Quotes about inverse (132 quotes) | Quotes of famous people

“In general, complexity and precision bear an inverse relation to one another in the sense that, as the complexity of a problem increases, the possibility of analysing it in precise terms diminishes. Thus 'fuzzy thinking' may not be deplorable, after all, if it makes possible the solution of problems which are much too complex for precise analysis.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Zadeh (1972) "Fuzzy languages and their relation to human intelligence". in: Proceedings of the International Conference Man and Computer, Bordeaux, France. Basel: S. Karger, pp. 130-165. cited in Gaines (1976) "Foundations of fuzzy reasoning" in: International Journal of Man-Machine Studies 8(6), p. 624
1970s

Problem , Thinking , Sense

“My happiness grows in direct proportion to my acceptance, and in inverse proportion to my expectations.”

Michael J. Fox (1961) Canadian-American actor

Happy , Happiness

“Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion. This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide the necessity of the atmospheric medium for the transmission of sonorous vibrations; and we may conceive of the possibility of determining by experiment the duration of the propagation, in the air, and then through other media; but the general laws of the vibrations of sonorous bodies escape immediate observation. We should know almost nothing of the whole case if the mathematical theory did not come in to connect the different phenomena of sound, enabling us to substitute for direct observation an equivalent examination of more favorable cases subjected to the same law. For instance, when the analysis of the problem of vibrating chords has shown us that, other things being equal, the number of oscillations is hi inverse proportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law enables us to direct our attention to very slow vibrations. The same substitution is at our command in many cases in which it is less direct.”

Auguste Comte (1798–1857) French philosopher

Bk. 3, chap. 4; as cited in: Moritz (1914, 240)
System of positive polity (1852)

Law , Way , Mathematics , Question

“Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.”

William Osler (1849–1919) Canadian pathologist, physician, educator, bibliophile, historian, author, cofounder of Johns Hopkins Hospi…

"Teaching and Thinking" in The Montreal Medical Journal (1895).

Education , Sense

“The degree of one's emotion varies inversely with one's knowledge of the facts – the less you know the hotter you get.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Attributed to Russell in Distilled Wisdom (1964) by Alfred Armand Montapert, p. 145
1960s

Knowledge

“My friend Peter Schmidt used to talk about ‘not doing the things that nobody had ever thought of not doing’, which is an inverse process – where you leave out an assumption that everybody has always made and see what happens (e. g. music has to be made of intentionally produced sounds was the assumption that Cage left out). In that version of this process, you discover a value in the absence of something – in fact you discover that the absence of something is the revelation of something else (Buñuel, the film-maker, said, "Every object conceals another"”

Brian Eno (1948) English musician, composer, record producer and visual artist

a message that I often relay in the studio when overdubbing starts).
December 15, 1995, p. 178
A Year With Swollen Appendices (1996)

Music

“A promise is binding in the inverse ratio of the numbers to whom it is made.”

Thomas De Quincey book Confessions of an English Opium-Eater

Appendix.
Confessions of an English Opium-Eater (1822-1856)

“If our Bodily Life is a burning, our Spiritual Life is a being burnt, a Combustion (or, is precisely the inverse the case?); Death, therefore, perhaps a Change of Capacity.”

Novalis (1772–1801) German poet and writer

Novalis (1829)

Life , Death , Change

“I tend to follow a very nocturnal sort of existence mainly because I don't much care for sunlight. Bright colors of any kind depress me, in fact. And my moods are more or less inversely related to the clarity of the sky, on any given day. A matter of fact, my private motto has always been that behind every silver lining there is a cloud.”

Glenn Gould (1932–1982) Canadian pianist

transcribed from The Life and Times of Glenn Gould

Color , Mood

“In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposition in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

(ca. 1716) A Catalogue of the Portsmouth Collection of Books and Papers Written by Or Belonging to Sir Isaac Newton https://books.google.com/books?id=3wcjAAAAMAAJ&pg=PR18 (1888) Preface
Also partially quoted in Sir Sidney Lee (ed.), The Dictionary of National Biography Vol.40 http://books.google.com/books?id=NycJAAAAIAAJ (1894)

Books , Age , Thinking , Winter

“Bureaucracy and social harmony are inversely proportional to each other.”

Leon Trotsky book The Revolution Betrayed

Source: The Revolution Betrayed (1936), p. 41

“If in all ideology men and their circumstances appear upside down as in a camera obscura, this phenomenon arises just as much from their historical life-process as the inversion of objects on the retina does from their physical life-process.”

Karl Marx book The German Ideology

The German Ideology (1845/46)
Context: The fact is, therefore, that definite individuals who are productively active in a definite way enter into these definite social and political relations. Empirical observation must in each separate instance bring out empirically, and without any mystification and speculation, the connection of the social and political structure with production. The social structure and the state are continually evolving out of the life-process of definite individuals, but of individuals, not as they appear in their own or other people's imagination, but as they really are; i. e. as they are effective, produce materially, and are active under definite material limits, presuppositions and conditions independent of their will.
The production of ideas, of conceptions, of consciousness, is at first directly interwoven with the material activity and the material intercourse of men, the language of real life. Conceiving, thinking, the mental intercourse of men, appear at this stage as the direct efflux of their material behaviour. The same applies to mental production as expressed in the language of the politics, laws, morality, religion, metaphysics of a people. Men are the producers of their conception, ideas, etc. — real, active men, as they are conditioned by a definite development of their productive forces and of the intercourse corresponding to these, up to its furthest forms. Consciousness can never be anything else than conscious existence, and the existence of men is their actual life-process. If in all ideology men and their circumstances appear upside down as in a camera obscura, this phenomenon arises just as much from their historical life-process as the inversion of objects on the retina does from their physical life-process.

