On Scientific Communities

"A theoretical science unaware that those of its constructs considered relevant and momentous are destined eventually to be framed in concepts and words that have a grip on the educated community and become part and parcel of the general world picture - a theoretical science, I say, where this is forgotten, and where the initiated continue musing to each other in terms that are, at best, understood by a small group of close fellow travelers, will necessarily be cut off from the rest of cultural mankind; in the long run it is bound to atrophy and ossify however virulently esoteric chat may continue within its joyfully isolated groups of experts." (Erwin Schrödinger, "Are There Quantum Jumps?", The British Journal for the Philosophy of Science Vol. 3, 1952)

"A theoretical science unaware that those of its constructs considered relevant and momentous are destined eventually to be framed in concepts and words that have a grip on the educated community and become part and parcel of the general world picture - a theoretical science [...]" (Erwin Schrödinger, "Are There Quantum Jumps?", The British Journal for the Philosophy of Science Vol. 3, 1952)

"The subject matter of the scientist is a crowd of natural events at all times; he presupposes that this crowd is not real but apparent, and seeks to discover the true place of events in the system of nature. The subject matter of the poet is a crowd of historical occasions of feeling recollected from the past; he presupposes that this crowd is real but should not be, and seeks to transform it into a community. Both science and art are primarily spiritual activities, whatever practical applications may be derived from their results. Disorder, lack of meaning, are spiritual not physical discomforts, order and sense spiritual not physical satisfactions." (Wystan H Auden, "The Dyer’s Hand and Other Essays", 1965)

"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)

"A scientist should not cheat or falsify data or quote out of context or do any other thing that is intellectually dishonest. Of course, as always, some individuals fail; but science as a whole disapproves of such action. Indeed, when transgressors are detected, they are usually expelled from the community." (Michael Ruse, "Response to the Commentary: Pro Judice", Science, Technology and Human Values Vol. 7" (41), 1982)

"A theory is only ‘true’ for as long as the majority of the scientific community maintain the view that the theory is the one best able to explain the observations." (Jim Baggott, "The Meaning of Quantum Theory", 1992)

"It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only ‘true’ for as long as the majority of the scientific community maintain the view that the theory is the one best able to explain the observations." (Jim Baggott,"The Meaning of Quantum Theory", 1992)

"There are many possible definitions of chaos. In fact, there is no general agreement within the scientific community as to what constitutes a chaotic dynamical system." (Robert L Devaney, "A First Course in Chaotic Dynamical Systems: Theory and Experiment", 1992)

"In the new systems thinking, the metaphor of knowledge as a building is being replaced by that of the network. As we perceive reality as a network of relationships, our descriptions, too, form an interconnected network of concepts and models in which there are no foundations. For most scientists such a view of knowledge as a network with no firm foundations is extremely unsettling, and today it is by no means generally accepted. But as the network approach expands throughout the scientific community, the idea of knowledge as a network will undoubtedly find increasing acceptance." (Fritjof Capra," The Web of Life: a new scientific understanding of living systems", 1996)

🥀On Style in Science

"I think that science may be styled the knowledge of universals, or abstract wisdom; and art is science reduced to practice - or science is reason, and art the mechanism of it - and may be called practical science. Science, in fine, is the theorem, and art the problem." (Richard Griffith, 1779) [attributed to Laurence Sterne] 

"Both science and art form in the course of the centuries a human language by which we can speak about the more remote parts of reality, and the coherent sets of concepts as well as the different styles of art are different words or groups of words in this language." (Werner K Heisenberg, "Physics and Philosophy", 1958)

"When terms [...] evolve and change definition with time; and when the social reality which terms are intended to organize and render intelligible is also seen to be in flux, capturing the truth in a net of words becomes a matter of intuition and style more than of any scientific method that can be replicated by others and made to achieve the same result every time someone asks the same question, or undertakes the same operations." (William H McNeill, "Discrepancies among the Social Sciences", 1981)

"The body of mathematics to which the calculus gives rise embodies a certain swashbuckling style of thinking, at once bold and dramatic, given over to large intellectual gestures and indifferent, in large measure, to any very detailed description of the world. It is a style that has shaped the physical but not the biological sciences, and its success in Newtonian mechanics, general relativity and quantum mechanics is among the miracles of mankind. But the era in thought that the calculus made possible is coming to an end. Everyone feels this is so and everyone is right." (David Berlinski, "A Tour of the Calculus", 1995)

"Modeling involves a style of scientific thinking in which the argument is structured by the model, but in which the application is achieved via a narrative prompted by an external fact, an imagined event or question to be answered." (Uskali Mäki, "Fact and Fiction in Economics: Models, Realism and Social Construction", 2002)

"[...] the scientific models of concrete things are symbolic rather than iconic: they are systems of propositions, not pictures. Besides, such models are seldom if ever completely accurate, if only because they involve more or less brutal simplifications, such as pretending that a metallic surface is smooth, a crystal has no impurities, a biopopulation has a single predator, or a market is in equilibrium. These are all fictions. However, they are stylizations rather than wild fantasies. Hence, introducing and using them to account for real existents does not commit us to fictionism, just as defending the role of experience need not make us empiricists, nor is admitting the role of intuition enough to qualify as intuitionist." (Mario Bunge, "Chasing Reality: Strife over Realism", 2006)

"Scientists reach their conclusions for the damnedest of reasons: intuition, guesses, redirections after wild-goose chases, all combing with a dollop of rigorous observation and logical reasoning to be sure […] This messy and personal side of science should not be disparaged, or covered up, by scientists for two major reasons. First, scientists should proudly show this human face to display their kinship with all other modes of creative human thought […] Second, while biases and references often impede understanding, these mental idiosyncrasies may also serve as powerful, if quirky and personal, guides to solutions." (Stephen J Gould,"Dinosaur in a Haystack: Reflections in natural history", 1995)

On History of Science (1950-1974)

"Most important for the history of science is the fact that Liber de Ludo Aleae,'The Book of Games of Chance', contains the first study of the principles of probability. [...] it would seem much more just to date the beginnings of probability theory from Cardano's treatise rather than the customary reckoning from Pascal's discussions with his friend de Méré and the ensuing correspondence with Fermat [...] at least a century after Cardano [...]" (Oystein Ore [Ed.], "Cardano the Gambling Scholar", 1953)

"The history of science is rich in the example of the fruitfulness of bringing two sets of techniques, two sets of ideas, developed in separate contexts for the pursuit of new truth, into touch with one another." (J. Robert Oppenheimer, "Science and the common understanding", 1954)

"In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skillful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them." (Thomas Gold, "Cosmology", 1956) 

"Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. […] Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge." (Richard J. Blackwell, "Discovery in the Physical Sciences", 1969)

