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

"Hasheesh helped a great deal, and once sent him to a part of space where form does not exist, but where glowing gases study the secrets of existence. And a violet-coloured gas told him that this part of space was outside what he had called infinity. The gas had not heard of planets and organisms before, but identified Kuranes merely as one from the infinity where matter, energy, and gravitation exist." (Howard P Lovecraft, "Celephais", 1922)

"Man has natural three-dimensional limits, and he also has four-dimensional ones, considering time as an extension. When he reaches those limits, he ceases to grow and mature, and forms rigidly within the mold of those limiting walls. It is stasis, which is retrogression unless all else stands still as well. A man who reaches his limits is tending toward subhumanity. Only when he becomes superhuman in time and space can immortality become practical." (Henry Kuttner & C L Moore, "Time Enough", 1946)

"There are and have been worlds and cultures without end, each nursing the proud illusion that it is unique in space and time. There have been men without number suffering from the same megalomania; men who imagined themselves unique, irreplaceable, irreproducible. There will be more [...] more plus infinity." (Alfred Bester, "The Demolished Man", 1953)

"The 'romance' of space - drivel written in the old days. When you’re not blasting, you float in a cramped hotbox, crawl through dirty mazes of greasy pipe and cable to tighten a lug, scratch your arms and bark your shins, get sick and choked up because no gravity helps your gullet get the food down." (Walter M Miller Jr., "Death of a Spaceman", 1954)

"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)

"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)

"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)

"We’re free out here, really free for the first time. We’re floating, literally. Gravity can’t bow our backs or break our arches or tame our ideas. You know, it’s only out here that stupid people like us can really think. The weightlessness gets our thoughts and we can sort them. Ideas grow out here like nowhere else - it’s the right environment for them. Anyone can get into space, if he wants to hard enough. The ticket is a dream." (Fritz Leiber," The Beat Cluster", 1961)

"[...] for the 5th dimension [...] you can travel through space without having to go the long way around.. .In other words a straight line is not the shortest distance between two points." (Madeleine L'Engle, "A Wrinkle in Time", 1962)

"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 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)

"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)

"[...] the universe was scrawled [...] along all its dimensions [...] space didn't exist and perhaps had never existed." (Italo Calvino, "A Sign in Space", 1965)

"His vessel found itself between two vortices of gravitation called Bakhrida and Scintilla; Bakhrida speeds up time, Scintilla on the other hand slows it down, and between them lies a zone of stagnation, in which the present, becalmed, flows neither backward nor forward. There Heptodius froze alive, and remains to this day, along with the countless frigates and galleons of other astromariners, pirates, and spaceswashers, not aging in the least, suspended in the silence and excruciating boredom that is Eternity." (Stanislaw Lem, "How Erg the Self-Inducing Slew a Paleface", 1965)

"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)

"Someday, the real masters of space would be machines, not men - and he was neither. Already conscious of his destiny, he took a somber pride in his unique loneliness - the first immortal midway between two orders of creation.

He would, after all, be an ambassador; between the old and the new - between the creatures of carbon and the creatures of metal who must one day supersede them.

Both would have need of him in the troubled centuries that lay ahead." (Arthur C Clarke, "A Meeting with Medusa", 1971)

"It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death. Perhaps we are merely sliding down a gentle ripple that has been set up, accidently and very temporarily, in a quiet pond, and it is only the limitation of our own infinitesimal range of viewpoint in space and time that makes it seem to ourselves that we are hurtling down a cosmic waterfall of increasing entropy, a waterfall of colossal size and duration." (Isaac Asimov, 1976)

"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)

"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)

"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)

"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)

"The dimension of the imagination is much more complex than those of time and space, which are very junior dimensions indeed." (Terry Pratchett, "The Colour of Magic", 1983)

"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 0 it is a matter of simple extrapolation." (Kim S Robinson, "Red Mars", 1992)

"Once we overcome our fear of being tiny, we find ourselves on the threshold of a vast and awesome Universe that utterly dwarfs - in time, in space, and in potential - the tidy anthropocentric proscenium of our ancestors." (Carl Sagan, "Pale Blue Dot: A Vision of the Human Future in Space", 1994)

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

"A mighty maze! but not without a plan [...]" (Alexander Pope, "An Essay on Man", 1733-34)

"Language gradually varies, and with it fade away the writings of authors who have flourished their allotted time; otherwise, the creative powers of genius would overstock the world, and the mind would be completely bewildered in the endless mazes of literature." (Washington Irving, "The Sketch Book of Geoffrey Crayon", 1819–1820)

