Science: On Conjecture (Quotes)

"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)

"The art of discovering the causes of phenomena, or true hypothesis, is like the art of deciphering, in which an ingenious conjecture greatly shortens the road." (Gottfried W Leibniz, "New Essays Concerning Human Understanding", 1704 [published 1765])

"We define the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman." (Jacob Bernoulli, "Ars Conjectandi", 1713)

"One of the most intimate of all associations in the human mind is that of cause and effect. They suggest one another with the utmost readiness upon all occasions; so that it is almost impossible to contemplate the one, without having some idea of, or forming some conjecture about the other." (Joseph Priestley, "The History and Present State of Electricity", 1767)

"On the other hand, if we add observation to observation, without attempting to draw no only certain conclusions, but also conjectural views from them, we offend against the very end for which only observations ought to be made." (Friedrich W Herschel, "On the Construction of the Heavens", Philosophical Transactions of the Royal Society of London Vol. LXXV, 1785)

"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Conjectures in philosophy are termed hypotheses or theories; and the investigation of an hypothesis founded on some slight probability, which accounts for many appearances in nature, has too often been considered as the highest attainment of a philosopher. If the hypothesis (sic) hangs well together, is embellished with a lively imagination, and serves to account for common appearances - it is considered by many, as having all the qualities that should recommend it to our belief, and all that ought to be required in a philosophical system." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture." (Charles C Colton, "Lacon", 1820)

"Life is not the object of Science: we see a little, very little; And what is beyond we can only conjecture." (Samuel Johnson, "Causes Which Produce Diversity of Opinion", 1840)

"The philosophical study of nature rises above the requirements of mere delineation, and does not consist in the sterile accumulation of isolated facts. The active and inquiring spirit of man may therefore be occasionally permitted to escape from the present into the domain of the past, to conjecture that which cannot yet be clearly determined, and thus to revel amid the ancient and ever-recurring myths [...]." (Alexander von Humboldt, "Views of Nature: Or Contemplation of the Sublime Phenomena of Creation", 1850)

"The rules of scientific investigation always require us, when we enter the domains of conjecture, to adopt that hypothesis by which the greatest number of known facts and phenomena may be reconciled." (Matthew F Maury, "The Physical Geography of the Sea", 1855)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact." (Samuel L Clemens [Mark Twain], "Life on the Mississippi", 1883)

"It is best to prove things by actual experiment; then you know; whereas if you depend on guessing and supposing and conjecturing, you will never get educated."  (Samuel L Clemens [Mark Twain], "Eve’s Diary", 1906)

"Scientific theories are not the digest of observations, but they are inventions - conjectures boldly put forward for trial, to be eliminated if they clashed with observations; with observations which were rarely accidental, but as a rule undertaken with the definite intention of testing a theory by obtaining, if possible, a decisive refutation." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"We wish to see [...] the typical attitude of the scientist who uses mathematics to understand the world around us [...] In the solution of a problem [...] there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude." (George Pólya, "Mathematical Methods in Science", 1963) 

"We defined the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman." (Bertrand de Jouvenel, "The Art of Conjecture", 1967)

"All advances of scientific understanding, at every level, begin with a speculative adventure, an imaginative preconception of what might be true.[...] [This] conjecture is then exposed to criticism to find out whether or not that imagined world is anything like the real one. Scientific reasoning is, therefore, at all levels an interaction between two episodes of thought - a dialogue between two voices, the one imaginative and the other critical [...]" (Sir Peter B Medawar,  "The Hope of Progress", 1972)

"In moving from conjecture to experimental data, (D), experiments must be designed which make best use of the experimenter's current state of knowledge and which best illuminate his conjecture. In moving from data to modified conjecture, (A), data must be analyzed so as to accurately present information in a manner which is readily understood by the experimenter." (George E P Box & George C Tjao, "Bayesian Inference in Statistical Analysis", 1973)

"Statistical methods are tools of scientific investigation. Scientific investigation is a controlled learning process in which various aspects of a problem are illuminated as the study proceeds. It can be thought of as a major iteration within which secondary iterations occur. The major iteration is that in which a tentative conjecture suggests an experiment, appropriate analysis of the data so generated leads to a modified conjecture, and this in turn leads to a new experiment, and so on." (George E P Box & George C Tjao, "Bayesian Inference in Statistical Analysis", 1973)

"[Great scientists] are men of bold ideas, but highly critical of their own ideas: they try to find whether their ideas are right by trying first to find whether they are not perhaps wrong. They work with bold conjectures and severe attempts at refuting their own conjectures." (Karl R Popper, "The Problem of Demarcation", 1974)

"The essential function of a hypothesis consists in the guidance it affords to new observations and experiments, by which our conjecture is either confirmed or refuted." (Ernst Mach, "Knowledge and Error: Sketches on the Psychology of Enquiry", 1976)

"The verb 'to theorize' is now conjugated as follows: 'I built a model; you formulated a hypothesis; he made a conjecture.'" (John M Ziman, "Reliable Knowledge", 1978)