 "By showing us the extreme diversity of the factors involved in scientific creativity, the history of science teaches us that we should open the doors of our laboratories more widely. If we put that lesson into practice, our reflection on the past will have had a beneficial effect on the future." (Jean Rostand, "Humanly Possible: A Biologist’s Note on the Future of Mankind", 1970)

"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)

"The history of science is full of revolutionary advances that required small insights that anyone might have had, but that, in fact, only one person did." (Isaac Asimov, "The Three Numbers", Ellery Queen's Mystery Magazine, 1974)

On History of Science (-1949)

"We might venture the statement that the history of science is science itself. We cannot really know what we possess until we have learned to know what others have possessed before us." (Johann Wolfgang von Goethe, "On Theory of Color", 1810)

"In applying dynamical principles to the motion of immense numbers of atoms, the limitation of our faculties forces us to abandon the attempt to express the exact history of each atom, and to be content with estimating the average condition of a group of atoms large enough to be visible. This method [...] which I may call the statistical method, and which in the present state of our knowledge is the only available method of studying the properties of real bodies, involves an abandonment of strict dynamical principles, and an adoption of the mathematical methods belonging to the theory of probability. […] If the actual history of Science had been different, and if the scientific doctrines most familiar to us had been those which must be expressed in this way, it is possible that we might have considered the existence of a certain kind of contingency a self evident truth, and treated the doctrine of philosophical necessity as a mere sophism." (James C Maxwell, "Introductory Lecture on Experimental Physics", "The Scientific Papers of James Clerk Maxwell", 1890)

"Anyone who is practically acquainted with scientific work is aware that those who refuse to go beyond fact, rarely get as far as fact; and anyone who has studied the history of science knows that almost every great step therein has been made by the 'anticipation of Nature.'" (Thomas H Huxley, "Method and Results", 1893)

"If we study the history of science we see happen two inverse phenomena […] Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities. […] No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations." (Henri Poincaré, "Science and Hypothesis", 1901)

"Knowledge for the sake of knowledge, as the history of science proves, is an aim with an irresistible fascination for mankind, and which needs no defense. The mere fact that science does, to a great extent, gratify our intellectual curiosity, is a sufficient reason for its existence." (John W N Sullivan, "The Limitations of Science", 1915)

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein’s special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein’s amazing revelations have likewise sunk into the commonplaces of educated thought." (Arthur S Eddington, "The Theory of Relativity and its Influence on Scientific Thought", 1922)

"From the point of view of the history of science, transmission is as essential as discovery." (George Sarton, "Introduction to the History of Science" Vol. 2, 1927)

"The study of history, and especially of the history of science, may thus be regarded, not only as a source of wisdom and humanism, but also as a regulator for our consciences: it helps us not to be complacent, arrogant, too sanguine of success, and yet remain grateful and hopeful, and never to cease working quietly for the accomplishment of our own task." (George Sarton, "The History of Science and the New Humanism", 1928)

"The history of science is the only history which can illustrate the progress of mankind. In fact, progress has no definite and unquestionable meaning in fields other than the fields of science." (George Sarton,"The Study of The History of Science", 1936)

”We can put it down as one of the principles learned from the history of science that a theory is only overthrown by a better theory, never merely by contradictory facts.” (James B Conant, “On Understanding Science”, 1947)

On History of Science (1975-)

"Philosophy of science without history of science is empty; history of science without philosophy of science is blind." (Imre Lakatos, "The Methodology of Scientific Research Programmes" Vol. 1, 1980)

"Things are similar: this makes science possible. Things are different: this makes science necessary. At various times in the history of science important advances have been made either by abstracting away differences to reveal similarity or by emphasizing the richness of variation within a seeming uniformity. But either choice by itself is ultimately misleading. The general does not completely contain the particular as cases, but the empiricist refusal to group, generalize, and abstract reduces science to collecting - if not specimens, then examples." (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"It is a remarkable fact that the second law of thermodynamics has played in the history of science a fundamental role far beyond its original scope. Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s discovery of quantum theory or Einstein’s theory of spontaneous emission, which were all based on the second law of thermodynamics." (Ilya Prigogine, 'Time, Structure and Fluctuations", 1993

"Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science - by far the most successful claim to knowledge accessible to humans - teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)

"Tektology was the first attempt in the history of science to arrive at a systematic formulation of the principles of organization operating in living and nonliving systems." (Fritjof Capra, "The Web of Life", 1996)

"Scientific and religious ways of speaking also resemble each other in that they often purport to offer absolute know ledge. I find that parallel also quite amusing at times. The belief of some scientists to propagate the truth can easily be revealed a delusion because in the history of science nothing ever stays the same; theories and models of reality constantly change." (Ernst von Glasersfeld) [in (Bernhard Poerksen, "The Certainty of Uncertainty: Dialogues Introducing Constructivism", 2004)]

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

"Of all the fantastic ideas that belong to science fiction, the most remarkable - and, perhaps, the most fascinating - is that of time travel [...] Indeed, so fantastic a notion does it seem, and so many apparently obvious absurdities and bewildering paradoxes does it present, that some of the most imaginative students of science refuse to consider it as a practical proposition." (Idrisyn O Evans, "Can We Conquer Time?", Tales of Wonder, 1940)

"The aim of science is to discover and illuminate truth. And that, I take it, is the aim of literature, whether biography or history or fiction. It seems to me, then, that there can be no separate literature of science." (Rachel Carson, [acceptance speech of the National Book Award for Nonfiction] 1952) 

"[Science fiction is] that class of prose narrative treating of a situation that could not arise in the world we know, but which is hypothesised on the basis of some innovation in science or technology, or pseudo-science or pseudo-technology, whether human or extra-terrestrial in origin. It is distinguished from pure fantasy by its need to achieve verisimilitude and win the 'willing suspension of disbelief' through scientific plausibility." (Kingsley Amis, "New Maps of Hell", 1960)

"Science fiction is no more written for scientists than ghost stories are written for ghosts." Brian Aldiss, Penguin Science Fiction, 1961

"Science fiction is, very strictly and literally, analogous to science facts. It is a convenient analog system for thinking about new scientific, social, and economic ideas - and for re-examining old ideas." (John W Campbell Jr., "Prologue to Analog", 1962)

"Science fiction makes the implausible possible, while science fantasy makes the impossible plausible." (Rod Serling, "The Twilight Zone", "The Fugitive", 1962)

"A science fiction story is a story built around human beings, with a human problem and a human solution, which would not have happened at all without its scientific content." (Theodore Sturgeon, "The Issue at Hand: Studies in Contemporary Magazine Science Fiction", 1964)

"A scientist can not be measured quantitatively by the number of degrees or the accumulation of information. A true scientist should have a measure of courage to correct error and seek truth - no matter how painful. The alternative is more painful. To build error upon error is to drift into dogmas, metaphysics, science fiction, and mythology." (Alexander Wilf, "Origin and Destiny of the Moral Species", 1969)

