On Insight (1950-1959)

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

"Another approach for a given problem is to try to restate it in just as many different forms as you can. Change the words. Change the viewpoint. Look at it from every possible angle. After you’ve done that, you can try to look at it from several angles at the same time and perhaps you can get an insight into the real basic issues of the problem, so that you can correlate the important factors and come out with the solution." (Claude E Shannon, "Creative Thinking", 1952)

"Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practice to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuitions of man." (Morris Kline, "Mathematics in Western Culture", 1953)

"Finally, students must learn to realize that mathematics is a science with a long history behind it, and that no true insight into the mathematics of the present day can be obtained without some acquaintance with its historical background. In the first-place time gives an additional dimension to one's mental picture both of mathematics as a whole, and of each individual branch." (André Weil, "The Mathematical Curriculum", 1954)

"Mathematics, springing from the soil of basic human experience with numbers and data and space and motion, builds up a far-flung architectural structure composed of theorems which reveal insights into the reasons behind appearances and of concepts which relate totally disparate concrete ideas." (Saunders MacLane, "Of Course and Courses"The American Mathematical Monthly, Vol 61, No 3, 1954)

"By far the most important consequence of the conceptual revolution brought about in physics by relativity and quantum theory lies not in such details as that meter sticks shorten when they move or that simultaneous position and momentum have no meaning, but in the insight that we had not been using our minds properly and that it is important to find out how to do so." (Percy W Bridgman, "Quo Vadis", 1958)

On Insight (1900-1949)

"Not only virtue, but also insight, not only sanctity but also wisdom, are the duties and tasks of mankind." (Otto Weininger, "Sex and Character", 1903)

"The introduction into geometrical work of conceptions such as the infinite, the imaginary, and the relations of hyperspace, none of which can be directly imagined, has a psychological significance well worthy of examination. It gives a deep insight into the resources and working of the human mind. We arrive at the borderland of mathematics and psychology." (John Theodore Merz, "History of European Thought in the Nineteenth Century", 1903)

"The mathematical formula is the point through which all the light gained by science passes in order to be of use to practice; it is also the point in which all knowledge gained by practice, experiment, and observation must be concentrated before it can be scientifically grasped. The more distant and marked the point, the more concentrated will be the light coming from it, the more unmistakable the insight conveyed. All scientific thought, from the simple gravitation formula of Newton, through the more complicated formulae of physics and chemistry, the vaguer so called laws of organic and animated nature, down to the uncertain statements of psychology and the data of our social and historical knowledge, alike partakes of this characteristic, that it is an attempt to gather up the scattered rays of light, the different parts of knowledge, in a focus, from whence it can be again spread out and analyzed, according to the abstract processes of the thinking mind. But only when this can be done with a mathematical precision and accuracy is the image sharp and well-defined, and the deductions clear and unmistakable. As we descend from the mechanical, through the physical, chemical, and biological, to the mental, moral, and social sciences, the process of focalization becomes less and less perfect, - the sharp point, the focus, is replaced by a larger or smaller circle, the contours of the image become less and less distinct, and with the possible light which we gain there is mingled much darkness, the sources of many mistakes and errors. But the tendency of all scientific thought is toward clearer and clearer definition; it lies in the direction of a more and more extended use of mathematical measurements, of mathematical formulae." (John T Merz, "History of European Thought in the 19th Century" Vol. 1, 1904)

"The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And the value of mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason." (William E Chancellor,"A Theory of Motives, Ideals and Values in Education" 1907)

"In fact, the opposition of instinct and reason is mainly illusory. Instinct, intuition, or insight is what first leads to the beliefs which subsequent reason confirms or confutes; but the confirmation, where it is possible, consists, in the last analysis, of agreement with other beliefs no less instinctive. Reason is a harmonising, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new." (Bertrand Russell, "Our Knowledge of the External World", 1914)

"No student ought to complete a course in mathematics without the feeling that there must be something in it, without catching a glimpse, however fleeting, of its possibilities, without at least a few moments of pleasure in achievement and insight." (Helen A Merrill, 'Why Students Fail in Mathematics", The Mathematics Teacher, 1918) 

