Quotes about number (3111 quotes, page 3)

“I just wonder what it would be like to be reincarnated in an animal whose species had been so reduced in numbers than it was in danger of extinction. What would be its feelings toward the human species whose population explosion had denied it somewhere to exist… I must confess that I am tempted to ask for reincarnation as a particularly deadly virus.”

Prince Philip, Duke of Edinburgh (1921) member of the British Royal Family, consort to Queen Elizabeth II

Foreword to If I Were an Animal (1987) by Fleur Cowles ISBN 9780688061500
1980s

Feeling , Animals

“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Über unendliche, lineare Punktmannigfaltigkeiten" in Mathematische Annalen 20 (1882)  Quoted in "Cantor's Grundlagen and the paradoxes of Set Theory" by William W. Tait

Reality , Sense , Parting , Falseness

“In case of actual danger, the social democracy banks not on the "Iron Front" but on the Prussian police. It is reckoning without its host! The fact that the police was originally recruited in large numbers from among social-democratic workers is absolutely meaningless. Consciousness is determined by environment even in this instance. The worker who becomes a policeman in the service of the capitalist state, is a bourgeois cop, not a worker. Of late years, these policemen have had to do much more fighting with revolutionary workers than with Nazi students. Such training does not fail to leave its effects. And above all: every policeman knows that though governments may change, the police remains.”

Leon Trotsky (1879–1940) Marxist revolutionary from Russia

Source: Fascism: What It Is and How to Fight It (1944), Ch. 4

Democracy , Change , Fight , Training

“You say your life's a bum deal 'n yer up against the wall. Well, people, you ain't even got no deal at all. 'Cause what they do in Washington. They just takes care of Number One. An' Number One ain't you. You ain't even Number Two!”

Frank Zappa (1940–1993) American musician, songwriter, composer, and record and film producer

"The Meek Shall Inherit Nothing"
You Are What You Is (1981)

Life , People

“England was nothing, compared to continental nations until she had become commercial…until about the middle of the last century, when a number of ingenious and inventive men, without apparent relation to each other, arose in various parts of the kingdom, succeeded in giving an immense impulse to all the branches of the national industry; the result of which has been a harvest of wealth and prosperity, perhaps without a parallel in the history of the world.”

Samuel Smiles (1812–1904) Scottish author

Lives of the Engineers (1862).

Men , World , History , Parting

“Legal plunder can be committed in an infinite number of ways. Thus we have an infinite number of plans for organizing it: tariffs, protection, benefits, subsidies, encouragements, progressive taxation, public schools, guaranteed jobs, guaranteed profits, minimum wages, a right to relief, a right to the tools of labor, free credit, and so on, and so on. All these plans as a whole — with their common aim of legal plunder — constitute socialism.”

Frédéric Bastiat book The Law

The Law (1850)

School , Way

“Surely it is a great thing to increase the numerous host of fixed stars previously visible to the unaided vision, adding countless more which have never before been seen, exposing these plainly to the eye in numbers ten times exceeding the old and familiar stars.”

Galileo Galilei book Sidereus Nuncius

Translation by Stillman Drake in Discoveries and Opinions of Galileo (1957)
Sidereus Nuncius (Venice, 1609)

Star , Time

“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)

“I know there are some people in Germany who become sick when they see these black uniforms, we understand the reason for this, and do not expect we shall be loved by all that number of people; those who come to fear us in any way or at any time must have a bad conscience towards the Fuhrer and the nation. For these persons we have established an organisation called the Security Service.”

Heinrich Himmler (1900–1945) Nazi officer, Commander of the SS

From his treatise The Security Squadron as an Anti-Bolshevik Battle Organisation, 1936
1930s

Love , People , Fear , Way

“The relational model provides different categories, different underlying structures into which experience can be organized. Here the establishment of strong connections to others, in reality or in fantasy, is presumed to be primary. Forms of relationship are seen as fundamental, and life is understood largely as an array of metaphors for expressing and playing out relational patterns: discovery, penetration, domination, surrender, control, longing, evasion, revelation, envelopment, merger, differentiation, and so on. The body is still centrally important. Sexuality and bodily experiences are viewed as particularly apt arenas for this activity, since sexuality is enormously multiform and plastic. The number of different body parts, the variability of interactions, the poignancy of the sensations, the immense number of combinations — the almost infinite variety of human sexual possibilities make this an enormously fertile reservoir of metaphors for expressing different types of relationships, different configurations of connections, between self and others.”

Stephen Mitchell (1946–2000) American psychologist

Relational Concepts in Psychoanalysis (Cambridge, Massachusetts: Harvard University Press, 1988), p. 91

Life , Reality , Strong , Parting

“Hermann went out of his mind, and is now confined in room Number 17 of the Obukhov Hospital. He never answers any questions, but he constantly mutters with unusual rapidity: "Three, seven, ace!"”

Aleksandr Pushkin book The Queen of Spades

"Three, seven, queen!"
VI.
The Queen of Spades (1833)

Question

“The number of elements that have to go into a hit would break a computer down…. the right season for that play, the right historical moment, the right tonality.”

Arthur Miller (1915–2005) playwright from the United States

The New York Times (9 May 1984)

Season

“He got out of the van to see how many other suppliers were ahead of him and thus calculate, more or less accurately, how long he would have to wait. He was number thirteen, he counted again, no, there was no doubt about it. Although he was not a suspirations person, he knew about that number’s bad reputation, in any conversation about chance, fate or destiny, someone always chips in with some real-life experience of the negative, even fatal influence of the number thirteen. He tried to remember if he had ever been in this place in the queue before, but the long and the short of it was that either it had never happened or else he had simply forgotten. he got annoyed with himself, it was nonsense, utterly absurd to worry about something that has no real existence, yes, that was right, he had never thought of that before, numbers don’t really exist, things couldn’t care less what number we give them, its all the same to them if we say they’re number thirteen or number forty-four, we can conclude, at the very least, that they do not even notice the position they happen to end up in. people aren’t things, people always want to be in first place”

José Saramago book The Cave

Source: The Cave (2000), p. 9 (Vintage 2003)

Life , Fate , People , Chance

“The streaming plain, seamed and seared with long parallel canals and scooped into water-holes, is an immensity, and these castaways who strive to exhume themselves from it are legion. But the thirty million slaves, hurled upon one another in the mud of war by guilt and error, uplift their human faces and reveal at last a bourgeoning Will. The future is in the hands of these slaves, and it is clearly certain that the alliance to be cemented some day by those whose number and whose misery alike are infinite will transform the old world.”

Henri Barbusse book Under Fire

Under Fire (1916), Ch. 1 - The Vision

War , World , Error , Water

“We, in the UAE, have no such word as “impossible”; it does not exist in our lexicon. Such a word is used by the lazy and the weak, who fear challenges and progress. When one doubts his potential and capabilities as well as his confidence, he will lose the compass that leads him to success and excellence, thus failing to achieve his goal. I require you, youth, to insist on number one.”

Mohammed bin Rashid al-Maktoum (1949) Emirati politician

Ten best quotes: HH Sheikh Mohammed, http://www.arabianbusiness.com/photos/ten-best-quotes-hh-sheikh-mohammed-503777.html?img=0, Arabian Business.

Youth , Fear , Confidence , Success

“As a square number is known to be the product of a number multiplied by itself, so every polygonal number, multiplied by one number and added to another, both of which depend upon the number of its angles, produces a square number. I shall prove this, and shall show also how from a given side to find its polygon and conversely. Some auxiliary propositions must first be proved.”

Diophantus Arithmetica

As quoted by James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884)
Arithmetica (c. 250 AD)

Dependency

“When we attempt to conceive the number of particles in an atmosphere, it is somewhat like attempting to conceive the number of stars in the universe; we are confounded with the thought. But if we limit the subject, by taking a given volume of any gas, we seem persuaded that, let the divisions be ever so minute, the number of particles must be finite; just as in a given space of the universe, the number of stars and planets cannot be infinite.”

John Dalton book A New System of Chemical Philosophy

Source: A New System of Chemical Philosophy (1808), Ch. III On Chemical Synthesis

Star , Universe

“Socrates having heard Plato read the Lysis, said, "O Hercules! what a number of lies the young man has told about me." For he had set down a great many things as sayings of Socrates which he never said.”

