📓On Literature: On Discovery (From Fiction to Science-Fiction)

"He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind if it is applied to no larger system than the starry one." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1849)

"My desire for knowledge is intermittent; but my desire to bathe my head in atmospheres unknown to my feet is perennial and constant. The highest that we can attain to is not Knowledge, but Sympathy with Intelligence. I do not know that this higher knowledge amounts to anything more definite than a novel and grand surprise on a sudden revelation of the insufficiency of all that we called Knowledge before - a discovery that there are more things in heaven and earth than are dreamed of in our philosophy. It is the lighting up of the mist by the sun." (Henry D Thoreau, "Walking", 1851)

"Consequently, these laws of nature need only be discovered, and then man will no longer be answerable for his actions, and his life will become extremely easy. Needless to say, all human actions will then be calculated according to these laws, mathematically, like a table of logarithms, up to 108,000, and entered into a calendar; or, better still, some well-meaning publications will appear, like the present-day encyclopedic dictionaries, in which everything will be so precisely calculated and designated that there will no longer be any actions or adventures in the world." (Fyodor Dostoevsky, "Notes from Underground", 1864)

"Phenomena may well be suspected of anything, are capable of anything. Hypothesis proclaims the infinite; that is what gives hypothesis its greatness. Beneath the surface fact it seeks the real fact. It asks creation for her thoughts, and then for her second thoughts. The great scientific discoverers are those who hold nature suspect." (Victor Hugo, "The Toilers of the Sea", 1866)

"The world is devoted to physical science, because it believes theses discoveries will increase its capacity of luxury and self-indulgence. But the pursuit of science only leads to the insoluble." (Benjamin Disraeli, "Lothair", 1870)

"A piece of scientific fiction is a narrative of an imaginary invention or discovery in the natural sciences and consequent adventures and experiences." (James O Bailey, "Pilgrims through Space and Time", 1947)

"The machine is only a tool after all, which can help humanity progress faster by taking some of the burdens of calculations and interpretations off its back. The task of the human brain remains what it has always been; that of discovering new data to be analyzed, and of devising new concepts to be tested." (Isaac Asimov, "I, Robot", 1950)

"The urge to explore, to discover, to ‘follow knowledge like a sinking star’, is a primary human impulse which needs and can receive no further justification than its own existence." (Arthur C. Clarke, "The Challenge of the Spaceship", 1959)

"The only way of discovering the limits of the possible is to venture a little way past them into the impossible." (Arthur C Clarke, "Profiles of the Future", 1962)

"There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before." (Isaac Asimov, "Adding a Dimension", 1964)

"We cannot predict the new forces, powers, and discoveries that will be disclosed to us when we reach the other planets and set up new laboratories in space. They are as much beyond our vision today as fire or electricity would be beyond the imagination of a fish." (Arthur C Clarke, "Space and the Spirit of Man", 1965)

"It is only when science asks why, instead of simply describing how, that it becomes more than technology. When it asks why, it discovers Relativity. When it only shows how, it invents the atomic bomb, and then puts its hands over its eyes and says, 'My God what have I done?'" (Ursula K Le Guin, "The Stalin in the Soul", 1973)

"Metaphysics attempts to discover the ultimate nature of reality, and in this sense, the innerspace of science fiction is metaphysical fiction." (Kate Wilhelm, 1974)

"There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarrely inexplicable. There is another theory which states that this has already happened." (Douglas Adams, "The Hitch-Hiker’s Guide to the Galaxy", [radio series episode] 1978) 

"It is only when science asks why, instead of simply describing how, that it becomes more than technology. When it asks why, it discovers Relativity. When it only shows how, it invents the atomic bomb." (Ursula K Le Guin, "Language of the Night", 1979)

"If we assume the existence of an omniscient and omnipotent being, one that knows and can do absolutely everything, then to my own very limited self, it would seem that existence for it would be unbearable. Nothing to wonder about? Nothing to ponder over? Nothing to discover? Eternity in such a heaven would surely be indistinguishable from hell." (Isaac Asimov, "'X' Stands for Unknown", 1984)

"We are only the beginning of humanity, the larval stage, the species preparing for its discovery of what intelligence is for. We will survive and develop, each crest a little higher than the one before." (George Turner, "Drowning Towers", 1987)

"Coincidence is just the word we use when we have not yet discovered the cause." (Orson Scott Card, "The Call Of Earth", 1992)

"The rationality of our universe is best suggested by the fact that we can discover more about it from any starting point, as if it were a fabric that will unravel from any thread." (George Zebrowski, "Is Science Rational?", OMNI Magazine, 1994)

Scientific Experience VII: Discovery

"In that pure enjoyment experienced on approaching to the ideal, in that eagerness to draw aside the veil from the hidden truth, and even in that discord which exists between the various workers, we ought to see the surest pledges of further scientific success. Science thus advances, discovering new truths, and at the same time obtaining practical results." (Dmitry I Mendeleev, "The Principles of Chemistry" Vol. 1, 1891)

"Experience teaches that one will be led to new discoveries almost exclusively by means of special mechanical models." (Ludwig Boltzmann, "Lectures on Gas Theory", 1896)

"Theoretical philosophy aimed to discover the unity of experience, namely, in the form of some universal explanation. It strived to yield a world picture, one which is harmoniously integral and completely understandable." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"For tektology the unity of experience is not 'discovered', but actively created by organizational means: ‘philosophers wanted to explain the world, but the main point is it change it’ said the greater precursor of organizational science, Karl Marx. The explanation of organizational forms and methods by tektology is directed not to a contemplation of their unity, but to a practical mastery over them." (Alexander Bogdanov, "Tektology: The Universal Organizational Science", 1922)

"A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery." (George Polya, "How to solve it", 1944)

"A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more." (J. Robert Oppenheimer, Science and the Common Understanding, 1954)

"A change in science, whether novelty or discovery, when properly understood, when the linguistic problem is adequately solved, will even then provide only a hunch, a starting point for looking at an area of experience other than the science in which it was nourished and born." (J Robert Oppenheimer, "The Growth of Science and the Structure of Culture", Daedalus, 1958)