"Mathematics is the foe of nature and of insight into nature. A human being who possesses mathematical knowledge, the lingo of formulas, and with it approaches nature, must be like a woman who, with soaped hands, wants to grab a fish: surely, she will not seize it. Yet it is an unprecedented arrogance of mathematicians to pose in front of the world and of nature, and to say that they only had eyes for things." (Alfred Döblin, "Die abscheuliche Relativitätslehre" ["The Abominable Relativity Theory"], Berliner Tageblatt, 1923)

"The axioms and provable theorems (i.e. the formulas that arise in this alternating game [namely formal deduction and the adjunction of new axioms]) are images of the thoughts that make up the usual procedure of traditional mathematics; but they are not themselves the truths in the absolute sense. Rather, the absolute truths are the insights (Einsichten) that my proof theory furnishes into the provability and the consistency of these formal systems." (David Hilbert; "Die logischen Grundlagen der Mathematik." Mathematische Annalen 88 (1), 1923)

"The primary purposes of the teaching of mathematics should be to develop those powers of understanding und analyzing relations of quantity and of space which are necessary to an insight into and a control over our environment and to an appreciation of the progress of civilization its various aspects, and to develop those habits of thought and of action which will make those powers in effective in the life of the individual." (J W Young [Ed] The Reorganization of Mathematics in Secondary Education, 1927)

"It is his intuition, his mystical insight into the nature of things, rather than his reasoning which makes a great scientist." (Karl R Popper, "The Open Society and Its Enemies", 1945)

"The theory [of categories] also emphasizes that, whenever new abstract objects are constructed in a specified way out of given ones, it is advisable to regard the construction of the corresponding induced mappings on these new objects as an integral part of their definition. The pursuit of this program entails a simultaneous consideration of objects and their mappings (in our terminology, this means the consideration not of individual objects but of categories). This emphasis on the specification of the type of mappings employed gives more insight onto the degree of invariance of the various concepts involved." (Samuel Eilenberg & Saunders Mac Lane, "A general theory of natural equivalences", Transactions of the American Mathematical Society 58, 1945)

💠On Problem Solving 12: On Theories

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

"No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down, or if it is a larger complex of statements and theories, to turn definitions into propositions, and propositions into definitions, the hot invention into icy beauty. This then if it has affected teaching matter, is the didactical inversion, which as it happens may be anti-didactical." (Hans Freudenthal, "The Concept and the Role of the Model in Mathematics and Natural and Social Sciences", 1961)

"The final test of a theory is its capacity to solve the problems which originated it." (George Dantzig, "Linear Programming and Extensions", 1963)

"If we deal with our problem not knowing, or pretending not to know the general theory encompassing the concrete case before us, if we tackle the problem 'with bare hands', we have a better chance to understand the scientist's attitude in general, and especially the task of the applied mathematician." (George Pólya, "Mathematical Methods in Science", 1977)

"[...] two related deficiencies have prevented real progress in understanding insight and its role in problem solving. First, we do not yet have a system of classifying problems into those in which insight occurs versus those in which it does not. However, only if we can isolate problems in which insight occurs will we be able to set on a firm base our theories of the mechanisms underlying insight. Second, formulation of such a taxonomic system requires that we agree on a definition of insight." (Robert W Weisberg, "Prolegomena to theories of insight in problem solving: a taxonomy of problems", 1995)

"Mathematics is not a matter of 'anything goes', and every mathematician is guided by explicit or unspoken assumptions as to what counts as legitimate – whether we choose to view these assumptions as the product of birth, experience, indoctrination, tradition, or philosophy. At the same time, mathematicians are primarily problem solvers and theory builders, and answer first and foremost to the internal exigencies of their subject." (Jeremy Avigad, "Methodology and Metaphysics in the Development of Dedekind’s Theory of Ideals", 2006)

"Therefore, although the notion of insight as a distinct process has a long history in the psychological study of problem solving, it might be useful at this point to refrain from using analytic and insight as theoretical terms applied a priori to problems." (Jason M Chein et al, "Working memory and insight in the nine-dot problem", Memory & Cognition 38, 2010)

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💠On Problem Solving 19: On Insight