Socrates (-470–-399 BC) classical Greek Athenian philosopher

Diogenes Laertius

Reading

“Motion at low Reynolds number is very majestic, slow, and regular.”

Edward M. Purcell (1912–1997) American physicist

"Life at Low Reynolds Number" in the American Journal of Physics (January 1977)

“The final sin of man, said Luther truly, is his unwillingness to concede that he is a sinner. The significant contribution of modern culture to this perennial human inclination lies in the number of plausible reasons which it was able to adduce in support of man's good opinion of himself.”

Reinhold Niebuhr (1892–1971) American protestant theologian

vol. 1, p. 121
The Nature and Destiny of Man: A Christian Interpretation (1941)

Support

“And I do further proclaim, declare, and make known, that whenever, in any of the States of Arkansas, Texas, Louisiana, Mississippi, Tennessee, Alabama, Georgia, Florida, South Carolina, and North Carolina, a number of persons, not less than one-tenth in number of the votes cast in such State at the Presidential election of the year of our Lord one thousand eight hundred and sixty, each having taken the oath aforesaid and not having since violated it, and being a qualified voter by the election law of the State existing immediately before the so-called act of secession, and excluding all others, shall re-establish a State government which shall be republican, and in no wise contravening said oath, such shall be recognized as the true government of the State, and the State shall receive thereunder the benefits of the constitutional provision which declares that "The United States shall guaranty to every State in this union a republican form of government, and shall protect each of them against invasion; and, on application of the legislature, or the executive, (when the legislature cannot be convened,) against domestic violence."”

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

1860s, Proclamation of Amnesty and Reconstruction (1863)

Law , Personality

“I was obliged to retract, like a good Catholic, this opinion of mine; and as a punishment my dialogue was prohibited; and after five months being dismissed from Rome (at the time that the city of Florence was infected with plague), the habitation which with generous pity was assigned to me, was that of the dearest friend I had in Siena, Monsignor the Archbishop Piccolomini, whose most agreeable conversation I enjoyed with such quite and satisfaction of mind, that having there resumed my studies, I discovered and demonstrated a great number on the mechanical conclusions on the resistance of solids … after about five months, the pestilence having ceased, the confinement of that house was changed by His Holiness for the freedom of the country so agreeable to me, whence I returned to the villa of Bellosguardo, and afterwards to Arcetri, where I still breathe salubrious air near my dear native-country Florence. Stay sane.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Source: Letter to Fr. Vincenzo Renieri (c. 1633), p. 251-253

Study , Freedom , Change , Time

“Your wonderment 'what I have against religion' reminds me of your recent Vagrant essay… To my mind, that essay misses one point altogether. Your "agnostic" has neglected to mention the very crux of all agnosticism—namely that the Judaeo-Christian mythology is NOT TRUE. I can see that in your philosophy truth per se has so small a place, that you can scarcely realise what it is that Galpin and I are insisting upon. In your mind, MAN is the centre of everything, and his exact conformation to certain regulations of conduct HOWEVER EFFECTED, the only problem in the universe. Your world (if you will pardon my saying so) is contracted. All the mental vigour and erudition of the ages fail to disturb your complacent endorsement of empirical doctrines and purely pragmatical notions, because you voluntarily limit your horizon—excluding certain facts, and certain undeniable mental tendencies of mankind. In your eyes, man is torn between only two influences; the degrading instincts of the savage, and the temperate impulses of the philanthropist. To you, men have but two types of emotion—lovers of the self and lovers of the race…. You are forgetting a human impulse which, despite its restriction to a relatively small number of men, has all through history proved itself as real and as vital as hunger—as potent as thirst or greed. I need not say that I refer to that simplest yet most exalted attribute of our species—the acute, persistent, unquenchable craving TO KNOW. Do you realise that to many men it makes a vast and profound difference whether or not the things about them are as they appear?… If TRUTH amounts to nothing, then we must regard the phantasma of our slumbers just as seriously as the events of our daily lives…. I recognise a distinction between dream life and real life, between appearances and actualities. I confess to an over-powering desire to know whether I am asleep or awake—whether the environment and laws which affect me are external and permanent, or the transitory products of my own brain. I admit that I am very much interested in the relation I bear to the things about me—the time relation, the space relation, and the causative relation. I desire to know approximately what my life is in terms of history—human, terrestrial, solar, and cosmical; what my magnitude may be in terms of extension,—terrestrial, solar, and cosmical; and above all, what may be my manner of linkage to the general system—in what way, through what agency, and to what extent, the obvious guiding forces of creation act upon me and govern my existence. And if there be any less obvious forces, I desire to know them and their relation to me as well.”

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

Letter to Maurice W. Moe (15 May 1918), in Selected Letters I, 1911-1924 edited by August Derleth and Donald Wandrei, p. 60
Non-Fiction, Letters

Life , Men , Hunger , Truth

“Henceforward the Christian Churches having a form of godliness, but denying the power thereof, came into the hands of the Encratites: and the Heathens, who in the fourth century came over in great numbers to the Christians, embraced more readily this sort of Christianity, as having a greater affinity with their old superstitions, than that of the sincere Christians; who by the lamps of the seven Churches of Asia, and not by the lamps of the Monasteries, had illuminated the Church Catholic during the three first centuries.”

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

Vol. I, Ch. 13: Of the King who did according to his will, and magnified himself above every God, and honored Mahuzzims, and regarded not the desire of women
Observations upon the Prophecies of Daniel, and the Apocalypse of St. John (1733)

Sincerity

“Priestley was the first (unless it was Beccaria) who taught my lips to pronounce this sacred truth — that the greatest happiness of the greatest number is the foundation of morals and legislation.”

Jeremy Bentham (1748–1832) British philosopher, jurist, and social reformer

"Extracts from Bentham's Commonplace Book", in Collected Works, x, p. 142; He credits Priestley in his Essay on the First Principles of Government (1768) or Beccaria with inspiring his use of the phrase, often paraphrased as "The greatest good for the greatest number", but the statement "the greatest happiness for the greatest number" actually originates with Francis Hutcheson, in his Inquiry concerning Moral Good and Evil (1725), sect. 3. In an unpublished manuscript on utilitarianism, written for James Mill, he later criticized this formulation: "Greatest happiness of the greatest number. Some years have now elapsed since, upon a closer scrutiny, reason, altogether incontestable, was found for discarding this appendage. On the surface, additional clearness and correctness given to the idea: at bottom, the opposite qualities. Be the community in question what it may, divide it into two equal parts, call one of them the majority, the other minority, layout of the account of the feelings of the minority, include in the account no feelings but those in the majority, the result you will find is that of this operation, that to the aggregate stock of happiness of the community, loss not profit is the result of the operation. Of this proposition the truth will be the more palpable, the greater the ration of the number of the minority to that of the majority: in other words, the less difference between the two unequal parts: and suppose the condivident part equal, the quantity of the error will then be at its maximum." — as quoted in The Classical Utilitarians : Bentham and Mill (2003) by John Troyer, p. 92;

Truth , Happiness

“I think that it’s important always to retain awareness of what you call core ideas, including those in the tradition of political philosophy. I think keeping in touch with those earlier political philosophers, being aware of them as part of our training, I think that’s still quite worthwhile. I know, or I would guess less and less of that may be taking place. But at the same time, I think that we should try to remain aware of the richness and complexity of the world that we deal with out there, and how much more, in a way—[laughing] it’s always been complex, but how much more complex it’s grown. Especially the field of democracy now, in just the sheer number and varieties.”

Robert A. Dahl (1915–2014) American political scientist

A Conversation with Robert A. Dahl (2009)

World , Way , Democracy , Idea

“I should have sent you news of myself long ago, for I know how much pleasure one derives from a letter during one's first days in the regiment. One needs it to be reminded that one is something more than a registered number and that in the past one's existence was different from that of beast. Anyway that is how I felt about the army. I was unable to connect my present existence with my former life as a civilian.... Here [in Paris in his studio in La Rue Pigalle] I am leading a studious and quite exemplary life... I am working on an important picture which is progressing well and which will be exhibited, I hope, at the [Salon des] 'Indépendants. In addition I am planning to do a screen which will also be shown at the exhibition. Otherwise nothing is happening. I may go with Vuillard to see a music publisher, but I do not expect any success as yet in that direction. I have abandoned chromolithography (ouf!) for the moment, but I shall take it up again whenever I feel impelled to interrupt my oil painting, in order to vary my pleasure's.”

