Quotes about number
page 27

John Ruskin photo
Robert Gascoyne-Cecil, 3rd Marquess of Salisbury photo

“Numbers instill a feeling for the lie of the land, and furnish grist for the mathematical mill that is the physicist's principal tool.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 6, The Book of Life, Genetic information, p. 48

Paul Erdős photo

“If numbers aren't beautiful, I don't know what is.”

Paul Erdős (1913–1996) Hungarian mathematician and freelancer

Frequent remark, as quoted in My Brain Is Open : The Mathematical Journeys of Paul Erdos (1998) by Bruce Schechter, p. 14

Geoffrey Hodgson photo
Georg Cantor photo

“I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.”

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

Grundlagen einer allgemeinen Mannigfaltigkeitslehre [Foundations of a General Theory of Aggregates] (1883)

Winston S. Churchill photo
Kate Bush photo

“He does love his numbers
And they run, they run, they run him
In a great big circle
In a circle of infinity
3.14159 26535897932 3846 264 338 3279…”

Kate Bush (1958) British recording artist; singer, songwriter, musician and record producer

Song lyrics, Aerial (2005), A Sea of Honey (Disc 1)

Joseph Chamberlain photo
Donald J. Trump photo
Bonnie Koppell photo
Philip Hammond photo
Frederick Douglass photo

“The days of Black Power are numbered. Its course, indeed is onward. But with the swiftness of an arrow, it rushes to the tomb. While crushing its millions, it is also crushing itself. The sword of Retribution, suspended by a single hair, hangs over it. That sword must fall. Liberty must triumph.”

Frederick Douglass (1818–1895) American social reformer, orator, writer and statesman

As quoted in "Sustaining Black Studies", by Winston A. Van Horne, Journal of Black Studies, Vol. 37, No. 3, (January 2007)
1850s

Jane Espenson photo
Zlatan Ibrahimović photo

“I'm only warming up. I had a fantastic season, I proved age is just a number, Everything is in your head. Whatever you want to do you will do it. It's a master mind game. If I want to make it I'll make it. If I want to do it I'll do it.”

Zlatan Ibrahimović (1981) Swedish association football player

Talking about his age doesn't affect his game http://www.espn.in/football/soccer-transfers/story/2880702/zlatan-ibrahimovic-has-made-choice-amid-manchester-united-talk
Attributed

Muhammad of Ghor photo

“When the army was mustered, it was found to amount to "fifty thousand mounted men clad in armour and coats of mail," with which they advanced to fight against the Rai of Benares… The Rai of Benares, Jai Chand, the chief of idolatry and perdition, advanced to oppose the royal troops with an army… The Rai of Benares, who prided himself on the number of his forces and war elephants," seated on a lofty howdah, received a deadly wound from an arrow, and "fell from his exalted seat to the earth." His head was carried on the point of a spear to the commander, and " his body was thrown to the dust of contempt." "The impurities of idolatry were purged by the water of the sword from that land, and the country of Hind was freed from vice and superstition."… From that place the royal army proceeded towards Benares 'which is the centre of the country of Hind, and here they destroyed nearly one thousand temples, and raised mosques on their foundations; and the knowledge of the law became promulgated, and the foundations of religion were established.”

Muhammad of Ghor (1160–1206) Ghurid Sultan

About the fight with the Rai of Banares and capture of Asni and of Benares. Hasan Nizami: Taju’l-Ma’sir, in Elliot and Dowson, Vol. II : Elliot and Dowson, History of India as told by its own Historians, 8 Volumes, Allahabad Reprint, 1964. pp. 222-223 Also quoted in Jain, Meenakshi (2011). The India they saw: Foreign accounts.

Julian of Norwich photo
Reggie Fils-Aimé photo

“Now I know many of you today walked in with numbers already swimming in your heads: 360, 16x9, 1080, 8.2 GHz. Well, we'd like to add one more number to the mix. And that number is two.”

Reggie Fils-Aimé (1961) American businessman

Reference to the big numbers in hardware power and specifications that Microsoft and Sony had mentioned about their upcoming video game consoles
'2' refers to Nintendo having sold two billion games since the NES
On Nintendo
Source: E3 2005 Press Event

Sergey Lavrov photo
Otto Ohlendorf photo

“There were a large number of Jews who held more favorable positions than they should have, according to their percentage of the population. Germans should have held those positions.”