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

"Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not." (Isaac Asimov, "How Easy to See the Future", Natural History magazine, 1975) 

"Science fiction, because it ventures into no man's lands, tends to meet some of the requirements posed by Jung in his explorations of archetypes, myth structures and self-understanding. It may be that the primary attraction of science fiction is that it helps us understand what it means to be human." (Frank Herbert, "Men on other planets", [in "The Craft of Science Fiction"] 1976)

"The idea of making machines that think has an unfailing fascination, not only for science fiction readers, but for all who can see it is a possible way of gaining some understanding of the working of our own minds. Thinking, however, is not an easily defined phenomenon, although it is often considered to be the process of solving problems." (Edward Ihnatowicz, "The Relevance of Manipulation to the Process of Perception", 1977)

"Individual science fiction stories may seem as trivial as ever to the blinder critics and philosophers of today - but the core of science fiction, its essence, the concept around which it revolves, has become crucial to our salvation if we are to be saved at all." (Isaac Asimov, "My Own View" [in "The Encyclopedia of Science Fiction"], 1978)

"In the face of all this, many of the standard ideas of science fiction seem to me to pale by comparison. I see the relative absence of these things and the distortions of scientific thinking often encountered in science fiction as terrible wasted opportunities. Real science is as amenable to exciting and engrossing fiction as fake science, and I think it is important to exploit every opportunity to convey scientific ideas in a civilization which is both based upon science and does almost nothing to ensure that science is understood." (Carl Sagan, "Broca's Brain", 1979)

"Many scientists deeply involved in the exploration of the solar system (myself among them) were first turned in that direction by science fiction. And the fact that some of that science fiction was not of the highest quality is irrelevant. Ten-year-olds do not read the scientific literature." (Carl Sagan, "Broca's Brain", 1979)

"First-rate science fiction was, and remains, more interesting than second-rate art." (Clive James, "From the Land of Shadows", 1982)

"This is an exercise in fictional science, or science fiction, if you like that better. Not for amusement: science fiction in the service of science. Or just science, if you agree that fiction is a part of it, always was, and always will be as long as our brains are only miniscule fragments of the universe, much too small to hold all the facts of the world but not too idle to speculate about them." (Valentino Braitenberg," Vehicles: Experiments in Synthetic Psychology", 1984)

"A science fiction writer is - or should be - constrained by what is, or logically might be. That can mean simple fidelity to facts (which, in science, are always more important than theories - though Lord knows the two help shape each other, undermining the convenient, complacent separation of observer and observed). To me it also means heeding the authentic, the actual and concrete. Bad fiction uses the glossy generality; good writing needs the smattering of detail, the unrelenting busy mystery of the real." (Gregory Benford, "Afterword to Exposures", [in Alien Flesh] 1986)

"Science fiction offers its writers chances of embarrassment that no other form of fiction does." (Isaac Asimov, "Robot Dreams" [introduction] 1986)

"General fiction is pretty much about ways that people get into problems and screw their lives up. Science fiction is about everything else." (Marvin Minsky, "The Society of Mind", 1987)

"Space or science fiction has become a dialect for our time." (Doris Lessing, The Guardian, 1988) 

"If science fiction is the mythology of modern technology, then its myth is tragic." (Ursula K. Le Guin, "Dancing at the Edge of the World", 1989)

"Science fiction properly conceived, like all serious fiction, however funny, is a way of trying to describe what is in fact going on, what people actually do and feel, how people relate to everything else in this vast sack, this belly of the universe, this womb of things to be and tomb of things that were, this unending story." (Ursula K Le Guin, "Dancing at the Edge of the World", 1989)

"[...] science fiction is about what could be but isn't; fantasy is about what couldn't be." (Orson Scott Card, "How to Write Science Fiction and Fantasy", 1990)

"Speculative fiction by definition is geared toward an audience that wants strangeness, an audience that wants to spend time in worlds that absolutely are not like the observable world around them." (Orson Scott Card, "How to Write Science Fiction & Fantasy", 1990)

"Science fiction rarely is about scientists doing real science, in its slowness, its vagueness, the sort of tedious quality of getting out there and digging amongst rocks and then trying to convince people that what you're seeing justifies the conclusions you're making. The whole process of science is wildly under-represented in science fiction because it's not easy to write about. There are many facets of science that are almost exactly opposite of dramatic narrative. It's slow, tedious, inconclusive, it's hard to tell good guys from bad guys [...]" (Kim S Robinson, [interview] 1997)

"To describe how quantum theory shapes time and space, it is helpful to introduce the idea of imaginary time. Imaginary time sounds like something from science fiction, but it is a well-defined mathematical concept: time measured in what are called imaginary numbers. […] Imaginary numbers can then be represented as corresponding to positions on a vertical line: zero is again in the middle, positive imaginary numbers plotted upward, and negative imaginary numbers plotted downward. Thus imaginary numbers can be thought of as a new kind of number at right angles to ordinary real numbers. Because they are a mathematical construct, they don't need a physical realization […]" (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"Change is the principal feature of our age and literature should explore how people deal with it. The best science fiction does that, head-on." (David Brin, Orbit, [interview] 2002)

"Once confined to fantasy and science fiction, time travel is now simply an engineering problem." (Michichio Kaku, Wired Magazine, 2003)

"Life isn’t divided into genres. It’s a horrifying, romantic, tragic, comical, science-fiction cowboy detective novel." (Alan Moore, "The Mustard magazine interview", 2005)

"Every so often I come up with a different definition of what science fiction and fantasy do, and I'm always looking for one that describes what they both do, rather than separating them. Currently I'm saying that one of the things they do is look at the effects of large-scale social change on both populations and individuals. Fantasy tends to look to the past, and science fiction to the future, but what is common to many of the stories is change: huge societal upheaval." (Nalo Hopkinson, "Nalo Hopkinson: Multiplicity", LocusMag, 2007) 

"Science fiction pretends to look into the future but it’s really looking at a reflection of what is already in front of us." (Ray Bradbury, The Paris Review, [interview] 2010) 

"Science fiction at its best should be crazy and dangerous, not sane and safe." (Paul di Filippo, "How To Write Science Fiction", cca. 2011) 

"The other buzzword that epitomizes a bias toward substitution is 'big data'. Today’s companies have an insatiable appetite for data, mistakenly believing that more data always creates more value. But big data is usually dumb data. Computers can find patterns that elude humans, but they don’t know how to compare patterns from different sources or how to interpret complex behaviors. Actionable insights can only come from a human analyst (or the kind of generalized artificial intelligence that exists only in science fiction)." (Peter Thiel & Blake Masters, "Zero to One: Notes on Startups, or How to Build the Future", 2014)