Pierre Bonnard (1867–1947) French painter and printmaker

in his letter to Lugné-Poë, End of 1890; as quoted in Pierre Bonnard, by John Rewald; MoMA - distribution, Simon & Schuster, New York, 1918, p. 17 - note 11
Lugné-Poe was just called then in the French army; Bonnard had left the army already, c. one year ago

Life , Pleasure , Hope , Music

“Our nation is unique. We grew out of a desire to worship God in a certain way; we grew from a number of other nations who were being prosecuted because of their faith. We have a wonderful culture, a wonderful, vibrant language. I want my people to be proud of who they are again.”

Eugène Terre'Blanche (1941–2010) South African police officer, farmer, political activist, white supremacist

Interview by Antoinette Keyser http://www.mg.co.za/articlePage.aspx?articleid=249083&area=/insight/insight__national/, (25 August 2005).

God , People , Faith , Way

“It seems to me, that if the matter of our sun and planets and all the matter of the universe, were evenly scattered throughout all the heavens, and every particle had an innate gravity towards all the rest, and the whole of space throughout which this matter was scattered was but finite, the matter on [toward] the outside of this space would, by its gravity, tend towards all the matter on the inside, and, by consequence, fall down into the middle of the whole space, and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space it could never convene into one mass; but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one another throughout all that infinite space.”

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

Four Letters to Bentley (1692) first letter

Universe , Sun

“The provision of a whole new system of electric generation emancipated industry from the leather belt and line shaft, for it eventually became possible to provide each tool with its own electric motor. This may seem only a detail of minor importance. In fact, modern industry could not be carried out with the belt and line shaft for a number of reasons. The motor enabled machinery to be arranged in the order of the work, and that alone has probably doubled the efficiency of industry, for it has cut out a tremendous amount of useless handling and hauling. The belt and line shaft were also tremendously wasteful – so wasteful indeed that no factory could be really large, for even the longest line shaft was small according to modern requirements. Also high speed tools were impossible under the old conditions – neither the pulleys nor the belts could stand modern speeds. Without high speed tools and the finer steels which they brought about, there could be nothing of what we call modern industry.”

Henry Ford (1863–1947) American industrialist

Henry Ford and Samuel Crowther (1930). Edison as I Know Him. Cosmopolitan Book Company. p. 15

Speed

“If you actually took the number of Muslims Americans, we'd be one of the largest Muslim countries in the world.”

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

Interview with Laura Haim, Canal Plus, France. http://www.whitehouse.gov/the_press_office/Transcript-of-the-Interview-of-the-President-by-Laura-Haim-Canal-Plus-6-1-09/, White House Library (1 June 2009)
2009

World , Country

“But for Socrates, tragedy did not even seem to "tell what's true", quite apart from the fact that it addresses "those without much wit", not the philosopher: another reason for giving it a wide berth. Like Plato, he numbered it among the flattering arts which represent only the agreeable, not the useful, and therefore required that his disciples abstain most rigidly from such unphilosophical stimuli — with such success that the young tragedian, Plato, burnt his writings in order to become a pupil of Socrates.”

Friedrich Nietzsche book The Birth of Tragedy

Nun aber schien Sokrates die tragische Kunst nicht einmal "die Wahrheit zu sagen": abgesehen davon, dass sie sich an den wendet, der "nicht viel Verstand besitzt", also nicht an den Philosophen: ein zweifacher Grund, von ihr fern zu bleiben. Wie Plato, rechnete er sie zu den schmeichlerischen Künsten, die nur das Angenehme, nicht das Nützliche darstellen und verlangte deshalb bei seinen Jüngern Enthaltsamkeit und strenge Absonderung von solchen unphilosophischen Reizungen; mit solchem Erfolge, dass der jugendliche Tragödiendichter Plato zu allererst seine Dichtungen verbrannte, um Schüler des Sokrates werden zu können.
Source: The Birth of Tragedy (1872), p. 68

Art , Success

“Why have stockholders?… What contribution do they make, entitling them to heirship of half the profits of the industrial system, receivable partly in the form of dividends, and partly in the form of increased market values resulting from undistributed corporate gains? Stockholders toil not, neither do they spin, to earn that reward. They are beneficiaries by position only. Justification for their inheritance must be sought outside classic economic reasoning…. [and] can be founded only upon social grounds… that justification turns on the distribution as well as the existence of wealth. Its force exists only in direct ratio to the number of individuals who hold such wealth. Justification for the stockholder's existence thus depends on increasing distribution within the American population. Ideally the stockholder's position will be impregnable only when every American family has its fragment of that position and of the wealth by which the opportunity to develop individuality becomes fully actualized.”

Adolf A. Berle (1895–1971) American diplomat

1967, p. xxiii
The Modern Corporation and Private Property. 1932/1967

Family , Dependency , Wealth

“It is a complaint without foundation that "to very few people is granted the faculty of comprehending what is imparted to them, and that most, through dullness of understanding, lose their labor and their time." On the contrary, you will find the greater number of men both ready in conceiving and quick in learning, since such quickness is natural to man. As birds are born to fly, horses to run, and wild beasts to show fierceness, so to us peculiarly belong activity and sagacity of understanding.”
Falsa enim est querela, paucissimis hominibus vim percipiendi quae tradantur esse concessam, plerosque vero laborem ac tempora tarditate ingenii perdere. Nam contra plures reperias et faciles in excogitando et ad discendum promptos. Quippe id est homini naturale, ac sicut aves ad volatum, equi ad cursum, ad saevitiam ferae gignuntur, ita nobis propria est mentis agitatio atque sollertia.

Quintilian (35–96) ancient Roman rhetor

Book I, Chapter I, 1; translation by Rev. John Selby Watson
De Institutione Oratoria (c. 95 AD)

Men , People , Understanding , Nature

“As regards capital cases, the trouble is that emotional men and women always see only the individual whose fate is up at the moment, and neither his victim nor the many millions of unknown individuals who would in the long run be harmed by what they ask. Moreover, almost any criminal, however brutal, has usually some person, often a person whom he has greatly wronged, who will plead for him. If the mother is alive she will always come, and she cannot help feeling that the case in which she is so concerned is peculiar, that in this case a pardon should be granted. It was really heartrending to have to see the kinfolk and friends of murderers who were condemned to death, and among the very rare occasions when anything governmental or official caused me to lose sleep were times when I had to listen to some poor mother making a plea for a "criminal" so wicked, so utterly brutal and depraved, that it would have been a crime on my part to remit his punishment.
On the other hand, there were certain crimes where requests for leniency merely made me angry. Such crimes were, for instance, rape, or the circulation of indecent literature, or anything connected with what would now be called the "white slave" traffic, or wife murder, or gross cruelty to women or children, or seduction and abandonment, or the action of some man in getting a girl whom he seduced to commit abortion. In an astonishing number of these cases men of high standing signed petitions or wrote letters asking me to show leniency to the criminal. In two or three of the cases — one where some young roughs had committed rape on a helpless immigrant girl, and another in which a physician of wealth and high standing had seduced a girl and then induced her to commit abortion — I rather lost my temper, and wrote to the individuals who had asked for the pardon, saying that I extremely regretted that it was not in my power to increase the sentence. I then let the facts be made public, for I thought that my petitioners deserved public censure. Whether they received this public censure or not I did not know, but that my action made them very angry I do know, and their anger gave me real satisfaction.”

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

Source: 1910s, Theodore Roosevelt — An Autobiography (1913), Ch. VIII : The New York Governorship

Death , Women , Men , Fate

“The number 2 thought of by one man cannot be added to the number 2 thought of by another man so as to make up the number 4.”

Simone Weil (1909–1943) French philosopher, Christian mystic, and social activist

Oppression and Liberty (1958), p. 82

“Win with ability, not with numbers.”

