Repasa las siete abominaciones de Proverbios 6: Es otra ma- nera de indicar la realidad de la promesa de Pablo, que dice: Atar la Ley en los dedos de la persona Prov. En la Biblia, la Palabra de Dios o su Ley se comparan con la luz: Junto con Proverbios 6: Este principio representa la espiritualidad verdadera: Esto puede suceder aun en casos de adulterio.
La pobreza y la necesidad no justifican el robo: Los dos pecados son un tanto similares. Sin embargo, hay una diferencia vital entre el robar y el adulterar: Tampoco ayuda el hecho de que la cultura popular a menudo exalta el adulterio y otras maldades. No pertenece a nadie en particular, sino a toda la humanidad, ya sea que la humanidad lo reconozca o no. Por supuesto, este paralelo no debe sor- prendernos pues Dios, como Creador de todas las cosas ver Juan 1: Muchos viven sin ninguna esperanza o con esperanzas falsas.
Toda la riqueza del mundo no sig- nifica nada ver Ecl.
My collection of quotations
Cier- tamente, caminar con nuestra propia luz es caminar en oscuridad. Y Dios bendice ese momento de pausa: Strand, The Sabbath in Scripture and History, p. El mismo lenguaje se usa en Salmo La segunda sentencia describe una actitud: En ambos casos, el requisito implica un esfuerzo con- tinuo. Los siete pilares que ha la- brado vers. La insensatez ofrece nada de comer o de beber; sencillamente, se jacta acerca de provisiones robadas vers.
Eternalmente tuve el principado [ La justicia es un don, que proviene de Dios. Lo opuesto es insensatez e infidelidad. La idea principal es que la maldad o la deficiencia moral no recompensan, aunque uno sea rico; y segundo, que la jus- ticia siempre trae su recompensa, de una manera u otra, aunque uno sea pobre. La lengua puede ser el mejor de los dones que se nos ha dado, o el peor de ellos. Se usa con referencia a Dios Sal. Proverbios 14; Daniel 7: Vemos muy poco, y lo que vemos siempre resulta filtrado por nuestras propias mentes.
Por el contrario, debemos confiar en Dios, quien controla el curso de los eventos aun cuando todo parezca ir mal. El necio habla con soberbia Prov. La idea de la vara, asociada con los labios del necio, implica su castigo final. El necio es impulsivo Prov. El necio oprime a otros Prov. El sabio habla con humildad Prov.
El sabio refrena sus labios. El sabio valora el aprendizaje y el conocimiento Prov. El sabio es cauto Prov. El sabio es apacible y paciente Prov. Su fe en Dios le permite relajarse y ejercer control propio Isa. El temor de Dios le da confianza Prov. El sabio es compasivo y sensible Prov. Del mismo modo, Job describe a Dios como mirando hasta los fines de la Tierra, y ve todo lo que sucede bajo los cielos Job La Escritura no nos promete una vida sin pruebas. Por esto la fe en Dios es tan importante; por eso es vital que conozcamos por nosotros mismos, por nuestra propia experiencia, la realidad de Dios y de su amor.
Como ya vimos en Proverbios, nuestras palabras tienen poder; pueden hacer mucho bien o mucho mal. La Biblia reconoce el valor de la responsabilidad y la libertad humanas. La Biblia no deja lugar para el azar. Pues aun cuando pensemos que el curso de los eventos es guiado por el azar, podemos confiar en que Dios sigue estando en los controles.
Proverbios 17; 1 Corintios Como lo destaca un pro- verbio egipcio: Cuando alguien comete un error, es muy tentador difundir la historia, con- tarla a otros. Sin embargo, esto no implica que debamos esconder el pecado, actuar como si nunca hubiera ocurrido, como si la persona nunca hubiese hecho nada malo. Solo mediante el amor aprendemos a no juzgar a otros porque, a causa de nuestras propias faltas y errores, podemos ser tan culpa- bles como ellos.
