William L Schaaf - Collected Quotes

"A formula is simply a mathematical statement of a principle or a rule describing the relation between two or more quantities. This mathematical statement shows that there is an equality between certain quantities; in other words, the formula translates a verbal rule into algebraic symbols. Thus a formula is very similar to an equation." (William L Schaaf, "Mathematics for Mechanics", 1942)

"A graph, as the name itself suggests, can go a step further than the formula - it can make visible what the formula represents - it can give an actual picture of the mathematical relationship. The relationship literally becomes more graphic; the relative magnitudes of the variables become apparent to the eye, as do extreme maximum and minimum values, if any; so do the rates at which they change; trends become clear; extrapolation and interpolation become more meaningful; any special features of the relationship are emphasized; general types of relationships are recognizable; two or more relationships can frequently be directly compared with one another." (William L Schaaf, "Mathematics for Mechanics", 1942)

"A type of picture-graph less commonly used than formerly is the pictorial representation of an object which has been arbitrarily subdivided to show certain numerical relationships; as, for example, the pictorial representation of the food values of beefsteak. This is a very poor type of graphic representation, and should definitely be avoided. The irregular outline of the picture as a whole, and of each of the shaded areas, makes a comparison of the areas difficult, if not altogether impossible; the shading only to the confusion." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"Geometric lines are fictions in the sense that, while we draw them, we think of them as having no width, simply length. Lines may be curved or straight." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"Graphs showing time changes, or the increases and decreases in the amount of something over a period of time, are generally of two kinds: (1) vertical bar graphs, and (2) broken- or smooth-line graphs. Both kinds differ from the categorical charts [...] in that they have two scales instead of only one; that is why it is preferable to call them graphs rather than charts, although these terms are used rather freely and interchangeably, and there is no standard convention." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"If a number or a quantity is thought of as being broken up, or subdivided into any number of equal parts, and then a certain number of those parts is considered separately in relation to the total number of such parts, we arrive at the idea of a fraction." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"In [...] horizontal bar-charts, showing comparisons between different kinds of things, or between different places, only one numerical scale is required, viz., the scale representing the amounts involved. No other numerical scale is needed, since we are dealing with various categories. While not always the most effective device for exhibiting such comparisons, horizontal bar-charts are simple and convenient." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"In mathematics, a definite quantitative relation between two or more variables, whether expressed verbally, by a formula, or by a graph, is called a functional relationship, or simply a mathematical function. Each variable is said to be a function of the other. The word function, as used here, has nothing to do with use or purpose; it simply calls attention to the fact that the quantities in question are quantitatively related to each other in a definite manner." (William L Schaaf, "Mathematics for Mechanics", 1942)

"It is clear that for any given point on a graph, its horizontal distance from the vertical scale (abscissa) represents the magnitude of the independent variable, while the vertical distance above or below the horizontal scale (ordinate) represents the corresponding magnitude of the dependent variable. Thus the position of the curve with respect to the axes depicts the actual magnitudes of the variables. But in studying changing variables and functional relationships, it is frequently desirable to inquire as to the rate at which a quantity is changing, i.e., how fast it is increasing or decreasing, rather than how large or how small it is. Rate implies a ratio; a rate of change means the amount of change in the function (or dependent variable) per unit change in the independent variable." (William L Schaaf, "Mathematics for Mechanics", 1942)

"Many forms in Nature exhibit the geometric property of symmetry. Anything symmetrical, whether natural or manmade, is usually pleasing in appearance, since it is 'balanced', and appeals to the eye. Symmetry is one of the most important principles of ornament, design and architecture. It is not, however, the only one; others are repetition and rhythm." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The mathematical concept of chance, or probability, must not be confused with the psychological notion of likelihood. If a coin upon being tossed six times in succession has come up 'heads' each of the six times, we may be impelled to feel that upon the seventh toss it is 'more likely' to turn 'tails' in view of the six previous heads; but this is only an emotional reaction and not a mathematical probability. Mathematically [...] on any single throw, the chances are even for heads or tails, irrespective of what the previous trials may have been. In the long run, the greater the number of trials, the more nearly equal will become the number of heads and tails." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The methods of algebra are essentially an extension of arithmetic. In other words, the numbers, symbols and operations used in algebra are the same as those used in arithmetic, only they are more general in character. This means (1) that letters as well as numbers are are “used te to represent quantities, and (2) that ‘numbers are re‘garded as having quality as well as quantity." (William L Schaaf, "Mathematics for Mechanics", 1942)

"There is no such thing as an absolute or perfect measurement. An object can be thought of as having an actual, real, or 'true' length; but that length can never be found completely, it can only be found approximately. How 'exact' any particular measurement happens to be depends upon the nature of the instruments used, the skill of the operator, and the conditions under which it is made. The difference between the true length and the measured length is technically known as the error. An error is not a mistake. The careless use, or the misuse, of a measuring instrument leads to mistakes. The proper use of a measuring instrument always involves errors. The errors may be large or small; they can never be completely eliminated. The extent of the approximation is known as the degree of accuracy of the measurement; a numerical measure of the extent of the error is known as the precision of the measurement. What particu. lar degree of accuracy is sought depends chiefly upon the purpose for which the measurement is made, or the "use to which the object is to be put." (William L Schaaf, "Mathematics for Mechanics", 1942)

"Practical geometry deals with the nature and properties of various geometric forms, such as rectangles, triangles, circles, etc., and emphasizes especially the measurement of such figures. Hence the chief value of practical geometry is in problems of design and construction." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The operation of adding two numbers is essentially a process of grouping, or, more accurately, regrouping. When we add two numbers we do not increase anything; we regroup the numbers in accordance  with the standard pattern or number system based on groups of ten." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"When statistical data are of such a nature that it is permissible to assume that 'in-between values' vary continuously and uniformly (or very nearly so) from one observed or measured value to the next, a modification of the broken-line graph may be used. Instead of connecting the plotted points with straightline segments, a 'smooth' curved line is drawn between the points [...]. Such curvedline graphs may be drawn either 'free hand' or with the aid of drafting instruments known as French curves." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"You may expect to find graphs anywhere: in books, in periodicals, in newspapers, in pamphlets, on show cards in advertisements, in business reports, and so on. Their use, however, is sometimes limited. For one thing, they are of necessity less accurate than the figures on which they are based, which, of course, doesn’t matter too much in many cases. In the second place, they are sometimes misleading, which may or may not be intentional. It is also possible that the reader of a chart or graph may misinterpret it." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"A mathematical point is an idea - an abstraction - something we can think about. It cannot be defined logically. Fortunately, our common experience with physical objects makes it relatively certain that each of us has the same idea in mind when he uses the word point, and so the lack of a logical definition presents no particular difficulty." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Having brought our story down to the present, we may well ask: What is geometry? Is it a system of logic, of pure mathematics, or is it a practical art to serve as the handmaiden to science, engineering, astronomy, and kindred technical fields? The answer is simple: it is both a logical science and a practical art." (William L Schaaf, "Plane and solid geometry for home study", [forward] 1944)

