Quotes about fraction

A collection of quotes on the topic of fraction, time, other, timing.

Quotes about fraction

“Consider again that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar", every "supreme leader", every saint and sinner in the history of our species lived there — on a mote of dust suspended in a sunbeam.
The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.
Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.
The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.
It has been said that astronomy is a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we've ever known.”

Carl Sagan book Pale Blue Dot

Source: Pale Blue Dot: A Vision of the Human Future in Space (1994), p. 8, Supplemental image at randi.org http://www.randi.org/images/122801-BlueDot.jpg

Love, Life, World, Religion

“As a fraction of the lifespan of the universe as measured from the beginning to the evaporation of the last black hole, life as we know it is only possible for one-thousandth of a billion billion billionth, billion billion billionth, billion billion billionth, of a percent (10^-84). And that's why, for me, the most astonishing wonder of the universe isn't a star or a planet or a galaxy. It isn't a thing at all. It's an instant in time. And that time is now. Humans have walked the earth for just the shortest fraction of that briefest of moments in deep time. But in our 200,000 years on this planet we've made remarkable progress. It was only 2,500 years ago that we believed that the sun was a god and measured its orbit with stone towers built on the top of a hill. Today the language of curiosity is not sun gods, but science. And we have observatories that are almost infinitely more sophisticated than those towers, that can gaze out deep into the universe. And perhaps even more remarkably through theoretical physics and mathematics we can calculate what the universe will look like in the distant future. And we can even make concrete predictions about its end. And I believe that it's only by continuing our exploration of the cosmos and the laws of nature that govern it that we can truly understand ourselves and our place in this universe of wonders.”

Brian Cox (physicist) (1968) English physicist and former musician

Conclusion in Wonders of the Universe - Destiny

Life, God, Law, Star

“That electrical energy can be economically transmitted without wires to any terrestrial distance, I have unmistakably established in numerous observations, experiments and measurements, qualitative and quantitative. These have demonstrated that is practicable to distribute power from a central plant in unlimited amounts, with a loss not exceeding a small fraction of one per cent, in the transmission, even to the greatest distance, twelve thousand miles — to the opposite end of the globe.”

Nikola Tesla (1856–1943) Serbian American inventor

A Means for Furthering Peace (1905)

Loss

“Welcome to my library! Ever since my high school days, books and magazines have been to my mind what friends are in the flesh. Each and every one of these books and articles-- a fraction of the 12,000 volumes that I share my house with-- has contributed to expanding my dream.”

Patch Adams (1945) Physician, activist, diplomat, author

Source: House Calls: How we can all heal the world one visit at a time (1998), p. 129

Books, School, Dreams, Housing

“[W]hat makes patriotic and religious fanatics such dangerous opponents is not the deaths of the fanatics themselves, but their willingness to accept the deaths of a fraction of their number in order to annihilate or crush their infidel enemy.”

Jared Diamond book Guns, Germs, and Steel

Source: Guns, Germs, and Steel: The Fates of Human Societies

Death

“We cannot turn against one another by letting this fight be defined as a war between America and Islam. That, too, is what groups like ISIL want. ISIL does not speak for Islam. They are thugs and killers, part of a cult of death, and they account for a tiny fraction of more than a billion Muslims around the world -- including millions of patriotic Muslim Americans who reject their hateful ideology. Moreover, the vast majority of terrorist victims around the world are Muslim. If we’re to succeed in defeating terrorism we must enlist Muslim communities as some of our strongest allies, rather than push them away through suspicion and hate.”

Barack Obama (1961) 44th President of the United States of America

2015, Address to the Nation by the President on San Bernardino (December 2015)

Death, Hate, War, World

“Any scientific treatment of the history of art must encompass not only the concepts of ‘social class’ and ‘class struggle, but also all the terms which describe particular social groups such as social category, autonomous fraction of a class, fraction of a class, and social stratum.”

Nicos Hadjinicolaou (1938) Art historian of Marxist-methodology and historian of visual ideology; El Greco scholar and Professor, El Greco …

Art History And Class Struggle (1978)

Art, History

“Not one of us knows what effect his life produces, and what he gives to others; that is hidden from us and must remain so, though we are often allowed to see some little fraction of it, so that we may not lose courage.”

Albert Schweitzer (1875–1965) French-German physician, theologian, musician and philosopher

Source: The Spiritual Life (1947), p. 164

Life, Courage

“The theories that I (and others) helped develop explained why unfettered markets often not only do not lead to social justice, but do not even produce efficient outcomes. Interestingly, there has been no intellectual challenge to the refutation of Adam Smith’s invisible hand: individuals and firms, in the pursuit of their self-interest, are not necessarily, or in general, led as if by an invisible hand, to economic efficiency. The only question that has been raised concerns the ability of government to remedy the deficiencies of the market. Within academia, a significant fraction of economists are involved with developing and expanding on the ideas of imperfect information (and imperfect markets) that I explored. For instance, Edmund Phelps, this year’s Nobel Prize winner, belongs to this "school" of thought. But in political discourse, simplistic “market fundamentalism” continues to exert enormous influence.”

Joseph E. Stiglitz (1943) American economist and professor, born 1943.

Interview on Bebbe Grillo's Blog http://www.beppegrillo.it/eng/2007/01/stiglitz.html, January 2007.

School, Justice, Idea, Question

“To the Youth in Europe and North America,
The recent events in France and similar ones in some other Western countries have convinced me to directly talk to you about them. I am addressing you, [the youth], not because I overlook your parents, rather it is because the future of your nations and countries will be in your hands; and also I find that the sense of quest for truth is more vigorous and attentive in your hearts.
I don’t address your politicians and statesmen either in this writing because I believe that they have consciously separated the route of politics from the path of righteousness and truth.
I would like to talk to you about Islam, particularly the image that is presented to you as Islam. Many attempts have been made over the past two decades, almost since the disintegration of the Soviet Union, to place this great religion in the seat of a horrifying enemy. The provocation of a feeling of horror and hatred and its utilization has unfortunately a long record in the political history of the West.
Here, I don’t want to deal with the different phobias with which the Western nations have thus far been indoctrinated. A cursory review of recent critical studies of history would bring home to you the fact that the Western governments’ insincere and hypocritical treatment of other nations and cultures has been censured in new historiographies.
The histories of the United States and Europe are ashamed of slavery, embarrassed by the colonial period and chagrined at the oppression of people of color and non-Christians. Your researchers and historians are deeply ashamed of the bloodsheds wrought in the name of religion between the Catholics and Protestants or in the name of nationality and ethnicity during the First and Second World Wars. This approach is admirable.
By mentioning a fraction of this long list, I don’t want to reproach history; rather I would like you to ask your intellectuals as to why the public conscience in the West awakens and comes to its senses after a delay of several decades or centuries. Why should the revision of collective conscience apply to the distant past and not to the current problems? Why is it that attempts are made to prevent public awareness regarding an important issue such as the treatment of Islamic culture and thought?
You know well that humiliation and spreading hatred and illusionary fear of the “other” have been the common base of all those oppressive profiteers. Now, I would like you to ask yourself why the old policy of spreading “phobia” and hatred has targeted Islam and Muslims with an unprecedented intensity. Why does the power structure in the world want Islamic thought to be marginalized and remain latent? What concepts and values in Islam disturb the programs of the super powers and what interests are safeguarded in the shadow of distorting the image of Islam? Hence, my first request is: Study and research the incentives behind this widespread tarnishing of the image of Islam.
My second request is that in reaction to the flood of prejudgments and disinformation campaigns, try to gain a direct and firsthand knowledge of this religion. The right logic requires that you understand the nature and essence of what they are frightening you about and want you to keep away from.”

