that cause and effect are always proportional to each other. If one plotted on a graph the cause against the effect, the result would be a straight line. In nonlinear systems, however, a small push may produce a small effect, a slightly larger push produces a proportionately larger effect, but increase that push by a hair’s breadth and suddenly the system does something radically different." (F David Peat, "From Certainty to Uncertainty", 2002)

"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)

"Linearity means that the rule that determines what a piece of a system is going to do next is not influenced by what it is doing now. More precisely, this is intended in a differential or incremental sense: For a linear spring, the increase of its tension is proportional to the increment whereby it is stretched, with the ratio of these increments exactly independent of how much it has already been stretched. Such a spring can be stretched arbitrarily far, and in particular will never snap or break. Accordingly, no real spring is linear." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science" 2nd Ed., 2004)

"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) 

"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)

"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)

"[…] 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)

"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)

"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)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 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)

"Complexity is a relative term. It depends on the number and the nature of interactions among the variables involved. Open loop systems with linear, independent variables are considered simpler than interdependent variables forming nonlinear closed loops with a delayed response." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"Nature's tendency for iteration, pattern formation, and creation of order out of chaos creates expectations of predictability. It seems, however, that nature, because of varying degrees of interaction between chance and choice, and the nonlinearity of systems, escapes the boredom of predictability." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"Remember that to map the dynamic behavior of a system is to capture the interaction of positive and negative feedback loops. These interactions, in essence, define the interdependencies, which in turn are responsible for nonlinearity in the system. It is the interdependency that poses the major challenge to our cognitive abilities. It is this challenge that we need to overcome by using operational modeling. Pattern recognition is critical for understanding and changing undesirable behavior. This leads us to the need for development of interactive operational representation of the phenomenon under investigation." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"Complex systems are full of interdependencies - hard to detect - and nonlinear responses." (Nassim N Taleb, "Antifragile: Things That Gain from Disorder", 2012)

"Where simplifications fail, causing the most damage, is when something nonlinear is simplified with the linear as a substitute. That is the most common Procrustean bed." (Nassim N Taleb, "Antifragile: Things that Gain from Disorder", 2012)

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

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"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)

"There is no linear additive process that, if all the parts are taken together, can be understood to create the total system that occurs at the moment of self-organization; it is not a quantity that comes into being. It is not predictable in its shape or subsequent behavior or its subsequent qualities. There is a nonlinear quality that comes into being at the moment of synchronicity." (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)

"[...] perhaps one of the most important features of complex systems, which is a key differentiator when comparing with chaotic systems, is the concept of emergence. Emergence 'breaks' the notion of determinism and linearity because it means that the outcome of these interactions is naturally unpredictable. In large systems, macro features often emerge in ways that cannot be traced back to any particular event or agent. Therefore, complexity theory is based on interaction, emergence and iterations." (Luis Tomé & Şuay Nilhan Açıkalın, "Complexity Theory as a New Lens in IR: System and Change" [in "Chaos, Complexity and Leadership 2017", Şefika Şule Erçetin & Nihan Potas], 2019)

"Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. […] The emergence of exponential growth from a multivariable nonlinear network is not mathematically intuitive. This indicates that the network structure and the flux functions of the modeled system must be subjected to constraints to result in long-term exponential dynamics." (Wei-Hsiang Lin et al, "Origin of exponential growth in nonlinear reaction networks", PNAS 117 (45), 2020)

16 December 2020

Systems Thinking: On Systems Thinking (Quotes)

"Tektology must clarify the modes of organization that are perceived to exist in nature and human activity; then it must generalize and systematize these modes; further it must explain them, that is, propose abstract schemes of their tendencies and laws; finally, based on these schemes, determine the direction of organizational methods and their role in the universal process. This general plan is similar to the plan of any natural science; but the objective of tektology is basically different. Tektology deals with organizational experiences not of this or that specialized field, but of all these fields together. In other words, tektology embraces the subject matter of all the other sciences and of all the human experience giving rise to these sciences, but only from the aspect of method, that is, it is interested only in the modes of organization of this subject matter." (Alexander Bogdanov, "Tektologia: Vseobshchaya Organizatsionnaya Nauka" ["Tektology: The Universal Organizational Science"], 1922)

"Creative evolution synthesises from the parts a new entity not only different from them, but quite transcending them. That is the essence of a whole. It is always transcendent to its parts, and its character cannot be inferred from the characters of its parts." (Jan Smuts, "Holism and Evolution", 1926)

"[Holism is] the tendency in nature to form wholes that are greater than the sum of the parts through creative evolution […]" (Jan Smuts, "Holism and Evolution", 1926)

"An ecological approach to public administration builds, then, quite literally from the ground up; from the elements of a place - soils, climate, location, for example - to the people who live there - their numbers and ages and knowledge, and the ways of physical and social technology by which from the place and in relationships with one another, they get their living. It is within this setting that their instruments and practices of public housekeeping should be studied so that they may better understand what they are doing, and appraise reasonably how they are doing it. Such an approach is of particular interest to us as students seeking to co-operate in our studies; for it invites - indeed is dependent upon - careful observation by many people in different environments of the roots of government functions, civic attitudes, and operating problems." (John Merriman Gaus, "Reflections on public administration", 1947)