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

"Some problems are just too complicated for rational logical solutions. They admit of insights, not answers." (Jerome B Wiesner, The New Yorker, 1963)

"[...] two related deficiencies have prevented real progress in understanding insight and its role in problem solving. First, we do not yet have a system of classifying problems into those in which insight occurs versus those in which it does not. However, only if we can isolate problems in which insight occurs will we be able to set on a firm base our theories of the mechanisms underlying insight. Second, formulation of such a taxonomic system requires that we agree on a definition of insight." (Robert W Weisberg, "Prolegomena to theories of insight in problem solving: a taxonomy of problems", 1995)

"Therefore, although the notion of insight as a distinct process has a long history in the psychological study of problem solving, it might be useful at this point to refrain from using analytic and insight as theoretical terms applied a priori to problems." (Jason M Chein et al, "Working memory and insight in the nine-dot problem", Memory & Cognition 38, 2010)

"A feeling of insight is a kind of 'Aha!' characterized by suddenness and obviousness (and often relief!) - like a revelation. You are relatively confident that your solution is correct without having to check it. In contrast, you experienced no Aha! if the solution occurs to you slowly and stepwise. As an example, imagine a light bulb that is switched on all at once in contrast to slowly dimming it up." (Amory H Danek et al, "Working wonders? Investigating insight with magic tricks", Cognition 130, 2014)

"If insight involves an abrupt change from a state of not knowing how to solve the problem to a state of knowing [...], with no conscious awareness of what caused the change, the person experiencing the insight can still be expected to be able to report that the change occurred." (Edward Bowden & Kristin Grunewald, "Whose insight is it anyway?", [in "Insight], 2018)

"In the problem-solving literature, the term 'insight' is used to designate the clear and sudden understanding of how to solve a problem. Insight is thought to arise as the result of a solver breaking free of unwarranted assumptions, or forming novel, task-related connections between existing concepts or skills. Although it would be preferable to have a single, clear, universally accepted definition of insight, this may not be possible – and almost certainly will not be possible until we start to assess on a regular basis the single feature that seems to be widely acknowledged as distinguishing insight solutions from other solutions: the 'Aha!'" (Edward Bowden & Kristin Grunewald, "Whose insight is it anyway?", [in "Insight], 2018)

"If insight involves an abrupt change from a state of not knowing how to solve the problem to a state of knowing how to solve the problem (or, in some cases, knowing the solution), with no conscious awareness of what caused the change, the person experiencing the insight can still be expected to be able to report that the change occurred." (Edward Bowden & Kristin Grunewald, "Whose insight is it anyway?", [in "Insight], 2018)

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🅽Winifred E Newman - Collected Quotes