Alexander Suvorov (1730–1800) Russian military commander

Quoted in Danchenko and Vydrin, Military Pedagogy, 1973.

“I believe that there is a necessary connection in both directions between the physical and the mental, but that it cannot be discovered a priori. Opinion is strongly divided on the credibility of some kind of functionalist reductionism, and I won't go through my reasons for being on the antireductionist side of that debate. Despite significant attempts by a number of philosophers to describe the functional manifestations of conscious mental states, I continue to believe that no purely functionalist characterization of a system entails — simply in virtue of our mental concepts — that the system is conscious.”

Thomas Nagel (1937) American philosopher

"Conceiving the Impossible and the Mind-Body Problem," Royal Institute of Philosophy annual lecture, given in London on February 18, 1998, published in Philosophy vol. 73 no. 285, July 1998, pp 337-352, Cambridge University Press, p. 337.

“We must resist the temptation to be “normal,” because those who are now considered normal accept the values and practices of an insane world. In modern society, for example, normal people strive to accumulate as many commodities as possible, because they believe that their success and personal worth are linked to the number of possessions they have acquired. As the joke goes, “The one who dies with the most toys, wins.” If we espouse this viewpoint, the toys we have to play with form the measure of our personal worth. Unfortunately, this notion confuses acquired material worth with our inherent worth as spiritual beings.”

Bhakti Tirtha Swami (1950–2005) American Hindu writer

Source: Books, Spiritual Warrior, Volume III: Solace for the Heart in Difficult Times (Hari-Nama Press, 2000), Chapter 8 - How To Strengthen Ourselves

People , World , Success , Personality

“…reciprocity is barter. I always understood that barter was the last effort of civilization that it was exactly that state of human exchange that separated civilization from savagery; and if reciprocity is only barter, I fear that would hardly help us out of our difficulty. My noble friend read some extracts from the speeches of those who had the misfortune to be in Parliament at that time, and he honoured me by reading an extract from the speech I then made in the other House of Parliament. That was a speech in favour of reciprocity, and indicated the means by which reciprocity could be obtained. That is to say…by the negotiation of a treaty of commerce, by reciprocal exchange and the lowering of duties, the products of the two negotiating countries would find a freer access and consumption in the two countries than they formerly possessed. But when he taunts me with his quotation of some musty phrases of mine 40 years ago, I must remind him that we had elements then on which treaties of reciprocity could be negotiated. At that time, although the great changes of Sir Robert Peel had taken place, there were 168 articles in the tariff which were materials by which you could have negotiated, if that was a wise and desirable policy, commercial treaties of reciprocity. What is the number you now have in the tariff? Twenty-two. Those who talk of negotiating treaties of reciprocity…have they the materials for negotiating treaties of reciprocity? You have lost the opportunity. I do not want to enter into the argument at the present moment; but England cannot pursue that policy.”

Benjamin Disraeli (1804–1881) British Conservative politician, writer, aristocrat and Prime Minister

Speech in the House of Lords (29 April 1879), reported in The Times (30 April 1879), p. 8.
1870s

Fear , Effort , Change , Time

“It is almost impossible to win a VC. In the hundred-and-fifty years since it was created, the number of British and Commonwealth troops who've seen action is in the tens of millions, but only 1,351 of them have been awarded the Victoria Cross. The chances of surviving a VC action are just one in ten, but if you do survive, the medal can never be taken away from you. You can go to the gallows wearing it. And no matter how many letters you have after your name, VC always comes first.”

Jeremy Clarkson (1960) English broadcaster, journalist and writer

The Victoria Cross: For Valour (2003)

Chance

“When there are such lands there should be profitable things without number.”

Cristoforo Colombo (1451–1506) Explorer, navigator, and colonizer

27 November 1492
Journal of the First Voyage

“The undulation of these infinite numbers of mountains, whose snowy summits make them look as if covered by foam, recalled to my remembrance the surface of a storm-beaten ocean. If I looked towards the west, the ocean lay before me in all its majestic grandeur, a continuation as it were, of these fleecy hilltops. Where the earth ended and the sea began it was impossible for the eye to distinguish.

I soon felt that strange and mysterious sensation which is awakened in the mind when looking down from lofty hilltops, and now I was able to do so without any feeling of nervousness, having fortunately hardened myself to that kind of sublime contemplation. I wholly forgot who I was, and where I was. I became intoxicated with a sense of lofty sublimity, without thought of the abysses into which my daring was soon about to plunge me.”

Jules Verne book A Journey to the Center of the Earth

<p>Les ondulations de ces montagnes infinies, que leurs couches de neige semblaient rendre écumantes, rappelaient à mon souvenir la surface d'une mer agitée. Si je me retournais vers l'ouest, l'Océan s'y développait dans sa majestueuse étendue, comme une continuation de ces sommets moutonneux. Où finissait la terre, où commençaient les flots, mon oeil le distinguait à peine.</p><p>Je me plongeais ainsi dans cette prestigieuse extase que donnent les hautes cimes, et cette fois, sans vertige, car je m'accoutumais enfin à ces sublimes contemplations. Mes regards éblouis se baignaient dans la transparente irradiation des rayons solaires, j'oubliais qui j'étais, où j'étais, pour vivre de la vie des elfes ou des sylphes, imaginaires habitants de la mythologie scandinave; je m'enivrais de la volupté des hauteurs, sans songer aux abîmes dans lesquels ma destinée allait me plonger avant peu.</p>
Source: Journey to the Center of the Earth (1864), Ch. XVI: Boldly down the crater

Feeling , Mountain , Sense , Sea

“We have been the recipients of the choicest bounties of Heaven. We have been preserved, these many years, in peace and prosperity. We have grown in numbers, wealth and power, as no other nation has ever grown. But we have forgotten God. We have forgotten the gracious hand which preserved us in peace, and multiplied and enriched and strengthened us; and we have vainly imagined, in the deceitfulness of our hearts, that all these blessings were produced by some superior wisdom and virtue of our own. Intoxicated with unbroken success, we have become too self-sufficient to feel the necessity of redeeming and preserving grace, too proud to pray to the God that made us!”

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

Upon proclaiming a National Fast Day (30 March 1863)
1860s

Wisdom , God , Peace , Feeling

“The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space. Therefore an infinite number of lines may be conceived of as intersecting each other at a point, which has no dimensions and is only of the thickness (if thickness it may be called) of one single line.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), II Linear Perspective

Idea , Nature

“I had translated the first twelve books of the Odyssey. For a while I learnt English also, merely so as to gain an accurate knowledge of Shakespeare; and I made a metrical translation of Romeo's monologue. Though I soon left English on one side, yet Shakespeare remained my exemplar, and I projected a great tragedy which was almost nothing but a medley of Hamlet and King Lear. The plan was gigantic in the extreme; two- and-forty human beings died in the course of this piece, and I saw myself compelled, in its working-out, to call the greater number back as ghosts, since otherwise I should have been short of characters for my last Acts. This play occupied my leisure for two whole years.”

Richard Wagner (1813–1883) German composer, conductor

Autobiographical Sketch (1843)

Books , Knowledge

“No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

“More often than not, the classes of objects encountered in the real physical world do not have precisely deﬁned criteria of membership. For example, the class of animals clearly includes dogs, horses, birds, etc. as its members, and clearly excludes such objects as rocks, ﬂuids, plants, etc. However, such objects as starfish, bacteria, etc. have an ambiguous status with respect to the class of animals. The same kind of ambiguity arises in the case of a number such as 10 in relation to the “class” of all real numbers which are much greater than 1.”

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

Source: 1960s, Fuzzy sets (1965), p. 338

World , Dogs , Bird , Animals

“The ideal of strictly scientific method in mathematics which I have tried to realise here, and which perhaps might be named after Euclid I should like to describe in the following way… The novelty of this book does not lie in the content of the theorems but in the development of the proofs and the foundations on which they are based… With this book I accomplish an object which I had in view in my Begriffsschrift of 1879 and which I announced in my Grundlagen der Arithmetik. I am here trying to prove the opinion on the concept of number that I expressed in the book last mentioned.”