Life , Men , Appearance

“The severity of the itch is inversely proportional to the ability to reach it.” – Chloe Traeger”

Jill Shalvis (1963) American writer

Source: Head Over Heels

“There is no inverse relationship between freedom and security. Less of one does not lead to more of the other. People with no rights are not safe from terrorist attack.”

Molly Ivins (1944–2007) American journalist

People , Freedom

“Researchers from Britain's Keele University have found that swearing after an injury may help alleviate pain. Evidently, the pain that you feel is inversely proportional to the number of middle names you give Jesus.”

Stephen Colbert (1964) American political satirist, writer, comedian, television host, and actor

Pain , Feeling , Universe , Help

“It was a distorted form of inverse logic: If hopes never come true, then hope for what you don't want.”

Amy Tan The Hundred Secret Senses

Source: The Hundred Secret Senses

Hope

“I smiled back, the importance of manners, my mother always said, is inversely related to how inclined one is to use them, or, in other words, sometimes politeness is all that stands between oneself and madness.”

Nicole Krauss book Great House

Source: Great House

Smile , Madness

“I have long held the opinion that the amount of noise that anyone can bear undisturbed stands in inverse proportion to his mental capacity and therefore be regarded as a pretty fair measure of it.”

Arthur Schopenhauer (1788–1860) German philosopher

“Hope and reality lie in inverse proportions, inside the walls of a hospital… Doubt is like dye. Once is spreads into the fabric of excuses you've woven, you'll never get rid of the stain.”

Jodi Picoult book Lone Wolf

Source: Lone Wolf

Lie , Hope , Reality

“Assigning central importance to the aesthetic in human experience may seem to be a radical inversion, placing what is usually considered secondary and peripheral at the center of the human world as its nourishing source. Isn’t this an ingenuous simplification of the vast range and complexity of experience?”

Arnold Berleant (1932) American philosopher

Sensibility and Sense: The Aesthetic Transformation of the Human World (2010), Introduction

World

“By induction we gain no certain knowledge; but by observation, and the inverse use of deductive reasoning, we estimate the probability that an event which has occurred was preceded by conditions of specified character, or that such conditions will be followed by the event. …I have no objection to use the words cause and causation, provided they are never allowed to lead us to imagine that our knowledge of nature can attain to certainty. …We can never recur too often to the truth that our knowledge of the laws and future events of the external world are only probable.”

William Stanley Jevons (1835–1882) English economist and logician

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, pp. 257, 260 & 271

Truth , World , Law , Imagination

“But now, as throughout history, financial capacity and political perspicacity are inversely correlated. Long run salvation by men of business has never been highly regarded if it means disturbance of orderly life and convenience in the present. So inaction will be advocated in the present even though it means deep trouble in the future. Here, at least equally with communism, lies the threat to capitalism. It is what causes men who know that things are going quite wrong to say that things are fundamentally sound.”

John Kenneth Galbraith book The Great Crash, 1929

Source: The Great Crash, 1929 (1954 and 1997 https://openlibrary.org/books/OL25728842M/The_Great_Crash_1929), Chapter X, Cause and Consequence, p. 199

Life , Men , History , Communication

“The approach that dominates organizational theory, teaching, and practice for most of the twentieth century looked at organizations from the top-down, starting with a view of the CEO as the "leader" who shapes the organization's strategy, structure, culture, and performance potential. The nature of work and the role of the workforce enter the analysis much later, after considerations of technology and organization design have been considered. However, if the key source of value in the twenty-first-century organization is to be derived from the workforce itself, an inversion of the dominant approach will be needed. The new perspective will start not at the top of the organization, but at but at the front lines, with people and the work itself — which is where value is created. Such an inversion will lead to a transformation in the management and organization of work workers, and knowledge.”

Thomas A. Kochan (1947) American academic

Source: "Beyond McGregor’s Theory Y", 2002, p. 2: introduction; Republished in: Douglas McGregor. The Human Side of Enterprise 1960/2006. p. 366

People , Nature , Knowledge

“The state, [Kierkegaard] argues, bears a direct relation to numbers. When a state decays, numbers decline and the state disappears. The whole concept is void. The relation of Christianity to numbers is different. A single Christian gives it reality. Christianity bears indeed an inverse relation to numbers. When all become Christians, the concept of Christianity is void. The concept is indeed a polemical one. One can be a Christian only in opposition. When opposition is suppressed, there is no more sense in saying “Christian.” Christendom has astutely abolished Christianity by making us all Christians. … In Christendom there is not the slightest idea of what Christianity is. People cannot see or understand that Christianity has been abolished by its propagation. Again, history probably does not offer any other example of a religion being abolished by reason of its success.”

Jacques Ellul (1912–1994) French sociologist, technology critic, and Christian anarchist

Source: The Subversion of Christianity (1984), pp. 35-36

People , Religion , History , Idea

“The appearance in nineteenth-century psychiatry, jurisprudence, and literature of a whole series of discourses on the species and subspecies of homosexuality, inversion, pederasty, and "psychic hermaphroditism" made possible a strong advance of social controls into this area of "perversity"; but it also made possible the formation of a "reverse" discourse: homosexuality began to speak in its own behalf, to demand that its legitimacy or "naturality" be acknowledged, often in the same vocabulary, using the same categories by which it was medically disqualified.”

