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

"The mathematicians and physics men have their mythology; they work alongside the truth, never touching it; their equations are false But the things work. Or, when gross error appears, they invent new ones; they drop the theory of waves In universal ether and imagine curved space." (Robinson Jeffers, "The Beginning and the End and Other Poems, The Great Wound", 1963

"Their minds sang with the ecstatic knowledge that either what they were doing was completely and utterly and totally impossible or that physics had a lot of catching up to do." (Douglas Adams, "So Long, and Thanks for All the Fish", 1985)

"All reality is a game. Physics at its most fundamental, the very fabric of our universe, results directly from the interaction of certain fairly simple rules, and chance; the same description may be applied to the best, most elegant and both intellectually and aesthetically satisfying games. By being unknowable, by resulting from events which, at the sub-atomic level, cannot be fully predicted, the future remains malleable, and retains the possibility of change, the hope of coming to prevail; victory, to use an unfashionable word. In this, the future is a game; time is one of its rules." (Iain Banks, "The Player of Games", 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)

"It does highlight the irony that everything you go to see is changed by the very action of going to see it, which is the sort of problem which physicists have been wrestling with for most of this century." (Douglas Adams, "Last Chance to See", 1990)

"Almost every credible physicist will tell you there’s nothing in physics that says time travel can’t happen [...]" (Peter Clines, "The End of the Experiment", [in J W Schnarrv (ed), "Timelines"] 2010)

"Physics admits of a lovely unification, not just at the level of fundamental forces, but when considering its extent and implications. Classifications like "optics" or "thermodynamics" are just straitjackets, preventing physicists from seeing countless intersections." (Ted Chiang, "Arrival: Film tie-in", 2016)

"'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 Literature: About Mathematicians (From Fiction to Science-Fiction)

"The mathematicians and physics men have their mythology; they work alongside the truth, never touching it; their equations are false But the things work. Or, when gross error appears, they invent new ones; they drop the theory of waves In universal ether and imagine curved space." (Robinson Jeffers, "The Beginning and the End and Other Poems, The Great Wound", 1963)

"The natural world is full of irregularity and random alteration, but in the antiseptic, dust-free, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please". (William A M Boyd, "Brazzaville Beach", 1990)

"History too has an inertia. In the four dimensions of spacetime, particles (or events) have directionality; mathematicians, trying to show this, draw what they call 'world lines' on graphs. In human affairs, individual world lines form a thick tangle, curling out of the darkness of prehistory and stretching through time: a cable the size of Earth itself, spiraling round the sun on a long curved course. That cable of tangled world lines is history. Seeing where it has been, it is clear where it is going - it is a matter of simple extrapolation." (Kim S Robinson, "Red Mars", 1992)

"People reach their peak ability as military commanders much earlier than we thought. Most of them in their late teens. The same age when poets do their most passionate and revolutionary work. And mathematicians. They peak, and then it falls off. They coast on what they learned back when they were still young enough to learn." (Orson Scott Card, "First Meetings in Ender's Universe", 2002)

"How do you know you shouldnt? The core question is not how you do math but how does the unconscious do it. How is it that it’s demonstrably better at it than you are? You work on a problem and then you put it away for a while. But it doesnt go away. It reappears at lunch. Or while you’re taking a shower. It says: Take a look at this. What do you think? Then you wonderwhy the shower is cold. Or the soup. Is this doing math? I’m afraid it is. How is it doing it? We dont know. I’ve posed the question to some pretty good mathematicians. How does the unconscious do math? Some who’d thought about it and some who hadnt. For the most part they seemed to think it unlikely that the unconscious went about it the same way we did. What was surprising to me was the insouciance with which they greeted this news. As if the very nature of mathematics had not just been hauled into the dock. A few thought that if it had a better way of doing mathematics it ought to tell us about it. Well, maybe. Or maybe it thinks we’re not smart enough to understand it." (Cormac McCarthy, "Stella Maris", 2022)

Brian W Aldiss - Collected Quotes

"If a machine had broken down, it would have been quickly replaced. But who can replace a man?" (Brian W Aldiss, "Who Can Replace a Man?", 1958)

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

"What was that epigram that he had trotted forth too often, about civilization being the distance man placed between himself and his excreta? But it was nearer the truth to say that civilization was the distance man had placed between himself and everything else." (Brian W Aldiss, "The Dark Light Years", 1964)

"The waking brain is perpetually lapped by the unconscious." (Brian W Aldiss, "Man in His Time", 1966)

"Science fiction is the search for a definition of man and his status in the universe which will stand in our advanced but confused state of knowledge (science), and is characteristically cast in the Gothic or post-Gothic mould." (Brian W Aldiss, "Billion Year Spree: The True History of Science Fiction", 1973)

"Over most of the universe, God was spread in fossil radiation, too old, too thin." (Brian W. Aldiss, "Non-Isotropic", 1978)

"We take foul medicines to improve our health; so we must entertain foul thoughts on occasion, to strengthen wisdom." (Brian W Aldiss, "The Small Stones of Tu Fu", 1978)

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

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

"A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history." (Lev N Tolstoy, "War and Peace", 1867)

"Arriving at infinitesimals, mathematics, the most exact of sciences, abandons the process of analysis and enters on the new process of the integration of unknown, infinitely small, quantities." (Lev N Tolstoy, "War and Peace", 1867)

"What logarithms are to mathematics that mathematics are to the other sciences." (Friederich von Hardenberg [Novalis], "Schriften", 1901)

"The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write." (Herbert G Wells, "Mankind in the Making", 1903)

"The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language." (Herbert G Wells, "Mankind in the Making", 1903)

"The demonstration must be against learning-science. But not every science will do. The attack must have all the shocking senselessness of gratuitous blasphemy. Since bombs are your means of expression, it would be really telling if one could throw a bomb into pure mathematics. But that is impossible... What do you think of having a go at Astronomy?" (Joseph Conrad, "The Secret Agent: A Simple Tale", 1907) 

"The function of man’s highest faculty, his reason, consists precisely of the continuous limitation of infinity, the breaking up of infinity into convenient, easily digestible portions - differentials. This is precisely what lends my field, mathematics, its divine beauty." (Yevgeny Zamiatin, "We", 1924)

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

*He was well on the way to inventing differential calculus when his mother called him down to breakfast." (Poul Anderson, "Brain Wave", 1954)

"First his math interest seemed to evaporate after the special calculus course, although he never blew an exam. Then he switched to the pre-college anthropology panel the school was trying. Here he made good grades and acted very motivated, until the semester when the visiting research team began pounding on sampling techniques and statistical significance. Hobie had no trouble with things like Chi square, of course. But after making his A in the final he gave them his sweet, unbelieving smile and faded." (James Tiptree Jr, "Beam Uds Home", 1969)

"If everything, everything were known, statistical estimates would be unnecessary. The science of probability gives mathematical expression to our ignorance, not to our wisdom." (Samuel R Delany, "Time Considered as a Helix of Semi-Precious Stones", 1969)

"The temporal engineers shrugged, and so did the mathematicians. They told her that paradoxes were accumulating elsewhere in the society by that time, too, even though only a few supra-legal heavy persons owned jumpers. Alternate time-tracks, perhaps? Time-independent hysteresis maybe? Paradoxes of course were wrong. They shouldn’t happen." (James Tiptree Jr, "Forever to a Hudson Bay Blanket", Fantastic, 1972)

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house." (Robert A Heinlein, "Time Enough for Love", 1973)

"Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm." (Douglas N Adams, "Life, the Universe and Everything", 1982)

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts. [...] A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data." (William Gibson, "Neuromancer", 1984)