"No step should ever be taken, and no statement should ever be made, without giving a legitimate reason therefor. A 'legitimate' reason means a reference to a definition, to an assumption, or to a proposition previously proved; it may also include reference to a statement in the hypothesis, or to a line arbitrarily drawn at the outset of the demonstration." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"To define a term adequately means to describe it in such a way that no doubt or ambiguity arises as to its meaning when that term is used. A good definition should indicate to what larger group of objects the object defined belongs, as well as how that object differs from other objects of that group. The larger group is sometimes called the genus, and the smaller, special group is called the species. Geometric objects, i.e., figures, are for the most part easy to define with precision." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Whenever we discuss a geometric statement in order to prove it, we refer to previously proved statements for 'evidence'. In this process of referring back to earlier statements that have already been established by proof, it is clear that some few of the earliest statements must of necessity remain unproved - that is, they have to be taken for granted, since we must begin our chain of reasoning somewhere. It is not possible to prove every statement. Those statements which are thus taken for granted without proof are called assumptions. Hence in all logical reasoning, two considerations are of prime importance: (1) the meanings of the terms used, and (2) the basic assumptions made." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders." (William L Schaaf, "Mathematics: Our Great Heritage: Essays on the Nature and Cultural Significance of Mathematics", 1948)

"A cylinder is a quadric surface if and only if its right section is a conic. As will be seen shortly, a quadric surface is one whose equation is of the second degree. A quadric cylinder is called parabolic, elliptic, or hyperbolic according as its right section is a parabola, an ellipse, or a hyperbola. The cylinder of revolution, or circular cylinder, is a special case of the elliptic cylinder." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"A cylindrical surface is any surface generated by a moving straight line which constantly intersects a given fixed curve and which remains parallel to a fixed straight line. The fixed curve is called the directrix, and the generating line is known as the generatrix. Thus a cylinder is a ruled surface, that is, the surface is comprised of straight lines (the generators), all of which are parallel." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"A transformation by translation has the effect of moving the origin to a new position without changing the directions of the axes. A transformation by rotation has the effect of turning the axes through an angle about the origin as a pivot, but without changing the position of the origin. Either transformation may be effected by itself, or both may be effected jointly; although, in such case, the rotation is normally performed first and the translation second." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"If each segment of a broken line in space be given the direction determined in passing continuously from one terminal to the other, then the algebraic sum of the projections of the segments upon any directed line equals the projection of the closing line. If the broken line in question should be a closed polygon, the sum of the projections of the sides upon any directed line is zero." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"In algebra, when we plot the graph of an equation, the curve so obtained represents the locus of the equation. In analytic geometry, the word 'curve' refers to any locus; it may be a straight line, a curved line, or a group of lines. We therefore see that: (1) The locus of an equation is a curve containing all those points, and only those points, whose coordinates satisfy the given equation. (2) The equation of a locus is an equation such that the coordinates of every point on the locus satisfy the equation, and every ordered pair of numbers which satisfy the equation are the coordinates of a point on the locus." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is possible, however, to determine the general shape and salient features of a curve by a more searching method. This is accomplished by examining more closely the equation of the curve, rather than by computing a more extensive table of values. Certain characteristic features of curves can be determined by inspection of the form of the equation, and by computing only certain special values of the variables. These characteristic properties include the intercepts, extent, symmetry, and asymptotes of the curve." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is possible, however, to express geometric facts by using algebraic methods. In other words, the properties of figures and the relationships between them can be described by means of numbers and equations. Conversely, algebraic expressions and equations can be represented or interpreted geometrically. When we translate from the language of geometry to the language of algebra, or vice versa, we are using analytical methods. Geometry when studied in this way is called analytic geometry." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is to be understood that by an algebraic equation is meant an equation which involves only integral and fractional powers of the variables x and y. If the equation is of degree higher than two, the equation represents an algebraic higher plane curve. Any equation which is not algebraic is known as a transcendental equation; functions defined by such equations are said to be transcendental functions. For example, y = cos x, y = a log x, and y = k"" are transcendental functions."  (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"The empirical data are usually available in the form of a table exhibiting pairs of corresponding values of the variables. Since the given values do not lie exactly along a straight hne, a parabola, an exponential curve or a power curve, it is necessar}' to find a curve that fits the given data approximately. This process is called curve fitting, and the equation of the curve which fits the data approximately is called an empirical equation. When fitting a curve to a set of given points, we must assume a general form for the equation which we are going to use to represent the curve." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"Very little can be learned about the nature of a surface merely by locating points on the surface. Instead, we study (1) its intercepts and traces in the coordinate planes; (2) its extent; (3) its symmetry, and (4) plane sections." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"When either the translation or the rotation transformations are applied to an equation, they change the coordinates of all points in the plane (except the origin in the case of a rotation). These transformations actually move the axes with relation to the curve, but they do not alter the shape of the curve represented by the original equation and by the transformed equation. Beside this constant or unvarying feature, i.e., the preservation of the geometric form of the curve, there are also certain algebraic expressions whose values remain unchanged in both equations. Mathematical forms which are preserved or do not vary when other changes take place are called invariants." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"When plotting or drawing the locus of a given equation, the position selected for the coordinate axes is, of course, immaterial. Hence, after the locus has been drawn, we may change the position of the axes arbitrarily, as we wish. Naturally, if the locus remains where it was drawn, but the position of the axes is changed, then the equation will have to be changed to correspond to the new position of the axes if the equation is to describe the same locus. In other words, a given locus may be described by more than one equation; each of the equations describes the locus in question with reference to a different set of axes."(William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"A maximum value of a function is one that is greater than any values immediately preceding or following; a minimum value of a function is one that is less than any values immediately preceding or following."  (William L Schaaf, "The Calculus, a college course guide", 1963)

"Emerson once said that it didn’t matter much where a man was, so long as you knew the direction in which he was moving. In somewhat the same way, the significance of a graph or curve often lies not so much in what height a point on the curve has reached, as it does in how fast its height is changing, and whether it is increasing or decreasing." (William L Schaaf, "The Calculus, a college course guide", 1963)

"If a function increases as the independent variable increases, or decreases as the independent variable decreases, the function is said to be increasing; if the function decreases as the independent variable increases, or increases as the independent variable decreases, the function is decreasing." (William L Schaaf, "The Calculus, a college course guide", 1963)

"When a curve approaches an axis or any other straight line in this fashion, the line is said to be an asymptote of the curve. As a working definition, we may say: An asymptote of a curve is any straight line which a curve approaches continuously as the curve moves on to infinity." (William L Schaaf, "The Calculus, a college course guide", 1963)

"In other words, we may think of the instantaneous speed at a certain instant as the limiting value which the average speed would approach tf the interval were indefinitely shortened, while always including the instant in question." (William L Schaaf, "The Calculus, a college course guide", 1963)

"It hardly need be pointed out that to use the calculus skillfully requires considerable practice with standard formulas for differentiating various functions. Among the most commonly used formulas are those for the power function, for a product, and for a quotient. The exercise below affords further practice in the use of these formulas" (William L Schaaf, "The Calculus, a college course guide", 1963)

"It is apparent, therefore, that for a function to have a maximum or a minimum value, it is necessary for the value of f’(x) to be zero or infinite, but that this alone is not a sufficient condition. In addition to f’(x) having a zero or infinite value, f’ (x) must change in sign as it passes through zero (or infinity)." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Once more we must remind the reader not to confuse the amount of change with the rate of change. A function may increase or decrease by a very small amount in a short interval, and yet be changing very rapidly - just as a bullet may travel only a small distance in one thousandth of a second and yet be moving at a very high speed." (William L Schaaf, "The Calculus, a college course guide", 1963)