Michel Foucault (1926–1984) French philosopher

Vol. I, p. 101
History of Sexuality (1976–1984)

Literature , Nature , Strong , Appearance

“Darwin himself told us in his last book (The Formation of Vegetable Mould Through the Action of Worms) that we should never underestimate the power of worms on the move…. The inversion of a humble worm, especially when disturbed, may bring down empires. Shakespeare told us that "the smallest worm will turn being trodden on." And Cervantes wrote in his author's preface to Don Quixote that "even a worm when trod upon, will turn again." …Geoffrey, it seems, was correct after all - not in every detail, of course, but at least in basic vision and theoretical meaning. And the triumph of surprise, the inversion of nuttiness to apparent truth, stands as a premier example of the most exciting general development in evolutionary theory during our times.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Brotherhood by Inversion", p. 329-330
Leonardo's Mountain of Clams and the Diet of Worms (1998)

Truth , Books , Time

“Baseball skill relates inversely to age. The older a man gets, the better a ball player he was when young, according to the watery eye of memory.”

Roger Kahn (1927–2020) American baseball writer

Source: The Boys Of Summer, Chapter 1, The Trolley Car That Ran By Ebbets Field, p. 10

Age , Memory

“It may fairly be said that the germs of the modern algebra of linear substitutions and concomitants are to be found in the fifth section of the Disquisitiones Arithmeticae; and inversely, every advance in the algebraic theory of forms is an acquisition to the arithmetical theory.”

George Ballard Mathews (1861–1922) British mathematician

Part 1, sect. 48.
Theory of Numbers, 1892

“Superficially at least the forces of electricity and magnetism seem to present the same kind of problem as gravitation. Experiment shows that two electrically charged bodies attract one another (or repel if their charges are of the same kind) with a force which conforms to the same mathematical law as the force of gravitation - both forces fall off inversely as the inverse square of the distance. The same is true of the magnetic force also; two magnetic poles attract or repel one another with a force which again follows the law of the inverse square of the distance.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

Law , Mathematics , Problem

“Suggestibility varies as the amount of disaggregation, and inversely as the unification of consciousness.”

Boris Sidis (1867–1923) American psychiatrist

The Psychology of Suggestion: a Research into the Subconscious Nature of Man and Society (1889), p. 90

“The value of a book about dealing with children is inversely proportional to the number of times it contains the word behavior. When our primary focus is on discrete behaviors, we end up ignoring the whole child.”

Alfie Kohn (1957) American author and lecturer

"Unconditional Teaching," Educational Leadership

Children , Books , Behavior , Time

“It is above all the impersonal and economically rationalized (but for this very reason ethically irrational) character of purely commercial relationships that evokes the suspicion, never clearly expressed but all the more strongly felt, of ethical religions. For every purely personal relationship of man to man, of whatever sort and even including complete enslavement, may be subjected to ethical requirements and ethically regulated. This is true because the structures of these relationships depend upon the individual wills of the participants, leaving room in such relations for manifestations of the virtue of charity. But this is not the situation in the realm of economically rationalised relationships, where personal control is exercised in inverse ratio to the degree of rational differentiation of the economic structure.”

Max Weber (1864–1920) German sociologist, philosopher, and political economist

Source: Sociology of Religion (1922), pp. 216-217

Religion , Exercises , Dependency , Personality

“[D]o not expect Americans to believe that freedom of speech is some disguised puppetry of the powerful. It is, to the contrary, an indispensable ingredient in the recipe for preventing tyrannies, be they of the left or right, be they in the name of the Fatherland, the Volk, or the workers. To say otherwise is merely to perform what Michael Polanyi called a “moral inversion”—an intellectual juggling act in which we are asked, in Orwellian terms, to regard freedom as slavery, discrimination as nondiscrimination, and truth as power.”

Allen C. Guelzo (1953) American historian

2010s, Free Speech and Its Present Crisis (2018)

Truth , Freedom

“A slowly moving queue does not move uniformly. Rather, waves of motion pass down the queue. The frequency and amplitude of these waves is inversely related to the speed at which the queue is served.”

Anthony Stafford Beer (1926–2002) British theorist, consultant, and professor

Source: Management Science (1968), Chapter 4, An Alphabet of Models, p. 108.

Speed

“Solidarity can grow only in inverse ratio to personality.”

Émile Durkheim (1858–1917) French sociologist (1858-1917)

Source: The Division of Labor in Society (1893), p. 129 (in 1933 edition)

Personality

“In electromagnetism… the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as "singularities" in the field. So far this transformation from the force to the potential, from the action at a distance to the field, is only a purely mathematical operation.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Law , Mathematics , Change

“Although the classic theoretical foundation of distance measurement in physics is the 'rigid rod', nearly all distances in surveying, whether terrestrial or celestial, are made to depend on the properties of light. The two simplest properties so employed are the principle of propogation in straight lines and the principle that the intensity of light diminishes inversely as the square of the distance.”