Otto Ohlendorf (1907–1951) German general

To Leon Goldensohn, March 1, 1946, from "The Nuremberg Interviews" by Leon Goldensohn, Robert Gellately - History - 2004.

E. W. Hobson photo

“A new point is determined in Euclidean Geometry exclusively in one of the three following ways:
Having given four points A, B, C, D, not all incident on the same straight line, then
(1) Whenever a point P exists which is incident both on (A, B) and on (C, D), that point is regarded as determinate.
(2) Whenever a point P exists which is incident both on the straight line (A, B) and on the circle C(D), that point is regarded as determinate.
(3) Whenever a point P exists which is incident on both the circles A(B), C(D), that point is regarded as determinate.
The cardinal points of any figure determined by a Euclidean construction are always found by means of a finite number of successive applications of some or all of these rules (1), (2) and (3). Whenever one of these rules is applied it must be shown that it does not fail to determine the point. Euclid's own treatment is sometimes defective as regards this requisite.
In order to make the practical constructions which correspond to these three Euclidean modes of determination, correponding to (1) the ruler is required, corresponding to (2) both ruler and compass, and corresponding to (3) the compass only.
…it is possible to develop Euclidean Geometry with a more restricted set of postulations. For example it can be shewn that all Euclidean constructions can be carried out by means of (3) alone…”

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

Source: Squaring the Circle (1913), pp. 7-8

Max Scheler photo

“"Another situation generally exposed to ressentiment danger is the older generation's relation with the younger. The process of aging can only be fruitful and satisfactory if the important transitions are accompanied by free resignation, by the renunciation of the values proper to the preceding stage of life. Those spiritual and intellectual values which remain untouched by the process of aging, together with the values of the next stage of life, must compensate for what has been lost. Only if this happens can we cheerfully relive the values of our past in memory, without envy for the young to whom they are still accessible. If we cannot compensate, we avoid and flee the “tormenting” recollection of youth, thus blocking our possibilities of understanding younger people. At the same time we tend to negate the specific values of earlier stages. No wonder that youth always has a hard fight to sustain against the ressentiment of the older generation. Yet this source of ressentiment is also subject to an important historical variation. In the earliest stages of civilization, old age as such is so highly honored and respected for its experience that ressentiment has hardly any chance to develop. But education spreads through printing and other modern media and increasingly replaces the advantage of experience. Younger people displace the old from their positions and professions and push them into the defensive. As the pace of “progress” increases in all fields, and as the changes of fashion tend to affect even the higher domains (such as art and science), the old can no longer keep up with their juniors. “Novelty‟ becomes an ever greater value. This is doubly true when the generation as such is seized by an intense lust for life, and when the generations compete with each other instead of cooperating for the creation of works which outlast them. “Every cathedral,” Werner Sombart writes, “every monastery, every town hall, every castle of the Middle Ages bears testimony to the transcendence of the individual's span of life: its completion spans generations which thought that they lived for ever. Only when the individual cut himself loose from the community which outlasted him, did the duration of his personal life become his standard of happiness.” Therefore buildings are constructed ever more hastily—Sombart cites a number of examples. A corresponding phenomenon is the ever more rapid alternation of political regimes which goes hand in hand with the progression of the democratic movement. But every change of government, every parliamentary change of party domination leaves a remnant of absolute opposition against the values of the new ruling group. This opposition is spent in ressentiment the more the losing group feels unable to return to power. The “retired official” with his followers is a typical ressentiment figure. Even a man like Bismarck did not entirely escape from this danger."”

Max Scheler (1874–1928) German philosopher

Das Ressentiment im Aufbau der Moralen (1912)

Eric Hoffer photo

“I have written a number of good sentences. I have kept free of delusions. I know I am going to die soon.”

Eric Hoffer (1898–1983) American philosopher

Entry (1977)
Eric Hoffer and the Art of the Notebook (2005)
Context: Disraeli felt that "nothing could compensate his obscure youth, not even a glorious old age." Practically all writers and artists are aware of their destiny and see themselves as actors in a fateful drama. With me, nothing is momentous: obscure youth, glorious old age, fateful coincidences — nothing really matters. I have written a number of good sentences. I have kept free of delusions. I know I am going to die soon.