"All advances of scientific understanding, at every level, begin with a speculative adventure, an imaginative preconception of what might be true - a preconception that always, and necessarily, goes a little way (sometimes a long way) beyond anything which we have logical or factual authority to believe in. It is the invention of a possible world, or of a tiny fraction of that world. The conjecture is then exposed to criticism to find out whether or not that imagined world is anything like the real one. Scientific reasoning is therefore at all levels an interaction between two episodes of thought - a dialogue between two voices, the one imaginative and the other critical; a dialogue, as I have put it, between the possible and the actual, between proposal and disposal, conjecture and criticism, between what might be true and what is in fact the case." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"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 everyday usage of 'theory' is for an idea whose outcome is as yet undetermined, a conjecture, or for an idea contrary to evidence. But scientists use the word in exactly the opposite sense. [In science] 'theory' [...] refers only to a collection of hypotheses and predictions that is amenable to experimental test, preferably one that has been successfully tested. It has everything to do with the facts." (Tony Rothman & George Sudarshan, "Doubt and Certainty: The Celebrated Academy: Debates on Science, Mysticism, Reality, in General on the Knowable and Unknowable", 1998) 

Systems Thinking: On Bounded Rationality (Quotes)

"The principle of bounded rationality [is] the capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solution is required for objectively rational behavior in the real world - or even for a reasonable approximation to such objective rationality." (Herbert A Simon, "Administrative Behavior", 1947)

"The first consequence of the principle of bounded rationality is that the intended rationality of an actor requires him to construct a simplified model of the real situation in order to deal with it. He behaves rationally with respect to this model, and such behavior is not even approximately optimal with respect to the real world. To predict his behavior we must understand the way in which this simplified model is constructed, and its construction will certainly be related to his psychological properties as a perceiving, thinking, and learning animal." (Herbert A Simon, "Models of Man", 1957)

[*]"A decision theory that rests on the assumptions that human cognitive capabilities are limited and that these limitations are adaptive with respect to the decision environments humans frequently encounter. Decision are thought to be made usually without elaborate calculations, but instead by using fast and frugal heuristics. These heuristics certainly have the advantage of speed and simplicity, but if they are well matched to a decision environment, they can even outperform maximizing calculations with respect to accuracy. The reason for this is that many decision environments are characterized by incomplete information and noise. The information we do have is usually structured in a specific way that clever heuristics can exploit." (E Ebenhoh, "Agent-Based Modelnig with Boundedly Rational Agents", 2007)

"Bounded rationality [...] is the rationality that takes into account the limitations of the decision maker in terms of information, cognitive capacity, and attention as opposed to substantive rationality, which is not limited to satisficing, but rather aims at fully optimized solutions." (Jean-Charles Pomerol & Frédéric Adam, "Understanding the Legacy of Herbert Simon to Decision Support Systems", 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)

[*] "Conceptual model that assumes individuals are intentionally rational, i.e. they try to maximize their decisions. However, this ideal model is almost impossible to apply in practice: actions and decisions are taken and performed by individuals whose knowledge of the alternatives and the consequences is incomplete; in addition, preferences are subject to change and are not always clearly orderable." (Maddalena Sorrentino & Marco De Marco, "Developing an Interdisciplinary Approach to the Evaluation of E-Government Implementation", 2009)

[*] "The assumption that agents have limited ability to acquire and process information and to solve complex economic problems. These limitations imply that expectations can diverge from RE [Rational Expectationa]." (Sebastiano Manzan, Agent Based Modeling in Finance", 2009)

[*] "Refers to the difficulties faced by an individual in obtaining, memorizing, and processing information in an actionable manner. Although he/she may want to act rationally, the individual can only do so in a limited way, without being able to take into account all desirable information or all possible options. This limited way consists in acting on the basis of knowledge that is deemed acceptable and sufficient, rather than complete knowledge, and of simple rules, rather than a comprehensive method; and in taking shortcuts whenever possible." (Humbert Lesca & Nicolas Lesca, "Weak Signals for Strategic Intelligence: Anticipation Tool for Managers", 2011)

[*] "The theory that personal rationality is bounded by our ability to process information, our cognitive limitations, and the finite time we have to make a decision. Although our decisions are still rational, they are rational within these constraints and, therefore, may not always appear to be rational or optimal." (Evan Stubbs, "Delivering Business Analytics: Practical Guidelines for Best Practice", 2013)

[*] "The principle that the rationality of human beings is constrained ('bounded') by the limits of their cognition and capacity to process information." (Robert M Grant, "Contemporary Strategy Analysis" 10th Ed., 2018)

[*] "A situation in which people have a limited capacity to anticipate, solve complex problems, or enumerate all options." (Jeffrey M Perloff & James A Brander, "Managerial Economics and Strategy" 2nd Ed., 2016)

[*] "A concept that explains behavior that diverges from the standard assumption of a fully rational economic agent. It occurs due to limitations of cognitive ability and access to information for decision making." (Ashlesha Khedekar-Swaminathan, "Behavioral Strategies to Achieve Financial Stability in Uncertain Times", 2019)

