Quotes about number
page 15

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“There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are
(1) ab(u) = ba (u),
(2) a(u + v) = a (u) + a (v),
(3) am. an. u = am + n. u.
The first of these laws is called the commutative law, and symbols which are subject to it are called commutative symbols. The second law is called distributive, and the symbols subject to it distributive symbols. The third law is not so much a law of combination of the operation denoted by a, but rather of the operation performed on a, which is indicated by the index affixed to a. It may be conveniently called the law of repetition, since the most obvious and important case of it is that in which m and n are integers, and am therefore indicates the repetition m times of the operation a.”

Duncan Gregory (1813–1844) British mathematician

That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation.
p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Examples of the processes of the differential and integral calculus, (1841)

Theodore Schultz photo
Delia Ephron photo

“Doyouwantogoona--Who is this? Oh, I have the wrong number.”

Delia Ephron (1944) American writer and film producer

Teenage Romance (Viking, 1981)
Quoted in Girls: 10 Gutsy, God-Centered Sessions on Issues That Matter to Girls By Helen Musick, Dan Jessup, Crystal Kirgiss

Paul Klee photo

“To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.”

Paul Klee (1879–1940) German Swiss painter

Diary entry (March 1906), # 759, in The Diaries of Paul Klee, 1898-1918; University of California Press, 1968
1903 - 1910

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Sören Kierkegaard photo

“You have surely noticed among schoolboys, that the one that is regarded by all as the boldest is the one who has no fear of his father, who dares to say to the others, "Do you think I am afraid of him?" On the other hand, if they sense that one of their number is actually and literally afraid of his father, they will readily ridicule him a little. Alas, in men’s fear-ridden rushing together into a crowd (for why indeed does a man rush into a crowd except because he is afraid!) there, too, it is a mark of boldness not to be afraid, not even of God. And if someone notes that there is an individual outside the crowd who is really and truly afraid – not of the crowd, but of God, he is sure to be the target of some ridicule. The ridicule is usually glossed over somewhat and it is said: a man should love God. Yes, to be sure, God knows that man’s highest consolation is that God is love and that man is permitted to love Him. But let us not become too forward, and foolishly, yes, blasphemously, dismiss the tradition of our fathers, established by God Himself: that really and truly a man should fear God. This fear is known to the man who is himself conscious of being an individual, and thereby is conscious of his eternal responsibility before God.”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Søren Kierkegaard, Purity of Heart, 1847 Steere translation p. 196-197
1840s, Upbuilding Discourses in Various Spirits (1847), Purity of Heart (1847)

