🏷️Knowledge Representation: On Idealization (Quotes)

"We may be thinking out a chain of reasoning in abstract Geometry, but if we draw a figure, as we usually must do in order to fix our ideas and prevent our attention from wandering owing to the difficulty of keeping a long chain of syllogisms in our minds, it is excusable if we are apt to forget that we are not in reality reasoning about the objects in the figure, but about objects which ore their idealizations, and of which the objects in the figure are only an imperfect representation. Even if we only visualize, we see the images of more or less gross physical objects, in which various qualities irrelevant for our specific purpose are not entirely absent, and which are at best only approximate images of those objects about which we are reasoning." (Ernest W Hobson, "Squaring the Circle", 1913)

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

"For the mathematician, the physical way of thinking is merely the starting point in a process of abstraction or idealization. Instead of being a dot on a piece of paper or a particle of dust suspended in space, a point becomes, in the mathematician's ideal way of thinking, a set of numbers or coordinates. In applied mathematics we must go much further with this process because the physical problems under consideration are more complex. We first view a phenomenon in the physical way, of course, but we must then go through a process of idealization to arrive at a more abstract representation of the phenomenon which will be amenable to mathematical analysis." (Peter Lancaster, "Mathematics: Models of the Real World", 1976)

"[…] 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)

"Through modeling, scientists manipulate symbols with meanings to represent an environment with structure. Such manipulations take place to fulfill a human need, solve a problem, or create a product. When constructing a model, one works in the cognitive space of ideas. Models are used to encapsulate, highlight, replicate or represent patterns of events and the structures of things. Of course, no model provides an exact duplication of the subject matter being modeled. Details are hidden, features are skewed, and certain properties are emphasized. Models are abstract and idealized. As an abstraction, a model omits some features of the subject matter, while retaining only significant properties. As an idealization, a model depicts a subject's properties in a more perfect form." (Daniel Rothbart [Ed.], "Modeling: Gateway to the Unknown", 2004)

"The intent of these representations is to capture the relevant characteristics of reality, which may overlap but are not identical in each case. The engineer has to ascertain what those are, and then incorporate appropriate assumptions and simplifications accordingly. Two common strategies are abstraction, which involves neglecting certain aspects of reality in order to gain a better understanding of the remaining aspects; and idealization, which involves replacing a complicated and/or complex aspect of reality with a simplified version." (Jon A Schmidt, "Representation and Reality", Structure [magazine], 2015)

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

🦋Science: On Trial and Error (Quotes)

"The one lesson that comes out of all our theorizing and experimenting is that there is only one really scientific progressive method; and that is the method of trial and error." (George B Shaw, "The Doctor's Dilemma: Preface on Doctors", 1909)

"There are many men now living who were in the habit of using the age-old expression: 'It is as impossible as flying.' The discoveries in physical science, the triumphs in invention, attest the value of the process of trial and error. In large measure, these advances have been due to experimentation." (Louis Brandeis, "Dissent, New State Ice Co. v. Liebmann, 285 U.S. 262", 1932)

"The discoveries in physical science, the triumphs in invention, attest the value of the process of trial and error. In large measure, these advances have been due to experimentation." (Louis Brandeis, "Judicial opinions", 1932)

"But I believe that there is no philosophical high-road in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed. We do not find signposts at cross-roads, but our own scouts erect them, to help the rest." (Max Born, "Experiment and Theory in Physics", 1943)

"The method of learning by trial and error - of learning from our mistakes - seems to be fundamentally the same whether it is practised by lower or by higher animals, by chimpanzees or by men of science." (Karl Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"The difference between the amoeba and Einstein is that, although both make use of the method of trial and error elimination, the amoeba dislikes erring while Einstein is intrigued by it [...]" (Karl R Popper, "Objective Knowledge: An Evolutionary Approach", 1972) 

"Science progresses by trial and error, by conjectures and refutations. Only the fittest theories survive." (Alan Chalmers, "What Is This Thing Called Science?", 1976)

