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)

Jean-Baptiste-Joseph Fourier - Direct Perspectives

"It is true that Fourier had the opinion that the principal object of mathematics was public use and the explanation of natural phenomena; but a philosopher like him ought to know that the sole object of the science is the honor of the human spirit and that under this view a problem of [the theory of] numbers is worth as much as a problem on the system of the world." (Carl G J Jacobi [letter to Adrien-Marie Legendre], 1830)

"Nearly fifty years had passed without any progress on the question of analytic representation of an arbitrary function, when an assertion of Fourier threw new light on the subject. Thus a new era began for the development of this part of Mathematics and this was heralded in a stunning way by major developments in mathematical Physics." (Bernhard Riemann, 1854)

"Since Fermat introduced the conception of infinitely small differences between consecutive values of a function and arrived at the principle for finding the maxima and minima, it was maintained by Lagrange, Laplace, and Fourier, that Fermat may be regarded as the first inventor of the differential calculus. This point is not well taken, as will be seen from the words of Poisson, himself a Frenchman, who rightly says that the differential calculus "consists in a system of rules proper for finding the differentials of all functions, rather than in the use which may be made of these infinitely small variations in the solution of one or two isolated problems." (Florian Cajori, "A History of Mathematics", 1893)

"It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment. - judgment, that is, in matters not admitting of certainty - balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service." (Cassius J Keyser, "Lectures on Science, Philosophy and Art", 1908)

"Why are nonlinear systems so much harder to analyze than linear ones? The essential difference is that linear systems can be broken down into parts. Then each part can be solved separately and finally recombined to get the answer. This idea allows a fantastic simplification of complex problems, and underlies such methods as normal modes, Laplace transforms, superposition arguments, and Fourier analysis. In this sense, a linear system is precisely equal to the sum of its parts." (Steven H Strogatz, "Non-Linear Dynamics and Chaos, 1994)

"To understand, how noise is related to scale-freeness, we have to do some mathematics again. Noise is usually characterized by a mathematical trick. The seemingly random fluctuation of the signal is regarded as a sum of sinusoidal waves. The components of the million waves giving the final noise structure are characterized by their frequency. To describe noise, we plot the contribution (called spectral density) of the various waves we use to model the noise as a function of their frequency. This transformation is called a Fourier transformation [...]" (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)

"It has been said that the three most effective problem-solving devices in mathematics are calculus, complex variables, and the Fourier transform." (Peter D Lax & Lawrence Zalcman, "Complex proofs of real theorems", 2012)

"The significance of Fourier’s theorem to music cannot be overstated: since every periodic vibration produces a musical sound (provided, of course, that it lies within the audible frequency range), it can be broken down into its harmonic components, and this decomposition is unique; that is, every tone has one, and only one, acoustic spectrum, its harmonic fingerprint. The overtones comprising a musical tone thus play a role somewhat similar to that of the prime numbers in number theory: they are the elementary building blocks from which all sound is made." (Eli Maor, "Music by the Numbers: From Pythagoras to Schoenberg", 2018)

On Calculus: On Fluxions

"And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?" (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"And yet in the calculus differentialis, which method serves to all the same intents and ends with that of fluxions, our modern analysts are not content to consider only the differences of finite quantities: they also consider the differences of those differences, and the differences of the differences of the first differences. And so on ad infinitum. That is, they consider quantities infinitely less than the least discernible quantity; and others infinitely less than those infinitely small ones; and still others infinitely less than the preceding infinitesimals, and so on without end or limit. Insomuch that we are to admit an infinite succession of infinitesimals, each infinitely less than the foregoing, and infinitely greater than the following. As there are first, second, third, fourth, fifth, &c. fluxions, so there are differences, first, second, third, fourth, &c., in an infinite  progression towards nothing, which you still approach and never arrive at. And (which is most strange) although you should take a million of millions of these infinitesimals, each whereof is supposed infinitely greater than some other real magnitude, and add them to the least given quantity, it shall never be the bigger. For this is one of the modest postulata of our modern mathematicians, and is a cornerstone or ground-work of their speculations."  (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"He who can digest a second or third fluxion, a second or third difference, need not, we think, be squeamish about any point of divinity." (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"The foreign mathematicians are supposed by some, even of our own, to proceed in a manner less accurate, perhaps, and geometrical, yet more intelligible. Instead of flowing quantities and their fluxons, they consider the variable finite quantities as increasing or diminishing by the continual addition or subduction of infinitely small quantities. Instead of the velocities wherewith increments are generated, they consider the increments or decrements themselves, which they call differences, and which are supposed to be infinitely small. The difference of a line is an infinitely little line; of a plane an infinitely little plane. 