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Isaac Barrow photo

“Mathematics is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to Human Affairs. In which last Respect, we may be said to receive from the Mathematics, the principal Delights of Life, Securities of Health, Increase of Fortune, and Conveniences of Labour: That we dwell elegantly and commodiously, build decent Houses for ourselves, erect stately Temples to God, and leave wonderful Monuments to Posterity: That we are protected by those Rampires from the Incursions of the Enemy; rightly use Arms, skillfully range an Army, and manage War by Art, and not by the Madness of wild Beasts: That we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea, and come to the designed Ports by the uncertain Impulse of the Winds: That we rightly cast up our Accounts, do Business expeditiously, dispose, tabulate, and calculate scattered 248 Ranks of Numbers, and easily compute them, though expressive of huge Heaps of Sand, nay immense Hills of Atoms: That we make pacifick Separations of the Bounds of Lands, examine the Moments of Weights in an equal Balance, and distribute every one his own by a just Measure: That with a light Touch we thrust forward vast Bodies which way we will, and stop a huge Resistance with a very small Force: That we accurately delineate the Face of this Earthly Orb, and subject the Oeconomy of the Universe to our Sight: That we aptly digest the flowing Series of Time, distinguish what is acted by due Intervals, rightly account and discern the various Returns of the Seasons, the stated Periods of Years and Months, the alternate Increments of Days and Nights, the doubtful Limits of Light and Shadow, and the exact Differences of Hours and Minutes: That we derive the subtle Virtue of the Solar Rays to our Uses, infinitely extend the Sphere of Sight, enlarge the near Appearances of Things, bring to Hand Things remote, discover Things hidden, search Nature out of her Concealments, and unfold her dark Mysteries: That we delight our Eyes with beautiful Images, cunningly imitate the Devices and portray the Works of Nature; imitate did I say? nay excel, while we form to ourselves Things not in being, exhibit Things absent, and represent Things past: That we recreate our Minds and delight our Ears with melodious Sounds, attemperate the inconstant Undulations of the Air to musical Tunes, add a pleasant Voice to a sapless Log and draw a sweet Eloquence from a rigid Metal; celebrate our Maker with an harmonious Praise, and not unaptly imitate the blessed Choirs of Heaven: That we approach and examine the inaccessible Seats of the Clouds, the distant Tracts of Land, unfrequented Paths of the Sea; lofty Tops of the Mountains, low Bottoms of the Valleys, and deep Gulphs of the Ocean: That in Heart we advance to the Saints themselves above, yea draw them to us, scale the etherial Towers, freely range through the celestial Fields, measure the Magnitudes, and determine the Interstices of the Stars, prescribe inviolable Laws to the Heavens themselves, and confine the wandering Circuits of the Stars within fixed Bounds: Lastly, that we comprehend the vast Fabrick of the Universe, admire and contemplate the wonderful Beauty of the Divine 249 Workmanship, and to learn the incredible Force and Sagacity of our own Minds, by certain Experiments, and to acknowledge the Blessings of Heaven with pious Affection.”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

Source: Mathematical Lectures (1734), p. 27-30

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Didier Sornette photo

“The acceleration of the number of traders buying into the market in the inflating bubble captures the oft-quoted observation that bubbles are times when the "greater fool theory" applies.”

Didier Sornette (1957) French scientist

Source: Why Stock Markets Crash - Critical Events in Complex Systems (2003), Chapter 6, Hierarchies, Complex Fractal Dimensions, And Log Periodicity, p. 185.

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Harry Turtledove photo

“"With these victories to which you refer, the Confederate States do seem to have retrieved their falling fortunes," Lord Lyons said. "I have no reason to doubt that Her Majesty's government will soon recognize that fact." "Thank you, your excellency," Lee said quietly. Even had Lincoln refused to give up the war- not impossible, with the Mississippi valley and many coastal pockets held by virtue of Northern naval power and hence relatively secure from rebel AK-47s- recognition by the greatest empire on earth would have assured Confederate independence. Lord Lyons held up a hand. "Many among our upper classes will be glad enough to welcome you to the family of nations, both as a result of your successful fight for self-government and because you have given a black eye to the often vulgar democracy of the United States. Others, however, will judge your republic a sham, with its freedom for white men based upon Negro slavery, a notion loathsome to the civilized world. I should be less than candid if I failed to number myself among that latter group." "Slavery was not the reason the Southern states chose to leave the Union," Lee said. He was aware he sounded uncomfortable, but went on, "We sought only to enjoy the sovereignty guaranteed us under the constitution, a right the North wrongly denied us. Our watchword all along has been, we wish but to be left alone."”

Source: The Guns of the South (1992), p. 182-183

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“Attention must be given to the study of the given operations. Their study with due allowance made for the existing means of warfare will make it possible to reach a number of useful theoretical conclusions for conducting operations in the initial phase of a war.”