"Typically, scientific discovery is a two-part process. The first thing that happens is that a scientist experiences a sudden insight. Then, if he is lucky he finds that the insight has logical consequences that will clear up an outstanding scientific problem, or explain baffling experimental results." (Richard Morris)

On Discovery (Unsourced)

"A great discovery is not a terminus, but an avenue leading to regions hitherto unknown. We climb to the top of the peak and find that it reveals to us another higher than any we have yet seen, and so it goes on. The additions to our knowledge of physics made in a generation do not get smaller or less fundamental or less revolutionary, as one generation succeeds another. The sum of our knowledge is not like what mathematicians call a convergent series […] where the study of a few terms may give the general properties of the whole. Physics corresponds rather to the other type of series called divergent, where the terms which are added one after another do not get smaller and smaller, and where the conclusions we draw from the few terms we know, cannot be trusted to be those we should draw if further knowledge were at our disposal." (Sir Joseph J Thomson, [letter to G P Thomson], 1930)

"All great insights and discoveries are not only usually thought by several people at the same time, they must also be re-thought in that unique effort to truly say the same thing about the same thing." (Martin Heidegger)

"Discovering the unexpected is more important than confirming the known." (George E P Box)

"In signs, one sees an advantage for discovery that is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed, the labor of thought is wonderfully diminished” (Gottfried W Leibniz)

"It is notorious that the same discovery is frequently made simultaneously and quite independently, by different persons. […] It would seem, that discoveries are usually made when the time is ripe for them - that is to say, when the ideas from which they naturally flow are fermenting in the minds of many men." (Sir Francis Galton)

"It is the truth alone that we desire to know and what a joy there is in discovering it." (Carl W Scheele)

"The interpreter of the wonders of nature is experience. It never misleads us, only our grasp can do it with us. Until we can establish a general rule, we must accept the help of experience. Although nature begins with the cause, and with the experiment, we must do it inversely, we must discover the cause with experiments." (Leonardo da Vinci)

🧩Out of Context: On Science (Definitions)

"Science is, I believe, nothing but trained and organized common sense [...]" (Thomas H Huxley, "On the Educational Value of the Natural History Sciences", 1854)

"Science is organized knowledge; and before knowledge can be organized, some of it must first be possessed." (Herbert Spencer, "The Art of Education", The North British Review, 1854)

"In its broadest sense science is organised knowledge, and its methods consist of the observation and classification of the phenomena of which we become conscious through our senses, and the investigation of the causes of which these are the effects." (Richard Strachey, Nature Vol. 12 [E], 1875)

"Science is the observation of things possible, whether present or past; prescience is the knowledge of things which may come to pass, though but slowly." (Leonardo da Vinci, "The Notebooks of Leonardo da Vinci", 1883)

"Science is not the monopoly of the naturalist or the scholar, nor is it anything mysterious or esoteric. Science is the search for truth, and truth is the adequacy of a description of facts." (Paul Carus, "Philosophy as a Science", 1909)

"Science is the only truth and it is the great lie. It knows nothing, and people think it knows everything. It is misrepresented. People think that science is electricity, automobilism, and dirigible balloons. It is something very different. It is life devouring itself. It is the sensibility transformed into intelligence. It is the need to know stifling the need to live. It is the genius of knowledge vivisecting the vital genius." (Rémy de Gourmont, "Art and Science", cca. 1905-1909)

"Science is frankly empirical in method and aim; it seeks to discover the laws of concrete being and becoming, and to formulate these in the simplest terms, which are either immediate data of experience or verifiably derived therefrom." (J Arthur Thomson, "The System of Animate Nature" Vol. 1, 1920)

"Science is simply setting out on a fishing expedition to see whether it cannot find some procedure which it can call measurement of space and some procedure which it can call the measurement of time, and something which it can call a system of forces, and something which it can call masses." (Alfred N Whitehead, "The Concept of Nature", 1920)

"Science is a magnificent force, but it is not a teacher of morals." (William J Bryan, "Undelivered Trial Summation Scopes Trial", 1925)

"Science is either an important statement of systematic theory correlating observations of a common world or is the daydream of a solitary intelligence with a taste for the daydream of publication." (Alfred N Whitehead, "Process and Reality: An Essay in Cosmology", 1929)

"Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear." (Paul Valéry, "Moralités" ["Morality"], 1932)

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

"Science, in the broadest sense, is the entire body of the most accurately tested, critically established, systematized knowledge available about that part of the universe which has come under human observation." (Austin L Porterfield, "Creative Factors in Scientific Research", 1941)

"Physics is not about the real world, it is about ‘abstractions’ from the real world, and this is what makes it so scientific." (Anthony Standen, "Science is a Sacred Cow", 1950)

"Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined." (George Santayana, "The Life of Reason, or the Phases of Human Progress", 1954)

"Science is the creation of concepts and their exploration in the facts." (Jacob Bronowski, "Science and Human Values", 1956)

"Science is the reduction of the bewildering diversity of unique events to manageable uniformity within one of a number of symbol systems [...]" (Aldous L Huxley, "Essay", Daedalus, 1962)

"Science is what scientists do. Science is knowledge, a body of information about the external world. Science is the ability to predict. Science is power, it is engineering. Science explains, or gives causes and reasons." (John Bremer "What Is Science?" [in "Notes on the Nature of Science"], 1962)

"Science is the combined effort to find out what sort of behavior ensues when various conditions are fulfilled." (H Rom Harré, "Philosophical Issues and Conceptual Change", Theory Into Practice Vol. 10 (2), 1971)

"Science is a product of the human mind, but this product is as objective as a cathedral."  (Karl R Popper, "The Logic and Evolution of Scientific Theory", [in "All Life is Problem Solving", 1999] 1972)

"Science is systematic organisation of knowledge about the universe on the basis of explanatory hypotheses which are genuinely testable." (Francisco J Ayala, "Studies in the Philosophy of Biology: Reduction and Related Problems", 1974)