"A systems approach begins when first you see the world through the eyes of another." (C West Churchman, "The Systems Approach", 1968)

"The parallelism of general conceptions or even special laws in different fields therefore is a consequence of the fact that these are concerned with 'systems' and that certain general principles apply to systems irrespective of their nature. Hence principles such as those of wholeness and sum, mechanization, hierarchic order, approached to steady states, equifinality, etc., may appear in quite different disciplines. The isomorphism found in different realms is based of the existence of general system principles, of a more or less well-developed ‘general system theory’." (Ludwig von Bertalanffy, "General System Theory", 1968)

"We may state as characteristic of modern science that this scheme of isolable units acting in one-way causality has proven to be insufficient. Hence the appearance, in all fields of science, of notions like wholeness, holistic, organismic, gestalt, etc., which all signify that, in the last resort, we must think in terms of systems of elements in mutual interaction […]." (Ludwig von Bertalanffy, "General System Theory", 1968)

"In the selection of papers for this volume, two problems have arisen, namely what constitutes systems thinking and what systems thinking is relevant to the thinking required for organizational management. The first problem is obviously critical. Unless there were a meaningful answer there would be no sense in producing a volume of readings in systems thinking in any subject. A great many writers have manifestly believed that there is a way of considering phenomena which is sufficiently different from the well-established modes of scientific analysis to deserve the particular title of systems thinking." (Frederick E Emery (ed.),"Systems thinking: selected readings", 1969)

"There are different levels of organization in the occurrence of events. You cannot explain the events of one level in terms of the events of another. For example, you cannot explain life in terms of mechanical concepts, nor society in terms of individual psychology. Analysis can only take you down the scale of organization. It cannot reveal the workings of things on a higher level. To some extent the holistic philosophers are right." (Anatol Rapoport, "General Systems" Vol. 14, 1969) 

"The systems approach to problems focuses on systems taken as a whole, not on their parts taken separately. Such an approach is concerned with total - system performance even when a change in only one or a few of its parts is contemplated because there are some properties of systems that can only be treated adequately from a holistic point of view. These properties derive from the relationship between parts of systems: how the parts interact and fit together." (Russell L Ackoff, "Towards a System of Systems Concepts", 1971)

"Early scientific thinking was holistic, but speculative - the modern scientific temper reacted by being empirical, but atomistic. Neither is free from error, the former because it replaces factual inquiry with faith and insight, and the latter because it sacrifices coherence at the altar of facticity. We witness today another shift in ways of thinking: the shift toward rigorous but holistic theories. This means thinking in terms of facts and events in the context of wholes, forming integrated sets with their own properties and relationships."(Ervin László, "Introduction to Systems Philosophy", 1972) 

“The notion of ‘system’ has gained central importance in contemporary science, society and life. In many fields of endeavor, the necessity of a ‘systems approach’ or ‘systems thinking’ is emphasized, new professions called ‘systems engineering’, ‘systems analysis’ and the like have come into being, and there can be little doubt that this this concept marks a genuine, necessary, and consequential development in science and world-view.” (Ervin László, “Introduction to Systems Philosophy: Toward a New Paradigm of Contemporary Thought”, 1972)

"A company is a multidimensional system capable of growth, expansion, and self-regulation. It is, therefore, not a thing but a set of interacting forces. Any theory of organization must be capable of reflecting a company's many facets, its dynamism, and its basic orderliness. When company organization is reviewed, or when reorganizing a company, it must be looked upon as a whole, as a total system." (Albert Low, "Zen and Creative Management", 1976)

"There is a strong current in contemporary culture advocating ‘holistic’ views as some sort of cure-all […] Reductionism implies attention to a lower level while holistic implies attention to higher level. These are intertwined in any satisfactory description: and each entails some loss relative to our cognitive preferences, as well as some gain [...] there is no whole system without an interconnection of its parts and there is no whole system without an environment." (Francisco Varela, "On being autonomous: The lessons of natural history for systems theory", 1977)

"Holism traditionally says that a collection of beings may have a collective property that cannot be inferred from the properties of its members." (C West Churchman, "The Systems Approach and Its Enemies" , 1979) 

"Systems thinking is a special form of holistic thinking - dealing with wholes rather than parts. One way of thinking about this is in terms of a hierarchy of levels of biological organization and of the different 'emergent' properties that are evident in say, the whole plant (e.g. wilting) that are not evident at the level of the cell (loss of turgor). It is also possible to bring different perspectives to bear on these different levels of organization. Holistic thinking starts by looking at the nature and behaviour of the whole system that those participating have agreed to be worthy of study. This involves: (i) taking multiple partial views of 'reality' […] (ii) placing conceptual boundaries around the whole, or system of interest and (iii) devising ways of representing systems of interest." (C J Pearson and R L Ison, "Agronomy of Grassland Systems", 1987)