"In every language, from Arabic to Zulu to calligraphy to shorthand to math to music to art to wrought stone, everything from the Unified Field Theory to a curse to a sixpenny nail to an orbiting satellite, anything expressed is a net around some idea." (Richard Bach, "One", 1988)

"If we envision the entire System of Mathematics as a great Engine for proving theorems, then we must say, through the agency of the Modus, that such an Engine lives, and could indeed prove its own life, should it develop the capacity to look upon itself." (William Gibson & Bruce Sterling, "The Difference Engine", 1991)

"How do you know you shouldnt? The core question is not how you do math but how does the unconscious do it. How is it that it’s demonstrably better at it than you are? You work on a problem and then you put it away for a while. But it doesnt go away. It reappears at lunch. Or while you’re taking a shower. It says: Take a look at this. What do you think? Then you wonderwhy the shower is cold. Or the soup. Is this doing math? I’m afraid it is. How is it doing it? We dont know. I’ve posed the question to some pretty good mathematicians. How does the unconscious do math? Some who’d thought about it and some who hadnt. For the most part they seemed to think it unlikely that the unconscious went about it the same way we did. What was surprising to me was the insouciance with which they greeted this news. As if the very nature of mathematics had not just been hauled into the dock. A few thought that if it had a better way of doing mathematics it ought to tell us about it. Well, maybe. Or maybe it thinks we’re not smart enough to understand it." (Cormac McCarthy, "Stella Maris", 2022)

"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)

"If mathematical objects exist independently of human thought what else are they independent of? The universe, I suppose." (Cormac McCarthy, "Stella Maris", 2022)

"You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions." (Herbert G Wells)

George Zebrowski - Collected Quotes

"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)

"Apocalypse is the eye of a needle, through which we pass into a different world." (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"Part of human life is the need to reassure ourselves about the future that we may never live to see, rather than fool ourselves, as many did in the last century, that there won’t be any future and they might as well lie down and die." (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"Picture this: a mobile space colony, supporting more than a million people. No, not a colony, but an organism which can move and grow as long as it can obtain resources and maintain a food supply within its ecology. It’s a living organism because it can respond to stimuli through its optical and sensory nervous system. It thinks with the intellects of its human and cybernetic intelligences. And it can reproduce, which is what we expect from a living organism." (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"Progress is a tension between the notion of perfection and the notion that striving, not finding, is important." (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"She reached out across the cathedral of space-time to those hopelessly distant candle-furnaces, where all the material elements had been forged again and again inside the generation of suns, where alien sunspaces were certain to contain other humanities, however different, and she wondered if someone there might be her friend." (George Zebrowski, "Macrolife: A Mobile Utopia", 1979)

"In a perfectly rational universe, infinities turn back on themselves [...]" (George Zebrowski, "Is Science Rational?", OMNI Magazine, 1994)

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

"Time is a relationship that we have with the rest of the universe; or more accurately, we are one of the clocks, measuring one kind of time." (George Zebrowski, OMNI Magazine, 1994)

"Science, when it runs up against infinities, seeks to eliminate them, because a proliferation of entities is the enemy of explanation." (George Zebrowski, "Time Is Nothing But A Clock" , OMNI Magazine Vol. 17 (1), 1994)

On Literature: On Time Travel (From Fiction to Science-Fiction)

"At that I understood. At the risk of disappointing Richardson I stayed on, waiting for The Time Traveler; waiting for the second, perhaps still stranger story, and the specimens and photographs he would bring with him. But I am beginning now to fear that I must wait a lifetime. The Time Traveler vanished three years ago. And, as everybody knows now, he has never returned." (Herbert G Wells, "The Time Machine: An Invention", 1895)

"'Upon that machine',said the Time Traveller, holding the lamp aloft, 'I intend to explore time'." (Herbert G Wells, "The Time Machine: An Invention", 1895)

"If you don’t stop this senseless theorizing upon something that’s an obvious impossibility, you’ll find yourself working alone! Your ridiculous ideas sound like the ravings of a madman. Anyone with average intelligence realizes that the mere thought of traveling through time is absurd." (L Arthur Eshbach, "Out of the Past", Tales of Wonder, 1938)

'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) 

"To my way of thinking it is precisely because time travel involves such fascinating paradoxes that we can conclude, even in the absence of other evidence, that time travel is impossible." (Isaac Asimov, 1954)

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

"A simple proof. If time travel is - or ever will be - possible, where are the time travelers? Every moment of history should be mobbed with them, so where are they?" (Peter Clines, "The End of the Experiment", [in J W Schnarrv (ed), "Timelines"] 2010)

"A whole new branch of science started. It’s called paradoxology. Paradoxologists study the implications of time travel. The main question they try to answer is what happened to the reality Saul Baron came from. Did it cease to exist or does it still exist parallel to this reality?" (Daliso Chaponda, "By His Sacrifice", [in J W Schnarrv (ed), "Timelines"] 2010)

"Almost every credible physicist will tell you there’s nothing in physics that says time travel can’t happen [...]" (Peter Clines, "The End of the Experiment", [in J W Schnarrv (ed), "Timelines"] 2010)

"Beneath the cylindrical brass shield was an emerald, nearly fifteen centimeters in length and precision-cut into an orthorhombic dipyramidal crystal. It was this shape, combined with the high-energy potentiality of this particular variant of beryl that made time travel possible. It had taken him ten years and most of his inheritance to find and modify the emerald." (Mark Onspaugh, "Time’s Cruel Geometry", [in J W Schnarrv (ed), "Timelines"] 2010)

"Project Boomerang was a time travel experiment, headed by Howard, which had achieved some great success. They had managed to travel only backwards in time and the traveling worked on a pre-existing displacement principle. What this meant, Howard explained, was that the traveler could only jump to a time and place where they had previously existed. The traveling version of the person would take the place in the world of the old version, with all the knowledge they had gained since that time kept intact. That is, until the boomerang effect kicked in and the traveler was pulled back to the present, whereupon the original version of the person would resume back in the past. [...] it was the first step towards full time travel, and a massive achievement. He also pointed out that the boomerang effect could be, effectively, switched off and travelers could remain in the past reliving their lives any way they wanted to." (Harper Hull," Perpetual Motion Blues", [in J W Schnarrv (ed), "Timelines"] 2010)

"Time travel’s possible, but it’s only possible in that air-turning-into-gold way." (Peter Clines, "The End of the Experiment", [in J W Schnarrv (ed), "Timelines"] 2010)

"Time travel was quite notable in its own right, and as the world turned one way, opinions turned the other." (Jacob Edwards, "Professor Figwort Comes to an Understanding", [in J W Schnarrv (ed), "Timelines"] 2010)

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

"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." (Robert A Heinlein, "Time Enough for Love", 1973)

"Don’t dismiss the computer as a new type of fetters. Think of it rationally, as the most liberating device ever invented, the only tool capable of serving the multifarious needs of modern man." (John Brunner, "The Shockwave Rider", 1975)

"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)

"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)

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts. [...] A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data." (William Gibson, "Neuromancer", 1984)

"In cyberspace, she noted, there are no shadows." (William Gibson, "Mona Lisa Overdrive", 1988)

"Donna can feel computers dreaming, or so she says. She collects the dreams of machines, or so she thinks. The dreams of people are in the machines, a planet network of active imaginations hooked into their made-up, makebelieve worlds. Artificial reality is taking over; it has its own children. Donna feels the dreams of people. There are others like her. She is not unique." (Storm Constantine, ‘‘Immaculate’’ (1991)

"Computers bootstrap their own offspring, grow so wise and incomprehensible that their communiqués assume the hallmarks of dementia: unfocused and irrelevant to the barely-intelligent creatures left behind. And when your surpassing creations find the answers you asked for, you can't understand their analysis and you can't verify their answers. You have to take their word on faith." (Peter Watts, "Blindsight", 2006)

