🏷️Knowledge Representation: On Venn Diagrams (Quotes)

"[...] for merely theoretical purposes the rule of formation would be very simple. It would merely be to begin by drawing any closed figure, and then proceed [sic] to draw others, subject to the one condition that each is to intersect once and once only all the existing subdivisions produced by those which had gone before." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"[…] it must be noticed that these diagrams do not naturally harmonize with the propositions of ordinary life or ordinary logic. […] The great bulk of the propositions which we commonly meet with are founded, and rightly founded, on an imperfect knowledge of the actual mutual relations of the implied classes to one another. […] one very marked characteristic about these circular diagrams is that they forbid the natural expression of such uncertainty, and are therefore only directly applicable to a very small number of such propositions as we commonly meet with." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"[...] we can not readily break up a complicated problem into successive steps which can be taken independently. We have, in fact, to solve the problem first, by determining what are the actual mutual relations of the classes involved, and then to draw the circles to represent this final result; we cannot work step-by-step towards the conclusion by aid of our figures." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"Whereas the Eulerian plan endeavoured at once and directly to represent propositions, or relations of class terms to one another, we shall find it best to begin by representing only classes, and then proceed to modify these in some way so as to make them indicate what our propositions have to say. How, then, shall we represent all the subclasses which two or more class terms can produce? Bear in mind that what we have to indicate is the successive duplication of the number of subdivisions produced by the introduction of each successive term. and we shall see our way to a very important departure from the Eulerian conception. All that we have to do is to draw our figures, say circles, so that each successive one which we introduce shall intersect once, and once only, all the subdivisions already existing, and we then have what may be called a general framework indicating every possible combination producible by the given class terms." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"It will be found that there is a tendency for the resultant outlines thus successively drawn to assume a comb-like shape after the first four or five [...]The fifth-term figure will have two teeth, the sixth four, and so on. [...] There is no trouble in drawing such a diagram for any number of terms which our paper will find room for. But, as has already been repeatedly remarked, the visual aid for which mainly such diagrams exist is soon lost on such a path."  (John Venn, "Symbolic Logic", [footnote], 1881)

"There is no need here to exhibit such figures, as they would probably be distasteful to any but the mathematician, and he would see his way to drawing them readily enough for himself [...]" (John Venn, "Symbolic Logic", 1881)

"We endeavour to employ only symmetrical figures, such as should not only be an aid to reasoning, through the sense of sight, but should also be to some extent elegant in themselves." (John Venn, "Symbolic Logic", 1881)

"At the basis of our Symbolic Logic, however represented, whether by words by letters or by diagrams, we shall always find the same state of things. What we ultimately have to do is to break up the entire field before us into a definite number of classes or compartments which are mutually exclusive and collectively exhaustive." (John Venn, "Symbolic Logic" 2nd Ed., 1894)

"The best way of introducing this question will be to enquire a little more strictly whether it is really classes that we thus represent, or merely compartments into which classes may be put? […] The most accurate answer is that our diagrammatic subdivisions, or for that matter our symbols generally, stand for compartments and not for classes. We may doubtless regard them as representing the latter, but if we do so we should never fail to keep in mind the proviso, 'if there be such things in existence'. And when this condition is insisted upon, it seems as if we expressed our meaning best by saying that what our symbols stand for are compartments which may or may not happen to be occupied." (John Venn, "Symbolic Logic" 2nd Ed., 1894)

 "My Method of Diagrams resembles Mr. Venn's, in having separate Compartments assigned to the various Classes, and in marking these Compartments as occupied or as empty; but it differs from his Method, in assigning a closed area to the Universe of Discourse, so that the Class which, under Mr. Venn's liberal sway, has been ranging at will through Infinite Space, is suddenly dismayed to find itself "cabin'd, cribb'd, confined" in a limited Cell like any other Class! Also I use rectilinear, instead of curvilinear Figures" (Charles Dogson [Lews Carroll], 1896)

"This is why a 'web' of notes with links (like references) between them is far more useful than a fixed hierarchical system. When describing a complex system, many people resort to diagrams with circles and arrows. Circles and arrows leave one free to describe the interrelationships between things in a way that tables, for example, do not. The system we need is like a diagram of circles and arrows, where circles and arrows can stand for anything." (Tim Berners-Lee, "Information Management: A Proposal", 1989)

"Venn diagrams are widely used to solve problems in set theory and to test the validity of syllogisms in logic. […] However, it is a fact that Venn diagrams are not considered valid proofs, but heuristic tools for finding valid formal proofs." (Sun-Joo Shin, "Situation-Theoretic Account of Valid Reasoning with Venn Diagrams", [in "Logical Reasoning with Diagrams"], 1996)

"Venn diagrams provide us with a formalism that consists of a standardized system of representations, together with rules for manipulating them. In this regard, they could be considered a primitive visual analog of the formal systems of deduction developed in logic." (Jon Barwise & John Etchemendy, "Visual Information and Valid Reasoning", [in "Logical Reasoning with Diagrams"], 1996)

"A Venn diagram is a simple representation of the sample space, that is often helpful in seeing 'what is going on'. Usually the sample space is represented by a rectangle, with individual regions within the rectangle representing events. It is Often helpful to imagine that the actual areas Of the various regions in a Venn diagram are in proportion to the corresponding probabilities. However, there is no need to spend a long time drawing these diagrams - their use is simply as a reminder of what is happening." (Graham Upton & Ian Cook, "Introducing Statistics", 2001)

"Two types of graphic organizers are commonly used for comparison: the Venn diagram and the comparison matrix [...] the Venn diagram provides students with a visual display of the similarities and differences between two items. The similarities between elements are listed in the intersection between the two circles. The differences are listed in the parts of each circle that do not intersect. Ideally, a new Venn diagram should be completed for each characteristic so that students can easily see how similar and different the elements are for each characteristic used in the comparison." (Robert J. Marzano et al, "Classroom Instruction that Works: Research-based strategies for increasing student achievement, 2001)

"It is a curious fact that if you draw an endless line on a piece of paper so that it cuts itself any number of times (but never cuts itself more than once at the same point), then you can color the resulting regions using only two colors without any adjoining regions being the same color. [...] Venn diagrams also possess this property, but for a separate reason, which at first sight seems to be nicely demonstrated by induction." (Anthony W F Edwards, "Cogwheels of the mind: The story of Venn diagrams", 2004)

"The notion of outcomes covering a space is a very useful mental image, as it ties in strongly with the use of Venn diagrams and tables for clarifying the nature of possible events resulting from a trial. There are two important aspects to this. First, when enumerating the various outcomes that comprise an event, the number of (equally. likely) outcomes should correspond, visually, with the area of that part of the diagram represented by the event in question - the greater the probability, the larger the area. Secondly, where events overlap (for example, when rolling a die, consider the two events 'getting an even score' and 'getting a score greater than 2' ), the various regions in the Venn diagram help to clarify the various combinations of events that might occur." (Alan Graham, "Developing Thinking in Statistics", 2006)

"Venn diagrams visually ground symbolic logic and abstract set operations. They do not ground probability. Their common overuse in introducing probability, especially in teaching, can have undesirable consequences." (R W Oldford & W H Cherry, "Picturing Probability: the poverty of Venn diagrams, the richness of Eikosograms", 2006)

❄️Systems Thinking: On Regulation (Quotes)

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

"For if society lacks the unity that derives from the fact that the relationships between its parts are exactly regulated, that unity resulting from the harmonious articulation of its various functions assured by effective discipline and if, in addition, society lacks the unity based upon the commitment of men's wills to a common objective, then it is no more than a pile of sand that the least jolt or the slightest puff will suffice to scatter." (Émile Durkheim, 1903)    

"It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage of their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"The qualitative type of any stable discontinuity does not depend on the specific nature of the potential involved, merely on its existence. It does not depend on the specific conditions regulating behavior, merely on their number. It does not depend on the specific quantitative, cause-and-effect relationship between the conditions and the resultant behavior, merely on the empirical fact that such a relationship exists." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"We should scarcely be excused in concluding this essay without calling the reader's attention to the beneficent and wise laws established by the author of nature to provide for the various exigencies of the sublunary creation, and to make the several parts dependent upon each other, so as to form one well-regulated system or whole." (John Dalton, "Experiments and Observations to Determine whether the Quantity of Rain and Dew is Equal to the Quantity of Water carried off by the Rivers and Raised by Evaporation", Memoirs Manchester Literary and Philosophical Society, 1803)

