Quotes about direction
page 13

Henry Gantt photo
Pauline Kael photo
Vincent Van Gogh photo

“Some good must come by clinging to the right. Conscience is a man's compass, and though the needle sometimes deviates, though one often perceives irregularities in directing one's course by it, still one must try to follow its direction.”

Vincent Van Gogh (1853–1890) Dutch post-Impressionist painter (1853-1890)

Quote in a letter of Vincent to brother Theo, from The Hague, between c. 13 and c. 18 December 1882; as cited in Dear Theo: the Autobiography of Vincent Van Gogh; ed. Irving Stone and Jean Stone, (1995) p. 181 - ISBN 0452275040
1880s, 1882

Marcel Duchamp photo
Vytautas Juozapaitis photo
Norman Mailer photo
Nina Kiriki Hoffman photo

“Never rush into anything—unless into is the direction you want to go.”

Nina Kiriki Hoffman (1955) American writer

Source: The Thread That Binds the Bones (1993), Chapter 5 (p. 46)

Edward Hopper photo
Andy Goldsworthy photo
Ethan Allen photo
Thomas Young (scientist) photo
Calvin Coolidge photo

“Ever since the last great conflict the world has been putting a renewed emphasis, not on preparation to succeed in war, but on an attempt by preventing war to succeed in peace. This movement has the full and complete approbation of the American Government and the American people. While we have been unwilling to interfere in the political relationship of other countries and have consistently refrained from intervening except when our help has been sought and we have felt that it could be effectively given, we have signified our willingness to become associated with other nations in a practical plan for promoting international justice through the World Court. Such a tribunal furnishes a method of the adjustment of international differences in accordance with our treaty rights and under the generally accepted rules of international law. When questions arise which all parties agree ought to be adjudicated but which do not yield to the ordinary methods of diplomacy, here is a forum to which the parties may voluntarily repair in the consciousness that their dignity suffers no diminution and that their cause will be determined impartially, according to the law and the evidence. That is a sensible, direct, efficient, and practical method of adjusting differences which can not fail to appeal to the intelligence of the American people.”

Calvin Coolidge (1872–1933) American politician, 30th president of the United States (in office from 1923 to 1929)

1920s, Ways to Peace (1926)

Henry Brougham, 1st Baron Brougham and Vaux photo
J. C. R. Licklider photo

“Present-day computers are designed primarily to solve preformulated problems or to process data according to predetermined procedures. The course of the computation may be conditional upon results obtained during the computation, but all the alternatives must be foreseen in advance. … The requirement for preformulation or predetermination is sometimes no great disadvantage. It is often said that programming for a computing machine forces one to think clearly, that it disciplines the thought process. If the user can think his problem through in advance, symbiotic association with a computing machine is not necessary.
However, many problems that can be thought through in advance are very difficult to think through in advance. They would be easier to solve, and they could be solved faster, through an intuitively guided trial-and-error procedure in which the computer cooperated, turning up flaws in the reasoning or revealing unexpected turns in the solution. Other problems simply cannot be formulated without computing-machine aid. … One of the main aims of man-computer symbiosis is to bring the computing machine effectively into the formulative parts of technical problems.
The other main aim is closely related. It is to bring computing machines effectively into processes of thinking that must go on in "real time," time that moves too fast to permit using computers in conventional ways. Imagine trying, for example, to direct a battle with the aid of a computer on such a schedule as this. You formulate your problem today. Tomorrow you spend with a programmer. Next week the computer devotes 5 minutes to assembling your program and 47 seconds to calculating the answer to your problem. You get a sheet of paper 20 feet long, full of numbers that, instead of providing a final solution, only suggest a tactic that should be explored by simulation. Obviously, the battle would be over before the second step in its planning was begun. To think in interaction with a computer in the same way that you think with a colleague whose competence supplements your own will require much tighter coupling between man and machine than is suggested by the example and than is possible today.”

Man-Computer Symbiosis, 1960

Mark Zuckerberg photo
John Ruysbroeck photo
Philip Roth photo

“New Directions is a reviewer’s nightmare; it’s enough punishment to read it all, without writing about it too.”