José Guilherme Merquior photo

“[A] number of points are worth making at once [that challenge Foucault’s Madness and Civilization]: (1) There is ample evidence of medieval cruelty towards the insane; (2) In the late Middle Ages and the Renaissance, the mad were already confined, to cells, jails or even cages; (3) ‘dialogue’ or no ‘dialogue’, even madness during those times was frequently connected with sin -- even in the Ship of Fools mythology; and, to that extent, it was regarded in a far less benevolent light than suggested by Foucault (pre-modern minds accepted the reality of madness -- ‘madness as a part of truth’ -- just as they accepted the reality of sin; but this does not mean they valued madness, any more than sin; (4) as Martin Schrenk (himself a severe critic Foucault) has shown, early modern madhouses developed from medieval hospitals and monasteries rather than as reopened leprosaria; (5) the Great Confinement was primarily aimed not at deviance but at poverty -- criminal poverty, crazy poverty or just plain poverty; the notion that it heralded (in the name of the rising bourgeoise) a moral segregation does not bear close scrutiny; (6) at any rate, as stressed by Klaus Doerner, another of critic of Foucault (Madmen and the Bourgeoisie, 1969), that there was no uniform state-controlled confinement: the English and German patterns, for example, strayed greatly from the Louis Quatorzian Grand Renfermement; (7) Foucault’s periodization seems to me amiss. By the late eighteenths century, confinement of the poor was generally deemed a failure; but it is then that confinement of the mad really went ahead, as so conclusively shown in statistics concerning England, France, and the United States; (8) Tuke and Pinel did not ‘invent’ mental illness. Rather, they owe much to prior therapies and often relied also on their methods; (9) moreover, in nineetenth-century England moral treatment was not that central in the medicalization of madness. Far from it: as shown by Andrew Scull, physicians saw Tukean moral therapy as a lay threat to their art, and strove to avoid it or adapt it to their own practice. Once more, Foucault’s epochal monoliths crumble before the contradictory wealth of the historical evidence.”

Source: Foucault (1985), pp. 28-29

Bill Bryson photo
Joseph Massad photo

“The more recent practice of writing numbers on the arms of thousands of Palestinians who have been crammed in Israeli detention camps since February 2002 through the present further demonstrates the Nazi system as a model for the Israeli army.”

Joseph Massad (1963) Associate Professor of Arab Studies

Massad, "The Ends of Zionism: Racism and the Palestinian Struggle", Interventions, 2003
On Comparisons of Israel to Nazi Germany

Joseph Massad photo
Muhammad bin Qasim photo

“Muhammad took the fort [of Rawar] and stayed there for two or three days. He put six thousand fighting men, who were in the fort, to the sword, and shot some with arrows. The other dependents and servants were taken prisoners, with their wives and children… When the number of the prisoners was calculated, it was found to amount to thirty thousand persons, amongst whom thirty were the daughters of chiefs, and one of them was Rai Dahir's sister's daughter, whose name was Jaisiya. They were sent to Hajjaj. The head of Dahir and the fifth part of the prisoners were forwarded in charge of Ka'ab, son of Mharak. When the head of Dahir, the women, and the property all reached Hajjaj, he prostrated himself before Allah, offered thanksgivings and praises… Hajjaj then forwarded the head, the umbrellas, and wealth, and the prisoners to Walid the Khalifa. When the Khalifa of the time had read the letter, he praised Almighty Allah. He sold some of those daughters of the chiefs, and some he granted as rewards. When he saw the daughter of Rai Dahir’s sister he was much struck with her beauty and charms, and began to bite his finger with astonishment…. It is said that after the conquest was effected and the affairs of the country were settled and the report of the conquest had reached Hajjaj, he sent a reply to the following effect. 'O my cousin! I received your life-inspiring letter. I was much pleased and overjoyed when it reached me. The events were recounted in an excellent and beautiful style, and I learnt that the ways and rules you follow are conformable to the Law. Except that you give protection to all, great and small alike, and make no difference between enemy and friend. God says, - Give no quarter to Infidels, but cut their throats. Then know that this is the command of the great God [Allah]. You shall not be too ready to grant protection, because it will prolong your work. After this, give no quarter to any enemy except to those who are of rank.”