Gerald James Whitrow (1912–2000) British mathematician

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

Light , Dependency

“By keeping historical events in their proper perspective, theology helps safeguard society and the Church from regarding as permanent what is only temporary. Critical reflection thus always plays the inverse role of an ideology which rationalizes and justifies a given social and ecclesial order.”

Gustavo Gutiérrez (1928) Peruvian theologian

Source: A Theology of Liberation (1971), p. 12

Help

“My obsession was the preservation of the Gaelic language so that there would be people left in the world who could hear its great songs as they really were. No poetry could be translated, still less could song poetry, and the great language of Gaelic song made me fanatical about the beauty of the Gaelic language and its astonishing ability to indicate shades and positions of emphasis with natural inversions and the use of particles.”

Sorley MacLean (1911–1996) Scottish poet

Sorley MacLean, 1982, quoted in Krause, Corinna. Eadar Dà Chànan: Self-Translation, the Bilingual Edition and Modern Scottish Gaelic Poetry https://www.era.lib.ed.ac.uk/bitstream/handle/1842/3453/Krause2007.pdf?sequence=1&isAllowed=y
Letters and interviews

People , World , Beauty , Nature

“You have all heard the old bromide to the effect that man has his eyes on the stars and his feet in the mud. It is usually taken to mean that man's reason and his physical senses are the element pulling him down to the mud while his mystical, super-rational emotions are the element that lifts him to the stars. This is the grimmest inversion of many in mankind's history. But, last summer, reality offered you a literal dramatization of the truth. It is man's irrational emotions that bring him down to the mud. It is man's reason that lifts him to the stars.”

Ayn Rand (1905–1982) Russian-American novelist and philosopher

Apollo and Dionysus (1969)

Truth , History , Star , Reality

“Greatness of individuality is inversely proportional to the mass of the social aggregate.”

Boris Sidis The Source and Aim of Human Progress

The Source and Aim of Human Progress (1919)

“Gaskell could not abide this indecorous version of his beloved linear progress theory. He could not bear to imagine that the grand procession from jellyfish to man, orchestrated by an ever-increasing mass of nervous tissue, once paused in its stately and orderly march toward human consciousness in order to execute a fancy little flip, a clever jig of inversion, just at the sublime and definitive moment of entrance into the vertebral home stretch.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Brotherhood by Inversion", p. 327
Leonardo's Mountain of Clams and the Diet of Worms (1998)

Home , Imagination

“If we study the history of science we see happen two inverse phenomena… Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities.
…No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations.”

Henri Poincaré book Science and Hypothesis

Science and Hypothesis (1901)

History , Reality , Study , Appearance

“The painter is turning his eyes towards us only in so far as we happen to occupy the same position as his subject. We, the spectators, are an additional factor. Though greeted by that gaze, we are also dismissed by it, replaced by that which was always there before we were: the model itself. But, inversely, the painter's gaze, addressed to the void confronting him outside the picture, accepts as many models as there are spectators; in this precise but neutral place, the observer and the observed take part in a ceaseless exchange.”

Michel Foucault (1926–1984) French philosopher

Las Menias
The Order of Things: An Archaeology of the Human Sciences (1970)

Parting

“There is an inverse relationship between imagination and money.”

Alan Moore (1953) English writer primarily known for his work in comic books

About the film adaptation of V for Vendetta, in an MTV interview "Alan Moore : The Last Angry Man" http://www.mtv.com/shared/movies/interviews/m/moore_alan_060315/

Money , Imagination

“Addition is the combination of any arbitrary repetitions of the above-mentioned simplest act into a single act; from it in a similar way arises multiplication. While the performance of these two operations is always possible, that of the inverse operations, subtraction and division, proves to be limited. Whatever the immediate occasion may have been, whatever comparisons or analogies with experience, or intuition, may have led thereto; it is certainly true that just this limitation in performing the indirect operations has in each case been the real motive for a new creative act; thus negative and fractional numbers have been created by the human mind; and in the system of all rational numbers there has been gained an instrument of infinitely greater perfection. This system, which I shall denote by R, possesses first of all a completeness and self-containedness which I have designated… as characteristic of a body of numbers [Zahlkőrper] and which consists in this, that the four fundamental operations are always performable with any two individuals in R, i. e., the result is always an individual of R, the single case of division by the number zero being excepted.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Way , Motivation , Perfection

“The creationist is a sham religious person who, curiously, has no true sense of religion. In the language of religion, it is the facts we observe in the world around us that must be seen to constitute the words of God. Documents, whether the Bible, Qur'an or those writings that held such force for Velikovsky, are only the words of men. To prefer the words of men to those of God is what one can mean by blasphemy. This, we think, is the instinctive point of view of most scientists who, curiously again, have a deeper understanding of the real nature of religion than have the many who delude themselves into a frenzied belief in the words, often the meaningless words, of men. Indeed, the lesser the meaning, the greater the frenzy, in something like inverse proportion.”

Fred Hoyle (1915–2001) British astronomer

Our Place in the Cosmos (1993), p. 14

Men , God , World , Religion

“Give me such evidence as would justify me in believing in anything else and I will believe that. Why should I not? It is not half so wonderful as the conservation of force, or the indestructibility of matter. Whoso clearly appreciates all that is implied in the falling of a stone can have no difficulty about any doctrine simply on account of its marvelousness But the longer I live, the more obvious it is to me that the most sacred act of a man's life is to say and to feel, 'I believe such and such to be true.' All the greatest rewards and all the heaviest penalties of existence cling about that act. The universe is one and the same throughout; and if the condition of my success in unraveling some little difficulty of anatomy or physiology is that I shall rigorously refuse to put faith in that which does not rest on sufficient evidence, I cannot believe that the great mysteries of existence will be laid open to me on other terms…. I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and hopes upon weaker convictions. I dare not if I would.”

