On Mechanisms I: Pendulum

"Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'." (Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de Rotation de la Terre", 1851)

"The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i. e., the inertial and the gravitational mass are the same." (Willem de Sitter, "The Astronomical Aspect of the Theory of Relativity", 1933)

"[…] we must be clear about how a 'system' is to be defined. Our first impulse is to point at the pendulum and to 'the system is that thing there' . This method, however, has a fundamental disadvantage: every material object contains no less than an infinity of variables and therefore of possible systems. The real pendulum, for instance, has not only length and position; it has also mass, temperature, electric conductivity, crystalline structure, chemical impurities, some radio-activity, velocity, reflecting power, tensile strength, a surface film of moisture, bacterial contamination, an optical absorption, elasticity, shape, specific gravity, and so on and on. Any suggestion that we should study 'all' the facts is unrealistic, and actually the attempt is never made. What is try is that we should pick out and study the facts that are relevant to some main interest that is already given." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"[…] the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks." (George Pólya, "Mathematical Methods in Science", 1977)

"Dynamical systems that vary continuously, like the pendulum and the rolling rock, and evidently the pinball machine when a ball’s complete motion is considered, are technically known as flows. The mathematical tool for handling a flow is the differential equation. A system of differential equations amounts to a set of formulas that together express the rates at which all of the variables are currently changing, in terms of the current values of the variables." (Edward N Lorenz, "The Essence of Chaos", 1993)

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

"Financial markets are supposed to swing like a pendulum: They may fluctuate wildly in response to exogenous shocks, but eventually they are supposed to come to rest at an equilibrium point and that point is supposed to be the same irrespective of the interim fluctuations." (George Soros, "The Crisis of Global Capitalism", 1998)

"According to quantum theory, the ground state, or lowest energy state, of a pendulum is not just sitting at the lowest energy point, pointing straight down. That would have both a definite position and a definite velocity, zero. This would be a violation of the uncertainty principle, which forbids the precise measurement of both position and velocity at the same time. The uncertainty in the position multiplied by the uncertainty in the momentum must be greater than a certain quantity, known as Planck's constant - a number that is too long to keep writing down, so we use a symbol for it: ħ." (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"So the ground state, or lowest energy state, of a pendulum does not have zero energy, as one might expect. Instead, even in its ground state a pendulum or any oscillating system must have a certain minimum amount of what are called zero point fluctuations. These mean that the pendulum won't necessarily be pointing straight down but will also have a probability of being found at a small angle to the vertical. Similarly, even in the vacuum or lowest energy state, the waves in the Maxwell field won't be exactly zero but can have small sizes. The higher the frequency (the number of swings per minute) of the pendulum or wave, the higher the energy of the ground state." (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"[…] some systems (system is just a jargon for anything, like the swinging pendulum or the Solar System, or water dripping from a tap)  are very sensitive to their starting conditions, so that a tiny difference in the initial ‘push’ you give them causes a big difference in where they end up, and there is feedback, so that what a system does affects its own behavior."(John Gribbin, "Deep Simplicity", 2004)

"In this world, there are two times. There is mechanical time and there is body time. The first is as rigid and metallic as a massive pendulum of iron that swings back and forth, back and forth, back and forth. The second squirms and wriggles like a bluefish in a bay. The first is unyielding, predetermined. The second makes up its mind as it goes along." (Alan Lightman, "Einstein's Dreams", 2012)

"In mathematics, pendulums stimulated the development of calculus through the riddles they posed. In physics and engineering, pendulums became paradigms of oscillation. […] In some cases, the connections between pendulums and other phenomena are so exact that the same equations can be recycled without change. Only the symbols need to be reinterpreted; the syntax stays the same. It’s as if nature keeps returning to the same motif again and again, a pendular repetition of a pendular theme. For example, the equations for the swinging of a pendulum carry over without change to those for the spinning of generators that produce alternating current and send it to our homes and offices. In honor of that pedigree, electrical engineers refer to their generator equations as swing equations." (Steven H Strogatz, "Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics", 2019)

On Prediction V (Chaos)

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

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

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

"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 subject of probability begins by assuming that some mechanism of uncertainty is at work giving rise to what is called randomness, but it is not necessary to distinguish between chance that occurs because of some hidden order that may exist and chance that is the result of blind lawlessness. This mechanism, figuratively speaking, churns out a succession of events, each individually unpredictable, or it conspires to produce an unforeseeable outcome each time a large ensemble of possibilities is sampled."  (Edward Beltrami, "Chaos and Order in Mathematics and Life", 1999)

"A Black Swan is a highly improbable event with three principal characteristics: It is unpredictable; it carries a massive impact; and, after the fact, we concoct an explanation that makes it appear less random, and more predictable, than it was. […] The Black Swan idea is based on the structure of randomness in empirical reality. [...] the Black Swan is what we leave out of simplification." (Nassim N Taleb, "The Black Swan", 2007)