El amor verdadero no es ciego. El amor y la justicia van juntos. Los dos conceptos deben estar unidos. El hecho de que Proverbios El Ser sin pecado se compadece de las debilidades de la pecadora, y le tiende una mano ayudadora. Los sabios no son superficiales. Por eso debemos ser cuidadosos al usar esta potente herramienta. Sus mentes cerradas se conjugan con sus bocas abiertas. Dios tiene la capacidad de ver todos los lados de un asunto. El testigo, por lo tanto, debe dar un testimonio veraz.
Esto deshonra a Dios. Proverbios 20; 1 Corintios Hasta cierto punto y en un grado elevado, realmente , todos somos pro- ductos de nuestro ambiente. Desde la infancia, nos impacta lo que vemos y lo que escuchamos. A los Corintios, Pablo les habla de nuestras diferencias, y enfatiza que no deben darnos un sentido de superioridad sino ayudarnos a ver nuestra ne- cesidad mutua. No te necesito, ni tampoco la cabeza a los pies: El pecado es otro igualador universal. Es un don absolutamente gra- tuito. El hijo hasta pudo haber tramado la muerte de sus padres, a fin de obtener la herencia.
Si refrenas tu venganza, promete Proverbios El libro de Proverbios enfatiza y explica esta prioridad. Por causa de Dios: Por causa de los pobres: El futuro de nuestra sociedad y de nuestros hijos depende de lo que hemos sembrado. Piensa acerca de tu ejemplo: No procuran educarlos para que empleen sus talentos para honra de su Redentor. Medita en la idea de Proverbios Algunos de los proverbios de esta semana tienen paralelos en los textos egipcios.
Algunas verdades se aplican univer- salmente, y a todos. La frase hebrea en Proverbios Tomar algo de alguien que tiene menos de lo que uno tiene es peor que robar: En realidad, Proverbios La referencia al Redentor, el goel Prov. En Inglaterra, algunos ateos pusieron este lema en los buses de la ciudad: Realmente, todos los que han cometido grandes males y parecen haber escapado, realmente han escapado. No obstante, esa es una perspectiva de las cosas muy estrecha y de corto alcance.
Debemos odiar el pecado porque es pecado. Debemos odiarlo por lo que nos hizo, lo que hizo a nuestro mundo y a nuestro Dios. Es cierto, no todo el que bebe se embriaga hasta caer junto al camino. Piensa en alguien que conozcas y cuya vida fuera destruida por el alcohol. Pronto, los gritos de la mujer se detu- vieron. Podemos no ser capaces de actuar contra un crimen, pero si nos mantenemos en silencio sobre lo que vemos, compartimos la culpa con el criminal.
Este acto se compara con un beso en los labios, que- riendo decir que la persona se preocupa y se interesa en la otra.
No tenemos un momento que perder. Todos ejercemos una influencia en favor o en contra de la verdad. Exaltad su santo nombre. Otra vez, ese logo puesto en los buses de Londres: The Beginning of Infinity: Explanations That Trans- form the World. Ubicado en Kindle Hay cosas acerca de Dios que sencillamente no podemos comprender.
En un instante, eventos aparen- temente al azar pueden significar la diferencia entre la vida y la muerte. Algunas personas van de una tragedia a otra, mientras que a otras les va bien. Es decir, lo que es verdad para una persona o una cultura puede no ser verdad para otra. Al fin, siempre tenemos que someter nuestros conceptos a la Palabra de Dios y a las verdades que en ella se encuentran. Como ya hemos visto, ninguno de nosotros comprendemos todas las cosas; en realidad, no entendemos nada completamente.
Pero, al hacer precisamente eso, perdemos todas las oportunidades que la vida nos ofrece. Nunca gozaremos de la belleza de la rosa, si no corremos el riesgo de lastimarnos con sus espinas. Los que piensan que tienen todas las respuestas, generalmente no las tienen. Por eso, Proverbios nos advierte que a veces el amigo se comporta como un enemigo, y un enemigo como un amigo. El amor no tiene que ver solo con besos y palabras dulces.
Sin guardianes del orden no hay vida civilizada. They said also that this king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But every one from whose part the river tore away anything, had to go to him and notify what had happened; he then sent the overseers, who had to measure out by how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed.