"Bounded rationality means rationality within limits or bounds set by incomplete information, cognitive limitations of mind and limited time available for taking the decision." (Anubhuti Dwivedi, "Peace in Economic Equilibrium: A Micro-Perspective", 2019)

[*] "Paradigm that explains agents’ strategic decision-making based on the imperfect information available to them and the expectations they have that dictate whether they will view the results as satisfactory. It leads on to the idea of adaptive learning and trial-and-error processes." (César Camisón, "Neurostrategy", 2021)

[*] "The idea that decision making deviates from rationality due to such inherently human factors as limitations in cognitive capacity and willpower, and situational constraints." (Shaun Ruysenaar, "Thinking Critically About the Fourth Industrial Revolution as a Wicked Problem", 2021)

Systems Thinking: On Issues/Problems (Quotes)

"The making of decisions, as everyone knows from personal experience, is a burdensome task. Offsetting the exhilaration that may result from correct and successful decision and the relief that follows the termination of a struggle to determine issues is the depression that comes from failure, or error of decision, and the frustration which ensues from uncertainty." (Chester I Barnard, "The Functions of the Executive", 1938)

"Systems engineering embraces every scientific and technical concept known, including economics, management, operations, maintenance, etc. It is the job of integrating an entire problem or problem to arrive at one overall answer, and the breaking down of this answer into defined units which are selected to function compatibly to achieve the specified objectives. [...] Instrument and control engineering is but one aspect of systems engineering - a vitally important and highly publicized aspect, because the ability to create automatic controls within overall systems has made it possible to achieve objectives never before attainable, While automatic controls are vital to systems which are to be controlled, every aspect of a system is essential. Systems engineering is unbiased, it demands only what is logically required. Control engineers have been the leaders in pulling together a systems approach in the various technologies." (Instrumentation Technology, 1957) 

"Systems engineering is the name given to engineering activity which considers the overall behavior of a system, or more generally which considers all factors bearing on a problem, and the systems approach to control engineering problems is correspondingly that approach which examines the total dynamic behavior of an integrated system. It is concerned more with quality of performance than with sizes, capacities, or efficiencies, although in the most general sense systems engineering is concerned with overall, comprehensive appraisal." (Ernest F Johnson, "Automatic process control", 1958)

"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)

"It is a commonplace of modern technology that there is a high measure of certainty that problems have solutions before there is knowledge of how they are to be solved." (John K Galbraith, "The New Industrial State", 1967)

"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)

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

"General systems theory deals with the most fundamental concepts and aspects of systems. Many theories dealing with more specific types of systems (e. g., dynamical systems, automata, control systems, game-theoretic systems, among many others) have been under development for quite some time. General systems theory is concerned with the basic issues common to all these specialized treatments. Also, for truly complex phenomena, such as those found predominantly in the social and biological sciences, the specialized descriptions used in classical theories (which are based on special mathematical structures such as differential or difference equations, numerical or abstract algebras, etc.) do not adequately and properly represent the actual events. Either because of this inadequate match between the events and types of descriptions available or because of the pure lack of knowledge, for many truly complex problems one can give only the most general statements, which are qualitative and too often even only verbal. General systems theory is aimed at providing a description and explanation for such complex phenomena." (Mihajlo D. Mesarovic & Yasuhiko Takahare, "General Systems Theory: Mathematical foundations", 1975)

"The world is a complex, interconnected, finite, ecological–social–psychological–economic system. We treat it as if it were not, as if it were divisible, separable, simple, and infinite. Our persistent, intractable global problems arise directly from this mismatch." (Donella Meadows, "Whole Earth Models and Systems", 1982)

"Models are often used to decide issues in situations marked by uncertainty. However statistical differences from data depend on assumptions about the process which generated these data. If the assumptions do not hold, the inferences may not be reliable either. This limitation is often ignored by applied workers who fail to identify crucial assumptions or subject them to any kind of empirical testing. In such circumstances, using statistical procedures may only compound the uncertainty." (David A Greedman & William C Navidi, "Regression Models for Adjusting the 1980 Census", Statistical Science Vol. 1 (1), 1986)

"If we want to solve problems effectively […] we must keep in mind not only many features but also the influences among them. Complexity is the label we will give to the existence of many interdependent variables in a given system. The more variables and the greater their interdependence, the greater the system's complexity. Great complexity places high demands on a planner's capacity to gather information, integrate findings, and design effective actions. The links between the variables oblige us to attend to a great many features simultaneously, and that, concomitantly, makes it impossible for us to undertake only one action in a complex system." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)

"The real leverage in most management situations lies in understanding dynamic complexity, not detail complexity. […] Unfortunately, most 'systems analyses' focus on detail complexity not dynamic complexity. Simulations with thousands of variables and complex arrays of details can actually distract us from seeing patterns and major interrelationships. In fact, sadly, for most people 'systems thinking' means 'fighting complexity with complexity', devising increasingly 'complex' (we should really say 'detailed') solutions to increasingly 'complex' problems. In fact, this is the antithesis of real systems thinking." (Peter M Senge, "The Fifth Discipline: The Art and Practice of the Learning Organization", 1990)