Ali Khamenei (1939) Iranian Shiite faqih, Marja' and official independent islamic leader

Message of Ayatollah Seyyed Ali Khamenei To the Youth in Europe and North America http://english.khamenei.ir//index.php?option=com_content&task=view&id=2001, Khamenei.ir (January 21, 2015) 2015

War, People, Truth, Youth

“In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents. This varies enormously in amount in different species, but, in all, there has been, before the offspring is able to lead an independent existence, a certain expenditure of nutriment in addition, almost universally, to some expenditure of time or activity, which the parents are induced by their instincts to make for the advantage of their young. Let us consider the reproductive value of these offspring at the moment when this parental expenditure on their behalf has just ceased. If we consider the aggregate of an entire generation of such offspring it is clear that the total reproductive value of the males in this group is exactly equal to the total value of all the females, because each sex must supply half the ancestry of all future generations of the species. From this it follows that the sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal; for if this were not so and the total expenditure incurred in producing males, for instance, were less than the total expenditure incurred in producing females, then since the total reproductive value of the males is equal to that of the females, it would follow that those parents, the innate tendencies of which caused them to produce males in excess, would, for the same expenditure, produce a greater amount of reproductive value; and in consequence would be the progenitors of a larger fraction of future generations than would parents having a congenital bias towards the production of females. Selection would thus raise the sex-ratio until the expenditure upon males became equal to that upon females.”

Ronald Fisher book The Genetical Theory of Natural Selection

On natural selection acting on sex ratio: Fisher's principle, Ch. 6, p. 141.
The Genetical Theory of Natural Selection (1930)

Children, Sex, Nature, Parent

“We know today that nothing will restore the pre-machine condition of reasonably universal employment save an artificial allocation of working hours involving the use of more men than formerly to perform a given task.... The primary function of society, in spite of all the sophistries spurred of selfishness, is to give men better conditions than they could get without it; and the basic need today is jobs for all—not for "property" for a few of the luck and the acquisitive.... In view of the urgent need for change, there is something almost obscene in the chatter of the selfish about various psychological evils allegedly inherent in a New Deal promising decent economic security and humane leisure for all instead of for a few.... What is worth answering is the kindred outcry about "regimentation", "collective slavery", "violation of Anglo-Saxon freedom", "destruction of the right of the individual to make his own way" and so on; with liberal references to Stalin, Hitler, Mustapha Kemal, and other extremist dictators who have sought to control men's personal, intellectual, and artistic lives, and traditional habits and folkways, as well as their economic fortunes. Naturally the Anglo-Saxon balks at any programme calculated to limit his freedom as a man and a thinker or to disturb his inherited perspectives and daily customs—and need we say that no plan ever proposed in an Anglo-Saxon country would conceivably seek to limit such freedom or disturb such perspectives and customs? Here we have a deliberate smoke-screen—conscious and malicious confusion of terms. A decent planned society would indeed vary to some extent the existing regulations (for there are such) governing commercial and economic life. Yet who save a self-confessed Philistine or Marxist (the plutocrat can cite "Das Kapital" for his purpose!) would claim that the details and conditions of our merely economic activities form more than a trivial fraction of our whole lives and personalities? That which is essential and distinctive about a man is not the routine of material struggle he follows in his office; but the civilised way he lives, outside his office, the life whose maintenance is the object of his struggle. So long as his office work gains him a decently abundant and undisputedly free life, it matters little what that work is—what the ownership of the enterprise, and what and how distributed its profits, if profits there be. We have seen that no system proposes to deny skill and diligence an adequate remuneration. What more may skill and diligence legitimately ask? Nor is any lessening in the pride of achievement contemplated. Man will thrill just as much at the overcoming of vast obstacles, and the construction of great works, whether his deeds be performed for service or for profit. As it is, the greatest human achievements have never been for profit. Would Keats or Newton or Lucretius or Einstein or Santayana flourish less under a rationally planned society? Any intimation that a man's life is wholly his industrial life, and that a planned economic order means a suppression of his personality, is really both a piece of crass ignorance and an insult to human nature. Incidentally, it is curious that no one has yet pointed to the drastically regulated economic life of the early Mass. Bay colony as something "American!"”

H.P. Lovecraft (1890–1937) American author

Unpublished (and probably unsent) letter to the Providence Journal (13 April 1934), quoted in Collected Essays, Volume 5: Philosophy, edited by J. T. Joshi, pp. 115-116
Non-Fiction, Letters

Life, Men, Way, Nature

“The ambition for broad acres leads to poor farming, even with men of energy. I scarcely ever knew a mammoth farm to sustain itself; much less to return a profit upon the outlay. I have more than once known a man to spend a respectable fortune upon one; fail and leave it; and then some man of more modest aims, get a small fraction of the ground, and make a good living upon it. Mammoth farms are like tools or weapons, which are too heavy to be handled. Ere long they are thrown aside, at a great loss.”

Abraham Lincoln (1809–1865) 16th President of the United States

1850s, Address before the Wisconsin State Agricultural Society (1859)

Men, Loss

“Instructors can impart only a fraction of the teaching. It is through your own devoted practice that the mysteries of the Art of Peace are brought to life.”

Morihei Ueshiba (1883–1969) founder of aikido

The Art of Peace (1992)

Life, Peace, Art

“The danger is that global warming may become self-sustaining, if it has not done so already. The melting of the Arctic and Antarctic ice caps reduces the fraction of solar energy reflected back into space, and so increases the temperature further. Climate change may kill off the Amazon and other rain forests, and so eliminate once one of the main ways in which carbon dioxide is removed from the atmosphere. The rise in sea temperature may trigger the release of large quantities of carbon dioxide, trapped as hydrides on the ocean floor. Both these phenomena would increase the greenhouse effect, and so global warming further. We have to reverse global warming urgently, if we still can.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

ABC News interview (16 August 2006)

Way, Change, Sea

“Our public life depends primarily not upon the men who occupy public positions for the moment, because they are but an infinitesimal fraction of the whole. Our public life depends upon men who take an active interest in that public life; who are bound to see public affairs honestly and competently managed; but who have the good sense to know what honesty and competency actually mean.”

Theodore Roosevelt (1858–1919) American politician, 26th president of the United States

1900s, Address at the Prize Day Exercises at Groton School (1904)
Context: You often hear people speaking as if life was like striving upward toward a mountain peak. That is not so. Life is as if you were traveling a ridge crest. You have the gulf of inefficiency on one side and the gulf of wickedness on the other, and it helps not to have avoided one gulf if you fall into the other. It shall profit us nothing if our people are decent and ineffective. It shall profit us nothing if they are efficient and wicked. In every walk of life, in business, politics; if the need comes, in war; in literature, science, art, in everything, what we need is a sufficient number of men who can work well and who will work with a high ideal. The work can be done in a thousand different ways. Our public life depends primarily not upon the men who occupy public positions for the moment, because they are but an infinitesimal fraction of the whole. Our public life depends upon men who take an active interest in that public life; who are bound to see public affairs honestly and competently managed; but who have the good sense to know what honesty and competency actually mean. And any such man, if he is both sane and high-minded, can be a greater help and strength to any one in public life than you can easily imagine without having had yourselves the experience. It is an immense strength to a public man to know a certain number of people to whom he can appeal for advice and for backing; whose character is so high that baseness would shrink ashamed before them; and who have such good sense that any decent public servant is entirely willing to lay before them every detail of his actions, asking only that they know the facts before they pass final judgment.

Life, Men, Sense, Dependency

“It can take years to mold a dream. It takes only a fraction of a second for it to be shattered.”

Mary E. Pearson book The Kiss of Deception

Source: The Kiss of Deception

Dreams

“Is a woman a thinking unit at all, or a fraction always wanting its integer?”

Thomas Hardy (1840–1928) English novelist and poet

Thinking

“We imagined we knew everything the other thought, even when we did not necessarily want to know it, but in fact, I have come to see, we knew not the smallest fraction of what there was to know.”

Joan Didion The Year of Magical Thinking

Source: The Year of Magical Thinking

Imagination

“And in that fraction of a second before anything actually happened, Santino Corleone knew he was a dead man.”

Mario Puzo The Godfather

Source: The Godfather

Dead

“The one word love means too little for what it is. It doesn't communicate even a fraction of the feelings involved. Love. The word is not enough for what it is. Love. Love.”