"The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature." (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"Newton started out from another principle; and one can say that the metaphysics of this great mathematician on the calculus of fluxions is very exact and illuminating, even though he allowed us only an imperfect glimpse of his thoughts. He never considered the differential calculus as the study of infinitely small quantities, but as the method of first and ultimate ratios, that is to say, the method of finding the limits of ratios. Thus this famous author has never differentiated quantities but only equations; in fact, every equation involves a relation between two variables and the differentiation of equations consists merely in finding the limit of the ratio of the finite differences of the two quantitiescontained in the equation." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"It appears that Fermat, the true inventor of the differential calculus, considered that calculus as derived from the calculus of finite differences by neglecting infinitesimals of higher orders as compared with those of a lower order [...] Newton, through his method of fluxions, has since rendered the calculus more analytical, he also simplified and generalized the method by the invention of his binomial theorem. Leibnitz has enriched the differential calculus by a very happy notation." (Pierre-Simon Laplace, "Exposition du système du monde" ["Exposition of the System of the World"], 1796)

"This great geometrician expresses by the character E the increment of the abscissa; and considering only the first power of this increment, he determines exactly as we do by differential calculus the subtangents of the curves, their points of inflection, the maxima and minima of their ordinates, and in general those of rational functions. We see likewise by his beautiful solution of the problem of the refraction of light inserted in the Collection of the Letters of Descartes that he knows how to extend his methods to irrational functions in freeing them from irrationalities by the elevation of the roots to powers. Fermat should be regarded, then, as the true discoverer of Differential Calculus. Newton has since rendered this calculus more analytical in his Method of Fluxions, and simplified and generalized the processes by his beautiful theorem of the binomial. Finally, about the same time Leibnitz has enriched differential calculus by a notation which, by indicating the passage from the finite to the infinitely small, adds to the advantage of expressing the general results of calculus, that of giving the first approximate values of the differences and of the sums of the quantities; this notation is adapted of itself to the calculus of partial differentials." (Pierre-Simon Laplace, "Essai philosophique sur le calcul des probabilities", 1812)

"Every man is ready to join in the approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton’s Quaternions, and show us wherein it is superior to Newton’s Fluxions?" (Thomas Hill, 'Imagination in Mathematics', North American Review 85, 1857)

"In reality the origin of the notion of derivatives is in the vague feeling of the mobility of things, and of the greater or less speed with which phenomena take place; this is well expressed by the terms fluent and fluxion, which were used by Newton and which we may believe were borrowed from the ancient mathematician Heraclitus." (Émile Picard, [address to the section of Algebra and Analysis] 1904)

On Calculus (-1799)

"[…] it is not necessary that these hypotheses should be true, or even probably; but it is enough if they provide a calculus which fits the observations […]" (Andrew Osiander, "On the Revolutions of the Heavenly Spheres", 1543)

"Even though these are called imaginary, they continue to be useful and even necessary in expressing real magnitudes analytically. For example, it is impossible to express the analytic value of a straight line necessary to trisect a given angle without the aid of imaginaries. Just so it is impossible to establish our calculus of transcendent curves without using differences which are on the point of vanishing, and at last taking the incomparably small in place of the quantity to which we can assign smaller values to infinity." (Gottfried W Leibniz, [letter to Varignon], 1702)

"The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there […] If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little." (Bernard Le Bovier de Fontenelle, "Elements de la géométrie de l'infini", 1727)

"This method of subjecting the infinite to algebraic manipulations is called differential and integral calculus. It is the art of numbering and measuring with precision things the existence of which we cannot even conceive. Indeed, would you not think that you are being laughed at, when told that there are lines infinitely great which form infinitely small angles? Or that a line which is straight so long as it is finite would, by changing its direction infinitely little, become an infinite curve? Or that there are infinite squares, infinite cubes, and infinities of infinities, one greater than another, and that, as compared with the ultimate infinitude, those which precede it are as nought. All these things at first appear as excess of frenzy; yet, they bespeak the great scope and subtlety of the human spirit, for they have led to the discovery of truths hitherto undreamt of." (Voltaire, "Letters on the English", 1733)

"And yet in the calculus differentialis, which method serves to all the same intents and ends with that of fluxions, our modern analysts are not content to consider only the differences of finite quantities: they also consider the differences of those differences, and the differences of the differences of the first differences. And so on ad infinitum. That is, they consider quantities infinitely less than the least discernible quantity; and others infinitely less than those infinitely small ones; and still others infinitely less than the preceding infinitesimals, and so on without end or limit. Insomuch that we are to admit an infinite succession of infinitesimals, each infinitely less than the foregoing, and infinitely greater than the following. As there are first, second, third, fourth, fifth, &c. fluxions, so there are differences, first, second, third, fourth, &c., in an infinite  progression towards nothing, which you still approach and never arrive at. And (which is most strange) although you should take a million of millions of these infinitesimals, each whereof is supposed infinitely greater than some other real magnitude, and add them to the least given quantity, it shall never be the bigger. For this is one of the modest postulata of our modern mathematicians, and is a cornerstone or ground-work of their speculations."  (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"What concerns us most here is the metaphysics of the differential calculus. This metaphysics, of which so much has been written, is even more important and perhaps more difficult to explain than the rules of this calculus themselves: various mathematicians, among them Rolle, who were unable to accept the assumption concerning infinitely small quantities, have rejected it entirely, and have held that the principle was false and capable of leading to error. Yet in view of the fact that all results obtained by means of ordinary Geometry can be established similarly and much more easily by means of the differential calculus, one cannot help concluding that, since this calculus yields reliable, simple, and exact methods, the principles on which it depends must also be simple and certain." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"Those quantities that depend on others in this way, namely, those that undergo a change when others change, are called functions of these quantities. This definition applies rather widely and includes all ways in which one quantity could be determined by another." (Leonhard Euler, "Foundations of differential calculus, with applications to finite analysis and series", 1755)

"I see with much pleasure that you are working on a large work on the integral Calculus [...] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics." (Pierre-Simon Laplace [letter to Sylvestre F Lacroix] 1792)

