🗼On Philosophy of Science: On Mysticism (Trivia)

"It is in fact wonderful how physics - as soon as it is concerned not with technical purposes but with general results - without knowing it gets into cosmogony, astrology, theosophy, or whatever you wish to call it, in short, into a mystic discipline of the whole." (K W Friedrich von Schlegel, "Dialogue on Poetry and Literary Aphorisms", 1797)

"Wit is the appearance, the external flash of imagination. Thus its divinity, and the witty character of mysticism." (K W Friedrich von Schlegel, "Dialogue on Poetry and Literary Aphorisms", [Aphorism 26] 1797)

"Although we gladly acknowledge Nature's mysterious encheiresis, her faculty of creating and furthering life, and, without being mystics, admit the existence of ultimate limits to our explorations, we are nevertheless convinced that man, if he is serious about it, cannot desist from the attempt to keep encroaching upon the region of the unexplorable. In the end, of course, he has to give up and willingly concede his defeat." (Johann Wolfgang von Goethe, 1832)

"Metaphysics, or the attempt to conceive the world as a whole by means of thought, has been developed, from the first, by the union and conflict of two very different human impulses, the one urging men towards mysticism, the other urging them towards science." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1919)

"We are constantly hatching an enormous number of false ideas, conceits, Utopias, mystical explanations, suspicions, and megalomaniacal fantasies, which disappear when brought into contact with other people." (Jean Piaget, "Le jugement et le raisonnement chez l'enfant" ["Judgment and Reasoning in the Child"], 1924)

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

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

"The conceptual framework of quantum mechanics, supported by massive volumes of experimental data, forces contemporary physicists to express themselves in a manner that sounds, even to the uninitiated, like the language of mystics." (Gary Zukav, "The Dancing Wu Li Masters", 1979)

"There is no such thing as a Scientific Mind. Scientists are people of very dissimilar temperaments doing different things in very different ways. Among scientists are collectors, classifiers and compulsive tidiers-up; many are detectives by temperament and many are explorers; some are artists and others artisans. There are poet-scientists and philosopher-scientists and even a few mystics. What sort of mind or temperament can all these people be supposed to have in common? Obligative scientists must be very rare, and most people who are in fact scientists could easily have been something else instead." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"Zero is not a point of non-existence. Zero is always a balance point of existents. The human understanding of 'zero' must undergo the most radical of all transformations. Most people, especially scientists, associate it with absolute nothingness, with non-existence. This is absolutely untrue. Or, to put it another way, we can define it in two ways: 1) nothing as non-existence, in which case it has absolutely no consequences but leads to all manner of abstract paradoxes and contradictions, or 2) nothing as existence, in which case it is always a mathematical balance point for somethings. It is purely mathematical, not scientific, or religious, or spiritual, or emotional, or sensory, or mystical. It is analytic nothing and whenever you encounter it you have to establish the exact means by which it is maintaining its balance of zero." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

🗼On Philosophy of Science: On Mysticism in Mathematics (1990-)

"Virtually all mathematical theorems are assertions about the existence or nonexistence of certain entities. For example, theorems assert the existence of a solution to a differential equation, a root of a polynomial, or the nonexistence of an algorithm for the Halting Problem. A platonist is one who believes that these objects enjoy a real existence in some mystical realm beyond space and time. To such a person, a mathematician is like an explorer who discovers already existing things. On the other hand, a formalist is one who feels we construct these objects by our rules of logical inference, and that until we actually produce a chain of reasoning leading to one of these objects they have no meaningful existence, at all." (John L Casti, "Reality Rules: Picturing the world in mathematics" Vol. II, 1992) 

"A real number that satisfies (is a solution of) a polynomial equation with integer coefficients is called algebraic. […] A real number that is not algebraic is called transcendental. There is nothing mystic about this word; it merely indicates that these numbers transcend (go beyond) the realm of algebraic numbers."  (Eli Maor, "e: The Story of a Number", 1994)

"An aura of mysticism still surrounds the concept that has since been called 'imaginary numbers', and anyone who encounters these numbers for the first time is intrigued by their strange properties. But 'strange' is relative: with sufficient familiarity, the strange object of yesterday becomes the common thing of today." (Eli Maor, "e: The Story of a Number", 1994)

