Mental Models LXVII: On Causal Maps

"Causal maps are representations of individuals (or groups) beliefs about causal relations. They include elements, with only two kinds of properties. The first property is 'relevance'. The second  is the possibility of being in one (of two) 'influence relationships' (positive or negative) with one (of three) strengths (weak. moderate, or strong)." (Kivia Markoczy & Jeff Goldberg, "A method for eliciting and comparing causal maps", 1995)

"Short-term memory can hold 7 ± 2 chunks of information at once. This puts a rather sharp limit on the effective size and complexity of a causal map. Presenting a complex causal map all at once makes it hard to see the loops, understand which are important, or understand how they generate the dynamics. Resist the temptation to put all the loops you and your clients have identified into a single comprehensive diagram." (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)

"A causal map is an abstract representation of the causal relationships among kinds of objects and events in the world. Such relationships are not, for the most part, directly observable, but they can often be accurately inferred from observations. This includes both observations of patterns of contingency and correlation among events as well as observations of the effects of experimental interventions. We can think of everyday theories and theory-formation processes as cognitive systems that allow us to recover an accurate causal map of the world." (Alison Gopnik & Clark Glymour, "Causal maps and Bayes nets: a cognitive and computational account of theory-formation" [in "The cognitive basis of science"], 2002)

"Causal mapping is a simple and useful technique for addressing situations where thinking - as an individual or as a group - matters. A causal map is a word-and-arrow diagram in which ideas and actions are causally linked with one another through the use of arrows. The arrows indicate how one idea or action leads to another. Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that people can know what to do in an area of concern, how to do it and why, because the arrows indicate the causes and consequences of an idea or action." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping is [...]  a technique for linking strategic thinking and acting, helping make sense of complex problems, and communicating to oneself and others what might be done about them. With practice, the use of causal mapping can assist you in moving from 'winging it' when thinking matters to a more concrete and rigorous approach that helps you and others achieve success in an easy and far more reliable way" (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that we can better understand an area of concern. Causal mapping also helps us know what to do about the issue, what it would take to do those things, and what we would like to get out of having done so. Causal mapping is therefore a particularly powerful technique for making sense of complex problems, linking strategic thinking and acting, and helping to communicate to others what might or should be done. " (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"When an individual uses causal mapping to help clarify their own thinking, we call this technique cognitive mapping, because it is related to personal thinking or cognition. When a group maps their own ideas, we call it oval mapping, because we often use oval-shaped cards to record individuals’ ideas so that they can be arranged into a group’s map. Cognitive maps and oval maps can be used to create a strategic plan, because the maps include goals, strategies and actions, just like strategic plans." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal maps include elements called nodes, which are allowed to have causal relationships of different strengths of positive or negative loading depicted with a number, usually in the range of from 1 (weak) to 3 (strong). The relationships of the nodes are depicted with arcs or links labeled with the assumed polarity and loading factor or strength of causality, Links with positive polarity refer to dependency (when A increases B increases proportionally to the loading factor) and negative to inverse dependency (when A increases, B decreases)." (Hannu Kivijärvi et al, "A Support System for the Strategic Scenario Process", Encyclopedia of Decision Making and Decision Support Technologies, 2008)

"Fifth principle: (a) in finding solutions for systemic problems do not be content with symptomatic solutions but look for systemic-structural levers that can produce the more incisive effect; (b) if there are several systemic levers, choose the most efficient, that which produces the maximum effects with the minimum effort; (c) to activate the chosen structural lever identify the most effective decisional lever (action variable) taking into account the time necessary to produce the desired effect; (d) the choice of structural and decisional levers, as well as the intensity of the actions to modify their values, must follow from a careful construction, interpretation and assessment of the system’s causal map." (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"(1) The causal maps are only models of a world of variables and processes; (2) They are models suitable for depicting that world only if they represent a logical image; (3) A logical image is made up of a network of arrows that depict the cause and effect connections among the variables and processes in the world; this network cannot be in contradiction to the world; (4) This depiction of the world relates to the boundaries between the represented and the external systems; the causal maps always depict a portion of a vaster world;" (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"In constructing causal maps, whatever technique is adopted, there is always the problem of identifying or defining the system’s boundaries, either if we zoom in or broaden our perspective by zooming out." (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"A Causal Map is hierarchical in structure (linking means to ends) and built with a focus on achieving goals. The process of creating the maps is ideally a group process and this in itself will add lots of value to a collective understanding of goals around EDI, what is required to achieve these and some of the potential challenges around this." (Nicola Morrill, "Supporting Your Efforts on Diversity", 2021)

On Causality (1200-1699)

"The universal cause is one thing, a particular cause another. An effect can be haphazard with respect to the plan of the second, but not of the first. For an effect is not taken out of the scope of one particular cause save by another particular cause which prevents it, as when wood dowsed with water, will not catch fire. The first cause, however, cannot have a random effect in its own order, since all particular causes are comprehended in its causality. When an effect does escape from a system of particular causality, we speak of it as fortuitous or a chance happening […]" (Thomas Aquinas, “Summa Theologica”, cca. 1266-1273)

"Among all the studies of natural causes and reasoning, Light chiefly delights the beholder; and among the great features of mathematics the certainty of its demonstrations is what preeminently tends to elevate the mind of the investigator: Perspective, therefore, might be preferred to all the discourses and systems of the human learning." (Leonardo da Vinci, 1497)

"In the discovery of hidden things and the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort […]" (William Gilbert, "De Magnete", 1600)

"As we divided natural philosophy in general into the inquiry of causes, and productions of effects: so that part which concerneth the inquiry of causes we do subdivide according to the received and sound division of causes. The one part, which is physic, inquireth and handleth the material and efficient causes; and the other, which is metaphysic, handleth the formal and final causes." (Francis Bacon, "The Advancement of Learning", 1605)

"The end of our foundation is the knowledge of causes, and secret motions of things; and the enlarging of the bounds of human empire, to the effecting of all things possible." (Francis Bacon, "New Atlantis", 1627)