"The 'romance' of space - drivel written in the old days. When you’re not blasting, you float in a cramped hotbox, crawl through dirty mazes of greasy pipe and cable to tighten a lug, scratch your arms and bark your shins, get sick and choked up because no gravity helps your gullet get the food down." (Walter M Miller Jr., "Death of a Spaceman", 1954)

"A promise is a direction taken, a self-limitation of choice. [...] if no direction is taken, if one goes nowhere, no change will occur. One’s freedom to choose and to change will be unused, exactly as if one were in jail, a jail of one’s own building, a maze in which no one way is better than any other." (Ursula K. Le Guin, "The Dispossessed: An Ambiguous Utopia", 1974)

"The best maze is the mind.' (Ursula K Le Guin, "Mazes", 1975)

"Any path that narrows future possibilities may become a lethal trap. Humans are not threading their way through a maze; they scan a vast horizon filled with unique opportunities. The narrowing viewpoint of the maze should appeal only to creatures with their noses buried in the sand." (Frank Herbert, "Children of Dune", 1976)

"There is in Fantastica a certain place from which one can go anywhere and which can be reached from anywhere. We call it the Temple of a Thousand Doors. No one has ever seen it from outside. The inside is a maze of doors. Anyone wishing to know it must dare to enter it." (Michael Ende, "The Neverending Story", 1979)

"The truth of life is that every year we get farther away from the essence that is born within us. We get shouldered with burdens, some of them good, some of them not so good. Things happen to us. Loved ones die. People get in wrecks and get crippled. People lose their way, for one reason or another. It's not hard to do, in this world of crazy mazes. Life itself does its best to take that memory of magic away from us." (Robert McCammon, "Boy's Life", 1991)

"The maze itself is the sum of a man's life: choices he makes, dreams he hangs on to. And there at the center, there's a legendary man who had been killed over and over again countless times, but always clawed his way back to life. The man returned for the last time and vanquished all his oppressors in a tireless fury. He built a house. Around that house he built a maze so complicated, only he could navigate through it. I reckon he'd seen enough of fighting." (The Adversary" Westworld (TV series), 2016)

"We depend on nature not only for our physical survival. We also need nature to show us the way home, the way out of the prison of our own minds. We got lost in doing, thinking, remembering, anticipating–lost in a maze of complexity and a world of problems." (Eckhart Tolle, "Stillness Speaks", 2003)

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

"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) 

"The forceps of our minds are clumsy forceps, and crush the truth a little in taking hold of it." (Herbert G Wells, "Scepticism of the Instrument: A Modern Utopia", 1905)

"No honest historian can take part with - or against - the forces he has to study. To him even the extinction of the human race should be merely a fact to be grouped with other vital statistics." (Henry Adams, "The Education of Henry Adams", 1907)

"The humans have a curious force they call ambition. It drives them, and, through them, it drives us. This force which keeps them active, we lack. Perhaps, in time, we machines will acquire it." (John Wyndham, "The Lost Machine", 1932)

"It was in this world that we found in its most striking form a social disease which is perhaps the commonest of all world-diseases—namely, the splitting of the  population into two mutually unintelligible castes through the influence of economic forces." (Olaf Stapledon, "Star Maker", 1937)

"Scientific study and reflection had taught us that the known universe of three dimensions embraces the merest fraction of the whole cosmos of substance and energy. In this case an overwhelming preponderance of evidence from numerous authentic sources pointed to the tenacious existence of certain forces of great power and, so far as the human point of view is concerned, exceptional malignancy." (Howard P Lovecraft, "The Shunned House", 1937)

"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)

"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 universe is full of matter and force. Yet in all that force, amongst all the bulks and gravities, the rains of cosmic light, the bombardment of energy - how little spirit, how small the decimal points of intelligence." (Ray Bradbury et al, "Mars and the Mind of Man", 1973)

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

"Belief is a force. It’s a weak force, by comparison with gravity; when it comes to moving mountains, gravity wins every time. But it still exists." (Terry Pratchett, "Pyramids", 1989)

"Of all the forces in the universe, the hardest to overcome is the force of habit. Gravity is easy-peasy by comparison." (Terry Pratchett, "Johnny and the Dead", 1993)

"Grief can have a quality of profound healing because we are forced to a depth of feeling that is usually below the threshold of awareness." (Stephen Levine, "Who Dies?: An Investigation of Conscious Living and Conscious Dying", 2012)

"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)

On Measures (-1849)

"Numbers prime to one another are those which are measured by a unit alone as a common measure." (Euclid, "The Elements", Book VII)