Clifford D Simak - Collected Quotes

"The chain of life runs smoothly from one generation to the next and none of the links stand out except here and there a link one sees by accident." (Clifford D Simak, "Time and Again", 1951)

"To cover up actual lack of knowledge, the tale develops an explanation which amounts to divine intervention. It is an easy and, to the primitive mind, a plausible and satisfactory way to explain something of which nothing at all is known." (Clifford D Simak, "City", 1952)

"We thought all the time that we were passing through time when we really weren’t, when we never have. We’ve just been moving along with time. We said, there’s another second gone, there’s another minute and another hour and another day, when, as a matter of fact the second or the minute or the hour was never gone. It was the same one all the time. It had just moved along and we had moved with it." (Clifford D Simak, "City", 1952)

"And time itself? Time was a never-ending medium that stretched into the future and the past - except there was no future and no past, but an infinite number of brackets, extending either way, each bracket enclosing its single phase of the Universe." (Clifford D Simak,"Ring Around the Sun", 1954)

"Once again the universe was spread far out before him and it was a different and in some ways a better universe, a more diagrammatic universe, and in time, he knew, if there were such a thing as time, he'd gain some completer understanding and acceptance of it." (Clifford D Simak, "All the Traps of Earth", 1960)

"It was a place without a single feature of the space-time matrix that he knew. It was a place where nothing yet had happened - an utter emptiness. There was neither light nor dark: there was nothing here but emptiness. There had never been anything in this place, nor was anything ever intended to occupy this place [...]" (Clifford D Simak, "Time is the Simplest Thing", 1961)

"There was so much knowledge in the galaxy and he knew so little of it, understood so little of the little that he knew. [...] Out among the stars lay a massive body of knowledge, some of it an extension of what mankind knew, some of it concerning matters which Man had not yet suspected, and used in ways and for purposes that Man had not as yet imagined. And never might imagine, if left on his own." (Clifford D Simak, "Way Station", 1963)

"It's not the machine itself that does the trick. The machine merely acts as an intermediary between the sensitive and the spiritual force. It is an extension of the sensitive. It magnifies the capability of the sensitive and acts as a link of some sort. It enables the sensitive to perform his function." (Clifford D Simak, "Way Station", 1963)

"There was a comfort in the thought, a strange sort of personal comfort in being able to believe that some intelligence might have solved the riddle of that mysterious equation of the universe. And how, perhaps, that mysterious equation might tie in with the spiritual force that was idealistic brother to time and space and all those other elemental factors that held the universe together." (Clifford D Simak, "Way Station", 1963)

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

"These kind never change. The machine does something to a man. It brutalizes him. It serves as a buffer between himself and his environment and he is the worst for it. It arouses an opportunistic instinct and makes possible a greed that makes a man inhuman." (Clifford D Simak, "A Choice of Gods", 1972)

"If mankind were to continue in other than the present barbarism, a new path must be found, a new civilization based on some other method than technology. Space is an illusion, and time as well. There is no such factor as either time or space. We have been blinded by our own cleverness, blinded by false perceptions of those qualities that we term eternity and infinity. There is another factor that explains it all, and once this universal factor is recognized, everything grows simple. There is no longer any mystery, no longer any wonder, no longer any doubt; for the simplicity of it all lies before us [...]" (Clifford D Simak,"A Heritage of Stars", 1977)

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

“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” (Sir Arthur C Doyle, “The Adventures of Sherlock Holmes”, 1892)

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

"In a way, science might be described as paranoid thinking applied to Nature: we are looking for natural conspiracies, for connections among apparently disparate data." (Carl Sagan, "The Dragons of Eden", 1977)

"Data in isolation are meaningless, a collection of numbers. Only in context of a theory do they assume significance […]" (George Greenstein, "Frozen Star", 1983)

"Intelligence takes chances with limited data in an arena where mistakes are not only possible but also necessary." (Frank Herbert, "Chapterhouse: Dune", 1985)

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts. [...] A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data." (William Gibson, "Neuromancer", 1984)

"Science demands a tolerance for ambiguity. Where we are ignorant, we withhold belief. Whatever annoyance the uncertainty engenders serves a higher purpose: It drives us to accumulate better data. This attitude is the difference between science and so much else. Science offers little in the way of cheap thrills. The standards of evidence are strict. But when followed they allow us to see far, illuminating even a great darkness." (Carl Sagan, "Pale Blue Dot: A Vision of the Human Future in Space", 1994)

"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)

Poul Anderson - Collected Quotes

*He was well on the way to inventing differential calculus when his mother called him down to breakfast." (Poul Anderson, "Brain Wave", 1954)

"No one person can change a whole culture." (Poul Anderson, "Ghetto", 1954)

"Memory is not a passive filing cabinet, but a continuous process beneath the level of consciousness; in a way, you are always reliving your entire past." (Poul Anderson, "Journeys End", 1957)

"Time is the bridge that always burns behind us." (Poul Anderson, "The Burning Bridge", 1960)

"We live with our archetypes, but can we live in them?" (Poul Anderson, "The Fatal Fulfillment", 1970

"Homo can truly be called sapiens when he practices his specialty of being unspecialized. His repeated attempts to freeze himself into an all-answering pattern or culture or ideology, or whatever he has named it, have repeatedly brought ruin. Give him the pragmatic business of making his living, and he will usually do rather well. He adapts, within broad limits." (Poul Anderson, "The Queen of Air and Darkness", 1971)

"The best foundation that a decision is ever allowed is our fallible assessment of the probabilities." (Poul Anderson, "The People of the Wind", 1973)

"The fact is that thresholds exist throughout reality, and that things on their far sides are altogether different from things on their hither sides." (Poul Anderson, "The Saturn Game", 1981)

"Absolute proof of absolute knowledge is impossible." (Poul Anderson, "The Boat of a Million Years" 1989)

"I don’t pretend to understand what the physicists mean by time, but for people, it isn’t so-and-so many measured units; it’s events, experiences. A man who crowds his life and dies young has lived longer than one who got old sitting in tame sameness." (Poul Anderson, "The Boat of a Million Years" 1989)

"Before the spirit could seek into it, the mind must. She studied the tensor equations as once she studied the sutras, she meditated upon the koans of science, and at last she began to feel her oneness with all that was, and in the vision find peace." (Poul Anderson, "The Boat of a Million Years" 1989)

On Category Theory (2000-)

"What was clearly useful was the use of diagrams to prove certain results either in algebraic topology, homological algebra or algebraic geometry. It is clear that doing category theory, or simply applying category theory, implies manipulating diagrams: constructing the relevant diagrams, chasing arrows by going via various paths in diagrams and showing they are equal, etc. This practice suggests that diagram manipulation, or more generally diagrams, constitutes the natural syntax of category theory and the category-theoretic way of thinking. Thus, if one could develop a formal language based on diagrams and diagrams manipulation, one would have a natural syntactical framework for category theory. However, moving from the informal language of categories which includes diagrams and diagrammatic manipulations to a formal language based on diagrams and diagrammatic manipulations is not entirely obvious." (Jean-Pierre Marquis, "From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory", 2009)

"Category theory has developed classically, beginning with definitions and axioms and proceeding to a long list of theorems. Category theory is not topology (and so will not be described here), but it can be used to understand some of the relationships that exist among classes of topological spaces. It can be used to bring unity to diversity. [...] the theory of categories is not complete, it may not be completable, but it is a step forward in understanding foundational questions in mathematics." (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)