"For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it ‘works’ and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed." (Bertram N Brockhouse, [lecture] 1994)

"In sharp contrast (with the traditional social planning) the systems design approach seeks to understand a problem situation as a system of interconnected, interdependent, and interacting issues and to create a design as a system of interconnected, interdependent, interacting, and internally consistent solution ideas." (Béla H Bánáthy, "Designing Social Systems in a Changing World", 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)

"The theory of Tipping Points requires, however, that we reframe the way we think about the world. [...] We have trouble estimating dramatic, exponential change. [...] There are abrupt limits to the number of cognitive categories we can make and the number of people we can truly love and the number of acquaintances we can truly know. We throw up our hands at a problem phrased in an abstract way, but have no difficulty at all solving the same problem rephrased as a social dilemma. All of these things are expressions of the peculiarities of the human mind and heart, a refutation of the notion that the way we function and communicate and process information is straightforward and transparent. It is not. It is messy and opaque." (Malcolm T Gladwell, "The Tipping Point: How Little Things Can Make a Big Difference", 2000)

"A model is an imitation of reality and a mathematical model is a particular form of representation. We should never forget this and get so distracted by the model that we forget the real application which is driving the modelling. In the process of model building we are translating our real world problem into an equivalent mathematical problem which we solve and then attempt to interpret. We do this to gain insight into the original real world situation or to use the model for control, optimization or possibly safety studies." (Ian T Cameron & Katalin Hangos, "Process Modelling and Model Analysis", 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)

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

"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)

"We often hear warnings that some social problem is 'epidemic'. This expression suggests that the problem's growth is rapid, widespread, and out of control. If things are getting worse, and particularly if they're getting worse fast, we need to act." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"Internal friction is exacerbated by the fact that in business as in war, we are operating in a nonlinear, semi-chaotic environment in which our endeavors will collide and possibly clash with the actions of other independent wills (customers, suppliers, competitors, regulators, lobbyists, and so on). The internal and external worlds are in constant contact and the effects of our actions are the result of their reciprocal interaction. Friction gives rise to three gaps: the knowledge gap, the alignment gap, and the effects gap. To execute effectively, we must address all three. Our instinctive reaction to the three gaps is to demand more detail. We gather more data in order to craft more detailed plans, issue more detailed instructions, and exercise more detailed control. This not only fails to solve the problem, it usually makes it worse. We need to think about the problem differently and adopt a systemic approach to solving it." (Stephen Bungay, "The Art of Action: How Leaders Close the Gaps between Plans, Actions, and Results", 2010)

[system dynamics:] "The interactions of connected and interdependent components, which may cause change over time and give rise to interconnected risks; emerging, unforeseeable issues; and unclear, disproportional cause-and-effect relationships." (Project Management Institute, "Navigating Complexity: A Practice Guide", 2014)

"System dynamics [...] uses models and computer simulations to understand behavior of an entire system, and has been applied to the behavior of large and complex national issues. It portrays the relationships in systems as feedback loops, lags, and other descriptors to explain dynamics, that is, how a system behaves over time. Its quantitative methodology relies on what are called 'stock-and-flow diagrams' that reflect how levels of specific elements accumulate over time and the rate at which they change. Qualitative systems thinking constructs evolved from this quantitative discipline." (Karen L Higgins, "Economic Growth and Sustainability: Systems Thinking for a Complex World", 2015)

"Man is not born to solve the problems of the universe, but to find out where the problems begin, and then to take his stand within the limits of the intelligible." (Johann Wolfgang von Goethe)

"Some problems are just too complicated for rational logical solutions. They admit of insights, not answers." (Jerome B Wiesner)

Systems Thinking: On Perturbation (Quotes)

"A real system is subject to perturbations and it is never possible to control its initial state exactly. This raises the question of stability: under a slight perturbation will the system remain near the equilibrium state or not?" Joseph P LaSalle & Solomon Lefschetz, "Stability by Liapunov's Direct Method with Applications", 1961) 

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

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

"Open systems, in contrast to closed systems, exhibit a principle of equifinality, that is, a tendency to achieve a final state independent of initial conditions. In other words, open systems tend to 'resist' perturbations that take them away from some steady state. They can exhibit homeostasis." (Anatol Rapaport, "The Uses of Mathematical Isomorphism in General System Theory", 1972)

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

"Regarding stability, the state trajectories of a system tend to equilibrium. In the simplest case they converge to one point (or different points from different initial states), more commonly to one (or several, according to initial state) fixed point or limit cycle(s) or even torus(es) of characteristic equilibrial behaviour. All this is, in a rigorous sense, contingent upon describing a potential, as a special summation of the multitude of forces acting upon the state in question, and finding the fixed points, cycles, etc., to be minima of the potential function. It is often more convenient to use the equivalent jargon of 'attractors' so that the state of a system is 'attracted' to an equilibrial behaviour. In any case, once in equilibrial conditions, the system returns to its limit, equilibrial behaviour after small, arbitrary, and random perturbations." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

