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

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

"How do you attack the unknown, or defend yourself from it?" (Jules Verne, "Twenty Thousand Leagues under the Sea", 1870)

"Sitting there on the heather, on our planetary grain, I shrank from the abysses that opened up on every side, and in the future. The silent darkness, the featureless unknown, were more dread than all the terrors that imagination had mustered." (Olaf Stapledon, "Star Maker", 1937)

"All unknowns are organically inimical to man, and homo sapiens is human in the full sense of the word only when his grammar is entirely free of question marks." (Yevgeny Zamiatin, "We", 1924)

"The unknown is a terrible place. There are monsters out there." (Philip K Dick, "Solar Lottery", 1955)

"There are people who run at the sight of the unknown, others who advance to meet it." (Fredric Brown, "Puppet Show", 1962)

"The exploration of the unknown is always a fraud." (James Gunn, "Station in Space", 1958)

"He knew the unknown. It was beyond all comprehension and Guy thought that it was no more than a set of words: a black, empty World preceding the appearance of the World Light; a dead, icy World when the World Light was extinguished; an endless Wasteland with many World Lights. No one could explain what this meant." (Arkady Strugatsky &Boris Strugatsky, "Prisoners of Power", 1969)

"The unknown is always worse than the known." (Eando Binder, "Menace of the Saucers", 1969)

"What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what ‘the stars foretell,’ avoid opinion, care not what the neighbors think, never mind the unguessable ‘verdict of history', - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your only clue. Get the facts!" (Robert A Heinlein, "Time Enough for Love", 1973)

"An infinity of universes swim in superspace, all passing through their own cycles of birth and death; some are novel, others repetitious; some produce macrolife, others do not; still others are lifeless. In time, macrolife will attempt to reach out from its cycles to other space-time bubbles, perhaps even to past cycles, which leave their echoes in superspace, and might be reached. In all these ambitions, only the ultimate pattern of development is unknown, drawing macrolife toward some future transformation still beyond its view. There are times when the oldest macrolife senses that vaster intelligences are peering in at it from some great beyond [...]" (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"So together they left the office and walked into the uncertainty of the rest of their lives. That, in the final analysis, is the great adventure in which each of us takes part; what more courageous thing is there, after all, than facing the unknown we all share, the danger and joy that awaits us in the unread pages of the Book of the Future [...]" (George Alec Effinger," The World of Pez Pavilion: Preliminary to the Groundbreaking Ceremony", 1983)

"The Sioux had outlived their way of life, had turned it over to the white technicians, who would map everything. That was what he most disliked about them: that they sought to know all things, and did not realize that a forest without dark places has value only to the woodcutter." (Jack McDevitt, "Ancient Shores", 1996)

"'Do you really believe in physics?'  'I dont know what that means. Physics tries to draw a numerical picture of the world. I dont know that it actually explains anything. You cant illustrate the unknown. Whatever that might mean.'" (Cormac McCarthy, "Stella Maris", 2022)

On Unknowns - Systems

"The state of a system at a given moment depends on two things - its initial state, and the law according to which that state varies. If we know both this law and this initial state, we have a simple mathematical problem to solve, and we fall back upon our first degree of ignorance. Then it often happens that we know the law and do not know the initial state. It may be asked, for instance, what is the present distribution of the minor planets? We know that from all time they have obeyed the laws of Kepler, but we do not know what was their initial distribution. In the kinetic theory of gases we assume that the gaseous molecules follow rectilinear paths and obey the laws of impact and elastic bodies; yet as we know nothing of their initial velocities, we know nothing of their present velocities. The calculus of probabilities alone enables us to predict the mean phenomena which will result from a combination of these velocities. This is the second degree of ignorance. Finally it is possible, that not only the initial conditions but the laws themselves are unknown. We then reach the third degree of ignorance, and in general we can no longer affirm anything at all as to the probability of a phenomenon. It often happens that instead of trying to discover an event by means of a more or less imperfect knowledge of the law, the events may be known, and we want to find the law; or that, instead of deducing effects from causes, we wish to deduce the causes." (Henri Poincaré, "Science and Hypothesis", 1902)