"In many ways, the mathematical quest to understand infinity parallels mystical attempts to understand God. Both religions and mathematics attempt to express the relationships between humans, the universe, and infinity. Both have arcane symbols and rituals, and impenetrable language. Both exercise the deep recesses of our mind and stimulate our imagination. Mathematicians, like priests, seek ‘ideal’, immutable, nonmaterial truths and then often try to apply theses truth in the real world." (Clifford A Pickover, "The Loom of God: Mathematical Tapestries at the Edge of Time", 1997)

"How beautifully simple is Wessel’s idea. Multiplying by √-1 is, geometrically, simply a rotation by 90 degrees in the counter clockwise sense [...] Because of this property √-1 is often said to be the rotation operator, in addition to being an imaginary number. As one historian of mathematics has observed, the elegance and sheer wonderful simplicity of this interpretation suggests 'that there is no occasion for anyone to muddle himself into a state of mystic wonderment over the grossly misnamed ‘imaginaries'. This is not to say, however, that this geometric interpretation wasn’t a huge leap forward in human understanding. Indeed, it is only the start of a tidal wave of elegant calculations." (Paul J Nahin, "An Imaginary Tale: The History of √-1", 1998)

"The primes have been a constant companion in our exploration of the mathematical world yet they remain the most enigmatic of all numbers. Despite the best efforts of the greatest mathematical minds to explain the modulation and transformation of this mystical music, the primes remain an unanswered riddle." (Marcus du Sautoy, "The Music of the Primes", 2003)

"To survive, mathematical ideas must be beautiful, they must be seductive, and they must be illuminating, they must help us to understand, they must inspire us. […] Part of that beauty, an essential part, is the clarity and sharpness that the mathematical way of thinking about things promotes and achieves. Yes, there are also mystic and poetic ways of relating to the world, and to create a new math theory, or to discover new mathematics, you have to feel comfortable with vague, unformed, embryonic ideas, even as you try to sharpen them."  (Gregory Chaitin, "Meta Math: The Quest for Omega", 2005)

"Mathematical language is littered with pejorative and mystical terms - such as irrational, imaginary, surd, transcendental - that were once used to ridicule supposedly impossible objects. And these are just terms applied to numbers. Geometry also has many concepts that seem impossible to most people, such as the fourth dimension, finite universes, and curved space - yet geometers (and physicists) cannot do without them. Thus there is no doubt that  mathematics flirts with the impossible, and seems to make progress by doing so." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics", 2006)

"Zero is not a point of non-existence. Zero is always a balance point of existents. The human understanding of 'zero' must undergo the most radical of all transformations. Most people, especially scientists, associate it with absolute nothingness, with non-existence. This is absolutely untrue. Or, to put it another way, we can define it in two ways: 1) nothing as non-existence, in which case it has absolutely no consequences but leads to all manner of abstract paradoxes and contradictions, or 2) nothing as existence, in which case it is always a mathematical balance point for somethings. It is purely mathematical, not scientific, or religious, or spiritual, or emotional, or sensory, or mystical. It is analytic nothing and whenever you encounter it you have to establish the exact means by which it is maintaining its balance of zero." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

🗼On Phylosophy of Science: On Mysticism & Mathematics (-1989)

"All things began in order, so shall they end, and so shall they begin again; according to the ordainer of order and mystical mathematics of the city of heaven." (Sir Thomas Browne, "The Garden of Cyrus", 1658)

"In the beginning of algebra, even the most intelligent child finds, as a rule, very great difficulty. The use of letters is a mystery, which seems to have no purpose except mystification. It is almost impossible, at first, not to think that every letter stands for some particular number, if only the teacher would reveal what number it stands for." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1910)

"The popularity of the problem among non-Mathematicians may seem to require some explanation. No doubt, the fact of its comparative obviousness explains in part at least its popularity; unlike many Mathematical problems, its nature can in some sense be understood by anyone; although, as we shall presently see, the very terms in which it is usually stated tend to suggest an imperfect apprehension of its precise import. The accumulated celebrity which the problem attained, as one of proverbial difficulty, makes it an irresistible attraction to men with a certain kind of mentality. An exaggerated notion of the gain which would accrue to mankind by a solution of the problem has at various times been a factor in stimulating the efforts of men with more zeal than knowledge. The man of mystical tendencies has been attracted to the problem by a vague idea that its solution would, in some dimly discerned manner, prove a key to a knowledge of the inner connections of things far beyond those with which the problem is immediately connected." (Ernest W Hobson, "Squaring the Circle", 1913)