"The great revolutions in science are almost always the result of unexpected intuitive leaps. After all, what is science if not the posing of difficult puzzles by the universe? Mother Nature does something interesting, and challenges the scientist to figure out how she does it. In many cases the solution is not found by exhaustive trial and error […] or even by a deduction based on the relevant knowledge." (Martin Gardner, "Aha! Insight", 1978)

"I believe people can solve complex problems eventually. By repeated trial and error they will get there; but they need a long time. At this point I agree with Herbert Simon. People do not learn immediately, as those rational expectations models seem to imply. I don't believe that. The statement that assumptions do not matter is nonsense. It is funny. Yes, I assume people are consistent in their behavior. I assume that not because I believe everybody actually is, but because I believe, on the average, you do not get too far from it." (Franco Modigliani, "Conversations with Economists", 1983)

"Science usually amounts to a lot more than blind trial and error. Good statistics consists of much more than just significance tests; there are more sophisticated tools available for the analysis of results, such as confidence statements, multiple comparisons, and Bayesian analysis, to drop a few names. However, not all scientists are good statisticians, or want to be, and not all people who are called scientists by the media deserve to be so described." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"Whatever humans have learned had to be learned as a consequence only of trial and error experience. Humans have learned only through mistakes." (R Buckminster Fuller, "Intuition", 1983)

"Growth is a process of experimentation, a series of trials, errors, and occasional victories. The failed experiments are as much as part of the process as the experiments that work." (Chérie Carter-Scott, "If Life Is a Game, These Are the Rules", 1998)

"The natural as well as the social sciences always start from problems, from the fact that something inspires amazement in us, as the Greek philosophers used to say. To solve these problems, the sciences use fundamentally the same method that common sense employs, the method of trial and error. To be more precise, it is the method of trying out solutions to our problem and then discarding the false ones as erroneous. This method assumes that we work with a large number of experimental solutions. One solution after another is put to the test and eliminated." (Karl R Popper, "All Life is Problem Solving", 1999)

"We can simplify the relationships between fragility, errors, and antifragility as follows. When you are fragile, you depend on things following the exact planned course, with as little deviation as possible - for deviations are more harmful than helpful. This is why the fragile needs to be very predictive in its approach, and, conversely, predictive systems cause fragility. When you want deviations, and you don’t care about the possible dispersion of outcomes that the future can bring, since most will be helpful, you are antifragile. Further, the random element in trial and error is not quite random, if it is carried out rationally, using error as a source of information. If every trial provides you with information about what does not work, you start zooming in on a solution - so every attempt becomes more valuable, more like an expense than an error. And of course you make discoveries along the way." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

❄️Systems Thinking: On Idealization (Quotes)

"It is difficult, however, to learn all these things from situations such as occur in everyday life. What we need is a series of abstract and quite impersonal situations to argue about in which one side is surely right and the other surely wrong. The best source of such situations for our purposes is geometry. Consequently we shall study geometric situations in order to get practice in straight thinking and logical argument, and in order to see how it is possible to arrange all the ideas associated with a given subject in a coherent, logical system that is free from contradictions. That is, we shall regard the proof of each proposition of geometry as an example of correct method in argumentation, and shall come to regard geometry as our ideal of an abstract logical system. Later, when we have acquired some skill in abstract reasoning, we shall try to see how much of this skill we can apply to problems from real life." (George D Birkhoff & Ralph Beately, "Basic Geometry", 1940)

"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12 (4), 1945)

"In fact, it is empirically ascertainable that every event is actually produced by a number of factors, or is at least accompanied by numerous other events that are somehow connected with it, so that the singling out involved in the picture of the causal chain is an extreme abstraction. Just as ideal objects cannot be isolated from their proper context, material existents exhibit multiple interconnections; therefore the universe is not a heap of things but a system of interacting systems." (Mario Bunge, "Causality: The place of the casual principles in modern science", 1959)

"There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction." (Thomas Merton, "The Secular Journal of Thomas Merton", 1959)

"[…] if a system is sufficiently complicated, the time it takes to return near a state already visited is huge (think of the hundred fleas on the checkerboard). Therefore if you look at the system for a moderate amount of time, eternal return is irrelevant, and you had better choose another idealization." (David Ruelle, "Chance and Chaos", 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)