"'Computational thinking', an idea borrowed from computer science, quickly radicalized design disciplines and created productive debate around what and how to represent data in the design process. Making complex maps using large datasets is one option enabling designers to bridge the gap between human and machine observation. Maps are efficient, evocative, and indeterminate. They model data well enough for us to infer relations, forecast possibilities, while maintaining data consistency. Additionally, maps are reproducible and transmittable to other designers." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Making a map is the physical production including conceptualization and design. Mapping is the mental interpretation of the world and although it must precede the map, it does not necessarily result in a map artifact. Mapping defined in mathematics is the correspondence between each element of a given set with each element of another. Similarly in linguistics emphasis is on the correspondence between associated elements of different types. For designers all drawings are maps - they represent relationships between objects, places and ideas." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Mapping is based on our perceptions of what we are experiencing and our conceptions framing how we interpret sensorial input. The map isn’t ‘real’ but the objects in the map are at some point in the world or of the world. Just as we have to disabuse ourselves of the idea maps, as semiotic texts are value neutral, similarly mapping calls into question how we interpret perceptions." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"[...] mapping is the collective set of practices structuring correspondence between physical phenomena, lived experience, or conceptual frameworks." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Maps are parenthetical - maps frame what you want to hold apart from the real in the world. Maps do this by creating conceptual representations of the milieu using symbols and relations between symbols. [...] Maps, any map and every map, begin with a frame. This is the literal and conceptual demarcation between what is in the map and what is not. Making a map begins with an observation which is both a thought about thinking and the object of thought itself. The undifferentiated world cannot be apprehended, therefore; all maps have a frame whether a concept or a cosmography." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"The presence of structure distinguishes maps from diagrams. They are similar in kind but not degree. Diagrams share some of the structure but don’t quantify or qualify spatio-temporal relationships in the same way as maps. They are ‘simplified figures to convey essential meaning,’ whereas maps tend toward robust meaning relative to the subject. Symbols in diagrams have multiple possible significations until we specify or point to their meaning through context using an index. Diagrams are indexical, i.e. they point to something, but they aren’t indexed: they don’t order or organize within a larger context nor do they have a spatio-temporal dimension like maps." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"The utility of mapping as a form of data visualization isn’t in accuracy or precision, but rather the map’s capacity to help us make and organize hypothesis about the world of ideas and things. hypothesis-making through the map isn’t strictly inductive or deductive, although it can use the thought process of either, but it is often based on general observations." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Using maps as communication tools masks their complexity as a mode of thinking. Maps act like language: we attribute the signs or marks in the map to a natural extension of thought. But post-structuralism exposed maps (like language) as artificial signs whose meaning is tethered to time, place, culture, gesture, smell - in short, a plethora of cognitive and phenomenal attributes of our communication ecology." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Visual representations of data engage our cognitive perceptions, graphic skills, and rational capacity to synthesize complex ideas. For designers, maps represent observations about places, ideas or relationships. Being able to frame, represent, and order data through maps empowers the process of thinking, including thinking visually. In the twenty-first century, synthesis of complex data is a hallmark of critical thinking in all areas of knowledge. organizing information means creating links between chains of data, links between quantitative and qualitative data, and links between ideas through data. Visually organizing data means managing these links at the intersection of visual perception, representation, and the imagination." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

🅼Mark S Monmonier - Collected Quotes

"A good map tells a multitude of little white lies; it suppresses truth to help the user see what needs to be seen. Reality is three-dimensional, rich in detail, and far too factual to allow a complete yet uncluttered two-dimensional graphic scale model. Indeed, a map that did not generalize would be useless. But the value of a map depends on how well its generalized geometry and generalized content reflect a chosen aspect of reality." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Enhancement adds detail to give map symbols a more realistic appearance. Lines representing streams, for instance, might be given typical meander loops, whereas shorelines might be made to look more coast-like. Enhanced map symbols are more readily interpreted as well as more aesthetic." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Graphic scales are not only the most helpful means of communicating map scale but also the safest. An alternative to blind trust in the user's sense of distance and skill in mental arithmetic, the simple bar scale typically portrays a series of conveniently rounded distances appropriate to the map's function and the area covered." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Graphic symbols complement map scale and projection by making visible the features, places, and other locational information represented on the map. By describing and differentiating features and places, map symbols serve as a graphic code for storing and retrieving data in a two-dimensional geographic framework." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Map projections distort five geographic relationships: areas, angles, gross shapes, distances, and directions. Although some projections preserve local angles but not areas, others preserve areas but not local angles. All distort large shapes noticeably (but some distort continental shapes more than others), and all distort at least some distances and some directions." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Maps have three basic attributes: scale, projection, and symbolization. Each element is a source of distortion. As a group, they describe the essence of the map's possibilities and limitations. No one can use maps or make maps safely and effectively without understanding map scales, map projections, and map symbols." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Not only is it easy to lie with maps, it's essential. To portray meaningful relationships for a complex, three-dimensional world on a flat sheet of paper or a video screen, a map must distort reality. As a scale model, the map must use symbols that almost always are proportionally much bigger or thicker than the features they represent. To avoid hiding critical information in a fog of detail, the map must offer a selective, incomplete view of reality. There's no escape from the cartographic paradox: to present a useful and truthful picture, an accurate map must tell white lies." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Smoothing, which also diminishes detail and angularity, might displace some points and add others to the list. A prime objective of smoothing is to avoid a series of abruptly joined straight line segments." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Some maps fail because of the mapmaker's ignorance or oversight. The range of blunders affecting maps includes graphic scales that invite users to estimate distances from world maps, maps based on incompatible sources, misspelled place-names, and graytone symbols changed by poor printing by poor planning. By definition a blunder is not a lie, but the informed map user must be aware of cartographic fallibility; and even of a bit of mischief." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