Thomas Henry Huxley (1825–1895) English biologist and comparative anatomist

1860s, Reply to Charles Kingsley (1860)

Life , Faith , Law , Penalty

“Concrete presents, besides a coefficient of thermal expansion, a coefficient of hygroscopic dilation which is more appreciable. While concrete is kept wet… it expands; and as it dries, it contracts, in inverse proportion to the hygroscopic degree of the ambient air. …The shrinkage …will vary with the porosity of the concrete and with the thickness used in the structural member. …Shrinkage is much greater in structures consisting of thin elements subjected to intemperateness of dry climate, and disappears or becomes negligible in underground structures”

Eduardo Torroja (1899–1961) Spanish architect

e.g., foundations
Philosophy of Structures (1958)

“He knows that every piece of selfknowledge which one cannot keep to oneself makes one smaller and smaller, he knows that he who cannot keep silent his wishes to be recognized in the greatness of his selfknowledge which is no selfknowledge if it cannot be kept silent, and one becomes hypersensitive one feels betrayed because one wants to be recognized by people, one becomes ridiculous ambitious in inverse ratio to ones selfknowledge”

Max Frisch book Gantenbein

Gantenbein (1964)

People , Feeling

“I maintain that inversion is the effect of neither a prenatal choice nor an endocrinal malformation nor even the passive and determined result of complexes. It is an outlet that a child discovers when he is suffocating.”

Jean Paul Sartre book Saint Genet

Saint Genet, Actor and Martyr (1952)

“…inversion…is an outlet that a child discovers when he is suffocating.”

Jean Paul Sartre book Saint Genet

91
Saint Genet, Actor and Martyr (1952)

“The approach that dominates organizational theory, teaching, and practice for most of the twentieth century looked at organizations from the top-down, starting with a view of the CEO as the "leader" who shapes the organization's strategy, structure, culture, and performance potential. The nature of work and the role of the workforce enter the analysis much later, after considerations of technology and organization design have been considered. However, if the key source of value in the twenty-first-century organization is to be derived from the workforce itself, an inversion of the dominant approach will be needed. The new perspective will start not at the top of the organization, but at but at the front lines, with people and the work itself — which is where value is created. Such an inversion will lead to a transformation in the management and organization of work workers, and knowledge. This transformation was signalled by McGregor, but we must go further.”

Wanda Orlikowski American computer scientist

Thomas Kochan, Wanda Orlikowski, and Joel Cutcher-Gershenfeld. "Beyond McGregor's theory Y," in: Douglas McGregor (1960), The Human Side of Enterprise; Annotated Edition, 2006, p. 366

People , Nature , Knowledge

“I had not thought of this regular decrease of gravity, namely that it is as the inverse square of the distance; this is a new and highly remarkable property of gravity.”

Christiaan Huygens (1629–1695) Dutch mathematician and natural philosopher

(1691) quoted in Popular Astronomy, Vol. 56 (1948), pp. 189–190.

“Let me close by reminding you of what Newton actually did on the day that he conceived G = k \frac{mm'}{r^2}. …Newton did not have any subsidies, grants, funds, Secret Service money. But he had the moon. He said, "… I cannot throw a ball round the world, but let me picture the moon as if it were a ball which has been flung around the world… How long will it take to go round the world?" …He knew the value of gravity at the earth's surface …but he did not know the value of the earth's gravity for the moon. He said, "Let us suppose that it is given by an inverse square law. Now, how long will it take the moon to go around?"”

Jacob Bronowski (1908–1974) Polish-born British mathematician

It comes out at twenty-eight days. As Newton said, "They agreed pretty nearly."
The Origins of Knowledge and Imagination (1978)

Money , Secret , World , Law

“It is understandable then that tragic heroes, unlike the baroque characters who had preceded them, could never be mad, and that inversely madness could never take on the tragic value we have known since Nietzsche and Artaud. In the classical epoch, tragic characters and the mad face each other without any possible dialogue or common language, for the one can only pronounce the decisive language of being, where the truth of light and the depths of night meet in a flash, and the other repeats endlessly an indifferent murmur where the empty chatter of the day is cancelled out by the deceptive lies of the shadows.”

Michel Foucault (1926–1984) French philosopher

Part Two: 2. The Transcendence of Delirium
History of Madness (1961)

Truth , Understanding , Decision , Light

“There is a deep irony in the fact that the more nearly an ideal is brought to realization, the more acutely do the saints and heroes who have committed themselves to the task, experience a vehement sense of failure in not having perfected their ideal in its totality; and inversely, the more perfunctory is the pursuit of an ideal, the less are people troubled by discrepancies between practice and principle.”

William H. McNeill (1917–2016) Canadian historian

Discrepancies among the Social Sciences (1981)

People , Failure , Sense , Perfection

“The line of march of all spirits is always progressive, never retrograde. They raise themselves gradually In the hierarchy of existence they never descend from the rank at which they have once arrived. In the course of their different corporeal existences they may descend in rank as men, but not as spirits. Thus the soul of one who has been at the pinnacle of earthly power may, in a subsequent incarnation, animate the humblest day-labourer, and vice versa; for the elevation of ranks among men is often In the inverse ratio of that of the moral sentiments. Herod was a king, and Jesus, a carpenter.”