"Formulation of a mathematical model is the first step in the process of analyzing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to be modelled and to the specific information one is interested in. Thus, the aim of modelling is to produce an idealized description of reality, which is both expressible in a tractable mathematical form and sufficiently close to reality as far as the physical mechanisms of interest are concerned." (Francois Axisa, "Discrete Systems" Vol. I, 2001)

"A first important remark is that nature gives us mathematical hints. […] A second important remark is that mathematical physics deals with idealized systems. […] The third important remark is that nature may hint at a theorem but does not state clearly under which conditions is true." (David Ruelle, "The Mathematician's Brain", 2007)

"Cellular automata (CA) are idealizations of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states." (Andreas Schadschneider et al, "Vehicular Traffic II: The Nagel–Schreckenberg Model", 2011)

"Abstract formulations of simply stated concrete ideas are often the result of efforts to create idealized models of complex systems. The models are 'idealized' in the sense that they retain only the most fundamental properties of the original systems. The vocabulary is chosen to be as inclusive as possible so that research into the model reveals facts about a wide variety of similar systems. Unfortunately, it is often the case that over time the connection between a model and the systems on which it was based is lost, and the interested reader is faced with something that looks as if it were created to be deliberately complicated - deliberately confusing - but the original intention was just the opposite. Often, the model was devised to be simpler and more transparent than any of the systems on which it was based." (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)

"Stated loosely, models are simplified, idealized and approximate representations of the structure, mechanism and behavior of real-world systems. From the standpoint of set-theoretic model theory, a mathematical model of a target system is specified by a nonempty set - called the model’s domain, endowed with some operations and relations, delineated by suitable axioms and intended empirical interpretation." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])

🏷️Knowledge Representation: On Causal Maps (Quotes)

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

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

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

"The concepts a person uses are represented as points, and the causal links between these concepts are represented as arrows between these points. This gives a pictorial representation of the causal assertions of a person as a graph of points and arrows. This kind of representation of assertions as a graph will be called a cognitive map. The policy alternatives, all of the various causes and effects, the goals, and the ultimate utility of the decision maker can all be thought of as concept variables, and represented as points in the cognitive map. The real power of this approach ap pears when a cognitive map is pictured in graph form; it is then relatively easy to see how each of the concepts and causal relation ships relate to each other, and to see the overall structure of the whole set of portrayed assertions." (Robert Axelrod, "The Cognitive Mapping Approach to Decision Making" [in "Structure of Decision: The Cognitive Maps of Political Elites"], 1976)

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

"A fuzzy cognitive map or FCM draws a causal picture. It ties facts and things and processes to values and policies and objectives. And it lets you predict how complex events interact and play out. [...] Neural nets give a shortcut to tuning an FCM. The trick is to let the fuzzy causal edges change as if they were synapses in a neural net. They cannot change with the same math laws because FCM edges stand for causal effect not signal flow. We bombard the FCM nodes with real data. The data state which nodes are on or off and to which degree at each moment in time. Then the edges grow among the nodes."  (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"Under the label 'cognitive maps', mental models have been conceived of as the mental representation of spatial aspects of the environment. A mental model, in this sense, comprises the topology of an area, including relevant districts, landmarks, and paths." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)

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

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

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

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

"Causal mapping is a technique that is used to elicit and represent domain knowledge of experts in the form of a graphical network called a causal map. A causal map (also called an influence diagram or a cause map) is a directed graph in which causal concepts (or nodes) represent the important variables that make up a domain. Causal connections are the directed arrows that connect these concepts to represent causal relationships between the variables." (S Nadkarni, Aggregated causal maps: An approach to elicit and aggregate the knowledge of multiple experts, 2003) 

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

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

🏷️Knowledge Representation: On Mind Maps (Quotes)

"A mind map harnesses the full range of cortical skills—word, image, number, logic, rhythm, color, and spatial awareness - in a single, uniquely powerful technique. In doing so, it gives you the freedom to roam the infinite expanse of your brain." (Tony Buzan, Barry Buzan, "The Mind Map Book: How to Use Radiant Thinking to Maximize Your Brain's Untapped Potential", 1996)