"Category theory studies relationships between things and builds on this in various ways: characterising things by what properties they have, finding the pond in which things are the biggest fish, putting things in context, expressing subtle notions of things being ‘more or less the same’." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"In category theory there is always a tension between the idealism and the logistics. There are many structures that naturally want to have infinite dimensions, but that is too impractical, so we try and think about them in the context of just a finite number of dimensions and struggle with the consequences of making these logistics workable."(Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"This is how category theory arose, as a new piece of maths to study maths. In a way category theory is an ultimate abstraction. To study the world abstractly you use science; to study science abstractly you use maths; to study maths abstractly you use category theory. Each step is a further level of abstraction. But to study category theory abstractly you use category theory." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

On Category Theory (1975-1999)

"The point is simply that when explaining the general notion of structure and of particular kinds of structures such as groups, rings, categories, etc., we implicitly presume as understood the ideas of operation and collection." (Solomon Feferman, "Categorical foundations and foundations of category theory", 1975)

"A theory is a category with certain operations (defined up to isomorphism) [...] The notion of theory is thus 'intrinsic', i.e., independent of a particular presentation via formal languages and axiomatic systems. In this sense, categorical logic may be viewed as 'synthetic' or 'intrinsic' logic by opposition to the usual 'analytic', 'formal' logic." (André Joyal & Gonyalo E Reyes, "Forcing and generic models in categorical logic", 1977)

"But the question automatically arises as to exactly why, in introducing ordinary mathematical notions into the theory, one must make a detour through the somewhat opaque notion of discrete category. It is difficult to see how this can be explained except by appeal to the notion of 'unstructured' category, i.e. set." (John L Bell, "Category theory and the foundations of mathematics", The British Journal for the Philosophy of Science 32(4), 1981)

"But this seems to me highly dubious, for it is surely the case that the unstructured notion of class is epistemically prior to any more highly structured notion such as category: in order to understand what a category is, you first have to know what a class is." (John L Bell, "Category theory and the foundations of mathematics", The British Journal for the Philosophy of Science 32(4), 1981)

"[…] it would be technically possible to give a purely category-theoretic account of all mathematical notions expressible within axiomatic set theory, and so formally possible for category theory to serve as a foundation for mathematics insofar as axiomatic set theory does." (John L Bell, "Category theory and the foundations of mathematics", The British Journal for the Philosophy of Science 32(4), 1981)

"It is a remarkable empirical fact that mathematics can be based on set theory. More precisely, all mathematical objects can be coded as sets (in the cumulative hierarchy built by transfinitely iterating the power set operation, starting with the empty set). And all their crucial properties can be proved from the axioms of set theory. (. . . ) At first sight, category theory seems to be an exception to this general phenomenon. It deals with objects, like the categories of sets, of groups etc. that are as big as the whole universe of sets and that therefore do not admit any evident coding as sets. Furthermore, category theory involves constructions, like the functor category, that lead from these large categories to even larger ones. Thus, category theory is not just another field whose set-theoretic foundation can be left as an exercise. An interaction between category theory and set theory arises because there is a real question: What is the appropriate set-theoretic foundation for category theory?" (Andreas Blass, "The interaction between category theory and set theory", 1983)

"We consider forcing over categories as a way of constructing objects by geometric approximation, including a construction of a generic model of a geometric theory as its special case." (Andrej Scedrov, "Forcing and Classifying Topoi", Memoirs of the American Mathematical Society Vol. 48, 1984)

"Symmetries of a geometric object are traditionally described by its automorphism group, which often is an object of the same geometric class (a topological space, an algebraic variety, etc.). Of course, such symmetries are only a particular type of morphisms, so that Klein’s Erlanger program is, in principle, subsumed by the general categorical approach." (Yuri I Manin, "Topics in Noncommutative Geometry", 1991)

"[…] categorical logic is, to a great degree, autonomous, even in matters syntactical. ([203], 54.)" (Michael Makkai, "Generalized sketches as a framework for completeness theorems", Journal of Pure and Applied Algebra, 115(1), 1997)

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

"'Upon that machine',said the Time Traveller, holding the lamp aloft, 'I intend to explore time'." (Herbert G Wells, "The Time Machine: An Invention", 1895)

"The one reasonable goal of social life was affirmed to be the creation of a world of awakened, of sensitive, intelligent, and mutually understanding personalities, banded together for the common purpose of exploring the universe and developing the human spirit's manifold potentialities." (Olaf Stapledon, "Star Maker", 1937)

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

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

"Man has gone out to explore other worlds and other civilizations without having explored his own labyrinth of dark passages and secret chambers, and without finding what lies behind doorways that he himself has sealed." (Stanislaw Lem, "Solaris", 1961)

"The biggest developments of the immediate future will take place, not on the Moon or Mars, but on Earth, and it is inner space, not outer, that needs to be explored. The only truly alien planet is Earth." (James G Ballard, "Which Way to Inner Space?", 1962)

"Space... the final frontier. These are the voyages of the starship Enterprise. Its five-year mission: to explore strange, new worlds; to seek out new life, and new civilizations; to boldly go where no man has gone before." (] Gene Roddenberry, "Star Trek" (TV series), [opening narration] 1966)

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

"The exploration of alien worlds was just a monotonous and exhausting game." (Arkady Strugatsky & Boris Strugatsky, "Prisoners of Power", 1969)

"He enters pain’s cold regions as an explorer, an objective visitor. It is a country of ice and glass, monochromatic plains and valleys filled with washblue shards of ice, crystal pyramids and pinnacles, squares, oblongs, and all manner of polyhedron - block upon block of painted blue pain." (Jack Dann, "Camps", 1979)

"We’re all trying to fulfill ourselves, understand ourselves, get in touch with ourselves, face the reality of ourselves, explore ourselves, expand ourselves. Ever since we dispensed with God, we’ve got nothing but our selves to explain this meaningless horror of life." (Paddy Chayefsky, "Altered States", [film] 1980)

"If we knew exactly what to expect throughout the Solar System, we would have no reason to explore it." (Poul Anderson, "The Saturn Game, 1981)

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

"It was beyond him how someone could voluntarily let himself get involved in this game of dimension-shifting and mutant-battling. But it takes all sorts to make a continuum." (Robert Silverberg, "MUgwump 4" 1959)

"The exploration of alien worlds was just a monotonous and exhausting game." (Arkady Strugatsky & Boris Strugatsky, "Prisoners of Power", 1969)

"In a smoke-congested back room of the universe the God of my agnostic imagination oversees this crooked card game." (Robert Thurston, "Good-Bye, Shelley, Shirley, Charlotte, Charlene", 1972)

"The catastrophe story, whoever may tell it, represents a constructive and positive act by the imagination rather than a negative one, an attempt to confront the terrifying void of a patently meaningless universe by challenging it at its own game. [. . .] Each one of these fantasies represents an arraignment of the finite, an attempt to dismantle the formal structure of time and space which the universe wraps around us at the moment we first achieve consciousness." (James G Ballard, "Cataclysms and Dooms" 1977)

"Human brains back then had become such copious and irresponsible generators of suggestions as to what might be done with life, that they made acting for the benefit of future generations seem one of many arbitrary games which might be played by narrow enthusiasts - like poker or polo or the bond market, or the writing of science-fiction novels." (Kurt Vonnegut Jr, "Galapagos" 1985)

"All reality is a game. Physics at its most fundamental, the very fabric of our universe, results directly from the interaction of certain fairly simple rules, and chance; the same description may be applied to the best, most elegant and both intellectually and aesthetically satisfying games. By being unknowable, by resulting from events which, at the sub-atomic level, cannot be fully predicted, the future remains malleable, and retains the possibility of change, the hope of coming to prevail; victory, to use an unfashionable word. In this, the future is a game; time is one of its rules." (Iain Banks, "The Player of Games", 1988)

"The very first-rank games acknowledge the element of chance, even if they rightly restrict raw luck." (Iain Banks, "The Player of Games", 1988)