"Mathematics and poetry move together between two extremes of mysticism, the mysticism of the commonplace where ideas illuminate and create facts, and the mysticism of the extraordinary where God, the Infinite, the Real, poses the riddles of desire and disappointment, sin and salvation, effort and failure, question and paradoxical answer."(Scott Buchanan, "Poetry and Mathematics", 1929)

"For centuries [the concept of complex numbers] figured as a sort of mystic bond between reason and imagination." (Tobias Dantzig, "Number: The Language of Science", 1930)

"A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say." (Eric T Bell, "The Handmaiden of the Sciences", 1937

"Life, this anti-entropy, ceaselessly reloaded with energy, is a climbing force, toward order amidst chaos, toward light, among the darkness of the indefinite, toward the mystic dream of Love, between the fire which devours itself and the silence of the Cold. Such a Nature does not accept abdication, nor skepticism." (Albert Claude, [Nobel lecture] 1974) 

📒🅺Dean Koontz - Collected Quotes

"Each smallest act of kindness, reverberates across great distances and spans of time - affecting lives unknown to the one who’s generous spirit, was the source of this good echo. Because kindness is passed on and grows each time it’s passed until a simple courtesy becomes an act of selfless courage, years later, and far away. Likewise, each small meanness, each expression of hatred, each act of evil." (Dean Koontz, "From the Corner of His Eye", 2000)

"Change isn't easy. Changing the way you live means changing the way you think, means changing what you believe about life. That's hard." (Dean Koontz, "One Door Away from Heaven", 2001)

"Truth is always stranger than fiction. We craft fiction to match our sense of how things ought to be, but truth cannot be crafted. Truth is, and truth has a way of astonishing us to our knees. Reminding us, that the universe does not exist to fulfill our expectations. Because we are imperfect beings who are self-blinded to the truth of the world’s stunning complexity, we shave reality to paper thin theories and ideologies that we can easily grasp - and we call them truths. But the truth of a sea in all it’s immensity cannot be embodied in one tidewashed pebble." (Dean Koontz, "Dean Koontz, A Big Little Life: A Memoir of a Joyful Dog", 2009)

"Nothing can be imagined, nothing can be visualized in our minds, until we have a word for it." (Dean Koontz, "Odd Apocalypse", 2012)

"Without faith to act as a governor, the human mind is a runaway worry generator, a dynamo of negative expectations." (Dean Koontz, "Odd Apocalypse", 2012)

"Each book is a mind alive, a life revealed, a world awaiting exploration, but living people are all those things, as well - and more, because their stories haven’t yet been completely told." (Dean Koontz, "Innocence", 2013)

"To understand the universe, our world, and all life in the world, you have to step out of time, which for living humanity is not an option, because we are a part of this painting, characters within it, able to perceive it only as a continuing series of events, episodes. However, because we are conscious creatures with the gift of reason, we can seek and learn and extrapolate from what we learn, and conceive the truth."  (Dean Koontz, "Innocence", 2013)

🪸On Systems Thinking: On Small Scale

"[...] the task of the theory consists in constructing a picture of the external world that exists purely internally and must be our guiding star in all thought and experiment; that is in completing, as it were, the thinking process and carrying out globally what on a small scale occurs within us whenever we form an idea.” (Ludwig E Boltzmann, “On the Significance of Theories”, 1890)

"If the organism carries a ‘small-scale model’ of external reality and of its possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future simulations before they arise, utilize the knowledge of past events in dealing with the present and the future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it." (Kenneth Craik, "The Nature of Explanation", 1943)

"Thus there are instances of symbolisation in nature; we use such instances as an aid to thinking; there is evidence of similar mechanisms at work in our own sensory and central nervous systems; and the function of such symbolisation is plain. If the organism carries a ’small-scale model’ of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise […]" (Kenneth Craik, "The Nature of Explanation", 1943)

"[…] the intrinsic value of a small-scale model is that it compensates for the renunciation of sensible dimensions by the acquisition of intelligible dimensions." (Claude Levi- Strauss,"The Savage Mind", 1962