"Feedback is a method of controlling a system by reinserting into it the results of its past performance. If these results are merely used as numerical data for the criticism of the system and its regulation, we have the simple feedback of the control engineers. If, however, the information which proceeds backward from the performance is able to change the general method and pattern of performance, we have a process which may be called learning." (Norbert Wiener, 1954)

"Many of the activities of living organisms permit this double aspect. On the one hand the observer can notice the great deal of actual movement and change that occurs, and on the other hand he can observe that throughout these activities, so far as they are coordinated or homeostatic, there are invariants and constancies that show the degree of regulation that is being achieved." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Cybernetics is concerned with scientific investigation of systemic processes of a highly varied nature, including such phenomena as regulation, information processing, information storage, adaptation, self-organization, self-reproduction, and strategic behavior. Within the general cybernetic approach, the following theoretical fields have developed: systems theory (system), communication theory, game theory, and decision theory." (Fritz B Simon et al, "Language of Family Therapy: A Systemic Vocabulary and Source Book", 1985)

"[…] the standard theory of chaos deals with time evolutions that come back again and again close to where they were earlier. Systems that exhibit this eternal return" are in general only moderately complex. The historical evolution of very complex systems, by contrast, is typically one way: history does not repeat itself. For these very complex systems with one-way evolution it is usually clear that sensitive dependence on initial condition is present. The question is then whether it is restricted by regulation mechanisms, or whether it leads to long-term important consequences." (David Ruelle, "Chance and Chaos", 1991)

"Neural nets have no central control in the classical sense. Processing is distributed over the network and the roles of the various components (or groups of components) change dynamically.  This does not preclude any part of the network from developing a regulating function, but that will be determined by the evolutionary needs of the system." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"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)

"Incidentally, the butterfly effect also has a good side to it. Since a butterfly in Brazil can disturb the serene weather in Florida, the same butterfly could calm a hurricane in Texas by simply flapping its wings in a certain fashion. This process is called 'controlling chaos' and has been put to use with some success in dealing with heart fibrillation. By applying small shocks at precisely the right moment, an erratic heartbeat can be regularized and a heart attack avoided." (George Szpiro, "Kepler’s Conjecture", 2002)

"Most systems displaying a high degree of tolerance against failures are a common feature: Their functionality is guaranteed by a highly interconnected complex network. A cell's robustness is hidden in its intricate regulatory and metabolic network; society's resilience is rooted in the interwoven social web; the economy's stability is maintained by a delicate network of financial and regulator organizations; an ecosystem's survivability is encoded in a carefully crafted web of species interactions. It seems that nature strives to achieve robustness through interconnectivity. Such universal choice of a network architecture is perhaps more than mere coincidences." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"A self-organizing system not only regulates or adapts its behavior, it creates its own organization. In that respect it differs fundamentally from our present systems, which are created by their designer. We define organization as structure with function. Structure means that the components of a system are arranged in a particular order. It requires both connections, that integrate the parts into a whole, and separations that differentiate subsystems, so as to avoid interference. Function means that this structure fulfils a purpose." (Francis Heylighen & Carlos Gershenson, "The Meaning of Self-organization in Computing", IEEE Intelligent Systems, 2003)

"The notion of feedback to regulate servomechanisms is the control engineer’s contribution to understanding how systems can be sensed, and then sufficient sense made of this for the purpose of having the system behave agreeably. The cleverness of control has been to influence systems behavior when a priori knowledge of that system is difficult or impossible to achieve. Usually you need to know what it is you are controlling to have a chance of regulating its behavior; that is one consequence of the law of requisite variety." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"In negative feedback regulation the organism has set points to which different parameters (temperature, volume, pressure, etc.) have to be adapted to maintain the normal state and stability of the body. The momentary value refers to the values at the time the parameters have been measured. When a parameter changes it has to be turned back to its set point. Oscillations are characteristic to negative feedback regulation […]" (Gaspar Banfalvi, "Homeostasis - Tumor – Metastasis", 2014)

❄️Systems Thinking: On Self-Regulation (Quotes)

 "The concept of teleological mechanisms however it be expressed in many terms, may be viewed as an attempt to escape from these older mechanistic formulations that now appear inadequate, and to provide new and more fruitful conceptions and more effective methodologies for studying self-regulating processes, self-orienting systems and organisms, and self-directing personalities. Thus, the terms feedback, servomechanisms, circular systems, and circular processes may be viewed as different but equivalent expressions of much the same basic conception." (Lawrence K Frank, 1948)

"Biological communities are systems of interacting components and thus display characteristic properties of systems, such as mutual interdependence, self-regulation, adaptation to disturbances, approach to states of equilibrium, etc." (Ludwig von Bertalanffy, "Problems of Life", 1952)

"Feedback […] is the fundamental principle that underlies all self-regulating systems, not only machines but also the processes of life and the tides of human affairs." (Arnold Tustin, 1952)

"Today our main problem is that of organized complexity. Concepts like those of organization, wholeness, directiveness, teleology, control, self-regulation, differentiation and the like are alien to conventional physics. However, they pop up everywhere in the biological, behavioural and social sciences, and are, in fact, indispensable for dealing with living organisms or social groups. Thus, a basic problem posed to modern science is a general theory of organization." (Ludwig von Bertalanff, "General System Theory, 1956)

"The famous balance of nature is the most extraordinary of all cybernetic systems. Left to itself, it is always self-regulated." (Joseph W Krutch, Saturday Review, 1963)

"Basically, self-regulation requires a functional distinction between perception, decision-making, and action. This is normally achieved by a structural distinction between perceptor elements, control elements and effector elements in the system. Behaviorally, a system may be defined as a “black box” characterized by a given set or range of inputs and outputs. Adequate knowledge of any system requires both structural-functional analysis and behavioral analysis." (Charles R Decher, "The Development of Cybernetics" [in "The Social Impact of Cybernetics", 1967)

"A structure is a system of transformations. Inasmuch as it is a system and not a mere collection of elements and their properties, these transformations involve laws: the structure is preserved or enriched by the interplay of its transformation laws, which never yield results external to the system nor employ elements that are external to it. In short, the notion of structure is composed of three key ideas: the idea of wholeness, the idea of transformation, and the idea of self-regulation." (Jean Piaget, "Structuralism", 1968)

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

❄️Systems Thinking: On Scale (Quotes)

"There seems to be a time scale in all natural processes beyond which structural stability and calculability become incompatible." (René Thom, "Structural Stability and Morphogenesis", 1972)

"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)

"What is renormalization? First of all, if scaling is present we can go to smaller scales and get exactly the same result. In a sense we are looking at the system with a microscope of increasing power. If you take the limit of such a process you get a stability that is not otherwise present. In short, in the renormalized system, the self-similarity is exact, not approximate as it usually is. So renormalization gives stability and exactness." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder."  (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

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

"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"At an anatomical level - the level of pure, abstract connectivity - we seem to have stumbled upon a universal pattern of complexity. Disparate networks show the same three tendencies: short chains, high clustering, and scale-free link distributions. The coincidences are eerie, and baffling to interpret." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)

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

"When parts are acting independently, the fine scale behavior is more complex. When they are working together, the fine scale complexity is much smaller, but the behavior is on a larger scale. This means that complexity is always a trade-off, more complex at a large scale means simpler at a fine scale. This trade-off is a basic conceptual tool that we need in order to understand complex systems." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004) 