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

"An effective mind map is one that works for you and therefore it is your tailoring and your emphasis, images, colours, codes and style that will determine its effectiveness. Try to develop the habit of taking down all your notes in mind map format. If you are required to give presentations, do this from a mind map. When you are at meetings, take down the minutes in mind map layout and just notice the difference in your ability to retain exactly what happened at that meeting and compare it with your usual logical/analytical method of recording minutes." (Peter F Haddon, Mastering Personal and Interpersonal Skills, 1999)

"Mind mapping is a technique whereby information is summarised in a form of pictorial representation which depends very much on the creativity of the individual involved. The idea is that when information is pictured in colourful word associations backed up by sketches or even stick drawings of the key words, it is far more easily remembered, much like when looking at a photograph you can recall in detail the happenings that led up to and followed the incident." (Peter F Haddon, Mastering Personal and Interpersonal Skills, 1999)

"Knowledge maps are node-link representations in which ideas are located in nodes and connected to other related ideas through a series of labeled links. They differ from other similar representations such as mind maps, concept maps, and graphic organizers in the deliberate use of a common set of labeled links that connect ideas. Some links are domain specific (e.g., function is very useful for some topic domains...) whereas other links (e.g., part) are more broadly used. Links have arrowheads to indicate the direction of the relationship between ideas." (Angela M O’Donnell et al, "Knowledge Maps as Scaffolds for Cognitive Processing", Educational Psychology Review Vol. 14 (1), 2002) 

"Mind Mapping uses the full range of the brain's abilities, placing an image in the center of the page in order to facilitate memorization and the creative generation of ideas, and subsequently branches out in associative networks that mirror externally the brain's internal structures. By using this approach, the preparation of speeches can be reduced in time from days to minutes; problems can be solved both more comprehensively and more rapidly; memory can be improved from absent to perfect; and creative thinkers can generate a limitless number of ideas rather than a truncated list." Marshall Goldsmith et al, "The Many Facets of Leadership", 2002)

"[a mind map is a] "visual note-taking process that includes key words and pictures illustrating the relationships among concepts." (Ruth Colvin Clark, Chopeta Lyons, "Graphics for Learning: Proven guidelines for planning, designing, and evaluating visuals in training materials" 2nd ed., 2011)

"Data visualizations can also play a critical role when it is time to disseminate and communicate evaluation findings. Data visualization engages and supports program stakeholders by increasing their capacity to understand data and participate in the evaluation process. Collaboratively developed mind maps, logic models, and graphic illustrations can facilitate understanding of the findings and their implications by depicting a program’s most important activities, outcomes, and ultimate goal in a concise and clear manner. Well-designed interactive visualizations for reporting and community engagement help stakeholders answer questions of import within context and place engaged stakeholders in the driver’s seat in terms of defining variables and interpreting results." (Tarek Azzam et al, "Data Visualization and Evaluation", "Data visualization, part 1: New Directions for Evaluation", 139], 2013)

"Paradoxically one of the greatest advantages of mind maps is that they are seldom needed again. The very act of constructing a map is itself so effective in fixing ideas in memory that very often a whole map can recalled without going back to it at all. A mind map is so strongly visual and uses so many of the natural functions of memory that frequently it can be simply read off in the mind's eye." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 2013)

"With the adoption of a more schematic and abstract construct, deprived of realistic arboreal features, a tree diagram could sometimes be rotated along its axis and depicted horizontally, with its ranks arranged most frequently from left to right. Horizontal trees probably emerged as an alternative to vertical trees to address spatial constraints and layout requirements, but they also provide unique advantages. The nesting arrangement of horizontal trees resembles the grammatical construct of a sentence, echoing a natural reading pattern that anyone can relate to. This alternative scheme was often deployed on facing pages of a manuscript, with the root of the tree at the very center, creating a type of mirroring effect that is still found in many digital and interactive executions. Horizontal trees have proved highly efficient for archetypal models such as classification trees, flow charts, mind maps, dendrograms, and, notably, in the display of files on several software applications and operating systems." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"Essentially, a mind map is a type of node-link diagram in which the nodes represent concepts and the links represent relationships between concepts. The central idea to be explored is placed in the middle of the page and it is expanded out from there. Usually mind maps are drawn as tree structures with no cross links between branches, but this can be restrictive." (Colin Ware, "Information Visualization: Perception for Design" 4th Ed., 2021)