"Systems thinking is a framework of thought that helps us to deal with complex things in a holistic way. The formalization of (giving an explicit, definite, and conventional form to) this thinking is what we have termed systems theory." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Systems thinking is a discipline for seeing the 'structures' that underlie complex situations, and for discerning high from low leverage change. That is, by seeing wholes we learn how to foster health. To do so, systems thinking offers a language that begins by restructuring how we think." (Peter Senge, "The Fifth Discipline", 1990)

"Systems thinking is a discipline for seeing wholes. It is a framework for seeing interrelationships rather than things, for seeing patterns of change rather than static 'snapshots'. It is a set of general principles- distilled over the course of the twentieth century, spanning fields as diverse as the physical and social sciences, engineering, and management. [...] During the last thirty years, these tools have been applied to understand a wide range of corporate, urban, regional, economic, political, ecological, and even psychological systems. And systems thinking is a sensibility for the subtle interconnectedness that gives living systems their unique character." (Peter Senge, "The Fifth Discipline", 1990)

"Systems thinking is a framework for seeing interrelationships rather than things, for seeing patterns rather than static snapshots. It is a set of general principles spanning fields as diverse as physical and social sciences, engineering and management." (Peter Senge, "The Fifth Discipline", 1990) 

"Systems philosophy brings forth a reorganization of ways of thinking. It creates a new worldview, a new paradigm of perception and explanation, which is manifested in integration, holistic thinking, purpose-seeking, mutual causality, and process-focused inquiry.” (Béla H. Bánáthy, "Systems Design of Education”, 1991)

"The new paradigm may be called a holistic world view, seeing the world as an integrated whole rather than a dissociated collection of parts. It may also be called an ecological view, if the term 'ecological' is used in a much broader and deeper sense than usual. Deep ecological awareness recognizes the fundamental interdependence of all phenomena and the fact that, as individuals and societies we are all embedded in (and ultimately dependent on) the cyclical process of nature." (Fritjof Capra & Gunter A Pauli, "Steering business toward sustainability", 1995)

"In the new systems thinking, the metaphor of knowledge as a building is being replaced by that of the network. As we perceive reality as a network of relationships, our descriptions, too, form an interconnected network of concepts and models in which there are no foundations. For most scientists such a view of knowledge as a network with no firm foundations is extremely unsettling, and today it is by no means generally accepted. But as the network approach expands throughout the scientific community, the idea of knowledge as a network will undoubtedly find increasing acceptance." (Fritjof Capra," The Web of Life: a new scientific understanding of living systems", 1996)

"It [system dynamics] focuses on building system dynamics models with teams in order to enhance team learning, to foster consensus and to create commitment with a resulting decision […] System dynamics can be helpful to elicit and integrate mental models into a more holistic view of the problem and to explore the dynamics of this holistic view […] It must be understood that the ultimate goal of the intervention is not to build a system dynamics model. The system dynamics model is a means to achieve other ends […] putting people in a position to learn about a messy problem [...] create a shared social reality […] a shared understanding of the problem and potential solutions [...] to foster consensus within the team [..]" (Jac A M Vennix, "Group Model Building: Facilitating Team Learning Using System Dynamics", 1996)

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

"One of the strongest benefits of the systems thinking perspective is that it can help you learn to ask the right questions. This is an important first step toward understanding a problem. […] Much of the value of systems thinking comes from the different framework that it gives us for looking at problems in new ways." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"Systems thinking is most effective when it’s used to look at a problem in a new way, not to advocate a predetermined solution. Strong advocacy will create resistance - both to your ideas, and to systems thinking itself. Present systems thinking in the spirit of inquiry, not inquisition." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"[Systems thinking is] A new way to view and mentally frame what we see in the world; a worldview and way of thinking whereby we see the entity or unit first as a whole, with its fit and relationship to its environment as primary concerns." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"The beauty of this [systems thinking] mindset is that its mental models are based on natural laws, principles of interrelationship, and interdependence found in all living systems. They give us a new view of ourselves and our many systems, from the tiniest cell to the entire earth; and as our organizations are included in that great range, they help us define organizational problems as systems problems, so we can respond in more productive ways. The systems thinking mindset is a new orientation to life. In many ways it also operates as a worldview - an overall perspective on, and understanding of, the world." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"The Systems Thinking Approach is an absolute necessity to make sense of and succeed in today’s complex world." (Stephen G Haines, 1998)

 "[...] information feedback about the real world not only alters our decisions within the context of existing frames and decision rules but also feeds back to alter our mental models. As our mental models change we change the structure of our systems, creating different decision rules and new strategies. The same information, processed and interpreted by a different decision rule, now yields a different decision. Altering the structure of our systems then alters their patterns of behavior. The development of systems thinking is a double-loop learning process in which we replace a reductionist, narrow, short-run, static view of the world with a holistic, broad, long-term, dynamic view and then redesign our policies and institutions accordingly." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000)