"The word model is used as a noun, adjective, and verb, and in each instance it has a slightly different connotation. As a noun 'model' is a representation in the sense in which an architect constructs a small-scale model of a building or a physicist a large-scale model of an atom. As an adjective 'model' implies a degree or perfection or idealization, as in reference to a model home, a model student, or a model husband. As a verb 'to model' means to demonstrate, to reveal, to show what a thing is like." (Russell L Ackoff, "Scientific method: optimizing applied research decisions", 1962) 

"In general a small-scale test or experiment will not detect a small effect, or small differences among various products." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"The evident power of simple heuristics […] teaches us the important lesson that global behavior patterns, and social organization, can emerge out of local interactions. Organisms do not necessarily need to have an over-riding plan nor do they require awareness of the large-scale. Grand patterns and processes can emerge as the nett effect of small-scale, local behavior."(David G Green, 2000) 

"The self-similarity on different scales arises because growth often involves iteration of simple, discrete processes (e.g. branching). These repetitive processes can often be summarized as sets of simple rules." (David G Green, 2000)

"According to mental model theory, human reasoning relies on the construction of integrated mental representations of the information that is given in the reasoning problem's premises. These integrated representations are the mental models. A mental model is a mental representation that captures what is common to all the different ways in which the premises can be interpreted. It represents in 'small scale' how "reality" could be— according to what is stated in the premises of a reasoning problem. Mental models, though, must not be confused with images. A mental model often forms the basis of one or more visual images, but some of them represent situations that cannot be visualized. Instead, mental models are often likened to diagrams since, as with diagrams, their structure is analogous to the structure of the states of affairs they represent." (Carsten Held et al, "Mental Models and the Mind", 2006)

"Physics deals with both the large and the small. Its domain of study includes the interior of the nucleus of an atom as well as the exterior of a galaxy. It is, therefore, natural for the scope of physical theories to switch between global, or large-scale, and local, or small-scale regimes. Such an interplay between the local and the global has existed ever since Newton and others discovered the mathematical translation of this interplay: Derivatives are defined as local objects while integrals encompass global properties." (Sadri Hassani, "Mathematical Methods: For Students of Physics and Related Fields", 2009)

"[…] there’s atomic physics - electrons and protons and neutrons, all the stuff of which atoms are made. At these very, very, very small scales, the laws of physics are much the same, but there is also a force you ignore, which is the gravitational force. Gravity is present everywhere because it comes from the entire mass of the universe. It doesn’t cancel itself out, it doesn’t have positive or negative value, it all adds up." (Michael F Atiyah, [interview] 2013)

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

"We know the truth not only through our reason but also through our heart. It is through the latter that we know first principles, and reason, which has nothing to do with it, tries in vain to refute them." (Blaise Pascal, "Pensées", 1670)

"We are made happy when reason can discover no occasion for it. The memory of some past moments is more persuasive than the experience of present ones. There have been visions of such breadth and brightness that these motes were invisible in their light." (Henry D Thoreau, "Letters to Various Persons", 1865)

"Human reason needs only to will more strongly than fate, and she is fate." (Thomas Mann, "The Magic Mountain", 1924)

"If we would guide by the light of reason, we must let our minds be bold." (Louis Brandeis, [dissenting opinion in Jay Burns Baking Co. v. Bryan], 1924)

"I accept nothing on authority. A hypothesis must be backed by reason, or else it is worthless." (Isaac Asimov, "I, Robot", 1950)

"The will is never free - it is always attached to an object, a purpose. It is simply the engine in the car - it can't steer. It is the mind, the reason, the imagination that steers." (Joyce Cary, The Paris Review, 1954)

"Her dance spoke of nothing more and nothing less than the tragedy of being alive, and being human. It spoke, most eloquently, of pain. It spoke, most knowingly, of despair. It spoke of the cruel humor of limitless ambition yoked to limited ability, of eternal hope invested in an ephemeral lifetime, of the driving need to try and create an inexorably predetermined future. It spoke of fear, and of hunger, and, most clearly, of the basic loneliness and alienation of the human animal. It described the universe through the eyes of man: a hostile environment, the embodiment of entropy, into which we are all thrown alone, forbidden by our nature to touch another mind save secondhand, by proxy. It spoke of the blind perversity which forces man to strive hugely for a peace which, once attained, becomes boredom. And it spoke of folly, of the terrible paradox by which man is simultaneously capable of reason and unreason, forever unable to cooperate even with himself." (Spider Robinson & Jeanne Robinson, "Stardance", 1977)