Allan Kardec (1804–1869) systematizer of Spiritism

Source: The Spirits' Book, p. 128.

Men , Soul , Animals

“Mankind has never been renowned for accepting logical solutions to its most serious problems. As a rule, the degre of logicality of solutions seemed to vary inversely with the urgency or seriousness of the problems.”

Edmund Cooper book Five to Twelve

Five to Twelve (1968)

Problem

“Gaskell… had to keep his stately soldiers upright and uniformly oriented… by crafting the brain and spinal cord from an arthropod digestive tube, while forming a completely new gut below. …Gaskell thought that his move would rescue the theory of linear progress, with its necessary transition of arthropod into vertebrate, from the absurdities of the old inversion theory.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Brotherhood by Inversion", p. 327
Leonardo's Mountain of Clams and the Diet of Worms (1998)

“With a few exceptions, lower population [density] means fewer problems [for survivalist retreats]. When the Schumer Hits the Fan, there will be a mass exodus from the cities. Think of it as an army that is spreading out across a battlefield: The wider they are spread, the less effective they are. The inverse-square law hasn’t been repealed.”

James Wesley Rawles (1960) Survivalist-fiction author and blogger

How to Survive the End of the World as We Know It, Plume, New York (2009)

Law , Problem , Thinking

“Infanticide and infant neglect exist in inverse ratio to the accessibility of abortion services.”

Sheri S. Tepper (1929–2016) American fiction writer

Source: Gibbon's Decline & Fall (1996), Chapter 10 (p. 173)

“[T]here is an inverse correlation between the cleanliness of a bathroom and my 3-year-old daughter's need to move her bowels.”

Ayelet Waldman (1964) American- Israeli writer

Salon.com column http://www.salon.com/mwt/col/waldman/2005/04/11/baby_lust/

Daughters

“They are unfettered by precedent in the administration of justice. Customs have been handed down by ages of repetition, but the punishment for ignoring a custom is a matter for individual treatment by a jury of the culprit’s peers, and I may say that justice seldom misses fire, but seems rather to rule in inverse ratio to the ascendency of law. In one respect at least the Martians are a happy people; they have no lawyers.”

Edgar Rice Burroughs book A Princess of Mars

Source: A Princess of Mars (1917), Chapter 9

People , Age , Justice , Law

“As every bird-watcher knows, the beauty of a bird's song is inversely correlated with the colourfulness of its plumage.”

Matt Ridley (1958) economist

Source: The Red Queen (1993), Ch. 5

Beauty , Bird

“In no sense other than an utterly trivial one is reproduction the inverse of chemical disintegration. It is a misunderstanding of genetics to suppose that reproduction is only 'intended' to make facsimiles, for parasexual processes of genetical exchange are to be found in the simplest living things.”

Peter Medawar (1915–1987) scientist

1960s, Review of Teilhard de Chardin's "The Phenomenon of Man", 1961

Sense

“The value of a book about dealing with children is inversely proportional to the number of times it contains the word behavior.”

Alfie Kohn (1957) American author and lecturer

Published in Education Leadership, September 2005 http://www.alfiekohn.org/teaching/uncondtchg.htm

Children , Books , Behavior , Time

“That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If for instance, +1, -1, √-1 had been called direct, inverse, and lateral units, instead of positive, negative, and imaginary (or even impossible) such an obscurity would have been out of question.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

In Theoria residiorum biquadraticorum, Commentatio secunda; Werke, Bd. 2 (Goettingen, 1863), p.177. As quoted by Robert Edouard Moritz in Memorabilia mathematica: the philomath's quotation book (1914) p. 282.

Question

“The refraction of light agrees with the grand principle that Nature always uses the simplest means to accomplish its effects. From this principle, can be derived whenever light passes from one medium to another, the ratio of the sine of the angle of refraction to the sine of the angle of refraction equals the inverse ratio of the speeds at which light moves in each medium.
But this "budget", this expense of action that Nature minimizes in the refraction of light, is it also minimized in the direct propagation and reflection of light? Yes, it always has the smallest possible value.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

Nature , Light , Speed

“I have throughout introduced the Integral Calculus in connexion with the Differential Calculus…. Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction? The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold…”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Advertisement, pp.3-4
The Differential and Integral Calculus (1836)

Learning

“Even children know that drafting rule is easier to bend flat than across the edges; and… they will not be much surprised if told that for the same width of the rule its resistance is proportional to the square of the thickness and the deflection is inversely proportional to the cube of the thickness. Nevertheless some modern designers seem to be unaware… since they require… beams of such slenderness that they resemble springboards…”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

Children

“Now it is the practice of astronomers to assume that brightness falls off inversely with the square of the "distance" of an object—as it would do in Euclidean space, if there were no absorption… We must therefore examine the relation between this astronomer's "distance" d… and the distance r which appears as an element of the geometry.”