"Within a Metaphysics of Quality, science is a set of static intellectual patterns describing this reality, but the patterns are not the reality they describe." (Robert M Pirsig, "Zen and the Art of Motorcycle Maintenance", 1974)

"Science is a quintessentially human activity, not a mechanized, robot-like accumulation of objective information, leading by laws of logic to inescapable interpretation." (Stephen J Gould, "Ever Since Darwin", 1977)

"Engineering or Technology is the making of things that did not previously exist, whereas science is the discovering of things that have long existed." (David Billington, "The Tower and the Bridge: The New Art of Structural Engineering", 1983)

"Science is human experience systematically extended (by intent, methodology and instrumentation) for the purpose of learning more about the natural world and for the critical empirical testing and possible falsification of all ideas about the natural world." (Robert E Kofahl, Correctly Redefining Distorted Science: A Most Essential Task", Creation Research Society Quarterly Vol. 23, 1986)

"Science is a mechanism. It's a way of trying to improve your knowledge of nature. It's a system for testing your thoughts against the universe and seeing whether they match." (Isaac Asimov, [Interview by Bill Moyers] 1988)

"Science is more than a mere attempt to describe nature as accurately as possible. Frequently the real message is well hidden, and a law that gives a poor approximation to nature has more significance than one which works fairly well but is poisoned at the root." (Robert H March, "Physics for Poets", 1996)

"Science is like photographing a series of close-ups with your back to the sun. No matter which way you move, your shadow always falls across the scene you photograph. No matter what you do, you can never efface yourself from the photographed scene." (F David Peat, "From Certainty to Uncertainty", 2002)

"Science is that story our society tells itself about the cosmos." (F David Peat, "From Certainty to Uncertainty", 2002)

"Science is the art of the appropriate approximation." (Byron K Jennings, "On the Nature of Science", Physics in Canada Vol. 63 (1), 2007)

"Science is not only the enterprise of harnessing nature to serve the practical needs of humankind. It is also part of man’s unending search for knowledge about the universe and his place within it." (Henry P Stapp, "Mindful Universe: Quantum Mechanics and the Participating Observer", 2007)

"Science is about discovery, but it is also about communication. An idea can hardly be said to exist if you do not awaken that same idea in someone else." (Marcus du Sautoy, "Symmetry: A Journey into the Patterns of Nature", 2008)

"Science isn’t about being right. It is about convincing others of the correctness of an idea through a methodology all will accept using data everyone can trust. New ideas take time to be accepted because they compete with others that have already passed the test." (Tom Koch, "Commentary: Nobody loves a critic: Edmund A Parkes and John Snow’s cholera", International Journal of Epidemiology Vol. 42 (6), 2013)

"Science, at its core, is simply a method of practical logic that tests hypotheses against experience." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

"Science is an endeavor to understand and describe the real world out there to (at best) alleviate and enrich human existence." (Achim Zielesny, "From Curve Fitting to Machine Learning" 2^nd Ed., 2016)

"Science is a game - but a game with reality, a game with sharpened knives." (Erwin Schrödinger)

"Science is not a technique or a body of knowledge, though it uses both. It is rather an attitude of inquiry, or observation and reasoning, with respect to the world. It can be developed, not by memorizing facts or juggling formulas to get an answer, but only by actual practice of scientific observation and reasoning." (Karl T Compton)

"Science is the knowledge of the many, orderly and methodically-arranged, so as to become comprehended by one." (Sir John Herschel)

📁 On DIKW: On Knowledge (2000-2009)

"Storytelling is the art of unfolding knowledge in a way that makes each piece contribute to a larger truth." (Philip Gerard, "Writing a Book That Makes a Difference", 2000)

"There is a strong tendency today to narrow specialization. Because of the exponential growth of information, we can afford (in terms of both economics and time) preparation of specialists in extremely narrow fields, the various branches of science and engineering having their own particular realms. As the knowledge in these fields grows deeper and broader, the individual's field of expertise has necessarily become narrower. One result is that handling information has become more difficult and even ineffective." (Semyon D Savransky, "Engineering of Creativity", 2000)

"All human knowledge - including statistics - is created  through people's actions; everything we know is shaped by our language, culture, and society. Sociologists call this the social construction of knowledge. Saying that knowledge is socially constructed does not mean that all we know is somehow fanciful, arbitrary, flawed, or wrong. For example, scientific knowledge can be remarkably accurate, so accurate that we may forget the people and social processes that produced it." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Defined from a societal standpoint, information may be seen as an entity which reduces maladjustment between system and environment. In order to survive as a thermodynamic entity, all social systems are dependent upon an information flow. This explanation is derived from the parallel between entropy and information where the latter is regarded as negative entropy (negentropy). In more common terms information is a form of processed data or facts about objects, events or persons, which are meaningful for the receiver, inasmuch as an increase in knowledge reduces uncertainty." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Knowledge is factual when evidence supports it and we have great confidence in its accuracy. What we call 'hard fact' is information supported by  strong, convincing evidence; this means evidence that, so far as we know, we cannot deny, however we examine or test it. Facts always can be questioned, but they hold up under questioning. How did people come by this information? How did they interpret it? Are other interpretations possible? The more satisfactory the answers to such questions, the 'harder' the facts."(Joel Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, 2001)

"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) 

"Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003)

"The networked world continuously refines, reinvents, and reinterprets knowledge, often in an autonomic manner." (Donald M Morris et al, "A revolution in knowledge sharing", 2003) 

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

"Evolution moves towards greater complexity, greater elegance, greater knowledge, greater intelligence, greater beauty, greater creativity, and greater levels of subtle attributes such as love. […] Of course, even the accelerating growth of evolution never achieves an infinite level, but as it explodes exponentially it certainly moves rapidly in that direction." (Ray Kurzweil, "The Singularity is Near", 2005)

“It makes no sense to seek a single best way to represent knowledge - because each particular form of expression also brings its particular limitations. For example, logic-based systems are very precise, but they make it hard to do reasoning with analogies. Similarly, statistical systems are useful for making predictions, but do not serve well to represent the reasons why those predictions are sometimes correct.” (Marvin Minsky, "The Emotion Machine: Commonsense Thinking, Artificial Intelligence, and the Future of the Human Mind", 2006)