"The creation of Analytic Geometry by Descartes in the early part of the seventeenth century was a milestone of tremendous significance. Indeed, it was the beginning of modern mathematics in the broad perspective of history. ('Modern' mathematics in the sense of contemporary mathematics did not commence until about 1900, with the advent of functional analysis, abstract spaces, set theory, and symbolic logic.) This great step of recognizing the relation between the numbers of algebra and the entities of geometry once having been taken, it is perhaps not surprising that further advances were soon to follow, culminating in the invention of the Calculus by Isaac Newton and by Gottfried Leibniz. This was a classic illustration of nearly simultaneous, but presumably independent creation." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Thus far we have regarded integration as the inverse of the operation of differentiation, and the integral was thought of as an anti-derivative. It is possible, however, to consider integration from another point of view, namely, as a process of summation, or as the addition of many similar elements. Indeed, it is largely from this point of view that the Integral Calculus developed historically, growing out of early attempts to determine the area bounded by various curves. A given area was subdivided into many small parts, and these 'infinitesimal parts' were then added." (William L Schaaf, "The Calculus, a college course guide", 1963)

"When comparing infinitesimals, we refer to their order. This is a relative term, suggesting comparative degree of smallness. If the limit of the quotient of two infinitesimals is a constant, not zero, they are said to be of the same order; if this limit is zero, the first differential (the numerator) is said to be of higher order than the second, and the second of lower order than the first. If the limit is infinite, the first differential (the numerator) is said to be of lower order than the second, and the second of higher order than the first." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number π." (William L Schaaf, "Nature and History of π", 1967)

Alessandro Negro - Collected Quotes

"A graph is a simple and quite old mathematical concept: a data structure consisting of a set of vertices (or nodes/points) and edges (or relationships/lines) that can be used to model relationships among a collection of objects." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"A widely adopted technique for solving the data sparsity issue and the cold-start problem is based on graph representation, navigation, and processing. Graph navigation methods (like the pathfinding example [...]) and graph algorithms (such as PageRank) are applied to fill some gaps and create a denser representation of [a] dataset."

"GNNs are capable of generating representations of nodes that depend on the structure of the graph as well as on any feature information we have. These features could be nodes’ properties, relationship types, and relationship properties. That’s why GNNs could drive the final tasks to better results. These embeddings represent the input for tasks such as node classification, link prediction, and graph classification." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"[...] graphs are extremely useful for encoding information, and data in graph format is increasingly plentiful. In many areas of machine learning - including natural language processing, computer vision, and recommendations - graphs are used to model local relationships between isolated data items (users, items, events, and so on) and to construct global structures from local information. Representing data as graphs is often a necessary step (and at other times only a desirable one) in dealing with problems arising from applications in machine learning or data mining." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are powerful structures useful not only for representing connected information, but also for supporting multiple types of analysis. Their simple data model, consisting of two basic concepts such as nodes and relationships, is flexible enough to store complex information. If you also store properties in nodes and relationships, it is possible to represent practically everything of any size." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are useful for representing how things are either physically or logically linked in simple or complex structures. A graph in which we assign names and meanings to the edges and vertices becomes what is known as a network. In these cases, a graph is the mathematical model for describing a network, whereas a network is a set of relations between objects, which could include people, organizations, nations, items found in a Google search, brain cells, or electrical transformers." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can be used to model and analyze the relationships between entities as well as their properties. This aspect brings an additional dimension of information that graph-powered machine learning can harness for prediction and categorization. The schema flexibility provided by graphs also allows different models to coexist in the same dataset." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can support machine learning by doing what they do best: representing data in a way that is easily understandable and easily accessible. Graphs make all the necessary processes faster, more accurate, and much more effective. Moreover, graph algorithms are powerful tools for machine learning practitioners. Graph community detection algorithms can help identify groups of people, page rank can reveal the most relevant keywords in a text, and so on." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs, with multiple node types and different types of relationships, are far from being a Euclidean space. This task is where graph neural networks (GNNs) comes in. GNNs are deep learning-based methods that operate on a graph domain to perform complex tasks such as node classification (the bot example), link prediction (the disease example), and so on. Due to its convincing performance, GNN has become a widely applied graph analysis method." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"In many areas of machine learning, graphs are used to model local relationships between data elements and to build global structures from local information. Building graphs is sometimes necessary for dealing with problems arising from applications in machine learning or data mining, and at other times, it's helpful for managing data. It's important to note that the transformation from the original data to a graph data representation can always be performed in a lossless manner. The opposite is not always true." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

📓Walter M Miller Jr. - Collected Quotes

"There is some wisdom, and some foolishness in every people’s way." (Walter M Miller Jr., "The Soul-Empty Ones", 1951)

"Space is my harp, and I touch it lightly with fingers of steel. Space sings." (Walter M. Miller, Jr, "The Big Hunger", 1952)

"A lot of human thinking occurred beneath the level of consciousness, downin the darker regions of the mind where it was not allowed to become conscious lest it bring shame to the thinker. And perhaps he had reasoned it all out in that mental half-world where thoughts are inner ghosts, haunting the possessed man with vague stirrings of uneasiness, leading him into inexplicable behavior." (Walter M Miller Jr, "Way of a Rebel", 1954)

"The machinery of civilization was a living body, with organismic Man as its brain." (Walter M Miller Jr., "Way of a Rebel", 1954)

"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 man could change his politics, his friends, his religion, his country, but Men’s tools were a part of his body. Having used a high-powered rifle, the man subsumed the weapon, made it a part of himself. Trading it for a stone axe would be like cutting off his arm. Man was a user of tools, a shaper of environments." (Walter M Miller Jr, "Way of a Rebel", 1954)

"Earth - it was a place where you could stop being afraid, a place where fear of suffocation was not, where fear of blowout was not, where nobody went berserk with the chokers or dreamed of poisoned air or worried about shorthorn cancer or burn blindness or meteorite dust or low-gravity muscular atrophy. A place where there was wind to blow your sweat away." (Walter M Miller Jr, "The Lineman", 1957)

"There were still some meteorites coming in, making bright little winks of fire where they bit into the plain. Deadly stingers out of nowhere, heading nowhere, impartially orbiting, random as rain, random as death. The debris of creation." (Walter M Miller Jr, "The Lineman", 1957)

"Apparently the expectation of humor was enough to produce the illusion of humor, and the comedian could elicit laughter with gesture and expression, regardless of what he said." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"During the last age of reason, certain proud thinkers had claimed that valid knowledge was indestructible - that ideas were deathless and truth immortal." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"Insofar as thought could be governed at all, it could only be commanded to follow what reason affirmed anyhow; command it otherwise and it would not obey." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"It was a species which often considered itself to be, basically, a race of divinely inspired toolmakers; any intelligent entity from Arcturus would instantly have perceived them to be, basically, a race of impassioned after-dinner speech-makers." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"Men must fumble awhile with error to separate it from truth, I think - as long as they don’t seize the error hungrily because it has a pleasanter taste." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

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

"The laws of society are what makes something a crime or not a crime." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

Robert Silverberg - Collected Quotes

"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)

"He swung dizzily along the line of time, as he had done so often before. He saw himself, here and here, and saw others, shadow-figures, dream-figures, lurking behind the curtains of time." (Robert Silverberg, "Open the Sky", 1966)

"Forget it. No, don't forget it. Don't forget anything. Take a lesson from it: collect all the data before shouting nonsense." (Robert Silverberg, "The Man in the Maze", 1969)