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

"Feedback and its big brother, control theory, are such important concepts that it is odd that they usually find no formal place in the education of physicists. On the practical side, experimentalists often need to use feedback. Almost any experiment is subject to the vagaries of environmental perturbations. Usually, one wants to vary a parameter of interest while holding all others constant. How to do this properly is the subject of control theory. More fundamentally, feedback is one of the great ideas developed (mostly) in the last century, with particularly deep consequences for biological systems, and all physicists should have some understanding of such a basic concept." (John Bechhoefer, "Feedback for physicists: A tutorial essay on control", Reviews of Modern Physics Vol. 77, 2005)

"Of course, the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So, the direct impact of this phenomenon on weather prediction is often somewhat overstated." (James Annan & William Connolley, "Chaos and Climate", 2005)

"Physically, the stability of the dynamics is characterized by the sensitivity to initial conditions. This sensitivity can be determined for statistically stationary states, e.g. for the motion on an attractor. If this motion demonstrates sensitive dependence on initial conditions, then it is chaotic. In the popular literature this is often called the 'Butterfly Effect', after the famous 'gedankenexperiment' of Edward Lorenz: if a perturbation of the atmosphere due to a butterfly in Brazil induces a thunderstorm in Texas, then the dynamics of the atmosphere should be considered as an unpredictable and chaotic one. By contrast, stable dependence on initial conditions means that the dynamics is regular." (Ulrike Feudel et al, "Strange Nonchaotic Attractors", 2006)

"This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment." (Greg Rae, Chaos Theory: A Brief Introduction, 2006)

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

"A perturbation in a system with a negative feedback mechanism will be reduced whereas in a system with positive feedback mechanisms, the perturbation will grow. Quite often, the system dynamics can be reduced to a low-order description. Then, the growth or decay of perturbations can be classified by the systems’ eigenvalues or the pseudospectrum." (Gerrit Lohmann, "Abrupt Climate Change Modeling", 2009)

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

Systems Thinking: Bifurcation Theory (Quotes)

"It is not enough to know the critical stress, that is, the quantitative breaking point of a complex design; one should also know as much as possible of the qualitative geometry of its failure modes, because what will happen beyond the critical stress level can be very different from one case to the next, depending on just which path the buckling takes. And here catastrophe theory, joined with bifurcation theory, can be very helpful by indicating how new failure modes appear." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"The study of changes in the qualitative structure of the flow of a differential equation as parameters are varied is called bifurcation theory. At a given parameter value, a differential equation is said to have stable orbit structure if the qualitative structure of the flow does not change for sufficiently small variations of the parameter. A parameter value for which the flow does not have stable orbit structure is called a bifurcation value, and the equation is said to be at a bifurcation point." (Jack K Hale & Hüseyin Kocak, "Dynamics and Bifurcations", 1991)

"Fundamental to catastrophe theory is the idea of a bifurcation. A bifurcation is an event that occurs in the evolution of a dynamic system in which the characteristic behavior of the system is transformed. This occurs when an attractor in the system changes in response to change in the value of a parameter. A catastrophe is one type of bifurcation. The broader framework within which catastrophes are located is called dynamical bifurcation theory." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"The existence of equilibria or steady periodic solutions is not sufficient to determine if a system will actually behave that way. The stability of these solutions must also be checked. As parameters are changed, a stable motion can become unstable and new solutions may appear. The study of the changes in the dynamic behavior of systems as parameters are varied is the subject of bifurcation theory. Values of the parameters at which the qualitative or topological nature of the motion changes are known as critical or bifurcation values." (Francis C Moona, "Nonlinear Dynamics", 2003)

"In parametrized dynamical systems a bifurcation occurs when a qualitative change is invoked by a change of parameters. In models such a qualitative change corresponds to transition between dynamical regimes. In the generic theory a finite list of cases is obtained, containing elements like ‘saddle-node’, ‘period doubling’, ‘Hopf bifurcation’ and many others." (Henk W Broer & Heinz Hanssmann, "Hamiltonian Perturbation Theory (and Transition to Chaos)", 2009)

"The concept of bifurcation, present in the context of non-linear dynamic systems and theory of chaos, refers to the transition between two dynamic modalities qualitatively distinct; both of them are exhibited by the same dynamic system, and the transition (bifurcation) is promoted by the change in value of a relevant numeric parameter of such system. Such parameter is named 'bifurcation parameter', and in highly non-linear dynamic systems, its change can produce a large number of bifurcations between distinct dynamic modalities, with self-similarity and fractal structure. In many of these systems, we have a cascade of numberless bifurcations, culminating with the production of chaotic dynamics." (Emilio Del-Moral-Hernandez, "Chaotic Neural Networks", Encyclopedia of Artificial Intelligence, 2009)

