Why is it that we entertain the belief that for every purpose odd numbers are the most effectual?
The relative freedom which we enjoy depends of public opinion. The law is no protection. Governments make laws, but whether they are carried out, and how the police behave, depends on the general temper in the country. If large numbers of people are interested in freedom of speech, there will be freedom of speech, even if the law forbids it; if public opinion is sluggish, inconvenient minorities will be persecuted, even if laws exist to protect them.
Judging by contemporary literature, there are numbers of highly cultivated and indeed superior persons to whom the material world is altogether contemptible; who can see nothing in a handful of garden soil, or a rusty nail, but types of the passive and the corruptible.
By magic numbers and persuasive sound.
Nec pluribus impar=--Not an unequal match for numbers.
Even if it were in the power of the employers to make a large addition to the rates of wages which they at present pay, it is very questionable whether any real good would result from their doing so. A considerable augmentation of the incomes of the working class is indeed very greatly to be desired if it proceeds from the limitation of their numbers, and increased efficiency of their labor. But where wages are kept at a low rate by their improvidence, or inferior qualities as workmen, any increase in their incomes, effected without merit on their part, is very likely to aggravate their improvidence, and perpetuate their inefficiency. [ An Essay on the Relations Between Labour and Capital , 1854.]
Nature always begins the same things again, years, days, and hours, and in like manner spaces and numbers follow each other, end without end. So is made a sort of infinity and eternity, not that any thing of these is infinite and eternal, but these finite entities are infinitely multiplied.
In the struggle for the means of enjoyment, the qualities which ensure success are energy, industry, intellectual capacity, tenacity of purpose, and, at least as much sympathy as is necessary to make a man understand the feelings of his fellows. Were there none of those artificial arrangements by which fools and knaves are kept at the top of society instead of sinking to their natural place at the bottom, the struggle for the means of enjoyment would ensure a constant circulation of the human units of the social compound, from the bottom to the top and from the top to the bottom. The survivors of the contest, those who continued to form the great bulk of the polity, would not be those "fittest" who got to the very top, but the great body of the moderately "fit," whose numbers and superior propagative power enable them always to swamp the exceptionally endowed minority.
Tell me not, in mournful numbers, "Life is but an empty dream!" For the soul is dead that slumbers, And things are not what they seem.
Only now are increasing numbers of political and social scientists beginning to realize that [Kelso’s] theories provide a private-property-based alternative to the imminent passage of a government-distributed “guaranteed income” or “negative income tax.” [ Harvard Business Review , September-October 1969.]
we do not have anything directly comparable to continued-fraction expansions for a complex quadratic irrationality. In fact, the simple, but true, answer to the problem of how to find an infinite number of rational numbers that converge to such an irrationality is that you cannot! Correspondingly, the analogue of the Pell equation has only finitely many solutions.
The curious switch, from initially perceiving an obstruction to a problem to eventually embodying this obstruction as a number or an algebraic object of some sort that we can effectively study, is repeated over and over again, in different contexts, throughout mathematics. Much later, complex quadratic irrationalities also made their appearance. Again these were not at first regarded as “numbers as such,” but rather as obstructions to the solution of problems.
Defendit numerus junct?que umbone phalanges=--Their numbers protect them and their compact array.
The collection of all real or complex numbers that are integral linear combinations of 1 and τd is closed under addition, subtraction, and multiplication, and is therefore a ring, which we denote by Rd. That is, Rd is the set of all numbers of the form a + bτd where a and b are ordinary integers. These rings Rd are our first, basic, examples of rings of algebraic integers beyond that prototype, , and they are the most important rings that are receptacles for quadratic irrationalities. Every quadratic irrational algebraic integer is contained in exactly one Rd.
It is forbidden to kill; therefore all murderers are punished unless they kill in large numbers and to the sound of trumpets.
"Anyone attempting to generate random numbers by deterministic means is, of
Round numbers are always false.
One murder made a villain, Millions a hero. Princes were privileged To kill, and numbers sanctified the crime.