Matvei Zakharov (1898–1972) Soviet military commander

Quoted in "Timely Lessons of History: The Manchurian Model for Soviet Strategy" - Page 4 - by John Despres, Lilita Dzirkals, Barton Whaley - History - 1976

“A complex system can fail in an infinite number of ways”

John Gall (1925–2014) American physician

Source: General systemantics, an essay on how systems work, and especially how they fail..., 1975, p. 92, cited in: Erik Hollnagel (2004) Barriers and accident prevention. p. 182

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“31 Proposition. The visible marks of the Beast, are the abused characters, of λρς and crosses of all kindes, taken out of the number of the first beasts name.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

Isaac Watts photo

“Hush! my dear, lie still and slumber,
Holy angels guard thy bed!
Heavenly blessings without number
Gently falling on thy head.”

Isaac Watts (1674–1748) English hymnwriter, theologian and logician

Song 35: "A Cradle Hymn".
1710s, Divine Songs Attempted in the Easy Language of Children (1715)

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John Napier photo

“27 Proposition. The image, marke, name, and number of the beast: are of the first great Romane beast, and whole Latine impyre universallie, and not of the second beaste, or Antichrist alone in particular.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

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“A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

Leonhard Euler (1707–1783) Swiss mathematician

§4
Introduction to the Analysis of the Infinite (1748)

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Joseph Strutt photo

“A number of little birds, to the amount, I believe, of twelve or fourteen, being taken from different cages, were placed upon a table in the presence of the spectators; and there they formed themselves into ranks like a company of soldiers: small cones of paper bearing some resemblance to grenadiers caps were put upon their heads, and diminutive imitations of muskets made with wood, secured under their left wings. Thus equipped, they marched to and fro several times; when a single bird was brought forward, supposed to be a deserter, and set between six of the musketeers, three in a row, who conducted him from the top to the bottom of the table, on the middle of which a small brass cannon charged with a little gunpowder had been previously placed, and the deserter was situated in the front part of the cannon; his guards then divided, three retiring on one side, and three on the other, and he was left standing by himself. Another bird was immediately produced; and, a lighted match being put into one of his claws, he hopped boldly on the other to the tail of the cannon, and, applying the match to the priming, discharged the piece without the least appearance of fear or agitation. The moment the explosion took place, the deserter fell down, and lay, apparently motionless, like a dead bird; but, at the command of his tutor he rose again; and the cages being brought, the feathered soldiers were stripped of their ornaments, and returned into them in perfect order.”

Joseph Strutt (1749–1802) British engraver, artist, antiquary and writer

pg. 250
The Sports and Pastimes of the People of England (1801), Public entertainment

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“If we were to do the Second Coming of Christ in color for a full hour, there would be a considerable number of stations which would decline to carry it on the grounds that a Western or a quiz show would be more profitable.”

Edward R. Murrow (1908–1965) Television journalist

On receiving the "Family of Man" Award (1964); as quoted in Prime Time: The Life of Edward R. Murrow by Alexander Kendrick (1969)

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“On the question of the "origin of species" Mr. Haughton enlarges considerably; but his chief arguments are reduced to the setting-up of "three unwarrantable assumptions," which he imputes to the Lamarckians and Darwinians, and then, to use his own words, "brings to the ground like a child's house of cards." The first of these is "the indefinite variation of species continuously in the one direction." Now this is certainly never assumed by Mr. Darwin, whose argument is mainly grounded on the fact that variations occur in every direction. This is so obvious that it hardly needs insisting on. In every large family there is almost always one child taller, one darker, one thinner than the rest; one will have a larger nose, another a larger eye: they vary morally as well; some are more poetical, others more morose; one has a genius for numbers, another for painting. It is the same in animals: the puppies, or kittens, or rabbits of one litter differ in many ways from each other - in colour, in size, in disposition; so that, though they do not "vary continuously in one direction," they do vary continuously in many directions; and thus there is always material for natural selection to act upon in some direction that may be advantageous. […] I will only, in conclusion, quote from it a short paragraph which contains an important truth, but which may very fairly be applied in other quarters than those for which the author intended it: - "No progress in natural science is possible as long as men will take their rude guesses at truth for facts, and substitute the fancies of their imagination for the sober rules of reasoning."”