"From a given determined cause an effect follows of necessity, and on the other hand, if no determined cause is granted, it is impossible that an effect should follow." (Baruch Spinoza, "Ethics", 1677)

"I understand that to be CAUSE OF ITSELF (causa sui) whose essence involves existence and whose nature cannot be conceived unless existing." (Baruch Spinoza, "Ethics", 1677)

"[...] that all men are born ignorant of the causes of things, and that all have a desire of acquiring what is useful; [...]" (Baruch Spinoza, "Ethics", 1677)

"To this purpose the philosophers say, that Nature does nothing in vain, and more is in vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes. Therefore to the same natural effects we must, as far as possible, assign the same causes." (Sir Isaac Newton, “The Mathematical Principles of Natural Philosophy”, Voll. II, 1687)

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On Causality (1990-1999)

"To live, it seems is to explain, to justify, and to find coherence among diverse outcomes, characteristics, and causes." (Thomas Gilovich, 1991)

"Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"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)

"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)

"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)

"First, social systems are inherently insensitive to most policy changes that people choose in an effort to alter the behavior of systems. In fact, social systems draw attention to the very points at which an attempt to intervene will fail. Human intuition develops from exposure to simple systems. In simple systems, the cause of a trouble is close in both time and space to symptoms of the trouble. If one touches a hot stove, the burn occurs here and now; the cause is obvious. However, in complex dynamic systems, causes are often far removed in both time and space from the symptoms. True causes may lie far back in time and arise from an entirely different part of the system from when and where the symptoms occur. However, the complex system can mislead in devious ways by presenting an apparent cause that meets the expectations derived from simple systems." (Jay W Forrester, "Counterintuitive Behavior of Social Systems", 1995)

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

“The term mental model refers to knowledge structures utilized in the solving of problems. Mental models are causal and thus may be functionally defined in the sense that they allow a problem solver to engage in description, explanation, and prediction. Mental models may also be defined in a structural sense as consisting of objects, states that those objects exist in, and processes that are responsible for those objects’ changing states.” (Robert Hafner & Jim Stewart, “Revising Explanatory Models to Accommodate Anomalous Genetic Phenomena: Problem Solving in the ‘Context of Discovery’”, Science Education 79 (2), 1995)

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

"A good model makes the right strategic simplifications. In fact, a really good model is one that generates a lot of understanding from focusing on a very small number of causal arrows." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)

"A model is a deliberately simplified representation of a much more complicated situation. […] The idea is to focus on one or two causal or conditioning factors, exclude everything else, and hope to understand how just these aspects of reality work and interact." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)

"Delay time, the time between causes and their impacts, can highly influence systems. Yet the concept of delayed effect is often missed in our impatient society, and when it is recognized, it’s almost always underestimated. Such oversight and devaluation can lead to poor decision making as well as poor problem solving, for decisions often have consequences that don’t show up until years later. Fortunately, mind mapping, fishbone diagrams, and creativity/brainstorming tools can be quite useful here." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"Our simplistic cause-effect analyses, especially when coupled with the desire for quick fixes, usually lead to far more problems than they solve - impatience and knee-jerk reactions included. If we stop for a moment and take a good look our world and its seven levels of complex and interdependent systems, we begin to understand that multiple causes with multiple effects are the true reality, as are circles of causality-effects." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"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)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world."  (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

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On Causality (2010-2019)

"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)

"Cybernetics is the art of creating equilibrium in a world of possibilities and constraints. This is not just a romantic description, it portrays the new way of thinking quite accurately. Cybernetics differs from the traditional scientific procedure, because it does not try to explain phenomena by searching for their causes, but rather by specifying the constraints that determine the direction of their development." (Ernst von Glasersfeld, "Partial Memories: Sketches from an Improbable Life", 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)

"System dynamics is an approach to understanding the behaviour of over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. It also helps the decision maker untangle the complexity of the connections between various policy variables by providing a new language and set of tools to describe. Then it does this by modeling the cause and effect relationships among these variables." (Raed M Al-Qirem & Saad G Yaseen, "Modelling a Small Firm in Jordan Using System Dynamics", 2010)

"In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Generally, at a bifurcation, the local stability properties of equilibria, periodic orbits or other invariant sets changes." (Gregory Faye, "An introduction to bifurcation theory",  2011)

"Each systems archetype embodies a particular theory about dynamic behavior that can serve as a starting point for selecting and formulating raw data into a coherent set of interrelationships. Once those relationships are made explicit and precise, the 'theory' of the archetype can then further guide us in our data-gathering process to test the causal relationships through direct observation, data analysis, or group deliberation." (Daniel H Kim, "Systems Archetypes as Dynamic Theories", The Systems Thinker Vol. 24 (1), 2013)

"Multiple regression, like all statistical techniques based on correlation, has a severe limitation due to the fact that correlation doesn't prove causation. And no amount of measuring of 'control' variables can untangle the web of causality. What nature hath joined together, multiple regression cannot put asunder." (Richard Nisbett, "2014 : What scientific idea is ready for retirement?", 2013)

"Statisticians set a high bar when they assign a cause to an effect. [...] A model that ignores cause–effect relationships cannot attain the status of a model in the physical sciences. This is a structural limitation that no amount of data - not even Big Data - can surmount." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 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", 2013)

"A basic problem with MRA is that it typically assumes that the independent variables can be regarded as building blocks, with each variable taken by itself being logically independent of all the others. This is usually not the case, at least for behavioral data. […] Just as correlation doesn’t prove causation, absence of correlation fails to prove absence of causation. False-negative findings can occur using MRA just as false-positive findings do—because of the hidden web of causation that we’ve failed to identify." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"The theory behind multiple regression analysis is that if you control for everything that is related to the independent variable and the dependent variable by pulling their correlations out of the mix, you can get at the true causal relation between the predictor variable and the outcome variable. That’s the theory. In practice, many things prevent this ideal case from being the norm." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"The work around the complex systems map supported a concentration on causal mechanisms. This enabled poor system responses to be diagnosed as the unanticipated effects of previous policies as well as identification of the drivers of the sector. Understanding the feedback mechanisms in play then allowed experimentation with possible future policies and the creation of a coherent and mutually supporting package of recommendations for change."  (David C Lane et al, "Blending systems thinking approaches for organisational analysis: reviewing child protection", 2015)