Tell me not, in mournful numbers, / "Life is but an empty dream," / For the soul is dead that slumbers, / And things are not what they seem.
Beyond a critical point within a finite space, freedom diminishes as numbers increase. . . . the human question is not how many can possibly survive within the system, but what kind of existence is possible for those who do survive.
The first apostles of Christ were in the eyes of the world “unlearned and ignorant” men: it was not until the Church had endured a persecution and had grown largely in numbers that Christ called a learned man to be His apostle.31
We should ask, critically and with appeal to the numbers, whether the best site for a growing advancing industrial society is Earth, the Moon, Mars, some other planet, or somewhere else entirely. Surprisingly, the answer will be inescapable — the best site is "somewhere else entirely."
As yet a child, nor yet a fool to fame, I lisp'd in numbers, for the numbers came.
This is the third time; I hope good luck lies in odd numbers. . . . There is divinity in odd numbers, either in nativity, chance, or death.
Thoughts that voluntary move / Harmonious numbers.
The term "just war" contains an internal contradiction. War is inherently unjust, and the great challenge of our time is how to deal with evil, tyranny, and oppression without killing huge numbers of people.
If I may speak of myself (the only person of whom I can speak with certainty), _my_ happy hours have far exceeded, and far exceed, the scanty numbers of the caliph of Spain; and I shall not scruple to add that many of them are due to the pleasing labor of the present composition.--_Gibbon._
(_Translation by Darius Lyman. The numbers are those of the translator._) As men, we are all equal in the presence of death.
The Hebrews were accustomed to divide numbers, and to place the smaller first, so that seven and sixty-two make sixty-nine. Of this seventy there will then rest the seventieth: that is to say the seven last years of which he will speak next, and after these sixty-two weeks which have followed the seven first, the Christ should be killed, and a people would come with its prince, who should destroy the city, and the sanctuary, and overwhelm all, and the end of that war will accomplish the desolation. Christ shall be killed after the sixty-nine weeks, that is to say, in the last week.
It is notorious that, to the unthinking mass of mankind, nine-tenths of the facts of fife do not suggest the relation of cause and effect; and they practically deny the existence of any such relation by attributing them to chance. Few gamblers but would stare if they were told that the falling of a die on a particular face is as much the effect of a definite cause as the fact of its falling; it is a proverb that "the wind bloweth where it listeth"; and even thoughtful men usually receive with surprise the suggestion, that the form of the crest of every wave that breaks, wind-driven, on the sea-shore, and the direction of every particle of foam that flies before the gale, are the exact effects of definite causes; and, as such, must be capable of being determined, deductively, from the laws of motion and the properties of air and water. So again, there are large numbers of highly intelligent persons who rather pride themselves on their fixed belief that our volitions have no cause; or that the will causes itself, which is either the same thing, or a contradiction in terms.
"Then here goes another," says he, "to make sure, For there 's luck in odd numbers," says Rory O'More.
The key elements in human thinking are not numbers but labels of fuzzy sets.
As yet a child, not yet a fool to fame, / I lisp'd in numbers, for the numbers came.
The considerable actions in the world have usually very small beginnings. Of a few letters, how many thousand words are made! Of ten figures, how many thousand numbers! A point is the beginning of all geometry. A little stone flung into a pond makes a little circle, then a greater, till it enlarges itself to both the sides. So from small beginnings God doth cause an efflux through the whole world.--_Charnock._
To add to golden numbers golden numbers.
Round Numbers are always false.
There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful.
Boggies are an unattractive but annoying people whose numbers have increased rather precipitously since the bottom fell out of the fairy-tale market. Slow and sullen, and yet dull, they prefer to lead simple lives of pastoral squalor. They don't like machines more complicated than a garotte, a blackjack, or a luger, and they have always been shy of the 'big folk' or 'biggers' as they call us. As a rule they avoid us, except on rare occasions when a hundred or so will get together to dry-gulch a lone farmer or hunter. They seldom exceed three feet in height, but are fully capable of overpowering creatures half their size when they get the drop on them ... Their beginnings lie far back in the Good Ole Days when the planet was populated with the kind of colorful creatures you have to drink a quart of Old Overcoat to see nowadays.