In this way, it appears to me, geometry originated, which passed thence to Hellas. American Mathematical Society, Chelsea publishing, Esto se hizo sin ton ni son, y ha generado una enorme incertidumbre. Edwards dans le n. Berlin, Heidelberg, New York: El Colegio de Abogados de la Ciudad de Buenos Aires y varios juristas se han manifestado en contra de esta iniciativa. Es de esperar que la iniciativa no prospere y sea rechazada sobre tablas.
Jueves 16 de mayo, Lo bueno fue cuando descubrimos el yeite , que era ver a la Argentina desde Tailandia. La antena estaba en Uruguay. In this book we will develop the foundations of algebraic geometry using the language of schemes, starting with the next chapter. American Mathematical Society, Chelsea Publishing: Dice Nguyen Khac Vien, un viejo militante anticolonialista: No hay socialismo en la pobreza, y tampoco sin democracia. Es la zona fronteriza en el norte de Bolivia con Brasil. Gelblung mando el grito de: Citado por Jeffrey D.
Carter, en su libro Condemned to Repetitions , Princeton, Las cursivas aparecen en el original. Citado por Noam Chomsky, Estados Canallas. The political career of this eminent scientist was stained by servility and suppleness. After the 18th of Brumaire, the day when Napoleon was made emperor, laplace's ardour for republican principles suddenly gave way to a great devotion to the emperor.
Napoleon rewarded this devotion by giving him the post of ministere of the interior, but dismissed him after six months for incapacity. Alexandre Grothendieck en una carta a Jean-Pierre Serre del 16 de febrero de Alexandre Grothendieck en una carta a Jean-Pierre Serre del 5 de noviembre de La situation est absolument grotesque.
En tout cas, si tu ne dis rien, je me demande bien qui dirait quelque chose. Il est impossible de ne pas faire de politique. No en una democracia.
No; no creo que pueda. Schumpeter, Capitalismo, Socialismo y Democracia , vol.
The genealogical trees at the end of the Red Book of Westmarch are a small book in themselves, and all but Hobbits would find them exceedingly dull. Hobbits delighted in such things, if they were accurate: The Fellowship of the Ring. Ballentine Books, New York: Proudfoots , repeated Bilbo. Today is my one hundred and eleventh birthday: I am eleventy-one today! Bilbo was doing splendidly.
This was the sort of stull they liked: Y cuando no hay noticias concretas, la gente se las inventa. In accordance with Hilbert's prophecy, we are living in Cantor's paradise. So we are bound to be tempted. Providence, Rhode Island, The problems mentioned here are merely samples of problems, yet they will suffice to show how rich, how manifold and how extensive the mathematical science of to-day is, and the question is urged upon us whether mathematics is doomed to the fate of those other sciences that have split up into separate branches, whose representatives scarcely understand one another and whose connection becomes ever more loose.
I do not believe this nor wish it. Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditiones open the connection of its parts. For with all the variety of mathematica knowledge, we are still clearly conscious of the similarity of the logical devices, the relationships of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science.
So it happends that, with the extension of mathematics, its organic character is not lost but only manifests itself more clearly. But, we ask, with the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departemets of this knowledge? In answer let me point out how thoroughly it is integrated in mathematical science that every realadvance goes hand in hand with the invention of sharper tools and simpler methods which at the same time assist in understanding earlier theories and cast aside older more complicated developments.
It is therefore possiblefor the individual investigator, when he makes these sharper tools and simpler methods hiw own, to find his way more easily in the various branches of mathematics than is possible in any other science. The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena.
That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples. Del final de David Hilbert, Mathematical Problems. Traducido en Bulletin of the American Mathematical Society , vol. Collection Classiques Larousse, Larousse, Citado en Anne Henry, Proust. I am now about 23 yars of age. I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics.
I have not trodden through the conventional regular course which is followed in a University course, but I am strinking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as startling. Very recently I came across a tract published by you styled Orders of Infinity in page 36 of which I find the statement that no definite expression has been as yet found for the number of prime numbers less than any given number.
I have found an expression which very nearly approximates to the real result, the error being negligible. I would request you to go through the enclosed papers. Being poor, if you are convinced that there is anything of value I would like to have my theorems published. I have not given the actual investigations nor the expressions that I get but I have indicated the lines on which I proceed. Requesting to be excused for the toruble I give you,.