"Some might say that the processes are in effect the functions of the components of the system. This would not be quite correct. The processes indeed comprise these component functions, denoting a change in scale - from system level to component level - but the processes tie these component functions together in a very real structural sense, although this is integration of behavior of elements rather than of elements themselves. What we do find, however, is the continual interaction of the forces of separation and integration, and the interdependencies of structure, function, and process across. scales. This is the phenomenon of systems thinking. Greater depths of this thinking require attention be paid to these three: scale, moving across scale, and discovering new behaviors as we go to higher scales." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"Science reveals complexity unfolding in all dimensions and novel features emerging at all scales and organizational levels of the universe. The more we know the more we become aware of how much we do not know. […] Complexity itself is understood as a particular dynamic or 'movement' in time that is simultaneously stable and unstable, predictable and unpredictable, known and unknown, certain and uncertain." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"We are beginning to see the entire universe as a holographically interlinked network of energy and information, organically whole and self-referential at all scales of its existence. We, and all things in the universe, are non-locally connected with each other and with all other things in ways that are unfettered by the hitherto known limitations of space and time." (Ervin László,"Cosmos: A Co-creator's Guide to the Whole-World", 2010)

"Among complex systems, stability is typically meta-stability, which is preserved through cycling, whilst growth and shrinkage are often components of a larger-scale, cyclic wave." (Nick Land, "Eternal Return, and After", 2011)

"In other words, the web of life consists of networks within networks. At each scale, under closer scrutiny, the nodes of the network reveal themselves as smaller networks. We tend to arange these systems, all nesting within larger systems, in a hierarchical scheme by placing the larger systems above the smaller ones in pyramid fashion. But this is a human projection. In nature there is no 'above' or 'below', and there are no hierarchies. There are only networks nesting within other networks." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

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

"Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

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

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

🦋Science: On Statistical Models (Quotes)

"The most widely used mathematical tools in the social sciences are statistical, and the prevalence of statistical methods has given rise to theories so abstract and so hugely complicated that they seem a discipline in themselves, divorced from the world outside learned journals. Statistical theories usually assume that the behavior of large numbers of people is a smooth, average 'summing-up' of behavior over a long period of time. It is difficult for them to take into account the sudden, critical points of important qualitative change. The statistical approach leads to models that emphasize the quantitative conditions needed for equilibrium - a balance of wages and prices, say, or of imports and exports. These models are ill suited to describe qualitative change and social discontinuity, and it is here that catastrophe theory may be especially helpful." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"Statistical models for data are never true. The question whether a model is true is irrelevant. A more appropriate question is whether we obtain the correct scientific conclusion if we pretend that the process under study behaves according to a particular statistical model." (Scott Zeger, "Statistical reasoning in epidemiology", American Journal of Epidemiology, 1991)

"[…] it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model." (Sir David Cox, "Comment on ‘Model uncertainty, data mining and statistical inference’", Journal of the Royal Statistical Society, Series A 158, 1995)

"Building statistical models is just like this. You take a real situation with real data, messy as this is, and build a model that works to explain the behavior of real data." (Martha Stocking, New York Times, 2000)

"The role of graphs in probabilistic and statistical modeling is threefold: (1) to provide convenient means of expressing substantive assumptions; (2) to facilitate economical representation of joint probability functions; and (3) to facilitate efficient inferences from observations." (Judea Pearl, "Causality: Models, Reasoning, and Inference", 2000)

"It is impossible to construct a model that provides an entirely accurate picture of network behavior. Statistical models are almost always based on idealized assumptions, such as independent and identically distributed (i.i.d.) interarrival times, and it is often difficult to capture features such as machine breakdowns, disconnected links, scheduled repairs, or uncertainty in processing rates." (Sean Meyn, "Control Techniques for Complex Networks", 2008)

"Statistical cognition is concerned with obtaining cognitive evidence about various statistical techniques and ways to present data. It’s certainly important to choose an appropriate statistical model, use the correct formulas, and carry out accurate calculations. It’s also important, however, to focus on understanding, and to consider statistics as communication between researchers and readers." (Geoff Cumming, "Understanding the New Statistics", 2012)

"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 statistical model is a relatively simple approximation to account for complex phenomena that generate data. A statistical model consists of one or more equations involving both random variables and parameters. The random variables have stated or assumed distributions. The parameters are unknown fixed quantities. The random components of statistical models account for the inherent variability in most observed phenomena." (Richard M Heiberger & Burt Holland, "Statistics Concepts", 2015)

"An oft-repeated rule of thumb in any sort of statistical model fitting is 'you can't fit a model with more parameters than data points'. This idea appears to be as wide-spread as it is incorrect. On the contrary, if you construct your models carefully, you can fit models with more parameters than datapoints [...]. A model with more parameters than datapoints is known as an under-determined system, and it's a common misperception that such a model cannot be solved in any circumstance. [...] this misconception, which I like to call the 'model complexity myth' [...] is not true in general, it is true in the specific case of simple linear models, which perhaps explains why the myth is so pervasive." (Jake Vanderplas, "The Model Complexity Myth", 2015) [source]

"Machine learning takes many different forms and goes by many different names: pattern recognition, statistical modeling, data mining, knowledge discovery, predictive analytics, data science, adaptive systems, self-organizing systems, and more. Each of these is used by different communities and has different associations. Some have a long half-life, some less so." (Pedro Domingos, "The Master Algorithm", 2015)

"In machine learning, knowledge is often in the form of statistical models, because most knowledge is statistical [...] Machine learning is a kind of knowledge pump: we can use it to extract a lot of knowledge from data, but first we have to prime the pump." (Pedro Domingos, "The Master Algorithm", 2015)

"One final warning about the use of statistical models (whether linear or otherwise): The estimated model describes the structure of the data that have been observed. It is unwise to extend this model very far beyond the observed data." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"The central limit conjecture states that most errors are the result of many small errors and, as such, have a normal distribution. The assumption of a normal distribution for error has many advantages and has often been made in applications of statistical models." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"When we use algebraic notation in statistical models, the problem becomes more complicated because we cannot 'observe' a probability and know its exact number. We can only estimate probabilities on the basis of observations." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Any fool can fit a statistical model, given the data and some software. The real challenge is to decide whether it actually fits the data adequately. It might be the best that can be obtained, but still not good enough to use." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

🧬Cybernetics: Communication Theory (Quotes)

"We have decided to call the entire field of control and communication theory, whether in the machine or in the animal, by the name Cybernetics, which we form from the Greek [...] for steersman. In choosing this term, we wish to recognize that the first significant paper on feedback mechanisms is an article on governors, which was published by Clerk Maxwell in 1868, and that governor is derived from a Latin corruption [...] We also wish to refer to the fact that the steering engines of a ship are indeed one of the earliest and best-developed forms of feedback mechanisms." (Norbert Wiener, "Cybernetics", 1948)

"Incomplete knowledge of the future, and also of the past of the transmitter from which the future might be constructed, is at the very basis of the concept of information. On the other hand, complete ignorance also precludes communication; a common language is required, that is to say an agreement between the transmitter and the receiver regarding the elements used in the communication process [... The information of a message can] be defined as the 'minimum number of binary decisions which enable the receiver to construct the message, on the basis of the data already available to him.' These data comprise both the convention regarding the symbols and the language used, and the knowledge available at the moment when the message started." (Dennis Gabor, "Optical transmission" [in: "Information Theory: Papers Read at a Symposium on Information Theory"], 1952) 

"The theory of communication is partly concerned with the measurement of information content of signals, as their essential property in the establishment of communication links. But the information content of signals is not to be regarded as a commodity; it is more a property or potential of the signals, and as a concept it is closely related to the idea of selection, or discrimination. This mathematical theory first arose in telegraphy and telephony, being developed for the purpose of measuring the information content of telecommunication signals. It concerned only the signals themselves as transmitted along wires, or broadcast through the aether, and is quite abstracted from all questions of 'meaning'. Nor does it concern the importance, the value, or truth to any particular person. As a theory, it lies at the syntactic level of sign theory and is abstracted from the semantic and pragmatic levels. We shall argue [...] that, though the theory does not directly involve biological elements, it is nevertheless quite basic to the study of human communication - basic but insufficient." (Colin Cherry, "On Human Communication", 1957)

"A more viable model, one much more faithful to the kind of system that society is more and more recognized to be, is in process of developing out of, or is in keeping with, the modern systems perspective (which we use loosely here to refer to general systems research, cybernetics, information and communication theory, and related fields). Society, or the sociocultural system, is not, then, principally an equilibrium system or a homeostatic system, but what we shall simply refer to as a complex adaptive system." (Walter F Buckley, "Society as a complex adaptive system", 1968)