"The educational use of mind maps and concept maps would seem to fit well with constructivist theory. To construct such a map, students must actively draw out links between various concepts as they understand them. The problem is that the cognitive engagement tends to be somewhat superficial for mind maps, since it does not require that students think deeply about the nature of the links." (Colin Ware, "Information Visualization: Perception for Design" 4th Ed., 2021)

"Idea mapping offers the power to represent qualitative data, describe relationships, and enable one to see the 'big picture'. Further, mapping allows us to represent data in a way that facilitates the conceptualizing of its meaning. It provides a 'map', which makes it possible to observe macrophenomena, discover trends, and generate creative options. Idea mapping makes it possible to represent multiple dimensions of a situation without losing sight of any of its parts; it is an efficient way to manage an overwhelming amount of qualitative information. Finally, it offers a way to present information to clients in a graphic form that is both easy to understand and data rich. Often, an entire strategic plan can be represented in one map." (Terry Moore)

❄️Systems Thinking: On Sustainability (Quotes)

"Nature, displayed in its full extent, presents us with an immense tableau, in which all the order of beings are each represented by a chain which sustains a continuous series of objects, so close and so similar that their difference would be difficult to define. This chain is not a simple thread which is only extended in length, it is a large web or rather a network, which, from interval to interval, casts branches to the side in order to unite with the networks of another order." (Comte Georges-Louis Leclerc de Buffon, "Les Oiseaux Qui Ne Peuvent Voler", Histoire Naturelle des Oiseaux Vol. I, 1770)

"These, then, are some of the basic principles of ecology - interdependence, recycling, partnership, flexibility, diversity, and, as a consequence of all those, sustainability... the survival of humanity will depend on our ecological literacy, on our ability to understand these principles of ecology and live accordingly." (Fritjof Capra, "The Web of Life", 1996)

"The key to understanding the future is one word: sustainability." (Patrick Dixon, "Futurewise", 1998)

"Organizations need to undergo fundamental changes, both in order to adapt to the new business environment and to become ecologically sustainable." (Fritjof Capra, "The Hidden Connections", 2002)

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

"This new model of development would be based clearly on the goal of sustainable human well-being. It would use measures of progress that clearly acknowledge this goal. It would acknowledge the importance of ecological sustainability, social fairness, and real economic efficiency. Ecological sustainability implies recognizing that natural and social capital are not infinitely substitutable for built and human capital, and that real biophysical limits exist to the expansion of the market economy." (Robert Costanza, "Toward a New Sustainable Economy", 2008)

“Sustainability encompasses both financial sustainability (the ability to generate resources to meet the needs of the present without compromising the future) and programmatic sustainability (the ability to develop, mature, and cycle out programs to be responsive to constituencies over time).” (Jan Masaoka et al, "Nonprofit Sustainability", 2010)

"The term (Sustainability) has become so widely used that it is in danger of meaning nothing. It has been applied to all manner of activities in an effort to give those activities the gloss of moral imperative, the cachet of environmental enlightenment. 'Sustainable' has been used variously to mean 'politically feasible', 'economically feasible', 'not part of a pyramid or bubble' ,' socially enlightened', 'consistent with neoconservative small-government dogma' ,' consistent with liberal principles of justice and fairness', 'morally desirable' , and, at its most diffuse, 'sensibly far-sighted'.” (Eric Zencey, "Theses on Sustainability", Orion, 2010) 

"To find our steady state and solve the sustainability puzzle, we need to abandon the relentless quest for dominance. We need to abandon our visions of progress as growth... Only progress in diversity, equality, and beauty can stand the test of time. We need to live within our limits." (Steve Hallett,"The Efficiency Trap", 2013)

"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)