"Systems thinking practices the exact opposite of this analytic approach. Systems thinking studies the organization as a whole in its interaction with its environment. Then, it works backwards to understand how each part of that whole works in relation to, and support of, the entire system’s objectives. Only then can the core strategies be formulated. (Stephen G Haines, "The Systems Thinking Approach to Strategic Planning and Management", 2000)

"Systems, and organizations as systems, can only be understood holistically. Try to understand the system and its environment first. Organizations are open systems and, as such, are viable only in interaction with and adaptation to the changing environment." (Stephen G Haines, "The Systems Thinking Approach to Strategic Planning and Management", 2000)

"As a meta-discipline, systems science will transfer its content from discipline to discipline and address problems beyond conventional reductionist boundaries. Generalists, qualified to manage today’s problem better than the specialist, could be fostered. With these intentions, systems thinking and systems science should not replace but add, complement and integrate those aspects that seem not to be adequately treated by traditional science." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Systems thinking expands the focus of the observer, whereas analytical thinking reduces it. In other words, analysis looks into things, synthesis looks out of them. This attitude of systems thinking is often called expansionism, an alternative to classic reductionism. Whereas analytical thinking concentrates on static and structural properties, systems thinking concentrates on the function and behaviour of whole systems. Analysis gives description and knowledge; systems thinking gives explanation and understanding." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"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)

"Deep change in mental models, or double-loop learning, arises when evidence not only alters our decisions within the context of existing frames, but also feeds back to alter our mental models. As our mental models change, we change the structure of our systems, creating different decision rules and new strategies. The same information, interpreted by a different model, now yields a different decision. Systems thinking is an iterative learning process in which we replace a reductionist, narrow, short-run, static view of the world with a holistic, broad, long-term, dynamic view, reinventing our policies and institutions accordingly." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

"There exists an alternative to reductionism for studying systems. This alternative is known as holism. Holism considers systems to be more than the sum of their parts. It is of course interested in the parts and particularly the networks of relationships between the parts, but primarily in terms of how they give rise to and sustain in existence the new entity that is the whole whether it be a river system, an automobile, a philosophical system or a quality system." (Michael C. Jackson, "Systems Thinking: Creative Holism for Manager", 2003) 

"System Thinking is a common concept for understanding how causal relationships and feedbacks work in an everyday problem. Understanding a cause and an effect enables us to analyse, sort out and explain how changes come about both temporarily and spatially in common problems. This is referred to as mental modelling, i.e. to explicitly map the understanding of the problem and making it transparent and visible for others through Causal Loop Diagrams (CLD)." (Hördur V. Haraldsson, "Introduction to System Thinking and Causal Loop Diagrams", 2004)

"Systems thinking is only an epistemology, a particular way of describing the world. It does not tell us what the world is. Hence, strictly speaking, we should never say of something in the world: ‘It is a system’, only: ‘It may be described as a system.’" (John Mingers, Realising" Systems Thinking: Knowledge and Action in Management Science", 2006)

"At a time when the world is more messy, more crowded, more interconnected, more interdependent, and more rapidly changing than ever before, the more ways of seeing, the better. The systems-thinking lens allows us to reclaim our intuition about whole systems and hone our abilities to understand parts, see interconnections, ask 'what-if' questions about possible future behaviors, and be creative and courageous about system redesign. (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"In ecology, we are often interested in exploring the behavior of whole systems of species or ecosystem composed of individual components which interact through biological processes. We are interested not simply in the dynamics of each species or component in isolation, but the dynamics of each species or component in the context of all the others and how those coupled dynamics account for properties of the system as a whole, such as its persistence. This is what people seem to mean when they say that ecology is ‘holistic’, an otherwise rather vague term." (John Pastor, "Mathematical Ecology of Populations and Ecosystems", 2008)

"Systems thinking is a mental discipline and framework for seeing patterns and interrelationships. It is important to see organizational systems as a whole because of their complexity. Complexity can overwhelm managers, undermining confidence. When leaders can see the structures that underlie complex situations, they can facilitate improvement. But doing that requires a focus on the big picture." (Richard L Daft, "The Leadership Experience", 2008) 

"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" , 2008)

"Understanding interdependency requires a way of thinking different from analysis. It requires systems thinking. And analytical thinking and systems thinking are quite distinct. [...] Systems thinking is the art of simplifying complexity. It is about seeing through chaos, managing interdependency, and understanding choice. We see the world as increasingly more complex and chaotic because we use inadequate concepts to explain it. When we understand something, we no longer see it as chaotic or complex." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture", 2011)

"Systems thinking is a discipline or process that considers how individual elements interact with one another as part of a whole entity. As an approach to solving problems, systems thinking uses relationships among individual elements and the dynamics of these relationships to explain the behavior of systems such as an ecosystem, social system, or organization." (Karen L Higgins, "Economic Growth and Sustainability: Systems Thinking for a Complex World", 2015)