Gottlob Frege (1848–1925) mathematician, logician, philosopher

Vol. 1. pp. 137-140, as cited in: Ralph H. Johnson (2012), Manifest Rationality: A Pragmatic Theory of Argument, p. 87
Grundgesetze der Arithmetik, 1893 and 1903

Lie , Books , Way , Mathematics

“I get paid for seeing that my clients have every break the law allows. I have knowingly defended a number of guilty men. But the guilty never escape unscathed. My fees are sufficient punishment for anyone.”

F. Lee Bailey (1933) American lawyer

Los Angeles Times, January 9, 1972.

Men , Law

“Europe is a molehill. It has never had any great empires, like those of the Orient, numbering six hundred million souls.”

Napoleon I of France (1769–1821) French general, First Consul and later Emperor of the French

Napoleon : In His Own Words (1916)

Soul

“Let us assume that our problem is the intensification in the public mind of the prestige of a hotel. The problem for the public relations counsel is to create in the public mind the close relationship between the hotel and a number of ideas that represent the things the hotel desires to stand for in the public mind.”

Edward Bernays (1891–1995) American public relations consultant, marketing pioneer

Source: Crystallizing Public Opinion (1923), p. 168

Idea , Problem

“Part of the charm of synthetic organic chemistry derives from the vastness of the intellectual landscape along several dimensions. First, there is the almost infinite variety and number of possible target structures that lurk in the darkness waiting to be made. Then, there is the vast body of organic reactions that serve to transform one substance into another, now so large in number as to be beyond credibility to a non-chemist. There is the staggering range of reagents, reaction conditions, catalysts, elements, and techniques that must be mobilized in order to tame these reactions for synthetic purposes. Finally, it seems that new information is being added to that landscape at a rate that exceeds the ability of a normal person to keep up with it. In such a troubled setting any author, or group of authors, must be regarded as heroic if through their efforts, the task of the synthetic chemist is eased.”

Elias James Corey (1928) American chemist

Foreword of Name Reactions in Heterocyclic Chemistry (2004) by Jie Jack Li

Effort , Waiting , Parting , Personality

“O comfortable allurement, O ravishing persuasion to deal with a science whose subject is so ancient, so pure, so excellent, so surrounding all creatures, so used of the almighty and incomprehensible wisdom of the Creator, in distinct creation of all creatures: in all their distinct parts, properties, natures, and virtues, by order, and most absolute number, brought from nothing to the formality of their being and state.”

John Dee (1527–1608) English mathematican, astrologer and antiquary

The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara (1570)

Wisdom , Nature , Science , Parting

“It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Mathematics , Problem

“God created everything by number, weight and measure.”
Numero pondere et mensura Deus omnia condidit.

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

As quoted in Symmetry in Plants (1998) by Roger V. Jean and Denis Barabé, p. xxxvii, a translation of a Latin phrase he wrote in a student's notebook, elsewhere given as Numero pondere et mensura Deus omnia condidit. This is similar to Latin statements by Thomas Aquinas, and even more ancient statements of the Greek philosopher Pythagoras. See also Wisdom of Solomon 11:20 https://en.wikisource.org/wiki/Bible_(King_James)/Wisdom_of_Solomon#Chapter_11

God

“No one can escape the power of language, let alone those of English birth brought up from childhood, as Mrs. Hilbery had been, to disport themselves now in the Saxon plainness, now in the Latin splendor of the tongue, and stored with memories, as she was, of old poets exuberating in an infinity of vocables. Even Katharine was slightly affected against her better judgment by her mother's enthusiasm. Not that her judgment could altogether acquiesce in the necessity for a study of Shakespeare's sonnets as a preliminary to the fifth chapter of her grandfather's biography. Beginning with a perfectly frivolous jest, Mrs. Hilbery had evolved a theory that Anne Hathaway had a way, among other things, of writing Shakespeare's sonnets; the idea, struck out to enliven a party of professors, who forwarded a number of privately printed manuals within the next few days for her instruction, had submerged her in a flood of Elizabethan literature; she had come half to believe in her joke, which was, she said, at least as good as other people's facts, and all her fancy for the time being centered upon Stratford-on-Avon.”

Virginia Woolf book Night and Day

Source: Night and Day (1919), Ch. 24

People , Way , Literature , Idea

“… to put an end to the epidemics, we were forced to burn the bodies of an incalculable number of people who were destroyed by the disease. So we were forced to build crematoria, and on this account they are loosing a bond for us. "He also stated that he punished the culprit if the atrocities occurred in the camps." On the Einsatzgruppen: "The war on the Eastern front made the demands more difficult for our soldiers. A terrible climate, never-ending distances, an enemy population and constantly apparent partisans. Just because it was difficult, the troops prevailed. So they were forced to destroy entire villages if there was resistance and gunfire from such a village. Russians are not ordinary enemies, we can not understand their mentality. In the most desperate situations, they would refuse to capitulate. If, because of these difficulties in the East, the Jewish people suffered large casualties, it must be remembered that the German people also suffered severely."”

Heinrich Himmler (1900–1945) Nazi officer, Commander of the SS

April 20, 1945 in a meeting with Norbert Masur, a representative of the World Jewish Congress.

War , People , Disease , Understanding

“The rude, discursive Thinker is the Scholastic (Schoolman Logician). The true Scholastic is a mystical Subtlist; out of logical Atoms he builds his Universe; he annihilates all living Nature, to put an Artifice of Thoughts (Gedankenkunststuck, literally Conjuror's-trick of Thoughts) in its room. His aim is an infinite Automaton. Opposite to him is the rude, intuitive Poet: this is a mystical Macrologist: he hates rules and fixed form; a wild, violent life reigns instead of it in Nature; all is animate, no law; wilfulness and wonder everywhere. He is merely dynamical. Thus does the Philosophic Spirit arise at first, in altogether separate masses. In the second stage of culture these masses begin to come in contact, multifariously enough; and, as in the union of infinite Extremes, the Finite, the Limited arises, so here also arise "Eclectic Philosophers" without number; the time of misunderstanding begins. The most limited is, in this stage, the most important, the purest Philosopher of the second stage. This class occupies itself wholly with the actual, present world, in the strictest sense. The Philosophers of the first class look down with contempt on those of the second; say, they are a little of everything, and so nothing; hold their views as the results of weakness, as Inconsequentism. On the contrary, the second class, in their turn, pity the first; lay the blame on their visionary enthusiasm, which they say is absurd, even to insanity.”

Novalis (1772–1801) German poet and writer

Pupils at Sais (1799)

Life , Hate , World , Law

“It is forbidden to kill; therefore all murderers are punished unless they kill in large numbers and to the sound of trumpets.”

Voltaire (1694–1778) French writer, historian, and philosopher

Il est défendu de tuer; tout meurtrier est puni, à moins qu’il n’ait tué en grande compagnie, et au son des trompettes.
"Rights" (1771)
Citas, Questions sur l'Encyclopédie (1770–1774)

Funny

“[W]hile man exists, it is his duty to improve not only his own condition, but to assist in ameliorating mankind; and therefore, without entering upon the details of the question, I will simply say, that I am for those means which will give the greatest good to the greatest number.”

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

1860s, Speech to Germans at Cincinnati, Ohio (1861), Commercial version

Question

“"What's common across all human experience across all time? That's what Jung essentially meant by an archetype. We tend to think that what we see with our senses is real. And of course that's true, but what we see with our senses is what's real that works in the time frame that we exist in. So we see things that we can touch and pick up - we see tools, essentially, that are useful for our moment to moment activities. We don't see the structures of eternity, and we especially don't see the abstract structures of eternity. We have to imagine those with our imagination. Well that's partly what those stories are doing. They're saying that there are forms of stability that transcend our capacity to observe, which is hardly surprising. We know that if we are scientists, because we are always abstracting out things that we can't immediately observe. But there are moral, or metaphysical, or phenomenological realities that have the same nature. You can't see them in your life by observing them with your senses, but you can imagine them with your imagination, and sometimes the things that you imagine with your imagination are more real than the things that you see. Numbers are like that, for example. There are endless things like that. Same with fiction. A good work of fiction is more real than the stories from which it was derived. Otherwise it has no staying power. It's distilled reality. And some would say "it never happened," but it depends on what you mean by "happened." If it's a pattern that repeats in many many places, with variation, you can abstract out the central pattern. So the pattern never purely existed in any specific form, but the fact that you pulled a pattern out from all those exemplars means that you've extracted something real. I think the reason that the story of Adam and Eve has been immune to being forgotten is because it says things about the nature of the human condition that are always true."”