"The goal of a system dynamics approach is to understand how a dynamic pattern of behaviour is generated by a system and to find leverage points within the system structure that have the potential to change the problematic trend to a more desirable one. The key steps in a system dynamics approach are identifying one or more trends that characterise the problem, describing the structure of the system generating the behaviour and finding and testing leverage points in the system to change the problematic behaviour. System dynamics is an appropriate modelling approach for sustainability questions because of the long-term perspective and feedback dynamics inherent in such questions." (Bilash K Bala et al, "System Dynamics: Modelling and Simulation", 2017)

❄️Systems Thinking: On Connectedness (Quotes)

"The first attempts to consider the behavior of so-called 'random neural nets' in a systematic way have led to a series of problems concerned with relations between the 'structure' and the 'function' of such nets. The 'structure' of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of 'this' neuron synapsing on 'that' one, but rather in terms of tendencies and probabilities associated with points or regions in the net." (Anatol Rapoport, "Cycle distributions in random nets", The Bulletin of Mathematical Biophysics 10(3), 1948)

"A NETWORK is a collection of connected lines, each of which indicates the movement of some quantity between two locations. Generally, entrance to a network is via a source (the starting point) and exit from a network is via a sink (the finishing point); the lines which form the network are called links (or arcs), and the points at which two or more links meet are called nodes." (Cecil W Lowe, "Critical Path Analysis by Bar Chart", 1966)

"The essential vision of reality presents us not with fugitive appearances but with felt patterns of order which have coherence and meaning for the eye and for the mind. Symmetry, balance and rhythmic sequences express characteristics of natural phenomena: the connectedness of nature - the order, the logic, the living process. Here art and science meet on common ground." (Gyorgy Kepes, "The New Landscape: In Art and Science", 1956)

"In fact, it is empirically ascertainable that every event is actually produced by a number of factors, or is at least accompanied by numerous other events that are somehow connected with it, so that the singling out involved in the picture of the causal chain is an extreme abstraction. Just as ideal objects cannot be isolated from their proper context, material existents exhibit multiple interconnections; therefore the universe is not a heap of things but a system of interacting systems." (Mario Bunge, "Causality: The place of the casual principles in modern science", 1959)

"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […]  'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 1979)

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

"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. [...] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", 1988)

"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)

"Nodes and connectors comprise the structure of a network. In contrast, an ecology is a living organism. It influences the formation of the network itself." (George Siemens, "Knowing Knowledge", 2006)

"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"Networks may also be important in terms of view. Many models assume that agents are bunched together on the head of a pin, whereas the reality is that most agents exist within a topology of connections to other agents, and such connections may have an important influence on behavior. […] Models that ignore networks, that is, that assume all activity takes place on the head of a pin, can easily suppress some of the most interesting aspects of the world around us. In a pinhead world, there is no segregation, and majority rule leads to complete conformity - outcomes that, while easy to derive, are of little use." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"Complexity theory embraces things that are complicated, involve many elements and many interactions, are not deterministic, and are given to unexpected outcomes. […] A fundamental aspect of complexity theory is the overall or aggregate behavior of a large number of items, parts, or units that are entangled, connected, or networked together. […] In contrast to classical scientific methods that directly link theory and outcome, complexity theory does not typically provide simple cause-and-effect explanations." (Robert E Gunther et al, "The Network Challenge: Strategy, Profit, and Risk in an Interlinked World", 2009)

"The simplest basic architecture of an artificial neural network is composed of three layers of neurons - input, output, and intermediary (historically called perceptron). When the input layer is stimulated, each node responds in a particular way by sending information to the intermediary level nodes, which in turn distribute it to the output layer nodes and thereby generate a response. The key to artificial neural networks is in the ways that the nodes are connected and how each node reacts to the stimuli coming from the nodes it is connected to. Just as with the architecture of the brain, the nodes allow information to pass only if a specific stimulus threshold is passed. This threshold is governed by a mathematical equation that can take different forms. The response depends on the sum of the stimuli coming from the input node connections and is 'all or nothing'." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

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

"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)

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 2013) 

❄️Systems Thinking: On Boundaries (Quotes)