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

"In chaotic deterministic systems, the probabilistic description is not linked to the number of degrees of freedom (which can be just one as for the logistic map) but stems from the intrinsic erraticism of chaotic trajectories and the exponential amplification of small uncertainties, reducing the control on the system behavior." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"Strange attractors, unlike regular ones, are geometrically very complicated, as revealed by the evolution of a small phase-space volume. For instance, if the attractor is a limit cycle, a small two-dimensional volume does not change too much its shape: in a direction it maintains its size, while in the other it shrinks till becoming a 'very thin strand' with an almost constant length. In chaotic systems, instead, the dynamics continuously stretches and folds an initial small volume transforming it into a thinner and thinner 'ribbon' with an exponentially increasing length." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

On Prediction IV (Theories)

"In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict facts of the same kind. The  catch in this criterion lies in the world 'simplest'." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

"It is characteristic of a good scientific theory that it makes no more assumptions than are needed to explain the facts under consideration and predict a few more." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"A theory in its scientific context is not a static museum piece, but is always being extended and modified to account for new phenomena. […] Moreover, without a model, it will be impossible to use a theory for one of the essential purposes we demand of it, namely to make predictions in new domains of phenomena." (Mary B Hesse," Models and Analogies in Science", 1963)

"It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations. Confirmations should count only if they are the result of risky predictions. […] A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1970)

"But a theory is not like an airline or bus timetable. We are not interested simply in the accuracy of its predictions. A theory also serves as a base for thinking. It helps us to understand what is going on by enabling us to organize our thoughts. Faced with a choice between a theory which predicts well but gives us little insight into how the system works and one which gives us this insight but predicts badly, I would choose the latter, and I am inclined to think that most economists would do the same." (Ronald Coase, "How should economists choose?", 1981)

"The ability of a scientific theory to be refuted is the key criterion that distinguishes science from metaphysics. If a theory cannot be refuted, if there is no observation that will disprove it, then nothing can prove it - it cannot predict anything, it is a worthless myth." (Eric Lerner, "The Big Bang Never Happened", 1991)

"Good theories are the ones that get those predictions right; the best theories enable us to 'get right' the calculation of how the Universe came into being and then exploded into its present form. But that doesn’t mean that they convey ultimate truth, or that there ‘really are’ little hard particles rattling around against each other inside the atom. Such truth as there is in any of this work lies in the mathematics; the particle concept is simply a crutch ordinary mortals can use to help them towards an understanding of the mathematical laws." (John R Gribbin, "The Search of Superstrings, Symmetry, and the Theory of Everything", 1998)

"[...] the definitive property of good theory is predictiveness. Those theories endure that are precise in the predictions they make across many phenomena and whose predictions are easiest to test by observation and experiment." (Edward O Wilson, "Consilience: The Unity of Knowledge", 1998)

"A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized." (Jay Odenbaugh, "True Lies: Realism, Robustness, and Models", Philosophy of Science, Vol. 78, No. 5, 2011 

On Prediction VIII (Systems II)

"Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"When a system is predictable, it is already performing as consistently as possible. Looking for assignable causes is a waste of time and effort. Instead, you can meaningfully work on making improvements and modifications to the process. When a system is unpredictable, it will be futile to try and improve or modify the process. Instead you must seek to identify the assignable causes which affect the system. The failure to distinguish between these two different courses of action is a major source of confusion and wasted effort in business today." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

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

"The only way to look into the future is use theories since conclusive data is only available about the past." (Clayton Christensen et al, "Seeing What’s Next: Using the Theories of Innovation to Predict Industry Change", 2004)

"A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"Complexity carries with it a lack of predictability different to that of chaotic systems, i.e. sensitivity to initial conditions. In the case of complexity, the lack of predictability is due to relevant interactions and novel information created by them." (Carlos Gershenson, "Understanding Complex Systems", 2011)

"Complexity scientists concluded that there are just too many factors - both concordant and contrarian - to understand. And with so many potential gaps in information, almost nobody can see the whole picture. Complex systems have severe limits, not only to predictability but also to measurability. Some complexity theorists argue that modelling, while useful for thinking and for studying the complexities of the world, is a particularly poor tool for predicting what will happen." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

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

"The problem of complexity is at the heart of mankind’s inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", 2014)

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

Walter A Shewhart - Collected Quotes

"Every sentence in order to have definite scientific meaning must be practically or at least theoretically verifiable as either true or false upon the basis of experimental measurements either practically or theoretically obtainable by carrying out a definite and previously specified operation in the future. The meaning of such a sentence is the method of its verification." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"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)