James Frey book A Million Little Pieces

Source: A Million Little Pieces

Love, Feeling, Communication

“The happiness of life is made up of minute fractions — the little soon forgotten charities of a kiss or smile, a kind look, a heartfelt compliment, and the countless infinitesimals of pleasurable and genial feeling.”

Samuel Taylor Coleridge (1772–1834) English poet, literary critic and philosopher

"The Friend. The Improvisatore" (1828)

Life, Pleasure, Smile, Feeling

“Time is a funny thing. I was always puzzled with the way a single day could stretch itself out to the point of eternity in your mind, all while years melted down into the fraction of a second.”

Gloria Naylor book Mama Day

Source: Mama Day

Way, Time

“.. Think of the rivers of blood spilled by all those generals and emperors so that in glory and in triumph they could become the 'Momentary' masters of a 'Fraction' of a 'Dot”

Carl Sagan book Pale Blue Dot

Source: Pale Blue Dot: A Vision of the Human Future in Space

Thinking

“I was completely astonished by the beauty of nature. Our eyes see just a small fraction of the light in the world. It is a trick to make a colored world, which does not exist outside of human beings.”

Albert Hofmann (1906–2008) Swiss chemist

World, Beauty, Color, Nature

“Sometimes your whole life could hinge on a fraction of an inch. Or the beat of nanosecond. Or the knock on a door.
Kind of made a male believe in the divine. It really did.”

Jessica Bird (1969) U.S. novelist

Source: Lover Awakened

Life

“Sometimes your whole life could hinge on a fraction of an inch. Or the beat of a nanosecond. Or the knock on a door.”

Jessica Bird (1969) U.S. novelist

Source: Lover Awakened

Life

“Perhaps my life is nothing but an image of this kind; perhaps I am doomed to retrace my steps under the illusion that I am exploring, doomed to try and learn what I simply should recognize, learning a mere fraction of what I have forgotten.”

André Breton (1896–1966) French writer

Life, Learning

“Happy is what you realize you are a fraction of a second before it's too late.”

Ali Smith (1962) Scottish writer

Happiness

“The truly faithless one is the one who makes love to only a fraction of you. And denies the rest.”

Anaïs Nin (1903–1977) writer of novels, short stories, and erotica

February, 1932
Diary entries (1914 - 1974)

Love, Making love

“A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.”

Leo Tolstoy (1828–1910) Russian writer

Thinking

“Immaterial labor has become hegemonic in qualitative terms and has imposed a tendency on other forms of labor and society itself. Immaterial labor, in other words, is today in the same position that industrial labor was 150 years ago, when it accounted for only a small fraction of global production and was concentrated in a small part of the world but nonetheless exerted hegemony over all other forms of production. Just as in that pgase all forms of labor and society itself had to industrialize, today, labor and society have to informationalize, become intelligent, become communicative, become affective.”

Antonio Negri book Multitude: War and Democracy in the Age of Empire

109
Multitude: War and Democracy in the Age of Empire

World, Intelligence, Communication, Parting

“What to do? I see only two courses open to the likes of us. One is to go live on locusts in the wilderness, if there is any wilderness left. The other is surreptitiously to set up within the economic Juggernaut certain new cogs and wheels whereby the residual love of nature, inherent even in Rotarians, may be made to recreate at least a fraction of those values which their love of "progress" is destroying. A briefer way to put it is: if we want Mr. Babbitt to rebuild outdoor America, we must let him use the same tools wherewith he destroyed it. He knows no other.”

Aldo Leopold (1887–1948) American writer and scientist

"Game and Wild Life Conservation" [1932]; Published in The River of the Mother of God and Other Essays by Aldo Leopold, Susan L. Flader and J. Baird Callicott (eds.) 1991, p. 165-166.
1930s

Love, Way, Nature

“The mother as a social servant instead of a home servant will not lack in true mother duty…. From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.”

Charlotte Perkins Gilman (1860–1935) American feminist, writer, commercial artist, lecturer and social reformer

Source: Women and Economics (1898), Ch. 13.

Love, Life, Pleasure, Home

“The first period embraces the time between the first records of empirical determinations of the ratio of the circumference to the diameter of a circle until the invention of the Differential and Integral Calculus, in the middle of the seventeenth century. This period, in which the ideal of an exact construction was never entirely lost sight of, and was occasionally supposed to have been attained, was the geometrical period, in which the main activity consisted in the approximate determination of π by the calculation of the sides or the areas of regular polygons in- and circum-scribed to the circle. The theoretical groundwork of the method was the Greek method of Exhaustions. In the earlier part of the period the work of approximation was much hampered by the backward condition of arithmetic due to the fact that our present system of numerical notation had not yet been invented; but the closeness of the approximations obtained in spite of this great obstacle are truly surprising. In the later part of this first period methods were devised by which the approximations to the value of π were obtained which required only a fraction of the labour involved in the earlier calculations. At the end of the period the method was developed to so high a degree of perfection that no further advance could be hoped for on the lines laid down by the Greek Mathematicians; for further progress more powerful methods were required.”

E. W. Hobson (1856–1933) British mathematician

Source: Squaring the Circle (1913), pp. 10-11

Hope, Time, Parting, Perfection

“The fraction of Americans working in occupations concerned primarily with information has increased from 20 to nearly 50 percent of the work force.”

Edward O. Wilson book On Human Nature

On Human Nature (1978), Ch.4 Emergence

“Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the fraction, and the irrational, but in no other sense; all are alike mere symbols devised for the sake of representing the results of operations even when these results are not numbers (positive integers).”

Henry Burchard Fine (1858–1928) American academic

Source: The Number-System of Algebra, (1890), p. 86; Reported in Moritz (1914, 282)

Sense

“Hell is when we look back during that fraction of a second and know that we wasted an opportunity to dignify the miracle of life. Paradise is being able to say at that moment: “I made some mistakes, but I wasn’t a coward.”

Paulo Coelho book Aleph

I lived my life and did what I had to do.”
Aleph (2011)

Life, Hell

“Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic 31 geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence.”

James Joseph Sylvester (1814–1897) English mathematician

James Joseph Sylvester. "A Plea for the Mathematician, Nature," Vol. 1, p. 238; Collected Mathematical Papers, Vol. 2 (1908), pp. 655, 656.

Law, Mathematics, Idea, Effort

“We agree to recognise Lithuanian independence on condition that the desire of the Lithuanians for a military convention and a customs, monetary and postal union with Germany, communicated to us some time ago by a Lithuanian delegation, still remains. For to be candid, the idea of full independence for these peripheral countries seems to me to be purely theoretical and impracticable…The whole development of world politics shows that we have not only great and powerful individual countries like Germany on the one hand and Britain and France on the other, but associations of States fighting against each other…I do not believe in Wilson's universal League of Nations, I think that after the peace it will burst like a soap bubble. Great and powerful complexes of nations with hundreds of millions of inhabitants, armies of millions of men and exports amounting to thousands of millions, will be confronting each other. In the circumstances such small fractional nationalities will not be able to exist in complete independence, without seeking to lean on one side or the other. Just as there is no independent Belgium in the sense that it gravitates towards one side or the other, so it is not possible to conceive of a completely independent Lithuania, Balticum or Poland without that provisio.”

Gustav Stresemann (1878–1929) German politician, statesman, and Nobel Peace Prize laureate

1910s, Speech in the Reichstag, 18 March 1918

Men, World, Peace, Communication

“Here’s a test you can try at home: put a two-year-old in a playpen with an apple and a rabbit. If it plays with the apple and eats the rabbit, you’ve got a carnivore. According to numerous studies … vegetarians have 60% less cancer than meat-eaters, and a tiny fraction of the heart attack rate. It doesn’t take a rocket scientist to figure out we aren’t very well designed to eat meat.”