"Information is just bits of data. Knowledge is putting them together. Wisdom is transcending them." (Ram Dass, "One-Liners: A Mini-Manual for a Spiritual Life (ed. Harmony", 2007)

"Science is not only the enterprise of harnessing nature to serve the practical needs of humankind. It is also part of man’s unending search for knowledge about the universe and his place within it." (Henry P Stapp, "Mindful Universe: Quantum Mechanics and the Participating Observer", 2007)

"Critical thinking is essentially a questioning, challenging approach to knowledge and perceived wisdom. It involves ideas and information from an objective position and then questioning this information in the light of our own values, attitudes and personal philosophy." Brenda Judge et al, "Critical Thinking Skills for Education Students", 2009)

"Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge." (Robert P Crease, "The Great Equations", 2009)

"Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon."(Judea Pearl, "Causal inference in statistics: An overview", Statistics Surveys 3, 2009)

📁 On DIKW: On Knowledge (1800-1824)

"Knowledge is only real and can only be set forth fully in the form of science, in the form of system." (G W Friedrich Hegel, "The Phenomenology of Mind", 1807)

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretched out his arms for others." (Carl F Gauss, [Letter to Farkas Bolyai] 1808)

"Thus then does the Doctrine of Knowledge, which in its substance is the realisation of the absolute Power of intelligising which has now been defined, end with the recognition of itself as a mere Schema in a Doctrine of Wisdom, although indeed a necessary and indispensable means to such a Doctrine: - a Schema, the sole aim of which is, with the knowledge thus acquired, - by which knowledge alone a Will, clear and intelligible to itself and reposing upon itself without wavering or perplexity, is possible, - to return wholly into Actual Life; - not into the Life of blind and irrational Instinct which we have laid bare in all its nothingness, but into the Divine Life which shall become visible to us." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)

"The most important questions of life are, for the most part, really only problems of probability. Strictly speaking one may even say that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, induction and analogy, the principal means for discovering truth, are based on probabilities, so that the entire system of human knowledge is connected with this theory." (Pierre-Simon Laplace, "Theorie Analytique des Probabilités", 1812)

"One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814) 

"[...] all knowledge, and especially the weightiest knowledge of the truth, to which only a brief triumph is allotted between the two long periods in which it is condemned as paradoxical or disparaged as trivial." (Arthur Schopenhauer, "The World as Will and Representation", 1819)

"The highest knowledge can be nothing more than the shortest and clearest road to truth; all the rest is pretension, not performance, mere verbiage and grandiloquence, from which we can learn nothing." (Charles C Colton, "Lacon", 1820)

"We [...] are profiting not only by the knowledge, but also by the ignorance, not only by the discoveries, but also by the errors of our forefathers; for the march of science, like that of time, has been progressing in the darkness, no less than in the light." (Charles C Colton, "Lacon", 1820)

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

📁 On DIKW: On Knowledge (1825-1849)

"It is true that of far the greater part of things, we must content ourselves with such knowledge as description may exhibit, or analogy supply; but it is true likewise, that these ideas are always incomplete, and that at least, till we have compared them with realities, we do not know them to be just. As we see more, we become possessed of more certainties, and consequently gain more principles of reasoning, and found a wider base of analogy." (Samuel Johnson, 1825)

"The first steps in the path of discovery, and the first approximate measures, are those which add most to the existing knowledge of mankind." (Charles Babbage, "Reflections on the Decline of Science in England", 1830)

"Our knowledge of circumstances has increased, but our uncertainty, instead of having diminished, has only increased. The reason of this is, that we do not gain all our experience at once, but by degrees; so our determinations continue to be assailed incessantly by fresh experience; and the mind, if we may use the expression, must always be under arms." (Carl von Clausewitz, "On War", 1832)

"Truth in itself is rarely sufficient to make men act. Hence the step is always long from cognition to volition, from knowledge to ability. The most powerful springs of action in men lie in his emotions." (Carl von Clausewitz, "On War", 1832)

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"The peculiar character of mathematical truth is that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths." (William Whewell, "Principles of English University Education", 1838)

"[…] in order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conception which, applied for this purpose, gives distinct and definite results, such as can be steadily taken hold of and reasoned from […]" (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon their History" Vol. 2, 1840)

"But a thousand unconnected observations have no more value, as a demonstrative proof, than a single one. If we do not succeed in discovering causes by our researches, we have no right to create them by the imagination; we must not allow mere fancy to proceed beyond the bounds of our knowledge."(Justus von Liebig, "The Lancet", 1844)

"[…] there do exist among us doctrines of solid and acknowledged certainty, and truths of which the discovery has been received with universal applause. These constitute what we commonly term Sciences; and of these bodies of exact and enduring knowledge, we have within our reach so large and varied a collection, that we may examine them, and the history of their formation, with good prospect of deriving from the study such instruction as we seek." (William Whewell, "The Philosophy of the Inductive Sciences Founded upon Their History" Vol. 1, 1847)

📁 On DIKW: On Knowledge (1850-1874)

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." (James C Maxwell, [Letter to Lewis Campbell] 1851) 

"Remember that accumulated knowledge, like accumulated capital, increases at compound interest: but it differs from the accumulation of capital in this; that the increase of knowledge produces a more rapid rate of progress, whilst the accumulation of capital leads to a lower rate of interest. Capital thus checks its own accumulation: knowledge thus accelerates its own advance. Each generation, therefore, to deserve comparison with its predecessor, is bound to add much more largely to the common stock than that which it immediately succeeds." (Charles Babbage, "The Exposition of 1851: Or the Views of Industry, Science and Government of England", 1851)

"All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions." (Joseph Henry, "Report of the Secretary" [Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851], 1852)

"SYSTEM (σύστημα, σύν ἵστημιavu, to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound." (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857)