Randall Jarrell (1914–1965) poet, critic, novelist, essayist

In All Directions”, p. 87
Kipling, Auden & Co: Essays and Reviews 1935-1964 (1980)

Courtney Love photo
Adam Smith photo
Philip Schaff photo

“The charge that Luther adapted the translation to his theological opinions has become traditional in the Roman Church, and is repeated again and again by her controversialists and historians.
In both cases, the charge has some foundation, but no more than the counter-charge which may be brought against Roman Catholic Versions.
The most important example of dogmatic influence in Luther's version is the famous interpolation of the word alone in Rom. 3:28 (allein durch den Glauben), by which he intended to emphasize his solifidian doctrine of justification, on the plea that the German idiom required the insertion for the sake of clearness. But he thereby brought Paul into direct verbal conflict with James, who says (James 2:24), "by works a man is justified, and not only by faith" ("nicht durch den Glauben allein"). It is well known that Luther deemed it impossible to harmonize the two apostles in this article, and characterized the Epistle of James as an "epistle of straw," because it had no evangelical character ("keine evangelische Art").
He therefore insisted on this insertion in spite of all outcry against it. His defense is very characteristic. "If your papist," he says,
The Protestant and anti-Romish character of Luther's New Testament is undeniable in his prefaces, his discrimination between chief books and less important books, his change of the traditional order, and his unfavorable judgments on James, Hebrews, and Revelation. It is still more apparent in his marginal notes, especially on the Pauline Epistles, where he emphasizes throughout the difference between the law and the gospel, and the doctrine of justification by faith alone; and on the Apocalypse, where he finds the papacy in the beast from the abyss (Rev. 13), and in the Babylonian harlot (Rev. 17). The anti-papal explanation of the Apocalypse became for a long time almost traditional in Protestant commentaries.
There is, however, a gradual progress in translation, which goes hand in hand with the progress of the understanding of the Bible. Jerome's Vulgate is an advance upon the Itala, both in accuracy and Latinity; the Protestant Versions of the sixteenth century are an advance upon the Vulgate, in spirit and in idiomatic reproduction; the revisions of the nineteenth century are an advance upon the versions of the sixteenth, in philological and historical accuracy and consistency. A future generation will make a still nearer approach to the original text in its purity and integrity. If the Holy Spirit of God shall raise the Church to a higher plane of faith and love, and melt the antagonisms of human creeds into the one creed of Christ, then, and not before then, may we expect perfect versions of the oracles of God.”

Philip Schaff (1819–1893) American Calvinist theologian

How Luther's theology may have influenced his translating

“[W]omen under phallocratic rule are confined to the role of vessels/carriers, directed and controlled by men. Since that role is the basic base reversal of the very be-ing of Voyaging/Spiraling women, when we direct our own Crafts/Vessels we become reversers of that deadly reversal.”

Mary Daly (1928–2010) American radical feminist philosopher and theologian

Source: Gyn/Ecology: The Metaethics of Radical Feminism (1978–1990), p. xxvi (New Intergalactic Introduction).

Georges Bataille photo
Cyrus David Foss photo
Hermann Rauschning photo
Chris Hedges photo
Winston S. Churchill photo
Euclid Tsakalotos photo

“The overall framework of the euro zone is in crisis — not from Syriza or the left, but because of the policies of austerity. Unless Europe moves in a more just and socially democratic direction, then it’s in danger.”

Euclid Tsakalotos (1960) Greek economist and politician

" Greek impasse forces early elections and fears of a return to euro crisis https://www.washingtonpost.com/world/europe/greek-impasse-forces-early-elections-and-fears-of-euro-crisis-return/2014/12/29/3be75924-8f4e-11e4-ba53-a477d66580ed_story.html" (29 December 2014)

Newton Lee photo
Thomas Henry Huxley photo
Vitruvius photo
David Baddiel photo
Karl Jaspers photo
Hannah Arendt photo

“What stuck in the minds of these men who had become murderers was simply the notion of being involved in something historic, grandiose, unique ("a great task that occurs once in two thousand years"), which must therefore be difficult to bear. This was important, because the murderers were not sadists or killers by nature; on the contrary, a systematic effort was made to weed out all those who derived physical pleasure from what they did. The troops of the Einsatzgruppen had been drafted from the Armed S. S., a military unit with hardly more crimes in its record than any ordinary unit of the German Army, and their commanders had been chosen by Heydrich from the S. S. élite with academic degrees. Hence the problem was how to overcome not so much their conscience as the animal pity by which all normal men are affected in the presence of physical suffering. The trick used by Himmler — who apparently was rather strongly afflicted by these instinctive reactions himself — was very simple and probably very effective; it consisted in turning these instincts around, as it were, in directing them toward the self. So that instead of saying: What horrible things I did to people!, the murderers would be able to say: What horrible things I had to watch in the pursuance of my duties, how heavily the task weighed upon my shoulders!”