"[Disorganized complexity] is a problem in which the number of variables is very large, and one in which each of the many variables has a behavior which is individually erratic, or perhaps totally unknown. However, in spite of this helter-skelter, or unknown, behavior of all the individual variables, the system as a whole possesses certain orderly and analyzable average properties. [...] [Organized complexity is] not problems of disorganized complexity, to which statistical methods hold the key. They are all problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole. They are all, in the language here proposed, problems of organized complexity." (Warren Weaver, "Science and Complexity", American Scientist Vol. 36, 1948)

"[...] in a state of dynamic equilibrium with their environments. If they do not maintain this equilibrium they die; if they do maintain it they show a degree of spontaneity, variability, and purposiveness of response unknown in the non-living world. This is what is meant by ‘adaptation to environment’ […] [Its] essential feature […] is stability - that is, the ability to withstand disturbances." (Kenneth Craik, 'Living organisms', "The Nature of Psychology", 1966)

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?" (Deborah J Bennett, "Randomness", 1998)

"Of course, the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So, the direct impact of this phenomenon on weather prediction is often somewhat overstated." (James Annan & William Connolley, "Chaos and Climate", 2005)

"If you want a system - economic, social, political, or otherwise - to operate at a high level of efficiency, then you have to optimize its operation in such a way that its resilience is dramatically reduced to unknown - and possibly unknowable - shocks and/or changes in its operating environment. In other words, there is an inescapable price to be paid in efficiency in order to gain the benefits of adaptability and survivability in a highly uncertain environment. There is no escape clause!" (John L Casti, "X-Events: The Collapse of Everything", 2012)

"Order is not universal. In fact, many chaologists and physicists posit that universal laws are more flexible than first realized, and less rigid - operating in spurts, jumps, and leaps, instead of like clockwork. Chaos prevails over rules and systems because it has the freedom of infinite complexity over the known, unknown, and the unknowable." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

On Unknowns in Mathematics (-1949)

"It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, choosing rather to acknowledge their ignorance, than affirm anything rashly." (Isaac Barrow, "Mathematical Lecture", 1734)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.   Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter." (Augustus De Morgan, "Calculus of Functions" Encyclopaedia of Pure Mathematics, 1847)

"Thought is symbolical of Sensation as Algebra is of Arithmetic, and because it is symbolical, is very unlike what it symbolises. For one thing, sensations are always positive; in this resembling arithmetical quantities. A negative sensation is no more possible than a negative number. But ideas, like algebraic quantities, may be either positive or negative. However paradoxical the square of a negative quantity, the square root of an unknown quantity, nay, even in imaginary quantity, the student of Algebra finds these paradoxes to be valid operations. And the student of Philosophy finds analogous paradoxes in operations impossible in the sphere of Sense. Thus although it is impossible to feel non-existence, it is possible to think it; although it is impossible to frame an image of Infinity, we can, and do, form the idea, and reason on it with precision." (George H Lewes "Problems of Life and Mind", 1873)

"So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality." (Henri Poincaré, "The Value of Science", 1905)

"Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality." (Henri Poincaré, "The Value of Science", Popular Science Monthly, 1906

"It must be gently but firmly pointed out that analogy is the very corner-stone of scientific method. A root-and-branch condemnation would invalidate any attempt to explain the unknown in terms of the known, and thus prune away every hypothesis." (Archie E Heath, "On Analogy", The Cambridge Magazine, 1918)

"[…] mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediaeval slowness of the syllogisms expressed in our words." (Charles Nordmann, "Einstein and the Universe", 1922)

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

"[…] mathematicians progress only by doubt, through humble and constant attempts to impinge on the immense domain of the unknown." (Leopold Infeld, "Whom the Gods Love: The Story of Évariste Galois", 1948)

On Unknowns in Mathematics (2000-)

"The classification theorems of mathematics are among the ultimate triumphs of human intellectual achievement. A classification theorem provides a complete list of all objects in a given category as well as a scheme for matching an unknown object from the category with exactly one of the canonical examples." (Robert Messer & Philip Straffin, "Topology Now!", 2006)