"The universe is a perilous place. We do our best. Everything else is unimportant." (Robert Silverberg, "The Man in the Maze", 1969)

"You can make no meaningful evaluations of the universe without the confidence that you are seeing it clearly." (Robert Silverberg, "The Man in the Maze", 1969)

 "You have come to the place where all times are one, where all errors can be unmade, where past and future are fluid and subject to redefinition." (Robert Silverberg, "Breckenridge and the Continuum", 1973)

"He didn't have to observe the niceties of etiquette when talking to a computer." (Robert Silverberg, "Born with the Dead", 1974)

"To a dead the whole universe is plastic, nothing’s real, nothing matters a hell of a lot, it’s all only a joke." (Robert Silverberg, "Born with the Dead", 1974)

"In the absolute universe all events can be regarded as absolutely deterministic, and if we can't perceive the greater structures, it's because our vision is faulty. If we had a real grasp of causality down to the molecular level, we wouldn't need to rely on mathematical approximations, on statistics and probabilities, in making predictions. If our perceptions of cause and effect were only good enough, we'd be able to attain absolute knowledge of what is to come. We would make ourselves all-seeing." (Robert Silverberg, "The Stochastic Man", 1975)

"We are born by accident into a purely random universe." (Robert Silverberg, "The Stochastic Man", 1975)

"The only workable time machine ever invented is the science-fiction story." (Robert Silverberg, [introduction] "Trips in Time", 1977)

"The infinite fullness of time brings about everything, he thought: even intelligent lobsters, even a divine octopus." (Robert Silverberg, "Homefaring", 1983)

"Time devours everything. Entire histories vanish. What matters is endurance. The spirit survives and goes onward when the palaces crumble and the kings are forgotten." (Robert Silverberg, "Letters from Atlantis", 1990)

Clive S Lewis - Collected Quotes

"This is called the inductive method. Hypothesis, my dear young friend, establishes itself by a cumulative process: or, to use popular language, if you make the same guess often enough it ceases to be a guess and becomes a Scientific Fact." (Clive S Lewis, "The Pilgrim’s Regress: An Allegorical Apology for Christianity, Reason and Romanticism", 1933)

"If you find my arithmetic correct, then no amount of vapouring about my psychological condition can be anything but a waste of time. If you find my arithmetic wrong, then it may be relevant to explain psychologically how I came to be so bad at my arithmetic, and the doctrine of the concealed wish will become relevant - but only after you have yourself done the sum and discovered me to be wrong on purely arithmetical grounds. It is the same with all thinking and all systems of thought. If you try to find out which are tainted by speculating about the wishes of the thinkers, you are merely making a fool of yourself. You must first find out on purely logical grounds which of them do, in fact, break down as arguments. Afterwards, if you like, go on and discover the psychological causes of the error." (Clive S Lewis, "Bulverism", 1941)

"Humans are amphibians - half spirit and half animal. [...] As spirits they belong to the eternal world, but as animals they inhabit time." (Clive S Lewis, "The Screwtape Letters", 1942)

"The Historical Point of View, put briefly, means that when a learned man is presented with any statement in an ancient author, the one question he never asks is whether it is true. He asks who influenced the ancient writer, and how far the statement is consistent with what he said in other books, and what phase in the writer’s development, or in the general history of thought, it illustrates, and how it affected later writers, and how often it has been misunderstood (specially by the learned man’s colleagues) and what the general course of criticism on it has been for the last ten years, and what is the 'present state of the question'. To regard the ancient writer as a possible source of knowledge - to anticipate that what he said could possibly modify your thoughts or your behavior - this would be rejected as unutterably simple-minded. And since we cannot deceive the whole human race all the time, it is most important thus to cut every generation off from all others; for where learning makes a free commerce between the ages there is always the danger that the characteristic errors of one may be corrected by the characteristic truths of another. But thanks be to our Father and the Historical Point of View, great scholars are now as little nourished by the past as the most ignorant mechanic who holds that 'history is bunk." (C. S. Lewis, "The Screwtape Letters", 1942)

"A sum can be put right: but only by going back till you find the error and working it afresh from that point, never by simply going on." (Clive S Lewis, "The Great Divorce", 1945)

"A world of automata – of creatures that worked like machines – would hardly be worth creating." (Clive S Lewis, "Mere Christianity", 1952)

"It is not impossible that our own Model will die a violent death, ruthlessly smashed by an unprovoked assault of new facts […]." (Clive S Lewis, “The Discarded Image: An Introduction to Medieval and Renaissance Literature”, 1964)

"The laws of thought are also the laws of things: of things in the remotest space and the remotest time." (Clive S Lewis, "Christian Reflections", 1967)

“Education without values, as useful as it is, seems rather to make man a more clever devil.” (Clive S Lewis)

"Of course all children's literature is not fantastic, so all fantastic books need not be children's books. It is still possible, even in an age so ferociously anti-romantic as our own, to write fantastic stories for adults: though you will usually need to have made a name in some more fashionable kind of literature before anyone will publish them." (Clive S Lewis)

John W Campbell Jr. - Collected Quotes

"Can you appreciate the crushing hopelessness it brought to me? I, who love science, who see in it, or have seen in it, the salvation, the raising of mankind - to see those wondrous machines, of man’s triumphant maturity, forgotten and misunderstood. The wondrous, perfect machines that tended, protected, and cared for those gentle, kindly people who had - forgotten." (John W Campbell Jr, "Twilight", 1934)

"No average mind can either understand or enjoy science-fiction; it takes an amount of imagination beyond the average man." (John W. Campbell Jr, "Science-Fiction", 1938)

"Too darned good a machine can be a menace, not a help." (John W. Campbell Jr, [introduction] "Cloak of Aesir", 1951)

"Science fiction is the literature of the Technological Era. It, unlike other literatures, assumes that change is the natural order of things, that there are goals ahead larger than those we know." (John W Campbell Jr, [introduction to "The Astounding Science Fiction Anthology"] 1952)

"Science is not a sacred cow - but there are a large number of would-be sacred cowherds busily devoting quantities of time, energy and effort to the task of making it one, so they can be sacred cowherds." (John W Campbell Jr, "Prologue to Analog", [introduction] 1962)

"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)

"That group of writings which is usually referred to as 'mainstream literature' is, actually, a special subgroup of the field of science fiction - for science fiction deals with all places in the Universe, and all times in Eternity, so theliterature of here-and-now is, truly, a subset of science fiction." (John W Campbell Jr, [introduction] Analog I, 1963)

Howard P Lovecraft - Collected Quotes

 "I have often wondered if the majority of mankind ever pause to reflect upon the occasionally titanic significance of dreams, and of the obscure world to which they belong. [...] We may guess that in dreams life, matter, and vitality, as the earth knows such things, are not necessarily constant; and that time and space do not exist as our waking selves comprehend them. Sometimes I believe that this less material life is our truer life, and that our vain presence on the terraqueous globe is itself the secondary or merely virtual phenomenon." (Howard P Lovecraft, "Beyond the Wall of Sleep", 1919)

"Ocean is more ancient than the mountains, and freighted with the memories and the dreams of Time." (Howard P Lovecraft, "The White Ship", 1919)

"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)

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age." (Howard P Lovecraft, "The Call of Cthulhu", 1926)