"Science fiction these days is only half a step ahead of science. Astrophysicists and scientists are working in the same way as science fiction writers. They’re working things out in their imagination based on the slim scientific facts that they know. Hawking imagines a black hole and then discovers the mathematics that support his theory, and new possibilities come to light. That’s the imaginative flair that scientists have to have. For me as a sci-fi writer, spinning those ideas in your mind brings you to the point where you dream in science fiction. Suddenly you think of something in the middle of the night, and it’s so vivid you don’t need to write it down because you know you’ll remember it in the morning. That’s what these books, Zero G, reflect: a vivid imagination." (William Shatner, "William Shtner on Sci-Fi, Aging and the Environment", Saturday Evening Post, [interview] 2017)

"But if the general opinion of Mankind is optimistic then we're in for a period of extreme popularity for science fiction. If the general opinion is pessimistic, fantasy is going to hold its own." (David Eddings) 

"Fantasy and science fiction can be literal as well as allegorical and there’s nothing wrong with enjoying a monster like a giant squid for what it is, as well as searching for metaphor." (China Miéville) 

"Individual science fiction stories may seem as trivial as ever to the blinder critics and philosophers of today - but the core of science fiction, its essence [...] has become crucial to our salvation if we are to be saved at all." (Isaac Asimov)

"One of the biggest roles of science fiction is to prepare people to accept the future without pain and to encourage a flexibility of mind. Politicians should read science fiction, not westerns and detective stories. (Arthur C Clarke)

"Science fiction, outside of poetry, is the only literary field which has no limits, no parameters whatsoever. You can go not only into the future, but into that wonderful place called "other", which is simply another universe, another planet, another species." (Theodore Sturgeon)

"Science fiction encourages us to explore… all the futures, good and bad, that the human mind can envision." (Marion Z Bradley)

"The science fiction approach doesn't mean it's always about the future; it's an awareness that this is different." (Neal Stephenson) 

On Scientific Analysis

"The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. […] On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade." (Gilbert N Lewis, "The Anatomy of Science", 1926)

"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)

"Only by the analysis and interpretation of observations as they are made, and the examination of the larger implications of the results, is one in a satisfactory position to pose new experimental and theoretical questions of the greatest significance." (John A Wheeler, "Elementary Particle Physics", American Scientist, 1947)

"We have here no esoteric theory of the ultimate nature of concepts, nor a philosophical championing of the primacy of the 'operation'. We have merely a pragmatic matter, namely that we have observed after much experience that if we want to do certain kinds of things with our concepts, our concepts had better be constructed in certain ways. In fact one can see that the situation here is no different from what we always find when we push our analysis to the limit; operations are not ultimately sharp or irreducible any more than any other sort of creature. We always run into a haze eventually, and all our concepts are describable only in spiralling approximation." (Percy W Bridgman, "Reflections of a Physicist", 1950)

"Multiple equilibria are not necessarily useless, but from the standpoint of any exact science the existence of a uniquely determined equilibrium is, of course, of the utmost importance, even if proof has to be purchased at the price of very restrictive assumptions; without any possibility of proving the existence of (a) uniquely determined equilibrium - or at all events, of a small number of possible equilibria - at however high a level of abstraction, a field of phenomena is really a chaos that is not under analytical control." (Joseph A Schumpeter, "History of Economic Analysis", 1954)

"Intuition implies the act of grasping the meaning or significance or structure of a problem without explicit reliance on the analytical apparatus of one’s craft. It is the intuitive mode that yields hypotheses quickly, that produces interesting combinations of ideas before their worth is known. It precedes proof: indeed, it is what the techniques of analysis and proof are designed to test and check. It is founded on a kind of combinatorial playfulness that is only possible when the consequences of error are not overpowering or sinful." (Jerome S Bruner,"On Learning Mathematics", Mathematics Teacher Vol. 53, 1960)

"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)

"Discovery is a double relation of analysis and synthesis together. As an analysis, it probes for what is there; but then, as a synthesis, it puts the parts together in a form by which the creative mind transcends the bare limits, the bare skeleton, that nature provides."(Jacob Bronowski, "The Ascent of Man", 1973)

"Science does not need mysticism and mysticism does not need science, but man needs both. Mystical experience is necessary to understand the deepest nature of things, and science is essential for modern life. What we need, therefore, is not a synthesis, but a dynamic interplay between mystical intuition and scientific analysis." (Fritjof Capra,"The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"In the ultimate analysis science is born of myth and religion, all three being expressions of the ordering spirit of the human mind." (Lancelot L Whyte, "The Unconscious Before Freud", 1978)

"The most astonishing achievements of science, intellectually and practically, have been in physics, which many people take to be the ideal type of scientific knowledge. In fact, physics is a very special type of science, in which the subject matter is deliberately chosen so as to be amenable to quantitative analysis." (John M Ziman, "Reliable Knowledge: An Exploration of the Grounds for Belief in Science", 1978)

"Science is not impressed with a conglomeration of data. It likes carefully constructed analysis of each problem." (Daniel E Koshland Jr, Science, Volume 263" (5144), [editorial] 1994)

"The methods of science include controlled experiments, classification, pattern recognition, analysis, and deduction. In the humanities we apply analogy, metaphor, criticism, and (e)valuation. In design we devise alternatives, form patterns, synthesize, use conjecture, and model solutions." (Béla H Bánáthy, "Designing Social Systems in a Changing World", 1996)

On Idealization: Science

"The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. " (Cassius J Keyser, "The Humanization of the Teaching of Mathematics", 1912)

"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized. The universe, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"Scientific models have all these connotations. They are representations of states, objects, and events. They are idealized in the sense that they are less complicated than reality and hence easier to use for research purposes. These models are easier to manipulate and 'carry' than the real thing. The simplicity of models, compared with reality, lies in the fact that only the relevant properties of reality are represented." (Russell L Ackoff, "Scientific Method: optimizing applied research decisions", 1962) 

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

"The idea of approximation to the truth is, in my view, one of the most important ideas in the theory of science. [...] The idea of approximation to the truth - like the idea of truth as are gulative principle - presupposes a realistic view of the world. It does not presuppose that reality is as our scientific theories describe it; but it does presuppose that there is a reality and that we and our theories - which are ideas we have ourselves created and are therefore always idealizations - can draw closer and closer to an adequate description of reality, if we employ the four-stage method of trial and error." (Karl R Popper, "The Logic and Evolution of Scientific Theory", [in "All Life is Problem Solving", 1999] 1972)

"[…] it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model." (Sir David Cox, "Comment on ‘Model uncertainty, data mining and statistical inference’", Journal of the Royal Statistical Society, Series A 158, 1995)