"Equations are the mathematician's way of working out the value of some unknown quantity from circumstantial evidence. ‘Here are some known facts about an unknown number: deduce the number.’ An equation, then, is a kind of puzzle, centered upon a number. We are not told what this number is, but we are told something useful about it. Our task is to solve the puzzle by finding the unknown number." (Ian Stewart, "Why Beauty Is Truth", 2007)

"[…] statistics is the key discipline for predicting the future or for making inferences about the unknown, or for producing convenient summaries of data." (David J Hand, "Statistics: A Very Short Introduction", 2008)

"What could mathematics and poetry share, except that the mention of either one is sometimes enough to bring an uneasy chill into a conversation? [...] Both fields use analogies - comparisons of all sorts - to explain things, to express unknown or unknowable concepts, and to teach." (Marcia Birken & Anne C Coon, "Discovering Patterns in Mathematics and Poetry", 2008)

"The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown." (Michael P Starbird, [interview] 2009)

"To the average layperson, mathematics is a mass of abstruse formulae and bizarre technical terms (e.g., perverse sheaves, the monster group, barreled spaces, inaccessible cardinals), usually discussed by academics in white coats in front of a blackboard covered with peculiar symbols. The distinction between mathematics and physics is blurred and that between pure and applied mathematics is unknown. But to the professional, these are three different worlds, different sets of colleagues, with different goals, different standards, and different customs." (David Mumford, ["The Best Writing of Mathematics: 2012"] 2012)

"Mathematics does not merely describe the problem in an abstract way, it allows us to find a previously unknown 'solution' from the abstract description. It is surprising that the unknown can be transformed into the well known when we succeed in describing the problem mathematically." (Waro Iwane, "Mathematics in Our Company: What Does It Describe?", [in "What Mathematics Can Do for You"] 2013)

"Symbols transcend the medium of communication. They are ubiquitous in our language, and play a sizable role (though perhaps not a central one) in mathematical imagery linking the conscious and subconscious, the familiar and unknown, to give us cultural/emotional predispositions to meaning, all to enhance the creative process."(Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"Unlike symbols in poetry, mathematical symbols begin as deliberate designs created by mathematicians. That does not stop symbols from performing the same function that a poem would: to make connections between experience and the unknown and to transfer metaphorical thoughts capable of conveying meaning. As in poetry, there are archetypes in mathematics. If there are such things as self-evident truths, then there probably are things we know about the world that come with the human package at birth." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

On Unknowns in Mathematics (1950-1999)

"Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved." (Omar Khayyam [quoted by J.J. Winter and W. Arafat, "The Algebra of ‘Umar Khayyam’", Journal of the Royal Asiatic Society of Bengal, Volume 41, 1950)

"Unfortunately, when most people think of 'physics', they think of chalkboards covered with undecipherable symbols of an unknown mathematics. The fact is that physics is not mathematics. Physics, in essence, is simple wonder at the way things are and a divine (some call it compulsive) interest in how that is so. Mathematics is the tool of physics. Stripped of mathematics, physics becomes pure enchantment." (Gary Zukav, "The Dancing Wu Li Masters", 1979)

"The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient." (Benoit Mandelbrot, "The Fractal Geometry of Nature", 1977)

"To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas." (Ivars Peterson, "The Mathematical Tourist", 1988)

"Statistics as a science is to quantify uncertainty, not unknown." (Chamont Wang, "Sense and Nonsense of Statistical Inference: Controversy, Misuse, and Subtlety", 1993)

"In mathematical models, usually the qualitative effects are at least partially understood. Quantitative results are often unknown. When quantitative results are known (perhaps due to precise experiments), then mathematical models are desirable in order to discover which mechanisms best account for the known data, i.e., which quantities are important and which can be ignored. In complex problems sometimes two or more effects interact. Although each by itself is qualitatively and quantitatively understood, their interaction may need mathematical analysis in order to be understood even qualitatively." (Richard Haberman, "Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow", 1998)

Isaac Asimov - Collected Quotes

"Old men tend to forget what thought was like in their youth; they forget the quickness of the mental jump, the daring of the youthful intuition, the agility of the fresh insight. They become accustomed to the more plodding varieties of reason, and because this is more than made up by the accumulation of experience, old men think themselves wiser than the young." (Isaac Asimov, "Pebble in the Sky", 1950)