Dan Piraro (1958) cartoonist

"Are Humans Designed to Eat Meat?", in his official website Bizarro.com http://bizarro.com/are-humans-designed-to-eat-meat/

Home, Study, Heart

“The research questions that motivate most quantitative studies in the health, social and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population? Whether data can prove an employer guilty of hiring discrimination? What fraction of past crimes could have been avoided by a given policy? What was the cause of death of a given individual, in a specific incident? These are causal questions because they require some knowledge of the data-generating process; they cannot be computed from the data alone.”

Judea Pearl (1936) Computer scientist

Pearl, Judea (2008) "Causal Inference," in: Pearl, Judea. The science and ethics of causal modeling. (2010).

Death, Health, Behavior, Motivation

“Pearson shut out of science everything which the nineteenth-century had brought into it. He told his scholars that they must put up with a fraction of the universe, and a very small fraction at that — the circle reached by the senses, where sequence could be taken for granted.”

Henry Adams (1838–1918) journalist, historian, academic, novelist

Adams quotes — and takes the title of this chapter — from Karl Pearson's classic work The Grammar of Science: "In the chaos behind sensations, in the 'beyond' of sense-impressions, we cannot infer necessity, order or routine, for these are concepts formed by the mind of man on this side of sense-impressions." "Briefly chaos is all that science can logically assert of the supersensuous."
The Education of Henry Adams (1907)

Sense, Universe, Science

“Dust had dimmed only a fraction, not enough. Decay had brushed with its rotten fingers not nearly all it should. It was an enchanted sweet, stuck in the throat of time.”

Tanith Lee book Vazkor, Son of Vazkor

Book Two, Part II “The Wolf Hunt”, Chapter 1 (p. 166)
Vazkor, Son of Vazkor (1978)

Time

“Sex also concentrates the mind wonderfully, and that is why civilised man is so obsessed by it. It enables him to "savour every fraction of an inch," not merely of the act of sexual intercourse, but of living itself. But that, of course, only underlines the basic problem: after coitus, "man becomes sad," because he quickly returns to his unconcentrated and defocused state. In sexual excitement, it is the spirit itself that becomes erect, and becomes capable of penetrating the meaning of life. Normal consciousness is limp and flaccid; its attitude towards reality is defensive. This is what Sartre called contingency, that feeling of being at the mercy of chance.”

Colin Wilson book The Misfits: A Study of Sexual Outsiders

Source: The Misfits: A Study of Sexual Outsiders (1988), pp. 45-46

Life, Sadness, Sex, Feeling

“My one abiding principle has been to translate everything – even puns. For although this is… an 'unfinished' novel, it was written (and rewritten) by a great artist with his very lifeblood. I have therefore assumed that whatever I find in it is there for a purpose and must be dealt with somehow or other. I cannot pretend always to have done so successfully, but if I can convey to the reader even a fraction of the pleasure this Chinese novel has given me, I shall not have lived in vain.”

David Hawkes (sinologist) (1923–2009) British sinologist

Introduction to The Story of the Stone, Vol. 1: 'The Golden Days' (1973), p. 46
Preface to The Golden Days, 1973

Pleasure

“In the course of the fifteenth century, the sexagesimal division of the radius, in terms of which cords and goniometrical line-segments were expressed, was generally superseded, though not immediately replaced, by a decimal system of positional notation. Instead, mathematicians sought to avoid fractions by taking the Radius equal to a number of units of length of the form {\displaystyle 10^{n}} {\displaystyle 10^{n}}…The first to apply this method was the German astronomer Regiomontanus… the second half of the sixteenth and the first decades of the seventeenth century… observed of a gradual development of this method of Regiomontanus into a complete system of decimal positional fractions. Yet none of the steps taken by… writers is comparable in importance and scope with the progress achieved by Stevin in his De Thiende.”

Eduard Jan Dijksterhuis (1892–1965) Dutch historian

Source: Simon Stevin: Science in the Netherlands around 1600, 1970, p. 17-18

“The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Exercises, Imagination, Mathematics, Question

“b>One of the loveliest and most magnificent events that can happen in the country is when ponies take fright, particularly in a herd. A meadow-pippit has flown past. The ponies' fear is at first blended with play, even with mockery, amusement touched with a shudder, not unlike the behavior of the mentally ill. They trot as if they were retreating from a slow-moving stream of fire, but with lightning in every action, storm in every nerve; swinging their heads everywhere as if the front of their necks were made of elastic, gracefully flirting their tails. They can even pause for a moment, and start biting and boxing, with those romantic mating cries of theirs. Then all at once it is as if the fire has started flowing right under these strange creatures, they charge away like a storm incarnate over scree and bogs and landslides, dipping the tips of their toes for a fractional moment into the furnace that blazes beneath their hooves, cutting across waterfalls, gullys, and boulders, galloping steeply for a while until they stand trapped at last on some ledge high in the mountaintops, there to die and be eaten by birds.”

Halldór Laxness book The Atom Station

Atómstöðin (The Atom Station) (1948)

Fear, Behavior, Bird, Past

“Sometimes I have a sense of what I'm seeing being a small fraction of what's there. Not always there, but probably more often than I realize. Something will come up, and I'll realize I'm thinking about the world a little differently than my friends.”

Lisa Randall (1962) American theoretical physicist and an expert on particle physics and cosmology

The Discover Interview: Lisa Randall (July 2006)

World, Thinking, Sense

“I cannot believe that in the twentieth century the British people are by their deliberate vote going to constitute this assembly – a fraction of whom no doubt are men of real eminence and dignity, but the great majority of whom are quite ordinary people of the well-to-do class with all the narrowest prejudices and special interests of that class – I cannot believe that you by your votes are going to constitute them the main foundation on which the governing power in our land is reposed. I cannot believe the middle classes and the working classes, who after all have only to use their voting strength to get their own way, are going to degrade and cast away their own voting powers which their fathers won for them in the past…I cannot believe that the electors are going obsequiously to hand over their most vital constitutional right, namely, to choose the Chamber that governs the Government, to an antiquated body of titled persons utterly beyond their control.”

Winston S. Churchill (1874–1965) Prime Minister of the United Kingdom

The People's Rights [1909] (London: Jonathan Cape, 1970), pp. 65-66
Early career years (1898–1929)

Men, People, Way, Past

“Your body will never be more connected to your mind than when something is at stake. That's how you measure the value of a movement: by its consequences. Climb a tree, throw a rock, balance on the edge of a cliff-- you lose focus for a fraction of a second, you're screwed. It takes a very affluent and indulged culture to convince itself that standing around in weird poses is exercise.”

Erwan Le Corre (1971)

Christopher McDougall (2015). Natural Born Heroes: How A Daring Band of Misfits Mastered the Lost Secrets of Strength and Endurance, Vintage.

Exercises, Tree

“We are so accustomed to hear arithmetic spoken of as one of the three fundamental ingredients in all schemes of instruction, that it seems like inquiring too curiously to ask why this should be. Reading, Writing, and Arithmetic—these three are assumed to be of co-ordinate rank. Are they indeed co-ordinate, and if so on what grounds?
In this modern “trivium” the art of reading is put first. Well, there is no doubt as to its right to the foremost place. For reading is the instrument of all our acquisition. It is indispensable. There is not an hour in our lives in which it does not make a great difference to us whether we can read or not. And the art of Writing, too; that is the instrument of all communication, and it becomes, in one form or other, useful to us every day. But Counting—doing sums,—how often in life does this accomplishment come into exercise? Beyond the simplest additions, and the power to check the items of a bill, the arithmetical knowledge required of any well-informed person in private life is very limited. For all practical purposes, whatever I may have learned at school of fractions, or proportion, or decimals, is, unless I happen to be in business, far less available to me in life than a knowledge, say, of history of my own country, or the elementary truths of physics. The truth is, that regarded as practical arts, reading, writing, and arithmetic have no right to be classed together as co-ordinate elements of education; for the last of these is considerably less useful to the average man or woman not only than the other two, but than 267 many others that might be named. But reading, writing, and such mathematical or logical exercise as may be gained in connection with the manifestation of numbers, have a right to constitute the primary elements of instruction. And I believe that arithmetic, if it deserves the high place that it conventionally holds in our educational system, deserves it mainly on the ground that it is to be treated as a logical exercise. It is the only branch of mathematics which has found its way into primary and early education; other departments of pure science being reserved for what is called higher or university instruction. But all the arguments in favor of teaching algebra and trigonometry to advanced students, apply equally to the teaching of the principles or theory of arithmetic to schoolboys. It is calculated to do for them exactly the same kind of service, to educate one side of their minds, to bring into play one set of faculties which cannot be so severely or properly exercised in any other department of learning. In short, relatively to the needs of a beginner, Arithmetic, as a science, is just as valuable—it is certainly quite as intelligible—as the higher mathematics to a university student.”