"There is a sense of spectral whirling through liquid gulfs of infinity, of dizzying rides through reeling universes on a comet’s tail, and of hysterical plunges from the pit to the moon and from the moon back again to the pit, all livened by a cachinnating chorus of the distorted, hilarious elder gods and the green, bat-winged mocking imps of Tartarus." (Howard P Lovecraft, "The Call of Cthulhu", 1928)

"Non- Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of Gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension." (Howard P Lovecraft, "The Dreams in the Witch House and Other Weird Stories", 1933)

"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)

"Men of broader intellect know that there is no clear distinction between the real and the unreal, that things appear as they seem only by virtue of the delicate physical and mental instruments through which we perceive them." (Howard P Lovecraft)

Alfred E van Vogt - Collected Quotes

"There is nothing more futile than arguing with someone who has no basis for his opinions but a vague backlash of emotions." (Alfred E van Vogt, "The Gryb", 1940)

"What system do men follow if not that of logic?" (Algfred E van Vogt, "Vault of the Beast", 1940)

"He knew where the seesaw would stop. It would end in the very remote past, with the release of the stupendous temporal energy he had been accumulating with each of those monstrous swings. He would not witness, but he would cause the formation of the planets." (Alfred E van Vogt, "The Seesaw", 1941)

"Of all the energies in the universe, time is the most potent." (Alfred E van Vogt, "The Seesaw", 1941)

"Amnesia is the best method of escaping from reality." (Alfred E van Vogt, "The Players of Null-A", 1948)

"And the more technically developed a nation or race is, the more cruel, ruthless, predatory, and commercialized its systems tend to become [...]" (Alfred E van Vogt, "The World of Null-A", 1948)

"Words were subtle, and frequently had little connection with the facts they were supposed to represent." (Alfred E van Vogt, "The Players of Null-A", 1948)

"Space was vast, the journeys through it long and lonely, landing always a stimulating experience, with its prospect of new life forms to be seen and studied." (Alfred E van Vogt, "The Monster", 1948)

"It must be that robots predated all other life. It’s the only logical conclusion." (Alfred E van Vogt, "Final Command", 1949)

"When a people lose the courage to resist encroachment on their rights, then they can't be saved by an outside force. Our belief is that people always have the kind of government they want and that individuals must bear the risks of freedom, even to the extent of giving their lives." (Alfred E van Vogt," The Weapon Shops of Isher", 1951)

"Science fiction is a field of writing where, month after month, every printed word implies to hundreds of thousands of people: 'There is change. Look, today's fantastic story is tomorrow's fact.'" (Alfred E van Vogt)

George Orwell - Collected Quotes

"The energy that actually shapes the world springs from emotions - racial pride, leader-worship, religious belief, love of war - which liberal intellectuals mechanically write off as anachronisms, and which they have usually destroyed so completely in themselves as to have lost all power of action." (George Orwell, 1941)

"All animals are equal, but some animals are more equal than others." (George Orwell, "Animal Farm: A Fairy Story", 1945)

"The point is that we are all capable of believing things which we know to be untrue, and then, when we are finally proved wrong, impudently twisting the facts so as to show that we were right. Intellectually, it is possible to carry on this process for an indefinite time: the only check on it is that sooner or later a false belief bumps up against solid reality, usually on a battlefield." (George Orwell, "In Front of Your Nose", Tribune, 1946)

"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them." (George Orwell, "1984", 1949)

"Freedom is the freedom to say that two plus two make four. If that is granted, all else follows" (George Orwell, "1984", 1949)

"How could you communicate with the future? It was of its nature impossible. Either the future would resemble the present, in which case it would not listen to him: or it would be different from it, and his predicament would be meaningless." (George Orwell, "1984", 1949)

"If you want to keep a secret you must also hide it from yourself." (George Orwell, "1984", 1949)

"In general, the greater the understanding, the greater the delusion; the more intelligent, the less sane." (George Orwell, "1984", 1949)

"In the long run, a hierarchal society was only possible on a basis of poverty and ignorance." (George Orwell, "1984", 1949)

"It is impossible to found a civilization on fear and hatred and cruelty. It would never endure." (George Orwell, "1984", 1949)

"The best books [...] are those that tell you what you know already." (George Orwell, "1984", 1949)

"Throughout recorded time, and probably since the end of the Neolithic Age, there have been three kinds of people in the world, the High, the Middle, and the Low. They have been subdivided in many ways, they have borne countless different names, and their relative numbers, as well as their attitude toward one another, have varied from age to age; but the essential structure of society has never altered. Even after enormous upheavals and seemingly irrevocable changes, the same pattern has always reasserted itself, just as a gyroscope will always return to equilibrium, however far it is pushed one way or the other." (George Orwell, "1984", 1949)

"We shall meet in the place where there is no darkness." (George Orwell, "1984", 1949)

"Who controls the past [...] controls the future: who controls the present controls the past." (George Orwell, "1984", 1949)

📓Ray Bradbury - Collected Quotes

"There they go, off to Mars, just for the ride, thinking that they will find a planet like a seer’s crystal, in which to read a miraculous future. What they’ll find, instead, is the somewhat shopworn image of themselves. Mars is a mirror, not a crystal." (Ray Bradbury," A Few Notes on The Martian Chronicles", 1950)

"Coming out of space was like coming out of the most beautiful cathedral they had ever seen." (Ray Bradbury, "The Fire Balloons", 1951)

"The Machine howled. Time was a film run backward. Suns fled and ten million moons fled after them." (Ray Bradbury, "A Sound of Thunder", 1952)

"A book is a loaded gun in the house next door." (Ray Bradbury, "Fahrenheit 451", 1953)

"Books were only one type of receptacle where we stored a lot of things we were afraid we might forget. There is nothing magical in them, at all. The magic is only in what books say, how they stitched the patches of the universe together into one garment for us." (Ray Bradbury, "Fahrenheit 451", 1953)

"The books say nothing! Nothing you can teach or believe. They’re about nonexistent people, figments of imagination, if they’re fiction. And if they’re nonfiction, it’s worse, one professor calling another an idiot, one philosopher screaming down another’s gullet." (Ray Bradbury, "Fahrenheit 451", 1953)

"They are so confident that they will run on forever. But they won’t run on. They don’t know that this is all one huge big blazing meteor that makes a pretty fire in space, but that some day it’ll have to hit." (Ray Bradbury, "Fahrenheit 451", 1953)

"We must all be alike. Not everyone born free and equal, as the Constitution says, but everyone made equal. Each man the image of every other; then all are happy, for there are no mountains to make them cower, to judge themselves against." (Ray Bradbury, "Fahrenheit 451", 1953) 

"What traitors book can be! you think they’re backing you up, and they turn on you." (Ray Bradbury, "Fahrenheit 451", 1953)

"You don't have to burn books to destroy a culture. Just get people to stop reading them." (Ray Bradbury, "Fahrenheit 451", 1953)

"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)

"Life is a magic show or should be if people didn’t go to sleep on each other. Always leave folks with a bit of mystery." (Ray Bradbury, "Colonel Stonesteel’s Genuine Home-Made Truly Egyptian Mummy", 1981)

"That’s all science fiction was ever about. Hating the way things are, wanting to make things different." (Ray Bradbury, "No News, or, What Killed the Dog?", 1994)

"Do you know why teachers use me? Because I speak in tongues. I write metaphors. Every one of my stories is a metaphor you can remember. The great religions are all metaphor. We appreciate things like Daniel and the lion's den, and the Tower of Babel. People remember these metaphors because they are so vivid you can't get free of them and that's what kids like in school." (Ray Bradbury, The Paris Review, [interview] 2010)