Every day is a little life; and our whole life is but a day repeated: whence it is that old Jacob numbers his life by days; and Moses desires to be taught this point of holy arithmetic--to number not his years, but his days. Those, therefore, that dare lose a day, are dangerously prodigal; those that dare misspend it, desperate.--_Bishop Hall._
Don't compare floating point numbers solely for equality.
The generation of random numbers is too important to be left to chance.
Now night descending, the proud scene was o'er, But lived in Settle's numbers one day more.
I am further of opinion that it would be better for us to have at all than to have them in so prodigious numbers as we have.
There are three ways in which a man becomes a slave. He may be born into slavery, or forced into it, or he can deliberately accept his servitude. All three forms flourish in the modern world. Men are born and forced into slavery in Russia and her satellites states. Men in the free world invite slavery when they ask the government to provide complete security, when they surrender their freedom to the “Welfare State.” The slave states of Western world are an outgrowth of monopolistic capitalism — an economic system which is opposed to the wide distribution of private property in many hands. Instead, monopolistic capitalism concentrates productive wealth among a few men, allowing the rest to become a vast proletariat. Some representatives of monopolistic capitalism, sensing this evil in their system, have tried to silence criticism by pointing to the diffused ownership in the great corporations. They advertise, “No one owns more than 4 percent of the stock of this great company.” Or they print lists of stockholders, showing that these include farmers, schoolteachers, baseball players, taxi drivers, and even babies. But there is a catch to this argument, and it is this: although it is true that individuals of small means own shares in the company, it is not true that they run the company. Their responsibility for its policies is nil. Possession properly has two faces, two aspects: we all have a right to private property, but this is accompanied by our responsibility for its righteous use. These two things (which should be inseparable) are frequently divided today. Everyone admits that the farmer who own a horse is obligated to feed and care for it, but in the case of stocks and bonds, we often forget that the same principle should prevail. Monopolistic capitalism is to blame for this; it sunders the right to own property from responsibility that owning property involves. Those who own only a few stocks have no practical control of any industry. They vote by postcard proxy, but they have rarely even seen “their” company. The two elements which ought to be inextricably joined in any true conception of private property — ownership and responsibility — are separated. Those who own do not manage; those who manage; those who manage and work do not control or own. The workmen in a factory may have a shadowy, unknown absentee “employer” — the thousands of individual owners of stock — whom “management” represents and tries to please by extra dividends. The workman’s livelihood is at the disposition of strangers who make a single demand of their representatives: higher profits. Faced with such insecurity, labor unions seek a solution in demands for higher wages, shorter hours, pensions, and such things. But this approach takes monopolistic capitalism for granted, and accepts the unnatural division between property and responsibility as permanent. A much more radical solution is apt to come, and this may take either of two forms. One way of remedying the situation would be through a profound alternative of our political and economic life, with the aim of distributing the means of production more widely by giving every workman a share in profits, management, and ownership, all three. The other alternative which is not a constructive solution is confiscation: this may take the violent form of communism, or the less noticeable form of bureaucratic encroachment through taxation, as favored by the welfare state. [and/or outright confiscation likened to General Motors, AIG, and Banks, etc. etc. etc.] Confiscation in any form is an unhealthy solution for a real disease. It amounts to telling men that because they are economically crippled, they must abandon all efforts to get well and allow the state to provide them with free wheelchairs. The denial of the right of ownership to a man is a denial of his basic freedom: freedom without property is always incomplete. To be “secured” — but with no accompanying responsibility – is to be the slave of whatever group provides the security. A democracy flirts with the danger of becoming a slave in direct ratio to the numbers of its citizens who work, but do not own / or who own, but do not work; or who distribute, as politicians do, but do not produce. The danger of the “slave state” disappears in ratio to the numbers of people who own property and admit its attendant responsibilities under God. They can call their souls their own because they own and administer something other than their souls. Thus they are free. [“New Slavery: Freedom without Property is Incomplete,” originally published in On Being Human: Reflections, On Life and Living , New York: Doubleday & Co., 1982.]