"It appears that Fermat, the true inventor of the differential calculus, considered that calculus as derived from the calculus of finite differences by neglecting infinitesimals of higher orders as compared with those of a lower order [...] Newton, through his method of fluxions, has since rendered the calculus more analytical, he also simplified and generalized the method by the invention of his binomial theorem. Leibnitz has enriched the differential calculus by a very happy notation." (Pierre-Simon Laplace, "Exposition du système du monde" ["Exposition of the System of the World"], 1796)

On Analysis: On Differentials

"But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not." (Johann I Bernoulli, cca. 1691–1692

"Since the nature of differentials […] consists in their being infinitely small and infinitely changeable up to zero, in being only quantitates evanescentes, evanescentia divisibilia, they will be always smaller than any given quantity whatsoever. In fact, some difference which one can assign between two magnitudes which only differ by a differential, the continuous and imperceptible variability of that infinitely small differential, even at the very point of becoming zero, always allows one to find a quantity less than the proposed difference." (Johann Bernoulli, cca. 1692–1702)

"It is easy to see at first glance that the rule of the differential calculus which consists in equating to zero the differential of the expression of which one seeks a maximum or a minimum, obtained by letting the unknown of that expression vary, gives the same result, because it is the same fundamentally and the terms one neglects as infinitely small in the differential calculus are those which are suppressed as zeroes in the procedure of Fermat. His method of tangents depends on the same principle. In the equation involving the abscissa and ordinate which he calls the specific property of the curve, he augments or diminishes the abscissa by an indeterminate quantity and he regards the new ordinate as belonging both to the curve and to the tangent; this furnishes him with an equation which he treats as that for a case of a maximum or a minimum." (Joseph-Louis Lagrange, "Leçons sur le calcul des fonctions", 1806)

"It was long accepted as a fact that a metrical character could be described by means of a quadratic differential form, but the fact was not clearly understood. Riemann many years ago pointed out that the metrical groundform might, with equal right, essentially, be a homogeneous function of the fourth order in the differentials, or even a function built up in some other way. and that it need not even depend rationally on the differentials. But we dare not stop even at that point." (Hermann Weyl, "Space, Time, Matter", 1922)

"The conception of tensors is possible owing to the circumstance that the transition from one co-ordinate system to another expresses itself as a linear transformation in the differentials. One here uses the exceedingly fruitful mathematical device of making a problem "linear" by reverting to infinitely small quantities." (Hermann Weyl, "Space - Time - Matter", 1922)

"Mathematicians call this combination [space and time] a quadratic form of the differentials of four variables, but we may call it more briefly, with Minkowski, ‘the Universe’." (Émile Borel, "Space and Time", 1926)

"The great advantage of infinitesimals in general and differentials in particular is that they make calculations easier. They provide shortcuts. They free the mind for more imaginative thought, just as algebra did for geometry in an earlier era. […] The only thing wrong with infinitesimals is that they don’t exist, at least not within the system of real numbers." (Steven H Strogatz, "Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics", 2019)

"But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not." (Johann I Bernoulli [attributed]) 

On Analysis: On Infinitesimals (1925-1949)

"Most sciences progress by pursuing nature into the realms of infinitely small, but for astronomy and cosmogony progress lies in the direction of the infinitely great, or, to be more exact, of the unthinkably great." (James Jeans, "Annual Report of the Board of Regents of the Smithsonian Institution" 1926) 

"Number knows no limitations, either from the side of the infinitely great or from the side of the infinitely small, and the facility it offers for generalization is too great for us not to be tempted by it." (Émile Borel, "Space and Time", 1926)

"The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes. ...but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface." (Hans Reichenbach, "The Philosophy of Space and Time", 1928)

"The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes […] but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface." (Hans Reichenbach, "The Philosophy of Space and Time", 1928)

"It is enough for me to contemplate the mystery of conscious life perpetuating itself through all eternity, to reflect upon the marvelous structure of the universe which we dimly perceive, and to try humbly to comprehend an infinitesimal part of the intelligence manifested in nature." (Albert Einstein, "Mein Weltbild" ["My Worldview"], 1931)

"The individual contribution, the work of any single generation, is infinitesimal; the power and glory belong to human society at large, and are the long result of selection, conservation, sacrifice, creation, and renewal - the outcome of endless brave efforts to conserve values and ideas, and to hand them on to posterity, along with physical life itself. Each person is a temporary focus of forces, vitalities, and values that carry back into an immemorial past and that reach forward into an unthinkable future." (Lewis Mumford, "Faith for Living", 1940)

On Analysis: On Infinitesimals (1875-1899)

"For an understanding of Nature, questions about the infinitely large are idle questions. It is different, however, with questions about the infinitely small. Our knowledge of their causal relations depends essentially on the precision with which we succeed in tracing phenomena on the infinitesimal level." (Bernhard Riemann, "Gesammelte Mathematische Werke", 1876)

"To prove that, until this very day, life has never been shown to man as a product of the forces that govern matter, it could be useful the spiritual doctrine which has been very neglected elsewhere, but always finds at least a glorious refuge in your groups. Perhaps you know that in this difficult question concerning the origin of the infinitesimal, I will have brought experimental rigor that has grown weary of contradiction. Referring to the merit, however, we have inherited severe rules of the method from the great experimenters: Galileo, Pascal, Newton and their followers for two centuries." (Louis Pasteur, [Discours de réception de Louis Pasteur] 1882)