Jordan Peterson (1962) Canadian clinical psychologist, cultural critic, and professor of psychology

Concepts

Life , Imagination , Nature , Thinking

“If by "democracy" we mean the form which the Third Estate as such wishes to impart to public life as a whole, it must be concluded that democracy and plutocracy are the same thing under the two aspects of wish and actuality, theory and practice, knowing and doing. It is the tragic comedy of the world‑ improvers' and freedom‑ teachers' desperate fight against money that they are ipso facto assisting money to be effective. Respect for the big number—expressed in the principles of equality for all, natural rights, and universal suffrage—is just as much a class‑ ideal of the unclassed as freedom of public opinion (and more particularly freedom of the press) is so. These are ideals, but in actuality the freedom of public opinion involves the preparation of public opinion, which costs money; and the freedom of the press brings with it the question of possession of the press, which again is a matter of money; and with the franchise comes electioneering, in which he who pays the piper calls the tune. The representatives of the ideas look at one side only, while the representatives of money operate with the other. The concepts of Liberalism and Socialism are set in effective motion only by money. … There is no proletarian, not even a Communist movement, that has not operated in the interests of money, and for the time being permitted by money—and that without the idealists among its leaders having the slightest suspicion of the fact.”

Oswald Spengler book The Decline of the West

Source: Vol. II, Alfred A. Knopf, 1928, pp. 401–02 https://archive.org/details/in.ernet.dli.2015.49906/page/n893/mode/2up
Der Untergang des Abendlandes, Welthistorische Perspektiven (1922)
The Decline of the West (1918, 1923)

Democracy , Freedom , Money , Question

“Rocket engineering is not like ditch digging. With ditch digging you can get 100 people and dig a ditch, and you will dig it a hundred times as faster if you get 100 people versus one. With rockets, you have to solve the problem of a particular level of difficulty; one person who can solve the problem is worth an infinite number of people who can’t.”

Elon Musk (1971) South African-born American entrepreneur

Conversation: Elon Musk on Wired Science (2007)

People , Problem , Time , Personality

“I learnt to see philosophical systems in the context of the social milieu which produced them. I therefore learnt to look for social contention in philosophical systems. It is of course possible to see the history of philosophy in diverse ways, each way of seeing it being in fact an illumination of the type of problem dealt with in this branch of human thought. It is possible, for instance, to look upon philosophy as a series of abstract systems. When philosophy is so seen, even moral philosophers, with regrettable coyness, say that their preoccupation has nothing to do with life. They say that their concern is not to name moral principles or to improve anybody's character, but narrowly to elucidate the meaning of terms used in ethical discourse, and to determine the status of moral principles and ru1es, as regards the obligation which they impose upon us. When philosophy is regarded in the light of a series of abstract systems, it can be said to concern itself with two fundamental questions: first, the question 'what there is'; second, the question how 'what there is' may be explained. The answer to the first question has a number of aspects. It lays down a minimum number of general under which every item in the world can and must be brought. It does this without naming the items themselves, without furnishing us with an inventory, a roll-call of the items, the objects in the world. It specifies, not particu1ar objects, but the basic types of object. The answer further implies a certain reductionism; for in naming only a few basic types as exhausting all objects in the world, it brings object directly under one of the basic types.”

Kwame Nkrumah (1909–1972) Pan Africanist and First Prime Minister and President of Ghana

Source: Consciencism (1964), Philosophy In Retrospect, pp. 5-6.

Life , World , Way , History

“What a pity and what a poverty of spirit, to assert that beasts are machines deprived of knowledge and sentiment, which affect all their operations in the same manner, which learn nothing, never improve, &c. […] Some barbarians seize this dog, who so prodigiously excels man in friendship, they nail him to a table, and dissect him living, to show the mezarian veins. You discover in him all the same organs of sentiment which are in yourself. Answer me, machinist, has nature arranged all the springs of sentiment in this animal that he should not feel? Has he nerves to be incapable of suffering? Do not suppose this impertinent contradiction in nature. […] The animal has received those of sentiment, memory, and a certain number of ideas. Who has bestowed these gifts, who has given these faculties? He who has made the herb of the field to grow, and who makes the earth gravitate towards the sun.”

Voltaire (1694–1778) French writer, historian, and philosopher

" Beasts https://books.google.it/books?id=WQpJAQAAIAAJ&pg=PA8", in A Philosophical Dictionary, Volume 2, J. and H. L. Hunt, 1824, p. 9
Citas, Dictionnaire philosophique (1764)

Friendship , Dogs , Feeling , Spring

“The growth of cities has gone on beyond comparison faster than the growth of the country, and the upbuilding of the great industrial centers has meant a startling increase, not merely in the aggregate of wealth, but in the number of very large individual, and especially of very large corporate, fortunes. The creation of these great corporate fortunes has not been due to the tariff nor to any other governmental action, but to natural causes in the business world, operating in other countries as they operate in our own.”

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

1900s, First Annual Message to Congress (1901)

World , Business , Nature , Country

“Suppose that, at a given moment, a certain number of people are engaged in the manufacture of pins. They make as many pins as the world needs, working (say) eight hours a day. Someone makes an invention by which the same number of men can make twice as many pins: pins are already so cheap that hardly any more will be bought at a lower price. In a sensible world, everybody concerned in the manufacturing of pins would take to working four hours instead of eight, and everything else would go on as before. But in the actual world this would be thought demoralizing. The men still work eight hours, there are too many pins, some employers go bankrupt, and half the men previously concerned in making pins are thrown out of work. There is, in the end, just as much leisure as on the other plan, but half the men are totally idle while half are still overworked. In this way, it is insured that the unavoidable leisure shall cause misery all round instead of being a universal source of happiness. Can anything more insane be imagined?”

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

Source: 1930s, In Praise of Idleness and Other Essays (1935), Ch. 1: In Praise of Idleness.

Men , People , World , Way

“You'll be surprised how infinitely merciful they are. The prescription number is 96814. I think of it as the telephone number of God!”

Tennessee Williams Summer and Smoke

Alma, Scene Twelve
Summer and Smoke (1948)

God , Thinking

“If the immortal is also imperishable, the soul when attacked by death cannot perish; for the preceding argument shows that the soul will not admit of death, or even be dead, any more than three or the odd number will admit of the even…”

Socrates (-470–-399 BC) classical Greek Athenian philosopher

Plato, Phaedo

Death , Soul , Dead

“Random numbers should not be generated with a method chosen at random”

Donald Ervin Knuth book The Art of Computer Programming

Vol. II, Seminumerical Algorithms
The Art of Computer Programming (1968–2011)

“The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library.”

Bertrand Russell Principia Mathematica

Principia Mathematica, written with Alfred North Whitehead, (1910), vol. I, Introduction, ch. II: The Theory of Logical Types. This is a statement of the Berry paradox.
1910s

“Why is it that we entertain the belief that for every purpose odd numbers are the most effectual?”

Pliny the Elder book Natural History

Book XXVIII, sec. 23.
Naturalis Historia

“Women thought me charmingly shy, and sometimes stopped at nothing to “penetrate the disdainful shell of my fear,” as one of their number put it. Often as not, it was they who got penetrated.”

John Barth book The Floating Opera

The Floating Opera (1956)

Women , Fear

“If we glance at the most important revolutions in history, we are at no loss to perceive that the greatest number of these originated in the periodical revolutions of the human mind.”

Wilhelm Von Humboldt (1767–1835) German (Prussian) philosopher, government functionary, diplomat, and founder of the University of Berlin

Source: The Limits of State Action (1792), Ch. 16

History , Loss

“But, suppose, besides, that the making of the new machinery affords employment to a greater number of mechanics, can that be called compensation to the carpet makers, thrown on the streets?”