“The conception of the inconceivable [imaginary], this measurement of what not only does not, but cannot exist, is one of the finest achievements of the human intellect. No one can deny that such imaginings are indeed imaginary. But they lead to results grander than any which flow from the imagination of the poet. The imaginary calculus is one of the master keys to physical science. These realms of the inconceivable afford in many places our only mode of passage to the domains of positive knowledge. Light itself lay in darkness until this imaginary calculus threw light upon light. And in all modern researches into electricity, magnetism, and heat, and other subtile physical inquiries, these are the most powerful instruments.” (Thomas Hill, “The Imagination in Mathematics”, North American Review Vol. 85, 1857)

"Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained - a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas." (Chauncey Wright, "The Philosophy of Herbert Spencer", North American Review, 1865)

"One of the greatest obstacles to the free and universal movement of human knowledge is the tendency that leads different kinds of knowledge to separate into systems." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method." (Immanuel Kant, "Critique of Pure Reason", 1871)

"Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress." (William T Kelvin, "Elements of Natural Philosophy", 1873)

"Numerical facts, like other facts, are but the raw materials of knowledge, upon which our reasoning faculties must be exerted in order to draw forth the principles of nature. [...] Numerical precision is the soul of science [...]" (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

📁 On DIKW: On Knowledge (1930-1939)

"The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge is complete. We go beyond the mathematical formula at our own risk; we may find a [nonmathematical] model or picture that helps us to understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault." (James Jeans, "The Mysterious Universe", 1930)

"Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of them without any practical purpose whatsoever in view." (Max Planck, "Where is Science Going?", 1932)

"As facts and knowledge accumulate, the claim of the scientist to an understanding of the world in a certain sense diminishes." (Werner K Heisenberg, "Zur Geschichte der physikalischen Naturerklärung", 1933)

"The urge to knowledge is so deeply rooted in man that it can scarcely be omitted from a list of life's important needs." (Hans Reichenbach, "Atom and Cosmos: The World of Modern Physics", 1933)

"Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all. Thus it may be that some part of what one knows may pertain to relations […] between the two subsystems (we shall limit ourselves to two), as follows: if a particular measurement on the first system yields this result, then for a particular measurement on the second the valid expectation statistics are such and such; but if the measurement in question on the first system should have that result, then some other expectation holds for that one the second. […] In this way, any measurement process at all or, what amounts to the same, any variable at all of the second system can be tied to the not-yet-known value of any variable at all of the first, and of course vice versa also." (Erwin Schrödinger, "The Present Situation in Quantum Mechanics", 1935)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"We have discovered that it is actually an aid in the search for knowledge to understand the nature of the knowledge we seek." (Arthur S Eddington, "The Philosophy of Physical Science", 1938)

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

"The failure of the social sciences to think through and to integrate their several responsibilities for the common problem of relating the analysis of parts to the analysis of the whole constitutes one of the major lags crippling their utility as human tools of knowledge." (Robert S Lynd, "Knowledge of What?", 1939)

📁 On DIKW: On Knowledge (1970-1979)

"Inductive inference is the only process known to us by which essential new knowledge comes into the world." (Sir Ronald A Fisher, "The Design of Experiments", 1971)

"A discovery must be, by definition, at variance with existing knowledge." (Albert Szent-Gyorgyi, "Dionysians and Apollonians", Science 176, 1972)

"Nature is a network of happenings that do not unroll like a red carpet into time, but are intertwined between every part of the world; and we are among those parts. In this nexus, we cannot reach certainty because it is not there to be reached; it goes with the wrong model, and the certain answers ironically are the wrong answers. Certainty is a demand that is made by philosophers who contemplate the world from outside; and scientific knowledge is knowledge for action, not contemplation. There is no God’s eye view of nature, in relativity, or in any science: only a man’s eye view." (Jacob Bronowski, "The Identity of Man", 1972)

"The human condition can almost be summed up in the observation that, whereas all experiences are of the past, all decisions are about the future. It is the great task of human knowledge to bridge this gap and to find those patterns in the past which can be projected into the future as realistic images." (Kenneth E Boulding, [foreword] 1972)

"Human knowledge is personal and responsible, an unending adventure at the edge of uncertainty." (Jacob Bronowski, "The Ascent of Man", 1973)

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

"Discoveries are made by pursuing possibilities suggested by existing knowledge." (Michael Polanyi, "Meaning", 1975)

"Combining this observation with the insight that science has no special method, we arrive at the result that the separation of science and non-science is not only artificial but also detrimental to the advancement of knowledge. If we want to understand nature, if we want to master our physical surroundings, then we must use all ideas, all methods, and not just a small selection of them. The assertion, however, that there is no knowledge outside science - extra scientiam nulla salus." (Paul K Feyerabend, "Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)

"Knowledge is not a series of self-consistent theories that converges toward an ideal view; it is rather an ever increasing ocean of mutually incompatible (and perhaps even incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the others into greater articulation and all of them contributing, via this process of competition, to the development of our consciousness." (Paul K Feyerabend, "Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)

"Every judgment teeters on the brink of error. To claim absolute knowledge is to become monstrous. Knowledge is an unending adventure at the edge of uncertainty." (Frank Herbert, "Children of Dune", 1976)

"Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things […] are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge." (Alan R Beals, "Strategies of Resort to Curers in South India" [contributed in Charles M. Leslie (ed.), "Asian Medical Systems: A Comparative Study", 1976]) 

"Concepts form the basis for any science. These are ideas, usually somewhat vague (especially when first encountered), which often defy really adequate definition. The meaning of a new concept can seldom be grasped from reading a one-paragraph discussion. There must be time to become accustomed to the concept, to investigate it with prior knowledge, and to associate it with personal experience. Inability to work with details of a new subject can often be traced to inadequate understanding of its basic concepts." (William C Reynolds & Harry C Perkins, "Engineering Thermodynamics", 1977)

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

"Certainty, simplicity, vividness originate in popular knowledge. That is where the expert obtains his faith in this triad as the ideal of knowledge. Therein lies the general epistemological significance of popular science." (Ludwik Fleck, "Genesis and Development of a Scientific Fact", 1979)