🆃Barbara Tversky - Collected Quotes

"Bars are naturally interpreted as containers, as enclosing one set of things and separating that set from other sets. Lines, on the other hand, are naturally interpreted as connectors, as paths interrelating different points. Thus, in the context of representing data, a more natural way to represent discrete quantities is by bars and a more natural way to represent trends is by lines." (Barbara Tversky, "What does drawing reveal about thinking?", 1999)

"Drawings, then, are representations of reality, not presentations of reality. Drawings can omit things that are actually there, they can distort things that are there, they can add things that are not there. They need not have a consistent point of view or a point of view at all. As such, drawings are of even greater interest to art critics, designers, and psychologists alike. They can provide insights into conceptulizations not just imaginings." (Barbara Tversky, "What does drawing reveal about thinking?", 1999)

"Attention is selective, ignoring much incoming information. The perceptual systems level and sharpen the information that does come in; for example, the visual system searches for the boundaries that define figures by sharpening edges and corners, by filing in gaps, by normalizing shapes. Cognition filters, abstracts, and categorizes, continuing this process, and symbol systems carry these processes further." (Barbara Tversky, "Visualizing thought", Topics in Cognitive Science 3(3), 2010)

"Diagrams and other depictions are expressions and communications of thought, a class that includes gesture, action, and language. In common with gesture and action, diagrams use place and form in space to convey meanings, concrete and abstract, quite directly." (Barbara Tversky, "Visualizing thought", Topics in Cognitive Science 3(3), 2010)

"Because [images] persist, they can be subjected to myriad perceptual processes: Compare, contrast, assess similarity, distance, direction, shape, and size, reverse figure and ground, rotate, group and regroup; that is, they can be mentally assessed and rearranged in multiple ways that contribute to understanding, inference, and insight." (Barbara Tversky, "Visualizing thought", Topics in Cognitive Science 3(3), 2010)

"[...] maps, like many other kinds of visualizations, distort the 'truth' to tell a larger truth. The processes that abstract, schematize, supplement, and distort the world outside onto the world of a page, filtering, leveling, sharpening, categorizing, and otherwise transforming, are the same processes the nervous system and the brain apply to make sense of the barrage of stimuli the world provides." (Barbara Tversky, "Visualizing thought", Topics in Cognitive Science 3(3), 2010)

"When diagrams are cluttered with information, finding and integrating the relevant information takes working memory capacity. Schematization, that is, removing irrelevant details, exaggerating, perhaps distorting, relevant ones, even adding relevant but invisible information, can facilitate information processing in a variety of ways." (Barbara Tversky, "Visualizing thought", Topics in Cognitive Science 3(3), 2010)

🅼Ludwig von Mises - Collected Quotes

"Facts per se can neither prove nor refute anything. Everything is decided by the interpretation and explanation of the facts, by the ideas and the theories." (Ludwig von Mises, "Socialism: An Economic and Sociological Analysis", 1922)

"Figures alone prove or disprove nothing. Only the conclusions drawn from the collected material can do this. And these are theoretical." (Ludwig von Mises, "Socialism: An Economic and Sociological Analysis", 1922)

"Scientific criticism has no nobler task than to shatter false beliefs." (Ludwig von Mises, "Socialism: An Economic and Sociological Analysis", 1922)

"Human reasoning does not have the power to exhaust completely the content of the universe." (Ludwig Von Mises, "Epistemological Problems of Economics", 1933)

"One has to recognize that science is not metaphysics, and certainly not mysticism; it can never bring us the illumination and the satisfaction experienced by one enraptured in ecstasy. Science is sobriety and clarity of conception, not intoxicated vision." (Ludwig Von Mises, "Epistemological Problems of Economics", 1933)

"Historical knowledge is indispensable for those who want to build a better world." (Ludwig von Mises, "Omnipotent Government", 1944)

"Science is competent to establish what is. It can never dictate what ought to be." (Ludwig von Mises, "Planned Chaos", 1947)

"Changes in human conditions are brought about by the pioneering of the cleverest and most energetic men. They take the lead and the rest of mankind follows them little by little." Ludwig von Mises, "The Anti-Capitalistic Mentality", 1956)