"A state of equilibrium in a system does not mean, further, that the system is without tension. Systems can, on the contrary, also come to equilibrium in a state of tension (e.g., a spring under tension or a container with gas under pressure).The occurrence of this sort of system, however, presupposes a certain firmness of boundaries and actual segregation of the system from its environment (both of these in a functional, not a spatial, sense). If the different parts of the system are insufficiently cohesive to withstand the forces working toward displacement (i.e., if the system shows insufficient internal firmness, if it is fluid), or if the system is not segregated from its environment by sufficiently firm walls but is open to its neighboring systems, stationary tensions cannot occur. Instead, there occurs a process in the direction of the forces, which encroaches upon the neighboring regions with diffusion of energy and which goes in the direction of an equilibrium at a lower level of tension in the total region. The presupposition for the existence of a stationary state of tension is thus a certain firmness of the system in question, whether this be its own inner firmness or the firmness of its walls." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)

"A system is difficult to define, but it is easy to recognize some of its characteristics. A system possesses boundaries which segregate it from the rest of its field: it is cohesive in the sense that it resists encroachment from without […]" (Marvin G Cline, "Fundamentals of a theory of the self: some exploratory speculations‎", 1950)

"In the minds of many writers systems engineering is synonymous with component selection and interface design; that is, the systems engineer does not design hardware but decides what types of existing hardware shall be coupled and how they shall be coupled. Complete agreement that this function is the essence of systems engineering will not be found here, for, besides the very important function of systems engineering in systems analysis, there is the role played by systems engineering in providing boundary conditions for hardware design." (A Wayne Wymore, "A Mathematical Theory of Systems Engineering", 1967)

"To model the dynamic behavior of a system, four hierarchies of structure should be recognized: closed boundary around the system; feedback loops as the basic structural elements within the boundary; level variables representing accumulations within the feedback loops; rate variables representing activity within the feedback loops." (Jay W Forrester, "Urban Dynamics", 1969)

"General systems theory is the scientific exploration of 'wholes' and 'wholeness' which, not so long ago, were considered metaphysical notions transcending the boundaries of science. Hierarchic structure, stability, teleology, differentiation, approach to and maintenance of steady states, goal-directedness - these are a few of such general system properties." (Ervin László, "Introduction to Systems Philosophy", 1972)

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

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

"When a system has more than one attractor, the points in phase space that are attracted to a particular attractor form the basin of attraction for that attractor. Each basin contains its attractor, but consists mostly of points that represent transient states. Two contiguous basins of attraction will be separated by a basin boundary." (Edward N Lorenz, "The Essence of Chaos", 1993)

"To avoid policy resistance and find high leverage policies requires us to expand the boundaries of our mental models so that we become aware of and understand the implications of the feedbacks created by the decisions we make. That is, we must learn about the structure and dynamics of the increasingly complex systems in which we are embedded." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000)

"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

❄️Systems Thinking: On Loops (Quotes)

"A state of equilibrium in a system does not mean, further, that the system is without tension. Systems can, on the contrary, also come to equilibrium in a state of tension (e.g., a spring under tension or a container with gas under pressure).The occurrence of this sort of system, however, presupposes a certain firmness of boundaries and actual segregation of the system from its environment (both of these in a functional, not a spatial, sense). If the different parts of the system are insufficiently cohesive to withstand the forces working toward displacement (i.e., if the system shows insufficient internal firmness, if it is fluid), or if the system is not segregated from its environment by sufficiently firm walls but is open to its neighboring systems, stationary tensions cannot occur. Instead, there occurs a process in the direction of the forces, which encroaches upon the neighboring regions with diffusion of energy and which goes in the direction of an equilibrium at a lower level of tension in the total region. The presupposition for the existence of a stationary state of tension is thus a certain firmness of the system in question, whether this be its own inner firmness or the firmness of its walls." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)

"A system is difficult to define, but it is easy to recognize some of its characteristics. A system possesses boundaries which segregate it from the rest of its field: it is cohesive in the sense that it resists encroachment from without […]" (Marvin G Cline, "Fundamentals of a theory of the self: some exploratory speculations‎", 1950)

"In the minds of many writers systems engineering is synonymous with component selection and interface design; that is, the systems engineer does not design hardware but decides what types of existing hardware shall be coupled and how they shall be coupled. Complete agreement that this function is the essence of systems engineering will not be found here, for, besides the very important function of systems engineering in systems analysis, there is the role played by systems engineering in providing boundary conditions for hardware design." (A Wayne Wymore, "A Mathematical Theory of Systems Engineering", 1967)