"At base, science is no more than an investigation of a miracle we can never explain, and art is an interpretation of that miracle." (Ray Bradbury)

📓William Gibson - Collected Quotes

"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)

"The sky above the port was the color of television, tuned to a dead channel." (William Gibson, "Neuromancer", 1984)

"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)

"He’d used decks in school, toys that shuttled you through the infinite reaches of that space that wasn’t space, mankind’s unthinkably complex consensual hallucination, the matrix, cyberspace, where the great corporate hotcores burned like neon novas, data so dense you suffered sensory overload if you tried to apprehend more than the merest outline." (William Gibson, "Count Zero", 1986)

"Some things you teach yourself to remember to forget." (William Gibson, "Count Zero", 1986)

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

"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)

Rick Delmonico - Collected Quotes

"A quantum of action in a field creates the dimensions it inhabits. Fields contain waves of potential."  (Rick Delmonico, "Fractals all the way down", 2018)

"At every level of the fractal hierarchy, variation enters the system in different ways, so there is no scale invariance. All of the information is stored in the relationships of and in each level in the computational geometry." (Rick Delmonico, "Fractals all the way down", 2018)

"How can unity and infinity share the same space? There is only one way, as a fractal." (Rick Delmonico, "Fractals all the way down", 2018)

"In a fractal nested hierarchy there are an infinite number of boundaries and boundary conditions, this is important because this is where emergence comes from and this is why there are no perfect symmetries."  (Rick Delmonico, "Fractals all the way down", 2018)

"The computational geometry of space/time is fractal. The entire system is interwoven as a fractal and as each series of iterations occur, there is a dithering of sorts because the difference in possibilities can be matastable in many locations in the computation. Each layer of the system computes in a frequency that is probably following the phi ratio. Measurement is always described as ratio and scale may be, in a sense, an illusion. Light appears to be scale invariant and the cutoff frequency may be another illusion. If this is true, everything is fields and particles are just a smaller version of a field." (Rick Delmonico, "Fractals all the way down", 2018)

"The fractal nesting of the relationship between space and time at different scales causes phase transitions as the influence of one force changes with respect to another. From this we get the astonishing variety of behaviors in the material world." (Rick Delmonico, "Fractals all the way down", 2018)

"The particle/wave duality has something to do with the nature of time. Time is intimately linked to information, you cannot separate them. Information moving in time always contains meaning. This meaning has a truth value. There is a dynamic nature to these truth values with application and material expressions. Experience relies on these expressions, it is the perception or division of the expression that creates the experience. How much we are able to understand varies from experience to experience. In the quantum world these expressions have a probability. A fractal probability distribution." (Rick Delmonico, "Fractals all the way down", 2018)

"The structure of reality is a computational geometry that is fractal in nature. Truth is the highest energy state of the system, we are branching out in a fractal pattern into uncertainty. What we value matters, meaning is generated in a nested hierarchy. The intellect will only get you so far, beyond this are things like desire. Desire is a higher level of processing, it is deeper and more nuanced. There is something beyond the emotional realm that I will call spirit, as an organizing principle, spirit has the ability to transcend space and time and generates value and meaning that have harmonious relationships that keep the system going. Without harmony and some principle of organization, time or process would end."  (Rick Delmonico, "Fractals all the way down", 2018)

"There is a fractal nesting of time-like loops in spacetime. Both space and time emerge from a quantum of action in a field. Space and time are united but different. The scale of the dimensions is inversely proportional, as well as the density. The only infinity is one of scale." (Rick Delmonico, "Fractals all the way down", 2018)

"Waves travel according to their dimensionality. The idea is to find agreement in two unrelated fields that point to the same thing, a duality. Waves can't be quantized, interactions among the associated dimensions can. Fractal geometry and levels of description. It is the interaction of forces across scale, with ratio being the only thing that is discrete." (Rick Delmonico, "Fractals all the way down", 2018)

📓James G Ballard - Collected Quotes

"A few moments earlier the water had seemed cool and inviting, but now had become a closed world, the barrier of the surface like a plane between two dimensions." (James G Ballard, "The Drowned World", 1962)

"However selective the conscious mind may be, most biological memories are unpleasant ones, echoes of danger and terror. Nothing endures for so long as fear." (James G Ballard, "The Drowned World", 1962)

"Speculative fantasy, as I prefer to call the more serious fringe of science fiction, is an especially potent method of using one’s imagination to construct a paradoxical universe where dream and reality become fused together, each retaining its own distinctive quality and yet in some way assuming the role of its opposite, and where by an undeniable logic black simultaneously becomes white." (James G Ballard, "Time, Memory, and Inner Space’", 1963)

"It marked the beginning of the giant’s surrender to that all-demanding system of time in which the rest of humanity finds itself, and of which, like the million twisted ripples of a fragmented whirlpool, our finite lives are the concluding products." (James G Ballard, "The Drowned Giant", 1965)

"Our lives today are not conducted in linear terms. They are much more quantified; a stream of random events is taking place." (James G Ballard, [Conversation with George MacBeth on Third Programme - BBC], 1967)

"Everything is becoming science fiction. From the margins of an almost invisible literature has sprung the intact reality of the 20th century." (James G Ballard, "Fictions of Every Kind", 1971)

"The role of the writer today has totally changed - he is now merely one of a huge army of people filling the environment with fictions of every kind. To survive, he must become far more analytic, approaching his subject matter like a scientist or engineer. If he is to produce fiction at all, he must outimagine everyone else, scream louder, whisper more quietly. For the first time in the history of narrative fiction, it will require more than talent to become a writer." (James G Ballard, "Fictions of Every Kind", 1971)

"Even the vagal flushes that seized at my chest seemed extensions of that real world of violence calmed and tamed within our television programmes and the pages of news magazines." (James G Ballard, "Crash", 1973)

"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)

"I would sum up my fear about the future in one word: boring. And that’s my one fear: that everything has happened; nothing exciting or new or interesting is ever going to happen again [...] the future is just going to be a vast, conforming suburb of the soul." (James G Ballard, Re/Search 8–9, [interview with Andrea Juno and V. Vale], 1984)

Viktor Schauberger - Collected Quotes

"In Nature all life is a question of the minutest, but extremely precisely graduated differences in the particular thermal motion within every single body, which continually changes in rhythm with the processes of pulsation. This unique law, which manifests itself throughout Nature's vastness and unity and expresses itself in every creature and organism, is the 'law of ceaseless cycles' that in every organism is linked to a certain time span and a particular tempo. The slightest disturbance of this harmony can lead to the most disastrous consequences for the major life forms. In order to preserve this state of equilibrium, it is vital that the characteristic inner temperature of each of the millions of micro-organisms contained in the macro-organisms be maintained." (Viktor Schauberger," Callum Coats: Water Wizard", 1934)

"This civilization is the work of man, who high-handedly and ignorant of the true workings of Nature, has created a world without meaning or foundation, which now threatens to destroy him, for through his behavior and his activities, he, who should be her master, has disturbed Nature's inherent unity." (Viktor Schauberger, "Callum Coats: Water Wizard", 1934)