"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." (Greegory Faye, "An introduction to bifurcation theory",  2011)

"Catastrophe theory can be thought of as a link between classical analysis, dynamical systems, differential topology (including singularity theory), modern bifurcation theory and the theory of complex systems." (Werner Sanns, "Catastrophe Theory" [Mathematics of Complexity and Dynamical Systems, 2012])

"Roughly spoken, bifurcation theory describes the way in which dynamical system changes due to a small perturbation of the system-parameters. A qualitative change in the phase space of the dynamical system occurs at a bifurcation point, that means that the system is structural unstable against a small perturbation in the parameter space and the dynamic structure of the system has changed due to this slight variation in the parameter space." (Holger I Meinhardt, "Cooperative Decision Making in Common Pool Situations", 2012)

"Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of 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 behavior. Bifurcations can occur in both continuous systems (described by ODEs, DDEs, or PDEs) and discrete systems (described by maps)." (Tianshou Zhou, "Bifurcation", 2013)

"Most commonly applied to the mathematical study of 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 behavior. Bifurcations can occur in both continuous systems (described by ODEs, DDEs, or PDEs) and discrete systems (described by maps)." (Tianshou Zhou, "Bifurcation", 2013)

"The core of bifurcation theory of nonlinear system inevitably falls back to the dynamic analysis of linear ones. Because of that, the fundamental question one may ask is if there exist a linearized DAE system with the same qualitative behavior around fixed points of its nonlinear counterpart." (Ataíde S A.Netoa et al, "Nonlinear dynamic analysis of chemical engineering processes described by differential-algebraic equations systems", 2019)

Science: On Insight (Quotes)

"[…] it is from long experience chiefly that we are to expect the most certain rules of practice, yet it is withal to be remembered, that observations, and to put us upon the most probable means of improving any art, is to get the best insight we can into the nature and properties of those things which we are desirous to cultivate and improve." (Stephen Hales, "Vegetable Staticks", 1727)

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"Insight is not the same as scientific deduction, but even at that it may be more reliable than statistics." (Anthony Standen, "Science Is a Sacred Cow", 1950)

"The attempt to characterize exactly models of an empirical theory almost inevitably yields a more precise and clearer understanding of the exact character of a theory. The emptiness and shallowness of many classical theories in the social sciences is well brought out by the attempt to formulate in any exact fashion what constitutes a model of the theory. The kind of theory which mainly consists of insightful remarks and heuristic slogans will not be amenable to this treatment. The effort to make it exact will at the same time reveal the weakness of the theory." (Patrick Suppes," A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences", Synthese  Vol. 12 (2/3), 1960)

"Model-making, the imaginative and logical steps which precede the experiment, may be judged the most valuable part of scientific method because skill and insight in these matters are rare. Without them we do not know what experiment to do. But it is the experiment which provides the raw material for scientific theory. Scientific theory cannot be built directly from the conclusions of conceptual models." (Herbert G Andrewartha," Introduction to the Study of Animal Population", 1961)

"A point of view can be a dangerous luxury when substituted for insight and understanding." (Marshall McLuhan, "The Gutenberg Galaxy", 1962)

"The purpose of computing is insight, not numbers […] sometimes […] the purpose of computing numbers is not yet in sight." (Richard Hamming, "Numerical Methods for Scientists and Engineers", 1962)

"The mediation of theory and praxis can only be clarified if to begin with we distinguish three functions, which are measured in terms of different criteria: the formation and extension of critical theorems, which can stand up to scientific discourse; the organization of processes of enlightenment, in which such theorems are applied and can be tested in a unique manner by the initiation of processes of reflection carried on within certain groups toward which these processes have been directed; and the selection of appropriate strategies, the solution of tactical questions, and the conduct of the political struggle. On the first level, the aim is true statements, on the second, authentic insights, and on the third, prudent decisions." (Jürgen Habermas, "Introduction to Theory and Practice", 1963)

"[…] the human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight […] induction, which - like other forms of imagination - cannot be formalized." (Jacob Bronowski, "The Reach of Imagination", 1967)

"Insight doesn't happen often in the click of the moment, like a lucky snapshot, but it comes in its own time and more slowly and from nowhere but within." (Eudora Welty, "One Time, One Place", 1971)

"[...] it is rather more difficult to recapture directness and simplicity than to advance in the direction of ever more sophistication and complexity. Any third-rate engineer or researcher can increase complexity; but it takes a certain flair of real insight to make things simple again." (Ernst F Schumacher, "Small Is Beautiful", 1973)

"All of us must cross the line between ignorance and insight many times before we truly understand." (David Hawkins, "The Informed Vision: Essays on Learning and Human Nature", 1974)

"Every discovery, every enlargement of the understanding, begins as an imaginative preconception of what the truth might be. The imaginative preconception - a ‘hypothesis’ - arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, a product of a blaze of insight. It comes anyway from within and cannot be achieved by the exercise of any known calculus of discovery." (Sir Peter B Medawar, "Advice to a Young Scientist", 1979)