"The mark of the creative mind is that it defies a part of what it has learned." (Ludwig von Mises, "Theory and History: An Interpretation of Social and Economic Evolution", 1957)

"Even knowledge of the laws of nature does not make action free. It is never able to attain more than definite, limited ends. It can never go beyond the insurmountable barriers set for it. And even within the sphere allowed to it, it must always reckon with the inroads of uncontrollable forces, with fate." (Ludwig von Mises, "Epistemological Problems of Economics", 1960)

"Scientific research sooner or later, but inevitably, encounters something ultimately given that it cannot trace back to something else of which it would appear as the regular or necessary derivative. Scientific progress consists in pushing further back this ultimately given." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)

"Statistics is the description in numerical terms of experiences concerning phenomena not subject to regular uniformity. […] Statistic is therefore a specific method of history." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)

"The criterion of truth is that it works even if nobody is prepared to acknowledge it." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)

"The methods of the natural sciences cannot be applied to human behavior because this behavior lacks the peculiarity that characterizes events in the field of the natural sciences, viz., regularity." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)

"There always remains an orbit that to the limited knowledge of man appears as an orbit of pure chance and marks life as a gamble. Man and his works are always exposed to the impact of unforeseen and uncontrollable events." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)

"There is in the universe something for the description and analysis of which the natural sciences cannot contribute anything. There are events beyond the range of those events that the procedures of the natural sciences are fit to observe and describe. There is human action." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method" 1962)

"History speaks only to those people who know how to interpret it." (Ludwig von Mises, "Human Action", 1963)

"Man can never become omniscient. He can never be absolutely certain that his inquiries were not misled and that what he considers as certain truth is not error. All that man can do is to submit all his theories again and again to the most critical reexamination." (Ludwig von Mises, "Human Action", 1963)

"Statistics is a method for the presentation of historical facts concerning prices and other relevant data of human action. It is not economics and cannot produce economic theorems and theories. The statistics of prices is economic history." (Ludwig von Mises, "Human Action", 1963)

"Every branch of knowledge has its own merits and its own rights. Economists have never tried to belittle or deny the significance of economic history. Neither do real historians object to the study of economics." (Ludwig von Mises)

🅷Thomas Homer-Dixon - Collected Quotes

"Connectivity harbors other risks too. As we create more links among the nodes of our technological and social networks, these networks sometimes developed unexpected patterns of connections that make breakdown more likely. They can, for instance, develop harmful feedback loops - what people commonly call vicious circles - that reinforce instabilities and even lead to collapse." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"In a random network the loss of a small number of nodes can cause the overall network to become incoherent - that is, to break into disconnected subnetworks. In a scale-free network, such an event usually won’t disrupt the overall network because most nodes don’t have many links. But there’s a big caveat to this general principle: if a scale-free network loses a hub, it can be disastrous, because many other nodes depend on that hub." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"In the case of a complex system, nonlinear behavior can happen as disturbances or changes in the system, each one relatively small by itself, accumulate. Outwardly, everything seems to be normal: the system doesn’t generate any surprises. At some point, though, the behavior of the whole system suddenly shifts to a radically new mode. This kind of behavior is often called a threshold effect, because the shift occurs when a critical threshold - usually unseen and often unexpected - is crossed." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"Initially, increasing connectedness and diversity helps, but as the connections become increasingly dense, the system gets very strongly coupled so that a failure in one part reverberates throughout the entire network." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"People often use the words 'breakdown' and 'collapse' synonymously. But in my view, although both breakdown and collapse produce a radical simplification of a system, they differ in their long-term consequences. Breakdown may be serious, but it’s not catastrophic. Something can be salvaged after breakdown occurs and perhaps rebuilt better than before. Collapse, on the other hand, is far more harmful: the damage endures- it may even be permanent - and there’s far less knowledge, wealth, or information left behind to use in a process of renewal." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006) 