"Holism [is] the art - in contrast with reductionism - of seeing a complex system as a whole. Holism knows the limits to its understanding; it acknowledges that the system has its wildness, its privacy, its own reasons, its defenses against invasive explanation." (David Fleming, "Lean Logic", 2016)

"Systems thinking focuses on optimizing for the whole, looking at the overall flow of work, identifying what the largest bottleneck is today, and eliminating it." (Matthew Skelton & Manuel Pais, "Team Topologies: Organizing Business and Technology Teams for Fast Flow", 2019)

11 December 2020

Systems Thinking: Systems Theory (Quotes)

"Linking the basic parts are communication, balance or system parts maintained in harmonious relationship with each other and decision making. The system theory include both man-machine and interpersonal relationships. Goals, man, machine, method, and process are woven together into a dynamic unity which reacts." (George R Terry, "Principles of Management", 1960) 

"The aim of systems theory for business is to develop an objective, understandable environment for decision making; that is, if the system within which managers make the decisions can be provided as an explicit framework, then such decision making should be easier to handle." (Richard A Johnson et al, "Systems Theory and Management", Management Science Vol. 10 (2), 1964)

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

"Whereas traditional reductionism sought to find the commonality underlying diversity in reference to a shared substance, such as material atoms, contemporary systems theory seeks to find common features in terms of shared aspects of organization." (Ervin László, "The Systems View of the World: A Holistic Vision for Our Time", 1972)

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

"Systems theory is a scientific discipline concerned with the explanations of various phenomena, regardless of their specific nature, in terms of the formal relationships between the factors involved and the ways they are transformed under different conditions; the observations are explained in terms of the relationships between the components, i.e., in reference to the organization and functioning rather than with an explicit reference to the nature of the mechanisms involved (e.g., physical, biological, social, or even purely conceptual)." (Mihajlo D Mesarovic & Y Takahara, "Foundations for the mathematical theory of general systems", 1975)

"The subject of study in systems theory is not a 'physical object', a chemical or social phenomenon, for example, but a 'system': a formal relationship between observed features or attributes. For conceptual reasons, the language used in describing the behavior of systems is that of information processing and goal seeking (decision making control)." (Mihajlo D Mesarovic & Y Takahara, "Foundations for the mathematical theory of general systems", 1975)

"The most general form of systems theory is a set of logical or mathematical statements about all conceptual systems. A subset of this concerns all concrete systems. A subsubset concerns the very special and very important living systems, i. e., general living systems theory." (James G Miller, "Living systems", 1978)

"Systems theory looks at the world in terms of the interrelatedness and interdependence of all phenomena, and in this framework an integrated whole whose properties cannot be reduced to those of its parts is called a system. Living organisms, societies, and ecosystems are all systems." (Fritjof Capra, "The Turning Point: Science, Society, and the Turning Culture", 1982)

"The emphasis in system(s) theory is on the dynamic behaviour of these phenomena, i.e. how do characteristic features (such as input and output) change in time and what are the relationships, also as functions of time. One tries to design control systems such that a desired behaviour is achieved. In this sense mathematical system(s) theory (and control theory) distinguishes itself from many other branches of mathematics in the sense that it is prescriptive rather than descriptive." (G J Olsder & J.W. van der Woude, "Mathematical Systems Theory" 2nd Ed., 1983)

"For a long time, people have been trying to characterize or define the notion of system. After all, ‘systems’ are supposed to be what System Theory is about. The results so far have been contradictory and unsatisfactory. This confusion at the foundations has led many to conclude that there is no such thing as a ‘system’ and hence to deny that System Theory is about anything. Even those most sympathetic to the notion have difficulties at this level. The very founders of System Theory did not try to say what a system was; and as for System Theory, they characterized it only obliquely, by saying it comprised all studies of interest to more than one discipline. They thereby begged the entire question." (Robert Rosen, "Some comments on systems and system theory", 1986) 

"Systems theory pursues the scientific exploration and understanding of systems that exist in the various realms of experience, in order to arrive at a general theory of systems: an organized expressing of sets of interrelated concepts and principles that apply to all systems." (Béla H Bánáthy, "Systems Design of Education", 1991)

"Systems theory is antireductionist; it asserts that no system can be adequately understood or totally explained once it has been broken down into its component parts." (Charles Zastrow, "Introduction to Social Work and Social Welfare: Empowering People", 1993)

"Systems theory, in its concern for the whole and its emergent properties, ignores the components." (Walter F Buckley, "A Complex Adaptive System: Essays in Social Theory", 1998) 

"Systems theory is an interdisciplinary field of science concerned with the nature of complex systems, be they physical or natural or purely mathematical." (Thomas B Sheridan, The System Perspective on Human Factors in Aviation, 2010) 