"To model the dynamic behavior of a system, four hierarchies of structure should be recognized: closed boundary around the system; feedback loops as the basic structural elements within the boundary; level variables representing accumulations within the feedback loops; rate variables representing activity within the feedback loops." (Jay W Forrester, "Urban Dynamics", 1969)

"General systems theory is the scientific exploration of 'wholes' and 'wholeness' which, not so long ago, were considered metaphysical notions transcending the boundaries of science. Hierarchic structure, stability, teleology, differentiation, approach to and maintenance of steady states, goal-directedness - these are a few of such general system properties." (Ervin László, "Introduction to Systems Philosophy", 1972)

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

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

"When a system has more than one attractor, the points in phase space that are attracted to a particular attractor form the basin of attraction for that attractor. Each basin contains its attractor, but consists mostly of points that represent transient states. Two contiguous basins of attraction will be separated by a basin boundary." (Edward N Lorenz, "The Essence of Chaos", 1993)

"To avoid policy resistance and find high leverage policies requires us to expand the boundaries of our mental models so that we become aware of and understand the implications of the feedbacks created by the decisions we make. That is, we must learn about the structure and dynamics of the increasingly complex systems in which we are embedded." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000)

"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

❄️Systems Thinking: On Parsimony (Quotes)

"A mechanistic model has the following advantages: 1. It contributes to our scientific understanding of the phenomenon under study. 2. It usually provides a better basis for extrapolation (at least to conditions worthy of further experimental investigation if not through the entire range of all input variables). 3. It tends to be parsimonious (i. e, frugal) in the use of parameters and to provide better estimates of the response." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)

"It is part of the lore of science that the most parsimonious explanation of observed facts is to be preferred over convoluted and long-winded theories. Ptolemaic epicycles gave way to the Copernican system largely on this premise, and in general, scientific inquiry is governed by the oft-quoted dictum of the medieval cleric William of Occam that 'nunquam ponenda est pluralitas sine necesitate' , which may be paraphrased as 'choose the simplest explanation for the observed facts' ." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"A smaller model with fewer covariates has two advantages: it might give better predictions than a big model and it is more parsimonious (simpler). Generally, as you add more variables to a regression, the bias of the predictions decreases and the variance increases. Too few covariates yields high bias; this called underfitting. Too many covariates yields high variance; this called overfitting. Good predictions result from achieving a good balance between bias and variance. […] fiding a good model involves trading of fit and complexity." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"The model theory postulates that mental models are parsimonious. They represent what is possible, but not what is impossible, according to assertions. This principle of parsimony minimizes the load on working memory, and so it applies unless something exceptional occurs to overrule it." (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)

"Two systems concepts lie at the disposal of the architect to reflect the beauty of harmony: parsimony and variety. The law of parsimony states that given several explanations of a specific phenomenon, the simplest is probably the best. […] On the other hand, the law of requisite variety states that for a system to survive in its environment the variety of choice that the system is able to make must equal or exceed the variety of influences that the environment can impose on the system." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"What advantages do diagrams have over verbal descriptions in promoting system understanding? First, by providing a diagram, massive amounts of information can be presented more efficiently. A diagram can strip down informational complexity to its cor. e - in this sense, it can result in a parsimonious, minimalist description of a system. Second, a diagram can help us see patterns in information and data that may appear disordered otherwise. For example, a diagram can help us see mechanisms of cause and effect or can illustrate sequence and flow in a complex system. Third, a diagram can result in a less ambiguous description than a verbal description because it forces one to come up with a more structured description." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)

"The idea of a machine thinking is by no means repugnant to all of us. In fact, I find the converse idea, that the human brain may itself be a machine which could be possibly duplicated functionally with inanimate objects, quite attractive. Until clearly disproved, this hypothesis concerning the brain seems the natural scientific one in line with the principle of parsimony, etc., rather than hypothecating intangible and unreachable 'vital forces' , 'souls' and the like." (Claude E Shannon)