Joshua Girling Fitch (1824–1903) British educationalist

Source: Lectures on Teaching, (1906), pp. 267-268.

Life, Truth, Education, School

“In advanced capitalism it expresses the fundamental contradiction between, on the one hand, the increasing socialisation of consumption, and on the other hand, the capitalist logic of the production and distribution of its means of consumption, the outcome of which is a deepening crisis in this sector at the same time as popular protest demands an amelioration of the collective material conditions of daily existence. In an attempt to resolve these contradictions and their resulting conflicts, the state increasingly intervenes in the city; but, as an expression of a class society, the state in practice acts according to the relations of force between classes and social groups, generally in favour of the hegemonic fraction of the dominant classes.”

Manuel Castells (1942) Spanish sociologist (b.1942)

Source: City, Class and Power, 1978, p. 3

Time

“…A government as large as the modern megastate cannot conceivably be controlled by a well-informed public, since it is literally impossible to be knowledgeable about even a fraction of the many complex matters modern governments are called upon to govern. … The attraction of free markets … is that they have self-correcting features that place far smaller demands on anyone’s knowledge than democracy does. Each person concerns herself with her own life and the system, supposedly, runs itself. Interpreted in this way, the literature on public ignorance could form the basis of the consequentialist argument the postwar free-market economists sought, but never found … against all government economic intervention: for even if it cannot be shown, on economic grounds, that every intervention hurts more than it helps, it might be shown, on political grounds, that by opening the door to helpful interventions, we begin sliding toward the unhelpful ones on a slope slippery with public ignorance.”

Jeffrey Friedman (political scientist) (1959) American political scientist

Source: “What’s wrong with Libertarianism”, p. 455

Life, Way, Democracy, Literature

“… only a fraction of book learning will seep into practical life anyhow; and the more foolish the theory, the less of it.”

Carl von Clausewitz book On War

Source: On War (1832), Book 6, Chapter 17.

Life, Books, Learning

“Even traditionally well educated and literate individuals are significantly restricted by the fact that they are able to use only a fraction of the biological and conceptual thinking tools which are available”

Tony Buzan (1942–2019) British psychologist

the mind map
The Mind Map Book, Buzan and Buzan (1991)

Education, Thinking

“The first characteristic of interest is the fraction of the computational load which is associated with data management housekeeping. This fraction has been very nearly constant for about ten years, and accounts for 40% of the executed instructions in production runs.”

Gene Amdahl (1922–2015) American physicist

Source: Validity of the single processor approach... (1967), p. 483

“Another conspicuous failure of classical mechanics was with one aspect of the problem of radiation. …Imagine a crowd of steel balls rolling about on a steel floor. …There must… be a steady leakage of energy from… causes, such as air resistance and the friction of the floor, so the balls will eventually lose energy, and, after no great length of time, will be found standing at rest on the floor. The energy of their motion seems to have been lost… most of it has been transformed into heat. The classical mechanics predicts that this must happen; it shows that all energy of motion, except possibly a minute fraction of the whole, must be transformed into heat whenever such a transformation is physically possible. It is because of this that perpetual-motion machines are a practical impossibility.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

Imagination, Failure, Problem, Time

“You--i. e. the US--didn't wreck Iraq a fraction as much as we--i. e. Iraqis--did. The looting for instance destroyed orders of magnitude more infrastructure than the war ever did.”

Kanan Makiya (1949) American orientalist

"Kanan Makiya speaks about Iraq 5 years later...", Washington Post (March 20, 2008)

War

“Asjadi composed the following qaSida in honour of this expedition: When the King of kings marched to Somnat, He made his own deeds the standard of miracles' 'Once more he led his army against Somnat, which is a large city on the coast of the ocean, a place of worship of the Brahmans who worship a large idol. There are many golden idols there. Although certain historians have called this idol Manat, and say that it is the identical idol which Arab idolaters brought to the coast of Hindustan in the time of the Lord of the Missive (may the blessings and peace of God be upon him), this story has no foundation because the Brahmans of India firmly believe that this idol has been in that place since the time of Kishan, that is to say four thousand years and a fraction' The reason for this mistake must surely be the resemblance in name, and nothing else' The fort was taken and Mahmud broke the idol in fragments and sent it to Ghaznin, where it was placed at the door of the Jama' Masjid and trodden under foot.'….'In the year AH 402 (AD 1011) he set out for Thanesar and Jaipal, the son of the former Jaipal, offered him a present of fifty elephants and much treasure. The Sultan, however, was not to be deterred from his purpose; so he refused to accept his present, and seeing Thanesar empty he sacked it and destroyed its idol temples, and took away to Ghaznin, the idol known as Chakarsum on account of which the Hindus had been ruined; and having placed it in his court, caused it to be trampled under foot by the people… From thence he went to Mathra (Mathura) which is a place of worship of the infidels and the birthplace of Kishan, the son of Basudev, whom the Hindus Worship as a divinity - where there are idol temples without number, and took it without any contest and razed it to the ground. Great wealth and booty fell into the hands of the Muslims, among the rest they broke up by the orders of the Sultan, a golden idol.”

Mahmud of Ghazni (971–1030) Sultan of Ghazni

Muntakhabut-Tawarikh, translated into English by George S.A. Ranking, Patna Reprint 1973, Vol. I, p. 17-28
Quotes from Muslim medieval histories

God, People, Peace, Time

“It has ever been held the highest wisdom for a man not merely to submit to Necessity,—Necessity will make him submit,—but to know and believe well that the stern thing which Necessity had ordered was the wisest, the best, the thing wanted there. To cease his frantic pretension of scanning this great God's-World in his small fraction of a brain; to know that it had verily, though deep beyond his soundings, a Just Law, that the soul of it was Good;—that his part in it was to conform to the Law of the Whole, and in devout silence follow that; not questioning it, obeying it as unquestionable.”

Thomas Carlyle (1795–1881) Scottish philosopher, satirical writer, essayist, historian and teacher

1840s, Heroes and Hero-Worship (1840), The Hero as Prophet

Wisdom, God, World, Law

“By making this chair five times as expensive, three times heavier, half as comfortable, and only a fraction as beautiful, an architect can make a good name for himself.”

Poul Henningsen (1894–1967) Danish architect

cited in: Eric Reiss (2012), Usable Usability: Simple Steps for Making Stuff Better, p. 17: About the iconic Bentwood chair from Thonet.

Beauty, Time

“From the start, the bourgeois-positivistic fraction of enlightenment was uncomfortable about the unpredictable, subversive dimensions of the new category, the unconscious. With it, the motif of critical self-reflection was introduced into civilization in a way that could not please those who held themselves to be the representatives of civilization. If every ego is underlaid by an unconscious, then that is the end of the self-satisfaction of a consciousness that thinks it knows itself, and thus knows how to value itself. The “unconscious” touched on the cultural narcissism of all social classes.”

Peter Sloterdijk (1947) German philosopher

Source: Kritik der zynischen Vernunft [Critique of Cynical Reason] (1983), p. 50

Way, Thinking

“We have tried occasionally to buy toads at bargain prices with results that have been chronicled in past reports. Clearly our kisses fell flat. We have done well with a couple of princes — but they were princes when purchased. At least our kisses didn’t turn them into toads. And, finally, we have occasionally been quite successful in purchasing fractional interests in easily-identifiable princes at toad-like prices.”