Muhammad bin Qasim (695–715) Umayyad general

The Chach Nama, in: Elliot and Dowson, History of India as told by its own Historians, Volume I, p. 172-173. Also partially quoted in B.R. Ambedkar, Pakistan or The Partition of India (1946)
Quotes from The Chach Nama

Ben Croshaw photo
James Madison photo
Chris Anderson photo

“The Web is the ultimate marketplace of ideas, governed by the laws of big numbers.”

Source: The Long Tail: Why the Future of Business Is Selling Less of More (2006), Ch. 5, p. 70

Iain Banks photo
Abraham Cowley photo
J. R. D. Tata photo
John McCain photo

“Vietnam vet: We haven't heard why you voted against your colleagues' proposals to increase health care funding in 2004, '05, '06, and '07, when we had troops coming back from two wars.
Madow: Instead of the answer the questioner is looking for, McCain now takes credit for the GI bill and takes a political shot at Jim Webb.
McCain: On the issue of the GI bill, I was disappointed that Senator Webb didn't support making it permanent. Senator Graham, other veterans and I will be looking to extend that to all veterans, not just 2001. I hope you'll urge Senator Webb to agree with that.
McCain: I received every award from every major veterans' organization in America. The reason is I have a perfect voting record from organizations like Veterans of Foreign Wars, the American Legion, and all the other veterans service organizations because of my support of them.
Vietnam vet: You do not have a perfect voting record by the DIV and the VFW. That's where these votes [of yours against increasing vet health care] are recorded. The votes were proposals by your colleagues in the Senate to increase health care funding of the VA in 2003, '04, '05, and '06 for troops returning from Iraq and Afghanistan, and you voted against those proposals. I can give you specific Senate votes, the numbers of those Senate votes right now.
McCain: I thank you, and I'll examine your version of what my voting record is, but again, I've been endorsed in every election by all of the veterans' organizations that do that. I've been supported by them, and I've received their highest rewards, from all of those organizations, so I guess they don't know something you know.
Rieckoff: [McCain's] voting record is not very strong. The Disabled American Veterans gave him a 20% rating out of 100. Our organization, the IAVA, gave him a D rating in the last voting session. He does not have a perfect voting record from the VFW. He's consistently voted against increased funding of the VA, and he's been a major opponent of the new GI bill.”

John McCain (1936–2018) politician from the United States

Paul Rieckhoff of Iraq & Afghanistan Veterans for America and author of Chasing Ghosts, on Countdown, discussing a town hall exchange between McCain and another Vietnam vet; 9 July 2008; http://www.youtube.com/watch?v=OnyEMLXvgV8
IAVA ratings: McCain: D; Obama: B+ http://www.iava.org/full-ratings-list; DAV: McCain: 20%; Obama: 80%; the AL and VFW don't perform such voting record ratings http://www.factcheck.org/askfactcheck/does_mccain_have_a_perfect_voting_record.html http://www.youtube.com/watch?v=OnyEMLXvgV8
2000s, 2008

“They first sallied forth in a body of about 500 persons to attack the market place of the village known as Poorwa, where they slaughtered a cow. With the blood of the animal they defiled a Hindu temple. Then they hung up the four quarters (of the cow) in the different parts of the market place. They maltreated and wounded an unfortunate Brahmin and threatened to make him a Muslim… The village of Laoghatty in the Nadia district was their next object attack. Here they commenced operations by the repetition of the same outrage to the religious feelings of the Hindus which they had committed at Poorwa, viz, the slaughter of a cow in that part of the village exclusively occupied by Hindu residents. But being opposed by Hardeb Ray, a principal inhabitant of the village, and a Brahmin, at the head of a party of villagers, an affray ensued in which one Debnath Ray was killed and Hardeb Ray and a number of villagers were severely wounded… Titu’s party went on increasing and with growing confidence they went on killing cows in different places, making raids on the neighbouring villages, forcing from the raiyats agreements to furnish grain, compelling many of them to profess conformity to the tenets of their sect… They openly proclaimed themselves masters of the country, asserting that the Mussalmans from whom the English usurped it, were the rightful owners of the empire… The rebels issued parwanas to the principal zamindars of the district. Their tenor was as follows: “This country is now given to our Deen Mohammed. You must, therefore, immediately send grain to the army.’ In a written report the magistrate of Nadia states that a paper written in Bengali and signed in Arabic characters, was put into his hand, purporting to be an order of Allah to the Pal Chowdhuries of Ranaghat to supply russud (rations) to the army of fakirs who were about to fight with the government.”