We know truth, not only by the reason, but also by the heart, and it is from this last that we know first principles; and reason, which has nothing to do with it, tries in vain to combat them. The sceptics who desire truth alone labour in vain. We know that we do not dream, although it is impossible to prove it by reason, and this inability shows only the weakness of our reason, and not, as they declare, the general uncertainty of our knowledge. For our knowledge of first principles, as _space_, _time_, _motion_, _number_, is as distinct as any principle derived from reason. And reason must lean necessarily on this instinctive knowledge of the heart, and must found on it every process. We know instinctively that there are three dimensions in space, and that numbers are infinite, and reason then shows that there are no two square numbers one of which is double of the other. We feel principles, we infer propositions, both with certainty, though by different ways. It is as useless and absurd for reason to demand from the heart proofs of first principles before it will admit them, as it would be for the heart to ask from reason a feeling of all the propositions demonstrated before accepting them.
Far greater numbers have been lost by hopes / Than all the magazines of daggers, ropes, / And other ammunitions of despair, / Were ever able to despatch by fear.
Round numbers are always false.
Killing time isn't as difficult as it sounds. I can shoot a hundred numbers through the chest and watch them bleed decimal points in the palm of my hand.
No bravery in war can withstand overwhelming numbers.
We know that there is an infinite, but are ignorant of its nature. As we know it to be false that numbers are finite, it must therefore be true that there is an infinity in number, but what this is we know not. It can neither be odd nor even, for the addition of an unit can make no change in the nature of number; yet it is a number, and every number is either odd or even, at least this is understood of every finite number.
Of all evils in story-telling, the humour of telling tales one after another in great numbers is the least supportable.
Sweet and gentle and sensitive man With an obsessive nature and deep fascination For numbers And a complete infatuation with the calculation Of \xF0.
Genus immortale manet, multosque per annos / Stat fortuna domus, et avi numerantur avorum=--The race continues immortal, and through many years the fortune of the house stands steadfast, and it numbers grandsires of grandsires.
There is no wealth but life. Life, including all its powers of love, of joy, and of admiration. That country is the richest which nourishes the greatest numbers of noble and happy human beings; that man is richest, who, having perfected the functions of his own life to the utmost, has also the widest helpful influence, both personal, and by means of his possessions, over the lives of others.
No society can surely be flourishing and happy, of which by far the greater part of the numbers are poor and miserable.
Fundamental to understanding the arithmetic of Rd is the following question: which ordinary prime numbers p are irreducible elements of Rd and which ones factorize as products of irreducible elements in Rd? We will see shortly that if a prime number does factorize in Rd, it must be expressible as the product of precisely two irreducible factors.
Tell me not, in mournful numbers, "Life is but an empty dream!" For the soul is dead that slumbers, And things are not what they seem.
U.S. labor leaders will realize that automation can multiply man’s wealth far more rapidly than it is multiplying at present and that automation will leave all men free to search and research…. Realizing the direct competition with foreign industry on a straight labor basis will mean swiftly decreasing wages per hour and longer hours and decreasing buying power of the public…. American labor will realize that its function is not to increase jobs, but to multiply the wealth and to expand the numbers benefited by the wealth at the swiftest possible rate. [ Utopia or Oblivion. ]
They hide themselves in the crowd, and call numbers to their aid.
"This is lemma 1.1. We start a new chapter so the numbers all go back to one."
Therefore I do not here undertake to prove by natural reasons either the existence of God or the Trinity, or the immortality of the soul, nor anything of that sort, not only because I do not feel myself strong enough to find in nature proofs to convince hardened atheists, but also, because this knowledge without Jesus Christ is useless and barren. Though a man should be persuaded that the proportions of numbers are immaterial truths, eternal, and dependent on a first truth in whom they subsist, and who is called God, I should not consider him far advanced towards his salvation.