"When scientists need to explain difficult points of theory, illustration by hypothetical example - rather than by total abstraction - works well (perhaps indispensably) as a rhetorical device. Such cases do not function as speculations in the pejorative sense - as silly stories that provide insight into complex mechanisms - but rather as idealized illustrations to exemplify a difficult point of theory." (Stephen Jay Gould, "Leonardo's Mountain of Clams and the Diet of Worms", 1998)

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

On Heuristics: Trial and Error in Data Science

"We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, [Nobel Prize Lecture], 1974)

"Heuristics are rules of thumb that help constrain the problem in certain ways (in other words they help you to avoid falling back on blind trial and error), but they don't guarantee that you will find a solution. Heuristics are often contrasted with algorithms that will guarantee that you find a solution - it may take forever, but if the problem is algorithmic you will get there. However, heuristics are also algorithms." (S Ian Robertson, "Problem Solving", 2001)

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

"Another crowning achievement of deep learning is its extension to the domain of reinforcement learning. In the context of reinforcement learning, an autonomous agent must learn to perform a task by trial and error, without any guidance from the human operator." (Ian Goodfellow et al, "Deep Learning", 2015)

"Bayesian networks provide a more flexible representation for encoding the conditional independence assumptions between the features in a domain. Ideally, the topology of a network should reflect the causal relationships between the entities in a domain. Properly constructed Bayesian networks are relatively powerful models that can capture the interactions between descriptive features in determining a prediction." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015) 

"A learning algorithm for a robot or a software agent to take actions in an environment so as to maximize the sum of rewards through trial and error." (Tomohiro Yamaguchi et al, "Analyzing the Goal-Finding Process of Human Learning With the Reflection Subtask", 2018)

"Reinforcement learning is also a subset of AI algorithms which creates independent, self-learning systems through trial and error. Any positive action is assigned a reward and any negative action would result in a punishment. Reinforcement learning can be used in training autonomous vehicles where the goal would be obtaining the maximum rewards." (Vijayaraghavan Varadharajan & Akanksha Rajendra Singh, "Building Intelligent Cities: Concepts, Principles, and Technologies", 2021)

"Methodologically, much of modern machine learning practice rests on a variant of trial and error, which we call the train-test paradigm. Practitioners repeatedly build models using any number of heuristics and test their performance to see what works. Anything goes as far as training is concerned, subject only to computational constraints, so long as the performance looks good in testing. Trial and error is sound so long as the testing protocol is robust enough to absorb the pressure placed on it." (Moritz Hardt & Benjamin Recht, "Patterns, Predictions, and Actions: Foundations of Machine Learning", 2022)

On Heuristics: Trial and Error in Science

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

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

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

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

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

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

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

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

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

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

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

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

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

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

On Mistakes, Blunders and Errors X: Data Science

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"[…] it is not enough to say: 'There's error in the data and therefore the study must be terribly dubious'. A good critic and data analyst must do more: he or she must also show how the error in the measurement or the analysis affects the inferences made on the basis of that data and analysis." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Many scientists who work not just with noise but with probability make a common mistake: They assume that a bell curve is automatically Gauss's bell curve. Empirical tests with real data can often show that such an assumption is false. The result can be a noise model that grossly misrepresents the real noise pattern. It also favors a limited view of what counts as normal versus non-normal or abnormal behavior. This assumption is especially troubling when applied to human behavior. It can also lead one to dismiss extreme data as error when in fact the data is part of a pattern." (Bart Kosko, "Noise", 2006

"In bagging, generating complementary base-learners is left to chance and to the unstability of the learning method. In boosting, we actively try to generate complementary base-learners by training the next learner boosting on the mistakes of the previous learners." (Ethem Alpaydin, "Introduction to Machine Learning" 2nd Ed, 2010)

"When data is not normal, the reason the formulas are working is usually the central limit theorem. For large sample sizes, the formulas are producing parameter estimates that are approximately normal even when the data is not itself normal. The central limit theorem does make some assumptions and one is that the mean and variance of the population exist. Outliers in the data are evidence that these assumptions may not be true. Persistent outliers in the data, ones that are not errors and cannot be otherwise explained, suggest that the usual procedures based on the central limit theorem are not applicable." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"There are two kinds of mistakes that an inappropriate inductive bias can lead to: underfitting and overfitting. Underfitting occurs when the prediction model selected by the algorithm is too simplistic to represent the underlying relationship in the dataset between the descriptive features and the target feature. Overfitting, by contrast, occurs when the prediction model selected by the algorithm is so complex that the model fits to the dataset too closely and becomes sensitive to noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"[...] data often has some errors, outliers and other strange values, but these do not necessarily need to be individually identified and excluded. It also points to the benefits of using summary measures that are not unduly affected by odd observations [...] are known as robust measures, and include the median and the inter-quartile range." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Statistical models have two main components. First, a mathematical formula that expresses a deterministic, predictable component, for example the fitted straight line that enables us to make a prediction [...]. But the deterministic part of a model is not going to be a perfect representation of the observed world [...] and the difference between what the model predicts, and what actually happens, is the second component of a model and is known as the residual error - although it is important to remember that in statistical modelling, ‘error’ does not refer to a mistake, but the inevitable inability of a model to exactly represent what we observe." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"There are many ways for error to creep into facts and figures that seem entirely straightforward. Quantities can be miscounted. Small samples can fail to accurately reflect the properties of the whole population. Procedures used to infer quantities from other information can be faulty. And then, of course, numbers can be total bullshit, fabricated out of whole cloth in an effort to confer credibility on an otherwise flimsy argument. We need to keep all of these things in mind when we look at quantitative claims. They say the data never lie - but we need to remember that the data often mislead." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

On Mistakes, Blunders and Errors XIII: Science

"Knowledge being to be had only of visible and certain truth, error is not a fault of our knowledge, but a mistake of our judgment, giving assent to that which is not true." (John Locke, "An Essay Concerning Human Understanding", 1689)

"Assert nothing till after repeated experiments and examinations, in all lights, and in all positions. Truth alone is the matter that you are in search after; and if you have been mistaken, let not vanity seduce you to persist in your mistake." (Henry Baker, "The Microscope Made Easy", 1742)

"The only method of preventing such errors from taking place, and of correcting them when formed, is to restrain and simplify our reasoning as much as possible. This depends entirely upon ourselves, and the neglect of it is the only source of our mistakes." (Antoine-Laurent de Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)

"Hypotheses are scaffoldings erected in front of a building and then dismantled when the building is finished. They are indispensable for the workman; but you mustn't mistake the scaffolding for the building." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833) 

"Experimental science hardly ever affords us more than approximations to truth; and whenever many agents are concerned we are in great danger of being mistaken." (Sir Humphry Davy, cca. 1836)

"We learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a discovery." (Samuel Smiles, "Facilities and Difficulties", 1859)