"Progress in modifying our concept of control has been and will be comparatively slow. In the first place, it requires the application of certain modern physical concepts; and in the second place it requires the application of statistical methods which up to the present time have been for the most part left undisturbed in the journal in which they appeared." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Rule 1. Original data should be presented in a way that will preserve the evidence in the original data for all the predictions assumed to be useful." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Rule 2. Any summary of a distribution of numbers in terms of symmetric functions should not give an objective degree of belief in any one of the inferences or predictions to be made therefrom that would cause human action significantly different from what this action would be if the original distributions had been taken as evidence."  (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen."(Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

On Prediction XII (Behavior)

"Engage people with what they expect; it is what they are able to discern and confirms their projections. It settles them into predictable patterns of response, occupying their minds while you wait for the extraordinary moment - that which they cannot anticipate." (Sun Tzu, "The Art of War")

"What is big is easy to perceive: what is small is difficult to perceive. In short, it is difficult for large numbers of men to change position, so their movements can be easily predicted. An individual can easily change his mind, so his movements are difficult to predict."(Miyamoto Musashi, "The Book of Five Rings" , 1645)

"The doctrine called Philosophical Necessity is simply this: that, given the motives which are present to an individual's mind, and given likewise the character and disposition of the individual, the manner in which he will act might be unerringly inferred: that if we knew the person thoroughly, and knew all the inducements which are acting upon him, we could foretell his conduct with as much certainty as we can predict any physical event." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"How can we dare to predict the behavior of man? We may predict the movements of a machine, of an automaton; more than this, we many even try to predict the mechanisms or 'dynamisms' of the human psyche as well. But man is more than psyche." (Viktor E Frankl, "Man's Search for Meaning", 1984) 

"To assume you know someone well enough that you can and do predict their behavior and mental perspective is a gross and often tragic mistake, for it eliminates that person's freedom to create his or her own opinion and drastically affects the emerging picture of the relationship." (Meredith L Young-Sowers, "Agartha: a journey to the stars", 1984) 

"The challenge for individuals in primate societies is to be able to predict the behavior of others. One way would be for individuals to have a huge mental bank in their brains, which stored every possible action of their fellow troop members and their own appropriate actions." (Richard Leakey, "The Origin of Humankind", 1994)

"Even if someone knew the entire physical history of the world, and every mental event were identical with a physical, it would notfollow that he could predict or explain a single mental event (so described, of course)."(Donald Davidson, "Essays on Actions and Events", 2001)

"We need to stop, and admit it: we have a prediction problem. We love to predict things—and we aren't very good at it." (Nate Silver, "The Signal and the Noise", 2012)

On Prediction II

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "A Scientific Autobiography", 1949)

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"In the long run, qualitative changes always outweigh quantitative ones. Quantitative predictions of economic and social trends are made obsolete by qualitative changes in the rules of the game. Quantitative predictions of technological progress are made obsolete by unpredictable new inventions. I am interested in the long run, the remote future, where quantitative predictions are meaningless. The only certainty in that remote future is that radically new things will be happening." (Freeman J Dyson, "Disturbing the Universe", 1979)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985) 

"We can predict only those things we set up to be predictable, not what we encounter in the real world of living and reactive processes." (Bill Mollison, "Permaculture: A Designers' Manual", 1988)

"Prediction, not narration, is the real test of our understanding of the world." (Nassim N Taleb, "The Black Swan", 2007)

"The inability to predict outliers implies the inability to predict the course of history." (Nassim N Taleb, "The Black Swan", 2007)

"Relevance is not something you can predict. It is something you discover after the fact." (Thomas Sowell, "The Thomas Sowell Reader", 2011)

"The illusion that we understand the past fosters overconfidence in our ability to predict the future." (Daniel Kahneman, "Thinking, Fast and Slow", 2011) 

"Under complexity science, the more interacting factors, the more unpredictable and irregular the outcome. To be succinct, the greater the complexity, the greater the unpredictability." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

On Prediction X (Mathematics)

 "The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines but of its methods. Mathematics will ever remain the past perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"As a science progresses, its power of foresight rapidly increases, until the mathematician in his library acquires the power of anticipating nature, and predicting what will happen in circumstances which the eye of man has never examined." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success." (Max Born, "Einstein's Statistical Theories", 1951)

"What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations." (Celia Green, "The Lost Cause", 2003) 

"[…] because observations are all we have, we take them seriously. We choose hard data and the framework of mathematics as our guides, not unrestrained imagination or unrelenting skepticism, and seek the simplest yet most wide-reaching theories capable of explaining and predicting the outcome of today’s and future experiments." (Brian Greene, "The Fabric of the Cosmos", 2004)

"In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality - a point well made by George Box in his oft-cited remark that "all models are wrong, but some are useful". (David Hand, "Wonderful examples, but let's not close our eyes", Statistical Science 29, 2014)