"Systems theory is the interdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research. The term does not yet have a well-established, precise meaning, but systems theory can reasonably be considered a specialization of systems thinking; alternatively as a goal output of systems science and systems engineering, with an emphasis on generality useful across a broad range of systems (versus the particular models of individual fields)." (Gabriela Walker & Elizabeth Pattison, "Using Bronfenbrenner's Ecological Framework to Design Support Systems for Education and Special Education: Learning About Thought Systems", 2016)

"The assumption that quality of a part of a system can only be understood in its relationship to the whole and investigating the parts in isolation cannot explain their combined effect on the whole system." (Margaret S Suubi, "Education for Sustainable Development (ESD) in Higher Education", 2019) 

[Systems Theory:] "Framework of describing how smaller, multiple units and components work together to create a larger system that is designed to carry out a particular function or meet a certain goal." (RaMonda Horton, "Systems-Based Approaches to Speech-Language Pathology Service Delivery for School Age Children", 2020)

[Systems Theory:]"Is an interdisciplinary study of systems that takes a holistic approach to analysis that focuses on the elements within a system, how they interrelate, how they work over time and within the context of larger systems (e.g., natural or man-made)." (Tatiana C Valencia & Stephanie J Valencia, "Cultivating Flow and Happiness in Children", 2020)

"Systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science. It is a framework by which one can use to study, investigate and describe any group of objects that work in collaboration towards a common purpose/goal."
(Cheryl M Cordeiro et al, "Culture From a Value Systems Perspective", 2020)

[Systems Theory:] "The domain of systems inquiry that explores the principles and the description models of the abstract organization of phenomena, in an interdisciplinary manner and independently of their nature (natural or social systems) or scale of existence." (Evangelos C Papakitsos et al, "The Challenges of Work-Based Learning via Systemic Modelling in the European Union", 2020)

[Systems Theory:] "Theory that holds that systems in nature are holistic, interconnected and interdependent. If a change occurs in one part of a system, other parts of the system are affected as well." (Joe Monaco & Edward W Schneider, "Building Performance Systems That Last", 2020)

06 December 2020

Knowledge Representation: On Schema/Schemata (Quotes)

"That faculty which perceives and recognizes the noble proportions in what is given to the senses, and in other things situated outside itself, must be ascribed to the soul. It lies very close to the faculty which supplies formal schemata to the senses, or deeper still, and thus adjacent to the purely vital power of the soul, which does not think discursively […] Now it might be asked how this faculty of the soul, which does not engage in conceptual thinking, and can therefore have no proper knowledge of harmonic relations, should be capable of recognizing what is given in the outside world. For to recognize is to compare the sense perception outside with the original pictures inside, and to judge that it conforms to them." (Johannes Kepler, "Harmonices Mundi" ["Harmony of the World"] , 1619)

"This formal and pure condition of sensibility to which the employment of the concept of understanding is restricted, we shall entitle the schema of the concept. The procedure of understanding in these schemata we shall entitle the schematism of pure understanding.
 The schema is in itself always a product of imagination. Since, however, the synthesis of imagination aims at no special intuition, but only at unity in the determination of sensibility, the schema has to be distinguished from the image." (Immanuel Kant," Critique of Pure Reason", 1781)

“This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze.” (Immanuel Kant, “Critique of Pure Reason”, 1781)

"Thus then does the Doctrine of Knowledge, which in its substance is the realisation of the absolute Power of intelligising which has now been defined, end with the recognition of itself as a mere Schema in a Doctrine of Wisdom, although indeed a necessary and indispensable means to such a Doctrine: - a Schema, the sole aim of which is, with the knowledge thus acquired, - by which knowledge alone a Will, clear and intelligible to itself and reposing upon itself without wavering or perplexity, is possible, - to return wholly into Actual Life; - not into the Life of blind and irrational Instinct which we have laid bare in all its nothingness, but into the Divine Life which shall become visible to us." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)

"Everything which distinguishes man from the animals depends upon this ability to volatilize perceptual metaphors in a schema, and thus to dissolve an image into a concept. For something is possible in the realm of these schemata which could never be achieved with the vivid first impressions: the construction of a pyramidal order according to castes and degrees, the creation of a new world of laws, privileges, subordinations, and clearly marked boundaries - a new world, one which now confronts that other vivid world of first impressions as more solid, more universal, better known, and more human than the immediately perceived world, and thus as the regulative and imperative world." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)

"That immense framework and planking of concepts to which the needy man clings his whole life long in order to preserve himself is nothing but a scaffolding and toy for the most audacious feats of the liberated intellect. And when it smashes this framework to pieces, throws it into confusion, and puts it back together in an ironic fashion, pairing the most alien things and separating the closest, it is demonstrating that it has no need of these makeshifts of indigence and that it will now be guided by intuitions rather than by concepts. There is no regular path which leads from these intuitions into the land of ghostly schemata, the land of abstractions. There exists no word for these intuitions; when man sees them he grows dumb, or else he speaks only in forbidden metaphors and in unheard - of combinations of concepts. He does this so that by shattering and mocking the old conceptual barriers he may at least correspond creatively to the impression of the powerful present intuition." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)