Karl Marx (1818–1883) German philosopher, economist, sociologist, journalist and revolutionary socialist

Vol. I, Ch. 15, Section 6, pg. 479.
(Buch I) (1867)

“… behind me there were ghosts of people like a trailing fog as far as I could see - grandfathers of grandfathers and grandmothers of grandmothers without number.”

Black Elk (1863–1950) Oglala Lakota leader

Black Elk Speaks (1961)

People

“Do you think Arabs are dumb? They gave us our numbers. Try doing long division with Roman numerals.”

Kurt Vonnegut book A Man Without a Country

A Man Without a Country (2005)

Thinking

“[L]et us assign the figures that have come into being in our theory to fire and earth and water and air. To earth let us give the cubical form; for earth is least mobile of the four and most plastic of bodies: and that substance must possess this nature in the highest degree which has its bases most stable. Now of the triangles which we assumed as our starting-point that with equal sides is more stable than that with unequal; and of the surfaces composed of the two triangles the equilateral quadrangle necessarily is more stable than the equilateral triangle… Now among all these that which has the fewest bases must naturally in all respects be the most cutting and keen of all, and also the most nimble, seeing it is composed of the smallest number of similar parts… Let it be determined then… that the solid body which has taken the form of the pyramid [tetrahedron] is the element and seed of fire; and the second in order of generation let [octahedron] us say to be that of air, and the third [icosahedron] that of water. Now all these bodies we must conceive as being so small that each single body in the several kinds cannot for its smallness be seen by us at all; but when many are heaped together, their united mass is seen…”

Plato book Timaeus

Section 55e–56c, Tr. R. D. Archer-Hind, The Timaeus of Plato (1888) pp. 199-201. https://books.google.com/books?id=q2YMAAAAIAAJ&pg=PA199
Timaeus

Nature , Water , Parting

“[F]rom the earliest periods of time [man] alone has divided the empire of the world between him and Nature. …[H]e rather enjoys than possesses, and it is by constant and perpetual activity and vigilance that he preserves his advantage, for if those are neglected every thing languishes, changes, and returns to the absolute dominion of Nature. She resumes her power, destroys the operations of man; envelopes with moss and dust his most pompous monuments, and in the progress of time entirely effaces them, leaving man to regret having lost by his negligence what his ancestors had acquired by their industry. Those periods in which man loses his empire, those ages in which every thing valuable perishes, commence with war and are completed by famine and depopulation. Although the strength of man depends solely upon the union of numbers, and his happiness is derived from peace, he is, nevertheless, so regardless of his own comforts as to take up arms and to fight, which are never-failing sources of ruin and misery. Incited by insatiable avarice, or blind ambition, which is still more insatiable, he becomes callous to the feelings of humanity; regardless of his own welfare, his whole thoughts turn upon the destruction of his own species, which he soon accomplishes. The days of blood and carnage over, and the intoxicating fumes of glory dispelled, he beholds, with a melancholy eye, the earth desolated, the arts buried, nations dispersed, an enfeebled people, the ruins of his own happiness, and the loss of his real power.”

Georges-Louis Leclerc, Comte de Buffon (1707–1788) French natural historian

Buffon's Natural History (1797) Vol. 10, pp. 340-341 https://books.google.com/books?id=respAAAAYAAJ&pg=PA340, an English translation of Histoire Naturelle (1749-1804).

War , People , Age , World

“I define as a unit any magnitude that can serve for the numerical derivation of a series of magnitudes, and in particular I call such a unit an original unit if it is not derivable from another unit. The unit of numbers, that is one, I call the absolute unit, all others relative.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Zero can never be a unit.
Definition 3. Part 1. The Elementary Conjunctions of Extensive Magnitudes. Ch. 1. Addition, Subtraction, Multiples and Fractions of Extensive Magnitudes. 1. Concepts and laws of calculation. Extension Theory Hermann Grassman, History of Mathematics (2000) Vol. 19 Tr. Lloyd C. Kannenberg, American Mathematical Society, London Mathematical Society
Ausdehnungslehre (1844)

“As the Bajauris were rebels and at enmity with the people of Islam, and as, by reason of the heathenish and hostile customs prevailing in their midst, the very name of Islam was rooted out from their tribe, they were put to general massacre and their wives and children were made captive. At a guess more than 3000 men went to their death; as the fight did not reach to the eastern side of the fort, a few got away there. The fort taken, we entered and inspected it. On the walls, in houses, streets and alleys, the dead lay, in what numbers! Comers and goers to and fro were passing over the bodies… With mind easy about the important affairs of the Bajaur fort, we marched, on Tuesday the 9th of Muharram, one kuroh (2m) down the dale of Bajaur and ordered that a tower of heads should be set up on the rising ground. On Wednesday the 10th of Muharram, we rode out to visit the Bajaur fort. There was a wine-party in Khawaja Kalan's house, several goat-skins of wine having been brought.”

Babur (1483–1530) 1st Mughal Emperor

Babur-Nama, translated into English by A.S. Beveridge, New Delhi reprint, 1979, pp. 370-71.

Death , Men , Hostility , Children

“It is easy to get to a higher number when you are not asking anything difficult from yourself.”

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

In response to House Majority Leader Eric Cantor (R-Va.), who, on behalf of the Republican party, wanted steeper cuts, while opposing tax rises (also termed as revenue enhancements) in a meeting about the U.S. debt ceiling on July 13, 2011.
According to an unidentified source[citation needed], as reported by blogger Sam Stien, "Obama Warns Cantor 'Don't Call My Bluff' As Debt Talks Stall," http://www.huffingtonpost.com/2011/07/13/obama-debt-ceiling-meeting_n_897834.html The Huffington Post, 14 July 2011
2011, Remarks on the economy (July 2011)

“In mathematics there is a certain way of seeking the truth, a way which Plato is said first to have discovered and which was called "analysis" by Theon and was defined by him as "taking the thing sought as granted and proceeding by means of what follows to a truth which is uncontested"; so, on the other hand, "synthesis" is "taking the thing that is granted and proceeding by means of what follows to the conclusion and comprehension of the thing sought." And although the ancients set forth a twofold analysis, the zetetic and the poristic, to which Theon's definition particularly refers, it is nevertheless fitting that there be established also a third kind, which may be called rhetic or exegetic, so that there is a zetetic art by which is found the equation or proportion between the magnitude that is being sought and those that are given, a poristic art by which from the equation or proportion the truth of the theorem set up is investigated, and an exegetic art by which from the equation set up or the proportion, there is produced the magnitude itself which is being sought. And thus, the whole threefold analytic art, claiming for itself this office, may be defined as the science of right finding in mathematics…. the zetetic art does not employ its logic on numbers—which was the tediousness of the ancient analysts—but uses its logic through a logistic which in a new way has to do with species [of number]…”

François Viète (1540–1603) French mathematician

Source: In artem analyticem Isagoge (1591), Ch. 1 as quoted by Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1934-1936) Appendix.

Truth , Art , Way , Mathematics

“Some shows get great numbers, others don’t. I don’t get panicky over it. If an actor can’t live with the cyclic nature of our industry, I guess he/she is in the wrong profession.”

Sukirti Kandpal (1987) Indian actress

On TRP of televison shows http://www.tellychakkar.com/tv/tv-news/sukirti-kandpal-says-i-dont-get-panicky-over-trps/

Nature

“The last chapter modeled technological progress as an increase in the number of types of products, N. In this chapter, we allow for improvements in the quality or productivity of each type. This approach has come to be known as the Schumpeterian approach to endogenous growth. We can think of increases in N as basic innovations that amount to dramatically new kinds of goods or methods of production. In contrast, increases in the quality of the existing products involve a continuing series of improvements and refinements of goods and techniques.”