Source: Eichmann in Jerusalem (1963), Ch. VI.

Lynn Margulis photo

“Identity is not an object; it is a process with addresses for all the different directions and dimensions in which it moves, and so it cannot so easily be fixed with a single number.”

Lynn Margulis (1938–2011) American evolutionary biologist

with Richard Guerrero, "Two Plus Two Equals One: Individuals Emerge from Bacterial Communities" in Gaia 2: Emergence : the New Science of Becoming ed. William Irwin Thompson (1991).

Dylan Moran photo
Stephenie Meyer photo
Ogden Nash photo

“Every New Year is the direct descendant, isn't it, of a long line of proven criminals?”

Ogden Nash (1902–1971) American poet

"Good-by, Old Year, You Oaf or Why Don't They Pay the Bonus?" in The Primrose Path (1935)

Max Scheler photo
Narendra Modi photo

“Mahatma Buddha has also left a deep imprint on my life. In my personal room also, there are three-four statues of the Buddha…. In Buddhism, I see dharma entrenched in karuna (compassion). I believe compassion is the most valuable essence of life. When I formed the government, these values got ingrained even deeper. What attracts me about Buddha is his inclusive philosophy; secondly, his modernity; and thirdly, his belief in the importance of Sangathan—the idea of Sangha. This underlies all his philosophy. I would often wonder how Buddha managed to reach all over the world. What was it about him that lit sparks everywhere he went, took ordinary human beings towards their kartavya (duty) and appealed to the lower status groups as well? Buddhism does not have too much tam-jham or celebration of big utsavs. There is a direct connect of the individual with the Divine. That entire thought system touches me deeply. Moreover, wherever Buddha went, the region witnessed prosperity. Even though China had a different belief system but Buddha has maintained his influence on China as well. Recently, I went to China and found that their government was introducing me to Buddhist elements of their culture with great pride. I got to know that China is making a film on Hiuen-Tsang. I took a pro-active role and wrote to those people saying that they should not forget the part about his stay in Gujarat. Hiuen-Tsang lived for a long time in the village where I was born. He has written about a hostel in that village where 1,000 student monks resided. After I became chief minister, I got the area excavated and found archeological evidence of things described by Hiuen-Tsang. This means Mahatma Buddha’s philosophy would have had some influence on my ancestors.”

Narendra Modi (1950) Prime Minister of India

Narendra Modi quoted from Kishwar, Madhu (2014). Modi, Muslims and media: Voices from Narendra Modi's Gujarat. p.388-389
2013

Friedrich Wilhelm Joseph Schelling photo
Nathanael Greene photo

“Before I came into the department, your Excellency was obliged often to stand Quarter-master. However capable the principal was of doing his duty, he was hardly ever with you. The line and the staff were at war with each other. The country had been plundered in a way that would now breed a kind of civil war between the staff and the inhabitants. The manner of my engaging in this business, and your Excellency's declaration to the Committee of Congress, that you would stand Quarter-master no longer, are circumstances which I wish may not be forgotten; as I may have occasion, at some future day, to appeal to your Excellency for my own justification. One thing I can say, with truth and sincerity, that I have conducted the business with as much prudence and economy, as if my private fortune had been answerable for the disbursements. And I believe your Excellency will do me the justice to say, the department has cooperated with your measures as far as circumstances were to be governed by me; and this you had reason to apprehend would not have been the case had I not taken direction of the business. And here, in justice to my colleagues, I shall mention that I think them entitled to your Excellency's personal esteem, from the warmth of their wishes, and a desire to promote your ease and convenience.”

Nathanael Greene (1742–1786) American general in the American Revolutionary War

Letter to George Washington (24 April 1779)

Lester B. Pearson photo
Margaret Thatcher photo
Franklin D. Roosevelt photo
Gaurav Sharma (author) photo
Jon Cruddas photo
Sophie Swetchine photo

“To love deeply in one direction makes us more loving in all others”

Sophie Swetchine (1782–1857) Russian salon-holder

Source: Reported in, "Transform Your Life: 52 Brilliant Ideas for Becoming the Person You Want to Be" by Penny Ferguson, p. 167.