"Every definite image in the mind is steeped and dyed in the free water that flows around it. With it goes the sense of its relations, near and remote, the dying echo of whence it came to us, the dawning sense of whither it is to lead. The significance, the value, of the image is all in this halo or penumbra that surrounds and escorts it, - or rather that is fused into one with it and has become bone of its bone and flesh of its flesh; leaving it, it is true, an image of the same thing it was before, but making it an image of that thing newly taken and freshly understood. […] Great thinkers have vast premonitory glimpses of schemes of relations between terms, which hardly even as verbal images enter the mind, so rapid is the whole process. We all of us have this permanent consciousness of whither our thought is going." (William James, "The Principles of Psychology”, 1890)

"This is the greatest degree of impoverishment; the image, deprived little by little of its own characteristics, is nothing more than a shadow. It has become that transitional form between image and pure concept that we now term ‘generic image’, or one that at least resembles the latter. The image, then, is subject to an unending process of change, of suppression and addition, of dissociation and corrosion. 
This means that it is not a dead thing; it is not at all like a photographic plate with which one may reproduce copies indefinitely. Being dependent on the state of the brain, the image undergoes change like all living substance, - it is subject to gains and losses, especially losses. But each of the foregoing three classes has its use for the inventor. They serve as material for different kinds of imagination - in their concrete form, for the mechanic and the artist; in their schematic form, for the scientist and for others." (Théodule-Armand Ribot, "Essay on the Creative Imagination", 1900)

"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, [in "On the Foundations of Geometry and Formal Theories of Arithmetic" 1971] cca. 1903-1909)

"If the fresh facts which come to our knowledge all fit themselves into the scheme, then our hypothesis may gradually become a solution." (Arthur C Doyle, "The Adventure of Wisteria Lodge", 1908)

“A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To ‘visualise’ a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement” (Albert Einstein, “Geometry and Experience”, 1921)

"This is the reason why mechanical explanations are better understood than stories, even though they are more difficult to reproduce. The exposition, even if it is faulty, excites analogous schemas already existing in the listener’s mind; so that what takes place is not genuine understanding, but a convergence of acquired schemas of thought. In the case of stories, this convergence is not possible, and the schemas brought into play are usually divergent." (Jean Piaget, "The Language and Thought of the Child", 1926)

"At first sight the assimilative tendency shown by thought seems sufficient to secure stability in judgments. To assimilate, in psychology as in biology, is to reproduce oneself by means of the external world; it is to transform perceptions until they are identical with one’s own thought, i.e. with previous schemas. Assimilation is therefore preservation and, in a certain sense, identification." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)

"In the presence of certain objects of thought or of certain affirmations the child, in virtue of previous experiences, adopts a certain way of reacting and thinking which is always the same, and which might be called a schema of reasoning. Such schemas are the functional equivalents of general propositions, but since the child is not conscious of these schemas before discussion and a desire for proof have laid them bare and at the same time changed their character, they cannot be said to constitute implicit general propositions. They simply constitute certain unconscious tendencies which live their own life but are submitted to no general systematization and consequently lead to no logical exactitude. To put it in another way, they form a logic of action but not yet a logic of thought." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)

"It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture" (Werner K Heisenberg, "The Physical Principles of the Quantum Theory", 1930)

"The methods of progress in theoretical physics have undergone a vast change during the present century. The classical tradition has been to consider the world to be an association of observable objects (particles, fluids, fields, etc.) moving about according to definite laws of force, so that one could form a mental picture in space and time of the whole scheme. This led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects, to account for their behaviour in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies. (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)

"Generally speaking, one can say that motor intelligence contains the germs of completed reason. But it gives promise of more than reason pure and simple. From the moral as from the intellectual point of view, the child is born neither good nor bad, but master of his destiny. Now, if there is intelligence in the schemas of motor adaptation, there is also the element of play. The intentionality peculiar to motor activity is not a search for truth but the pursuit of a result, whether objective or subjective; and to succeed is not to discover a truth." (Jean Piaget, "The Moral Judgment of the Child", 1932)

"In this way things, external objects, are assimilated to more or less ordered motor schemas, and in this continuous assimilation of objects the child's own activity is the starting point of play. Not only this, but when to pure movement are added language and imagination, the assimilation is strengthened, and wherever the mind feels no actual need for accommodating itself to reality, its natural tendency will be to distort the objects that surround it in accordance with its desires or its fantasy, in short to use them for its satisfaction. Such is the intellectual egocentrism that characterizes the earliest form of child thought." (Jean Piaget, "The Moral Judgment of the Child", 1932)