"The general notion in communication theory is that of information. In many cases, the flow of information corresponds to a flow of energy, e. g. if light waves emitted by some objects reach the eye or a photoelectric cell, elicit some reaction of the organism or some machinery, and thus convey information." (Ludwig von Bertalanffy, "General System Theory", 1968) 

"The 'flow of information' through human communication channels is enormous. So far no theory exists, to our knowledge, which attributes any sort of unambiguous measure to this 'flow'." (Anatol Rapoport, "Modern Systems Research for the Behavioral Scientist", 1969)

"The term hypothesis testing arises because the choice as to which process is observed is based on hypothesized models. Thus hypothesis testing could also be called model testing. Hypothesis testing is sometimes called decision theory. The detection theory of communication theory is a special case." (Fred C Scweppe, "Uncertain dynamic systems", 1973)

"Communication theory deals with certain important but abstract aspects of communication. Communication theory proceeds from clear and definite assumptions to theorems concerning information sources and communication channels. In this it is essentially mathematical, and in order to understand it we must understand the idea of a theorem as a statement which must be proved, that is, which must be shown to be the necessary consequence of a set of initial assumptions. This is an idea which is the very heart of mathematics as mathematicians understand it." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals & Noise" 2nd Ed., 1980)

"Communication theory tells us how many bits of information can be sent per second over perfect and imperfect communication channels in terms of rather abstract descriptions of the properties of these channels. Communication theory tells us how to measure the rate at which a message source, such as a speaker or a writer, generates information. Communication theory tells us how to represent, or encode, messages from a particular message source efficiently for transmission over a particular sort of channel, such as an electrical circuit, and it tells us when we can avoid errors in transmission." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals & Noise" 2nd Ed., 1980)

"In communication theory we consider a message source, such as a writer or a speaker, which may produce on a given occasion any one of many possible messages. The amount of information conveyed by the message increases as the amount of uncertainty as to what message actually will be produced becomes greater. A message which is one out of ten possible messages conveys a smaller amount of information than a message which is one out of a million possible messages. The entropy of communication theory is a measure of this uncertainty and the uncertainty, or entropy, is taken as the measure of the amount of information conveyed by a message from a source. The more we know about what message the source will produce, the less uncertainty, the less the entropy, and the less the information." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals & Noise" 2nd Ed., 1980)

"The amount of information conveyed by the message increases as the amount of uncertainty as to what message actually will be produced becomes greater. A message which is one out of ten possible messages conveys a smaller amount of information than a message which is one out of a million possible messages. The entropy of communication theory is a measure of this uncertainty and the uncertainty, or entropy, is taken as the measure of the amount of information conveyed by a message from a source. The more we know about what message the source will produce, the less uncertainty, the less the entropy, and the less the information." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals and Noise", 1980)

"Thus, information is sometimes associated with the idea of knowledge through its popular use rather than with uncertainty and the resolution of uncertainty, as it is in communication theory." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals & Noise" 2nd Ed., 1980)

"Cybernetics is concerned with scientific investigation of systemic processes of a highly varied nature, including such phenomena as regulation, information processing, information storage, adaptation, self-organization, self-reproduction, and strategic behavior. Within the general cybernetic approach, the following theoretical fields have developed: systems theory (system), communication theory, game theory, and decision theory." (Fritz B Simon et al, "Language of Family Therapy: A Systemic Vocabulary and Source Book", 1985)

"General evolution theory, based on the integration of the relevant tenets of general system theory, cybernetics, information and communication theory, chaos theory, dynamical systems theory, and nonequilibrium thermodynamics, can convey a sound understanding of the laws and dynamics that govern the evolution of complex systems in the various realms of investigation [...]. The basic notions of this new discipline can be developed to give an adequate account of the dynamical evolution of human societies as well. Such an account could furnish the basis of a system of knowledge better able to orient human beings and societies in their rapidly changing milieu." (Ervin László et al, "The Evolution of Cognitive Maps: New Paradigms for the Twenty-first Century", 1993)

"Communication theory is enormously rich in the range of ideas that fall within its nominal scope, and new theoretical work on communication has recently been flourishing. Nevertheless, despite the ancient roots and growing profusion of theories about communication, I argue that communication theory as an identifiable field of study does not yet exist." (Robert T Craig "Communication Theory as a Field", 1999)

"The very essence of mass communication theory is a simple but all-embracing expression of technological determinism, since the essential features depend on what certain technologies have made possible, certain technologies have made possible, especially the following: communication at a distance, the multiplication and simultaneous distribution of diverse ‘messages’, the enormous capacity and speed of carriers, and the limitations on response. There is no escaping the implication that public communication as practised in modern societies is profoundly shaped by these general features." (Denis McQuail, "McQuail's Reader in Mass Communication Theory", 2002)

"Without an understanding of causality there can be no theory of communication. What passes as information theory today is not communication at all, but merely transportation." (Marshall McLuhan, "The Book of Probes : Marshall McLuhan", 2011) 

"Cybernetics is an interdisciplinary science. It originated ‘at the junction’ of mathematics, logic, semiotics, physiology, biology and sociology. Among its inherent features, we mention analysis and revelation of general principles and approaches in scientific cognition. Control theory, communication theory, operations research and others represent most weighty theories within cybernetics 1.0." (Dmitry A Novikov, "Cybernetics 2.0", 2016)

🪂Mind: On Rational Behavior (Quotes)

"To the rational being only the irrational is unendurable, but the rational is endurable." (Epictetus, "Discourses", cca. 100 AD)

"To him who looks upon the world rationally, the world in its turn presents a rational aspect. The relation is mutual." (Georg W F Hegel, "Lectures on the Philosophy of History", 1832)

"As a 'rational' being, he now places his behavior under the control of abstractions. He will no longer tolerate being carried away by sudden impressions, by intuitions." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)

"All rational action is economic. All economic activity is rational action. All rational action is in the first place individual action. Only the individual thinks. Only the individual reasons. Only the individual acts." (Ludwig von Mises, "Socialism", 1922)

"In the process of decision those alternatives are chosen which are considered to be appropriate means of reaching desired ends. Ends themselves, however, are often merely instrumental to more final objectives. We are thus led to the conception of a series, or hierarchy, of ends. Rationality has to do with the construction of means-ends chains of this kind." (Herbert A Simon, "Administrative Behavior", 1947)

"It is impossible for the behavior of a single, isolated individual to reach a high degree of rationality. The number of alternatives he must explore is so great, the information he would need to evaluate them so vast that even an approximation to objective rationality is hard to conceive. Individual choice takes place in rationality is hard to conceive. [...] Actual behavior falls short in at least three ways, of objective rationality." (Herbert A Simon, "Administrative Behavior", 1947)

"Rationality requires a choice among all possible alternative behaviors. In actual behavior, only a very few of all these possible alternatives come to mind." (Herbert A Simon, "Administrative Behavior", 1947)

"Rationality requires a complete knowledge and anticipation of the consequences that will follow on each choice. In fact, knowledge of consequences is always fragmentary." (Herbert A Simon, "Administrative Behavior", 1947)

"Roughly speaking, rationality is concerned with the selection of preferred behavior alternatives in terms of some system of values, whereby the consequences of behavior can be evaluated." (Herbert A Simon, "Administrative Behavior", 1947)

"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)

"More than ambition, more than ability, it is rules that limit contribution; rules are the lowest common denominator of human behavior. They are a substitute for rational thought." (Hyman G Rickover, [address] 1954)

"Unlike pure theorists, we shall not assume at the outset that rational behavior exists or that rational behavior constitutes the topic of economic analysis. We shall study economic behavior as we find it. In describing and classifying different reactions, as well as the circumstances that elicit them, we shall raise the question whether and in what sense certain reactions may be called rational. After having answered that question and thus defined our terms, we shall study the fundamental problem: Under what conditions do more and under what conditions do less rational forms of behavior occur?" (George Katona, "Psychological Analysis of Economic Behavior", 1951)