"What relation has the life of the individual to the life of the universe? [...] The former is absolutely subordinate, inconceivably infinitesimal compared with the latter. The becoming of the latter bears not the slightest apparent reference to the becoming of the former. [...] The one seems finite, limited, temporal, the other by comparison infinite, boundless, eternal. This disparity has forced itself upon the attention of man ever since his first childlike attempts at thought." (Karl Pearson, "The Ethic of Freethought", 1883) 

"During my slumber I had a dream. I thought I was once more by the side of the Sphere, whose lustrous hue betokened that he had exchanged his wrath against me for perfect placability. We were moving together towards a bright but infinitesimally small Point, to which my Master directed my attention." (Edwin Abbott, "Flatland: A Romance of Many Dimensions", 1884)

"In abstract mathematical theorems the approximation to absolute truth is perfect, because we can treat of infinitesimals. In physical science, on the contrary, we treat of the least quantities which are perceptible." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"A great deal of misunderstanding is avoided if it be remembered that the terms infinity, infinite, zero, infinitesimal must be interpreted in connexion with their context, and admit a variety of meanings according to the way in which they are defined." (George B Mathews, "Theory of Numbers", 1892)

"Accordingly, time logically supposes a continuous range of intensity of feeling. It follows then, from the definition of continuity, that when any particular kind of feeling is present, an infinitesimal continuum of all feelings differing infinitesimally from that, is present." (Charles S Peirce, "The Law of Mind", 1892)

"From these two immediate perceptions, we gain a mediate, or inferential perception of the relation of all four instants. This mediate perception is objectively, or as to the object being represented, spread over the four instants; but subjectively, or as itself the subject of duration, it is completely embraced in the second moment. (The reader will observe that I use the word instant to mean a point in time, and moment to mean an infinitesimal duration." (Charles S Peirce, "The Law of Mind", 1892)

"How can a past idea be present?… it can only be going, infinitesimally past, less past than any assignable past date. We are thus brought to the conclusion that the present is connected to the past by a series of real infinitesimal steps." (Charles S Peirce, "The Law of Mind", 1892)

"The first character of a general idea so resulting is that it is living feeling. A continuum of this feeling, infinitesimal in duration, but still embracing innumerable parts, and also, though infinitesimal, entirely unlimited, is immediately present. And in its absence of boundedness a vague possibility of more than is present is directly felt." (Charles S Peirce, "The Law of Mind", 1892)

"To ignore the subject would be an act of cowardice - an act of cowardice I feel no temptation to commit. To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but to go straight on; to explore up and down, inch by inch, with the taper his reason; to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp. I have nothing to retract. I adhere to my already published statements. Indeed, I might add much thereto. I regret only a certain crudity in those early expositions which, no doubt justly, militated against their acceptance by the scientific world. My own knowledge at that time scarcely extended beyond the fact that certain phenomena new to science had assuredly occurred, and were attested by my own sober senses and, better still, by automatic record. I was like some two-dimensional being who might stand at the singular point of a Riemann's surface, and thus find himself in infinitesimal and inexplicable contact with a plane of existence not his own." (William Crookes, [Presidential Address to the Society for Psychical Research] 1897)

"Consciousness arises with, or out of, and accompanies, these clay compounds called creatures, but it does not cause, nor in any way interfere with, their phenomena. If it were possible to construct artificial clods, chemically as accomplished as philosophers, but without any accompanying consciousness, these soulless mechanisms, without will, feeling, or conscious intelligence, simply acting out their chemical and physical affinities, would not behave otherwise in any infinitesimal particular than the real, conscious meditators on things." (J Howard Moore," Better-World Philosophy: A Sociological Synthesis", 1899)

On Analysis: On Infinitesimals (1750-1799)

"Newton started out from another principle; and one can say that the metaphysics of this great mathematician on the calculus of fluxions is very exact and illuminating, even though he allowed us only an imperfect glimpse of his thoughts. He never considered the differential calculus as the study of infinitely small quantities, but as the method of first and ultimate ratios, that is to say, the method of finding the limits of ratios. Thus this famous author has never differentiated quantities but only equations; in fact, every equation involves a relation between two variables and the differentiation of equations consists merely in finding the limit of the ratio of the finite differences of the two quantitiescontained in the equation." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"What concerns us most here is the metaphysics of the differential calculus. This metaphysics, of which so much has been written, is even more important and perhaps more difficult to explain than the rules of this calculus themselves: various mathematicians, among them Rolle, who were unable to accept the assumption concerning infinitely small quantities, have rejected it entirely, and have held that the principle was false and capable of leading to error. Yet in view of the fact that all results obtained by means of ordinary Geometry can be established similarly and much more easily by means of the differential calculus, one cannot help concluding that, since this calculus yields reliable, simple, and exact methods, the principles on which it depends must also be simple and certain." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"Any change involves at least two conditions, one preceding and one following, which are distinct from one another in such a way that the difference between the former and the latter can be established. Now the law of continuity prohibits the thing which is being changed to transcend abruptly from the former to the latter. It must pass through an intermediate condition which is as little distinct from the previous as from the subsequent one. And because the difference between this intermediate condition and the previous condition can be established still, there must be an intermediate condition between these two as well, and this must continue in the same way, until the difference between the previous condition and the one immediately succeeding it vanishes. As long as the set of these intermediate conditions can be established, every difference between one and the next can be established as well: hence their set must become larger than any given set if these differences shall vanish, and thus we imagine infinitely many conditions where one differs from the next to an infinitely small degree." (Abraham G Kästner, "Anfangsgründe der Analysis des Unendlichen" ["Beginnings of the Analysis of the Infinite"], 1766)