"Words are a pretty fuzzy substitute for mathematical equations." (Isaac Asimov, "Foundation and Empire", 1952)

"[…] infinity is not a large number or any kind of number at all; at least of the sort we think of when we say 'number'. It certainly isn't the largest number that could exist, for there isn't any such thing." (Isaac Asimov, "Asimov on Numbers", 1959)

"Scientific theories have a tendency to fit the intellectual fashions of the time." (Isaac Asimov, "The Weighting Game", 1962)

"The mysteries of the universe and the questions that scientists strive to answer never come to an end. For that we should be grateful. A universe in which their were no mysteries for curious men to ponder would be a very dull universe indeed."(Isaac Asimov, "The Search for the Elements", 1962) 

"[...] the orchard of science is a vast globe-encircling monster, without a map, and known to no one man; indeed, to no group of men fewer than the whole international mass of creative scientists. Within it, each observer clings to his own well-known and well-loved clump of trees. If he looks beyond, it is usually with a guilty sigh." (Isaac Asimov, "View from a Height", 1963)

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

"[…] it took men about five thousand years, counting from the beginning of number symbols, to think of a symbol for nothing." (Isaac Asimov, "Of Time and Space and Other Things", 1965)

"If it is exciting to probe the unknown and shed light on what was dark before, then more and more excitement surely lies ahead of us." (Isaac Asimov, "The Universe: From Flat Earth to Quasar", 1966)

"The easiest way to solve a problem is to deny it exists." (Isaac Asimov, "The Gods Themselves", 1972)

"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)

"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) 

"Self-education is, I firmly believe, the only kind of education there is. The only function of a school is to make self-education easier; failing that, it does nothing." (Isaac Asimov, "Science Past, Science Future", 1975)

"If entropy must constantly and continuously increase, then the universe is remorselessly running down, thus setting a limit (a long one, to be sure) on the existence of humanity. To some human beings, this ultimate end poses itself almost as a threat to their personal immortality, or as a denial of the omnipotence of God. There is, therefore, a strong emotional urge to deny that entropy must increase." (Isaac Asimov," Asimov on Physics", 1976) 

"People are entirely too disbelieving of coincidence. They are far too ready to dismiss it and to build arcane structures of extremely rickety substance in order to avoid it. I, on the other hand, see coincidence everywhere as an inevitable consequence of the laws of probability, according to which having no unusual coincidence is far more unusual than any coincidence could possibly be." (Isaac Asimov, "The Planet That Wasn't", 1976) 

"The force of gravity-though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate-is by far the weakest known force in nature. It is first and rearmost." (Isaac Asimov, 1976)

"It is one thing to be able to make predictions. It is another to listen to the predictions you have made and to act upon them." (Isaac Asimov, "The Road to Infinity", 1979)

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

"If arithmetical skill is the measure of intelligence, then computers have been more intelligent than all human beings all along. If the ability to play chess is the measure, then there are computers now in existence that are more intelligent than any but a very few human beings. However, if insight, intuition, creativity, the ability to view a problem as a whole and guess the answer by the 'feel' of the situation, is a measure of intelligence, computers are very unintelligent indeed. Nor can we see right now how this deficiency in computers can be easily remedied, since human beings cannot program a computer to be intuitive or creative for the very good reason that we do not know what we ourselves do when we exercise these qualities." (Isaac Asimov, "Machines that Think", 1983)

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

"Science does not promise absolute truth, nor does it consider that such a thing necessarily exists. Science does not even promise that everything in the Universe is amenable to the scientific process."(Isaac Asimov, "'X' Stands for Unknown", 1984)

"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)

"The process of science [...] involves a slow forward movement through the reachable portions of the Universe - a gradual unfolding of parts of the mystery." (Isaac Asimov, "'X' Stands for Unknown", 1984)

"Human beings are very conservative in some ways and virtually never change numerical conventions once they grow used to them. They even come to mistake them for laws of nature." (Isaac Asimov, "Foundation and Earth", 1986)