"The true foundation of all culture is the knowledge and understanding of water. Water is the ur-substance or ur-cause of all creation and for this reason is the ur-original accumulator, which readily absorbs both earthly and cosmic substances and conveys them to the body in a purely objective form. This must be done in such a way that the ur-attributes will in no way be modified and that change as such can only first come about in the effect, which the organically correctly structured body mediates and imparts. For this reason a good spirit dwells in a healthy body. Conversely a body full of vitality can be created, maintained and further developed by healing the inhering spirit." (Viktor Schauberger, 1936)

"All motion consists of two components. One component serves inwardness (internalisation) and the other outwardness (dispersion). Both preconditions for motion regulate the eternal flow of metamorphosis (panta Rhei)." (Viktor Schauberger, "Callum Coats: Energy Evolution", Implosion Magazine No. 57, 2000)

"If we wish to influence our own life in a particular direction, which is constantly threatened by the danger of the emergence of alien life-forms, and protect it from deterioration, then we must either allow Nature to rule or, if we wish to intervene, we must first acquaint ourselves with the simplest principles of life." (Viktor Schauberger, "Callum Coats: Energy Evolution", Implosion Magazine No. 86, 2000)

"We must look into unknown dimensions, into Nature, into that incalculable and imponderable life, whose carrier and mediator, the blood of the Earth that accompanies us steadfastly from the cradle to the grave, is water." (Viktor Schauberger, "Callum Coats: Energy Evolution", Implosion Magazine No. 103, 2000)

"Naturally moving water augments itself. It improves its quality and matures considerably. Its boiling and freezing points change, and wise Nature makes use of this phenomenon to raise water, without using pumping equipment, to the highest mountain peaks, to appear as mountain springs. This conception of raising water is not to be taken literally, since in this context it is concerned with the natural process of propagation and purification. This in turn helps towards the expansion of air by creating an air cover, which serves to develop a higher form of life." (Viktor Schauberger)

"Nothing falls entirely! Nothing dies away completely! Nothing can totally deprive another of its rights! On the contrary, the deeper the fall, the higher the reactive upswing!" (Viktor Schauberger, "Callum Coats: The Fertile Earth") 

"Our primeval Mother Earth is an organism that no science in the world can rationalize. Everything on her that crawls and flies is dependent upon her and all must hopelessly perish if that Earth dies that feeds us." (Viktor Schauberger)

David Bohm - Collected Quotes

"The principle of complementarity states that no single model is possible which could provide a precise and rational analysis of the connections between these phenomena [before and after measurement]. In such a case, we are not supposed, for example, to attempt to describe in detail how future phenomena arise out of past phenomena. Instead, we should simply accept without further analysis the fact that future phenomena do in fact somehow manage to be produced, in a way that is, however, necessarily beyond the possibility of a detailed description. The only aim of a mathematical theory is then to predict the statistical relations, if any, connecting the phenomena." (David Bohm, "A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables", 1952)

"Indeed, the laws of chance are just as necessary as the causal laws themselves." (David Bohm, "Causality and Chance in Modern Physics", 1957)

"We have reversed the usual classical notion that the independent 'elementary parts' of the world are the fundamental reality, and that the various systems are merely particular contingent forms and arrangements of these parts. Rather, we say that inseparable quantum interconnectedness of the whole universe is the fundamental reality, and that relatively independent behaving parts are merely particular and contingent forms within this whole." (David Bohm, "On the Intuitive Understanding of Nonlocality as Implied by Quantum Theory", Foundations of Physics Vol 5 (1), 1975)

“Man's general way of thinking of the totality, i.e. his general world view, is crucial for overall order of the human mind itself. If he thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken and without border (for every border is a division or break) then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole.” (David Bohm, “Wholeness and the Implicate Order”, 1980)

"My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc." (David Bohm,"Wholeness and the Implicate Order? ", 1980) 

"The prevailing trend in modern physics is thus much against any sort of view giving primacy to [...] undivided wholeness of flowing movement. Indeed, those aspects of relativity theory and quantum theory which do suggest the need for such a view tend to be de-emphasized and in fact hardly noticed by most physicists, because they are regarded largely as features of the mathematical calculus and not as indications of the real nature of things." (David Bohm, "Wholeness and the Implicate Order?", 1980)

"Although science literally means ‘knowledge’, the scientific attitude is concerned much more with rational perception through the mind and with testing such perceptions against actual fact, in the form of experiments and observations." (David Bohm & F David Peat, "Science, Order, and Creativity", 1987)

"We haven't worked on ways to develop a higher social intelligence […] We need this higher intelligence to operate socially or we're not going to survive. […] If we don't manage things socially, individual high intelligence is not going to make much difference. [...] Ordinary thought in society is incoherent - it is going in all sorts of directions, with thoughts conflicting and canceling each other out. But if people were to think together in a coherent way, it would have tremendous power." (David Bohm, "New Age Journal", 1989)

📓Terry Pratchett - Collected Quotes

"A stray thought, wandering through the dimensions in search of a mind to harbour it, slid into his brain." (Terry Pratchett, "The Colour of Magic", 1983)

"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)

"Real stupidity beats artificial intelligence every time." (Terry Pratchett, "Hogfather", 1996)

"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)

"It is now known to science that there are many more dimensions than the classical four. Scientists say that these don’t normally impinge on the world because the extra dimensions are very small and curve in on themselves, and that since reality is fractal most of it is tucked inside itself. This means either that the universe is more full of wonders than we can hope to understand or, more probably, that scientists make things up as they go along." (Terry Pratchett, Pyramids, 1989)

"Most people don’t listen. They use the time when someone else is speaking to think of what they’re going to say next. True Listeners have always been revered among oral cultures, and prized for their rarity value." (Terry Pratchett, "Pyramids", 1989)

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

"The gods of the Disc have always been fascinated by humanity’s incredible ability to say exactly the wrong thing at the wrong time." (Terry Pratchett, "Pyramids", 1989)

"science: A way of finding things out and then making them work. Science explains what is happening around us the whole time." (Terry Pratchett, "Wings", 1990)

"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." (Terry Pratchett, "Diggers", 1990)

"The trouble with being a god is that you’ve got no one to pray to." (Terry Pratchett, "Small Gods", 1992)

"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)

"Logic is a wonderful thing but doesn’t always beat actual thought." (Terry Pratchett, "The Last Continent", 1998)

Robert M Axelrod - Collected Quotes

"A cognitive map has only two basic types of elements: concepts and causal beliefs. The concepts are treated as variables, and the causal beliefs are treated as relationships between the variables." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A cognitive map is a particular kind of mathematical model of a person's belief system; in actual practice, cognitive maps are derived from assertions of beliefs. [...] Like all mathematical models, a cognitive map can be useful in two quite distinct ways: as a normative model and as an empirical model. Interpreted as a normative model, a cognitive map makes no claims to reflect accurately how a person deduces new beliefs from old ones, how he makes decisions, and so on, but instead claims to show how he should do these things. Interpreted as an empirical model, a cognitive map claims to indicate how a person actually does perform certain cognitive operations, in the sense that the results of the various operations that are possible with the model do, in fact, correspond to the behavior of the per son who is being modeled." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A cognitive map is a specific way of representing a person's assertions about some limited domain, such as a policy problem. It is designed to capture the structure of the person's causal assertions and to generate the consequences that follow front this structure. […]  a person might use his cognitive map to derive explanations of the past, make predictions for the future, and choose policies in the present." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A cognitive map is designed to capture the structure of the causal assertions of a person with respect to a particular policy domain, and generate the consequences that follow from this structure." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A decision maker must simplify the manifest complexities of the external world. He must be able to construct a manageable representation of the external world so that he can describe and cope with his environment. The use of this representation for the purposes of making reasoned decisions requires some beliefs that link possible choices with potential outcomes." (Robert M Axelrod, "Decision for Neoimperialism: The Deliberations of the British Eastern Committee in 1918", 1976)