"Correlation is not equivalent to cause for one major reason. Correlation is well defined in terms of a mathematical formula. Cause is not well defined." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Effects without an understanding of the causes behind them, on the other hand, are just bunches of data points floating in the ether, offering nothing useful by themselves. Big Data is information, equivalent to the patterns of light that fall onto the eye. Big Data is like the history of stimuli that our eyes have responded to. And as we discussed earlier, stimuli are themselves meaningless because they could mean anything. The same is true for Big Data, unless something transformative is brought to all those data sets… understanding." (Beau Lotto, "Deviate: The Science of Seeing Differently", 2017)

"The main differences between Bayesian networks and causal diagrams lie in how they are constructed and the uses to which they are put. A Bayesian network is literally nothing more than a compact representation of a huge probability table. The arrows mean only that the probabilities of child nodes are related to the values of parent nodes by a certain formula (the conditional probability tables) and that this relation is sufficient. That is, knowing additional ancestors of the child will not change the formula. Likewise, a missing arrow between any two nodes means that they are independent, once we know the values of their parents. [...] If, however, the same diagram has been constructed as a causal diagram, then both the thinking that goes into the construction and the interpretation of the final diagram change." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Again, classical statistics only summarizes data, so it does not provide even a language for asking [a counterfactual] question. Causal inference provides a notation and, more importantly, offers a solution. As with predicting the effect of interventions [...], in many cases we can emulate human retrospective thinking with an algorithm that takes what we know about the observed world and produces an answer about the counterfactual world." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Bayesian networks inhabit a world where all questions are reducible to probabilities, or (in the terminology of this chapter) degrees of association between variables; they could not ascend to the second or third rungs of the Ladder of Causation. Fortunately, they required only two slight twists to climb to the top." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Some scientists (e.g., econometricians) like to work with mathematical equations; others (e.g., hard-core statisticians) prefer a list of assumptions that ostensibly summarizes the structure of the diagram. Regardless of language, the model should depict, however qualitatively, the process that generates the data - in other words, the cause-effect forces that operate in the environment and shape the data generated." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"The calculus of causation consists of two languages: causal diagrams, to express what we know, and a symbolic language, resembling algebra, to express what we want to know. The causal diagrams are simply dot-and-arrow pictures that summarize our existing scientific knowledge. The dots represent quantities of interest, called 'variables', and the arrows represent known or suspected causal relationships between those variables - namely, which variable 'listens' to which others." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"We often say that causes precede effects and yet, in the elementary grammar of things, there is no distinction between 'cause' and 'effect'. There are regularities, represented by what we call physical laws, that link events of different times, but they are symmetric between future and past. In a microscopic description, there can be no sense in which the past is different from the future."(Carlo Rovelli, "The Order of Time", 2018)

"With Bayesian networks, we had taught machines to think in shades of gray, and this was an important step toward humanlike thinking. But we still couldn’t teach machines to understand causes and effects. [...] By design, in a Bayesian network, information flows in both directions, causal and diagnostic: smoke increases the likelihood of fire, and fire increases the likelihood of smoke. In fact, a Bayesian network can’t even tell what the 'causal direction' is." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

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On Causality (2000-2009)

"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)

"A model isolates one or a few causal connections, mechanisms, or processes, to the exclusion of other contributing or interfering factors - while in the actual world, those other factors make their effects felt in what actually happens. Models may seem true in the abstract, and are false in the concrete. The key issue is about whether there is a bridge between the two, the abstract and the concrete, such that a simple model can be relied on as a source of relevantly truthful information about the complex reality." (Uskali Mäki, "Fact and Fiction in Economics: Models, Realism and Social Construction", 2002)

"In a complex system, there is no such thing as simple cause and effect." (Margaret J Wheatley, "It's An Interconnected World", 2002)

"A causal map is a word-and-arrow diagram in which ideas and actions are causally linked with one another through the use of arrows. The arrows indicate how one idea or action leads to another. Causal mapping makesit possible to articulate a large number of ideas and their interconnections in such a way that people can know what to do in an area of concern, how to do it and why, because the arrows indicate the causes and consequences of an idea or action. Causal mapping is therefore a technique for linking strategic thinking and acting, helping make sense of complex problems, and communicating to oneself and others what might be done about them." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Nonetheless, the basic principles regarding correlations between variables are not that difficult to understand. We must look for patterns that reveal potential relationships and for evidence that variables are actually related. But when we do spot those relationships, we should not jump to conclusions about causality. Instead, we need to weigh the strength of the relationship and the plausibility of our theory, and we must always try to discount the possibility of spuriousness." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"We’re accustomed to thinking in terms of centralized control, clear chains of command, the straightforward logic of cause and effect. But in huge, interconnected systems, where every player ultimately affects every other, our standard ways of thinking fall apart. Simple pictures and verbal arguments are too feeble, too myopic." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous", 2004)

"Chance is just as real as causation; both are modes of becoming. The way to model a random process is to enrich the mathematical theory of probability with a model of a random mechanism. In the sciences, probabilities are never made up or 'elicited' by observing the choices people make, or the bets they are willing to place. The reason is that, in science and technology, interpreted probability exactifies objective chance, not gut feeling or intuition. No randomness, no probability." (Mario Bunge, "Chasing Reality: Strife over Realism", 2006)

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

"A system is a set of things – people, cells, molecules, or whatever - interconnected in such a way that they produce their own pattern of behavior over time. […] The system, to a large extent, causes its own behavior." (Donella H Meadows, “Thinking in Systems: A Primer”, 2008)