"To read fiction means to play a game by which we give sense to the immensity of things that happened, are happening, or will happen in the actual world. By reading narrative, we escape the anxiety that attacks us when we try to say something true about the world. This is the consoling function of narrative - the reason people tell stories, and have told stories from the beginning of time." (Umberto Eco, "Six Walks in the Fictional Woods", 1994)

"Programming is the Great Game. It consumes you, body and soul. When you're caught up in it, nothing else matters. When you emerge into daylight, you might well discover that you're a hundred pounds overweight, your underwear is older than the average first grader, and judging from the number of pizza boxes lying around, it must be spring already. But you don't care, because your program runs, and the code is fast and clever and tight. You won." (Orson Scott Card, "How Software Companies Die", Windows Sources: The Magazine for Windows Experts, 1995)

"The real training ground for leadership is in the game." (Orson Scott Card, "First Meetings in Ender's Universe", 2002)

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

"What will not be forgotten, and what will and should continue to obsess our imaginations, is this revelation of the possibilities of the universe, this destruction of our ignorant self-complacency, and this demonstration of how narrow is the path of our material existence, and what abysses may lie upon either side of it. Solemnity and humility are at the base of all our emotions to-day. May they be the foundations upon which a more earnest and reverent race may build a more worthy temple." (Arthur C Doyle, "The Poison Belt", 1913)

"Everything in human society is being continually perfected - and should be." (Yevgeny Zamiatin, "We", 1924)

"The function of man’s highest faculty, his reason, consists precisely of the continuous limitation of infinity, the breaking up of infinity into convenient, easily digestible portions - differentials. This is precisely what lends my field, mathematics, its divine beauty." (Yevgeny Zamiatin, "We", 1924)

"All stories, if continued far enough, end in death, and he is no true-story teller who would keep that from you. Especially do all stories of monogamy end in death, and your man who is monogamous while he often lives most happily, dies in the most lonely fashion." (Ernest Hemingway, "Death in the Afternoon", 1932)

"Memory is not a passive filing cabinet, but a continuous process beneath the level of consciousness; in a way, you are always reliving your entire past." (Poul Anderson, "Journeys End", 1957)

"It was beyond him how someone could voluntarily let himself get involved in this game of dimension-shifting and mutant-battling. But it takes all sorts to make a continuum." (Robert Silverberg, "MUgwump 4" 1959)

"No live organism can continue for long to exist sanely under conditions of absolute reality; even larks and katydids are supposed, by some, to dream." (Shirley Jackson, "The Haunting of Hill House", 1959)

"Change is what’s boring, monotonous. Sameness is a continual challenge, almost impossible to maintain. Repetition, knowing that you’ve done it right before and can do it right again, is satisfying." (Robert Thurston, "Good-Bye, Shelley, Shirley, Charlotte, Charlene", 1972) 

"Well it's a matter of continuity. Most people's lives have ups and downs that are gradual, a sinuous curve with first derivatives at every point. They're the ones who never get struck by lightning. No real idea of cataclysm at all. But the ones who do get hit experience a singular point. a discontinuity in the curve of life - do you know what the time rate of change is at a cusp? Infinity, that's what! A-and right across the point, it's minus infinity! How's that for sudden change, eh?" (Thomas Pynehon, Gravity's Rainbow, 1973)

"A continuity exists between inert matter, through the grand design of the early universe, and intelligent life today. Now accepted by all, this cosmic perspective may be seen as a culmination of all the ancient religions." (Gregory Benford, "Starswarmer", 1978)

"It is change, continuing change, inevitable change, that is the dominant factor in society today. No sensible decision can be made any longer without taking into account not only the world as it is, but the world as it will be - and naturally this means that there must be an accurate perception of the world as it will be. This, in turn, means that our statesmen, our businessmen, our everyman must take on a science fictional way of thinking, whether he likes it or not, or even whether he knows it or not. Only so can the deadly problems of today be solved." (Isaac Asimov, [foreword to Robert Holdstock (Ed.), "Encyclopedia of Science Fiction] 1978)

"The whole fabric of the space-time continuum is not merely curved, it is in fact totally bent." (Douglas N Adams, "The Restaurant at the End of the Universe", 1980)

"It was one of those nights, I quickly decided, when you slip into an alternate continuum, a city that looks exactly like the one where you live, except for the peculiar difference that it contains not one person you love or know or have even spoken to before." (William Gibson, "The Winter Market", 1985)

"The second law of thermodynamics!: energy is indestructible in quantity but continually changes in form. And it always runs down like water." (Ernesto Cardenal, "Cosmic Canticle", 1993)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

On Literature: On Prediction (From Fiction to Science Fiction)

"[…] anybody with a genuine system of prediction would be using it, not selling it." (Philip K Dick, "Solar Lottery", 1955) 

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

"You could not predict what would happen in a single instance, a single throw of the dice, a single pitch in the seventh inning, a single toss of the coin. But you could predict three out of five, four out of ten, seven out of sixteen, and to that extent chance governed everyone, all the time. Just as surely as two equals two." (Michael Crichton,"Odds On", 1966)

"When one culture has the big guns and the other has none, there is a certain predictability about the outcome." (Joanna Russ, ‘"When It Changed", 1972)

"All reality is a game. Physics at its most fundamental, the very fabric of our universe, results directly from the interaction of certain fairly simple rules, and chance; the same description may be applied to the best, most elegant and both intellectually and aesthetically satisfying games. By being unknowable, by resulting from events which, at the sub-atomic level, cannot be fully predicted, the future remains malleable, and retains the possibility of change, the hope of coming to prevail; victory, to use an unfashionable word. In this, the future is a game; time is one of its rules." (Iain Banks, "The Player of Games", 1988)

"Things rarely happen for a single reason. Even the cleverest and most skilled manipulators recognize that their real art lies in making use of that which they cannot predict." (Tom Clancy, "Debt of Honor", 1994)

"[...] you can’t stay committed to one pattern. It makes you too easy to predict." (Orson Scott Card, "First Meetings in Ender's Universe", 2002)

"Averages might mean something to bureaucrats and engineers, but the sea had no struck with statistics: it was a succession of unpredictable circumstances and extremes." (Frank Schätzing, "The Swarm", 2004)

On Systems (From Fiction to Science-Fiction)

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

"At the final stage you teach me that this wondrous and multicolored universe can be reduced to the atom and that the atom itself can be reduced to the electron. All this is good and I wait for you to continue. But you tell me of an invisible planetary system in which electrons gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know. Have I the time to become indignant? You have already changed theories. So that science that was to teach me everything ends up in a hypothesis, that lucidity founders in metaphor, that uncertainty is resolved in a work of art." (Albert Camus, "The Myth of Sisyphus", 1942)

"[…] anybody with a genuine system of prediction would be using it, not selling it." (Philip K Dick, "Solar Lottery", 1955)

 "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)

"A system has order, flowing from point to point. If something dams that flow, order collapses. The untrained might miss that collapse until it was too late. That's why the highest function of ecology is the understanding of consequences." (Frank Herbert, "Dune", 1965)

"Beyond a critical point within a finite space, freedom diminishes as numbers increase. This is as true of humans as it is of gas molecules in a sealed flask. The human question is not how many can possibly survive within the system, but what kind of existence is possible for those who do survive." (Frank Herbert, "Dune", 1965)

"Science offers a sounder basis on which to formulate systems of thought and ethics." (Michael Moorcock, "Behold the Man", 1967)

"Deception, in a system of this sort, can be defined simply as entropy [...] And of course, entropy, or degradation of order, is avoided by all civilized beings, since no local increase in complexity can offset entropic effects in the larger matrix." (James Tiptree Jr, "Faithful to Thee, Terra, in Our Fashion" ["Parimutuel Planet"], Galaxy, 1969)