"'Schema' refers to an active organisation of past reactions, or of past experiences, which must always be supposed to be operating in any well-adapted organic response. That is, whenever there is any order or regularity of behavior, a particular response is possible only because it is related to other similar responses which have been serially organised, yet which operate, not simply as individual members coming one after another, but as a unitary mass. Determination by schemata is the most fundamental of all the ways in which we can be influenced by reactions and experiences which occurred some time in the past. All incoming impulses of a certain kind, or mode, go together to build up an active, organised setting: visual, auditory, various types of cutaneous impulses and the like, at a relatively low level; all the experiences connected by a common interest: in sport, in literature, history, art, science, philosophy, and so on, on a higher level." (Frederic C Bartlett, "Remembering: A study in experimental and social psychology", 1932)

"[T]he sudden inventions characteristic of the sixth stage [of infant development] are in reality the product of a long evolution of schemata and not only of an internal maturation of perceptive structures. [..] This is revealed by the existence of a fifth stage, characterized by experimental groping. […] What does this mean if not that the practice of actual experience is necessary in order to acquire the practice of mental experience and that invention does not arise entirely preformed despite appearances? (Jean Piaget, "The origin of intelligence in children" 1936)

"The more the schemata are differentiated, the smaller the gap between the new and the familiar becomes, so that novelty, instead of constituting an annoyance avoided by the subject, becomes a problem and invites searching." (Jean Piaget, "The Construction Of Reality In The Child", 1950)

"Accommodation of mental structures to reality implies the existence of assimilatory schemata apart from which any structure would be impossible." (Jean Piaget, "The Construction Of Reality In The Child", 1950)

"What in fact is the schema of the object? In one essential respect it is a schema belonging to intelligence. To have the concept of an object is to attribute the perceived figure to a substantial basis, so that the figure and the substance that it thus indicates continue to exist outside the perceptual field. The permanence of the object seen from this viewpoint is not only a product of intelligence, but constitutes the very first of those fundamental ideas of conservation which we shall see developing within the thought process." (Jean Piaget, "The Psychology of Intelligence", 1950)

"A conceptual scheme is never discarded merely because of a few stubborn facts with which it cannot be reconciled; a conceptual scheme is either modified or replaced by a better one, never abandoned with nothing left to take its place."(James B Conant, "Science and Common Sense", 1951)

"Common sense […] may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do." (James B Conant, "Science and Common Sense", 1951)

"As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries - not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer." (Willard v O Quine, "From a Logical Point of View", 1953)

"As perceivers we select from all the stimuli falling on our senses only those which interest us, and our interests are governed by a pattern-making tendency, sometimes called a schema. In a chaos of shifting impressions each of us constructs a stable world in which objects have recognisable shapes, are located in depth and have permanence." (Mary Douglas, "Purity and Danger", 1966)

"We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality […]" (Ludwig von Bertalanffy, "General System Theory", 1968)

"Imagining is not perceiving, but images are indeed derivatives of perceptual activity. In particular, they are the anticipatory phases of that activity, schemata that the perceiver has detached from the perceptual cycle for other purposes. […] The experience of having an image is just the inner aspect of a readiness to perceive the imagined object. (Ulrich Neisser, "Cognition and reality" 1976)

"A schema is a configuration within the brain, either inborn or learned, against which the input of the nerve cells is compared. [...] the conscious mind [...] can fill in details that are missing from the actual sensory input and create a pattern in the mind which is not necessarily present in reality. In this way, the gestalt of objects - the impression [...] - is aided by the taxonomic powers of the schemata." (Edward O Wilson, "On Human Nature", 1978) 

"A schema, then is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts; those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. A schema theory embodies a prototype theory of meaning. That is, inasmuch as a schema underlying a concept stored in memory corresponds to the meaning of that concept, meanings are encoded in terms of the typical or normal situations or events that instantiate that concept." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)

"Once we have accepted a configuration of schemata, the schemata themselves provide a richness that goes far beyond our observations. […] In fact, once we have determined that a particular schema accounts for some event, we may not be able to determine which aspects of our beliefs are based on direct sensory information and which are merely consequences of our interpretation." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)

"Mental schemas are not rigid. By lasting and laborious processes the mental schemas accommodate themselves, in the long run, to the features of real situations and become progressively more fit to manage them and to solve the problems with which we are faced. Each period of mental development is characterized by a system. of basic mental schemas which determine the capacity of the child to learn, to interpret, and to use the information he gets." (Efraim Fischbein, "Intuition and Proof", For The Leaning of Mathematics 3 (2), 1982)

"The basic idea is that schemata are data structures for representing the generic concepts stored in memory. There are schemata for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions. Roughly, schemata are like models of the outside world. To process information with the use of a schema is to determine which model best fits the incoming information. Ultimately, consistent configurations of schemata are discovered which, in concert, offer the best account for the input. This configuration of schemata together constitutes the interpretation of the input. (David E Rumelhart, Paul Smolensky, James L McClelland & Geoffrey E Hinton, "Schemata and sequential thought processes in PDP models", 1986)

"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 1996)

[Schemata are] knowledge structures that represent objects or events and provide default assumptions about their characteristics, relationships, and entailments under conditions of incomplete information. (Paul J. DiMaggio, "Culture and Cognition", Annual Review of Sociology 23, 1997)

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