"For me, as I later came to say, cybernetics is the art of creating equilibrium in a world of possibilities and constraints. This is not just a romantic description, it portrays the new way of thinking quite accurately. Cybernetics differs from the traditional scientific procedure, because it does not try to explain phenomena by searching for their causes, but rather by specifying the constraints that determine the direction of their development." (Ernst von Glasersfeld, "The Cybernetics of Snow Drifts 1948", 2009)

"Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon." (Judea Pearl, "Causal inference in statistics: An overview", Statistics Surveys 3, 2009)

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On Causality (1975-1989)

"Causation depends on an extraordinary turning of reality at a particular instant such that one event transmutes into another." (David R Heise, "Causal Analysis", 1975)

"The invalid assumption that correlation implies cause is probably among the two or three most serious and common errors of human reasoning." (Stephen J Gould, "The Mismeasure of Man", 1980)

"All certainty in our relationships with the world rests on acknowledgement of causality. Causality is a genetic connection of phenomena through which one thing (the cause) under certain conditions gives rise to, causes something else (the effect). The essence of causality is the generation and determination of one phenomenon by another." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Every phenomenon is related to other phenomena by connections of more than one value. It is the result both of certain conditions and certain basic factors that act as its cause. That is why the cause-effect connection has to be artificially isolated from the rest of conditions so that we can see this connection in its 'pure form'. But this is achieved only by abstraction. In reality we cannot isolate this connection from the whole set of conditions. There is always a closely interwoven mass of extremely diverse secondary conditions, which leave their mark on the form in which the general connection emerges. This means that there can never be two exactly identical phenomena, even if they are generated by the same causes. They have always developed in empirically different conditions. So there can be no absolute identity in the world." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Physics is like that. It is important that the models we construct allow us to draw the right conclusions about the behaviour of the phenomena and their causes. But it is not essential that the models accurately describe everything that actually happens; and in general it will not be possible for them to do so, and for much the same reasons. The requirements of the theory constrain what can be literally represented. This does not mean that the right lessons cannot be drawn. Adjustments are made where literal correctness does not matter very much in order to get the correct effects where we want them; and very often, as in the staging example, one distortion is put right by another. That is why it often seems misleading to say that a particular aspect of a model is false to reality: given the other constraints that is just the way to restore the representation." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"The complexities of cause and effect defy analysis." (Douglas Adams, "Dirk Gently's Holistic Detective Agency", 1987)

"Correlation and causation are two quite different words, and the innumerate are more prone to mistake them than most." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

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On Causality (1900-1949)

"Some of the common ways of producing a false statistical argument are to quote figures without their context, omitting the cautions as to their incompleteness, or to apply them to a group of phenomena quite different to that to which they in reality relate; to take these estimates referring to only part of a group as complete; to enumerate the events favorable to an argument, omitting the other side; and to argue hastily from effect to cause, this last error being the one most often fathered on to statistics. For all these elementary mistakes in logic, statistics is held responsible." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"[...] the present contains nothing more than the past, and what is found in the effect was already in the cause." (Henri Bergson, "Creative Evolution", 1907)

"An exceedingly small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation 'approximately'. If that enabled us to predict the succeeding situation with 'the same approximation', that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon. (Jules H Poincaré, "Science and Method", 1908)

"To speak of the cause of an event is therefore misleading. Any set of antecedents from which the event can theoretically be inferred by means of correlations might be called a cause of the event. But to speak of the cause is to imply a uniqueness [...]." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1910)

"It is an enduring truth, which can never be altered, that every infraction of the Law of nature must carry its punitive consequences with it. We can never get beyond that range of cause and effect." (Thomas Troward, "The Edinburgh Lectures on Mental Science", 1915)

"What in the whole denotes a causal equilibrium process, appears for the part as a teleological event." (Ludwig von Bertalanffy, 1929)

"Postulate 1. All chance systems of causes are not alike in the sense that they enable us to predict the future in terms of the past. Postulate 2. Constant systems of chance causes do exist in nature. Postulate 3. Assignable causes of variation may be found and eliminated."(Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)

"When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us. Occurrences in this domain are beyond the reach of exact prediction because of the variety of factors in operation, not because of any lack of order in nature." (Albert Einstein, "Science and Religion", 1941)

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

"[...] the conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation." (Max Born, 1949)

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On Causality (-1199)

"Analysis is a method where one assumes that which is sought, and from this, through a series of implications, arrives at something which is agreed upon on the basis of synthesis; because in analysis, one assumes that which is sought to be known, proved, or constructed, and examines what this is a consequence of and from what this latter follows, so that by backtracking we end up with something that is already known or is part of the starting points of the theory; we call such a method analysis; it is, in a sense, a solution in reversed direction. In synthesis we work in the opposite direction: we assume the last result of the analysis to be true. Then we put the causes from analysis in their natural order, as consequences, and by putting these together we obtain the proof or the construction of that which is sought. We call this synthesis." (Pappus of Alexandria, cca. 4th century BC)

"All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion, desire." (Aristotle, 4th century BC)

"In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements." (Aristotle, "Physics", cca. 350 BC)

"We must rather seek for a cause, for every event whether probable or improbable must have some cause." (Polybius, "The Histories", cca. 120 BC)

"The Causes of events are ever more interesting than the events themselves." (Marcus Tullius Cicero, "Epistolae ad atticum" ["Letters to Atticus"], cca. 46-44 BC)

"The most important events are often determined by very trivial causes." (Marcus Tullius Cicero, "Orationes Philippicae", 44-43 BC)

"Constantly regard the universe as one living being, having one substance and one soul; and observe how all things have reference to one perception, the perception of this one living being; and how all things act with one movement; and how all things are the cooperating causes of all things which exist; observe too the continuous spinning of the thread and the contexture of the web." (Marcus Aurelius, "Meditations", cca. 121–180 AD)

"In the series of things those which follow are always aptly fitted to those which have gone before; for this series is not like a mere enumeration of disjointed things, which has only a necessary sequence, but it is a rational connection: and as all existing things are arranged together harmoniously, so the things which come into existence exhibit no mere succession, but a certain wonderful relationship." (Marcus Aurelius, "Meditations", cca. 180 AD)