"Broadly stated, the task is to replace the global rationality of economic man with a kind of rational behavior that is compatible with the access to information and the computational capacities that are actually possessed by organisms, including man, in the kinds of environments in which such organisms exist." (Herbert A Simon, "A behavioral model of rational choice", The Quarterly Journal of Economics, Vol. 69 (1), 1955)

"Because of the extended time image and the extended relationship images, man is capable of ‘rational behavior,’ that is to say, his response is not to an immediate stimulus but to an image of the future filtered through an elaborate value system.  His image contains not only what is, but what might be." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)

"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)

"The outcome of a non-constant-sum game may be dictated by the individual rationality of the respective players without satisfying a criterion of collective rationality." (Anatol Rapoport, "Game Theory as a Theory of Conflict Resolution", 1974)

"The tendency to be rational is the consistent and hence predictable element in human behavior." (David Friedman, "Price Theory: An Intermediate Text", 1986)

"Even though principles of rationality seem as often violated as followed, we still cling to the notion that human thought should be rational, logical, and orderly. Much of law is based upon the concept of rational thought and behavior. Much of economic theory is based upon the model of the rational human who attempts to optimize personal benefit, utility, or comfort. Many scientists who study artificial intelligence use the mathematics of formal logic - the predicate calculus - as their major tool to simulate thought. [...] Human thought is not like logic; it is fundamentally different in kind and spirit. The difference is neither worse nor better. But it is the difference that leads to creative discovery and to great robustness of behavior." (Donald Norman, "The Design of Everyday Things", 1988)

"Human rational behavior [...] is shaped by the scissors whose two blades are the structure of the task environment and the computational capabilities of the actor. (Herbert A Simon, "Invariants of Human Behavior", Annual Review of Psychology 41(1), 1990)

"The Minimax Theorem applies to games in which there are just two players and for which the total payoff to both parties is zero, regardless of what actions the players choose. The advantage of these two properties is that with two players whose interests are directly opposed we have a game of pure competition, which allows us to define a clear-cut mathematical notion of rational behavior that leads to a single, unambiguous rule as to how each player should behave." (John L Casti, "Five Golden Rules", 1995)

"Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has to choose his moves on the basis of what he thinks the other players' countermoves are likely to be." (John Harsanyi, "Games with Incomplete Information", The American Economic Review Vol. 85 (3), 1997)

"Behavior is imitated, then abstracted into play, formalized into drama and story, crystallized into myth and codified into religion—and only then criticized in philosophy, and provided, post-hoc, with rational underpinnings." (Jordan Peterson, "Maps of Meaning", 1999)

"The assumption of perfectly rational, maximizing behavior won out until recently in the art of modeling, not because it often reflects reality, but because it was useful." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Systems", 2003)

"A person's behavior is rational if it is in his best interests, given his information." (Robert Aumann, "War and Peace", 2005)

"Rational maximization should not be confused with conscious calculation. Economics is not a theory about consciousness. Behavior is rational when it conforms to the model of rational choice, whatever the state of mind of the chooser." (Richard Posner, "Economic Analysis of Law" 7th ed., 2007)

"Acting in conformity with reason, in the singular, and acting for good reasons, in the plural, are two different things insofar as reason is objective, whereas reasons are subjective. From an external point of view, we can evaluate a policy as being in conformity with reason or not. From an internal point of view, one can evaluate an action as being rational or not. From this difference it follows that only rationality can be used for explanatory ends. It is only insofar as the agent has made the demands of reason his own that the latter may give rise to, and possibly explain, specific behaviors. The assessment of the actor and that of the observer need not coincide." (Jon Elster, "Reason and Rationality", 2009)

"Game theory postulates rational behavior for each participant. Each player is conscious of the rules and behaves in accordance with them, each player has sufficient knowledge of the situation in which he or she is involved to be able to evaluate what the best option is when it comes to taking action (a move), and each player takes into account the decisions that might be made by other participants and their repercussions with respect to his or her own decision. Game theory about zero-sum games with two participants is relevant for chess. In this type of situation, each action that is favorable to one participant (player) is proportionally unfavorable for the opponent. Thus, the gain of one represents the loss of the other." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

❄️Systems Thinking: On Experience (Quotes)

"Every change of one of the factors of an equilibrium occasions a rearrangement of the system in such a direction that the factor in question experiences a change in a sense opposite to the original change." (Henri L Le Chatelier, "Recherches Experimentales et Theoriques sur les Equilibres Chimiques" ["Experimental and Theoretical Research on Chemical Equilibria"], Annales des Mines 8, 1888)

"No system would have ever been framed if people had been simply interested in knowing what is true, whatever it may be. What produces systems is the interest in maintaining against all comers that some favourite or inherited idea of ours is sufficient and right. A system may contain an account of many things which, in detail, are true enough; but as a system, covering infinite possibilities that neither our experience nor our logic can prejudge, it must be a work of imagination and a piece of human soliloquy: It may be expressive of human experience, it may be poetical; but how should anyone who really coveted truth suppose that it was true?" (George Santayana, "The Genteel Tradition in American Philosophy", 1911)

"A ‘representation’ of a system is not a knowledge of this system, but is this system itself becoming an object, an element of experience." (Florian Znaniecki, "Cultural reality?", 1919)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939)

"A […] difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare." (Lawrence J Henderson, "The Study of Man", 1941)

"The most fundamental concept in cybernetics is that of ‘difference’, either that two things are recognisably different or that one thing has changed with time. Its range of application need not be described now, for the subsequent chapters will illustrate the range abundantly. All the changes that may occur with time are naturally included, for when plants grow and planets age and machines move some change from one state to another is implicit. So our first task will be to develop this concept of 'change', not only making it more precise but making it richer, converting it to a form that experience has shown to be necessary if significant developments are to be made." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality. They are more or less isomorphic to transformations of reality. The transformational structures of which knowledge consists are not copies of the transformations in reality; they are simply possible isomorphic models among which experience can enable us to choose. Knowledge, then, is a system of transformations that become progressively adequate." (Jean Piaget, "Genetic Epistemology", 1968)

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

"Networks constitute the new social morphology of our societies, and the diffusion of networking logic substantially modifies the operation and outcomes in processes of production, experience, power, and culture. While the networking form of social organization has existed in other times and spaces, the new information technology paradigm provides the material basis for its pervasive expansion throughout the entire social structure." (Manuel Castells, "The Rise of the Network Society", 1996)

"Something of the previous state, however, survives every change. This is called in the language of cybernetics (which took it form the language of machines) feedback, the advantages of learning from experience and of having developed reflexes." (Guy Davenport, "The Geography of the Imagination: Forty Essays", 1997)

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

"Faced with the overwhelming complexity of the real world, time pressure, and limited cognitive capabilities, we are forced to fall back on rote procedures, habits, rules of thumb, and simple mental models to make decisions. Though we sometimes strive to make the best decisions we can, bounded rationality means we often systematically fall short, limiting our ability to learn from experience." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The self-reinforcing feedback between expectations and perceptions has been repeatedly demonstrated […]. Sometimes the positive feedback assists learning by sharpening our ability to perceive features of the environment, as when an experienced naturalist identifies a bird in a distant bush where the novice sees only a tangled thicket. Often, however, the mutual feedback of expectations and perception blinds us to the anomalies that might challenge our mental models and lead to deep insight." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Ecological rationality uses reason – rational reconstruction – to examine the behavior of individuals based on their experience and folk knowledge, who are ‘naïve’ in their ability to apply constructivist tools to the decisions they make; to understand the emergent order in human cultures; to discover the possible intelligence embodied in the rules, norms and institutions of our cultural and biological heritage that are created from human interactions but not by deliberate human design. People follow rules without being able to articulate them, but they can be discovered." (Vernon L Smith, "Constructivist and ecological rationality in economics", 2002)

"When we look at the world around us, we find that we are not thrown into chaos and randomness but are part of a great order, a grand symphony of life. Every molecule in our body was once a part of previous bodies-living or nonliving-and will be a part of future bodies. In this sense, our body will not die but will live on, again and again, because life lives on. We share not only life's molecules but also its basic principles of organization with the rest of the living world. Arid since our mind, too, is embodied, our concepts and metaphors are embedded in the web of life together with our bodies and brains. We belong to the universe, we are at home in it, and this experience of belonging can make our lives profoundly meaningful." (Fritjof Capra, "The Hidden Connections", 2002)