Xavier Sala-i-Martin (1962) Catalan economist

Robert J. Barro, Xavier Sala-i-Martin, Economic growth 2nd ed. (2004), Ch. 7 : Technological Change: Schumpeterian Models of Quality Ladders

Thinking

“Now the trickiest catch in the negro problem is the fact that it is really twofold. The black is vastly inferior. There can be no question of this among contemporary and unsentimental biologists—eminent Europeans for whom the prejudice-problem does not exist. But, it is also a fact that there would be a very grave and very legitimate problem even if the negro were the white man's equal. For the simple fact is, that two widely dissimilar races, whether equal or not, cannot peaceably coexist in the same territory until they are either uniformly mongrelised or cast in folkways of permanent and traditional personal aloofness. No normal being feels at ease amidst a population having vast elements radically different from himself in physical aspect and emotional responses. A normal Yankee feels like a fish out of water in a crowd of cultivated Japanese, even though they may be his mental and aesthetic superiors; and the normal Jap feels the same way in a crowd of Yankees. This, of course, implies permanent association. We can all visit exotic scenes and like it—and when we are young and unsophisticated we usually think we might continue to like it as a regular thing. But as years pass, the need of old things and usual influences—home faces and home voices—grows stronger and stronger; and we come to see that mongrelism won't work. We require the environing influence of a set of ways and physical types like our own, and will sacrifice anything to get them. Nothing means anything, in the end, except with reference to that continuous immediate fabric of appearances and experiences of which one was originally part; and if we find ourselves ingulphed by alien and clashing influences, we instinctively fight against them in pursuit of the dominant freeman's average quota of legitimate contentment.... All that any living man normally wants—and all that any man worth calling such will stand for—is as stable and pure a perpetuation as possible of the set of forms and appearances to which his value-perceptions are, from the circumstances of moulding, instinctively attuned. That is all there is to life—the preservation of a framework which will render the experience of the individual apparently relevant and significant, and therefore reasonably satisfying. Here we have the normal phenomenon of race-prejudice in a nutshell—the legitimate fight of every virile personality to live in a world where life shall seem to mean something.... Just how the black and his tan penumbra can ultimately be adjusted to the American fabric, yet remains to be seen. It is possible that the economic dictatorship of the future can work out a diplomatic plan of separate allocation whereby the blacks may follow a self-contained life of their own, avoiding the keenest hardships of inferiority through a reduced number of points of contact with the whites... No one wishes them any intrinsic harm, and all would rejoice if a way were found to ameliorate such difficulties as they have without imperilling the structure of the dominant fabric. It is a fact, however, that sentimentalists exaggerate the woes of the average negro. Millions of them would be perfectly content with servile status if good physical treatment and amusement could be assured them, and they may yet form a well-managed agricultural peasantry. The real problem is the quadroon and octoroon—and still lighter shades. Theirs is a sorry tragedy, but they will have to find a special place. What we can do is to discourage the increase of their numbers by placing the highest possible penalties on miscegenation, and arousing as much public sentiment as possible against lax customs and attitudes—especially in the inland South—at present favouring the melancholy and disgusting phenomenon. All told, I think the modern American is pretty well on his guard, at last, against racial and cultural mongrelism. There will be much deterioration, but the Nordic has a fighting chance of coming out on top in the end.”

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

Letter to James F. Morton (January 1931), in Selected Letters III, 1929-1931 edited by August Derleth and Donald Wandrei, p. 253
Non-Fiction, Letters, to James Ferdinand Morton, Jr.

Life , World , Penalty , Way

“Bourgeois society is ruled by equivalence. It makes the dissimilar comparable by reducing it to abstract quantities. To the enlightenment, that which does not reduce to numbers, and ultimately to the one, becomes illusion.”

Theodor W. Adorno (1903–1969) German sociologist, philosopher and musicologist known for his critical theory of society

John Cumming trans., p. 7
Dialektik der Aufklärung [Dialectic of Enlightenment] (1944)

“Philosophical problems can be compared to locks on safes, which can be opened by dialing a certain word or number, so that no force can open the door until just this word has been hit upon, and once it is hit upon any child can open it.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

Conversation of 1930, in Personal Recollections (1981) by Rush Rhees, Ch. 6
Variant: Philosophy is like trying to open a safe with a combination lock: each little adjustment of the dials seems to achieve nothing, only when everything is in place does the door open.
Source: 1930s-1951, Philosophical Occasions 1912-1951 (1993), Ch. 9 : Philosophy, p. 175

Problem

“It is in our own mind and not in exterior objects that we perceive most things; fools know scarcely anything because they are empty, and their heart is narrow; but great souls find in themselves a number of exterior things; they have no need to read or travel or to listen or to work to discover the highest truths; they have only to delve into themselves and search, if we may say so, their own thoughts.”

Luc de Clapiers, Marquis de Vauvenargues (1715–1747) French writer, a moralist

Source: Reflections and Maxims (1746), p. 186.

Truth , Fools , Travel , Soul

“1. Zero is a number.
2. The successor of any number is another number.
3. There are no two numbers with the same successor.
4. Zero is not the successor of a number.
5. Every property of zero, which belongs to the successor of every number with this property, belongs to all numbers.”

Giuseppe Peano (1858–1932) Italian mathematician

As expressed in "The Mathematical Philosophy of Giuseppe Peano" by Hubert C. Kennedy, in Philosophy of Science Vol. 30, No. 3 (July 1963)
Peano axioms

“Literature is idiosyncratic arrangements in horizontal lines in only twenty-six symbols, ten arabic numbers, and about eight punctuation marks.”

Kurt Vonnegut (1922–2007) American writer

Public conversation with Lee Stringer, in Like Shaking Hands With God (1999)
Various interviews

Literature

“He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."”

G. H. Hardy (1877–1947) British mathematician

Source: Ramanujan (1940), Ch. I : The Indian mathematician Ramanujan.

Hope , Way , Personality

“I cannot escape from the conclusion that the great ages of progress have depended upon a small number of individuals of transcendent ability.”

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

Source: 1930s, In Praise of Idleness and Other Essays (1935), Ch. 8: Western Civilisation

Age , Dependency

“A general is not easily overcome who can form a true judgment of his own and the enemy's forces. Valour is superior to numbers. The nature of the ground is often of more consequence than courage. (General Maxims)”
Amplius iuuat uirtus quam multitudo.

Publius Flavius Vegetius Renatus book De re militari

De Re Militari (also Epitoma Rei Militaris), Book III, "Dispositions for Action"

Courage , Nature

“The first Rudiments of Morality, broach'd by skilful Politicians, to render Men useful to each other as well as tractable, were chiefly contrived that the Ambitious might reap the more Benefit from, and govern vast Numbers of them with the greater Ease and Security.”

Bernard Mandeville book The Fable of the Bees

"An Enquiry into the Origin of Moral Virtue", p. 33
The Fable of the Bees (1714)

Men

“The Social-Democratic leaders glossed over and concealed from the masses the true class nature of fascism, and did not call them to the struggle against the increasingly reactionary measures of the bourgeoisie. They bear great historical responsibility for the fact that, at the decisive moment of the fascist offensive, a large section of the working people of Germany and of a number of other fascist countries failed to recognize in fascism the most bloodthirsty monster of finance capital, their most vicious enemy, and that these masses were not prepared to resist it.”

Georgi Dimitrov (1882–1949) Bulgarian politician

Source: The Fascist Offensive and the Tasks of the Communist International in the Struggle of the Working Class against Fascism, Ch. 1.

People , Nature , Decision , Country

“The white population of the world will soon cease to increase. The Asiatic races will be longer, and the negroes still longer, before their birth rate falls sufficiently to make their numbers stable without help of war and pestilence…. Until that happens, the benefits aimed at by socialism can only be partially realized, and the less prolific races will have to defend themselves against the more prolific by methods which are disgusting even if they are necessary.”

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

1920s, The Prospects of Industrial Civilization (1923)

War , World , Birth , Help

“… very often the laws derived by physicists from a large number of observations are not rigorous, but approximate.”

Augustin Louis Cauchy (1789–1857) French mathematician (1789–1857)

... très souvent les lois particulières déduites par les physiciens d'un grand nombre d'observations ne sont pas rigoureuses, mais approchées.
[Augustin Louis Cauchy, Sept leçons de physique, Bureau du Journal Les Mondes, 1868, 15]

Law

“The instant the atmosphere is illuminated it will be filled with an infinite number of images which are produced by the various bodies and colours assembled in it. And the eye is the target, a lodestone, of these images.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), II Linear Perspective

Quotes about number page 3

Quotes about number
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