"On the assumption that all happens by Cause, it is easy to discover the nearest determinants of any particular act or state to trace it plainly to them." (Plotinus, "Enneads", cca. 270 AD)

"Now it is established in the sciences that no knowledge is acquired save through the study of its causes and beginnings, if it has had causes and beginnings; nor completed except by knowledge of its accidents and accompanying essentials. Of these causes there are four kinds: material, efficient, formal, and final." (Ibn Sina [Avicenna] "On Medicine", cca. 1020)

"The knowledge of anything, since all things have causes, is not acquired or complete unless it is known by its causes." (Ibn Sina [Avicenna] "On Medicine", cca. 1020)

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On Causality (1950-1974)

"Keep in mind that a correlation may be real and based on real cause and effect, and still be almost worthless in determining action in any single case." (Darell Huff, "How to Lie with Statistics", 1954)

"The well-known virtue of the experimental method is that it brings situational variables under tight control. It thus permits rigorous tests of hypotheses and confidential statements about causation. The correlational method, for its part, can study what man has not learned to control. Nature has been experimenting since the beginning of time, with a boldness and complexity far beyond the resources of science. The correlator’s mission is to observe and organize the data of nature’s experiments." (Lee J Cronbach, "The Two Disciplines of Scientific Psychology", The American Psychologist Vol. 12, 1957)

"Nature is pleased with simplicity, and affects not the pomp of superfluous causes." (Morris Kline, "Mathematics and the Physical World", 1959)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1962)

"Every part of the system is so related to every other part that a change in a particular part causes a changes in all other parts and in the total system." (Arthur D Hall, "A methodology for systems engineering", 1962)

"Certain properties are necessary or sufficient conditions for other properties, and the network of causal relations thus established will make the occurrence of one property at least tend, subject to the presence of other properties, to promote or inhibit the occurrence of another. Arguments from models involve those analogies which can be used to predict the occurrence of certain properties or events, and hence the relevant relations are causal, at least in the sense of implying a tendency to co-occur." (Mary B Hesse," Models and Analogies in Science", 1963)

"Today we preach that science is not science unless it is quantitative. We substitute correlation for causal studies, and physical equations for organic reasoning. Measurements and equations are supposed to sharpen thinking, but [...] they more often tend to make the thinking non-causal and fuzzy." (John R Platt, "Strong Inference", Science Vol. 146 (3641), 1964)

"Cybernetics, based upon the principle of feedback or circular causal trains providing mechanisms for goal-seeking and self-controlling behavior." (Ludwig von Bertalanffy, "General System Theory", 1968)

"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)

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

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Virginia Anderson - Collected Quotes

"A system is a group of interacting, interrelated, or interdependent components that form a complex and unified whole." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"[…] dynamic behavior is produced by a combination of reinforcing and balancing loops. Behind any growth or collapse is at least one reinforcing loop, and for every sign of goal-seeking behavior, there is a balancing loop. A period of rapid growth or collapse followed by a slowdown typically signals a shift in dominance from a reinforcing loop that is driving the structure, to a balancing loop." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"[…] feedback is not necessarily transmitted and returned through the same system component - or even through the same system. It may travel through several intervening components within the system first, or return from an external system, before finally arriving again at the component where it started." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"Feedback is the transmission and return of information. […] A system has feedback within itself. But because all systems are part of larger systems, a system also has feedback between itself and external systems. In some systems, the feedback and adjustment processes happen so quickly that it is relatively easy for an observer to follow. In other systems, it may take a long time before the feedback is returned, so an observer would have trouble identifying the action that prompted the feedback." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"In a complex system, it is not uncommon for subsystems to have goals that compete directly with or diverge from the goals of the overall system. […] Feedback gathered from small, local subsystems for use by larger subsystems may be either inaccurately conveyed or inaccurately interpreted. Yet it is this very flexibility and looseness that allow large, complex systems to endure, although it can be hard to predict what these organizations are likely to do next." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"Left to themselves, systems seek to maintain their stability. […] Systems achieve this stability through the interactions, feedback, and adjustments that continually circulate among the system parts, and between the system and its environment." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"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)

"Reinforcing loops can be seen as the engines of growth and collapse. That is, they compound change in one direction with even more change in that direction. Many reinforcing loops have a quality of accelerating movement in a particular direction, a sense that the more one variable changes, the more another changes." (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)

On Principles V: Identity

"The topics of ontology, or metaphysic, are cause, effect, action, passion, identity, opposition, subject, adjunct, and sign." (Isaac Watts, "Logic, or The right use of reason, in the inquiry after truth", 1725)

"Science arises from the discovery of Identity amid Diversity." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle." (Henri Poincaré, "Science and Hypothesis", 1901)

"Metaphors deny distinctions between things: problems often arise from taking structural metaphors too literally. Because unexamined metaphors lead us to assume the identity of unidentical things, conflicts can arise which can only be resolved by understanding the metaphor (which requires its recognition as such), which means reconstructing the analogy on which it is based. […] The unexplained extension of concepts can too often result in the destruction rather than the expansion of meaning." (David Pimm,"Metaphor and Analogy in Mathematics", For the Learning of Mathematics Vol. 1 (3), 1981)

"The idea that one can 'introduce' a kind of objects simply by laying down an identity criterion for them really inverts the proper order of explanation. As Locke clearly understood, one must first have a clear conception of what kind of objects one is dealing with in order to extract a criterion of identity for them from that conception. […] So, rather than 'abstract' a kind of object from a criterion of identity, one must in general 'extract' a criterion of identity from a metaphysically defensible conception of a given kind of objects." (Edward J Lowe, The metaphysics of abstract objects, Journal of Philosophy 92 (10), 1995) 

"There is no unique, global, and universal relation of identity for abstract objects. [...] Abstract objects are of different sorts and this should mean, almost by definition, that there is no global, universal identity for sorts. Each sort X is equipped with an internal relation of identity but there is no identity relation that would apply to all sorts." (Jean-Pierre Marquis," Categorical foundations of mathematics, or how to provide foundations for abstract mathematics", The Review of Symbolic Logic Vol. 6 (1), 2012) 