Jacob Bronowski photo
African Spir photo

“To reform society, and with it humanity, there is only one mean; to transform the mentality of men, to direct them ("les orienter", Fr.) in a new spirit.”

African Spir (1837–1890) Russian philosopher

Source: Words of a Sage : Selected thoughts of African Spir (1937), p. 60.

Patrick Henry photo

“That religion, or the duty which we owe to our Creator, and the manner of discharging it, can be directed only by reason and conviction, not by force or violence; and therefore all men are equally entitled to the free exercise of religion, according to the dictates of conscience; and that it is the mutual duty of all to practice Christian forbearance, love, and charity towards each other.”

Patrick Henry (1736–1799) attorney, planter, politician and Founding Father of the United States

Virginia Bill of Rights, Article 16 (12 June 1776); Henry was on the committee which drafted the Virginia constitution and he supported this Bill, but it is not clear to what extent he was the author of any portion of it. This statement is also sometimes misattributed to James Madison who quoted it in his arguments for the United States Bill of Rights.
Misattributed

Ibn Khaldun photo
Isaac Asimov photo

“Plowboy: You truly feel that all the major changes in history have been caused by science and technology?
Asimov: Those that have proved permanent—the ones that affected every facet of life and made certain that mankind could never go back again—were always brought about by science and technology. In fact, the same twin "movers" were even behind the other "solely" historical changes. Why, for instance, did Martin Luther succeed, whereas other important rebels against the medieval church—like John Huss—fail? Well, Luther was successful because printing had been developed by the time he advanced his cause. So his good earthy writings were put into pamphlets and spread so far and wide that the church officials couldn't have stopped the Protestant Reformation even if they had burned Luther at the stake.
Plowboy: Today the world is changing faster than it has at any other time in history. Do you then feel that science—and scientists—are especially important now?
Asimov: I do think so, and as a result it's my opinion that anyone who can possibly introduce science to the nonscientist should do so. After all, we don't want scientists to become a priesthood. We don't want society's technological thinkers to know something that nobody else knows—to "bring down the law from Mt. Sinai"—because such a situation would lead to public fear of science and scientists. And fear, as you know, can be dangerous.
Plowboy: But scientific knowledge is becoming so incredibly vast and specialized these days that it's difficult for any individual to keep up with it all.
Asimov: Well, I don't expect everybody to be a scientist or to understand every new development. After all, there are very few Americans who know enough about football to be a referee or to call the plays … but many, many people understand the sport well enough to follow the game. It's not important that the average citizen understand science so completely that he or she could actually become involved in research, but it is very important that people be able to "follow the game" well enough to have some intelligent opinions on policy.
Every subject of worldwide importance—each question upon which the life and death of humanity depends—involves science, and people are not going to be able to exercise their democratic right to direct government policy in such areas if they don't understand what the decisions are all about.”

Isaac Asimov (1920–1992) American writer and professor of biochemistry at Boston University, known for his works of science fiction …

Mother Earth News interview (1980)

Adam Smith photo
Annette Lu photo
Roberto Clemente photo

“This is my ball park. Every game is played in daylight and I can see the ball good. And I can reach the stands in any direction. I hope I'm never traded but if I am, I wish it would be to the Cubs. I know I do well there in 77 games.”

Roberto Clemente (1934–1972) Puerto Rican baseball player

Discussing Wrigley Field (where he was currently hitting .693 for the season, with 9 hits in 13 AB, with 3 home runs and 9 RBI); as quoted in "Feast Then Famine For Pirates: Split Means Lost Ground In Race" https://news.google.com/newspapers?id=o2scAAAAIBAJ&sjid=Fk8EAAAAIBAJ&pg=4554%2C1706304 by Lester J. Biederman, in The Pittsburgh Press (Friday, July 7, 1961), p. 26. To access article, drag image from right to left, bringing relevant headline immediately into view, displayed on its side; continue dragging until you reach the fifth paragraph from the end.
Baseball-related, <big><big>1960s</big></big>, <big>1961</big>

Daniel Buren photo
Ivar Giaever photo
Eric Hargan photo
Bob Costas photo

“Our game today was produced by Ken Edmunson, directed by Bucky Guntz; Mike Weisman is the executive producer of NBC Sports, coordinating producer of baseball, Harry Coyle. The 1-1 pitch…He hits it to deep left field, LOOK OUT! DO YOU BELIEVE IT! IT'S GONE!!”