Alfred Russel Wallace (1823–1913) British naturalist, explorer, geographer, anthropologist and biologist

"Remarks on the Rev. S. Haughton's Paper on the Bee's Cell, And on the Origin of Species" (1863).

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“Even though something like Danny Hillis' "connection machine" is big, it's nothing compared with Avogadro's number of processors that nature has at her disposal.”

J. Doyne Farmer (1952) American physicist and entrepreneur (b.1952)

The Third Culture: Beyond the Scientific Revolution (1995)

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Stanley Baldwin photo

“I often wonder if all the people in this country realise the inevitable changes that are coming over the industrial system in England…owing to the peculiar circumstances of my own life, I have seen a great deal of this evolution taking place before my own eyes. I worked for many years in an industrial business, and had under me a large number, or what was then a large number, of men…I was probably working under a system that was already passing. I doubt if its like could have been found in any of the big modern industrial towns of this country, even at that time. It was a place where I knew, and had known from childhood, every man on the ground, a place where I was able to talk with the men not only about the troubles in the works, but troubles at home where strikes and lock-outs were unknown. It was a place where the fathers and grandfathers of the men then working there had worked, and where their sons went automatically into the business. It was also a place where nobody ever "got the sack," and where we had a natural sympathy for those who were less concerned in efficiency than is this generation, and where a number of old gentlemen used to spend their days sitting on the handle of a wheelbarrow, smoking their pipes. Oddly enough, it was not an inefficient community. It was the last survivor of that type of works, and ultimately became swallowed up in one of those great combinations towards which the industries of to-day are tending.”

Stanley Baldwin (1867–1947) Former Prime Minister of the United Kingdom

Speech http://hansard.millbanksystems.com/commons/1925/mar/06/industrial-peace in the House of Commons (6 March 1925).
1925

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“Reducing complexity by order formation is the number one skill needed by all leaders in the twenty-first century”

Peter Kruse (1955–2015) German psychologist

Peter Kruse, Google's Think Quarterly, "Soft Values, Hard Facts" (March 2011) Think Quarterly http://www.thinkwithgoogle.co.uk/quarterly/data/peter-kruse-next-practice.html

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“Among the names of those who have led the great advance of the industrial arts during the past thirty years, that of Frederick Winslow Taylor will hold an increasingly high place. Others have led in electrical development, in the steel industry, in industrial chemistry, in railroad equipment, in the textile arts, and in many other fields, but he has been the creator of a new science, which underlies and will benefit all of these others by greatly increasing their efficiency and augmenting their productivity. In addition, he has literally forged a new tool for the metal trades, which has doubled, or even trebled, the productive capacity of nearly all metal-cutting machines. Either achievement would entitle him to high rank among the notable men of his day; — the two combined give him an assured place among the world's leaders in the industrial arts.
Others without number have been organizers of industry and commerce, each working out, with greater or less success, the solution of his own problems, but none perceiving that many of these problems involved common factors and thus implied the opportunity and the need of an organized science. Mr. Taylor was the first to grasp this fact and to perceive that in this field, as in the physical sciences, the Baconian system could be applied, that a practical science could be created by following the three principles of that system, viz.: the correct and complete observation oi facts, the intelligent and unbiased analysis of such facts, and the formulating of laws by deduction from the results so reached. Not only did he comprehend this fundamental conception and apply it; he also grasped the significance and possibilities of the problem so fully that his codification of the fundamental principles of the system he founded is practically complete and will be a lasting monument to its founder.”

Henry R. Towne (1844–1924) American engineer

Henry R. Towne, in: Frank Barkley Copley, Frederick W. Taylor, father of scientific management https://archive.org/stream/frederickwtaylor01copl, 1923. p. xii.

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Jimmy Wales photo

“We've always had a love/hate relationship with numbers.”