"Scale-free networks are particularly vulnerable to intentional attack: if someone wants to wreck the whole network, he simply needs to identify and destroy some of its hubs. And here we see how our world’s increasing connectivity really matters. Scientists have found that as a scale-free network like the Internet or our food-distribution system grows- as it adds more nodes - the new nodes tend to hook up with already highly connected hubs." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"So the first cost of greater connectivity is that damage or a shock in one part of the system […] can cascade farther and faster to other parts of the system. This is especially true when the nodes in the network, or the elements in the system, are packed so closely together that the links among them are very short - that is, when they’re tightly coupled." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"Synergy happens when people, things, or events combine to produce a larger impact than they would if each acted separately." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"The breakdown of a system […] simplifies its internal organization and reduces its range of potential behaviors." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"The intricate networks that tightly connect us together - and through which people, materials, information, money and energy move - amplify and transmit any shock." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"When small things can make a big difference, and when it’s impossible to know which small things matter and which don’t, predicting the future becomes formidably difficult. This is especially true of human affairs." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

🅲John A Comenius - Collected Quotes

"All explanations should be given in a language that pupils understand." (John A Comenius)

"Education that associates learning with doing will replace the passive education of imparting the learning of others." (John A Comenius)

"[Education carries an impact] as long as the student has a need for it and applies it to some situation of his own. Every new idea should be worked out in application." (John A Comenius)

"It is by working that we learn how to work, just as we learn how to act by acting." (John A Comenius)

"It is impossible to find a remedy until we have discovered the real cause of the disease." (John A Comenius)

"It is never as easy to fulfill requirements in practice as it is to lay them down in theory." (John A Comenius)

"Languages should not be learned from grammar, but from real-life authors." (John A Comenius)

"Learners should first exercise their senses; then the memory; then the comprehension; and finally their judgment." (John A Comenius)

"Let us now speak of teaching, as the shipwright first sketches the blueprint of a ship in outline, laying down the lines of the keel before beginning construction, so we lay down here the blue-print for the voyage through life." (John A Comenius)

"Master the problems of experience, not the piling up of information." (John A Comenius)

"Mathematics should be learned through recreational games, the way the Egyptians do, through amusement and pleasure." (John A Comenius)

"Only in education - never in the life of farmer, sailor, merchant, physician, or laboratory experimenter- does knowledge mean primarily a store of information aloof from doing." (John A Comenius)

"Proceed from what is easy to what is more difficult. The subject matter should be so arranged that the learners first get to know that which lies nearest their mental vision, then that which lies moderately near, then that which is more remote, and lastly, that which is farthest off." (John A Comenius)

"Recognition of the natural course of development always starts with situations involving learning by doing." (John A Comenius)

"Schools are unfortunately better adapted, as John Stuart Mill said, to make disciples rather than inquirers." (John A Comenius)

"Students shall themselves seek, discover, discuss, do, and repeat by their own efforts, examine everything themselves without abdicating to the teacher's authority. The teacher should be left with the task of seeing that the task is completed." (John A Comenius)

"Teach everything through the medium of the senses. Show learners pictures of the things that they must learn. The illustrations should be derived from the events of everyday life. For all knowledge begins with sensuous perception. By appealing to the ear, the eye, and the hands (real world applications) what is learned is thoroughly impressed on the eyes, the ears, the understanding, and the memory." (John A Comenius)

"The desire to know should be excited in learners in every possible manner." (John A Comenius)

"The educational process is its own end, one of continually reorganizing, reconstructing, transforming."(John A Comenius)

"The method of instruction should lighten the drudgery of learning: relieve explanations through a humorous or less serious tone." (John A Comenius)

"The more the teacher 'teaches,' the less the student learns." (John A Comenius)

"The psyche, is characterized by three basic functions: knowing, feeling, will-to-action" (John A Comenius)

"The scientific interest which requires personal observation, reflection, and experimental activity will be added." (John A Comenius)

"The young always do better when the learning process is divided into brief but frequent intervals."(John A Comenius)

"To seek and to find a method of instruction by which teachers may teach less, and learners may learn more." (John A Comenius)

"To set forth a universal method of learning with such certainty that the desired result must of necessity follow. This is my goal." (John A Comenius)

"Unless goals are set, means provided to reach them, and a proper system devised for application of those means, it is easy for something to be omitted and for failure to step in." (John A Comenius)