History of Mathematics, vol. Hardy had one ruling passion—mathematics. Apart from that his main interest was in ball games, particularly cricket, of which he was a astylish player and an expert critic. Some of his interests and antipathies are revealed by this list of six New Year wished which he sent on a postcard to a friend in the 's: I am very much gratified onperusing your letter of the 8th February I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalss of divergent series.
I have found a friend in you who views my labours sympathetically. This is already some encouragement to me to proceed with my onward course. Y find in many a plave in your letter rigorous proofs are required and so on and you ask me to communicate the methods of proof. If I had given you my methods of proof I am sure you would follow the London Professor.
But as a fact I did not give him any proof but made some assertions as the followig under my theory. I told him that the sum of an infinite number of terms of the series: If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter.
You may ask how you can accept results based upon wrong premises. What I tell you is this. Verify the results I give and if they agree with your results, got by threading on the groove in which the present day mathematicians move, you should at least grant that there may be some truths in my fundamental basis. So what I now want at this stage is for eminent professors like you to recognize that there is some worth in me.
I am already a half starving man. To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarschip either from the University or from the Government. Citado en Bruce C. De la observacion de la irreductibilidad de las creencias ultimas he sacado la mayor leccion de mi vida.
Aprendi a respetar las ideas ajenas, a detenerme ante el secreto de las conciencias, a entender antes de discutir, a discutir antes de condenar. Y como estoy en vena de confesiones, hago una mas, quizas superflua: Hans Albert Einstein, hijo de Albert. Citado en Secretos de alcoba , vol. Todos saben que eso es falso. I'm sorry but I don't want to be an Emperor—that's not my business—I don't want to rule or conquer anyone. I should like to help everyone if possible, Jew, gentile, black man, white.
We all want to help one another, human beings are like that. We all want to live by each other's happiness, not by each other's misery. We don't want to hate and despise one another. In this world there is room for everyone and the earth is rich and can provide for everyone. The way of life can be free and beautiful. But we have lost the way. Greed has poisoned men's souls—has barricaded the world with hate; has goose-stepped us into misery and bloodshed. We have developed speed but we have shut ourselves in: Our knowledge has made us cynical, our cleverness hard and unkind.
We think too much and feel too little: More than machinery we need humanity; More than cleverness we need kindness and gentleness. Without these qualities, life will be violent and all will be lost. The aeroplane and the radio have brought us closer together. The very nature of these inventions cries out for the goodness in men, cries out for universal brotherhood for the unity of us all. Even now my voice is reaching millions throughout the world, millions of despairing men, women and little children, victims of a system that makes men torture and imprison innocent people.
To those who can hear me I say Do not despair. The misery that is now upon us is but the passing of greed, the bitterness of men who fear the way of human progress: Soldiers—don't give yourselves to brutes, men who despise you and enslave you—who regiment your lives, tell you what to do, what to think and what to feel, who drill you, diet you, treat you as cattle, as cannon fodder.
Don't give yourselves to these unnatural men, machine men, with machine minds and machine hearts. You are not machines. You are not cattle. You have the love of humanity in your hearts. You don't hate—only the unloved hate. Only the unloved and the unnatural. Soldiers—don't fight for slavery, fight for liberty. In the seventeenth chapter of Saint Luke it is written the kingdom of God is within man —not one man, nor a group of men—but in all men—in you, the people.
You the people have the power, the power to create machines, the power to create happiness. You the people have the power to make life free and beautiful, to make this life a wonderful adventure. Then in the name of democracy let's use that power—let us all unite.
Let us fight for a new world, a decent world that will give men a chance to work, that will give you the future and old age and security. By the promise of these things, brutes have risen to power, but they lie. They do not fulfil their promise, they never will. Dictators free themselves but they enslave the people. Now let us fight to fulfil that promise. Let us fight to free the world, to do away with national barriers, do away with greed, with hate and intolerance.