"It is hard for us today to assimilate all the new ideas that are being suggested in response to the new information we have. We must remember that our picture of the universe is based not only on our scientific knowledge but also on our culture and our philosophy. What new discoveries lie ahead no one can say. There may well be civilizations in other parts of our galaxy or in other galaxies that have already accomplished much of what lies ahead for mankind. Others may just be beginning. The universe clearly presents an unending challenge." (Necia H Apfel & J Allen Hynek, "Architecture of the Universe", 1979)

On Puzzles (- 1950)

"While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what anyone man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician." (Sir Arthur C Doyle, "The Sign of Four", 1890)

"Everything in nature is a puzzle until it finds its solution in man, who solves it in some way with God, and so completes the circle of creation. " (Theodore T Munger, "The Appeal to Life", 1891)

"The most ordinary things are to philosophy a source of insoluble puzzles. In order to explain our perceptions it constructs the concept of matter and then finds matter quite useless either for itself having or for causing perceptions in a mind. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time [...] The source of this kind of logic lies in excessive confidence in the so-called laws of thought." (Ludwig E Boltzmann, "On Statistical Mechanics", 1904)

"The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science." (Sir Oliver J Lodge, [Becquerel Memorial Lecture] Journal of the Chemical Society, Transactions 101 (2), 1912)

"The development of mathematics is largely a natural, not a purely logical one: mathematicians are continually answering questions suggested by astronomers or physicists; many essential mathematical theories are but the reflex outgrowth from physical puzzles." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"In her manifold opportunities Nature has thus helped man to polish the mirror of [man’s] mind, and the process continues. Nature still supplies us with abundance of brain-stretching theoretical puzzles and we eagerly tackle them; there are more worlds to conquer and we do not let the sword sleep in our hand; but how does it stand with feeling? Nature is beautiful, gladdening, awesome, mysterious, wonderful, as ever, but do we feel it as our forefathers did?" (Sir John A Thomson, "The System of Animate Nature", 1920)

"[while] the traditional way is to regard the facts of science as something like the parts of a jig-saw puzzle, which can be fitted together in one and only one way, I regard them rather as the tiny pieces of a mosaic, which can be fitted together in many ways. A new theory in an old subject is, for me, a new mosaic pattern made with the pieces taken from an older pattern. [...] Theories come into fashion and theories go out of fashion, but the facts connected with them stay." (William H George, "The Scientist in Action", 1936)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"Even if all parts of a problem seem to fit together like the pieces of a jigsaw puzzle, one has to remember that the probable need not necessarily be the truth and the truth not always probable." (Sigmund Freud, "Moses and Monotheism", 1939)

On Paradigms II

"The realm of the particularity of each experienced item differs from the formal realm of concepts. [...] The power of paradigmatic thought is to bring order to experience by seeing individual things as belonging to a category." (Donald E Polkinghorne, “Narrative configuration in qualitative analysis", International Journal of Qualitative Studies in Education Vol. 8 (1), 1995)

"Discovery commences with the awareness of anomaly, i.e., with the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science. It then continues with a more or less extended exploration of the area of anomaly. And it closes only when the paradigm theory has been adjusted so that the anomalous has become the expected. […] Until he has learned to see nature in a different way - the new fact is not quite a scientific fact at all." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"The transition from a paradigm to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field’s most elementary theoretical generalizations as well as many of its paradigm methods and applications." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"[…] paradigms, the core of the culture of science, are transmitted and sustained just as is culture generally: scientists accept them and become committed to them as a result of training and socialization, and the commitment is maintained by a developed system of social control." (Barry Barnes, "Thomas Kuhn", 1985)

"All scientific theories, even those in the physical sciences, are developed in a particular cultural context. Although the context may help to explain the persistence of a theory in the face of apparently falsifying evidence, the fact that a theory arises from a particular context is not sufficient to condemn it. Theories and paradigms must be accepted, modified or rejected on the basis of evidence." (Richard P Bentall,  "Madness Explained: Psychosis and Human Nature", 2003)

"A paradigm is a shared mindset that represents a fundamental way of thinking about, perceiving, and understanding the world." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

On Continuity XIV (Progress)

"Nothing is accomplished all at once, and it is one of my great maxims, and one of the most completely verified, that Nature makes no leaps: a maxim which I have called the law of continuity." (Gottfried W Leibniz, "New Essays Concerning Human Understanding with an Appealing", 1704)

"Harmonious order governing eternally continuous progress - the web and woof of matter and force interweaving by slow degrees, without a broken thread, that veil which lies between us and the Infinite - that universe which alone we know or can know; such is the picture which science draws of the world, and in proportion as any part of that picture is in unison with the rest, so may we feel sure that it is rightly painted." (Thomas H Huxley, "Darwiniana", 1893–94)

"Mathematics is not a world empire where one man can exert a dominating influence over work along all the lines, but it is continually splitting up into self-determining republics." (Geroge A Miller, "Felix Klein and the History of Modern Mathematics", 1927)

"The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. […] it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-Euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation." (Paul A M Dirac, "Quantities singularities in the electromagnetic field", Proceedings of the Royal Society of London, 1931)

"For it is true, generally speaking, that mathematics is not a popular subject, even though its importance may be generally conceded. The reason for this is to be found in the common superstition that mathematics is but a continuation, a further development, of the fine art of arithmetic, of juggling with numbers." (David Hilbert, "Anschauliche Geometrie", 1932)

"Science does not mean an idle resting upon a body of certain knowledge; it means unresting endeavor and continually progressing development toward an end which the poetic intuition may apprehend, but which the intellect can never fully grasp." (Max Planck, "The Philosophy of Physics", 1936)

"And yet, on looking into the history of science, one is overwhelmed by evidence that all too often there is no regular procedure, no logical system of discovery, no simple, continuous development. The process of discovery has been as varied as the temperament of the scientist." (Gerald Holton, "Thematic Origins of Scientific Thought: Kepler to Einstein", 1973)

On Conjecture (Unsourced)