"It is held because of this law in particular, that no change may occur suddenly, but rather that every change always passes by infinitely small stages, of which the trajectory of a point in a curved line provides a first example." (Abraham G Kästner, "Anfangsgründe der Analysis des Unendlichen" ["Beginnings of the Analysis of the Infinite"], 1766)

"When we have grasped the spirit of the infinitesimal method, and have verified the exactness of its results either by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of  shortening and simplifying our proofs." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

"At the time the book of Marquis de l'Hôpital had appeared, and almost all mathematicians began to turn to the new geometry of the infinite [that is, the new infinitesimal calculus], until then little known. The surprising universality of the methods, the elegant brevity of the proofs, the neatness and speed of the most difficult solutions, a singular and unexpected novelty, all attracted the mind and there was in the mathematical world a well marked revolution [une révolution bien marquée." (Bernard Le Bovier de Fontenelle, 1792) 

"The infinitely smallest part of space is always a space, something endowed with continuity, not at all a mere point or the boundary between specified places in space." (Johann G Fichte, "Grundriss des Eigenthümlichen der Wissenschaftslehre in Rücksicht auf das theoretische Vermögen", 1795)

"It appears that Fermat, the true inventor of the differential calculus, considered that calculus as derived from the calculus of finite differences by neglecting infinitesimals of higher orders as compared with those of a lower order [...] Newton, through his method of fluxions, has since rendered the calculus more analytical, he also simplified and generalized the method by the invention of his binomial theorem. Leibnitz has enriched the differential calculus by a very happy notation." (Pierre-Simon Laplace, "Exposition du système du monde" ["Exposition of the System of the World"], 1796)

On Analysis: On Infinitesimals (1700-1749)

"[…] even if someone refuses to admit infinite and infinitesimal lines in a rigorous metaphysical sense and as real things, he can still use them with confidence as ideal concepts (notions ideales) which shorten his reasoning, similar to what we call imaginary roots in the ordinary algebra, for example, √-2." (Gottfried W Leibniz, [letter to Varignon], 1702)

"Of late the speculations about Infinities have run so high, and grown to such strange notions, as have occasioned no small scruples and disputes among the geometers of the present age. Some there are of great note who, not contented with holding that finite lines may be divided into an infinite number of parts, do yet further maintain that each of these infinitesimals is itself subdivisible into an infinity of other parts or infinitesimals of a second order, and so on ad infinitum. These I say assert there are infinitesimals of infinitesimals, etc., without ever coming to an end; so that according to them an inch does not barely contain an infinite number of parts, but an infinity of an infinity of an infinity ad infinitum of parts." (George Berkeley, "The Principles of Human Knowledge', 1710)

"In fact, a similar principle of hardness cannot exist; it is a chimera which offends that general law which nature constantly observes in all its operations; I speak of that immutable and perpetual order, established since the creation of the Universe, that can be called the LAW OF CONTINUITY, by virtue of which everything that takes place, takes place by infinitely small degrees. It seems that common sense dictates that no change can take place at a jump; natura non operatur per saltion; nothing can pass from one extreme to the other without passing through all the degrees in between." (Johann Bernoulli, "Discours sur les Loix de la Communication du Mouvement", 1727)

"The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there […] If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little." (Bernard Le Bovier de Fontenelle, "Elements de la géométrie de l'infini", 1727)

"This method of subjecting the infinite to algebraic manipulations is called differential and integral calculus. It is the art of numbering and measuring with precision things the existence of which we cannot even conceive. Indeed, would you not think that you are being laughed at, when told that there are lines infinitely great which form infinitely small angles? Or that a line which is straight so long as it is finite would, by changing its direction infinitely little, become an infinite curve? Or that there are infinite squares, infinite cubes, and infinities of infinities, one greater than another, and that, as compared with the ultimate infinitude, those which precede it are as nought. All these things at first appear as excess of frenzy; yet, they bespeak the great scope and subtlety of the human spirit, for they have led to the discovery of truths hitherto undreamt of." (Voltaire, "Letters on the English", 1733)

"And yet in the calculus differentialis, which method serves to all the same intents and ends with that of fluxions, our modern analysts are not content to consider only the differences of finite quantities: they also consider the differences of those differences, and the differences of the differences of the first differences. And so on ad infinitum. That is, they consider quantities infinitely less than the least discernible quantity; and others infinitely less than those infinitely small ones; and still others infinitely less than the preceding infinitesimals, and so on without end or limit. Insomuch that we are to admit an infinite succession of infinitesimals, each infinitely less than the foregoing, and infinitely greater than the following. As there are first, second, third, fourth, fifth, &c. fluxions, so there are differences, first, second, third, fourth, &c., in an infinite  progression towards nothing, which you still approach and never arrive at. And (which is most strange) although you should take a million of millions of these infinitesimals, each whereof is supposed infinitely greater than some other real magnitude, and add them to the least given quantity, it shall never be the bigger. For this is one of the modest postulata of our modern mathematicians, and is a cornerstone or ground-work of their speculations."  (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities? [...] The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature." (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