"A hypothesis may be simply defined as a guess. A scientific hypothesis is an intelligent guess." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"A scientist is as weak and human as any man, but the pursuit of science may ennoble him even against his will."  (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Any increase in knowledge anywhere helps pave the way for an increase in knowledge everywhere." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Anyone who writes about science must know about science, which cuts down competition considerably." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Computers are better than we are at arithmetic, not because computers are so good at it, but because we are so bad at it."  (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Experimentation is the least arrogant method of gaining knowledge. The experimenter humbly asks a question of nature." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Facts are a heap of bricks and timber. It is only a successful theory that can convert the heap into a stately mansion." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"In mathematics, we say 'suppose' all the time and see if we can end up with something patently untrue or self-contradictory [...]" (Isaac Asimov, "Prelude to Foundation" 1988)

"It is hard to describe the exact route to scientific achievement, but a good scientist doesn't get lost as he travels it." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Physics is the basic science. One can easily argue that all other sciences are specialized aspects of physics." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Religion cannot object to science on moral grounds. The history of religious intolerance forbids it." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Religion considers the Universe deterministic and science considers it probabilistic - an important distinction." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Science can amuse and fascinate us all, but it is engineering that changes the world." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Science in the service of humanity is technology, but lack of wisdom may make the service harmful." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Science must be taught well, if a student is to understand the coming decades he must live through." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Scientific apparatus offers a window to knowledge, but as they grow more elaborate, scientists spend ever more time washing the windows." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"The law of conservation of energy tells us we can't get something for nothing, but we refuse to believe it." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"There is an art to science, and science in art; the two are not enemies, but different aspects of the whole." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"There is very little flexibility in the behavior of the Universe. What it does once, it does again." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"What makes it so hard to organize the environment sensibly is that everything we touch is hooked up to everything else." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"Theories are not so much wrong as incomplete." (Isaac Asimov, "The Relativity of Wrong", 1988)

"Scientific theories can always be improved and are improved. That is one of the glories of science. It is the authoritarian view of the Universe that is frozen in stone and cannot be changed, so that once it is wrong, it is wrong forever." (Isaac Asimov, "The Nearest Star", 1989)

"I believe that scientific knowledge has fractal properties; that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe." (Isaac Asimov, "Essay 400: A Way of Thinking, "The Magazine of Fantasy and Science Fiction", 1994)

"Science with all its faults has brought education and the arts to more people - a larger percentage - than has ever existed before science. In that respect it is science that is the great humanizer. And, if we are going to solve the problems that science has brought us, it will be done by science and in no other way." (Isaac Asimov, "Essay 400: A Way of Thinking, "The Magazine of Fantasy and Science Fiction", 1994)

"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)

"Once we learn to expect theories to collapse and to be supplanted by more useful generalizations, the collapsing theory becomes not the gray remnant of a broken today, but the herald of a new and brighter tomorrow." (Isaac Asimov)

On Equations: On Unknowns I

"Equations are the mathematician's way of working out the value of some unknown quantity from circumstantial evidence. ‘Here are some known facts about an unknown number: deduce the number.’ An equation, then, is a kind of puzzle, centered upon a number. We are not told what this number is, but we are told something useful about it. Our task is to solve the puzzle by finding the unknown number." (Ian Stewart, “Why Beauty Is Truth”, 2007)

“No equation, however impressive and complex, can arrive at the truth if the initial assumptions are incorrect.” (Arthur C Clarke, “Profiles of the Future”, 1973)

”It is sometimes said that the great discovery of the nineteenth century was that the equations of nature were linear, and the great discovery of the twentieth century is that they are not.” (Thomas W Körner, “Fourier Analysis”, 1988)

”Without the clear understanding that equations in physical science always have hidden limitations, we cannot expect to interpret or apply them successfully.” (Duane H D Roller, “Foundations of Modern Physical Science”, 1950)

“Being able to solve mathematical equations is useless if you don’t understand what the equation represents in real life.” (Robert S Root-Bernstein, “Discovering”, 1989)

"It often happens that understanding of the mathematical nature of an equation is impossible without a detailed understanding of its solution." (Freeman J Dyson)

“It is important to remember that the physical interpretation of the mathematical notions occurring in a physical theory must be compatible with the equations of the theory.” (Andrzej Trautman)

“I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.” (Paul A M Dirac)

“It would seem that more than function itself, simplicity is the deciding factor in the aesthetic equation. One might call the process beauty through function and simplification.” (Raymond Loewy)