"A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)

On Prediction XI (Mental Models)

"Some may object that this reduces thought to a mere ‘copy’ of reality and that we ought not to want such an internal ‘copy’; are not electrons, causally interacting, good enough? […] only this internal model of reality - this working model - enables us to predict events which have not yet occurred in the physical world, a process which saves time, expense, and even life." (Kenneth Craik, "The Nature of Explanation", 1943)

"Out of our image we predict the messages which will return to us as a result of our acts.  If this prediction is fulfilled the image is confirmed, if it is not fulfilled the image must be changed.  This is the essence of the logical-positivist view that definitions must be operational and hypotheses must be testable as an open system of a very different and much more complex character than that of the biological organism." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)

“People’s views of the world, of themselves, of their own capabilities, and of the tasks that they are asked to perform, or topics they are asked to learn, depend heavily on the conceptualizations that they bring to the task. In interacting with the environment, with others, and with the artifacts of technology, people form internal, mental models of themselves and of the things with which they are interacting. These models provide predictive and explanatory power for understanding the interaction.” (Donald A Norman, “Some observations on Mental Models”, 1983)

"Since mental models can take many forms and serve many purposes, their contents are very varied. They can contain nothing but tokens that represent individuals and identities between them, as in the sorts of models that are required for syllogistic reasoning. They can represent spatial relations between entities, and the temporal or causal relations between events. A rich imaginary model of the world can be used to compute the projective relations required for an image. Models have a content and form that fits them to their purpose, whether it be to explain, to predict, or to control." (Philip Johnson-Laird, "Mental models: Toward a cognitive science of language, inference, and consciousness", 1983)

"The purpose of a mental model is to allow the person to understand and to anticipate the behavior of a physical system. This means that the model must have predictive power, either by applying rules of inference or by procedural derivation (in whatever manner these properties may be realized in a person); in other words, it should be possible for people to ' run' their models mentally. This means that the conceptual mental model must also include a model of the relevant human information processing and knowledge structures that make it possible for the person to use a mental model to predict and understand the physical system." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models"], 1983)

"Mental models are the mechanisms whereby humans are able to generate descriptions of system purpose and form, explanations of system functioning and observed system states, and predictions of future system states." (William B Rouse & Nancy M Morris, "On looking into the black box: Prospects and limits in the search for mental models", Psychological Bulletin (3), 1986)

"Modeling underlies our ability to think and imagine, to use signs and language, to communicate, to generalize from experience, to deal with the unexpected, and to make sense out of the raw bombardment of our sensations. It allows us to see patterns, to appreciate, predict, and manipulate processes and things, and to express meaning and purpose. In short, it is one of the most essential activities of the human mind. It is the foundation of what we call intelligent behavior and is a large part of what makes us human. We are, in a word, modelers: creatures that build and use models routinely, habitually – sometimes even compulsively – to face, understand, and interact with reality."  (Jeff Rothenberg, "The Nature of Modeling. In: Artificial Intelligence, Simulation, and Modeling", 1989)

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

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

"People build practical, useful mental models all of the time. Seldom do they resort to writing a complex set of mathematical equations or use other formal methods. Rather, most people build models relating inputs and outputs based on the examples they have seen in their everyday life. These models can be rather trivial, such as knowing that when there are dark clouds in the sky and the wind starts picking up that a storm is probably on the way. Or they can be more complex, like a stock trader who watches plots of leading economic indicators to know when to buy or sell. The ability to make accurate predictions from complex examples involving many variables is a great asset." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

On Prediction VII (Nature)

"But the most powerful proof of the reality of phenomena (a proof which is, indeed, sufficient by itself) is success in predicting future phenomena from those which are past and present, whether the prediction be founded upon the success, so far, of a reason or hypothesis, or upon custom so far observed." (Gottfried W Leibniz, "De Modo Distinguendi phenomena realia ab imaginariis" ["On the Method of Distinguishing Real from Imaginary Phenomena"], cca. 1684)

"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)

"The world is not made up of empirical facts with the addition of the laws of nature: what we call the laws of nature are conceptual devices by which we organize our empirical knowledge and predict the future." (Richard B Braithwaite, "Scientific Explanation", 1953)

"The predictions of physical theories for the most part concern situations where initial conditions can be precisely specified. If such initial conditions are not found in nature, they can be arranged. Such arrangements are considerably easier to realize with inanimate than with animate matter, because the properties of animate matter are much more sensitive to being tampered with than inanimate matter. In particular, living tissue in vitro may behave quite differently than in situ. Controlled biological experiments are, of course, possible, but they are more difficult and their scope is more limited than that of physical experiments. For this reason, biology has had to depend to a greater extent than physics on theories of larger speculative scope, in which reasoning by imaginative analogy plays a more important role." (Anatol Rapoport, "The Search for Simplicity", 1956)