"In the study of Nature conjecture must be entirely put aside, and vague hypothesis carefully guarded against. The study of Nature begins with facts, ascends to laws, and raises itself, as far as the limits of man’s intellect will permit, to the knowledge of causes, by the threefold means of observation, experiment and logical deduction." (Jean Baptiste-Andre Dumas)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"The conjectures of the scientific intelligence are genuine creative novelties, inherently unpredictable and not determined by the character of the scientist’s physical environment. The thinking mind is not a causal mechanism." (Anthony M Quinton)

"The only use of an hypothesis is, that it should lead to experiments; that it should be a guide to facts. In this application, conjectures are always of use. The destruction of an error hardly ever takes place without the discovery of truth. [...] Hypothesis should be considered merely an intellectual instrument of discovery, which at any time may be relinquished for a better instrument. It should never be spoken of as truth; its highest praise is verisimility. Knowledge can only be acquired by the senses; nature has an archetype in the human imagination; her empire is given only to industry and action, guided and governed by experience." (Sir Humphry Davy) 

"The purpose of life is to conjecture and prove." (Paul Erdős)

"The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations." (Godfrey H Hardy)

"What certainty can there be in a Philosophy which consists in as many Hypotheses as there are Phaenomena to be explained. To explain all nature is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, & leave the rest for others that come after you, than to explain all things by conjecture without making sure of any thing." (Sir Isaac Newton)

On Conjecture (1750-1799)

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

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

"[...] the lofty aspirations of humanity and not delusions; they are realities. They link us to a purer order of existence, which makes us heirs of immortality. We repose order a confident and unwavering assurance that, in God’s own time, these earth-mists will be dispersed, and the dim twilight of conjecture will yield to the glorious, unclouded noonday of knowledge." (John LeConte, "The Nebular Hypothesis", The Popular Science Monthly Vol. 2, 1873)

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

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

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

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

On Creativity (Mathematics I)

"Creativity is the heart and soul of mathematics at all levels. The collection of special skills and techniques is only the raw material out of which the subject itself grows. To look at mathematics without the creative side of it, is to look at a black-and-white photograph of a Cezanne; outlines may be there, but everything that matters is missing." (Robert C Buck, "Teaching Machines and Mathematics Programs", American Mathematical Monthly 69, 1962)

"There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory." (Mark Kac, "Enigmas Of Chance", 1985)

"Music and higher mathematics share some obvious kinship. The practice of both requires a lengthy apprenticeship, talent, and no small amount of grace. Both seem to spring from some mysterious workings of the mind. Logic and system are essential for both, and yet each can reach a height of creativity beyond the merely mechanical." (Frederick Pratter, "How Music and Math Seek Truth in Beauty", Christian Science Monitor, 1995)

"Mathematics is a fascinating discipline that calls for creativity, imagination, and the mastery of rigorous standards of proof." (John Meier & Derek Smith, "Exploring Mathematics: An Engaging Introduction to Proof", 2017)

"Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say. Why play the violin? Because it is beautiful! Why engage in math? Because it too is beautiful!" (James Tanton, "Thinking Mathematics")

"Mathematics is the summit of human thinking. It has all the creativity and imagination that you can find in all kinds of art, but unlike art-charlatans and all kinds of quacks will not succeed there." (Meir Shalev)

"No discovery has been made in mathematics, or anywhere else for that matter, by an effort of deductive logic; it results from the work of creative imagination which builds what seems to be truth, guided sometimes by analogies, sometimes by an esthetic ideal, but which does not hold at all on solid logical bases. Once a discovery is made, logic intervenes to act as a control; it is logic that ultimately decides whether the discovery is really true or is illusory; its role therefore, though considerable, is only secondary." (Henri Lebesgue)

"The essential feature of mathematical creativity is the exploration, under the pressure of powerful implosive forces, of difficult problems for whose validity and importance the explorer is eventually held accountable by reality." (Alfred Adler)

K C Cole - Collected Quotes

"So much of science consists of things we can never see: light ‘waves’ and charged ‘particles’; magnetic ‘fields’ and gravitational ‘forces’; quantum ‘jumps’ and electron ‘orbits’. In fact, none of these phenomena is literally what we say it is. Light waves do not undulate through empty space in the same way that water waves ripple over a still pond; a field is only a mathematical description of the strength and direction of a force; an atom does not literally jump from one quantum state to another, and electrons do not really travel around the atomic nucleus in orbits. The words we use are merely metaphors." (K C Cole, "On Imagining the Unseeable", Discover Magazine, 1982)

"How deep truths can be defined as invariants – things that do not change no matter what; how invariants are defined by symmetries, which in turn define which properties of nature are conserved, no matter what. These are the selfsame symmetries that appeal to the senses in art and music and natural forms like snowflakes and galaxies. The fundamental truths are based on symmetry, and there’s a deep kind of beauty in that. (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997) 

"Math has its own inherent logic, its own internal truth. Its beauty lies in its ability to distill the essence of truth without the messy interference of the real world. It’s clean, neat, above it all. It lives in an ideal universe built on the geometer’s perfect circles and polygons, the number theorist’s perfect sets. It matters not that these objects don’t exist in the real world. They are articles of faith." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Mathematicians do not see their art as a way of simply calculating or ordering reality. They understand that math articulates, manipulates, and discovers reality. In that sense, it’s both a language and a literature; a box of tools and the edifices constructed from them." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Mathematics can function as a telescope, a microscope, a sieve for sorting out the signal from the noise, a template for pattern perception, a way of seeking and validating truth. […] A knowledge of the mathematics behind our ideas can help us to fool ourselves a little less often, with less drastic consequences." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Mathematics is a way of thinking that can help make muddy relationships clear. It is a language that allows us to translate the complexity of the world into manageable patterns. In a sense, it works like turning off the houselights in a theater the better to see a movie. Certainly, something is lost when the lights go down; you can no longer see the faces of those around you or the inlaid patterns on the ceiling. But you gain a far better view of the subject at hand." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Mathematics seems to have astonishing power to tell us how things work, why things are the way they are, and what the universe would tell us if we could only learn to listen. This comes as a surprise from a branch of human activity that is supposed to be abstract, objective, and devoid of sentiment." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"One of the main reasons that large numbers grow so explosively is that multiplication is a powerful engine for growth - even when the only number you happen to be multiplying is insignificantly puny, like the number two."  (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Another limit imposed by reality is its sheer complexity, which makes it impossible to predict some ordinary things (like weather) at the same time that it’s possible to predict truly extraordinary things (like the fate of the universe)." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"Abstractions are a way to distill the essence from an otherwise unfathomable situation." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"Imagining the unseeable is hard, because imagining means having an image in your mind. And how can you have a mental image of something you have never seen? Like perception itself, the models of science are embedded inextricably in the current worldview we call culture." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"Science [...] involves looking mostly at things we can never see." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"The abstractions of science are stereotypes, as two-dimensional and as potentially misleading as everyday stereotypes. And yet they are as necessary to the process of understanding as filtering is to the process of perception." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"The subjects of science are not only often unseeable; they are also untouchable, unmeasurable, and sometimes even unimaginable." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"If two quantum particles are entangled, they become, in effect, two parts of a single unit. What happens to one entangled particle happens to the other, no matter how far apart they are." (K C Cole, "Wormholes Untangle a Black Hole Paradox", 2015) [source] 