Warren Buffett (1930) American business magnate, investor, and philanthropist

1981 Chairman's Letter http://www.berkshirehathaway.com/letters/1981.html Letters to Shareholders (1957 - 2012)

Kiss, Success, Past

“Past, n. That part of Eternity with some small fraction of which we have a slight and regrettable acquaintance. A moving line called the Present parts it from an imaginary period known as the Future. These two grand divisions of Eternity, of which the one is continually effacing the other, are entirely unlike. The one is dark with sorrow and disappointment, the other bright with prosperity and joy. The Past is the region of sobs, the Future is the realm of song. In the one crouches Memory, clad in sackcloth and ashes, mumbling penitential prayer; in the sunshine of the other Hope flies with a free wing, beckoning to temples of success and bowers of ease. Yet the Past is the Future of yesterday, the Future is the Past of to-morrow. They are one--the knowledge and the dream.”

Ambrose Bierce book The Devil's Dictionary

The Devil's Dictionary (1911)

Dreams, Hope, Disappointment, Knowledge

“If those who support aggressive war had seen a fraction of what I've seen, if they'd watched children fry to death from Napalm and bleed to death from a cluster bomb, they might not utter the claptrap they do.”

John Pilger (1939) Australian journalist

John Pilger, This much i know http://www.guardian.co.uk/media/2005/nov/13/pressandpublishing.observermagazine, The Observer, 13 November 2005

Death, War, Children, Support

“The working of great administrations is mainly the result of a vast mass of routine, petty malice, self-interest, carelessness and sheer mistake. Only a residual fraction is thought.”

Giorgio De Santillana (1902–1974) American historian and philosopher

The Crime of Galileo http://books.google.com/books?id=34uQ6tlYHRgC&q=%22The+working+of+great+administrations+is+mainly+the+result+of+a+vast+mass+of+routine+petty+malice+self-interest+carelessness+and+sheer+mistake+Only+a+residual+fraction+is+thought%22&pg=PA290#v=onepage (1958)

“The very wise and wealthy financiers of the world--going way back, even before Rothschild's time--have observed that the world was a pretty rocky place to live in, and that nations were always fighting over something or other, there was always somebody who was trying to conquer somebody else, and wars were universal. Too bad about that, but that's the way it is. So we--the bankers--found out that if we loan money to them that we'll get paid back - they don't question what the interest rate is because they're fighting a war! And if they can win the war they can just plunder the victim and pay us whatever we want out of the plunder - it doesn't cost them anything really. Then the issue comes up of what happens if one of these nations decides not to pay us? Ah! The answer is very simple: if they refuse to pay us back we'll finance an opposing nation, a revolutionary group somewhere else to become an enemy of that nation and attack it, and destroy it, invade it. We'll create another war, in other words, in order to get our money back, we'll finance this side to attack that side. And so, by financing all sides in a war, and keeping the world divided up into warring fractions so that no one unit is particularly stronger than the other, the banks can continue to finance all sides of wars forever, and always collect their interest, because they have the ability of putting one nation against another nation against another nation to collect their debts.”

G. Edward Griffin (1931) American conspiracy theorist, film producer, author, and political lecturer

From the documentary Corporate Fascism: The Destruction of America's Middle Class (2011) http://www.youtube.com/embed/hTbvoiTJKIs?autoplay=1&start=2094&end=2183

Money, War, World, Way

“Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

Photo, Change, Time

“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 working of great administrations is mainly the result of a vast mass of routine, petty malice, self-interest, carelessness and sheer mistake. Only a residual fraction is thought.”

George Santayana (1863–1952) 20th-century Spanish-American philosopher associated with Pragmatism

Giorgio de Santillana (1902-1974) The Crime of Galileo http://books.google.com/books?id=34uQ6tlYHRgC&q=%22The+working+of+great+administrations+is+mainly+the+result+of+a+vast+mass+of+routine+petty+malice+self-interest+carelessness+and+sheer+mistake+Only+a+residual+fraction+is+thought%22&pg=PA290#v=onepage (1958) Many sources mistakenly attribute this quote to Santayana, and one http://books.google.com/books?id=e4tzpkw4caAC&q=%22The+working+of+great+institutions+is+mainly+the+result+of+a+vast+mass+of+routine+petty+malice+self-interest+carelessness+and+sheer+mistake+Only+a+residual+fraction+is+thought%22&pg=PA283#v=onepage even identifies the correct book, without realizing that George Santayana and Giorgio de Santillana are two different people Misattributed

“Are we making more mistakes now? I don't think so. Science is a high-risk activity. And when you do science—this is very important incidentally for the general public, and for policy makers—if you are not wasting some of your money, you are not doing good science. It's a funny way to say this. You've got to back high-risk opportunities. And high-risk opportunities means some fraction of them are going to fail. And I think in any science funding scenario, you've got to say, 10, 20, maybe even 30% of your funds are going to be invested in failures.”

Leon M. Lederman (1922–2018) American mathematician and physicist

Comments on need for failure in scientific research. From the Winding Your Way through DNA symposium http://www.accessexcellence.org/RC/CC/lederman.php at the University of California, San Francisco in 1992 (URL accessed on October 20, 2008)

Money, Way, Failure, Thinking

“[We may view the] economic organization as a system of prize relations. Seen in the large, free enterprise is an organization of production and distribution in which individuals or family units get their real income, their "living," by selling productive power for money to "business units" or "enterprises", and buying with the money income thus obtained the direct goods and services which they consume. This view, it will be remembered, ignores for the sake of simplicity the fact that an appreciable fraction of the productive power in use at any time is not really employed in satisfying current wants but to make provision for increased want-satisfaction in the future; it treats society as it would be, or would tend to become, with progress absent, or in a “static” state.”

Frank Knight (1885–1972) American economist

Source: The Economic Organization, 1933., p.59-60; on the circular-flow of income and the circular-flow diagram.

Money, Family, Business, Time

“Protocols:
Number 10, paras. 6,7
A scheme of government should come ready made from one brain, because it will never be clinched firmly if it is allowed to split into fractional parts in the minds of many. It is allowable, therefore, for us to have cognizance of the scheme of action but not to discuss it lest we disturb its artfulness, and interdependence of its component parts, the practical force of the secret meaning of each clause. To discuss and make alteration in a labor of this kind by means of numerous votings is to impress upon it the stamp of all ratiocinations and misunderstandings which have failed to penetrate the depth and nexus of its plottings….
These schemes will not turn existing institutions upside down just yet, They will only effect changes in their economy and consequently in the whole combined movement of their progress, which will thus be directed along the paths laid down in our schemes.”

Will Eisner (1917–2005) American cartoonist

The Plot: The Secret Story of the Protocols of the Elders of Zion (10/2/2005)

Secret, Art, Change, Parting

“Our school systems are all nonsynergetic. We take the whole child and fractionate the scope of his or her comprehending coordination by putting the children in elementary schools—to become preoccupied with elements or isolated facts only. Thereafter we force them to choose some specialization, forcing them to forget the whole. … We may well ask how it happened that the entire scheme of advanced education is devoted exclusively to ever narrower specialization. We find that the historical beginnings of schools and tutoring were established, and economically supported by illiterate and vastly ambitious warlords who required a wide variety of brain slaves with which to logistically and ballistically overwhelm those who opposed their expansion of physical conquest. They also simultaneously DIVIDED and CONQUERED any and all "bright ones" who might otherwise rise within their realms to threaten their supremacy. The warlord vitiated their threat by making them all specialists and reserving to himself exclusively the right to think about and act comprehensively. The warlord made all those about him differentiators and reserved the function of integration to himself.”

Buckminster Fuller (1895–1983) American architect, systems theorist, author, designer, inventor and futurist

Source: 1960s, Presentation to U.S. Congressional Sub-Committee on World Game (1969), p. 15

Children, Education, School, Support

“I must say a few words here concerning the solution of the Polish problem…Groeber has posed the question: Do I not overestimate the value of the military guarantees? Are not political guarantees in connection with good relations between Poland and Germany far better and more durable than it is possible fo military guarantees to be? …The past conduct of the Polish fraction in the Reichstag and the House of Deputies, and the attempts to have the German Ostmark question discussed as a question of international importance at world peace congresses, do not give my political friends a sufficient guarantee to think that future relations between Poland and Germany can be based solely on a formal paper friendship.”