"There is a tendency to mistake data for wisdom, just as there has always been a tendency to confuse logic with values, intelligence with insight. Unobstructed access to facts can produce unlimited good only if it is matched by the desire and ability to find out what they mean and where they lead." (Norman Cousins, "Human Options : An Autobiographical Notebook", 1981)

"The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases." (Paul Halmos, "Selecta: Expository writing", 1983)

"All the efforts of the researcher to find other models, conceptions, different mathematical forms, better linguistic modes of expression, to do justice to newly discovered layers of being mean self-transformation. The researcher in his place is the human being in self-transformation to more profound insight into what is given." (John Dessauer, Universitas: A Quarterly German Review of the Arts and Sciences Vol. 26 (4), 1984)

"[…] new insights fail to get put into practice because they conflict with deeply held internal images of how the world works [...] images that limit us to familiar ways of thinking and acting. That is why the discipline of managing mental models - surfacing, testing, and improving our internal pictures of how the world works - promises to be a major breakthrough for learning organizations." (Peter Senge, "The Fifth Discipline: The Art and Practice of the Learning Organization", 1990)

"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)

"Management is not founded on observation and experiment, but on a drive towards a set of outcomes. These aims are not altogether explicit; at one extreme they may amount to no more than an intention to preserve the status quo, at the other extreme they may embody an obsessional demand for power, profit or prestige. But the scientist's quest for insight, for understanding, for wanting to know what makes the system tick, rarely figures in the manager's motivation. Secondly, and therefore, management is not, even in intention, separable from its own intentions and desires: its policies express them. Thirdly, management is not normally aware of the conventional nature of its intellectual processes and control procedures. It is accustomed to confuse its conventions for recording information with truths-about-the-business, its subjective institutional languages for discussing the business with an objective language of fact and its models of reality with reality itself." (Stanford Beer, "Decision and Control", 1994)

"Ideas about organization are always based on implicit images or metaphors that persuade us to see, understand, and manage situations in a particular way. Metaphors create insight. But they also distort. They have strengths. But they also have limitations. In creating ways of seeing, they create ways of not seeing. There can be no single theory or metaphor that gives an all-purpose point of view, and there can be no simple 'correct theory' for structuring everything we do." (Gareth Morgan, "Imaginization", 1997)

"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)

"The purpose of analysis is insight. The best analysis is the simplest analysis which provides the needed insight." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"A model is an imitation of reality and a mathematical model is a particular form of representation. We should never forget this and get so distracted by the model that we forget the real application which is driving the modelling. In the process of model building we are translating our real world problem into an equivalent mathematical problem which we solve and then attempt to interpret. We do this to gain insight into the original real world situation or to use the model for control, optimization or possibly safety studies." (Ian T Cameron & Katalin Hangos, "Process Modelling and Model Analysis", 2001)

"Insight is not a lightbulb that goes off inside our heads. It is a flickering candle that can easily be snuffed out." (Malcolm Gladwell, "Blink: The Power of Thinking Without Thinking", 2005)

"A common mistake is that all visualization must be simple, but this skips a step. You should actually design graphics that lend clarity, and that clarity can make a chart 'simple' to read. However, sometimes a dataset is complex, so the visualization must be complex. The visualization might still work if it provides useful insights that you wouldn’t get from a spreadsheet. […] Sometimes a table is better. Sometimes it’s better to show numbers instead of abstract them with shapes. Sometimes you have a lot of data, and it makes more sense to visualize a simple aggregate than it does to show every data point." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"The other buzzword that epitomizes a bias toward substitution is 'big data'. Today’s companies have an insatiable appetite for data, mistakenly believing that more data always creates more value. But big data is usually dumb data. Computers can find patterns that elude humans, but they don’t know how to compare patterns from different sources or how to interpret complex behaviors. Actionable insights can only come from a human analyst (or the kind of generalized artificial intelligence that exists only in science fiction)." (Peter Thiel & Blake Masters, "Zero to One: Notes on Startups, or How to Build the Future", 2014)

"As business leaders we need to understand that lack of data is not the issue. Most businesses have more than enough data to use constructively; we just don't know how to use it. The reality is that most businesses are already data rich, but insight poor." (Bernard Marr, Big Data: Using SMART Big Data, Analytics and Metrics To Make Better Decisions and Improve Performance, 2015)

"While Big Data, when managed wisely, can provide important insights, many of them will be disruptive. After all, it aims to find patterns that are invisible to human eyes. The challenge for data scientists is to understand the ecosystems they are wading into and to present not just the problems but also their possible solutions." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"Big Data allows us to meaningfully zoom in on small segments of a dataset to gain new insights on who we are." (Seth Stephens-Davidowitz, "Everybody Lies: What the Internet Can Tell Us About Who We Really Are", 2017)

"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh, ”Mathematics as an Empirical Phenomenon, Subject to Modeling”, 2017)