"The foreign mathematicians are supposed by some, even of our own, to proceed in a manner less accurate, perhaps, and geometrical, yet more intelligible. Instead of flowing quantities and their fluxons, they consider the variable finite quantities as increasing or diminishing by the continual addition or subduction of infinitely small quantities. Instead of the velocities wherewith increments are generated, they consider the increments or decrements themselves, which they call differences, and which are supposed to be infinitely small. The difference of a line is an infinitely little line; of a plane an infinitely little plane. They suppose finite quantities to consist of parts infinitely little, and curves to be polygons, whereof the sides are infinitely little, which by the angles they make one with another determine the curvity of the line. Now to conceive a quantity infinitely small, that is, infinitely less than any sensible or imaginable quantity, or than any the least finite magnitude is, I confess, above my capacity. But to conceive a part of such infinitely small quantity that shall be still infinitely less than it, and consequently though multiplied infinitely shall never equal the minutest finite quantity, is, I suspect, an infinite difficulty to any man whatsoever; and will be allowed such by those who candidly say what they think; provided they really think and reflect, and do not take things upon trust." (George Berkeley, "The Analyst: A Discourse Addressed to an Infidel Mathematician...", 1734)

On Analysis: On Infinitesimals (2000-)

"[…] all roads in mathematics lead to infinity. At any rate, most of the attempts to do the impossible have called upon infinity in one way or another: not necessarily the infinitely large, not necessarily the infinitely small, but certainly the infinitely many." (John Stillwell, "Yearning for the impossible: the surpnsing truths of mathematics", 2006)

"The mathematician's circle, with its infinitely thin circumference and a radius that remains constant to infinitely many decimal places, cannot take physical form. If you draw it in sand, as Archimedes did, its boundary is too thick and its radius too variable." (Ian Stewart, "Letters to a Young Mathematician", 2006)

"Within a few decades of its discovery, the fantasy of infinitesimals had completely overpowered the honest method of exhaustion by joining forces with algebra to form an infinitesimal calculus - a symbolism for solving problems about curves by routine calculations, like those already known for the geometry of straight lines. The calculus, as we know it today, is perhaps the most powerful mathematical tool ever invented, yet it originated in the dream world of infinitesimals. We look at these strange origins in the next section." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics", 2006)

"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"Probability is often expressed using large but finite numbers: ‘one in a thousand’, ‘one in a million’. But perhaps the probability of life, intelligent life, appearing somewhere in our universe is infinitesimal. If so, a universe would need infinitely many planets to produce even a finite number of civilisations (i.e., one)." (Daniel Tammet, "Thinking in Numbers" , 2012)

"One of the remarkable features of these complex systems created by replicator dynamics is that infinitesimal differences in starting positions create vastly different patterns. This sensitive dependence on initial conditions is often called the butterfly-effect aspect of complex systems - small changes in the replicator dynamics or in the starting point can lead to enormous differences in outcome, and they change one’s view of how robust the current reality is. If it is complex, one small change could have led to a reality that is quite different." (David Colander & Roland Kupers, "Complexity and the art of public policy : solving society’s problems from the bottom up", 2014)

"In the applications of mathematics, infinitesimal quantities are often considered as variable points on the real number line. Cauchy took this viewpoint by defining an infinitesimal to be a variable quantity that becomes arbitrarily small. In modern notation, this idea can be represented as a null sequence, which is simply a sequence that tends to zero." (Ian Stewart & David Tall,"The Foundations of Mathematics" 2nd Ed., 2015)

"Newton explained naturally occurring phenomena, such as gravity and the movement of the planets, using a combination of Greek geometry and symbolic algebra to build his ideas in the calculus. Leibniz imagined quantities that could be infinitesimally small and produced a powerful symbolism for the calculus that has stood the test of time, despite widespread concerns about its logical foundation. Later giants in mathematical development focused on different aspects. Euler manipulated symbols algebraically using power series and complex numbers, and Cauchy imagined infinitesimals geometrically as variable quantities on the line or in the plane that become arbitrarily small. His approach led to major advances, using a blend of visual and symbolic methods in real and complex analysis, but it also generated significant criticism about the precise meaning. The critics had a point: the meaning had not then been fully worked out. What prevailed was more an act of faith, that everything would work out much as it always had done." (Ian Stewart & David Tall,"The Foundations of Mathematics" 2nd Ed., 2015)

"Calculus is the study of things that are changing. It is difficult to make theories about things that are always changing, and calculus accomplishes it by looking at infinitely small portions, and sticking together infinitely many of these infinitely small portions." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"But in another way infinitesimals were not like imaginaries. While it is true that imaginaries are not part of the ordinary number system, that system can easily be enlarged to accommodate them – for example, by defining imaginaries as ordered pairs of ordinary numbers, as Hamilton did in 1835. It is not nearly as easy, or convenient, to enlarge the number system to include infinitesimals. It was not even known to be possible until the twentieth century, long after mathematicians had decided that it was better to avoid infinitesimals the way Euclid and Archimedes avoided infinity." (John Stillwell, "A Concise History of Mathematics for Philosophers", 2019) 