"It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"It is surprising to learn the number of causes of error which enter into the simplest experiment, when we strive to attain rigid accuracy." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Perfect readiness to reject a theory inconsistent with fact is a primary requisite of the philosophic mind. But it, would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent. (William S Jevons, "The Principles of Science", 1874)

"There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind." (William T Kelvin, "Electrical Units of Measurement", 1883)

"It sounds paradoxical to say the attainment of scientific truth has been effected, to a great extent, by the help of scientific errors." (Thomas H Huxley, "The Progress of Science", 1887)

"The man of science, who, forgetting the limits of philosophical inquiry, slides from these formulæ and symbols into what is commonly understood by materialism, seems to me to place himself on a level with the mathematician, who should mistake the x's and y's with which he works his problems for real entities - and with this further disadvantage, as compared with the mathematician, that the blunders of the latter are of no practical consequence, while the errors of systematic materialism may paralyse the energies and destroy the beauty of a life." (Thomas H Huxley, "Method and Results", 1893)

"The scientific spirit is of more value than its products, and irrationally held truths may be more harmful than reasoned errors." (Thomas H Huxley, "Darwiniana", 1893–94)

"The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us." (Paul Valéry, "Introduction to the Method of Leonardo da Vinci", 1895)

"It is a great mistake to suppose that the mind of the active scientist is filled with pro-positions which, if not proved beyond all reasonable cavil, are at least extremely probable. On the contrary, he entertains hypotheses which are almost wildly incredible, and treats them with respect for the time being. Why does he do this? Simply because any scientific proposition whatever is always liable to be refuted and dropped at short notice. A hypothesis is something which looks as if it might be true and were true, and which is capable of verification or refutation by comparison with facts. The best hypothesis, in the sense of the one most recommending itself to the inquirer, is the one which can be the most readily refuted if it is false." (Charles S Peirce, 1896)

"The scientific value of truth is not, however, ultimate or absolute. It rests partly on practical, partly on aesthetic interests. As our ideas are gradually brought into conformity with the facts by the painful process of selection, - for intuition runs equally into truth and into error, and can settle nothing if not controlled by experience, - we gain vastly in our command over our environment. This is the fundamental value of natural science" (George Santayana, "The Sense of Beauty: Being the Outlines of Aesthetic Theory", 1896)

"It would be a mistake to suppose that a science consists entirely of strictly proved theses, and it would be unjust to require this. […] Science has only a few apodeictic propositions in its catechism: the rest are assertions promoted by it to some particular degree of probability. It is actually a sign of a scientific mode of thought to find satisfaction in these approximations to certainty and to be able to pursue constructive work further in spite of the absence of final confirmation." (Sigmund Freud, "Introductory Lectures on Psycho-Analysis", 1916)

"The mistake from which todays’ science suffers is that the theoreticians are concerned too unilaterally with precision mathematics, while the practitioners use a sort of approximate mathematics, without being in touch with precision mathematics through which they could reach a real approximation mathematics." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)

"More than any other science, mathematics develops through a sequence of consecutive abstractions. A desire to avoid mistakes forces mathematicians to find and isolate the essence of problems and the entities considered. Carried to an extreme, this procedure justifies the well-known joke that a mathematician is a scientist who knows neither what he is talking about nor whether whatever he is talking about exists or not." (Élie Cartan, 1940) 

"Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions." (George Sarton, "A History of Science" Vol 2, 1952)

"Nature is more subtle, more deeply intertwined and more strangely integrated than any of our pictures of her - than any of our errors. It is not merely that our pictures are not full enough; each of our pictures in the end turns out to be so basically mistaken that the marvel is that it worked at all." (Jacob Bronowski, "The Common Sense of Science", 1953) 

"Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions." (George Sarton, "A History of Science" Vol. 2, 1959)

"[…] the progress of science is a little like making a jig-saw puzzle. One makes collections of pieces which certainly fit together, though at first it is not clear where each group should come in the picture as a whole, and if at first one makes a mistake in placing it, this can be corrected later without dismantling the whole group." (Sir George Thomson, "The Inspiration of Science", 1961)

"All discoveries in art and science result from an accumulation of errors." (Marshall McLuhan, "Culture Is Our Business", 1970)

"Early scientific thinking was holistic, but speculative - the modern scientific temper reacted by being empirical, but atomistic. Neither is free from error, the former because it replaces factual inquiry with faith and insight, and the latter because it sacrifices coherence at the altar of facticity. We witness today another shift in ways of thinking: the shift toward rigorous but holistic theories. This means thinking in terms of facts and events in the context of wholes, forming integrated sets with their own properties and relationships." (Ervin László, "Introduction to Systems Philosophy", 1972)

"The point is that every experiment involves an error, the magnitude of which is not known beforehand and it varies from one experiment to another. For this reason, no matter what finite number of experiments have been carried out, the arithmetic mean of the values obtained will contain an error. Of course, if the experiments are conducted under identical conditions and the errors are random errors, then the error of the mean will diminish as the number of experiments is increased, but it cannot be reduced to zero for a finite number of experiments. […] The choice of entities for an experiment must be perfectly random, so that even an apparently inessential cause could not lead to erroneous conclusions." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"[…] in most sciences the question Why? is forbidden and the answer is actually to the question, How? Science is much better in explaining than in understanding, but it likes to mistake one for the other." (Erwin Chargaff, "Voices in the Labyrinth", Perspectives in Biology and Medicine Vol. 18, 1975)

"Early scientific thinking was holistic, but speculative - the modern scientific temper reacted by being empirical, but atomistic. Neither is free from error, the former because it replaces factual inquiry with faith and insight, and the latter because it sacrifices coherence at the altar of facticity. We witness today another shift in ways of thinking: the shift toward rigorous but holistic theories. This means thinking in terms of facts and events in the context of wholes, forming integrated sets with their own properties and relationships." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Whatever humans have learned had to be learned as a consequence only of trial and error experience. Humans have learned only through mistakes." (Buckminster Fuller, "R Buckminster Fuller on education", 1979)

"What shows a theory to be inadequate or mistaken is not, as a rule, the discovery of a mistake in the information that led us to propound it; more often it is the contradictory evidence of a new observation which we were led to make because we held that theory." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

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

"[...] we learn only through trial and error. Our trials, however, are always our hypotheses. They stem from us, not from the external world. All we learn from the external world is that some of our efforts are mistaken." (Karl R Popper, "The Epistemological Position of Evolutionary Epistemology", [in "All Life is Problem Solving", 1999] 1987)

"Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science - by far the most successful claim to knowledge accessible to humans - teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)