About the exploits of Titumir. Narahari Kaviraj, Wahabi And Faraizi Rebels of Bengal, New Delhi, 1982, Pp. 37-38, 43-44, 50-51. Quoted in Goel, Sita Ram (1995). Muslim separatism: Causes and consequences. ISBN 9788185990262

Jane Goodall photo
Alauddin Khalji photo
Jessica Drake photo
Geert Wilders photo
Henrietta Swan Leavitt photo

“It is hoped that systematic study of the light changes of all the variables, nearly two thousand in number, in the two Magellanic Clouds may soon be undertaken at this Observatory.”

Henrietta Swan Leavitt (1868–1921) astronomer

Periods of 25 Variable Stars in the Small Magellanic Cloud http://adsabs.harvard.edu/abs/1912HarCi.173....1L (1912)

John P. Kotter photo
Harry Turtledove photo
James Joseph Sylvester photo

“Number, place, and combination... the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.”

James Joseph Sylvester (1814–1897) English mathematician

James Joseph Sylvester, Collected Mathematical Papers, Vol. 1 (1904), p. 91.

Philolaus photo

“[Number is] the commanding and self-begotten container of the eternal duration of mundane concerns.”

Philolaus (-470–-390 BC) ancient greek philosopher

Quoted by Aristotle, Metaphysics (ca. 350 BC) Tr. Thomas Taylor, The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements (1792) Vol. 1 https://books.google.com/books?id=AD1WAAAAYAAJ, p. xix.

Charles A. Beard photo

“I present, for what it is worth, and may prove to be worth, the following bill of axioms or aphorisms on public administration, as fitting this important occasion.
# The continuous and fairly efficient discharge of certain functions by government, central and local, is a necessary condition for the existence of any great society.
# As a society becomes more complicated, as its division of labor ramifies more widely, as its commerce extends, as technology takes the place of handicrafts and local self-sufficiency, the functions of government increase in number and in their vital relationships to the fortunes of society and individuals.
# Any government in such a complicated society, consequently any such society itself, is strong in proportion to its capacity to administer the functions that are brought into being.
# Legislation respecting these functions, difficult as it is, is relatively easy as compared with the enforcement of legislation, that is, the effective discharge of these functions in their most minute ramifications and for the public welfare.
# When a form of government, such as ours, provides for legal changes, by the process of discussion and open decision, to fit social changes, then effective and wise administration becomes the central prerequisite for the perdurance of government and society — to use a metaphor, becomes a foundation of government as a going concern.
# Unless the members of an administrative system are drawn from various classes and regions, unless careers are open in it to talents, unless the way is prepared by an appropriate scheme of general education, unless public officials are subjected to internal and external criticism of a constructive nature, then the public personnel will become a bureaucracy dangerous to society and to popular government.
# Unless, as David Lilienthal has recently pointed out in an address on the Tennessee Valley Authority, an administrative system is so constructed and operated as to keep alive local and individual responsibilities, it is likely to destroy the basic well-springs of activity, hope, and enthusiasm necessary to popular government and to the following of a democratic civilization.”

Charles A. Beard (1874–1948) American historian

Administration, A Foundation of Government (1940)

Geoffrey of Monmouth photo

“After this, having invited over to him all persons whatsoever that were famous for valour in foreign nations, he began to augment the number of his domestics, and introduced such politeness into his court, as people of the remotest countries thought worthy of their imitation. So that there was not a nobleman who thought himself of any consideration, unless his clothes and arms were made in the same fashion as those of Arthur's knights.”
Tunc invitatis probissimis quibusque ex longe positis regnis, cepit familiam suam augmentare, tantamque facetiam in domo sua habere ita et emulationem longe manentibus populis ingereret. Unde nobilissimus quisque incitatus nichili pendebat se nisi sese sive in induendo sive in arma ferendo ad modo militum Arturi haberet.

Bk. 9, ch. 11; p. 239.
Historia Regum Britanniae (History of the Kings of Britain)

George Ballard Mathews photo
Lloyd Kenyon, 1st Baron Kenyon photo
Courtney Love photo

“My brother, Toby, is six-foot-six, [and] he [went to] Vassar; my other brother, Brown; my sister, without one penny from me or my [step]dad, NYU Law, number one in her class—Jesus, it's such a functional family, I don't know where I came from.”