"A mathematical model is a tremendous simplification of what it represents. But it does not simplify everything about its object, or there would be nothing left to model. Instead, it simplifies everything that is not to be examined, and leaves in the model what is to be examined." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"Cognitive mapping is one specific approach to belief systems. It focuses on causal beliefs and values and their structural relationships. Cognitive mapping is, therefore especially suitable to the study of the means-ends arguments people use when they try to evaluate the policy alternatives that they perceive are available to them." (Robert Axelrod, "Structure of Decision: The Cognitive Maps of Political Elites", 1976)

"The concepts a person uses are represented as points, and the causal links between these concepts are represented as arrows between these points. This gives a pictorial representation of the causal assertions of a person as a graph of points and arrows. This kind of representation of assertions as a graph will be called a cognitive map. The policy alternatives, all of the various causes and effects, the goals, and the ultimate utility of the decision maker can all be thought of as concept variables, and represented as points in the cognitive map. The real power of this approach ap pears when a cognitive map is pictured in graph form; it is then relatively easy to see how each of the concepts and causal relation ships relate to each other, and to see the overall structure of the whole set of portrayed assertions." (Robert Axelrod, "The Cognitive Mapping Approach to Decision Making" [in "Structure of Decision: The Cognitive Maps of Political Elites"], 1976)

"What cognitive mapping offers is a systematic way to proceed in our search for understanding how others will act. Its real strength (especially as compared to other formal approaches to decision making) is that it is able to employ the concepts of the decision maker who is being predicted, rather than the concepts of the person who is doing the predicting." (Robert Axelrod, "Structure of Decision: The Cognitive Maps of Political Elites", 1976)

"What difference does it make which cognitive map a person has on a policy issue? Why would we want to know about a person's cognitive map? There are two broad answers to these questions. The first is that we want to know about cognitive maps so that we can better understand the decision-making process. The second is that we want to know about cognitive maps so that we can improve the decision-making process." (Robert Axelrod, "Structure of Decision: The Cognitive Maps of Political Elites", 1976)

📓Philip K Dick - Collected Quotes

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

"It’s the highest goal of man - the need to grow and advance [...] to find new things [...] to expand. To spread out, reach areas, experiences, comprehend and live in an evolving fashion. To push aside routine and repetition, to break out of mindless monotony and thrust forward. To keep moving on [...]" (Philip K Dick, "Solar Lottery", 1955)

"A man is morally responsible to his community. That’s a good idea. But his community is also morally responsible to him." (Philip K Dick, "The Man Who Japed", 1956)

"Even if all life on our planet is destroyed, there must be other life somewhere which we know nothing of. It is impossible that ours is the only world; there must be world after world unseen by us, in some region or dimension that we simply do not perceive." (Philip K Dick, "The Man in the High Castle", 1962)

"Sometimes one must try anything, he decided. It is no disgrace. On the contrary, it is a sign of wisdom, of recognizing the situation." (Philip K Dick, "The Man in the High Castle", 1962)

"The paranoid seemed rational. The formal pattern of logical reasoning appeared undisturbed. Underneath, however, the paranoid suffered from the greatest mental disfigurement possible for a human being. He was incapable of empathy, unable to imagine himself in another person’s role. Hence for him others did not actually exist - except as objects in motion that did or did not affect his well-being." (Philip K Dick, "Clans of the Alphane Moon", 1964)

"These machines had become old and worn-out, had begun making mistakes; therefore they began to seem almost human." (Philip K Dick & Ray Nelson, "The Ganymede Takeover", 1967)

"A humanoid robot is like any other machine; it can fluctuate between being a benefit and a hazard very rapidly." (Philip K Dick, "Do Androids Dream of Electric Sheep?", 1968)

"No structure, even an artificial one, enjoys the process of entropy. It is the ultimate fate of everything, and everything resists it." (Philip K Dick, "Galactic Pot-Healer", 1969)

"Becoming what I call, for lack of a better term, an android, means as I said, to allow oneself to become a means, or to be pounded down, manipulated, made into a means without one’s knowledge or consent - the results are the same. But you cannot turn a human into an android if that human is going to break laws every chance he gets. Androidization requires obedience. And, most of all, predictability. It is precisely when a given person’s response to any given situation can be predicted with scientific accuracy that the gates are open for the wholesale production of the android life form." (Philip K Dick, "The Android and the Human", 1972)

"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)

"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)

"Reality is that which when you stop believing in it, it doesn’t go away." (Philip K Dick, "Valis", 1981)

📓James Tiptree Jr - Collected Quotes

"Analogic reasoning works when you have the right reference frame. We need a new one."(James Tiptree Jr, "Mamma Come Home" ["The Mother Ship"], The Worlds of IF Science Fiction, 1968)

"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) 

"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)

"Entropy! The development of reliable knowledge is anti-entropic. Science’s task in a social system is comparable to the function of intelligence in the individual. It holds against disorganization, oscillation, noise, entropy. But we, here - we’ve allied ourselves with an entropic subsystem. We’re not generating structure, we’re helping to degrade the system!" (James Tiptree Jr, "I’m Too Big But I Love to Play", Amazing, 1970)

"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) 

"You can understand why a system would seek information - but why in hell does it offer information? Why do we strive to be understood? Why is a refusal to accept communication so painful?" (James Tiptree Jr, "Ten Thousand Light-Years From Home", 1973)

"In the wastes of nonbeing it is born, flickers out, is born again and holds together, swells and spreads. In lifelessness it lives, against the gray tide of entropy it strives, improbably persists, gathering itself into ever richer complexities until it grows as a swelling wave." (James Tiptree Jr, "She Waits for All Men Born", 1976)

"There're two kinds of people - those who think there are two kinds of people and those who have more sense." (James Tiptree Jr, "Up the Walls of the World", 1978)

Cormac McCarthy - Collected Quotes

"If people knew the story of their lives how many would then elect to live them?" (Cormac McCarthy, "The Crossing", 1994)

"We think we are the victims of time. In reality, the way of the world isn't fixed anywhere. How could that be possible? We are our own journey. And therefore we are time as well. We are the same. Fugitive. Inscrutable. Ruthless." (Cormac McCarthy, "The Crossing", 1994)

"Our waking life's desire to shape the world to our convenience invites all manner of paradox and difficulty." (Cormac McCarthy, "Cities of the Plain", 1998)

"Because the question for me was always whether that shape we see in our lives was there from the beginning or whether these random events are only called a pattern after the fact. Because otherwise we are nothing." (Cormac McCarthy, "All the Pretty Horses", 2010)

"'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)

"A group of evil and aberrant and wholly malicious partial differential equations who had conspired to usurp their own reality from the questionable circuitry of the creator’s brain not unlike the rebellion which Milton describes and to fly their colors as an independent nation unaccountable to God or man alike." (Cormac McCarthy, "Stella Maris", 2022)

"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)

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

 "If the world has a mind then it's all worse than we thought." (Cormac McCarthy, "Stella Maris", 2022)

"The world has created no living thing that it does not intend to destroy." (Cormac McCarthy, "Stella Maris", 2022)