📁 On DIKW: On Mastery (-1899)

"The modern age has a false sense of superiority because of the great mass of data at its disposal. But the valid criterion of distinction is rather the extent to which man knows how to form and master the material at his command." (Johann Wolfgang von Goethe, "On Theory of Color", 1810)

“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)

"Whenever a man can get hold of numbers, they are invaluable: if correct, they assist in informing his own mind, but they are still more useful in deluding the minds of others. Numbers are the masters of the weak, but the slaves of the strong." (Charles Babbage, "Passages From the Life of a Philosopher", 1864)

"[Arithmetic] is another of the great master-keys of life. With it the astronomer opens the depths of the heavens; the engineer, the gates of the mountains; the navigator, the pathways of the deep. The skillful arrangement, the rapid handling of figures, is a perfect magician's wand." (Edward Everett,"Orations and Speeches", 1870)

"Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skillful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures."(Johann F Herbart, 1890)

"One of the most baneful delusions by which the minds, not only of students, but even of many teachers of mathematics in our classical colleges, have been afflicted is that mathematics can be mastered by the favored few, but lies beyond the grasp and power of the ordinary mind." (Florian Cajori, "The Teaching and History of Mathematics in the United States", 1890)

📁 On DIKW: On Mastery (1900-1924)

"In astronomy, the law of gravitation is plainly better worth knowing than the position of a particular planet on a particular night, or even on every night throughout a year. There are in the law a splendor and simplicity and sense of mastery which illuminate a mass of otherwise uninteresting details [...]" (Bertrand Russell, "On History,  Independent Review, 1904)

"The training which mathematics gives in working with symbols is an excellent preparation for other sciences; […] the world's work requires constant mastery of symbols." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"The progressive development of man is vitally dependent on invention. It is the most important product of his creative brain. Its ultimate purpose is the complete mastery of mind over the material world, the harnessing of the forces of nature to human needs. This is the difficult task of the inventor who is often misunderstood and unrewarded. But he finds ample compensation in the pleasing exercises of his powers and in the knowledge of being one of that exceptionally privileged class without whom the race would have long ago perished in the bitter struggle against pitiless elements. Speaking for myself, I have already had more than my full measure of this exquisite enjoyment; so much, that for many years my life was little short of continuous rapture." (Nikola Tesla, "My Inventions", 1919)

"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)

"The mind unconsciously assimilates evidence in favour of a pet hypothesis; and a pet hypothesis is apt to grow from a favoured child to a tyrannical master." (Joseph W Mellor, "A Comprehensive Treatise on Inorganic and Theoretical Chemistry", 1922)

"Architecture is the masterly, correct and magnificent play of masses brought together in light. Our eyes are made to see forms in light; light and shade reveal these forms; cubes, cones, spheres, cylinders or pyramids are the great primary forms which light reveals to advantage; the image of these is distinct and tangible within us without ambiguity. It is for this reason that these are beautiful forms, the most beautiful forms. Everybody is agreed to that, the child, the savage and the metaphysician." (Charles-Edouard Jeanneret [Le Corbusier], "Towards a New Architecture", 1923)

📁 On DIKW: On Mastery (1925-1949)

"For establishing the laws of nature one resorts (not deliberately but involuntarily) to the simplest formulas that seem to describe the phenomena with reasonable accuracy. […] Even those laws of nature that are the most general and important for the world view have always been proved experimentally only in a confined ambit and with limited accuracy. […] The exact formulation of the laws of nature by simple formulas is based on the desire to master external phenomena with the simplest tools possible." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)

"In mathematics as in the other sciences, the same processes can be observed again and again. First, new questions arise, for internal or external reasons, and draw researchers away from the old questions. And the old questions, just because they have been worked on so much, need ever more comprehensive study for their mastery. This is unpleasant, and so one is glad to turn to problems that have been less developed and therefore require less foreknowledge - even if it is only a matter of axiomatics, or set theory, or some such thing." (Felix Klein,"Development of Mathematics in the 19th Century", 1928)

"This civilization is the work of man, who high-handedly and ignorant of the true workings of Nature, has created a world without meaning or foundation, which now threatens to destroy him, for through his behavior and his activities, he, who should be her master, has disturbed Nature's inherent unity." (Viktor Schauberger, "Callum Coats: Water Wizard", 1934

"We know, since the theory of relativity at least, that empirical sciences are to some degree free in defining dynamical concepts or even in assuming laws, and that only a system as a whole which includes concepts, coordinating definitions, and laws can be said to be either true or false, to be adequate or inadequate to empirical facts. This 'freedom', however, is a somewhat doubtful gift. The manifold of possibilities implies uncertainty, and such uncertainty can become rather painful in a science as young as psychology, where nearly all concepts are open and unsettled. As psychology approaches the state of a logically sound science, definitions cease to be an arbitrary matter. They become far-reaching decisions which presuppose the mastering of the conceptual problems but which have to be guided entirely by the objective facts." (Kurt Lewin, "Principles of topological psychology", 1936)

"Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up. " (Albert Einstein & Leopold Infeld, "The Evolution of Physics ", 1938)

"There is no sharply drawn line between those contradictions which occur in the daily work of every mathematician, beginner or master of his craft, as a result of more or less easily detected mistakes, and the major paradoxes which provide food for logical thought for decades and sometimes centuries." (Nicholas Bourbaki), "Foundations of Mathematics for the Working Mathematician", The Journal of Symbolic Logic Vol. 14 (1), 1949

📁 On DIKW: On Mastery (1950-1974)

"Something more than impeccable logic is required in mathematics. An expert logician will not necessarily be a passable mathematician for all his skill in logic, any more than a scholarly prosodist will be a respectable poet for all his mastery of meter." (Eric T Bell, "Mathematics, Queen and Servant of Science", 1951)

"Understanding mathematical logic, or the theory of relativity, is not an indispensable attribute of the cultured mind. But if one wishes to learn anything about these subjects, one must learn something. It is necessary to master the rudiments of the language, to practice a technique, to follow step by step a characteristic sequence of reasoning and to see a problem through from beginning to end." (James R Newman, "The World of Mathematics” Vol. I, 1956)

"It is widely believed that only those who can master the latest quantum mathematics can understand anything of what is happening. That is not so, provided one takes the long view, for no one can see far ahead. Against a historical background, the layman can understand what is involved, for example, in the fascinating challenge of continuity and discontinuity expressed in the antithesis of field and particle." (Lancelot L Whyte, "Essay on Atomism: From Democritus to 1960", 1961)

"Nature does not seem full of circles and triangles to the ungeometrical; rather, mastery of the theory of triangles and circles, and later of conic sections, has taught the theorist, the experimenter, the carpenter, and even the artist to find them everywhere, from the heavenly motions to the pose of a Venus." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"But, really, mathematics is not religion; it cannot be founded on faith. And what was most important, the methods yielding such remarkable results in the hands of the great masters began to lead to errors and paradoxes when employed by their less talented students. The masters were kept from error by their perfect mathematical intuition, that subconscious feeling that often leads to the right answer more quickly than lengthy logical reasoning. But the students did not possess this intuition […]" (Naum Ya. Vilenkin, "Stories about Sets", 1968)

"The future masters of technology will have to be lighthearted and intelligent. The machine easily masters the grim and the dumb." (Marshall McLuhan, "Counterblast", 1969)

"[...] it seems self-evident that mathematics is not likely to be much help in discovering laws of nature. If a mathematician wants to make a contribution on this (and I admit it is the highest) level, he will have to master so much experimental material and train himself to think in a way so different from the one he has been accustomed to that he will, in effect, cease to be a mathematician." (Mark Kac, "On Applying Mathematics: Reflections and Examples", Quarterly of Applied Mathematics, 1972)

📁 On DIKW: On Mastery (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)

"In spite of its universality and good precision the linear model is very elementary in its means which are mainly those of linear algebra, so even people with very modest mathematical training can understand and master it. The last is very important for a creative and non-routine use of the analytical means which are given by the model." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975)

"When you have mastered the numbers, you will in fact no longer be reading numbers, any more than you read words when reading a book. You will be reading meanings." (Harold Geneen & Alvin Moscow, "Managing", 1984)

"The beauty of mathematics often makes the subject matter much more attractive and easier to master." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"Understanding the methods of calculus is vital to the creative use of mathematics... Without this mastery the average scientist or engineer, or any other user of mathematics, will be perpetually stunted in development, and will at best be able to follow only what the textbooks say; with mastery, new things can be done, even in old, well-established fields." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"Apparently an 'art' - which almost by definition cannot be put into words - is probably best communicated by approaching it from many sides and doing so repeatedly, hoping thereby students will finally master enough of the art, or if you wish, style, to significantly increase their future contributions to society." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)

"Science is not about control. It is about cultivating a perpetual condition of wonder in the face of something that forever grows one step richer and subtler than our latest theory about it. It is about reverence, not mastery." (Richard Power, “Gold Bug Variations”, 1993)

"In our analysis of complex systems (like the brain and language) we must avoid the trap of trying to find master keys. Because of the mechanisms by which complex systems structure themselves, single principles provide inadequate descriptions. We should rather be sensitive to complex and self-organizing interactions and appreciate the play of patterns that perpetually transforms the system itself as well as the environment in which it operates." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)

"There is no 'scientific worldview' just as there is no uniform enterprise 'science' - except in the minds of metaphysicians, school masters, and scientists blinded by the achievements of their own particular niche […]." (Paul Karl Feyerabend, "Conquest of Abundance", 1999)

"In an information economy, entrepreneurs master the science of information in order to overcome the laws of the purely physical sciences. They can succeed because of the surprising power of the laws of information, which are conducive to human creativity. The central concept of information theory is a measure of freedom of choice. The principle of matter, on the other hand, is not liberty but limitation - it has weight and occupies space." (George Gilder, "Knowledge and Power: The Information Theory of Capitalism and How it is Revolutionizing our World", 2013)

"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)

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