"Quantum Machine Learning is defined as the branch of science and technology that is concerned with the application of quantum mechanical phenomena such as superposition, entanglement and tunneling for designing software and hardware to provide machines the ability to learn insights and patterns from data and the environment, and the ability to adapt automatically to changing situations with high precision, accuracy and speed." (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 2018)

"The goal of data science is to improve decision making by basing decisions on insights extracted from large data sets. As a field of activity, data science encompasses a set of principles, problem definitions, algorithms, and processes for extracting nonobvious and useful patterns from large data sets. It is closely related to the fields of data mining and machine learning, but it is broader in scope. (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The patterns that we extract using data science are useful only if they give us insight into the problem that enables us to do something to help solve the problem." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"An insight is when you mix your creative and intellectual labor with a set of data points to create a point of view resulting in a useful assertion. You 'see into' an object of inquiry to reveal important characteristics about its nature." (Eben Hewitt, "Technology Strategy Patterns: Architecture as strategy" 2nd Ed., 2019)

"Some problems are just too complicated for rational logical solutions. They admit of insights, not answers." (Jerome B Wiesner)

Science: On Causality (Quotes)

"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)

"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)

"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)

"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)

"The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road." (Gottfried W Leibniz, "New Essays Concerning Human Understanding", 1704) [published 1765]

"All effects follow not with like certainty from their supposed causes." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"[…] chance, that is, an infinite number of events, with respect to which our ignorance will not permit us to perceive their causes, and the chain that connects them together. Now, this chance has a greater share in our education than is imagined. It is this that places certain objects before us and, in consequence of this, occasions more happy ideas, and sometimes leads us to the greatest discoveries […]" (Claude Adrien Helvetius, "On Mind", 1751)

"One of the most intimate of all associations in the human mind is that of cause and effect. They suggest one another with the utmost readiness upon all occasions; so that it is almost impossible to contemplate the one, without having some idea of, or forming some conjecture about the other." (Joseph Priestley, "The History and Present State of Electricity", 1767)

"But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability." (Pierre-Simon Laplace, "Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards", 1773)

"If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.” (Pierre-Simon Laplace, "Mémoire sur la Probabilité des Causes par les Événements", 1774)

"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge." (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783) 

"We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture." (Charles C Colton, "Lacon", 1820)

"Things of all kinds are subject to a universal law which may be called the law of large numbers. It consists in the fact that, if one observes very considerable numbers of events of the same nature, dependent on constant causes and causes which vary irregularly, sometimes in one direction, sometimes in the other, it is to say without their variation being progressive in any definite direction, one shall find, between these numbers, relations which are almost constant." (Siméon-Denis Poisson, "Poisson’s Law of Large Numbers", 1837)

"Man’s mind cannot grasp the causes of events in their completeness, but the desire to find those causes is implanted in man’s soul. And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: ‘This is the cause!’" (Leo Tolstoy, "War and Peace", 1867)

"It is surprising to learn the number of causes of error which enter into the simplest experiment, when we strive to attain rigid accuracy." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)

"If statistical graphics, although born just yesterday, extends its reach every day, it is because it replaces long tables of numbers and it allows one not only to embrace at glance the series of phenomena, but also to signal the correspondences or anomalies, to find the causes, to identify the laws." (Émile Cheysson, cca. 1877)

"Before we can completely explain a phenomenon we require not only to find its true cause, its chief relations to other causes, and all the conditions which determine how the cause operates, and what its effect and amount of effect are, but also all the coincidences." (George Gore, "The Art of Scientific Discovery", 1878)

"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)

"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)

"'Causation' has been popularly used to express the condition of association, when applied to natural phenomena. There is no philosophical basis for giving it a wider meaning than partial or absolute association. In no case has it been proved that there is an inherent necessity in the laws of nature. Causation is correlation. [...] perfect correlation, when based upon sufficient experience, is causation in the scientific sense." (Henry E. Niles, "Correlation, Causation and Wright's Theory of 'Path Coefficients'", Genetics, 1922)

"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)

"[...] 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)

"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)

"There is no correlation between the cause and the effect. The events reveal only an aleatory determination, connected not so much with the imperfection of our knowledge as with the structure of the human world." (Raymond Aron, "The Opium of the Intellectuals", 1955)

"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 W 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)

"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)

"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)

"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)

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

"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)

"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)

"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)

"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)

"What it means for a mental model to be a structural analog is that it embodies a representation of the spatial and temporal relations among, and the causal structures connecting the events and entities depicted and whatever other information that is relevant to the problem-solving talks. […] The essential points are that a mental model can be nonlinguistic in form and the mental mechanisms are such that they can satisfy the model-building and simulative constraints necessary for the activity of mental modeling." (Nancy J Nersessian, "Model-based reasoning in conceptual change", 1999)

"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)

"Nonetheless, the basic principles regarding correlations between variables are not that diffcult 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)

"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) 

"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)

"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)

"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)

"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)

"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)

"Although to penetrate into the intimate mysteries of nature and hence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena." (Leonhard Euler)

"Nature is pleased with simplicity, and affects not the pomp of superfluous causes." (Sir Issac Newton)