"How often people speak of art and science as though they were two entirely different things, with no interconnection. An artist is emotional, they think, and uses only his intuition; he sees all at once and has no need of reason. A scientist is cold, they think, and uses only his reason; he argues carefully step by step, and needs no imagination. That is all wrong. The true artist is quite rational as well as imaginative and knows what he is doing; if he does not, his art suffers. The true scientist is quite imaginative as well as rational, and sometimes leaps to solutions where reason can follow only slowly; if he does not, his science suffers." (Isaac Asimov, "The Roving Mind", 1983)

"The old knowledge had been difficult but not distressing. It had been all paradox and myth, and it had made sense. The new knowledge was all fact and reason, and it made no sense." (Ursula K Le Guin," "A Man of the People", 1995)

More quotes on Reasoning, Reasons

🪸On Systems Thinking: On Function (1970-1979)

"A living system, due to its circular organization, is an inductive system and functions always in a predictive manner: what happened once will occur again. Its organization," (genetic and otherwise) is conservative and repeats only that which works. For this same reason living systems are historical systems; the relevance of a given conduct or mode of behavior is always determined in the past." (Humberto Maturana, "Biology of Cognition", 1970)

"The definition of a problem and the action taken to solve it largely depend on the view which the individuals or groups that discovered the problem have of the system to which it refers. A problem may thus find itself defined as a badly interpreted output, or as a faulty output of a faulty output device, or as a faulty output due to a malfunction in an otherwise faultless system, or as a correct but undesired output from a faultless and thus undesirable system. All definitions but the last suggest corrective action; only the last definition suggests change, and so presents an unsolvable problem to anyone opposed to change." (Herbert Brün, "Technology and the Composer", 1971)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"Systems at each level of integration function as wholes with respect to their parts and parts with respect to higher level wholes." (Ervin László, "Introduction to Systems Philosophy", 1972)

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"[A] system is represented by a mathematical model which may take many forms, such as algebraic equations, finite state machines, difference equations, ordinary differential equations, partial differential equations, and functional equations. The system model may be uncertain, as the mathematical model may not be known completely." (Fred C Scweppe, "Uncertain dynamic systems", 1973)

"A system may be specified in either of two ways. In the first, which we shall call a state description, sets of abstract inputs, outputs and states are given, together with the action of the inputs on the states and the assignments of outputs to states. In the second, which we shall call a coordinate description, certain input, output and state variables are given, together with a system of dynamical equations describing the relations among the variables as functions of time. Modern mathematical system theory is formulated in terms of state descriptions, whereas the classical formulation is typically a coordinate description, for example a system of differential equations." (E S Bainbridge, "The Fundamental Duality of System Theory", 1975)

"Loose systems last longer and function better." (John Gall, "General Systemantics: How systems work, and especially how they fail", 1975)

"Systems Are Seductive. They promise to do a hard job faster, better, and more easily than you could do it by yourself. But if you set up a system, you are likely to find your time and effort now being consumed in the care and feeding of the system itself. New problems are created by its very presence. Once set up, it won't go away, it grows and encroaches. It begins to do strange and wonderful things. Breaks down in ways you never thought possible. It kicks back, gets in the way, and opposes its own proper function. Your own perspective becomes distorted by being in the system. You become anxious and push on it to make it work. Eventually you come to believe that the misbegotten product it so grudgingly delivers is what you really wanted all the time. At that point encroachment has become complete. You have become absorbed. You are now a systems person." (John Gall, "General Systemantics: How systems work, and especially how they fail", 1975)