Bob Costas (1952) American sportscaster

Calling Sandberg's second game-tying home run against Sutter in the 10th inning. The Cubs went on to win 12-11 in the 11th inning. June 23, 1984.

Ibrahim of Ghazna photo
Ralph Waldo Trine photo
Richard Feynman photo

“There is one feature I notice that is generally missing in cargo cult science. … It's a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty — a kind of leaning over backwards. For example, if you're doing an experiment, you should report everything that you think might make it invalid — not only what you think is right about it; other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked — to make sure the other fellow can tell they have been eliminated. Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can — if you know anything at all wrong, or possibly wrong — to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it. There is also a more subtle problem. When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition. In summary, the idea is to try to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgement in one particular direction or another.”

Richard Feynman (1918–1988) American theoretical physicist

" Cargo Cult Science http://calteches.library.caltech.edu/51/2/CargoCult.htm", adapted from a 1974 Caltech commencement address; also published in Surely You're Joking, Mr. Feynman!, p. 341

Ernst Mach photo

“There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime.”

Ernst Mach (1838–1916) Austrian physicist and university educator

Source: 19th century, Popular Scientific Lectures [McCormack] (Chicago, 1898), p. 197; On mathematics and counting.

Ralph Waldo Trine photo
Stephen L. Carter photo
Aron Ra photo
Eric R. Kandel photo
Noam Chomsky photo

“We might add now that we do have an authoritative account of why the United States bombed Serbia in 1999. It comes from Strobe Talbott, now the director of the Brookings Institution, but in 1999 he was in charge of the State Department-Pentagon team that supervised the diplomacy in the affair. He wrote the introduction to a recent book by his Director of Communications, John Norris, which presents the position of the Clinton administration at the time of the bombing. Norris writes that "it was Yugoslavia's resistance to the broader trends of political and economic reform - not the plight of Kosovar Albanians - that best explains NATO's war". In brief, they were resisting absorption into the U. S. dominated international socioeconomic system. Talbott adds that thanks to John Norris, anyone interested in the war in Kosovo "will know … how events looked and felt at the time to those of us who were involved" in the war, actually directing it. This authoritative explanation will come as no surprise at all to students of international affairs who are more interested in fact than rhetoric. And it will also come as no surprise, to those familiar with intellectual life, that the attack continues to be hailed as a grand achievement of humanitarian intervention, despite massive Western documentation to the contrary, and now an explicit denial at the highest level; which will change nothing, it's not the way intellectual life works.”

Noam Chomsky (1928) american linguist, philosopher and activist

Talk at the Englert Theatre in Iowa, April 10, 2006 http://www.greenteaphd.com/greenteablog/?p=252
Quotes 2000s, 2006