"To the paranoid, nothing is a surprise; everything happens exactly as he expected, and sometimes even more so. It all fits into his system. For us, though, there can be no system; maybe all systems - that is, any theoretical, verbal, symbolic, semantic, etc. formulation that attempts to act as an all-encompassing, all-explaining hypothesis of what the universe is about - are manifestations of paranoia. We should be content with the mysterious, the meaningless, the contradictory, the hostile, and most of all the unexplainably warm and giving." (Philip K Dick, "The Android and the Human", [speech] 1972)

"Thought is a matrix which engenders its own reality. The ideas, concepts, belief-systems that your ancestors trapped have become your trap." (Alfred A Attanasio, "Radix", 1981)

"Dangers lurk in all systems. Systems incorporate the unexamined beliefs of their creators. Adopt a system, accept its beliefs, and you help strengthen the resistance to change." (Frank Herbert, "God Emperor of Dune", 1984)

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

"The system of life on this planet is so astoundingly complex that it was a long time before man even realized that it was a system at all and that it wasn't something that was just there." (Douglas N Adams, "Last Chance to See", 1990)

"It is a concatenation of synergistic interactions; the whole system is on the period-doubling route to Chaos! [...] in layman’s terms, it means that everything gets twice as bad, twice as fast, until everything falls completely apart!" (William Gibson & Bruce Sterling, "The Difference Engine", 1991)

"Any information system of sufficient complexity will inevitably become infected with viruses - viruses generated from within itself." (Neal Stephenson, "Snow Crash", 1992)

"The thing the ecologically illiterate don't realize about an ecosystem is that it's a system. A system! A system maintains a certain fluid stability that can be destroyed by a misstep in just one niche." (Frank Herbert, "Dune: House Atreides", 1999)

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

"We naturally associate democracy, to be sure, with freedom of action, but freedom of action without freed capacity of thought behind it is only chaos." (John Dewey, "Democracy in Education", The Elementary School Teacher, 1903)

"Too little liberty brings stagnation, and too much brings chaos." (Bertrand Russell, "Authority and the Individual", 1949)

"We had our atomic wars - thousands of years ago. After that we fought with bows and arrows. Then, slowly, we learned that fighting is no solution - that aggression leads to chaos." (Edmund H North, "The Day the Earth Stood Still" [film script] 1951)

"He jaunted up the geodesic lines of space-time to an Elsewhere and an Elsewhen. He arrived in chaos. He hung in a precarious para-Now for a moment and then tumbled back into chaos." (Alfred Bester, "The Stars My Destination", 1956)

"In a chaotic universe, who expects justice?" (Raylyn Moore, "Trigononomy", 1973)

"It is a concatenation of synergistic interactions; the whole system is on the period-doubling route to Chaos! [...] in layman’s terms, it means that everything gets twice as bad, twice as fast, until everything falls completely apart!" (William Gibson & Bruce Sterling, "The Difference Engine", 1991)

"Storms of Cataclysm lashed the Cretaceous earth, vast fires raged, and cometary grit sifted through the roiling atmosphere, to blight and kill the wilting foliage, till the mighty Dinosauria, adapted to a world now shattered, fell in massed extinction, and the leaping machineries of Evolution were loosed in chaos, to re-populate the stricken Earth with strange new orders of being." (William Gibson & Bruce Sterling, "The Difference Engine", 1991)

"Chaos is found in greatest abundance wherever order is being sought. It always defeats order, because it is better organized." (Terry Pratchett, "Interesting Times", 1995)

"An elven trait, to believe that that government governs best which doesn’t govern at all. Chaos is more fun. Anarchy is the ideal." (Glen Cook, "Angry Lead Skies" 2002)

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

"The simplicity of nature is not that which may easily be read, but is inexhaustible. The last analysis can no wise be made." (Ralph W Emerson, "Essays, First Series", 1841)

"It requires a very unusual mind to undertake the analysis of the obvious." (Alfred N Whitehead,"Science in the Modern World", 1925)

"The double analysis kills the single analysis, and the treble kills the double, until at last a sufficiency of statistics comes very near to common sense." (Hilaire Belloc," The Silence of the Sea", 1940) 

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

"The evil are always foolish in the final analysis." (Gene Wolfe, "The Island of Doctor Death and Other Stories", 1970)

"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." (Robert A Heinlein, "Time Enough for Love", 1973)

"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 complexities of cause and effect defy analysis." (Douglas Adams, "Dirk Gently's Holistic Detective Agency", 1987)

"Computers bootstrap their own offspring, grow so wise and incomprehensible that their communiqués assume the hallmarks of dementia: unfocused and irrelevant to the barely-intelligent creatures left behind. And when your surpassing creations find the answers you asked for, you can't understand their analysis and you can't verify their answers. You have to take their word on faith." (Peter Watts, "Blindsight", 2006)

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

"The limit of man's knowledge in any subject possesses a high interest which is perhaps increased by its close neighbourhood to the realms of imagination." (Charles Darwin, "Journal of Researches Into the Geology and Natural History of the Various Countries Visited by H.M.S. Beagle: Under the Command of Captain FitzRoy, R. N., from 1832-6", 1836) 

"There is a fifth dimension beyond that which is known to Man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man’s fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call ... The Twilight Zone." (Rod Serling, "The Twilight Zone" [TV series] 1959)

"You’re traveling through another dimension, a dimension not only of sight and sound but of mind; a journey into a wondrous land whose boundaries are that of imagination. That’s the signpost up ahead - your next stop, The Twilight Zone." (Rod Serling, "The Twilight Zone", [opening narration] 1961)

"That perfected machines may one day succeed us is, I remember, an extremely commonplace notion on Earth. It prevails not only among poets and romantics but in all classes of society. Perhaps it is because it is so widespread, born spontaneously in popular imagination, that it irritates scientific minds. Perhaps it is also for this very reason that it contains a germ of truth. Only a germ: Machines will always be machines; the most perfected robot, always a robot." (Pierre Boulle, "Planet of the Apes", 1963)

"You unlock this door with the key of imagination. Beyond it is another dimension. A dimension of sound. A dimension of sight. A dimension of mind. You’re moving into a land of both shadow and substance, of things and ideas. You’ve just crossed over into The Twilight Zone." (Rod Serling, "The Twilight Zone", [opening narration] 1963)

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

"The simple truth is that interstellar distances will not fit into the human imagination." (Douglas N Adams, "The Hitchhiker's Guide to the Galaxy", 1979)

"The dreams of people are in the machines, a planet network of active imaginations hooked into their made-up, make-believe worlds. Artificial reality is taking over; it has its own children." (Storm Constantine, "Immaculate", 1991)

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

"The limit of man's knowledge in any subject possesses a high interest which is perhaps increased by its close neighbourhood to the realms of imagination." (Charles Darwin, "Journal of Researches Into the Geology and Natural History of the Various Countries Visited by H.M.S. Beagle: Under the Command of Captain FitzRoy, R. N., from 1832-6", 1836

"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)

"If the fresh facts which come to our knowledge all fit themselves into the scheme, then our hypothesis may gradually become a solution." (Arthur C Doyle, "The Adventure of Wisteria Lodge", 1908)

"Knowledge is the distilled essence of our intuitions, corroborated by experience." (Elbert Hubbard, "A Thousand & One Epigrams, 1911)

"As the traveller who has been once from home is wiser than he who has never left his own door step, so a knowledge of one other culture should sharpen our ability to scrutinise more steadily, to appreciate more lovingly, our own." (Margaret Mead, "Coming of Age in Samoa", 1928)