"It is important to distinguish between the scientific concept of law as a generalization, and the social concept of law which is prescriptive and normative. A desire for tolerance in respecting the laws of different social systems must not lead us into the mistake of attributing volition to the entities of science or relativism to scientific laws." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"The human mind delights in finding pattern - so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it." (Stephen J Gould, "The Flamingo's Smile: Reflections in Natural History", 2010)

"No definition of a social problem is perfect, but there are two principal ways such definitions can be flawed. On the one hand, we may worry that a definition is too broad, that it encompasses more than it ought to include. That is, broad definitions identify some cases as part of the problem that we might think ought not to be included; statisticians call such cases false positives (that is, they mistakenly identify cases as part of the problem). On the other hand, a definition that is too narrow excludes cases that we might think ought to be included; these are false negatives (incorrectly identified as not being part of the problem)." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"One should never mistake pattern for meaning." (Iain Banks, "The Hydrogen Sonata",  2012)

"A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes." (G Johnstone Stoney)

"Science with its strict analysis of the facts, its persevering search for new, more consummate truths, and its relentless struggle against discovered mistakes and prejudices - science must saturate all or technics, our culture, and everyday life." (Abram F Joffe)

On Science: Definitions

"By Science is understood a Knowledge acquired by, or founded on clear and self evident Principles, whence it follows that the Mathematicks may truly be stiled such." (Jacques Ozanam, "A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms", 1702)

"Science is nothing but the finding of analogy, identity, in the most remote parts." (Ralph W Emerson, 1837)

"Science is the systematic classification of experience." (George H Lewes, "The Physical Basis of Mind", 1877)

"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)

"Abstract as it is, science is but an outgrowth of life. That is what the teacher must continually keep in mind. […] Let him explain […] science is not a dead system - the excretion of a monstrous pedantism - but really one of the most vigorous and exuberant phases of human life." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"Science is but a method. Whatever its material, an observation accurately made and free of compromise to bias and desire, and undeterred by consequence, is science." (Hans Zinsser, "Untheological Reflections", The Atlantic Monthly, 1929)

"Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements." (Rudolf Carnap, "The Unity of Science", 1934)

"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 is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought." (Albert Einstein, "Considerations Concerning the Fundaments of Theoretical Physics", Science Vol. 91 (2369), 1940)

"Science is the organised attempt of mankind to discover how things work as causal systems. The scientific attitude of mind is an interest in such questions. It can be contrasted with other attitudes, which have different interests; for instance the magical, which attempts to make things work not as material systems but as immaterial forces which can be controlled by spells; or the religious, which is interested in the world as revealing the nature of God." (Conrad H Waddington, "The Scientific Attitude", 1941)

"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. For the most part this knowledge concerns the forces impinging upon human beings in the serious business of living and thus affecting man’s adjustment to and of the physical and the social world. […] Pure science is more interested in understanding, and applied science is more interested in control […]" (Austin L Porterfield, "Creative Factors in Scientific Research", 1941)

"Science is an interconnected series of concepts and schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observation."(James B Conant, "Science and Common Sense", 1951)

"Science is the creation of concepts and their exploration in the facts. It has no other test of the concept than its empirical truth to fact." (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, and technology is the art of using these symbol systems so as to control and organize unique events. Scientific observation is always a viewing of things through the refracting medium of a symbol system, and technological praxis is always handling of things in ways that some symbol system has dictated. Education in science and technology is essentially education on the symbol level." (Aldous L Huxley, "Essay", Daedalus, 1962)

"What, then, is science according to common opinion? 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 a matter of disinterested observation, patient ratiocination within some system of logically correlated concepts. In real-life conflicts between reason and passion the issue is uncertain. Passion and prejudice are always able to mobilize their forces more rapidly and press the attack with greater fury; but in the long run (and often, of course, too late) enlightened self-interest may rouse itself, launch a counterattack and win the day for reason." (Aldous L Huxley, "Literature and Science", 1963)

"Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show." (Richard P Feynman, "The Problem of Teaching Physics in Latin America", Engineering and Science, 1963)

"Science is a product of man, of his mind; and science creates the real world in its own image." (Frank E Egler, "The Way of Science", 1970)

"Science is systematic organisation of knowledge about the universe on the basis of explanatory hypotheses which are genuinely testable. Science advances by developing gradually more comprehensive theories; that is, by formulating theories of greater generality which can account for observational statements and hypotheses which appear as prima facie unrelated." (Francisco J Ayala, "Studies in the Philosophy of Biology: Reduction and Related Problems", 1974)

"Science is not a heartless pursuit of objective information. It is a creative human activity, its geniuses acting more as artists than information processors. Changes in theory are not simply the derivative results of the new discoveries but the work of creative imagination influenced by contemporary social and political forces." (Stephen J Gould, "Ever Since Darwin: Reflections in Natural History", 1977)

"Science is a process. It is a way of thinking, a manner of approaching and of possibly resolving problems, a route by which one can produce order and sense out of disorganized and chaotic observations. Through it we achieve useful conclusions and results that are compelling and upon which there is a tendency to agree." (Isaac Asimov, "‘X’ Stands for Unknown", 1984)

"Science is defined as a set of observations and theories about observations." (F Albert Matsen, "The Role of Theory in Chemistry", Journal of Chemical Education Vol. 62 (5), 1985)

"We believe that science, in all its sense, is a social process that both causes and is caused by social organisation."  (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"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. Scientific hypotheses may incorporate only elements of the natural empirical world, and thus may contain no element of the supernatural." (Robert E Kofahl, Correctly Redefining Distorted Science: A Most Essential Task", Creation Research Society Quarterly Vol. 23, 1986)

"Science is not a given set of answers but a system for obtaining answers. The method by which the search is conducted is more important than the nature of the solution. Questions need not be answered at all, or answers may be provided and then changed. It does not matter how often or how profoundly our view of the universe alters, as long as these changes take place in a way appropriate to science. For the practice of science, like the game of baseball, is covered by definite rules." (Robert Shapiro, "Origins: A Skeptic’s Guide to the Creation of Life on Earth", 1986)

"Science doesn't purvey absolute truth. 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. And this works, not just for the ordinary aspects of science, but for all of life. I should think people would want to know that what they know is truly what the universe is like, or at least as close as they can get to it." (Isaac Asimov, [Interview by Bill Moyers] 1988)

"Science doesn’t purvey absolute truth. Science is a mechanism, 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 with Bill Moyers in The Humanist] 1989)

"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)

"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)

"Clearly, science is not simply a matter of observing facts. Every scientific theory also expresses a worldview. Philosophical preconceptions determine where facts are sought, how experiments are designed, and which conclusions are drawn from them." (Nancy R Pearcey & Charles B. Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"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)

"Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding." (Gian-Carlo Rota, "Indiscrete Thoughts", 1997)

"Religion is the antithesis of science; science is competent to illuminate all the deep questions of existence, and does so in a manner that makes full use of, and respects the human intellect. I see neither need nor sign of any future reconciliation." (Peter W Atkins, "Religion - The Antithesis to Science", 1997)