"Measure, time and number are nothing but modes of thought or rather of imagination." (Baruch Spinoza, [Letter to Ludvicus Meyer] 1663)

"To measure motion, space is as necessary to be considered as time. [... They] are made use of to denote the position of finite: real beings, in respect one to another, in those infinite uniform oceans of duration and space." (John Locke, "An Essay Concerning Human Understanding", 1689)

"Most of our philosophical instruments are measures of effects. The progress made in natural philosophy increases every day by the number of these measures; by these it still continues to be improved." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them." (J B Joseph Fourier, "The Analytical Theory of Heat", 1822)

"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible, or all of which have the same chance." (Siméon-Denis Poisson, "Recherches sur la Probabilités des Jugemens" ["An Investigation of the Laws of Thought"], 1837)

"Yet time and space are but inverse measures of the force of the soul. The spirit sports with time." (Ralph W Emerson, "Essays", 1841)

On Measures (1850-1899)

"Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case we can only determine the more or less and not the how much." (Bernhard Riemann, "On the hypotheses which lie at the foundation of geometry", 1854)

"The purely formal sciences, logic and mathematics, deal with such relations which are independent of the definite content, or the substance of the objects, or at least can be. In particular, mathematics involves those relations of objects to each other that involve the concept of size, measure, number." (Hermann Hankel, "Theorie der Complexen Zahlensysteme", 1867)

"The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." (William James, "Clifford's Lectures and Essays", 1879)

"Nothing that we can measure is inconceivably large or inconceivably small in physical science." (William T Kelvin, 1883)

"She [Nature] works with reference to no measure of time, no limit of space, and with an abundance of material not expressed by exhaustless." (John Burroughs, "Birds and Poets With Other Papers", 1884)

"I call a sign which stands for something merely because it resembles it, an icon. Icons are so completely substituted for their objects as hardly to be distinguished from them. Such are the diagrams of geometry. A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing. So in contemplating a painting, there is a moment when we lose the consciousness that it is not the thing, the distinction of the real and the copy disappears, and it is for the moment a pure dream, - not any particular existence, and yet not general. At that moment we are contemplating an icon." (Charles S Peirce, "On The Algebra of Logic : A Contribution to the Philosophy of Notation" in The American Journal of Mathematics 7, 1885)

On Measure (1900-1949)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Jules H Poincaré, "Science and Hypothesis", 1905)

"So completely is nature mathematical that some of the more exact natural sciences, in particular astronomy and physics, are in their theoretic phases largely mathematical in character, while other sciences which have hitherto been compelled by the complexity of their phenomena and the inexactitude of their data to remain descriptive and empirical, are developing towards the mathematical ideal, proceeding upon the fundamental assumption that mathematical relations exist between the forces and the phenomena, and that nothing short, of the discovery and formulations of these relations would constitute definitive knowledge of the subject. Progress is measured by the closeness of the approximation to this ideal formulation." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"Just as data gathered by an incompetent observer are worthless - or by a biased observer, unless the bias can be measured and eliminated from the result - so also conclusions obtained from even the best data by one unacquainted with the principles of statistics must be of doubtful value." (William F White, "A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays", 1908)

"The second law of thermodynamics appears solely as a law of probability, entropy as a measure of the probability, and the increase of entropy is equivalent to a statement that more probable events follow less probable ones." (Max Planck, "A Survey of Physics", 1923)

"Our environment may and should mean something towards us which is not to be measured with the tools of the physicist or described by the metrical symbols of the mathematician." (Arthur S Eddington, "Science and the Unseen World", 1929)

"Search for measurable elements among your phenomena, and then search for relations between these measures of physical quantities." (Alfred N Whitehead, "Science and the Modern World", 1929)

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

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939)

"Hence the awkward expression ‘negative entropy’ can be replaced by a better one: entropy, taken with the negative sign, is itself a measure of order. Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness ( = fairly low level of entropy) really consists in continually sucking orderliness from its environment." (Erwin Schrödinger, "What is Life?", 1944)

On Measures (1950-1974)

"Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Clichés, for example, are less illuminating than great poems." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"The belief in science has replaced in large measure, the belief in God. Even where religion was regarded as compatible with science, it was modified by the mentality of the believer in scientific truth." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"Beauty had been born, not, as we so often conceive it nowadays, as an ideal of humanity, but as measure, as the reduction of the chaos of appearances to the precision of linear symbols. Symmetry, balance, harmonic division, mated and mensurated intervals - such were its abstract characteristics." (Herbert Read, "Icon and Idea: The Function of Art in the Development of Human Consciousness", 1955)