"How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature? Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as elegance of description really reflects the interconnectedness of Nature’s laws at different levels." (Murray Gell-Mann, 1969)

"The basis of this theory is that in nature there is an inherent uncertainty or unpredictability that manifests itself only on an atomic scale. For example, the position of a subatomic particle such as an electron may not be a well-defined concept at all; it should be envisaged as jiggling around in a random sort of a way. Energy, too, becomes a slightly nebulous concept, subject to capricious and unpredictable changes." (Paul C W Davies, "The Edge of Infinity: Where the Universe Came from and How It Will End", 1981)

"Today’s quarks and leptons can be viewed as metaphors of the underlying reality of nature, though metaphors that are objectively and rationally defied and are components of theories that have great predictive power. And that’s the difference between the metaphors of science and those of myth: scientific metaphors work." (Victor J Stenger, "Physics and Psychics: The Search for a World Beyond the Senses", 1990)

"Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use of knowledge gathered in a few observations, to predict by logical processes the outcomes in many other circumstances. Any logically sound theory satisfying this condition is a good theory, whether or not it be derived from ‘ultimate’ or ‘fundamental’ truth." (Clifford Truesdell and Walter Noll, "The Non-Linear Field Theories of Mechanics" 2nd Ed., 1992)

"I seek […] to show that - other things being equal - the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"[…] the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"Historically, science has pursued a premise that Nature can be understood fully, its future predicted precisely, and its behavior controlled at will. However, emerging knowledge indicates that the nature of Earth and biological systems transcends the limits of science, questioning the premise of knowing, prediction, and control. This knowledge has led to the recognition that, for civilized human survival, technological society has to adapt to the constraints of these systems." (Nari Narasimhan, "Limitations of Science and Adapting to Nature", Environmental Research Letters, 2007)

On Prediction IX (Science)

 "The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

"Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'." (Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de Rotation de la Terre", 1851)

"Science is the attempt to discover, by means of observation, and reasoning based upon it, first, particular facts about the world, and then laws connecting facts with one another and (in fortunate cases) making it possible to predict future occurrences." (Bertrand Russell, "Religion and Science, Grounds of Conflict", 1935)

"Those who are content with a positivist conception of the aims of science will feel that he is in an entirely satisfactory position; he has discovered the pattern of events, and so can predict accurately; what more can he want? A mental picture would be an added luxury, but also a useless luxury. For if the picture did not bear any resemblance at all to the reality it would be valueless, and if it did it would be unintelligible […]" (James H Jeans," Physics and Philosophy" 3rd Ed., 1943)

"A fundamental value in the scientific outlook is concern with the best available map of reality. The scientist will always seek a description of events which enables him to predict most by assuming least. He thus already prefers a particular form of behavior. If moralities are systems of preferences, here is at least one point at which science cannot be said to be completely without preferences. Science prefers good maps." (Anatol Rapoport, "Science and the goals of man: a study in semantic orientation", 1950)

"Prediction is all very well; but we must make sense of what we predict. The mainspring of science is the conviction that by honest, imaginative enquiry we can build up a system of ideas about Nature which has some legitimate claim to ‘reality’." (Stephen Toulmin, "The Philosophy of Science: An Introduction", 1953)

"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)

"Science has become a social method of inquiring into natural phenomena, making intuitive and systematic explorations of laws which are formulated by observing nature, and then rigorously testing their accuracy in the form of predictions. The results are then stored as written or mathematical records which are copied and disseminated to others, both within and beyond any given generation. As a sort of synergetic, rigorously regulated group perception, the collective enterprise of science far transcends the activity within an individual brain." (Lynn Margulis & Dorion Sagan, "Microcosmos", 1986)

"Prediction can never be absolutely valid and therefore science can never prove some generalization or even test a single descriptive statement and in that way arrive at final truth." (Gregory Bateson, Mind and Nature: A necessary unity", 1988)

"The point is that scientific descriptions of phenomena in all of these cases do not fully capture reality they are models. This is not a shortcoming but a strength of science much of the scientist's art lies in figuring out what to include and what to exclude in a model, and this ability allows science to make useful predictions without getting bogged down by intractable details." (Philip Ball," The Self-Made Tapestry: Pattern Formation in Nature", 1998)

"The progress of science requires more than new data; it needs novel frameworks and contexts. And where do these fundamentally new views of the world arise? They are not simply discovered by pure observation; they require new modes of thought. And where can we find them, if old modes do not even include the right metaphors? The nature of true genius must lie in the elusive capacity to construct these new modes from apparent darkness. The basic chanciness and unpredictability of science must also reside in the inherent difficulty of such a task." (Stephen J Gould)

On Prediction III (Systems I)