"Programming systems can, of course, be built without plan and without knowledge, let alone understanding, of the deep structural issues involved, just as houses, cities, systems of dams, and national economic policies can be similarly hacked together. As a system so constructed begins to get large, however, it also becomes increasingly unstable. When one of its subfunctions fails in an unanticipated way, it may be patched until the manifest trouble disappears. But since there is no general theory of the whole system, the system itself can be only a more or less chaotic aggregate of subsystems whose influence on one another's behavior is discoverable only piecemeal and by experiment. The hacker spends part of his time at the console piling new subsystems onto the structure he has already built - he calls them 'new features' - and the rest of his time in attempts to account for the way in which substructures already in place misbehave. That is what he and the computer converse about." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"In set theory, perhaps more than in any other branch of mathematics, it is vital to set up a collection of symbolic abbreviations for various logical concepts. Because the basic assumptions of set theory are absolutely minimal, all but the most trivial assertions about sets tend to be logically complex, and a good system of abbreviations helps to make otherwise complex statements. " (Keith Devlin, "Sets, Functions, and Logic: An Introduction to Abstract Mathematics", 1979)

🪸On Systems Thinking: On Large Scale

"Almost everyone now acknowledges that theory and experiment, model making, theory construction and linguistics all go together, and that the successful development of a science of behavior depends upon a ‘total approach’ in which, given that the computer ‘is the only large-scale universal model’ that we possess, ‘we may expect to follow the prescription of Simon and construct our models - or most of them - in the form of computer programs’." (Frank H George,"Cognition", 1962) [attributed to Alan M Turing] 

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

"The word model is used as a noun, adjective, and verb, and in each instance it has a slightly different connotation. As a noun 'model' is a representation in the sense in which an architect constructs a small-scale model of a building or a physicist a large-scale model of an atom. As an adjective 'model' implies a degree or perfection or idealization, as in reference to a model home, a model student, or a model husband. As a verb 'to model' means to demonstrate, to reveal, to show what a thing is like." (Russell L Ackoff, "Scientific method: optimizing applied research decisions", 1962)

"Simple rules can have complex consequences. This simple rule has such a wealth of implications that it is worth examining in detail. It is the far from self-evident guiding principle of reductionism and of most modern investigations into cosmic complexity. Reductionism will not be truly successful until physicists and cosmologists demonstrate that the large-scale phenomena of the world arise from fundamental physics alone. This lofty goal is still out of reach. There is uncertainty not only in how physics generates the structures of our world but also in what the truly fundamental rules of physics are." (William Poundstone, "The Recursive Universe", 1985)

"The large-scale computer models of systems ecology do not fit under the heading of holism at all. Rather they are forms of large-scale reductionism: the objects of study are the naively given 'parts' -abundances or biomasses of populations. No new objects of study arise at the community level. The research is usually conducted on a single system - a lake, forest, or prairie - and the results are measurements of and projections for that lake, forest, or prairie, with no attempts to find the properties of lakes, forests, or prairies in general. Such modeling requires vast amounts of data for its simulations, and much of the scientific effort goes into problems of estimation." (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"The evident power of simple heuristics […] teaches us the important lesson that global behavior patterns, and social organization, can emerge out of local interactions. Organisms do not necessarily need to have an over-riding plan nor do they require awareness of the large-scale. Grand patterns and processes can emerge as the nett effect of small-scale, local behavior."(David G Green, 2000) 

"The really crucial question in multi-object systems is whether local interactions do grow into large-scale patterns." (David G Green, 2000)

"Statistical mechanics is the science of predicting the observable properties of a many-body system by studying the statistics of the behaviour of its individual constituents, be they atoms, molecules, photons etc. It provides the link between macroscopic and microscopic states. […] classical thermodynamics. This is a subject dealing with the very large. It describes the world that we all see in our daily lives, knows nothing about atoms and molecules and other very small particles, but instead treats the universe as if it were made up of large-scale continua. […] quantum mechanics. This is the other end of the spectrum from thermodynamics; it deals with the very small. It recognises that the universe is made up of particles: atoms, electrons, protons and so on. One of the key features of quantum mechanics, however, is that particle behaviour is not precisely determined (if it were, it would be possible to compute, at least in principle, all past and future behaviour of particles, such as might be expected in a classical view). Instead, the behaviour is described through the language of probabilities." (A Mike Glazer & Justin S Wark, "Statistical Mechanics: A survival guide", 2001)

"Physics deals with both the large and the small. Its domain of study includes the interior of the nucleus of an atom as well as the exterior of a galaxy. It is, therefore, natural for the scope of physical theories to switch between global, or large-scale, and local, or small-scale regimes. Such an interplay between the local and the global has existed ever since Newton and others discovered the mathematical translation of this interplay: Derivatives are defined as local objects while integrals encompass global properties." (Sadri Hassani, "Mathematical Methods: For Students of Physics and Related Fields", 2009)