"To remedy chaotic situations requires a chaotic approach, one that is non-linear, constantly morphing, and continually sharpening its competitive edge with recurring feedback loops that build upon past experiences and lessons learned. Improvement cannot be sustained without reflection. Chaos arises from myriad sources that stem from two origins: internal chaos rising within you, and external chaos being imposed upon you by the environment. The result of this push/pull effect is the disequilibrium [...]." (Jeff Boss, "Navigating Chaos: How to Find Certainty in Uncertain Situations", 2015)

🪂Mind: On Experience (Quotes)

"Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience." (Roger Bacon, "Opus Majus", cca. 1267)

"[…] 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)

"Men always fool themselves when they give up experience for systems born of the imagination. Man is the work of nature, he exists in nature, he is subject to its laws, he can not break free, he can not leave even in thought; it is in vain that his spirit wants to soar beyond the bounds of the visible world, he is always forced to return." (Paul-Henri T d’ Holbach, "Système de la Nature", 1770)

"It falls into this difficulty without any fault of its own. It begins with principles, which cannot be dispensed with in the field of experience, and the truth and sufficiency of which are, at the same time, insured by experience. With these principles it rises, in obedience to the laws of its own nature, to ever higher and more remote conditions. But it quickly discovers that, in this way, its labours must remain ever incomplete, because new questions never cease to present themselves; and thus it finds itself compelled to have recourse to principles which transcend the region of experience, while they are regarded by common sense without distrust. It thus falls into confusion and contradictions, from which it conjectures the presence of latent errors, which, however, it is unable to discover, because the principles it employs, transcending the limits of experience, cannot be tested by that criterion. The arena of these endless contests is called Metaphysic." (Immanuel Kant, "The Critique of Pure Reason", 1781)

"In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty." (Johann H Lambert, "The System of the World", 1800)

"We construct concepts when we represent them in intuition a priori, without experience, or when we represent in intuition  the object which corresponds to our concept of it. - The mathematician can never apply his reason to mere concepts, nor the philosopher to the construction of concepts. - In mathematics  the reason is employed in concreto, however, the intuition is not  empirical, but the object of contemplation is something a priori." (Immanuel Kant, "Logic", 1800)

"Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth." (Pierre-Simon Laplace, "A Philosophical Essay on Probabilities", 1814)

"Theories are always very thin and unsubstantial; experience only is tangible." (Hosea Ballou, "Universalist Expositor", 1831)

"It is frequently analogy which guides the experienced to what are called good guesses." (Francis W Newman, "Lectures on Logic", 1838)

"A human being, what is a human being? Everything and nothing. Through the power of thought it can mirror everything it experiences. Through memory and knowledge it becomes a microcosm, carrying the world within itself. A mirror of things, a mirror of facts. Each human being becomes a little universe within the universe!" (Guy de Maupassant, [in "The Journal of a Madman"] 1851)

"By reducing imagination to the power of forming images, and by insisting that no image can be formed except out of the elements furnished by experience, I do not mean to confound imagination with memory; indeed, the frequent occurrence of great strength of memory with comparative feebleness of imagination, would suffice to warn us against such a conclusion." (George H Lewes, "The Principles of Success in Literature", 1865)

"To imagine - to form an image - we must have the numerous relations of things present to the mind, and see the objects in their actual order. In this we are of course greatly aided by the mass of organised experience, which allows us rapidly to estimate the relations of gravity or affinity just as we remember that fire burns and that heated bodies expand. But be the aid great or small, and the result victorious or disastrous, the imaginative process is always the same." (George H Lewes, "The Principles of Success in Literature", 1865)

"All experience attests the strength of the tendency to mistake mental abstractions, even negative ones, for substantive realities; and the Permanent Possibilities of sensation which experience guarantees arc so extremely unlike in many of their properties to actual sensations, that since we are capable of imagining something which transcends sensations, there is a great natural probability that we should suppose these to be it." (Hippolyte Taine, "On intelligence", 1871)

"Every word instantly becomes a concept precisely insofar as it is not supposed to serve as a reminder of the unique and entirely individual original experience to which it owes its origin; but rather, a word becomes a concept insofar as it simultaneously has to fit countless more or less similar cases - which means, purely and simply, cases which are never equal and thus altogether unequal. Every concept arises from the equation of unequal things. Just as it is certain that one leaf is never totally the same as another, so it is certain that the concept 'leaf' is formed by arbitrarily discarding these individual differences and by forgetting the distinguishing aspects." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)

"Ideas are substitutions which require a secondary process when what is symbolized by them is translated into the images and experiences it replaces; and this secondary process is frequently not performed at all, generally only performed to a very small extent. Let anyone closely examine what has passed in his mind when he has constructed a chain of reasoning, and he will be surprised at the fewness and faintness of the images which have accompanied the ideas." (George H Lewes "Problems of Life and Mind", 1873)

"The man who is guided by concepts and abstractions only succeeds by such means in warding off misfortune, without ever gaining any happiness for himself from these abstractions. And while he aims for the greatest possible freedom from pain, the intuitive man, standing in the midst of a culture, already reaps from his intuition a harvest of continually inflowing illumination, cheer, and redemption - in addition to obtaining a defense against misfortune. To be sure, he suffers more intensely, when he suffers; he even suffers more frequently, since he does not understand how to learn from experience and keeps falling over and over again into the same ditch." (Friedrich Nietzsche," On Truth and Lie in an Extra-Moral Sense", 1873)

"Human existence is girt round with mystery: the narrow region of our experience is a small island in the midst of a boundless sea. To add to the mystery, the domain of our earthly existence is not only an island of infinite space, but also in infinite time. The past and the future are alike shrouded from us: we neither know the origin of anything which is, nor its final destination." (John S Mill, "Nature, The Utility of Religion and Theism", 1874)

"Summing up, then, it would seem as if the mind of the great discoverer must combine contradictory attributes. He must be fertile in theories and hypotheses, and yet full of facts and precise results of experience. He must entertain the feeblest analogies, and the merest guesses at truth, and yet he must hold them as worthless till they are verified in experiment. When there are any grounds of probability he must hold tenaciously to an old opinion, and yet he must be prepared at any moment to relinquish it when a clearly contradictory fact is encountered." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Incidentally, naive intuition, which is in large part an inherited talent, emerges unconsciously from the in-depth study of this or that field of science. The word ‘Anschauung’ has not perhaps been suitably chosen. I would like to include here the motoric sensation with which an engineer assesses the distribution of forces in something he is designing, and even that vague feeling possessed by the experienced number cruncher about the convergence of infinite processes with which he is confronted. I am saying that, in its fields of application, mathematical intuition understood in this way rushes ahead of logical thinking and in each moment has a wider scope than the latter " (Felix Klein, "Über Arithmetisierung der Mathematik", Zeitschrift für mathematischen und naturwissen-schaftlichen Unterricht 27, 1896)

"The mind of man, learning consciously and unconsciously lessons of experience, gradually constructs a mental image of its surroundings - as the mariner draws a chart of strange coasts to guide him in future voyages, and to enable those that follow after him to sail the same seas with ease and safety." (William C Dampier, "The Recent Development of Physical Science", 1904)

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts." (William James, "A Pluralistic Universe", 1908)

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

"Abstraction is the detection of a common quality in the characteristics of a number of diverse observations […] A hypothesis serves the same purpose, but in a different way. It relates apparently diverse experiences, not by directly detecting a common quality in the experiences themselves, but by inventing a fictitious substance or process or idea, in terms of which the experience can be expressed. A hypothesis, in brief, correlates observations by adding something to them, while abstraction achieves the same end by subtracting something." (Herbert Dingle, Science and Human Experience, 1931)

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

"Concepts can only acquire content when they are connected, however indirectly, with sensible experience. But no logical investigation can reveal this connection; it can only be experienced. […] this connection […] determines the cognitive value of systems of concepts." (Albert Einstein, "The Problem of Space, Ether, and the Field in Physics", Mein Weltbild, 1934)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939)