"Religion and science are the two conjugated faces of phases of one and the same act of complete knowledge - the only one which can embrace the past and future of evolution so as to contemplate, measure and fulfill them." (Pierre T de Chardin, "The Phenomenon of Man", 1955)

"Since we are assured that the all-wise Creator has observed the most exact proportions of number, weight and measure in the make of all things, the most likely way therefore to get any insight into the nature of those parts of the Creation which come within our observation must in all reason be to number, weigh and measure." (Stephen Hales, "Vegetable Staticks", 1961)

"Entropy is a measure of the heat energy in a substance that has been lost and is no longer available for work. It is a measure of the deterioration of a system." (William B Sill & Norman Hoss (Eds.), "Popular Science Encyclopedia of the Sciences", 1963)

"If our model is to be at all realistic, it will also need to be rather complex, It will in fact be too complex for easy handling by the traditional analytic measures, even after suitable simplifications." (Charles P Bonini, "Simulation of Information and Decision System in the Firm" , 1963)

"It is a commonplace of modern technology that there is a high measure of certainty that problems have solutions before there is knowledge of how they are to be solved." (John K Galbraith, "The New Industrial State", 1967)

"The aim of science is not so much to search for truth, or even truths, as to classify our knowledge and to establish relations between observable phenomena in order to be able to predict the future in a certain measure and to explain the sequence of phenomena in relation to ourselves." (Pierre L du Noüy, "Between Knowing and Believing", 1967)

"The 'flow of information' through human communication channels is enormous. So far no theory exists, to our knowledge, which attributes any sort of unambiguous measure to this 'flow'." (Anatol Rapoport, "Modern Systems Research for the Behavioral Scientist", 1969)

On Measures (1975-1999)

 "The amount of information conveyed by the message increases as the amount of uncertainty as to what message actually will be produced becomes greater. A message which is one out of ten possible messages conveys a smaller amount of information than a message which is one out of a million possible messages. The entropy of communication theory is a measure of this uncertainty and the uncertainty, or entropy, is taken as the measure of the amount of information conveyed by a message from a source. The more we know about what message the source will produce, the less uncertainty, the less the entropy, and the less the information." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals and Noise", 1979)

"The term closed loop-learning process refers to the idea that one learns by determining what s desired and comparing what is actually taking place as measured at the process and feedback for comparison. The difference between what is desired and what is taking place provides an error indication which is used to develop a signal to the process being controlled." (Harold Chestnut, 1984)

"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases."  (Stephen Hawking, "A Brief History of Time", 1988)

"Engineers, always looking for optimal values for the measures of magnitudes which interest them, think of mathematicians as custodians of a fund of formulae, to be supplied to them on demand." (Jean Dieudonné, "Mathematics - The Music of Reason", 1992)

"It has long been appreciated by science that large numbers behave differently than small numbers. Mobs breed a requisite measure of complexity for emergent entities. The total number of possible interactions between two or more members accumulates exponentially as the number of members increases. At a high level of connectivity, and a high number of members, the dynamics of mobs takes hold. " (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Quantify. If whatever it is you’re explaining has some measure, some numerical quantity attached to it, you’ll be much better able to discriminate among competing hypotheses. What is vague and qualitative is open to many explanations." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)

"Yet everything has a beginning, everything comes to an end, and if the universe actually began in some dense explosion, thus creating time and space, so time and space are themselves destined to disappear, the measure vanishing with the measured, until with another ripple running through the primordial quantum field, something new arises from nothingness once again." (David Berlinski, "A Tour of the Calculus", 1995)

"Probabilities aren't just numbers, and they aren't just frequencies-on-average. They are also rather like a substance that flows, dividing according to the likelihood of various outcomes, subdividing when several trials are performed in succession, and adding together when several outcomes are combined to give an event. This is a metaphor, but an accurate and powerful one. It is, in a sense, the metaphor that mathematicians formalise when they offer a definition of probability. In this sense, probability behaves like volume, mass, or area. The technical term is 'measure'. The technical definition of probability is 'a measure such that various nice things happen'. Probability is a quantity that flows through the conceptual maze of possible events, and it behaves just like water flowing through pipes." (Ian Stewart, "The Magical Maze: Seeing the World Through Mathematical Eyes", 1997)

On Measures (2000-2009)

"One measure of the depth of a physical theory is the extent to which it poses serious challenges to aspects of our worldview that had previously seemed immutable." (Brian Greene, "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest, for the Ultimate Theory", 2000)