Gustav Stresemann (1878–1929) German politician, statesman, and Nobel Peace Prize laureate

Source: 1910s, Speech in the Reichstag, 21 June 1918, p. 175

Friendship, World, Peace, Question

“The miraculous powers of modern calculation are due to three inventions : the Arabic Notation, Decimal Fractions and Logarithms.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 161; Cited in: Moritz (1914, 263); Arithmetics

“Wasn’t all their effort worthless? Wouldn’t it be better to accept the impossibility of their mission? He began to think Krane was mad. If there were a threat, then inevitably they would die. Death was the future of all people, all planets, all universes. Their struggle was symbolic of the futility of living creatures who fought against their own inevitable extinction. What were a few more years of existence compared to the longevity of a cosmos? In those terms, the whole history of their species lasted for less than a fraction of a second. And then, sheltering beside him under the protection of the energy equalizer, she looked up for a second, and, obscurely, he understood that the effort always would be worth it. Always had been worth it.”

Michael Moorcock (1939) English writer, editor, critic

Source: Short fiction, The Lost Canal (2013), p. 371

Death, People, History, Thinking

“The Good Economist Hayek is the thinker who has mind-blowing insights into just why the competitive market system is such a marvelous societal device for coordinating our by now 7.2 billion-wide global division of labor. Few other economists imagined that Lenin’s centrally-planned economy behind the Iron Curtain was doomed to settle at a level of productivity 1/5 that of the capitalist industrial market economies outside. Hayek did so imagine. And Hayek had dazzling insights as to why. Explaining the thought of this Hayek requires not sociology or history of thought but rather appreciation, admiration, and respect for pure genius.The Bad Economist Hayek is the thinker who was certain that Keynes had to be wrong, and that the mass unemployment of the Great Depression had to have in some mysterious way been the fault of some excessively-profligate government entity (or perhaps of those people excessively clever with money–fractional-reserve bankers, and those who claim not the natural increase of flocks but rather the interest on barren gold). Why Hayek could not see with everybody else–including Milton Friedman–that the Great Depression proved that Say’s Law was false in theory, and that aggregate demand needed to be properly and delicately managed in order to make Say’s Law true in practice is largely a mystery. Nearly everyone else did: the Lionel Robbinses and the Arthur Burnses quickly marked their beliefs to market after the Great Depression and figured out how to translate what they thought into acceptable post-World War II Keynesian language. Hayek never did.
My hypothesis is that the explanation is theology: For Hayek, the market could never fail. For Hayek, the market could only be failed. And the only way it could be failed was if its apostles were not pure enough.”

J. Bradford DeLong (1960) American economist

Making Sense of Friedrich A. von Hayek: Focus/The Honest Broker for the Week of August 9, 2014 http://equitablegrowth.org/making-sense-friedrich-von-hayek-focusthe-honest-broker-week-august-9-2014/ (2014)

Money, War, People, World

“I will not be proposing a course which has been under some public discussion recently — deficit financing. It is wholly inappropriate to our economic situation. In its least extreme form it is based on the theory that additional money generated by a Government deficit (and given currency, as necessary, by use of the printing press) will stimulate consumption and thereby production, in time to match the excess money with goods before real inflationary harm is done. Unfortunately we don't, and can't, produce more than a small fraction of what we consume, and increased consumption would merely mean increased imports without matching exports; and a severe balance of payment crisis, which would destroy Hong Kong's credit and confidence in the Hong Kong dollar; and which we could not cure without coming close to ruining ourselves. Keynes was not writing with our situation in mind. In this hard world we have to earn before we spend.”

John James Cowperthwaite (1915–2006) British colonial administrator

February 27, 1963, page 50.
Official Report of Proceedings of the Hong Kong Legislative Council

Money, World, Confidence, Time

“This is the type of AI I am interested in—what can the human and machine do together, and not in the competition which can arise. …There are doubts as to what fraction of the population can compete with computers, even with nice interactive prompting menus.”

Richard Hamming (1915–1998) American mathematician and information theorist

The Art of Doing Science and Engineering: Learning to Learn (1991)

“Many people fail to grasp this point, apparently because they think of "scientific" evidence as only that produced in laboratories by controlled experiments. This leads them to treat field studies, however careful, thorough and well-documented, as "anecdotal"--mere preparation for the real thing, therefore properly ignored till it bears fruit entitled to be considered by learned persons. This attitude was much like that of cavalry generals in the First World War, waiting patiently for the infantry to clear the ground so that they could make the dashing charges that alone they thought entitled the name of warfare. Because these creatures are complex, only a tiny fraction of important truths about them can ever be seen in laboratories of expressed in control experiments. The same, of course, is true of the human race.”

Mary Midgley (1919–2018) British philosopher and ethicist

Beast and Man: The Roots of Human Nature (1979). 224.

War, People, Truth, World

“The mind is like a well-endowed museum, only a small fraction of its holdings on view at any one time.”

James Richardson (1950) American poet

#407
Vectors: Aphorisms and Ten Second Essays (2001)

Time

“Britain, with the most completely socialized health system in the West, now spends the lowest fraction of GNP on health care of any major nation. There are frequent complaints of excessive waits for elective surgery and other inconveniences, but British citizens live slightly longer than Americans, on average, and our overall health conditions are comparable.”

Robert Kuttner (1943) American journalist

Source: The Economic Illusion (1984), Chapter 6, Welfare, p. 250

Health, Waiting

“Of all the creative work produced by humans anywhere, a tiny fraction has continuing commercial value. For that tiny fraction, the copyright is a crucially important legal device. For that tiny fraction, the copyright creates incentives to produce and distribute the creative work. For that tiny fraction, the copyright acts as an "engine of free expression."
But even for that tiny fraction, the actual time during which the creative work has a commercial life is extremely short. As I've indicated, most books go out of print within one year. The same is true of music and film. Commercial culture is sharklike. It must keep moving. And when a creative work falls out of favor with the commercial distributors, the commercial life ends.”

Lawrence Lessig book Free Culture

Free Culture (2004)

Life, Books, Music, Time

“[N]early every political evil can be found on display in China: slavery, discrimination, religious persecution, xenophobia, tyranny, mass-political indoctrination, colonialism, cultural genocide, and so on. And yet, the outcry against these things in America and the West is a tiny fraction of what it was with regard to South Africa in the 1980s or Israel today. Why? Some of the political answers are pretty obvious — and have much merit. A few that come to mind: China is non-Western, and many of these sins are supposed to be unique to white Europeans; China is a victim (or “victim”) of colonialism, and so we shouldn’t judge it harshly; China is very powerful, and realpolitik dictates that we be diplomatic; and so on.”

Jonah Goldberg (1969) American political writer and pundit

2010s, 2018, When Evil Becomes Inconvenient (2018)

Evil

“However convergent it be, evolution cannot attain to fulfilment on earth except through a point of dissociation. With this we are introduced to a fantastic and inevitable event which now begins to take shape in our perspective, the event which comes nearer with every day that passes: the end of all life on our globe, the death of the planet, the ultimate phase of the phenomenon of man. …
Now when sufficient elements have sufficiently agglomerated, this essentially convergent movement will attain such intensity and such quality that mankind, taken as a whole, will be obliged—as happened to the individual forces of instinct—to reflect upon itself at a single point; that is to say, in this case, to abandon its organo-planetary foothold so as to shift its centre on to the transcendent centre of its increasing concentration. This will be the end and the fulfilment of the spirit of the earth.
The end of the world: the wholesale internal introversion upon itself of the noosphere, which has simultaneously reached the uttermost limit of its complexity and its centrality.
The end of the world: the overthrow of equilibrium, detaching the mind, fulfilled at last, from its material matrix, so that it will henceforth rest with all its weight on God-Omega. …
Are we to foresee man seeking to fulfil himself collectively upon himself, or personally on a greater than himself? Refusal or acceptance of Omega? … Universal love would only vivify and detach finally a fraction of the noosphere so as to consummate it—the part which decided to "cross the threshold", to get outside itself into the other. …
The death of the materially exhausted planet; the split of the noosphere, divided on the form to be given to its unity; and simultaneously (endowing the event with all its significance and with all its value) the liberation of that percentage of the universe which, across time, space and evil, will have succeeded in laboriously synthesising itself to the very end. Not an indefinite progress, which is an hypothesis contradicted by the convergent nature of noogenesis, but an ecstasy transcending the dimensions and the framework of the visible universe.”