"The principle of complementarity states that no single model is possible which could provide a precise and rational analysis of the connections between these phenomena [before and after measurement]. In such a case, we are not supposed, for example, to attempt to describe in detail how future phenomena arise out of past phenomena. Instead, we should simply accept without further analysis the fact that future phenomena do in fact somehow manage to be produced, in a way that is, however, necessarily beyond the possibility of a detailed description. The only aim of a mathematical theory is then to predict the statistical relations, if any, connecting the phenomena." (David Bohm, "A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables", 1952)

"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)

"Synergy is the only word in our language that means behavior of whole systems unpredicted by the separately observed behaviors of any of the system's separate parts or any subassembly of the system's parts." (Buckminster Fuller, "Operating Manual for Spaceship Earth", 1969)

"A living system, due to its circular organization, is an inductive system and functions always in a predictive manner: what happened once will occur again. Its organization, (genetic and otherwise) is conservative and repeats only that which works. For this same reason living systems are historical systems; the relevance of a given conduct or mode of behavior is always determined in the past." (Humberto Maturana, "Biology of Cognition", 1970)

"Synergy means behavior of whole systems unpredicted by the behavior of their parts taken separately." (R Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"Because of mathematical indeterminancy and the uncertainty principle, it may be a law of nature that no nervous system is capable of acquiring enough knowledge to significantly predict the future of any other intelligent system in detail. Nor can intelligent minds gain enough self-knowledge to know their own future, capture fate, and in this sense eliminate free will." (Edward O Wilson, "On Human Nature", 1978) 

"A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations." (Stephen Hawking, "A Brief History of Time: From Big Bang To Black Holes", 1988)

"Unfortunately, recognizing a system as chaotic will not tell us all that we might like to know. It will not provide us with a means of predicting the future course of the system. It will tell us that there is a limit to how far ahead we can predict, but it may not tell us what this limit is. Perhaps the best advice that chaos 'theory' can give us is not to jump at conclusions; unexpected occurrences may constitute perfectly normal behavior." (Edward N Lorenz, "Chaos, spontaneous climatic variations and detection of the greenhouse effect", 1991)

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

"The model [of reality] takes on a life of its own, in which its future is under perpetual construction through the micro interactions of the diverse entities comprising it. The "final" form toward which it moves is not given in the model itself, nor is it being chosen from outside the model. The forms continually emerge in an unpredictable way as the system moves into the unknown. However, there is nothing mysterious or esoteric about this. What emerges does so because of the transformative cause of the process of the micro interactions, the fluctuations themselves." (Ralph D Stacey et al, "Complexity and Management: Fad or Radical Challenge to Systems Thinking?", 2000)

On Prediction VI (Models I)

"A model is a good model if it:1. Is elegant 2. Contains few arbitrary or adjustable elements 3. Agrees with and explains all existing observations 4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results" (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)

"A model is a useful (and often indispensable) framework on which to organize our knowledge about a phenomenon. […] It must not be overlooked that the quantitative consequences of any model can be no more reliable than the a priori agreement between the assumptions of the model and the known facts about the real phenomenon. When the model is known to diverge significantly from the facts, it is self-deceiving to claim quantitative usefulness for it by appeal to agreement between a prediction of the model and observation." (John R Philip, 1966)

"It is of course desirable to work with manageable models which maximize generality, realism, and precision toward the overlapping but not identical goals of understanding, predicting, and modifying nature. But this cannot be done."(Richard Levins, "The strategy of model building in population biology", American Scientist Vol. 54 (4), 1966) 

"Any theory starts off with an observer or experimenter. He has in mind a collection of abstract models with predictive capabilities. Using various criteria of relevance, he selects one of them. In order to actually make predictions, this model must be interpreted and identified with a real assembly to form a theory. The interpretation may be prescriptive or predictive, as when the model is used like a blueprint for designing a machine and predicting its states. On the other hand, it may be descriptive and predictive as it is when the model is used to explain and predict the behaviour of a given organism." (Gordon Pask, "The meaning of cybernetics in the behavioural sciences", 1969)

"After all of this it is a miracle that our models describe anything at all successfully. In fact, they describe many things well: we observe what they have predicted, and we understand what we observe. However, this last act of observation and understanding always eludes physical description." (Yuri I Manin, "Mathematics and Physics", 1981)

"A model is generally more believable if it can predict what will happen, rather than 'explain' something that has already occurred." (James R Thompson, "Empirical Model Building", 1989)

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

"In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality - a point well made by George Box in his oft-cited remark that "all models are wrong, but some are useful". (David Hand, "Wonderful examples, but let's not close our eyes", Statistical Science 29, 2014) 

"Models are formal structures represented in mathematics and diagrams that help us to understand the world. Mastery of models improves your ability to reason, explain, design, communicate, act, predict, and explore." (Scott E Page, "The Model Thinker", 2018)