Autor | Antonio Gonzalez - nifaquniky.cf
Let us fight for a world of reason, a world where science and progress will lead to all men's happiness. The clouds are lifting—the sun is breaking through. We are coming out of the darkness into the light. We are coming into a new world. A kind new world where men will rise above their hate and brutality. The soul of man has been given wings—and at last he is beginning to fly. He is flying into the rainbow—into the light of hope—into the future, that glorious future that belongs to you, to me and to all of us.
La circoncision n'est rien, et l'incirconcision n'est rien; ce qui compte, c'est de garder les commandements de Dieu. Ne t'en soucie pas. Ne vous rendez pas exclaves des hommes. Citado parcialmente por Guillermo de Ockham, Breviloquium de principar tyrannicu super divina et humana specialiter autem super imperium et subjectos imperioa quibusdam vocatis summis pontificubus usurparo , — Por eso no dijo a Pedro: Sin embargo, le dijo: Guillermo de Ockham, Breviloquium de principar tyrannicu super divina et humana specialiter autem super imperium et subjectos imperioa quibusdam vocatis summis pontificubus usurparo , — Mais s'ils ne peuvent se contenir, qu'ils se marient: For whosoever hath, to him shall be given, and he shall have more abundance: William Blake, en Proverbs from hell.
The Marriage of Heaven and Hell. Los Cantos de la Inocencia. Los Cantos de la Experiencia. Hoy anduvo la muerte buscando entre mis libros alguna cosa La prueba de una inteligencia de primera clase es la capacidad para retener dos ideas opuestas en la mente al mismo tiempo, y seguir conservando la capacidad de funcionar.
Francis Scott Fitwgerald, en Crack-up. I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field in mathematics, with more solid fundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise.
Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable. Es necesario neutralizar la resistencia natural a matar civiles , dijo. Nota al pie en Las Kenningar , de Historia de la eternidad.
Or, il n'est plus un enfant. Il sait bien maintenant ce qu'il aime, il est peu probable qu'il change, et it est capable de se rendre compre de ce qui le rendra heureux dans l'existence. Il quitte de moins en moins la campagne. Je lui ai dit que je n'avais pas besoin d'invitation pour aller aux Invalides. Je n'ai pas besoin de cartes pour cela.
Je vous plains beaucoup. J'aurais voulu la saisir. Porque la experiencia de la quimio es aterradora en varios aspectos, pero no en el hecho de que se caiga el pelo sino que la forma en que se cae es signo de enfermedad. Hay gente que hasta cambia de tonalidad, llega a la palidez total, casi verdosa.
Y eso es cierto pero durante las primeras 48 horas. Por eso el cuerpo puede llegar a adquirir esa tonalidad tan rara, tan enfermiza. Una pollera larga y estaba para el ghetto. Me hubiera hecho millonaria. Nadie ni por asomo pensaba que yo estaba enferma. Sin teta fue otra imagen , sin pero es otra imagen. No es necesario ponerse verde y vomitar para estar enfermo.
Se pueden tener otros aspectos. Ahora, tampoco es mi objetivo parecer no enferma. Pero no es el eje. Pero no estoy todo el tiempo enferma. Incluso hay momentos en que me olvido. Volverse casi verde, estar vomitando es un momento. Pero hay muchos otros. Si yo me hubiera puesto verde me hubiera pintado los ojos de violeta para que combine. Se trata justamente de eso, de que estas mutaciones combinen con tu vida. Si te pisa un auto no hay mucho que elaborar al respecto. Sometimes, I just take out a blank piece of paper and write out a bunch of closing parentheses, to make up for all the unclosed parenthetical blocks out there in the world.
Nat Friendman, en su blog , el 6 de marzo de Il ne sait pas que je l'aime. J'essaierais de le sauver, mais davantage j'essaierais qu'il me sauve. Ignorance more frequently begets confidence than does knowledge: Un escritor de cuentos. Citado en Radar Libros por Carlos Gamerro. Aujourd'hui tout le monde est prince, il faut pourtant bien avoir quelque chose qui vous distingue; je prendrai un titre de prince quand je voudrai voyager incognito.