"[…] interval mathematics and fuzzy logic together can provide a promising alternative to mathematical modeling for many physical systems that are too vague or too complicated to be described by simple and crisp mathematical formulas or equations. When interval mathematics and fuzzy logic are employed, the interval of confidence and the fuzzy membership functions are used as approximation measures, leading to the so-called fuzzy systems modeling." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?" (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, [Page-Barbour lecture], 2004)

"All models (whether mental or those turned into computer maps/models) are developed using a particular lens of what we value - what we think is important to understand, or what performance we wish to develop or improve. Although organizations can build forum models focusing on the performance measure du jour, they would be well advised to use a systemic or integral framework for what to include." (Peggy Holman et al, "The Change Handbook", 2007)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, "A Many-Colored Glass: Reflections on the Place of Life in the Universe", 2007)

"This new model of development would be based clearly on the goal of sustainable human well-being. It would use measures of progress that clearly acknowledge this goal. It would acknowledge the importance of ecological sustainability, social fairness, and real economic efficiency. Ecological sustainability implies recognizing that natural and social capital are not infinitely substitutable for built and human capital, and that real biophysical limits exist to the expansion of the market economy." (Robert Costanza, "Toward a New Sustainable Economy", 2008)

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

"Science has gone down into the mines and coal-pits, and before the safety-lamp the Gnomes and Genii of those dark regions have disappeared [...] Sirens, mermaids, shining cities glittering at the bottom of quiet seas and in deep lakes, exist no longer; but in their place, Science, their destroyer, shows us whole coasts of coral reef constructed by the labours of minute creatures; points to our own chalk cliffs and limestone rocks as made of the dust of myriads of generations of infinitesimal beings that have passed away; reduces the very element of water into its constituent airs, and re-creates it at her pleasure." (Charles Dickens, Poetry of Science, [Book review of Robert Hunt]1848)

"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)

"Only by reducing this element of free will to the infinitesimal, that is, by regarding it as an infinitely small quantity, can we convince ourselves of the absolute inaccessibility of the causes, and then instead of seeking causes, history will take the discovery of laws as its problem." (Lev N Tolstoy, "War and Peace", 1867)

"Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history."  (Lev N Tolstoy, "War and Peace", 1867)

"To-day alone was real. Never was man brought into contact with reality save through the evanescent emotions and sensations of that single moment, that infinitesimal fraction of a second, which was passing now - and it was in the insignificance of this moment, precisely, that religious persons must believe. So ran the teachings of all dead and lingering faiths alike. Here was, perhaps, only another instance of mankind's abhorrence of actualities; and man's quaint dislike of facing reality was here disguised as a high moral principle. That was why all art, which strove to make the sensations of a moment soul-satisfying, was dimly felt to be irreligious. For art performed what religion only promised." (James B Cabell, "The Cream of the Jest", 1917)

"Measured objectively, what a man can wrest from Truth by passionate striving is utterly infinitesimal. But the striving frees us from the bonds of the self and makes us comrades of those who are the best and the greatest." (Albert Einstein, cca. 1920s)

"It is venturesome to think that a coordination of words (philosophies are nothing more than that) can resemble the universe very much. It is also venturesome to think that of all these illustrious coordinations, one of them - at least in an infinitesimal way - does not resemble the universe a bit more than the others." (Jorge L Borges, "Discussion", 1932)

"To be so closely caught up in the teeth of things that they kill you, no matter how infinitesimally kill you, is, truly, to be a poet: and to be a poet in fact it is additionally necessary that you should possess the tongues and instruments with which to record this series of infinitesimal deaths." (George Barker,"Therefore All Poems Are Elegies", 1940)

"An ugliness unfurled in the moonlight and soft shadow and suffused the whole world. If I were an amoeba, he thought, with an infinitesimal body, I could defeat ugliness. A man isn’t tiny or giant enough to defeat anything." (Yukio Mishima, "The Sailor Who Fell from Grace with the Sea", 1963)

"The creative element in the mind of man [...] emerges in as mysterious a fashion as those elementary particles which leap into momentary existence in great cyclotrons, only to vanish again like infinitesimal ghosts." (Loren Eiseley, "The Night Country", 1971)

"It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death. Perhaps we are merely sliding down a gentle ripple that has been set up, accidently and very temporarily, in a quiet pond, and it is only the limitation of our own infinitesimal range of viewpoint in space and time that makes it seem to ourselves that we are hurtling down a cosmic waterfall of increasing entropy, a waterfall of colossal size and duration." (Isaac Asimov, 1976)

"I wonder if being sane means disregarding the chaos that is life, pretending only an infinitesimal segment of it is reality." (Rabih Alameddine, "Koolaids: The Art of War", 1998)