Mental Models LIII (Conceptual Models II)

"But metaphor is an indispensable tool of thought and expression - a characteristic of all human communication, even of that of the scientist. The conceptual models of cybernetics and the energy theories of psycho-analysis are, after all, only labeled metaphors." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"[…] conceptual models, even when incorrect, are useful to the extent that criticism of the model may point to new theoretical developments."  (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"As the least conscious layer of the user experience, the conceptual model has the paradoxical quality of also having the most impact on usability. If an appropriate conceptual model is faithfully represented throughout the interface, after users recognize and internalize the model, they will have a fundamental understanding of what the application does and how to operate it." (Bob Baxley, "Making the Web Work: Designing Effective Web Applications", 2002) 

"A conceptual model of an interactive application is, in summary: the structure of the application - the objects and their operations, attributes, and relation-ships; an idealized view of the how the application works – the model designers hope users will internalize; the mechanism by which users accomplish the tasks the application is intended to support." (Jeff Johnson & Austin Henderson, "Conceptual Models", 2011)

"Conceptual models are best thought of as design-tools - a way for designers to straighten out and simplify the design and match it to the users’ task-domain, thereby making it clearer to users how they should think about the application. The designers’ responsibility is to devise a conceptual model that seems natural to users based on the users’ familiarity with the task domain. If designers do their job well, the conceptual model will be the basis for users’ mental models of the application." (Jeff Johnson & Austin Henderson, "Conceptual Models", 2011)

"The conceptual model is not the users’ mental model of the application. […] users of an application form mental models of it to allow them to predict its behavior. A mental model is the user’s high-level understanding of how the application works; it allows the user to predict what the application will do in response to various user-actions. Ideally, a user’s mental model of an application should be similar to the designers’ conceptual model, but in practice the two models may differ significantly. Even if a user’s mental model is the same as the designer’s conceptual model, they are distinct models." (Jeff Johnson & Austin Henderson, "Conceptual Models", 2011)

"Briefly, a conceptual model is the configuration of conceptual elements and the navigation between them. As such, a conceptual model is the foundation of the user interface of any interactive system." (Avi Parush, "Conceptual Design for Interactive Systems", 2015)

"A conceptual model is a framework that is initially used in research to outline the possible courses of action or to present an idea or thought. When a conceptual model is developed in a logical manner, it will provide a rigor to the research process." (N Elangovan & R Rajendran, "Conceptual Model: A Framework for Institutionalizing the Vigor in Business Research", 2015) 

"Once we understand our user's mental model, we can capture it in a conceptual model. The conceptual model is a representation of the mental model using elements, relationships, and conditions. Our design and final system will be the tangible result of this conceptual model." (Pau Giner & Pablo Perea, "UX Design for Mobile, 2017) 

"A model or conceptual model is a schematic or representation that describes how something works. We create and adapt models all the time without realizing it. Over time, as you gain more information about a problem domain, your model will improve to better match reality." (James Padolsey, "Clean Code in JavaScript", 2020)

Mental Models LII (Conceptual Models I)

"Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment." (C West Churchman, "Costs, Utilities, and Values", 1956)

"Sometimes, however, a conceptual model is only a first step, and the second step is a mathematical representation of the conceptual model." (Gregory N Derry, "What Science Is and How It Works", 2002) 

"A conceptual model is one which reflects reality by placing words which are concepts into the model in the same way that the model aeroplane builder puts wings, a fuselage, and a cockpit together." (Lynn Basford & ‎Oliver Slevin, "Theory and Practice of Nursing: An Integrated Approach to Caring Practice", 2003) 

"A conceptual model is simply a framework or schematic to understand the interaction of workforce education and development systems with other variables in a society." (Jay W Rojewski, "International Perspectives on Workforce Education and Development", 2004) 

"The role of conceptual modelling in information systems development during all these decades is seen as an approach for capturing fuzzy, ill-defined, informal 'real-world' descriptions and user requirements, and then transforming them to formal, in some sense complete, and consistent conceptual specifications." (Janis A Burbenko jr., "From Information Algebra to Enterprise Modelling and Ontologies", Conceptual Modelling in Information Systems Engineering, 2007) 

"Like a physical model, a conceptual model is an artificial system. It is however, made up of conceptual, and not physical components." (Ibrahim A Halloun, "Modeling Theory in Science Education", 2007) 

"The first function of a conceptual model is relating the research to the existing body of literature. With the help of a conceptual model a researcher can indicate in what way he is looking at the phenomenon of his research."(Jan Jonker & Bartjan Pennink, "The Essence of Research Methodology" , 2010) 

"A conceptual model is a qualitative description of 'some aspect of the behaviour of a natural system'. This description is usually verbal, but may also be accompanied by figures and graphs." (Howard S. Wheater et al., "Groundwater Modelling in Arid and Semi-Arid Areas, 2010) 