"Science is the art of the appropriate approximation. While the flat earth model is usually spoken of with derision it is still widely used. Flat maps, either in atlases or road maps, use the flat earth model as an approximation to the more complicated shape." (Byron K. Jennings, "On the Nature of Science", Physics in Canada Vol. 63 (1), 2007)

"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. Scientism, by contrast, is the worldview and value system that insists that the questions the scientific method can answer are the most important questions human beings can ask, and that the picture of the world yielded by science is a better approximation to reality than any other." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

Richard B Braithwaite - Collected Quotes

"It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics [...] required [...] had already been worked out by pure mathematicians for their own amusement [...] The moral for statesmen would seem to be that, for proper scientific 'planning' , pure mathematics should be endowed fifty years ahead of scientists." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

"[...] no batch of observations, however large, either definitively rejects or definitively fails to reject the hypothesis H0." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

"The peaks of science may appear to be floating in the clouds, but their foundations are in the hard facts of experience." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

"The peculiarity of [...] statistical hypotheses is that they are not conclusively refutable by any experience." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

"The ultimate justification for any scientific belief will depend upon the main purpose for which we think scientifically - that of predicting and thereby controlling the future." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

"The world is not made up of empirical facts with the addition of the laws of nature: what we call the laws of nature are conceptual devices by which we organize our empirical knowledge and predict the future." (Richard B Braithwaite, "Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science", 1953)

On Method VI (Scientific Method)

"[...] scientific method is simply the attempt to acquire knowledge of general laws directly or indirectly by experience, by the use of our five senses. The only limitations that can be assigned to the applicability of this process are those due to the character of experience. Anything that is logically related to experience by discoverable laws and is capable of description in general terms can be dealt with by the scientific method." (Arthur D Ritchie, "Scientific Method: An Inquiry Into the Character and Validity of Natural Laws", 1923)

"Science attempts to establish an understanding of all types of phenomena. Many different explanations can sometimes be given that agree qualitatively with experiments or observations. However, when theory and experiment quantitatively agree, then we can usually be more confident in the validity of the theory. In this manner mathematics becomes an integral part of the scientific method." (Richard Haberman, "Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow", 1998)

"Scientific method is not much different from our day-to-day ways of learning about the world. Without really thinking about the steps or the standards, common sense invokes the same process of evidence and reasoning as scientists more explicitly follow." (Peter Kosso, "A Summary of Scientific Method", 2011)

"Scientific method is the gateway into scientific discoveries that in turn prompt technological advances and cultural influences." (Hugh G Gauch Jr., "Scientific Method in Brief", 2012)

"The traditional scientific method is hypothesis driven. The researcher formulates a theory of how the world works, and then seeks to support or reject this hypothesis based on data." (Steven S Skiena, "The Data Science Design Manual", 2017)

"Its primary function was to make previously invisible phenomena subject to direct inspection in a graphic display […] The graphic method had another function, that of communication to the scientific community and educated readers. These displays made complex phenomena palpable and concrete." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"The general principles of starting with a well-defined question, engaging in careful observation, and then formulating hypotheses and assessing the strength of evidence for and against them became known as the scientific method." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"We are accustomed to intellectual diffusion taking place from the natural and physical sciences into the social sciences; certainly that is the direction taken for both calculus and the scientific method. But statistical graphics in particular, and statistics in general, took the reverse route." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

On Construction VIII: Science

"Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'." (Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de Rotation de la Terre", 1851)

"The invention of a new symbol is a step in the advancement of civilisation. Why were the Greeks, in spite of their penetrating intelligence and their passionate pursuit of Science, unable to carry Mathematics farther than they did? and why, having formed the conception of the Method of Exhaustions, did they stop short of that of the Differential Calculus? It was because they had not the requisite symbols as means of expression. They had no Algebra. Nor was the place of this supplied by any other symbolical language sufficiently general and flexible; so that they were without the logical instruments necessary to construct the great instrument of the Calculus." (George H Lewes "Problems of Life and Mind", 1873)

"We shall call this universal organizational science the 'Tektology'. The literal translation of this word from the Greek is 'the theory of construction'. 'Construction' is the most generaI and suitable synonym for the modern concept of 'organization'. [...] The aim of tektology is to systematize organizational experience; this science is clearly empirical and should draw its conclusions by way of induction." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"It would be a mistake to suppose that a science consists entirely of strictly proved theses, and it would be unjust to require this. […] Science has only a few apodeictic propositions in its catechism: the rest are assertions promoted by it to some particular degree of probability. It is actually a sign of a scientific mode of thought to find satisfaction in these approximations to certainty and to be able to pursue constructive work further in spite of the absence of final confirmation." (Sigmund Freud, "Introductory Lectures on Psycho-Analysis", 1916)

"Science is a magnificent force, but it is not a teacher of morals. It can perfect machinery, but it adds no moral restraints to protect society from the misuse of the machine. It can also build gigantic intellectual ships, but it constructs no moral rudders for the control of storm tossed human vessel. It not only fails to supply the spiritual element needed but some of its unproven hypotheses rob the ship of its compass and thus endangers its cargo." (William J Bryan, "Undelivered Trial Summation Scopes Trial", 1925)

"Science aims at constructing a world which shall be symbolic of the world of commonplace experience." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"No doctrinal system in physical science, or indeed perhaps in any science, will alter its content of its own accord. Here we always need the pressure of outer circumstances. Indeed the more intelligible and comprehensive a theoretical system is the more obstinately it will resist all attempts at reconstruction or expansion." (Max Planck, "Where is Science Going?", 1932)

"A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empirical sciences, more particularly, he constructs hypotheses, or systems of theories, and tests them against experience by observation and experiment." (Karl Popper, "The Logic of Scientific Discovery", 1934)

"Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science." (Richard Courant & Herbert Robbins, "What Is Mathematics?", 1941)

"A theoretical science unaware that those of its constructs considered relevant and momentous are destined eventually to be framed in concepts and words that have a grip on the educated community and become part and parcel of the general world picture - a theoretical science [...]" (Erwin Schrödinger, "Are There Quantum Jumps?", The British Journal for the Philosophy of Science Vol. 3, 1952)

"[...] sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain aesthetic criteria - that is, in relation to how much it describes, it must be rather simple." (John von Neumann, "Method in the physical sciences", 1955)

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

"Many people believe that reasoning, and therefore science, is a different activity from imagining. But this is a fallacy […] Reasoning is constructed with movable images just as certainly as poetry is." (Jacob Bronowski, "Visionary Eye", 1978)

"[…] the pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before." (John A Wheeler, "Geons, Black Holes, and Quantum Foam: A Life in Physics", 1998)