"Black Swans (capitalized) are large-scale unpredictable and irregular events of massive consequence - unpredicted by a certain observer, and such un - predictor is generally called the 'turkey' when he is both surprised and harmed by these events. [...] Black Swans hijack our brains, making us feel we 'sort of' or 'almost' predicted them, because they are retrospectively explainable. We don’t realize the role of these Swans in life because of this illusion of predictability. […] An annoying aspect of the Black Swan problem - in fact the central, and largely missed, point - is that the odds of rare events are simply not computable." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"The sensitivity of chaotic systems to initial conditions is particularly well known under the moniker of the 'butterfly effect', which is a metaphorical illustration of the chaotic nature of the weather system in which 'a flap of a butterfly’s wings in Brazil could set off a tornado in Texas'. The meaning of this expression is that, in a chaotic system, a small perturbation could eventually cause very large-scale difference in the long run." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

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

"It is no bad thing to be a king - to see one's house enriched and one's authority enhanced." (Homer, "The Odyssey", cca. 750-700 BC)

"Even the best of men in authority are liable to be corrupted by passion. We may conclude then that the law is reason without passion, and it is therefore preferable to any individual." (Aristotle, "Politics", cca. 335-323 BC)

"An evil nature wielding great authority brings misfortune upon the community." (Aeschines, "Ctesiphontem", 330 BC) 

"Old age, especially an honored old age, has so great authority, that this is of more value than all the pleasures of youth." (Marcus Tullius Cicero, "Cato Maior de Senectute" ["On Old Age"], 44 BC) 

"Almost all the opinions we have are taken on authority and on credit." (Michel de Montaigne, "De la phisionomie" ["Of Physiognomy"], 1588)

"For rightly is truth called the daughter of time, not of authority." (Francis Bacon, "Novum Organum", 1620)

"Authority without wisdom is like a heavy axe without an edge, fitter to bruise than polish." (Anne Bradstreet, "Meditations Divine and Moral", 1666)

"Lawful and settled authority is very seldom resisted when it is well employed." (Samuel Johnson, The Rambler no. 50, 1750)

"Authority - the fact, namely, that something has already happened or been said or decided, is of great value; but it is only a pedant who demands authority for everything." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"Wherever there is a man who exercises authority, there is a man who resists authority." (Oscar Wilde, "The Soul of Man Under Socialism", 1895)

"Always acknowledge a fault frankly. This will throw those in authority off their guard and give you opportunity to commit more." (Mark Twain, "More Maxims of Mark", 1927)

"Man cannot do without beauty, and this is what our era pretends to want to disregard. It steels itself to attain the absolute and authority; it wants to transfigure the world before having exhausted it, to set it to rights before having understood it. Whatever it may say, our era is deserting this world." (Albert Camus,"Helen's Exile", 1948)

"I accept nothing on authority. A hypothesis must be backed by reason, or else it is worthless." (Isaac Asimov, "I, Robot", 1950)

"Objective evidence is the ultimate authority. Recorders may lie, but Nature is incapable of it." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959) 

"Believing things on authority only means believing them because you have been told them by someone you think trustworthy. Ninety-nine per cent of the things you believe are believed on authority. [...] Every historical event in the world is believed on authority." (Clive S Lewis, "Mere Christianity", 1961)

"Freedom of conscience entails more dangers than authority and despotism." (Michel Foucault, "Madness and Civilization", 1961)

"The robots are not technologically minded. They were not built to be. They were built to bolster human vanity and pride, to meet a strange longing that seems to be built into the human ego - the need to have other humans (or a reasonable facsimile of other humans) to minister to our wants and needs, human slaves to be dominated, human beings over which a man or woman (or a child) can assert authority, thus building up a false feeling of superiority." (Clifford D Simak, "A Choice of Gods", 1972)

"It is unusual for us to discover an imperial power-system in space. As a rule, such archaic forms of authority wither long before the relevant species drags itself off the home planet." (Iain M Banks, "The Player of Games", 1988)

📓On Literature: On Edges (From Fiction to Science Fiction)