"Thus we do not try to prove the existence of the external world – we discover it, because the fundamental power of words or other symbols to represent events [...] permits us to put forward hypotheses and test their truth by reference to experience. [..] A particular type of symbolism may always fail in a particular case, as Euclidean geometry apparently fails to represent stellar space; but if all types of symbolism always failed, we should be unable to recognise any objects or exist at all." (Kenneth Craik, "The Nature of Explanation", 1943)

"A model, like a novel, may resonate with nature, but it is not a ‘real’ thing. Like a novel, a model may be convincing - it may ‘ring true’ if it is consistent with our experience of the natural world. But just as we may wonder how much the characters in a novel are drawn from real life and how much is artifice, we might ask the same of a model: How much is based on observation and measurement of accessible phenomena, how much is convenience? Fundamentally, the reason for modeling is a lack of full access, either in time or space, to the phenomena of interest." (Kenneth Belitz, Science, Vol. 263, 1944)

"The complete use of pure reason brings us finally from physical to metaphysical knowledge. But the concepts of metaphysical knowledge do not in themselves fully satisfy the demand of our integral being. They are indeed entirely satisfactory to the pure reason itself, because they are the very stuff of its own existence. But our nature sees things through two eyes always, for it views them doubly as idea and as fact and therefore every concept is incomplete for us and to a part of our nature almost unreal until it becomes an experience." (Sri Aurobindo, "The Life Divine", 1944)

"Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own way." (Albert Einstein, "The World as I See It", 1949)

"Every bit of knowledge we gain and every conclusion we draw about the universe or about any part or feature of it depends finally upon some observation or measurement. Mankind has had again and again the humiliating experience of trusting to intuitive, apparently logical conclusions without observations, and has seen Nature sail by in her radiant chariot of gold in an entirely different direction." (Oliver J Lee, "Measuring Our Universe: From the Inner Atom to Outer Space", 1950)

"In speaking here of ‘comprehensibility’, the expression is used in its most modest sense. It implies: the production being produced by the creation of general concepts, relations between these concepts and sense experience. It is in this sense that the world of our sense experiences is comprehensible. The fact that it is comprehensible is a miracle." (Albert Einstein, "Out of My Later Years", 1950)

"As our mental eye penetrates into smaller and smaller distances and shorter and shorter times, we find nature behaving so entirely differently from what we observe in visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be ‘true’. A complete satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think of it, but however we think it, it is wrong; not perhaps quite as meaningless as a ‘triangular circle’, but more so than a ‘winged lion’." (Erwin Schrödinger, "Science and Humanism", 1952)

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

"Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics; we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged." (Willard van Orman Quine, "From a Logical Point of View", 1953)

"[a pictorial representation] is not a faithful record of a visual experience, but the faithful construction of a relational model […] Such a model can be constructed to any required degree of accuracy . What is decisive here is clearly the word 'required'. The form of a representation cannot be divorced from its purpose and the requirements of the society in which the given visual language gains currency." (Ernst H Gombrich," Art and illusion", 1960)

"Mental pictures offer us an opportunity to practice new traits and attitudes, which otherwise we could not do. This is possible because again - your nervous system cannot tell the difference between an actual experience and one that is vividly imagined." (Maxwell Maltz, "Psycho-Cybernetics", 1960)

"What a man sees depends both upon what he looks at and also upon what his previous visual-conceptual experience has taught him to see." (Thomas Kuhn, "The Structure of Scientific Revolutions", 1962)

"People may come along and argue philosophically that they like one better than another; but we have learned from much experience that all philosophical intuitions about what nature is going to do fail." (Richard Feynman, "The Character of Physical Law", 1965)

"The most pervasive paradox of the human condition which we see is that the processes which allow us to survive, grow, change, and experience joy are the same processes which allow us to maintain an impoverished model of the world - our ability to manipulate symbols, that is, to create models. So the processes which allow us to accomplish the most extraordinary and unique human activities are the same processes which block our further growth if we commit the error of mistaking the model of the world for reality." (Richard Bandler & John Grinder, "The Structure of Magic", 1975)

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

"A mental image occurs when a representation of the type created during the initial phases of perception is present but the stimulus is not actually being perceived; such representations preserve the perceptible properties of the stimulus and ultimately give rise to the subjective experience of perception." (Stephen Kosslyn, "Image and Mind", 1980)

"These organizational processes result in our perceptions being structured into units corresponding to objects and properties of objects. It is these larger units that may be stored and later assembled into images that are experienced as quasi-pictorial, spatial entities resembling those evoked during perception itself [...] It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings." (Stephen Kosslyn, "Image and Mind", 1980)

"Time goes forward because energy itself is always moving from an available to an unavailable state. Our consciousness is continually recording the entropy change in the world around us. [...] we experience the passage of time by the succession of one event after another. And every time an event occurs anywhere in this world energy is expended and the overall entropy is increased. To say the world is running out of time then, to say the world is running out of usable energy. In the words of Sir Arthur Eddington, 'Entropy is time's arrow'." (Jeremy Rifkin, "Entropy", 1980)

"Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through." (Hannah Arendt, "The Life of the Mind", 1981)

"That is to say, intuition is not a direct perception of something existing externally and eternally. It is the effect in the mind of certain experiences of activity and manipulation of concrete objects (at a later stage, of marks on paper or even mental images). As a result of this experience, there is something (a trace, an effect) in the pupil's mind which is his representation of the integers. But his representation is equivalent to mine, in the sense that we both get die same answer to any question you ask - or if we get different answers, we can compare notes and figure out what's right. We do this, not because we have been taught a set of algebraic rules, but because our mental pictures match each other." (Philip J Davis & Reuben Hersh, "The Mathematical Experience", 1981)

"The thinking person goes over the same ground many times. He looks at it from varying points of view - his own, his arch-enemy’s, others’. He diagrams it, verbalizes it, formulates equations, constructs visual images of the whole problem, or of troublesome parts, or of what is clearly known. But he does not keep a detailed record of all this mental work, indeed could not. […] Deep understanding of a domain of knowledge requires knowing it in various ways. This multiplicity of perspectives grows slowly through hard work and sets the state for the re-cognition we experience as a new insight." (Howard E Gruber, "Darwin on Man", 1981)

"[...] without imagination, heightened awareness, moral sense, and some reference to the general culture, the engineering experience becomes less meaningful, less fulfilling than it should be." (Samuel C Florman, "The Civilized Engineer", 1985)

"Metaphor [is] a pervasive mode of understanding by which we project patterns from one domain of experience in order to structure another domain of a different kind. So conceived metaphor is not merely a linguistic mode of expression; rather, it is one of the chief cognitive structures by which we are able to have coherent, ordered experiences that we can reason about and make sense of. Through metaphor, we make use of patterns that obtain in our physical experience to organise our more abstract understanding. " (Mark Johnson, "The Body in the Mind", 1987)

"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)

"Each of us has many, many maps in our head, which can be divided into two main categories: maps of the way things are, or realities, and maps of the way things should be, or values. We interpret everything we experience through these mental maps. We seldom question their accuracy; we're usually even unaware that we have them. We simply assume that the way we see things is the way they really are or the way they should be."  (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)

"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)

"The more aware we are of our basic paradigms, maps, or assumptions, and the extent to which we have been influenced by our experience, the more we can take responsibility for those paradigms, examine them, test them against reality, listen to others and be open to their perceptions, thereby getting a larger picture and a far more objective view." (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)

"Many people would accept that we do not really have knowledge of the world; we have knowledge only of our representations of the world. Yet we seem condemned by our consitution to treat these representations as if they were the world, for our everyday experience feels as if it were of a given and immediate world." (Francisco Varela, "The Embodied Mind", 1991)

"The most persuasive positive argument for mental images as objects is [that] whenever one thinks one is seeing something there must be something one is seeing. It might be an object directly, or it might be a mental picture. [This] point is so plausible that it is deniable only at the peril of becoming arbitrary. One should concede that the question whether mental images are entities of some sort is not resolvable by logical or linguistic analysis, and believe what makes sense of experience." (Eva T H Brann, "The World of Imagination", 1991)