"A civilization is a heritage of beliefs, customs, and knowledge slowly accumulated in the course of centuries, elements difficult at times to justify by logic, but justifying themselves as paths when they lead somewhere, since they open up for man his inner distance." (Antoine de Saint-Exupéry, "Flight to Arras", 1942)

"Can any of us fix anything? No. None of us can do that. We're specialized. Each one of us has his own line, his own work. I understand my work, you understand yours. The tendency in evolution is toward greater and greater specialization. Man's society is an ecology that forces adaptation to it. Continued complexity makes it impossible for us to know anything outside our own personal field - I can't follow the work of the man sitting at the next desk over from me. Too much knowledge has piled up in each field. And there are too many fields." (Philip K. Dick, The Variable Man", 1952)

"There is a fifth dimension beyond that which is known to Man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man’s fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call ... The Twilight Zone." (Rod Serling, "The Twilight Zone" [TV series] 1959)

"The meeting between ignorance and knowledge, between brutality and culture - it begins in the dignity with which we treat our dead." (Frank Herbert, "Dune", 1965)

"These dwarfs amass knowledge as others do treasure; for this reason they are called Hoarders of the Absolute. Their wisdom lies in the fact that they collect knowledge but never use it." (Stanislaw Lem, "How Erg the Self-Inducing Slew a Paleface", 1965)

"But you must not change one thing, one pebble, one grain of sand, until you know what good and evil will follow on that act. The world is in balance, in Equilibrium. […] It is dangerous, that power. [...] It must follow knowledge, and serve need." (Ursula K Le Guin, "A Wizard of Earthsea", 1968)

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

"Their minds sang with the ecstatic knowledge that either what they were doing was completely and utterly and totally impossible or that physics had a lot of catching up to do." (Douglas Adams, "So Long, and Thanks for All the Fish", 1985)

"What is all your studying worth, all your learning, all your knowledge, if it doesn't lead to wisdom? And what's wisdom but knowing what is right, and what is the right thing to do?" (Iain Banks, "Use of Weapons", 1990)

"All knowledge is local, all truth is partial. [...] No truth can make another truth untrue. All knowledge is part of the whole knowledge. A true line, a true color. Once you have seen the larger pattern, you cannot get back to seeing the part as the whole." (Ursula K Le Guin, "A Man of the People", 1995)

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

"A single thought is that which it is from other thoughts as a wave of the sea takes its form and shape from the waves which precede and follow it." (Samuel T Coleridge, "Letters", 1836)

"The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology." (Sir D’Arcy W Thompson, "On Growth and Form", 1951)

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

"God created two acts of folly. First, He created the Universe in a Big Bang. Second, He was negligent enough to leave behind evidence for this act, in the form of the microwave radiation." (Paul Erdős)

"Reality is a wave function traveling both backward and forward in time." (John L Casti)

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

"We know that there is an infinite, and we know not its nature. As we know it to be false that numbers are finite, it is therefore true that there is a numerical infinity. But we know not of what kind; it is untrue that it is even, untrue that it is odd; for the addition of a unit does not change its nature; yet it is a number, and every number is odd or even (this certainly holds of every finite number). Thus, we may quite well know that there is a God without knowing what He is." (Blaise Pascal, "Pensées", 1670)

"Sometimes the gods themselves forget the answers to their own riddles." (Edwin L. Arnold, "Lieut. Gullivar Jones: His Vacation", 1905)

"People believe in God because they’ve been conditioned to believe in God." (Aldous Huxley, "Brave New World", 1932)

"All perfection comes from within, and the perfection that is imposed from without is as frivolous and stupid as the trimmings on gingercake. The free man may be bad, but only the free man can be good. And all the kingdom and the power and the glory—call it of God, call it of Cosmos - must arise from the free will of man." (Anthony Boucher, "The Barrier", 1942)

"The gods do not speak the language of men, any more than men can speak the language of the gods." (Miriam Allen deFord, "The Apotheosis of Ki", 1956)

"Only the man who has had to face despair is really convinced that he needs mercy. Those who do not want mercy never seek it. It is better to find God on the threshold of despair than to risk our lives in a complacency that has never felt the need of forgiveness. A life that is without problems may literally be more hopeless than one that always verges on despair." (Thomas Merton, "No Man Is an Island", 1955)

"Man does not create gods, in spite of appearances. The times, the age, impose them on him." (Stanislaw Lem, "Solaris", 1961)

"If there are any gods whose chief concern is man, they cannot be very important gods." (Arthur C Clarke, "Rocket to the Renaissance", [revised version] 1962)

"To be an atheist is to maintain God." (Ursula K Le Guin, "The Left Hand of Darkness", 1969)

"I have seen God creating the cosmos, watching its growth, and finally destroying it." (Olaf Stapledon, "Nebula Maker", 1976)

"Man and the true God are identical—as the Logos and the true God are - but a lunatic blind creator and his screwed-up world separate man from God. That the blind creator sincerely imagines that he is the true God only reveals the extent of his occlusion." (Philip K Dick, "Valis", 1981)

"All the universe is just a dream in God's mind, and as long as he's asleep, he believes in it, and things stay real." (Orson Scott Card, "The Tales of Alvin Maker: Seventh Son", 1987)

"People needed to believe in gods, if only because it was so hard to believe in people." (Terry Pratchett, "Pyramids", 1989)

"God created two acts of folly. First, He created the Universe in a Big Bang. Second, He was negligent enough to leave behind evidence for this act, in the form of the microwave radiation." (Paul Erdős)

On Algebra: On Lie Algebra

"During the last decade the methods of algebraic topology have invaded extensively the domain of pure algebra, and initiated a number of internal revolutions. [...] The invasion of algebra has occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. The three subjects have been given independent but parallel developments." (Henri P Cartan & Samuel Eilenberg, "Homological Algebra", 1956)

"Algebraic deformation represents a method for the quantization of Lie groups and Lie algebras. Quantum groups are not groups, but Hopf algebras. [3]

"Lie groups describe finite symmetries or symmetries which smoothly depend on a finite number of real parameters. Lie algebras are the linearization of Lie groups at the unit element. The passage from Lie groups to Lie algebras simplifies considerably the approach. Lie algebras are frequently called infinitesimal symmetries." (Eberhard Zeidler, "Quantum Field Theory III: Gauge Theory", 2006)

"Representations of symmetries with the aid of linear operators (e.g., matrices) play a crucial role in modern physics. In particular, this concerns the linear representations of groups, Lie algebras, and quantum groups (Hopf algebras)" (Eberhard Zeidler, "Quantum Field Theory III: Gauge Theory", 2006)

"Solvable Lie algebras are close to both upper triangular matrices and commutative Lie algebras. In contrast to this, semisimple Lie algebras are as far as possible from being commutative. By Levi’s decomposition theorem, any Lie algebra is built out of a solvable and a semisimple one. The nontrivial prototype of a solvable Lie algebra is the Heisenberg algebra." (Eberhard Zeidler, "Quantum Field Theory III: Gauge Theory", 2006)

"The fundamental Levi decomposition of a Lie algebra is the prototype of a semidirect product of Lie algebras." (Eberhard Zeidler, "Quantum Field Theory III: Gauge Theory", 2006)

"There is a fundamental relationship between Lie groupoids and Lie algebroids which is similar to the relationship between Lie groups and Lie algebras. There are, however, significant differences in the conventions involved, and it important to be aware of these." (Mike Crampin & David Saunders, "Cartan Geometries and their Symmetries: A Lie Algebroid Approach", 2016)