"[…] a conceptual model is a diagram connecting variables and constructs based on theory and logic that displays the hypotheses to be tested." (Mary Wolfinbarger Celsi et al, "Essentials of Business Research Methods", 2011) 

"Simply put, a conceptual model is a simplified representation of reality, devised for a certain purpose and seen from a certain point of view."(David W Emble & Bernhard Thalheim, "Handbook of Conceptual Modeling", 2012) 

Mental Models LI

"[…] reason is the thing without which our state would be the state of wild beasts, of children and lunatics; it is the thing whereby we picture our intellectual acts before they become manifest to the senses, so that we see them exactly as though we had sensed them; then we represent these pictures in our sensual acts so that they correspond exactly with what we have represented and imagined." (Rhazes [Abu Bakr Muhammad Ibn Zakariyya Al-Razi], "Spiritual Physick", cca 10th century) 

"This making or imagining of models (not necessarily or usually a material model, but a conceptual model) is a recognised way of arriving at an understanding of recondite and ultra-sensual occurring say in the ether or elsewhere." (Hugh MacColl, Mind: a quarterly review of psychology and philosophy Vol. 14, 1905)

"Mere deductive logic, whether you clothe it in mathematical symbols and phraseology or whether you enlarge its scope into a more general symbolic technique, can never take the place of clear relevant initial concepts of the meaning of your symbols, and among symbols I include words. If you are dealing with nature, your meanings must directly relate to the immediate facts of observation. We have to analyse first the most general characteristics of things observed, and then the more casual contingent occurrences. There can be no true physical science which looks first to mathematics for the provision of a conceptual model. Such a procedure is to repeat the errors of the logicians of the middle-ages." (Alfred N Whitehead, "Principle of Relativity", 1922)

"The 'physical' does not mean any particular kind of reality, but a particular kind of denoting reality, namely a system of concepts in the natural sciences which is necessary for the cognition of reality. 'The physical' should not be interpreted wrongly as an attribute of one part of reality, but not of the other ; it is rather a word denoting a kind of conceptual construction, as, e.g., the markers 'geographical' or 'mathematical', which denote not any distinct properties of real things, but always merely a manner of presenting them by means of ideas." (Moritz Schlick,"Allgemeine Erkenntnislehre", 1925)

"We never have any understanding of any subject matter except in terms of our own mental constructs of 'things' and 'happenings' of that subject matter." (Douglas T Ross, "Structured analysis (SA): A language for communicating ideas", IEEE Transactions on Software Engineering Vol. 3 (1), 1977) 

"In medical science arguments are going on between behaviorists who perceive the function of brain as a multitude of simple and unconscious conditioned reflexes, and cognitivists who insist that humans sensing the surrounding world create its mental image which can be considered as memory of facts." (Yevgeniy Chazov, "Tragedy and Triumph of Reason", 1985)

"When we focus consciously on an object - and create a mental image for eexample- it's not because the brain pattern is a copy or neural representation of the perceived object, but because the brain experiences a special kind of interaction with that object, preparing the brain to deal with it." (Roger W Sperry, "New Mindset on Consciousness", Sunrise magazine, 1987/1988)

"For a musician, visualization is the process of picturing in our minds eye what we hear in our mind's ear. Visualization is something we all do. In fact, putting a visual form before the mind's eye or forming a mental image is something that precedes most things that we do." (Jerry Bergonzi, "Melodic Structures", 1992)

"Suppose the reasoning centers of the brain can get their hands on the mechanisms that plop shapes into the array and that read their locations out of it. Those reasoning demons can exploit the geometry of the array as a surrogate for keeping certain logical constraints in mind. Wealth, like location on a line, is transitive: if A is richer than B, and B is richer than C, then A is richer than C. By using location in an image to symbolize wealth, the thinker takes advantage of the transitivity of location built into the array, and does not have to enter it into a chain of deductive steps. The problem becomes a matter of plop down and look up. It is a fine example of how the form of a mental representation determines what is easy or hard to think." (Steven Pinker, "How the Mind Works", 1997)

"Image theory is an attempt to describe decision making as it actually occurs. […] The concept of images is central to the theory. They represent visions held by individuals and organisations that constitute how they believe the world should exist. When considering individuals, the theory refers to these images as the value image, trajectory image and strategic image. The value image is based on an individual’s ethics, morals and beliefs. The trajectory images encompass the decision maker’s goals and aspirations. Finally, for each trajectory image, a decision maker may have one or more strategic images that contain their plans, tactics and forecasts for their goal. […] In an organisational decision-making setting, these images are referred to as culture, vision and strategy." (Christopher B Stephenson, "What causes top management teams to make poor strategic decisions?", 2012)