"Reason is indeed all about identity, or, rather, tautology. Mathematics is the eternal, necessary system of rational, analytic tautology. Tautology is not 'empty', as it is so often characterized by philosophers. It is in fact the fullest thing there, the analytic ground of existence, and the basis of everything. Mathematical tautology has infinite masks to wear, hence delivers infinite variety. Mathematical tautology provides Leibniz’s world that is 'simplest in hypothesis and the richest in phenomena'. No hypothesis cold be simpler than the one revolving around tautologies concerning 'nothing'. There is something - existence - because nothing is tautologous, and 'something' is how that tautology is expressed. If we write x = 0, where x is any expression that has zero as its net result, then we have a world of infinite possibilities where something ('x') equals nothing (0)." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

On Patterns (2000-2009)

"In a linear world of equilibrium and predictability, the sparse research into an evidence base for management prescriptions and the confused findings it produces would be a sign of incompetence; it would not make much sense. Nevertheless, if organizations are actually patterns of nonlinear interaction between people; if small changes could produce widespread major consequences; if local interaction produces emergent global pattern; then it will not be possible to provide a reliable evidence base. In such a world, it makes no sense to conduct studies looking for simple causal relationships between an action and an outcome. I suggest that the story of the last few years strongly indicates that human action is nonlinear, that time and place matter a great deal, and that since this precludes simple evidence bases we do need to rethink the nature of organizations and the roles of managers and leaders in them." (Ralph D Stacey, "Complexity and Organizational Reality", 2000)

"The central proposition in [realistic thinking] is that human actions and interactions are processes, not systems, and the coherent patterning of those processes becomes what it becomes because of their intrinsic capacity, the intrinsic capacity of interaction and relationship, to form coherence. That emergent form is radically unpredictable, but it emerges in a controlled or patterned way because of the characteristic of relationship itself, creation and destruction in conditions at the edge of chaos." (Ralph D Stacey et al, "Complexity and Management: Fad or Radical Challenge to Systems Thinking?", 2000)

"Although the detailed moment-to-moment behavior of a chaotic system cannot be predicted, the overall pattern of its 'random' fluctuations may be similar from scale to scale. Likewise, while the fine details of a chaotic system cannot be predicted one can know a little bit about the range of its 'random' fluctuation." (F David Peat, "From Certainty to Uncertainty", 2002)

"There are endless examples of elaborate structures and apparently complex processes being generated through simple repetitive rules, all of which can be easily simulated on a computer. It is therefore tempting to believe that, because many complex patterns can be generated out of a simple algorithmic rule, all complexity is created in this way." (F David Peat, "From Certainty to Uncertainty", 2002)

"Randomness is a difficult notion for people to accept. When events come in clusters and streaks, people look for explanations and patterns. They refuse to believe that such patterns - which frequently occur in random data - could equally well be derived from tossing a coin. So it is in the stock market as well." (Didier Sornette, "Why Stock Markets Crash: Critical events in complex financial systems", 2003)

"Learning is the process of creating networks. Nodes are external entities which we can use to form a network. Or nodes may be people, organizations, libraries, web sites, books, journals, database, or any other source of information. The act of learning (things become a bit tricky here) is one of creating an external network of nodes - where we connect and form information and knowledge sources. The learning that happens in our heads is an internal network (neural). Learning networks can then be perceived as structures that we create in order to stay current and continually acquire, experience, create, and connect new knowledge (external). And learning networks can be perceived as structures that exist within our minds (internal) in connecting and creating patterns of understanding." (George Siemens, "Knowing Knowledge", 2006)

"Some number patterns, like even and odd numbers, lie on the surface. But the more you learn about numbers, both experimentally and theoretically, the more you discover patterns that are not so obvious. […] After a hidden pattern is exposed, it can be used to find more hidden patterns. At the end of a long chain of patterned reasoning, you can get to very difficult theorems, exploring facts about numbers that you otherwise would not know were true." (Avner Ash & Robert Gross, "Fearless Symmetry: Exposing the hidden patterns of numbers", 2006)

"Still, in the end, we find ourselves drawn to the beauty of the patterns themselves, and the amazing fact that we humans are smart enough to prove even a feeble fraction of all possible theorems about them. Often, greater than the contemplation of this beauty for the active mathematician is the excitement of the chase. Trying to discover first what patterns actually do or do not occur, then finding the correct statement of a conjecture, and finally proving it - these things are exhilarating when accomplished successfully. Like all risk-takers, mathematicians labor months or years for these moments of success." (Avner Ash & Robert Gross, "Fearless Symmetry: Exposing the hidden patterns of numbers", 2006)

"There is a big debate as to whether logic is part of mathematics or mathematics is part of logic. We use logic to think. We notice that our thinking, when it is valid, goes in certain patterns. These patterns can be studied mathematically. Thus, logic is a part of mathematics, called 'mathematical logic'." (Avner Ash & Robert Gross, "Fearless Symmetry: Exposing the hidden patterns of numbers", 2006) 

"The system is highly sensitive to some small changes and blows them up into major alterations in weather patterns. This is popularly known as the butterfly effect in that it is possible for a butterfly to flap its wings in São Paolo, so making a tiny change to air pressure there, and for this tiny change to escalate up into a hurricane over Miami. You would have to measure the flapping of every butterfly’s wings around the earth with infinite precision in order to be able to make long-term forecasts. The tiniest error made in these measurements could produce spurious forecasts. However, short-term forecasts are possible because it takes time for tiny differences to escalate."  (Ralph D Stacey, "Strategic Management and Organisational Dynamics: The Challenge of Complexity" 5th Ed. , 2007)

"Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. [...] We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that out picture is clear and accurate. But is it?" (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Why is the human need to be in control relevant to a discussion of random patterns? Because if events are random, we are not in control, and if we are in control of events, they are not random. There is therefore a fundamental clash between our need to feel we are in control and our ability to recognize randomness. That clash is one of the principal reasons we misinterpret random events."  (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"In emergent processes, the whole is greater than the sum of the parts. A mathematical phenomenon that appears in certain dynamic systems also occurs within biological systems, from molecular interactions within the cells to the cognitive processes that we use to move within society. [...] Emergent patterns of ideas, beauty, desires, or tragicomedy wait, ready to trap the next traveler in their complex domain of neatly patterned squares - the never-ending world of chess metaphors." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought." (Clifford A Pickover, "The Math Book", 2009)

"The master of chess is deeply familiar with these patterns and knows very well the position that would be beneficial to reach. The rest is thinking in a logical way (calculating) about how each piece should be moved to reach the new pattern that has already taken shape in the chess player’s mind. This way of facing chess is closely related to the solving of theorems in mathematics. For example, a mathematician who wishes to prove an equation needs to imagine how the terms on each side of the equal sign can be manipulated so that one is reduced to the other. The enterprise is far from easy, to judge by the more than two hundred years that have been needed to solve theorems such as that of Fermat (z^n = x^n + y^n), using diverse tricks to prove the equation." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

On Patterns (1990-1999)

"Mathematics is an exploratory science that seeks to understand every kind of pattern - patterns that occur in nature, patterns invented by the human mind, and even patterns created by other patterns." (Lynn A Steen, "The Future of Mathematics Education", 1990)

"Phenomena having uncertain individual outcomes but a regular pattern of outcomes in many repetitions are called random. 'Random' is not a synonym for 'haphazard' but a description of a kind of order different from the deterministic one that is popularly associated with science and mathematics. Probability is the branch of mathematics that describes randomness." (David S Moore, "Uncertainty", 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)

"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)

"Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"In everyday language, the words 'pattern' and 'symmetry' are used almost interchangeably, to indicate a property possessed by a regular arrangement of more-or-less identical units […]” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

"Scientists have discovered many peculiar things, and many beautiful things. But perhaps the most beautiful and the most peculiar thing that they have discovered is the pattern of science itself. Our scientific discoveries are not independent isolated facts; one scientific generalization finds its explanation in another, which is itself explained by yet another. By tracing these arrows of explanation back toward their source we have discovered a striking convergent pattern - perhaps the deepest thing we have yet learned about the universe." (Steven Weinberg, "Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature", 1992)

"Searching for patterns is a way of thinking that is essential for making generalizations, seeing relationships, and understanding the logic and order of mathematics. Functions evolve from the investigation of patterns and unify the various aspects of mathematics." (Marilyn Burns, "About Teaching Mathematics: A K–8 Resource", 1992)

"Symmetry is bound up in many of the deepest patterns of Nature, and nowadays it is fundamental to our scientific understanding of the universe. Conservation principles, such as those for energy or momentum, express a symmetry that (we believe) is possessed by the entire space-time continuum: the laws of physics are the same everywhere." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"World view, a concept borrowed from cultural anthropology, refers to the culturally dependent, generally subconscious, fundamental organization of the mind. This conceptual organization manifests itself as a set of presuppositions that predispose one to feel, think, and act in predictable patterns." (Kenneth G Tobin, "The practice of constructivism in science education", 1993)

"[For] us to be able to speak and understand novel sentences, we have to store in our heads not just the words of our language but also the patterns of sentences possible in our language. These patterns, in turn, describe not just patterns of words but also patterns of patterns. Linguists refer to these patterns as the rules of language stored in memory; they refer to the complete collection of rules as the mental grammar of the language, or grammar for short." (Ray Jackendoff, "Patterns in the Mind", 1994)

"A neural network is characterized by A) its pattern of connections between the neurons (called its architecture), B) its method of determining the weights on the connections (called its training, or learning, algorithm), and C) its activation function." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

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

"Each of nature's patterns is a puzzle, nearly always a deep one. Mathematics is brilliant at helping us to solve puzzles. It is a more or less systematic way of digging out the rules and structures that lie behind some observed pattern or regularity, and then using those rules and structures to explain what's going on." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns. We call it mathematics. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"Patterns possess utility as well as beauty. Once we have learned to recognize a background pattern, exceptions suddenly stand out." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

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

"Symmetry is basically a geometrical concept. Mathematically it can be defined as the invariance of geometrical patterns under certain operations. But when abstracted, the concept applies to all sorts of situations. It is one of the ways by which the human mind recognizes order in nature. In this sense symmetry need not be perfect to be meaningful. Even an approximate symmetry attracts one's attention, and makes one wonder if there is some deep reason behind it." (Eguchi Tohru & ?K Nishijima , "Broken Symmetry: Selected Papers Of Y Nambu", 1995)

"Whatever the reasons, mathematics definitely is a useful way to think about nature. What do we want it to tell us about the patterns we observe? There are many answers. We want to understand how they happen; to understand why they happen, which is different; to organize the underlying patterns and regularities in the most satisfying way; to predict how nature will behave; to control nature for our own ends; and to make practical use of what we have learned about our world. Mathematics helps us to do all these things, and often it is indispensable." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"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)

"The methods of science include controlled experiments, classification, pattern recognition, analysis, and deduction. In the humanities we apply analogy, metaphor, criticism, and (e)valuation. In design we devise alternatives, form patterns, synthesize, use conjecture, and model solutions." (Béla H Bánáthy, "Designing Social Systems in a Changing World", 1996)

"The more complex the network is, the more complex its pattern of interconnections, the more resilient it will be." (Fritjof Capra, "The Web of Life: A New Scientific Understanding of Living Systems", 1996)

"The role of science, like that of art, is to blend proximate imagery with more distant meaning, the parts we already understand with those given as new into larger patterns that are coherent enough to be acceptable as truth. Biologists know this relation by intuition during the course of fieldwork, as they struggle to make order out of the infinitely varying patterns of nature." (Edward O Wilson, "In Search of Nature", 1996)