Courtney Love (1964) American punk singer-songwriter, musician, actress, and artist

On her siblings, The David Letterman Show https://www.youtube.com/watch?v=zzX8Zv_dosM (17 March 2004)
1996–2005

Henry Wadsworth Longfellow photo
Niccolao Manucci photo

“Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all 59 our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,—we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,—social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.”

Joshua Girling Fitch (1824–1903) British educationalist

Source: Lectures on Teaching, (1906), pp. 291-292

Louis Bromfield photo
Gene Wolfe photo
Calvin Coolidge photo
Kent Hovind photo
Amir Taheri photo

“It is not solely by weapons that ISIS imposes its control. More important is the terror it has instilled in millions in Syria, Iraq, Jordan, Lebanon and, increasingly, Saudi Arabia and Kuwait. Indeed, Jordan’s panic-driven decision to execute two jihadists in response to the burning of its captured pilot is another sign of the terror Daesh has instilled in Arab governments and much of the public. In the short run, terror is a very effective means of psychological control of unarmed and largely defenseless populations. Even in areas far from Daesh’s reach, growing numbers of preachers, writers, politicians and even sheiks and emirs, terrorized by unprecedented savagery, are hedging their bets. Today, Daesh is a menacing presence not only in Baghdad but in Arab capitals from Cairo to Muscat — an evil ghost capable of launching attacks in the Sinai and organizing deadly raids on Jordanian and Saudi borders. ISIS enjoys yet another advantage: It has a clear strategy of making areas beyond its control unsafe. No one thinks Daesh can seize Baghdad, but few Baghdadis feel they’re living anything close to a normal life. Daesh’s message is clear: No one is safe anywhere, including in non-Muslim lands, until the whole world is brought under “proper Islamic rule.””

Amir Taheri (1942) Iranian journalist

How ISIS is winning: The long reach of terror http://nypost.com/2015/02/05/how-isis-is-winning-the-long-reach-of-terror/, New York Post (February 5, 2015).
New York Post

Olavo de Carvalho photo
François Viète photo

“On symbolic use of equalities and proportions. Chapter II.
The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:
1. The whole is equal to the sum of its parts.
2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]
3. If equal quantities are added to equal quantities the resulting sums are equal.
4. If equals are subtracted from equal quantities the remains are equal.
5. If equal equal amounts are multiplied by equal amounts the products are equal.
6. If equal amounts are divided by equal amounts, the quotients are equal.
7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]
8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]
9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]
10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]
11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]
12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]
13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]
14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.
But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:
15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]
And conversely
10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]
We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.”

François Viète (1540–1603) French mathematician

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix
In artem analyticem Isagoge (1591)

Billy Collins photo
Dennis Kucinich photo
Maggie Stiefvater photo
George Stephenson photo
Roberto Mangabeira Unger photo
Rex Stout photo

“One trouble with living beyond your deserved number of years is that there's always some reason to live another year. And I'd like to live another year so that Nixon won't be President. If he's re-elected I'll have to live another four years.”

Rex Stout (1886–1975) American writer

Nixon was re-elected in 1972, but Stout survived his August 1974 resignation from the Presidency by more than a year.
The New York Times, "Rex Stout, 85, Gives Clues on Good Writing"

David Woodard photo
Georges Braque photo
Florian Cajori photo
Warren Farrell photo
George Holmes Howison photo

“Mathematics is the science of the functional laws and transformations which enable us to convert figured extension and rated motion into number.—Howison, G. H.”