"Infinitesimals were a bit like imaginary numbers. They seemed to contradict accepted principles – just as imaginaries contradicted the principle that squares are positive, infinitesimals contradicted the Archimedean axiom for geometric quantities, [...] yet they enabled calculations that were otherwise difficult or impossible. For mathematicians of the seventeenth and eighteenth centuries this was generally good enough reason to accept them." (John Stillwell, "A Concise History of Mathematics for Philosophers", 2019) 

On Analysis: On Infinitesimals (1800-1874)

"It is easy to see at first glance that the rule of the differential calculus which consists in equating to zero the differential of the expression of which one seeks a maximum or a minimum, obtained by letting the unknown of that expression vary, gives the same result, because it is the same fundamentally and the terms one neglects as infinitely small in the differential calculus are those which are suppressed as zeroes in the procedure of Fermat. His method of tangents depends on the same principle. In the equation involving the abscissa and ordinate which he calls the specific property of the curve, he augments or diminishes the abscissa by an indeterminate quantity and he regards the new ordinate as belonging both to the curve and to the tangent; this furnishes him with an equation which he treats as that for a case of a maximum or a minimum." (Joseph-Louis Lagrange, "Leçons sur le calcul des fonctions", 1806)

"What should one understand by ∫ ϕx · dx for x = a + bi? Obviously, if we want to start from clear concepts, we have to assume that x passes from the value for which the integral has to be 0 to x = a + bi through infinitely small increments (each of the form x = a + bi), and then to sum all the ϕx · dx. Thereby the meaning is completely determined. However, the passage can take placein infinitely many ways: Just like the realm of all real magnitudes can be conceived as an infinite straight line, so can the realm of all magnitudes, real and imaginary, be made meaningful by an infinite plane, in which every point, determined by abscissa = a and ordinate = b, represents the quantity a+bi. The continuous passage from one value of x to another a+bi then happens along a curve and is therefore possible in infinitely many ways. I claim now that after two different passages the integral ∫ ϕx · dx acquires the same value when ϕx never becomes equal to ∞ in the region enclosed by the two curves representing the two passages." (Carl F Gauss, [letter to Bessel] 1811)

"This great geometrician expresses by the character E the increment of the abscissa; and considering only the first power of this increment, he determines exactly as we do by differential calculus the subtangents of the curves, their points of inflection, the maxima and minima of their ordinates, and in general those of rational functions. We see likewise by his beautiful solution of the problem of the refraction of light inserted in the Collection of the Letters of Descartes that he knows how to extend his methods to irrational functions in freeing them from irrationalities by the elevation of the roots to powers. Fermat should be regarded, then, as the true discoverer of Differential Calculus. Newton has since rendered this calculus more analytical in his Method of Fluxions, and simplified and generalized the processes by his beautiful theorem of the binomial. Finally, about the same time Leibnitz has enriched differential calculus by a notation which, by indicating the passage from the finite to the infinitely small, adds to the advantage of expressing the general results of calculus, that of giving the first approximate values of the differences and of the sums of the quantities; this notation is adapted of itself to the calculus of partial differentials." (Pierre-Simon Laplace, "Essai philosophique sur le calcul des probabilities", 1812)

"[…] a function of the variable x will be continuous between two limits a and b of this variable if between two limits the function has always a value which is unique and finite, in such a way that an infinitely small increment of this variable always produces an infinnitely small increment of the function itself." (Augustin-Louis Cauchy, "Mémoire sur les fonctions continues" ["Memoir on continuous functions"], 1844)

"If they [mathematicians] find a quantity greater than any finite number of the assumed units, they call it infinitely great; if they find one so small that its every finite multiple is smaller than the unit, they call it infinitely small; nor do they recognise any other kind of infinitude than these two, together with the quantities derived from them as being infinite to a higher order of greatness or smallness, and thus based after all on the same idea." (Bernard Bolzano, "Paradoxien des Unedlichen" ["Paradoxes of the Infinite"], 1851)

"As professor in the Polytechnic School [autumn of 1858] in Zurich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt, more keenly than ever before, the lack of a really scientific foundation for arithmetic. In discussing the notion of the approach of a variable magnitude to a fixed limiting value, and especially in proving the theorem that every magnitude which grows continually, but not beyond all limits, must certainly approach a limiting value, I had recourse to geometric evidences. Even now such resort to geometric intuition in a first presentation of the differential calculus, I regard as exceedingly useful, from the didactic standpoint, and indeed indispensable, if one does not wish to lose too much time. But that this form of introduction into the differential calculus can make no claim to being scientific, no one will deny. For myself this feeling of dissatisfaction was so overpowering that I made the fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis." (Richard Dedekind," Stetigkeit und irrationale Zahlen", 1872) 

"The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner. Among these, for example, belongs the above mentioned theorem, and a more careful investigation convinced me that this theorem, or any one equivalent to it, can be regarded in some way as a sufficient basis for infinitesimal analysis. It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. I succeeded Nov. 24, 1858." (Richard Dedekind," Stetigkeit und irrationale Zahlen", 1872) 

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

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

"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)

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

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

"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)

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

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

"It does take great maturity to understand that the opinion we are arguing for is merely the hypothesis we favor, necessarily imperfect, probably transitory, which only very limited minds can declare to be a certainty or a truth." (Milan Kundera, "Encounter", 2009)

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

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

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)