"Moreover, the universe as a whole is infinite, for whatever is limited has an outermost edge to limit it, and such an edge is defined by something beyond. Since the universe has no edge, it has no limit; and since it lacks a limit, it is infinite and unbounded. Moreover, the universe is infinite both in the number of its atoms and in the extent of its void." (Epicurus," Letters", [Letter to Herodotus] cca. 305 BC)

"It is the sharpness of our mind that gives the edge to our pains and pleasures." (Michel de Montaigne, "Essais", 1580)

"Authority without wisdom is like a heavy axe without an edge, fitter to bruise than polish." (Anne Bradstreet, "Meditations Divine and Moral", 1666)

"A great Empire, like a great Cake, is most easily diminished at the Edges." (Benjamin Franklin, "Rules By Which A Great Empire May Be Reduced To A Small One", The Public Advertiser, 1773)

"Life as we call it, is nothing but the edge of the boundless ocean of existence when it comes upon soundings." (Oliver W Holmes Jr, "The Professor at the Breakfast Table", 1860)

"[...] only on the edge of the grave can man conclude anything." (Henry Adams, "The Education of Henry Adams", 1907)

"We have come to the edge of a world of which we have no experience, and where all our preconceptions must be recast." (D'Arcy W Thompson, "On Growth and Form" Vol. 1, 1917)

"Life is a travelling to the edge of knowledge, then a leap taken." (David H Lawrence, "Reflections on the Death of a Porcupine and Other Essays", 1988) 

"All our words from loose using have lost their edge." (Ernest Hemingway, "Death in the Afternoon", 19325

"We do not truly see light, we only see slower things lit by it, so that for us light is on the edge-the last thing we know before things become too swift for us." (Clive S Lewis, "Out of the Silent Planet", 1938)

"War creates no absolutely new situation: it simply aggravates the permanent human situation so that we can no longer ignore it. Human life has always been lived on the edge of a precipice." (Clive S Lewis, "Learning in War-Time", 1939)

"Sooner or later we will come to the edge of the Solar System and will be looking out across the ultimate abyss. Then we must choose whether we reach the stars — or whether we wait until the stars reach us." (Arthur C Clarke, "The Challenge of the Spaceship". 1959)

"When they [radio astronomers] grew weary at their electronic listening posts, when their eyes grew dim with looking at unrevealing dials and studying uneventful graphs, they could step outside their concrete cells and renew their dull spirits in communion with the giant mechanism they commanded, the silent, sensing instrument in which the smallest packets of energy, the smallest waves of matter, were detected in their headlong, eternal flight across the universe. It was the stethoscope with which they took the pulse of the all and noted the birth and death of stars, the probe with which, here on an insignificant planet of an undistinguished star on the edge of its galaxy, they explored the infinite." (James Gunn, "The Listeners", 1968)

"Whole worlds formed in a pregnant void: not spherical worlds merely, but dodeka-spherical, and those much more intricate than that. Not merely seven colors to play with, but seven to the seventh and to the seventh again. Stars vivid in the bright light. You who have seen stars only in darkness. be silent! Asteroids that they ate like peanuts, for now they were all metamorphic giants. Galaxies like herds of rampaging elephants. Bridges so long that both ends of them receded over the light-speed edges. Waterfalls, of a finer water, that bounced off galaxy clusters as if they were boulders." (Raphael A Lafferty, "Sky", 1971)

"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)

"The distinction between sanity and insanity is narrower than the razor's edge, sharper than a hound's tooth, more agile than a mule deer. It is more elusive than the merest phantom. Perhaps it does not even exist; perhaps it is a phantom." (Philip K Dick,"VALIS", 1981)

"Living systems are never in equilibrium. They are inherently unstable. They may seem stable, but they're not. Everything is moving and changing. In a sense, everything is on the edge of collapse. Michael Crichton, "Jurassic Park", 1990)

"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)

"Mechs built, that was inevitable. They sought to make of the world a place of straight lines and sharp edges, geometry made real. Eternal, rigid certainties. Men were of a different order. They sought the curved, the flexible, the liveand unenduring. They lived and died." (Gregory Benford, "At the Double Solstice", 1988)

"At the edge of chaos, unexpected outcomes occur. The risk to survival is severe." (Michael Crichton, "Jurassic World", 1997)