Pierre Teilhard De Chardin book The Phenomenon of Man

pp. 273, 287–289 https://archive.org/stream/ThePhenomenonOfMan/phenomenon-of-man-pierre-teilhard-de-chardin#page/n137/mode/1up/, The Phenomenon of Man (1955)

Love, Life, Death, God

“Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Law, Question

“Look up and below and all round and see the wonderful creations of God, not only our earth but the whole host of celestial worlds, planets, constellations etc. – many still unknown to us. See with what minute precision and order they move and are regulated. Only God could have created them. Ev all the accumulated genius of Mankind from the time of Creation through eons and eons of time and even to the end of existence, were all pooled together, yet it would not be able to evolve even a fraction of this order. God only could do so, and without him it would be utter chaos.”

Peter de Noronha (1897–1970) Indian businessman

The Pageant of Life (1964), On Planning for a Better World

God, World, Time

“If you use conventional data compression on the [human brain's] genome, you get about 23 million bytes (a small fraction of the size of Microsoft Word), which is a level of complexity we can handle.”

Ray Kurzweil (1948) Author, scientist, inventor, and futurist

"The Singularity," The New Humanists: Science at the Edge (2003)

“The Hindus saw clearly that if the arithmetic operations… were properly defined for negative numbers, these numbers could be employed to as good advantage as people had previously derived from positive numbers. …To people to whom the word number had always meant positive whole numbers and positive fractions, the very idea that there could be other numbers came hard. For many centuries negative numbers were either rejected or treated as second-class citizens.
What was especially difficult for mathematicians to swallow was that negative numbers could be acceptable roots of equations.”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 51.

People, Idea

“The truth of the matter is that, even under individualism, only a small fraction of the population is impelled chiefly by the profit motive, and that vast multitudes of men and women are motivated by other incentives than by the desire for profit. …nevertheless, they are strategic individuals whose activities are essential to efficiency in industry.”

Kirby Page (1890–1957) American clergyman

Property (1935)

Women, Men, Truth, Motivation

“Inventor of a new mythology and weaver of surprising folklore, Lord Dunsany stands dedicated to a strange world of fantastic beauty... unexcelled in the sorcery of crystalline singing prose, and supreme in the creation of a gorgeous and languorous world of incandescently exotic vision. No amount of mere description can convey more than a fraction of Lord Dunsany's pervasive charm.”

Lord Dunsany (1878–1957) Irish writer and dramatist

H. P. Lovecraft, quoted in the Del Rey edition of The Charwoman's Shadow
About

World, Beauty, Singing

“When something dies, it is usually disassembled, digested, and decomposed. Only rarely is anything ever fossilized, and even fewer things are very well-preserved. Because the conditions required for that process are so particular, the fossil record can only represent a tiny fraction of everything that has ever lived. Darwin provided many environmental dynamics explaining why no single quarry could ever provide a continuous record of biological events, and why it would be impossible to find all the fossilized ancestors of every lineage. But despite this, he predicted that future generations, -having the benefit of better understanding- would discover a substantial number of fossil species which he called “intermediate” or “transitional” between what we see alive today and their taxonomic ancestors at successive levels in paleontological history. In fact, in the century-and-a-half since then, we’ve found millions of evolutionary intermediaries in the fossil record, much more than Darwin said he could reasonably hope for. There are three different types of transitional forms and we have ample examples of each. But creationists still insist that we’ve never found a single one, because what they usually ask us to present are impossible parodies which evolution would neither produce nor permit.”

Aron Ra (1962) Aron Ra is an atheist activist and the host of the Ra-Men Podcast

"9th Foundational Falsehood of Creationism" https://www.youtube.com/watch?v=Qfoje7jVJpU, Youtube (May 8, 2008) Youtube, Foundational Falsehoods of Creationism

Hope, History, Understanding, Success

“The first Part. Of the Definitions of the Dismes. The first Definition. Disme is a kind of Arithmeticke, invented by the tenth progression, consisting in Characters of Cyphers; whereby a certaine number is described, and by which also all accounts which happen in humane affayres, are dispatched by whole numbers, without fractions or broken numbers.”

Simon Stevin (1548–1620) Flemish scientist, mathematician and military engineer

Disme: the Art of Tenths, Or, Decimall Arithmetike (1608)

Parting

“Gsell: What astonishes me, is that your way is so different from that of other sculptors. They prose the model. Instead of that, you wait till a model has instinctively or accidentally taken an Interesting pose, and thon you reproduce It. Instead of your giving orders to the model, the model gives orders to you.
Rodin: I am not at the model's orders; I am at Nature's. Doubtless my confreres have their reasons for proceeding as they do. But when one constrains Nature in that way and treats human beings as mannikins, one runs a risk of getting nothing but dead, artificial results. A hunter of truth and a trapper of life. I am careful not to follow their example. I seize upon the movements I observe, but I don't dictate them. when a subject requires a predetermined pose, I merely Indicate It. For I want only what reality will afford without being forced. In everything I obey Nature. I never assume to command her. My sole ambition Is a servile fidelity.
Gsell : And yet, you take liberties with nature. You make changes.
Rodin : Not at all. I should be false to myself if I did.
Gsell : But you finished work is never like the plaster sketch
Rodin : That is so, but the sketch is far less true than the finished work. It would Impossible for a model to keep a living attitude during all the time it takes to shape the clay. Still, I retain a general idea of the pose and require the model to conform to it. But this is not all. The sketch reproduces only the exterior. I must next reproduce the spirit, which is every whit as essential a part of Nature. I see the whole truth — not merely the fraction of it that lies upon the surface. I accentuate tho lines that best express the spiritual state I am Interpreting.”

Auguste Rodin (1840–1917) French sculptor

Rodin on realism, 1910

Life, Truth, Way, Idea

“You know, the cure for all this talk is really a good dose of incompetent government. You get that alternative and you'll never put Singapore together again: Humpty Dumpty cannot be put together again… my asset values will disappear, my apartments will be worth a fraction of what they were, my ministers' jobs will be in peril, their security will be at risk and their women will become maids in other people's countries, foreign workers. I cannot have that!”

Lee Kuan Yew (1923–2015) First Prime Minister of Singapore

Justifying million-dollar pay hike for Singapore ministers (Straits Times, 5 April 2007)
2000s

Women, People, Country

“Find a fraction which, multiplied by itself, shall give 6, or… find the square root of 6. This can be shown to be an impossible problem; for it can be shown that no fraction whatsoever multiplied by itself, can give a whole number, unless it be itself a whole number disguised in a fractional form, such as 4⁄2 or 21⁄3. To this problem, then, there is but one answer, that it is self-contradictory. But if we propose the following problem,—to find a fraction which, multiplied by itself, shall give a product lying between 6 and 6 + a; we find that this problem admits of solution in every case. It therefore admits of solution however small a may be… as small as you please.”

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

...there is such a thing as the square root of 6, and it is denoted by √6. But we do not say we actually find this, but that we approximate to it.
The Differential and Integral Calculus (1836)

Lying, Problem

“I do believe that in a race, it is naive to think Linux has a hope of making a dent against Microsoft starting from way behind with a fraction of the resources and amateur labor.”

Ken Thompson (1943) American computer scientist, creator of the Unix operating system

I feel the same about Unix.
"Ken Thompson clarifies matters", 1999

Hope, Way, Feeling, Thinking