On Edward Beltrami - Historical Perspectives

"Early mathematicians had no difficulty accepting the first four of Euclid’s axioms. But the fifth was thought not to be so obvious as the other four, and mathematicians tried into the 19th century to derive the fifth postulate from the first four. All such attempts were doomed to failure, but in making the effort, investigators developed a great deal of modern mathematics. It was finally discovered (in the 19th century by Bolyai, Gauss, Lobachevsky, Beltrami, and others) that the fifth postulate is in fact independent of the first four and that one gets a perfectly legitimate geometry by discarding Euclid’s parallel axiom and replacing it with a different one: 'The hyperbolic parallel axiom: Given a line l and a point P not on l, there are infinitely many lines through P that are parallel to l.'" (Bruce Crauder et al, "Functions and Change: A Modeling Approach to College Algebra and Trigonometry", 2008)

"At any rate, long before the curvature of space was first detected, Beltrami’s construction of the hyperbolic plane showed that more than one kind of geometry is possible. Beltrami assumed that Euclidean space exists, and constructed a non-Euclidean plane inside it, with nonstandard definitions of 'line' and 'distance' (namely, line segments in the unit disk and pseudodistance). This shows that the geometry of Bolyai and Lobachevsky is logically as valid as the geometry of Euclid: if there is a space in which 'lines' and 'distance' behave as Euclid thought they do, then there is also a surface in which 'lines' and 'distance' behave as Bolyai and Lobachevsky thought they might." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics" 2nd Ed., 2018)

"Beltrami started this train of thought in 1865, by asking which surfaces can be mapped onto the plane in such a way that their geodesics go to straight lines. He found that the answer is precisely the surfaces of constant Gaussian curvature. For example, great circles on the sphere can be mapped to lines on the plane, and the map that does the trick (to be precise, for the hemisphere) is central projection [...]. Rays from the center O to any great circle form a plane, which of course meets any other plane in a line. Thus projection from O to a plane sends great circles to lines, though only half of the sphere is mapped." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics" 2nd Ed., 2018)

"When real numbers are used as coordinates, the number of coordinates is the dimension of the geometry. This is why we call the plane two-dimensional and space three-dimensional. However, one can also expect complex numbers to be useful [...]. What is remarkable is that complex numbers are if anything more appropriate for spherical and hyperbolic geometry than for Euclidean geometry. With hindsight, it is even possible to see hyperbolic geometry in properties of complex numbers that were studied as early as 1800, long before hyperbolic geometry was discussed by anyone. This was noticed by the third great contributor to non-Euclidean geometry after Beltrami and Klein - the French mathematician Henri Poincaré [...]" (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics" 2nd Ed., 2018)

"[...] quaternions give a nice approach to symmetric objects in three-dimensional space: the regular polyhedra. But this leads in turn to the regular polytopes, a family of four-dimensional symmetrical objects as remarkable as the regular polyhedra. One then becomes convinced that four-dimensional space is not just a set of quadruples; it is a world of genuine geometry." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics" 2nd Ed., 2018)

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

"That is probable which for the most part usually comes to pass, or which is a part of the ordinary beliefs of mankind, or which contains in itself some resemblance to these qualities, whether such resemblance be true or false." (Marcus T Cicero, "De Inventione", cca. 86–84 BC)

"Take away probability, and you can no longer please the world; give probability, and you can no longer displease it." (Blaise Pascal, "Thoughts", 1670)

"Ignorance gives one a large range of probabilities." (George Eliot, "Daniel Deronda", 1876)

"When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." (Arthur C Doyle, "The Sign of Four", 1890

"Every probability - and most of our common, working beliefs are probabilities - is provided with buffers at both ends, which break the force of opposite opinions clashing against it […]" (Oliver W Holmes, "The Autocrat of the Breakfast-Table", 1891) 

"It is more than possible; it is probable." (Arthur C Doyle, "The Memoirs of Sherlock Holmes", 1893)

"If everything, everything were known, statistical estimates would be unnecessary. The science of probability gives mathematical expression to our ignorance, not to our wisdom." (Samuel R Delany, "Time Considered as a Helix of Semi-Precious Stones", 1969)

"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)

"In the real world irrational things happened, impossible coincidences happened, because probability required that coincidences rarely, but not never, occur." (Orson Scott Card, "Ender’s Game", 1985)

"One of the elementary rules of nature is that, in the absence of a law prohibiting an event or phenomenon, it is bound to occur with some degree of probability. To put it simply and crudely: Anything that can happen does happen." (Kenneth W Ford)

On Systems: On Paths

"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 recti-linear 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)

"It is not enough to know the critical stress, that is, the quantitative breaking point of a complex design; one should also know as much as possible of the qualitative geometry of its failure modes, because what will happen beyond the critical stress level can be very different from one case to the next, depending on just which path the buckling takes. And here catastrophe theory, joined with bifurcation theory, can be very helpful by indicating how new failure modes appear." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"The pinball machine is one of those rare dynamical systems whose chaotic nature we can deduce by pure qualitative reasoning, with fair confidence that we have not wandered astray. Nevertheless, the angles in the paths of the balls that are introduced whenever a ball strikes a pin and rebounds […] render the system some what inconvenient for detailed quantitative study." (Edward N Lorenz, "The Essence of Chaos", 1993)

"In a free-market economy, then, uncertainty is a necessary element. Only when the economy is in a state of uncertainty can the participants efficiently search for solutions to problems and find creative answers. In addition, only a system that depends on uncertainty can survive unexpected shocks. A complex process can take multiple paths to an optimal solution. It does not require 'ideal' conditions; in fact, shocks often force it to find a better solution, a higher hill in the fitness landscape. The 'creative destruction' identified by the Austrian school suggests that a free-market economy is not only resilient to shocks, but is also creative and capable of generating innovation. It can only do so while in a high state of uncertainty." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999)

"It is, however, fair to say that very few applications of swarm intelligence have been developed. One of the main reasons for this relative lack of success resides in the fact that swarm-intelligent systems are hard to 'program', because the paths to problem solving are not predefined but emergent in these systems and result from interactions among individuals and between individuals and their environment as much as from the behaviors of the individuals themselves. Therefore, using a swarm-intelligent system to solve a problem requires a thorough knowledge not only of what individual behaviors must be implemented but also of what interactions are needed to produce such or such global behavior." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)

"Complexity theory shows that great changes can emerge from small actions. Change involves a belief in the possible, even the 'impossible'. Moreover, social innovators don’t follow a linear pathway of change; there are ups and downs, roller-coaster rides along cascades of dynamic interactions, unexpected and unanticipated divergences, tipping points and critical mass momentum shifts. Indeed, things often get worse before they get better as systems change creates resistance to and pushback against the new. Traditional evaluation approaches are not well suited for such turbulence. Traditional evaluation aims to control and predict, to bring order to chaos. Developmental evaluation accepts such turbulence as the way the world of social innovation unfolds in the face of complexity. Developmental evaluation adapts to the realities of complex nonlinear dynamics rather than trying to impose order and certainty on a disorderly and uncertain world." (Michael Q Patton, "Developmental Evaluation", 2010)

"In the 'computation' that is the economy, large and small probabilistic events at particular non-repeatable moments determine the attractors fallen into, the temporal structures that form and die away, the technologies that are brought to life, the economic structures and institutions that result from these, the technologies and structures that in turn build upon these; indeed the future shape of the economy - the future path taken. The economy at all levels and at all times is path dependent. History again becomes important. And time reappears." (W Brian Arthur, "Complexity and the Economy", 2015)

"Feedback systems are closed loop systems, and the inputs are changed on the basis of output. A feedback system has a closed loop structure that brings back the results of the past action to control the future action. In a closed system, the problem is perceived, action is taken and the result influences the further action. Thus, the distinguishing feature of a closed loop system is a feedback path of information, decision and action connecting the output to input." (Bilash K Bala et al, "System Dynamics: Modelling and Simulation", 2017)