Soft is the strain when zephyr gently blows, And the smooth stream in smoother numbers flows; But when loud surges lash the sounding shore, The hoarse rough verse should like the torrent roar. When Ajax strives some rock's vast weight to throw, The line too labours, and the words move slow: Not so when swift Camilla scours the plain, Flies o'er th' unbending corn, and skims along the main.
In numbers warmly pure and sweetly strong.
When a man has no occasion to borrow, he finds numbers willing to lend him.
Science speaks to us indeed of much more than numbers of years. It defines degrees of Life. It explains a widening Environment. It unfolds the relation between a widening Environment and increasing complexity in organisms. And if it has no absolute contribution to the content of Religion, its analogies are not limited to a point. It yields to Immortality, and this is the most that Science can do in any case, the broad framework for a doctrine. Natural Law, Eternal Life, p. 217.
Thoughts that voluntary move Harmonious numbers.
Good luck lies in odd numbers.
Let us then repeat and firmly fix this main point: the evil, the root evil, of that to which the term Capitalism has come to be applied, is neither its functioning for profit nor its dependence upon legally protected private property; but the presence of a Proletariat, that is of men possessing political freedom, but dispossessed of economic freedom, and existing in such large numbers in any community as to determine the tone of all that community. [ The Crisis of Civilization, Being the Matter of a Course of Lectures Delivered at Fordham University, 1937 . Rockford, Illinois: Tan Books and Publishers, Inc., 1991, p. 141.]
The seven eyes of Ningauble the Wizard floated back to his hood as he reported to Fafhrd: "I have seen much, yet cannot explain all. The Gray Mouser is exactly twenty-five feet below the deepest cellar in the palace of Gilpkerio Kistomerces. Even though twenty-four parts in twenty-five of him are dead, he is alive. "Now about Lankhmar. She's been invaded, her walls breached everywhere and desperate fighting is going on in the streets, by a fierce host which out-numbers Lankhamar's inhabitants by fifty to one -- and equipped with all modern weapons. Yet you can save the city." "How?" demanded Fafhrd. Ningauble shrugged. "You're a hero. You should know." -- Fritz Leiber, "The Swords of Lankhmar"
"This is lemma 1.1. We start a new chapter so the numbers all go back to one." -- Prof. Seager, C&O 351
There are more dead people than living, and their numbers are increasing. -- Eugene Ionesco
Just don't make the '9' format pack/unpack numbers... :-) -- Larry Wall in <199710091434.HAA00838@wall.org>
Don't compare floating point numbers solely for equality.
Hack placidly amidst the noisy printers and remember what prizes there may be in Science. As fast as possible get a good terminal on a good system. Enter your data clearly but always encrypt your results. And listen to others, even the dull and ignorant, for they may be your customers. Avoid loud and aggressive persons, for they are sales reps. If you compare your outputs with those of others, you may be surprised, for always there will be greater and lesser numbers than you have crunched. Keep others interested in your career, and try not to fumble; it can be a real hassle and could change your fortunes in time. Exercise system control in your experiments, for the world is full of bugs. But let this not blind you to what virtue there is; many persons strive for linearity and everywhere papers are full of approximations. Strive for proportionality. Especially, do not faint when it occurs. Neither be cyclical about results; for in the face of all data analysis it is sure to be noticed. Take with a grain of salt the anomalous data points. Gracefully pass them on to the youth at the next desk. Nurture some mutual funds to shield you in times of sudden layoffs. But do not distress yourself with imaginings -- the real bugs are enough to screw you badly. Murphy's Law runs the Universe -- and whether or not it is clear to you, no doubt <Curl>B*n dS = 0. Therefore, grab for a piece of the pie, with whatever proposals you can conceive of to try. With all the crashed disks, skewed data, and broken line printers, you can still have a beautiful secretary. Be linear. Strive to stay employed. -- Technolorata, "Analog"