Samuel Vince photo

“What we mean by the laws of nature, are those laws which are deduced from that series of events, which, by divine appointment, follow each other in the moral and physical world; the former of which we shall here have occasion principally to consider, the present question altogether, respecting the moral government of God — a consideration which our author has entirely neglected, in his estimation of the credibility of miracles. Examining the question therefore upon this principle, it is manifest, that the extraordinary nature of the fact is no ground for disbelief, provided such a fact, in, a moral point of view, was, from the condition of man, become necessary; for in that case, the Deky, by dispensing his assistance in proportion to our wants, acted upon the same principle as in his more 'ordinary operations. For however ' opposite the physical effects may be, if their moral tendency be the same, they form a part of the jmoral law. Now in those actions which are called miracles, the Deity is directed by the same moral principle as in his usual dispensations; and therefore being influenced by the same motive to accomplish the same end, the laws of God's moral government are not violated, such laws being established by the motives and the ends produced, and not by the means employed. To prove therefore the moral laws to be the same in those actions called miraculous, as in common events, it is not the actions thetnselves which are to be considered, but the principles by which they were directed, and their consequences, for if these be the same, the Deity acts by the same laws. And here, moral analogy will be found to confirm the truth of the miracles recorded in scripture. But as the moral government of God is directed by motives which lie beyond the reach of human investigation, we have no principles by which we can judge concerning the probability of the happening of any new event which respects the moral world; we cannot therefore pronounce any extraordinary event of that nature to be a violation of the moral law of God's dispensations; but we can nevertheless judge of its agreement with that law, so far as it has fallen under our observation. But our author leaves out the consideration of God's moral government, and reasons simply -on the facts which arc said to have nappened, without any reference to an end; we will therefore examine how far his conclusions are just upon this principle.
He defines miracles to be "a violation of the laws of nature;" he undoubtedly means the physical laws, as no part of his reasoning has any reference to them in a moral point of view. Now these laws must be deduced, either from his own view of events only, or from that, and testimony jojntly; and if testimony beallowed on one part, it ought also to be admitted on the other, granting that there is no impossibility in the fact attested. But the laws by which the Deity governs the universe can, at best, only be inferred from the whole series of his dispensations from the beginning of the world; testimony must therefore necessarily be admitted in establishing these laws. Now our author, in deducing the laws of nature, rejects all well authenticated miraculous events, granted to be possible, and therefore not altogether incredible and to be rejected without examination, and thence establishes a law to prove against their credibility; but the proof of a position ought to proceed upon principles which are totally independent of any supposition of its being either true or falser. His conclusion therefore is not deduced by just reasoning from acknowledged principles, but it is a necessary consequence of his own arbitrary supposition. "Tis a miracle," says he, "that a dead man should come to life, because that has never been observed in any age or country." Now, testimony, confirmed by every proof which can tend to establish a true matter of fact, asserts that such an event; has happened. But our author argues against the credibility of this, because it is contrary to the laws of nature; and in establishing these laws, he rejects all such extraordinary facts, although they are authenticated by all the evidence which such facts can possibly admit of; taking thereby into consideration, events of that kind only which have fallen within the sphere of his own observations, as if the whole series of God's dispensations were necessarily included in the course of a few years. But who shall thus circumscribe the operations of divine power and infinite wisdom, and say, "Hitherto shall thou go, and no further."”

Samuel Vince (1749–1821) British mathematician, astronomer and physicist

Before he rejected circumstances of this kind in establishing the laws of nature, he should, at least, have shewn, that we have not all that evidence for them which we might "have had" upon supposition that they were true ; he should also have shewn, in a moral point of view, that the events were inconsistent with the ordinary operations of Providence ; and that there was no end to justify the means. Whereas, on the contrary, there is all the evidence for them which a real matter of fact can possibly have ; they are perfectly consistent with all the moral dispensations of Providence and at the same time that the resurrection of Jesus Christ is most unexceptionably attested, we discover a moral intention in the miracle, which very satisfactorily accounts for that exertion of divine power?
Source: The Credibility of Christianity Vindicated, p. 48; As quoted in " Book review http://books.google.nl/books?id=52tAAQAAMAAJ&pg=PA259," in The British Critic, Volume 12 (1798). F. and C. Rivington. p. 259-261

Gideon Levy photo
Cyril Connolly photo
Cecil Day Lewis photo
Akira Ifukube photo
Gordon R. Dickson photo
Henry Adams photo
Augustus De Morgan photo

“In order to see the difference which exists between… studies,—for instance, history and geometry, it will be useful to ask how we come by knowledge in each. Suppose, for example, we feel certain of a fact related in history… if we apply the notions of evidence which every-day experience justifies us in entertaining, we feel that the improbability of the contrary compels us to take refuge in the belief of the fact; and, if we allow that there is still a possibility of its falsehood, it is because this supposition does not involve absolute absurdity, but only extreme improbability.
In mathematics the case is wholly different… and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us. In geometry, of the principles alluded to, those which are most commonly used are—
I. If a magnitude is divided into parts, the whole is greater than either of those parts.
II. Two straight lines cannot inclose a space.
III. Through one point only one straight line can be drawn, which never meets another straight line, or which is parallel to it.
It is on such principles as these that the whole of geometry is founded, and the demonstration of every proposition consists in proving the contrary of it to be inconsistent with one of these.”

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

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

John Kenneth Galbraith photo
Fred Phelps photo
S. I. Hayakawa photo
David Attenborough photo