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

Appearance

“Conquest brings no lasting happiness unless the person conquered was possessed of free will. Only then can there be doubt and anxiety and those continual victories over habit and boredom which produce the keenest pleasures of all. The comely inmates of the harem are rarely loved, for they are prisoners. Inversely, the far too accessible ladies of present-day seaside resorts almost never inspire love, because they are emancipated. Where is love's victory when there is neither veil, modesty, nor self-respect to check its progress? Excessive freedom raises up the transparent walls of an invisible seraglio to surround these easily acquired ladies. Romantic love requires women, not that they should be inaccessible, but that their lives should be lived within the rather narrow limits of religion and convention. These conditions, admirably observed in the Middle-Ages, produced the courtly love of that time. The honoured mistress of the chateau remained within its walls while the knight set out for the Crusades and thought about his lady. In those days a man scarcely ever tried to arouse love in the object of his passion. He resigned himself to loving in silence, or at least without hope. Such frustrated passions are considered by some to be naive and unreal, but to certain sensitive souls this kind of remote admiration is extremely pleasurable, because, being quite subjective, it is better protected against deception and disillusion.”

André Maurois (1885–1967) French writer

Un Art de Vivre (The Art of Living) (1939), The Art of Loving

Love , Women , Pleasure , Age

“Corporate inversion, they're leaving the United States, we have almost $5 trillion sitting out there, where they can't get the money back, they can't bring it in because there's no mechanism to bring it back in and the tax is so high. I'm going to bring tremendous amounts of money, tremendous amounts of jobs, tremendous numbers of companies, and yes the tax is going to be cut from the highest tax nation anywhere in the world to a fairly low tax. Not the lowest in the world, but to a fairly low tax.”

Donald J. Trump (1946) 45th President of the United States of America

2010s, 2016, June

Money , World

“The number of one's possible fantasies is inversely proportional to the amount of one's liquid assets. For him who has everything dreams are no longer possible.”

Stanisław Lem book Peace on Earth

Peace on Earth (1987), tr. Elinor Ford (1994) from Pokój na Ziemi, Ch. 4

Dreams

“When I wrote about Hank Williams 'A hundred floors above me in the tower of song', it's not some kind of inverse modesty. I know where Hank Williams stands in the history of popular song. Your Cheatin' Heart, songs like that, are sublime, in his own tradition, and I feel myself a very minor writer.”

Hank Williams (1923–1953) American country music singer

Leonard Cohen, Who held a gun to Leonard Cohen's head? http://www.guardian.co.uk/arts/fridayreview/story/0,12102,1305765,00.html The Guardian (2006-06-20)
About

Feeling , History , Heart

“The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors”

Roger Shepard (1929) American psychologist

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

Color , Way , Optimism , Support

“His days were full of meaningless ceremonies whose sacredness appeared to be in inverse ratio to their comprehensibility or usefulness.”

Mervyn Peake (1911–1968) English writer, artist, poet and illustrator

Source: Gormenghast (1950), Chapter 80 (p. 802)

Appearance

“Your ability to deal w/surprise is in inverse relation to the amount of your backlog of "stuff."”

David Allen (1945) American productivity consultant and author

4 September 2010 https://twitter.com/gtdguy/status/22924717953
Official Twitter profile (@gtdguy) https://twitter.com/gtdguy

“Karl Marx was himself an anti-Semite: that is to say, an opponent of bourgeois Jewry. Inversely, most Jews are anti-Marxist.”

Konrad Heiden (1901–1966) German journalist and historian

Source: Hitler: A Biography (1936), p. 62

“Is there an inverse relation between knowledge and wisdom? At times it seems the more we know, the less we understand.
I am not the first to note this quandary. One scholar recently wrote, “Lysos and her followers chase the siren call of pastoralism, like countless romantics before them, idealizing a past Golden Age that never was, pursuing a serenity possible only in the imagination.””

David Brin book Glory Season

Introduction to Chapter 26 (p. 502)
Glory Season (1993)

Wisdom , Age , Imagination , Understanding

“Infinity is the land of mathematical hocus pocus. There Zero the magician is king. When Zero divides any number he changes it without regard to its magnitude into the infinitely small [great? ], and inversely, when divided by any number he begets the infinitely great [small? ]. In this domain the circumference of the circle becomes a straight line, and then the circle can be squared. Here all ranks are abolished, for Zero reduces everything to the same level one way or another. Happy is the kingdom where Zero rules!”

Paul Carus (1852–1919) American philosopher

"Logical and Mathematical Thought?" in The Monist, Vol. 20 (1909-1910), p. 69

Way , Mathematics , Change , Happiness

“I verily believe that a man’s way with women is in inverse ratio to his prowess among men. The weakling and the saphead have often great ability to charm the fair sex, while the fighting man who can face a thousand real dangers unafraid, sits hiding in the shadows like some frightened child.”

Edgar Rice Burroughs book A Princess of Mars

Source: A Princess of Mars (1917), Chapter 16

Women , Men , Sex , Way

“... our confidence in foretelling and influencing events increases in inverse ratio to our ability to do so. The farther we go from ourselves and from the present, the less we sense the probabilities, and it is easy for us to be "dead certain" about things we cannot possibly know anything about.**The Rules of Chaos (1969), p 23,24”

Stephen Vizinczey (1933) Hungarian-Canadian writer

Confidence , Sense , Dead

“It is so hard for an evolutionary biologist to write about extinction caused by human stupidity. […] Let me then float an unconventional plea, the inverse of the usual argument. […] The extinction of Partula is unfair to Partula. That is the conventional argument, and I do not challenge its primacy. But we need a humanistic ecology as well, both for the practical reason that people will always touch people more than snails do or can, and for the moral reason that humans are legitimately the measure of all ethical questions—for these are our issues, not nature's.”