George Holmes Howison (1834–1916) American philosopher

"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 170. Reported in Moritz (1914)
Journals

Yasunari Kawabata photo

“"Among those who give thoughts to things, is there one who does not think of suicide?" With me was the knowledge that that fellow Ikkyu twice contemplated suicide. I have "that fellow", because the priest Ikkyu is known even to children as a most amusing person, and because anecdotes about his limitlessly eccentric behavior have come down to us in ample numbers. It is said of him that children climbed his knee to stroke his beard, that wild birds took feed from his hand. It would seem from all this that he was the ultimate in mindlessness, that he was an approachable and gentle sort of priest. As a matter of fact he was the most severe and profound of Zen priests. Said to have been the son of an emperor, he entered a temple at the age of six, and early showed his genius as a poetic prodigy. At the same time he was troubled with the deepest of doubts about religion and life. "If there is a god, let him help me. If there is none, let me throw myself to the bottom of the lake and become food for fishes." Leaving behind these words he sought to throw himself into a lake, but was held back. … He gave his collected poetry the title "Collection of the Roiling Clouds", and himself used the expression "Roiling Clouds" as a pen name. In his collection and its successor are poems quite without parallel in the Chinese and especially the Zen poetry of the Japanese middle ages, erotic poems and poems about the secrets of the bedchamber that leave one in utter astonishment. He sought, by eating fish and drinking spirits and having commerce with women, to go beyond the rules and proscriptions of the Zen of his day, and to seek liberation from them, and thus, turning against established religious forms, he sought in the pursuit of Zen the revival and affirmation of the essence of life, of human existence, in a day civil war and moral collapse.”

Yasunari Kawabata (1899–1972) Japanese author, Nobel Prize winner

Japan, the Beautiful and Myself (1969)

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E. W. Hobson photo

“In the third period, which lasted from the middle of the eighteenth century until late in the nineteenth century, attention was turned to critical investigations of the true nature of the number π itself, considered independently of mere analytical representations. The number was first studied in respect of its rationality or irrationality, and it was shown to be really irrational. When the discovery was made of the fundamental distinction between algebraic and transcendental numbers, i. e. between those numbers which can be, and those numbers which cannot be, roots of an algebraical equation with rational coefficients, the question arose to which of these categories the number π belongs. It was finally established by a method which involved the use of some of the most modern of analytical investigation that the number π was transcendental. When this result was combined with the results of a critical investigation of the possibilities of a Euclidean determination, the inferences could be made that the number π, being transcendental, does not admit of a construction either by a Euclidean determination, or even by a determination in which the use of other algebraic curves besides the straight line and the circle are permitted. The answer to the original question thus obtained is of a conclusive negative character; but it is one in which a clear account is given of the fundamental reasons upon which that negative answer rests.”

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

Source: Squaring the Circle (1913), p. 12

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Edmund Burke photo

“Permit me, Sir, to add another circumstance in our colonies, which contributes no mean part towards the growth and effect of this untractable spirit. I mean their education. In no country perhaps in the world is the law so general a study. The profession itself is numerous and powerful; and in most provinces it takes the lead. The greater number of the deputies sent to the congress were lawyers. But all who read, and most do read, endeavour to obtain some smattering in that science. I have been told by an eminent bookseller, that in no branch of his business, after tracts of popular devotion, were so many books as those on the law exported to the plantations. The colonists have now fallen into the way of printing them for their own use. I hear that they have sold nearly as many of Blackstone's Commentaries in America as in England. General Gage marks out this disposition very particularly in a letter on your table. He states, that all the people in his government are lawyers, or smatterers in law; and that in Boston they have been enabled, by successful chicane, wholly to evade many parts of one of your capital penal constitutions. The smartness of debate will say, that this knowledge ought to teach them more clearly the rights of legislature, their obligations to obedience, and the penalties of rebellion. All this is mighty well. But my honourable and learned friend on the floor, who condescends to mark what I say for animadversion, will disdain that ground. He has heard, as well as I, that when great honours and great emoluments do not win over this knowledge to the service of the state, it is a formidable adversary to government. If the spirit be not tamed and broken by these happy methods, it is stubborn and litigious. Abeunt studia in mores. This study renders men acute, inquisitive, dexterous, prompt in attack, ready in defence, full of resources. In other countries, the people, more simple, and of a less mercurial cast, judge of an ill principle in government only by an actual grievance; here they anticipate the evil, and judge of the pressure of the grievance by the badness of the principle. They augur misgovernment at a distance; and snuff the approach of tyranny in every tainted breeze.”

Edmund Burke (1729–1797) Anglo-Irish statesman

Second Speech on Conciliation with America (1775)

James Whitbread Lee Glaisher photo

“Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics…. The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible…. I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s “Algebra” published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 466 : On the need of text-books on higher mathematics

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“It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained…. I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 466 : On the expansion of the field of mathematics, and on the importance of a well-chosen notation

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