"Like many a maturing beauty, string theory has gotten rich in relationships, complicated, hard to handle and widely influential. Its tentacles have reached so deeply into so many areas in theoretical physics, it’s become almost unrecognizable, even to string theorists." (K C Cole, "The Strange Second Life of String Theory", Quanta Magazine", 2016) [source] 

"String theory today looks almost fractal. The more closely people explore any one corner, the more structure they find. Some dig deep into particular crevices; others zoom out to try to make sense of grander patterns. The upshot is that string theory today includes much that no longer seems stringy. Those tiny loops of string whose harmonics were thought to breathe form into every particle and force known to nature (including elusive gravity) hardly even appear anymore on chalkboards at conferences." (K C Cole, "The Strange Second Life of String Theory", Quanta Magazine", 2016) [source]

"[…] Einstein showed, for 'stuff' like space and time, seemingly stable, unchangeable aspects of nature; in truth, it’s the relationship between space and time that always stays the same, even as space contracts and time dilates. Like energy and matter, space and time are mutable manifestations of deeper, unshakable foundations: the things that never vary no matter what." (K C Cole, "The Simple Idea Behind Einstein’s Greatest Discoveries", Quanta Magazine, 2019) [source] 

📁 On DIKW: On Facts (1800-1824)

"Isolated facts, those that can only be obtained by rough estimate and that require development, can only be presented in memoires; but those that can be presented in a body, with details, and on whose accuracy one can rely, may be expounded in tables." (Emmanuel Duvillard, "Memoire sur le travail du Bureau de statistique", 1806)

"The foundations of chemical philosophy are observation, experiment, and analogy. By observation, facts are distinctly and minutely impressed on the mind. By analogy, similar facts are connected. By experiment, new facts are discovered; and, in the progression of knowledge, observation, guided by analogy, lends to experiment, and analogy confirmed by experiment, becomes scientific truth." (Sir Humphry Davy, "Elements of Chemical Philosophy" Vol. 4, 1812)

"The theory of which we have just given an overview may be considered from a point of view apt to set aside the obscure in what it presents, and which seems to be the primary aim, namely: to establish new notions on imaginary quantities. Indeed, putting to one side the question of whether these notions are true or false, we may restrict ourselves to viewing this theory as a means of research, to adopt the lines in direction only as signs of the real or imaginary quantities, and to see, in the usage to which we have put them, only the simple employment of a particular notation. For that, it suffices to start by demonstrating, through the first theorems of trigonometry, the rules of multiplication and addition given above; the applications will follow, and all that will remain is to examine the question of didactics. And if the employment of this notation were to be advantageous? And if it were to open up shorter and easier paths to demonstrate certain truths? That is what fact alone can decide." (Jean-Robert Argand, "Essai sur une manière de représenter les quantités imaginaires, dans les constructions géométriques", Annales Tome IV, 1813)

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

"The substitution of analogy for fact is the bane of chemical philosophy; the legitimate use of analogy is to connect facts together and to guide to new experiments." (Sir Humphry Davy, "Journal of Science and the Arts", 1816)

"Force is not a fact at all, but an idea embodying what is approximately the fact." (William K Clifford, "The Common Sense of the Exact Sciences", 1823)

📁 On DIKW: On Facts (1860-1869)

"Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer would always be in arrears, and were doomed forever to arrive at imperfect conclusion; but the power to perceive a law is equally rare in all ages of the world, and depends but little on the number of facts observed." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

"The discoverer and the poet are inventors; and they are so because their mental vision detects the unapparent, unsuspected facts, almost as vividly as ocular vision rests on the apparent and familiar." (George H Lewes, "Principles of Success in Literature", 1865)

"Facts can be accurately known to us only by the most rigid observation and sustained and scrutinizing skepticism […]" (James A Froude, Short Studies on Great Subjects Vol. 2, 1867)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"The triumph of a theory is to embrace the greatest number and the greatest variety of facts." (Charles A Wurtz, "A History of Chemical Theory from the Age of Lavoisier to the Present Time", 1869)

📁 On DIKW: On Facts (1870-1879)

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts." (Louis Pasteur, "Étude sur la maladie des vers à soie", 1870)

"Therefore, the great business of the scientific teacher is, to imprint the fundamental, irrefragable facts of his science, not only by words upon the mind, but by sensible impressions upon the eye, and ear, and touch of the student, in so complete a manner, that every term used, or law enunciated, should afterwards call up vivid images of the particular structural, or other, facts which furnished the demonstration of the law, or the illustration of the term." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in Nature." (Augustus de Morgan, "A Budget of Paradoxes", 1872)

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

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

"In every physical science we have carefully to distinguish between the facts which form its subject-matter and the theories by which we attempt to explain these facts, and group them in our scientific systems." (Josiah P Cooke, "The New Chemistry", 1876)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)