"A world view is a system of co-ordinates or a frame of reference in which everything presented to us by our diverse experiences can be placed. It is a symbolic system of representation that allows us to integrate everything we know about the world and ourselves into a global picture, one that illuminates reality as it is presented to us within a certain culture. […] A world view is a coherent collection of concepts and theorems that must allow us to construct a global image of the world, and in this way to understand as many elements of our experience as possible." (Diederick Aerts et al, "World views: From Fragmentation to Integration", 1994)

"A mental model is not normally based on formal definitions but rather on concrete properties that have been drawn from life experience. Mental models are typically analogs, and they comprise specific contents, but this does not necessarily restrict their power to deal with abstract concepts, as we will see. The important thing about mental models, especially in the context of mathematics, is the relations they represent. […]  The essence of understanding a concept is to have a mental representation or mental model that faithfully reflects the structure of that concept. (Lyn D. English & Graeme S. Halford, "Mathematics Education: Models and Processes", 1995)

"We all depend on models to interpret our everyday experiences. We interpret what we see in terms of mental models constructed on past experience and education. They are constructs that we use to understand the pattern of our experiences." (David Bartholomew, "What is Statistics?", 1995)

"When we visually perceive the world, we do not just process information; we have a subjective experience of color, shape, and depth. We have experiences associated with other senses (think of auditory experiences of music, or the ineffable nature of smell experiences), with bodily sensations (e.g., pains, tickles, and orgasms), with mental imagery (e.g., the colored shapes that appear when one tubs one's eyes), with emotion (the sparkle of happiness, the intensity of anger, the weight of despair), and with the stream of conscious thought." (David Chalmers, "The Puzzle of Conscious Experience", Scientific American, 1995)

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

"The power of images consists largely in the fact that they integrate different types of knowledge and experience." (David Gooding, "Creative Rationality", 1996)

"Faced with the overwhelming complexity of the real world, time pressure, and limited cognitive capabilities, we are forced to fall back on rote procedures, habits, rules of thumb, and simple mental models to make decisions. Though we sometimes strive to make the best decisions we can, bounded rationality means we often systematically fall short, limiting our ability to learn from experience." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"In the language of mental models, such past experience provided the default assumptions necessary to fill the gaps in the emerging and necessarily incomplete framework of a relativistic theory of gravitation. It was precisely the nature of these default assumptions that allowed them to be discarded again in the light of novel information - provided, for instance, by the further elaboration of the mathematical formalism - without, however, having to abandon the underlying mental models which could thus continue to function as heuristic orientations." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", [in "The Universe of General Relativity"] 2000)

"When we acquire a language we don’t simply learn how to use the correct words, grammar and conventions for speaking appropriately in context, we also acquire a ‘world view’: an implicit set of assumptions and presuppositions regarding how to understand the world, who and what we are within it, and everything else that is entailed in categorising our experience." (Michael Forrester," Psychology of the Image", 2000)

"A mental model is a representation of some domain or situation that supports understanding, reasoning, and prediction. Mental models permit reasoning about situations not directly experienced. They allow people to mentally simulate the behavior of a system. Many mental models are based on generalizations and analogies from experience." (D Gentner, "Psychology of Mental Models" [in "International Encyclopedia of the Social & Behavioral Sciences"], 2001)

"In the definition of meaning, it is assumed that both the source and receiver have previously coded (and stored) signals of the same or similar referents, such that the messages may have meaning and relate to behaviour. That is, the used symbols must have the same signification for both sender and receiver. If not, the receiver will create a different mental picture than intended by the transmitter. Meaning is generated by individuals in a process of social interaction with a more or less common environment. It is a relation subsisting within a field of experience and appears as an emergent property of a symbolic representation when used in culturally accepted interaction. The relation between the symbolic representation and its meaning is random. Of this, however, the mathematical theory has nothing to say. If human links in the chain of communication are missing, of course no questions of meaning will arise." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"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)

"Ecological rationality uses reason – rational reconstruction – to examine the behavior of individuals based on their experience and folk knowledge, who are ‘naïve’ in their ability to apply constructivist tools to the decisions they make; to understand the emergent order in human cultures; to discover the possible intelligence embodied in the rules, norms and institutions of our cultural and biological heritage that are created from human interactions but not by deliberate human design. People follow rules without being able to articulate them, but they can be discovered." (Vernon L Smith, "Constructivist and ecological rationality in economics", 2002)

"A mental model is conceived […] as a knowledge structure possessing slots that can be filled not only with empirically gained information but also with ‘default assumptions’ resulting from prior experience. These default assumptions can be substituted by updated information so that inferences based on the model can be corrected without abandoning the model as a whole. Information is assimilated to the slots of a mental model in the form of ‘frames’ which are understood here as ‘chunks’ of knowledge with a well-defined meaning anchored in a given body of shared knowledge." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", "The Universe of General Relativity" Ed. by A.J. Kox & Jean Eisenstaedt, 2005)

"Patterns experienced again and again become intuitions. […] Intuitive judgments are made by our use of imagery; intuition is the result of mental model building. […] The mental model used and the form of the intuition is dependent upon the question being answered." (Roger Frantz, "Two Minds", 2005)

"We must begin by distinguishing between visual mental imagery and visual perception: Visual perception occurs while a stimulus is being viewed, and includes functions such as visual recognition (i. e., registering that a stimulus is familiar) and identification (i. e., recalling the name, context, or other information associated with the object). Two types of mechanisms are used in visual perception: ‘bottom-up’ mechanisms are driven by the input from the eyes; in contrast, ‘top-down’ mechanisms make use of stored information (such as knowledge, belief, expectations, and goals). Visual mental imagery is a set of representations that gives rise to the experience of viewing a stimulus in the absence of appropriate sensory input. In this case, information in memory underlies the internal events that produce the experience. Unlike afterimages, mental images are relatively prolonged." (Stephen M Kosslyn, "Mental images and the brain", Cognitive Neuropsychology 22, 2005)

"When a particular image appears in the mind's eye often enough it begins to connect apparently unrelated ideas leading to models and theories. […] Patterns experienced again and again become intuitions. […] Intuitive judgments are made by our use of imagery; intuition is the result of mental model building. […] The mental model used and the form of the intuition is dependent upon the question being answered." (Roger Frantz, "Two Minds", 2005)

"Often our mental models serve a very useful and practical purpose by helping us to make very quick sense of our experiences and interactions. However, the danger for us is that our mental models do not always reflect the truth, i.e. the way things really are. Often they reflect what we believe to be true, and sometimes we get it wrong." (John Middleton, "Upgrade Your Brain: 52 brilliant ideas for everyday genius", 2006)

"Our inner working models, therefore, function as interpretation schemes, on the basis of which we organize our experiences. But, such schemes also distort reality in the direction of our pattern of expectations. In short: such working models organize and screen our experiences. This means that such an inner working model organizes and colours our perception of things in such a way that it can be extremely stimulating but can also sometimes slow us down considerably." (M H M de Wolf, "Freud and Mahler", 2007)

"A worldview must be coherent, logical and adequate. Coherence means that the fundamental ideas constituting the worldview must be seen as proceeding from a single, unifying, overarching concept. A logical worldview means simply that the various ideas constituting it should not be contradictory. Adequate means that it is capable of explaining, logically and coherently, every element of contemporary experience." (M. G. Jackson, "Transformative Learning for a New Worldview: Learning to Think Differently", 2008)

"Actually, around 80% of the data we use to make decisions is already in our heads before we engage with a situation. Our power to perceive is governed and limited by cognitive filters, sometimes termed our ‘mental model’. Mental models are formed as a result of past experience, knowledge and attitudes. They are deeply ingrained, often subconscious, structures that limit what we perceive and also colour our interpretation of supposed facts." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010)

"We all have mental models: the lens through which we see the world that drive our responses to everything we experience. Being aware of your mental models is key to being objective." (Elizabeth Thornton, "Learn to Be an Objective Leader without Losing Everything", 2015)

"When a culture is founded on the principle of immediacy of experience, there is no need for numeracy. It is impossible to consume more than one thing at a time, so differentiating between 'a small amount', 'a larger amount' and 'many' is enough for survival." (The Open University, "Understanding the environment: learning and communication", 2016)