"Mathematics can function as a telescope, a microscope, a sieve for sorting out the signal from the noise, a template for pattern perception, a way of seeking and validating truth. […] A knowledge of the mathematics behind our ideas can help us to fool ourselves a little less often, with less drastic consequences." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Mathematics is a way of thinking that can help make muddy relationships clear. It is a language that allows us to translate the complexity of the world into manageable patterns. In a sense, it works like turning off the houselights in a theater the better to see a movie. Certainly, something is lost when the lights go down; you can no longer see the faces of those around you or the inlaid patterns on the ceiling. But you gain a far better view of the subject at hand." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"A formal system consists of a number of tokens or symbols, like pieces in a game. These symbols can be combined into patterns by means of a set of rules which defines what is or is not permissible (e.g. the rules of chess). These rules are strictly formal, i.e. they conform to a precise logic. The configuration of the symbols at any specific moment constitutes a ‘state’ of the system. A specific state will activate the applicable rules which then transform the system from one state to another. If the set of rules governing the behaviour of the system are exact and complete, one could test whether various possible states of the system are or are not permissible." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"Mathematics, in the common lay view, is a static discipline based on formulas taught in the school subjects of arithmetic, geometry, algebra, and calculus. But outside public view, mathematics continues to grow at a rapid rate, spreading into new fields and spawning new applications. The guide to this growth is not calculation and formulas but an open-ended search for pattern." (Lynn A Steen, "The Future of Mathematics Education", 1998)

"A neural network consists of large numbers of simple neurons that are richly interconnected. The weights associated with the connections between neurons determine the characteristics of the network. During a training period, the network adjusts the values of the interconnecting weights. The value of any specific weight has no significance; it is the patterns of weight values in the whole system that bear information. Since these patterns are complex, and are generated by the network itself (by means of a general learning strategy applicable to the whole network), there is no abstract procedure available to describe the process used by the network to solve the problem. There are only complex patterns of relationships." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"Mathematics has traditionally been described as the science of number and shape. […] When viewed in this broader context, we see that mathematics is not just about number and shape but about pattern and order of all sorts. Number and shape - arithmetic and geometry - are but two of many media in which mathematicians work. Active mathematicians seek patterns wherever they arise." (Lynn A Steen, "The Future of Mathematics Education", 1998)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Sequences of random numbers also inevitably display certain regularities. […] The trouble is, just as no real die, coin, or roulette wheel is ever likely to be perfectly fair, no numerical recipe produces truly random numbers. The mere existence of a formula suggests some sort of predictability or pattern." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world."  (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, 1999)

"Randomness is the very stuff of life, looming large in our everyday experience. […] The fascination of randomness is that it is pervasive, providing the surprising coincidences, bizarre luck, and unexpected twists that color our perception of everyday events." (Edward Beltrami, "Chaos and Order in Mathematics and Life", 1999)

"The first view of randomness is of clutter bred by complicated entanglements. Even though we know there are rules, the outcome is uncertain. Lotteries and card games are generally perceived to belong to this category. More troublesome is that nature's design itself is known imperfectly, and worse, the rules may be hidden from us, and therefore we cannot specify a cause or discern any pattern of order. When, for instance, an outcome takes place as the confluence of totally unrelated events, it may appear to be so surprising and bizarre that we say that it is due to blind chance." (Edward Beltrami. "What is Random?: Chance and Order in Mathematics and Life", 1999)

On Conjecture (Unsourced)

"In the study of Nature conjecture must be entirely put aside, and vague hypothesis carefully guarded against. The study of Nature begins with facts, ascends to laws, and raises itself, as far as the limits of man’s intellect will permit, to the knowledge of causes, by the threefold means of observation, experiment and logical deduction." (Jean Baptiste-Andre Dumas)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"The conjectures of the scientific intelligence are genuine creative novelties, inherently unpredictable and not determined by the character of the scientist’s physical environment. The thinking mind is not a causal mechanism." (Anthony M Quinton)

"The only use of an hypothesis is, that it should lead to experiments; that it should be a guide to facts. In this application, conjectures are always of use. The destruction of an error hardly ever takes place without the discovery of truth. [...] Hypothesis should be considered merely an intellectual instrument of discovery, which at any time may be relinquished for a better instrument. It should never be spoken of as truth; its highest praise is verisimility. Knowledge can only be acquired by the senses; nature has an archetype in the human imagination; her empire is given only to industry and action, guided and governed by experience." (Sir Humphry Davy) 

"The purpose of life is to conjecture and prove." (Paul Erdős)

"The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations." (Godfrey H Hardy)

"What certainty can there be in a Philosophy which consists in as many Hypotheses as there are Phaenomena to be explained. To explain all nature is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, & leave the rest for others that come after you, than to explain all things by conjecture without making sure of any thing." (Sir Isaac Newton)

On Gravity II

"The weight of any heavy body of known weight at a particular distance from the center of the world varies according to the variation of its distance therefrom: so that as often as it is removed from the center, it becomes heavier, and when brought near to it, is lighter. On this account, the relation of gravity to gravity is as the relation of distance to distance from the center." (Al Khazini, "Book of the Balance of Wisdom", cca. 12th century)

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." (Sir Isaac Newton, "Philosophiæ Naturalis Principia Mathematica" ["The Mathematical Principles of Natural Philosophy"], 1687)

"It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact [...]That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers." (Sir Isaac Newton, [letter to Bentley] 1693)

"And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion." (Sir Isaac Newton, "Opticks", 1704)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe." (Thomas Carlyle, "Sartor Resartus", 1836)

"Gravity. Surely this force must be capable of an experimental relation to electricity, magnetism, and the other forces, so as to bind it up with them in reciprocal action and equivalent effect." (Michael Faraday, [Notebook entry] 1849) 

"It is no valid objection that science as yet throws no light on the far higher problem of the essence or origin of life. Who can explain gravity? No one now objects to following out the results consequent on this unknown element of attraction" (Charles Darwin, "The Origin of Species", 1859)

"Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance." (James C Maxwell, [Letter to William Huggins] 1868)