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

"Experience is the child of Thought, and Thought is the child of Action. We cannot learn men from books." (Benjamin Disraeli, "Vivian Grey", 1826)

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

"If a book were written all in numbers, it would be true. It would be just. Nothing said in words ever came out quite even. Things in words got twisted and ran together, instead of staying straight and fitting together. But underneath the words, at the center, like the center of the Square, it all came out even. Everything could change, yet nothing would be lost. If you saw the numbers you could see that, the balance, the pattern. You saw the foundations of the world. And they were solid." (Ursula K Le Guin, "The Dispossessed: An Ambiguous Utopia", 1974)

"Only library books speak with such wordless eloquence of the power good stories hold over us." (Stephen King, "Salem's Lot", 1975)

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

"No book, however good, can survive a hostile reading." (Orson Scott Card, "Ender’s Game", 1985)

"The book designer strives for perfection; yet every perfect thing lives somewhere in the neighborhood of dullness and is frequently mistaken for it by the insensitive." (Jan Tschichold, "The form of the book: essays on the morality of good design", 1991)

"There are no stories without meaning. And I am one of those men who can find it even when others fail to see it. Afterwards the story becomes the book of the living, like a blaring trumpet that raises from the tomb those who have been dust for centuries." (Umberto Eco, "Baudolino", 2000)

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

"[...] out of monuments, names, words, proverbs, traditions, private records and evidences, fragments of stories, passages of books, and the like, we do save and recover somewhat from the deluge of time." (Francis Bacon) 

"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)

Olaf Stapledon - Collected Quotes

"Great are the stars, and man is of no account of them." (Olaf Stapledon, "Last and First Men: A Story of the Near and Far Future", 1930)

"Man himself, at the very least, is music, a brave theme that makes music also of its vast accompaniment, its matrix of storms and stars. Man himself in his degree is eternally a beauty in the eternal form of things. It is very good to have been man. And so we may go forward together with laughter in our hearts, and peace, thankful for the past, and for our own courage. For we shall make after all a fair conclusion to this brief music that is man." (Olaf Stapledon, "Last and First Men: A Story of the Near and Far Future", 1930)

"Presently nothing was left in the whole cosmos but darkness and the dark whiffs of dust that once were galaxies." (Olaf Stapledon, "Last and First Men: A Story of the Near and Far Future", 1930)

"This is the goal of all living, that the cosmos may be known, and admired, and that it may be crowned with further beauties. Nowhere and at no time, so far as we can tell, at least within our own galaxy, has the adventure reached further than in ourselves. And in us, what has been achieved is but a minute beginning. But it is a real beginning." (Olaf Stapledon, "Last and First Men: A Story of the Near and Far Future", 1930)

"All this long human story, most passionate and tragic in the living, was but an unimportant, a seemingly barren and negligible effort, lasting only for a few moments in the life of the galaxy. When it was over, the host of the planetary systems still lived on, with here and there a casualty, and here and there among the stars a new planetary birth, and here and there a fresh disaster." (Olaf Stapledon, "Star Maker", 1937)

"In such a universe as this what significance could there be in our fortuitous, our frail, our evanescent community?" (Olaf Stapledon, "Star Maker", 1937)

"In that instant when I had seen the blazing star that was the Star Maker, I had glimpsed, in the very eye of that splendour, strange vistas of being; as though in the depths of the hypercosmical past and the hypercosmical future also, yet coexistent in eternity, lay cosmos beyond cosmos." (Olaf Stapledon, "Star Maker", 1937)

"In the tide of these wild thoughts we checked our fancy, remembering that only on the rare grains called planets can life gain foothold, and that all this wealth of restless jewels was but a waste of fire." (Olaf Stapledon, "Star Maker", 1937)

"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)

"To say that the cosmos was expanding is equally to say that its members were contracting. The ultimate centers of power, each at first coincident with the punctual cosmos, themselves generated the cosmical space by their disengagement from each other." (Olaf Stapledon, "Star Maker", 1937)

"The expansion of the whole cosmos was but the shrinkage of all its physical units and of the wavelengths of light." (Olaf Stapledon, "Star Maker", 1937)

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

"The universe, or the maker of the universe, must be indifferent to the fate of worlds. That there should be endless struggle and suffering and waste must ofcourse be accepted; and gladly, for these were the very soil in which the spiritgrew. But that all struggle should be finally, absolutely vain, that a wholeworld of sensitive spirits should fail and die, must be sheer evil. In my horrorit seemed to me that Hate must be the Star Maker." (Olaf Stapledon, "Star Maker", 1937)

"When the cosmos wakes, if ever she does, she will find herself not the single beloved of her maker, but merely a little bubble adrift on the boundless and bottomless ocean of being." (Olaf Stapledon, "Star Maker", 1937)

"Is it credible that our world should have two futures? I have seen them. Two entirely distinct futures lie before mankind, one dark, one bright; one the defeat of all man’s hopes, the betrayal of all his ideals, the other their hardwon triumph." (Olaf Stapledon, "Darkness and the Light", 1942)

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

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

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

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

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

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

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

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

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

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

On Literature: About Mathematicians (From Fiction to Science-Fiction)

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

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

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

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

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

Brian W Aldiss - Collected Quotes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

"Neither mathematics nor death ever makes a mistake." (Yevgeny Zamiatin, "We", 1924)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

George Zebrowski - Collected Quotes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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