Jimmy Wales (1966) Wikipedia co-founder and American Internet entrepreneur

Wales to Computerworld, "Wikipedia founder gazes into site's future" (18 August 2006) http://computerworld.co.nz/news.nsf/0/E33CA972AD48588CCC2571C7001C3649?OpenDocument, based on an earlier interview at Wikimania

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“To an atheist […], there is no all-seeing all-loving god to keep us free from harm. But atheism is not a recipe for despair. I think the opposite. By disclaiming the idea of the next life, we can take more excitement in this one. The here and now is not something to be endured before eternal bliss or damnation. The here and now is all we have, an inspiration to make the most of it. So atheism is life-affirming, in a way religion can never be. Look around you. Nature demands our attention, begs us to explore, to question. Religion can provide only facile, ultimately unsatisfying answers. Science, in constantly seeking real explanations, reveals the true majesty of our world in all its complexity. People sometimes say "There must be more than just this world, than just this life". But how much more do you want? We are going to die, and that makes us the lucky ones. Most people are never going to die because they’re never going to be born. The number of people who could be here, in my place, outnumber the sand grains of Sahara. If you think about all the different ways in which our genes could be permuted, you and I are quite grotesquely lucky to be here, the number of events that had to happen in order for you to exist, in order for me to exist. We are privileged to be alive and we should make the most of our time on this world.”

Richard Dawkins (1941) English ethologist, evolutionary biologist and author

End of the part 2: "The Virus of Faith" https://www.youtube.com/watch?v=aMUG6qd98wc
The Root of All Evil? (January 2006)

Clement Attlee photo

“…nothing short of a world state will be really effective in preventing war. As long as you rely for security on a number of national armaments you will have the difficulty as to who shall bell the cat in case of need, while you will have general staffs in all countries planning future wars. I want us to come out boldly for a real long-range policy which will envisage the abolition of the conception of the individual sovereign state. … A united navy to police the seas of the world could be attained and would incidentally bring enormous pressure to bear on Japan. The next thing would be an international air force and an international air service. … The basis of such a move would have to be a frank recognition that all states must surrender a large degree of sovereignty and that the Peace Treaties must be revised. On this basis one must then proceed to build up a world structure politically and economically. … This may sound very visionary but I am convinced that unless we see the world we want it is vain to try to build a permanent habitation for Peace and that temporary structures will catch fire very soon if we wait any longer.”

Clement Attlee (1883–1967) Former Prime Minister of the United Kingdom

Letter to Tom Attlee (1 January 1933), quoted in W. Golant, 'The Emergence of C. R. Attlee as Leader of the Parliamentary Labour Party in 1935', The Historical Journal, Vol. 13, No. 2 (Jun., 1970), p. 323
Deputy Leader of the Opposition

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“The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. … Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.”

Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret. … [P]raetereaque scientiae dignitas requirere videtur, ut omnia subsidia ad solutionem problematis tam elegantis ac celebris sedulo excolantur.
Disquisitiones Arithmeticae (1801): Article 329

Jorge Luis Borges photo

“One of the heresiarchs of Uqbar had stated that mirrors and copulation are abominable, since they both multiply the numbers of man.”

Variant translation: Mirrors and copulation are obscene, for they increase the numbers of mankind.
Cf. "Hakim, the Masked Dyer of Merv", in A Universal History of Iniquity (1935)
Tlön, Uqbar, Orbis Tertius (1940)

Thomas Dekker photo

“To add to golden numbers golden numbers.”

Thomas Dekker (1572–1632) English dramatist and pamphleteer

Patient Grissell (1599), Act i. Sc. 1.

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Muhammad bin Qasim photo

“Of the prisoners captured a selection was made from the slaves and other spoils, “in order to detach the usual one-fifth share of the State. The number of the selected slaves came to about 20,000. The rest were distributed among the troops.””

Muhammad bin Qasim (695–715) Umayyad general

Chachnama, Kalichbeg, in Lal, K. S. (1994). Muslim slave system in medieval India. New Delhi: Aditya Prakashan. Chapter 10
Quotes from The Chach Nama

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