Stephen Jay Gould book Eight Little Piggies

"Unenchanted Evening", p. 39
Eight Little Piggies (1993)

People , Stupidity , Question , Nature

“Come, let us hasten to a higher plane
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain! I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in our bound partition never part. Cancel me not — for what then shall remain?
Abscissas, some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.<p”

Stanisław Lem book The Cyberiad

Love and Tensor Algebra, St. 1, 4, 6, in "The First Sally (A): or, Trurl's Electronic Bard"
The Cyberiad (1967)

Love , Heart , Parting

“The inverse relationship between the bold promises and the effectiveness of the proposed solutions, the frustrations with the so-called system, the subtle and not-so-subtle bigotry and animus towards members of my race made radicals and nationalists of many of us. Yes, I understand the reasons why this is attractive. But it is precisely this -- in its historic form, not its present-day diluted form that I have rejected. My question was whether as an individual I truly believed that I was the equal of individuals who were white. This I had answered with a resounding "yes" in 1964 during my sophomore year in the seminary. And that answer continues to be yes. Accordingly, my words and my deeds are consistent with this answer.”

Clarence Thomas (1948) Associate Justice of the Supreme Court of the United States

1990s, I Am a Man, a Black Man, an American (1998)

Understanding , Question

“Newton supposed that all matter attracted other matter inversely according to the square of the distance; and the hypothesis was found to account for the whole movements of the heavenly bodies; which all became verifications of what Newton supposed to be the law of the solar system. Adopt the hypothesis that Jesus was what He is represented, and the whole of the books and the history becomes a verification.”

James McCosh (1811–1894) British philosopher

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 58.

Books , Law , History

“There has been an inversion in the hierarchy of the two principles of antiquity, “Take care of yourself” and “Know yourself.” In Greco-Roman culture, knowledge of oneself appeared as the consequence of the care of the self. In the modern world, knowledge of oneself constitutes the fundamental principle.”

Michel Foucault (1926–1984) French philosopher

“Technologies of the Self,” Ethics, Subjectivity and Truth (1994), p. 228

World , Knowledge , Appearance

“Where does this road lead?
And where does it go from there?
Even if I imagine [the possibilities]
Of course, I have no clue.
I feel the more I wish to be strong
The weaker my heart becomes
In inverse proportion”

Ayumi Hamasaki (1978) Japanese recording artist, lyricist, model, and actress

Fated
Lyrics, Guilty

Feeling , Imagination , Strong , Heart

“It's bad to use words like 'genius' unless you are talking about the late Jean-Michel Basquiat, the black Chatterton of the 80s who, during a picturesque career as sexual hustler, addict and juvenile art-star, made a superficial mark on the cultural surface by folding the conventions of street graffiti into those of art brut before killing himself with an overdose at the age of twenty-seven. The first stage of Basquiat's fate, in the mid-80s, was to be effusively welcomed by an art industry so trivialized by fashion and blinded by money that it couldn't tell a scribble from a Leonardo. Its second stage was to be dropped by the same audience, when the novelty of his work wore off. The third was an attempt at apotheosis four years after his death, with a large retrospective at the Whitney Museum designed to sanitise his short, frantic life and position him as a kind of all-purpose, inflatable martyr-figure, thus restoring the dollar value of his oeuvre in a time of collapsing prices for American contemporary art. One contributor to the catalogue proclaimed that "Jean remains wrapped in the silent purple toga of immortality"; another opined that "he is as close to Goya as American painting has ever produced." A third, not to be outdone, extolled Basquiat's "punishing regime of self-abuse" as part of "the disciplines imposed by the principle of inverse ascetism to which he was so resolutely committed."”

Robert Hughes (1938–2012) Australian critic, historian, writer

These disciplines of inverse ascetism, one sees, mean shooting smack until you drop dead.
Page 195
Culture of Complaint (1993)

Life , Death , Money , Fate

“What would happen if everyone did it? If everyone gave their wealth away what would we do for capital? If everyone loved their enemies who would ward off the Communists? This argument could be met on other levels, but here our only point is to observe that such reasoning would have been preposterous in the early church and remains ludicrous whenever committed Christians accept realistically their minority status. Far more fitting than "What if everybody did it" would be its inverse, "What if nobody else acted like a Christian, but we did?"”

John Howard Yoder (1927–1997) 20th century American Mennonite theologian

Source: The Priestly Kingdom (1984), p. 139

Love , Wealth

“There is generally, therefore, an inverse ratio between the worship of goddesses and the granting of rights to human women. Nor are the goddesses by and large compassionate; they are generally a pretty bloodthirsty lot. Goddesses are not the solution.”

Wendy Doniger (1940) American Indologist

Wendy Doniger, Quoted in The Washington Post. Quoted in Antonio de Nicolas, Krishnan Ramaswamy, and Aditi Banerjee (eds.) (2007), Invading the Sacred: An Analysis Of Hinduism Studies In America (Publisher: Rupa & Co., p. 13), also in Rajiv Malhotra: Wendy's Child Syndrome https://rajivmalhotra.com/library/articles/risa-lila-1-wendys-child-syndrome/, also in Rajiv Malhotra: Academic Hinduphobia: A Critique of Wendy Doniger's Erotic School of Indology (2016)

Women