Well, my art of midwifery is in most respects like theirs; but differs, in that I attend men and not women; and look after their souls when they are in labour, and not after their bodies: And like the midwives, I am barren, and the reproach which is often made against me, that I ask questions of others and have not the wit to answer them myself, is very just--the reason is, that the god compels me to be a midwife, but does not allow me to bring forth. And therefore I am not myself at all wise, nor have I anything to show which is the invention or birth of my own soul, but those who converse with me profit.
Some of them appear dull enough at first, but afterwards, as our acquaintance ripens, if the god is gracious to them, they all make astonishing progress; and this in the opinion of others as well as in their own. It is quite dear that they never learned anything from me; the many fine discoveries to which they cling are of their own making. But to me and the god they owe their delivery. John Kerry, durante un debate con George W. Cuanto puede expresarse, puede expresarse claramente.
Chesterton consideraba tan importante para las humanidades: La ciencia tiene dos misiones: Freud mencionaba tres de estas revoluciones: Es algo que destroza la certidumbre complaciente y al mismo tiempo aviva los fuegos del intelecto. Alejandra Pizarnik, en el poema Fuga en lila , de El Infierno musical. Una chica que conozco apenas de vista me dijo: As a parent, I applauded Bush's resolve at the time. I understood, as did most adults, that confessing to the drug use rampant on college campuses in the late '60s and the '70s risked giving children permission to behave likewise.
Children inevitably would infer: Kathleen Parker, columnista, comentando que, en unas grabaciones de conversaciones privadas, George W. Citado en The National Ledger. Usted afirma que es para prevenir el sida. Todos queremos que nadie sea aquejado por semejante enfermedad. Pan queda poco si no propiciamos la cultura del trabajo. There are those who dream of a perfect world in which copyrighted text is translated into copyrighted glyphs through copyrighted rules with no more human intervention than it takes to feed a tape to a machine, while money flows in perpetuity to everyone involved.
There are also those who think that putting chairs and air-conditioners in hell will make it just as good as heaven. Actually, working with type is an earthly task, much less like sitting down and turning on TV than like walking on our hands across an ever-varied, never-ending landscape that is otherwise too far away to see. Logograms pose a more difficult question.
An increasing number of persons and institutions, from e. In the earlier days it was kings and deities whose agents demanded that their names be written in a larger size or set in a specially ornate typeface; now it is business firms and mass-market products demanding an extra helping of capitals, or a proprietary face, and poets pleading, by contrast, to be left entirely in the vernacular lower case. But type is visible speech, in which gods and men, saints and sinners, poets and business executives are fundamentally treated alike.
And the typographer, by virtue of his trade, honors stewardship of texts and implicitly opposes private ownership of words. Pepe Mugica, ministro del gobierno uruguayo. It seems clear that, today, there is no selective advantage in being a mathematician. I suspect that it might even be a disadvantage. Mathematically inclined purists have a tendency to end up in poorly paid academic jobs—or sometimes without a job at all—as a result of their curious passions and predilections! In previous Chapters we have seen that interesting and challenging questions can arise even in the lowest dimensions, and that the methods used to resolve these problems often rely more on ingenuity and hard work than on particularly sophisticated concepts—the proofs may be involved, but they have the satisfying concreteness of geometrical arguments, and something of the charm of antique music.
Nevertheless, it is futile to deny the decisive influence which has been wrought upon the shape of modern mathematics by the daemonic spirit of functorial constructions. So it is appropriate that this book end with a topic thatrepresents one of the triumphs of machinery in mathematics. Here, at last, connections in principal bundles play their predestined role, the invariant form of the Bianchi identities prove their superiority, and connections on arbitrary bundles are frequently invoked.
As a final affirmation thatwe have plunged into the icy stream of modern mathematics, hardly a picture appears. Publish or Perish, To Paul Dirac who saw that it must be true, Laurent Schwartz who proved it and George Temple who showed how simple it could be made. Lighthill, en la dedicatoria de Introductions to Fourier Analysis and generalized functions.
Hay algo raro en los actos de escribir y hablar: Quem dera Que sintas! Mignon la vit ainsi, ivre de tragique. From looking at species as only strongly-marked and well-defined varieties, I was led to anticipate that the species of the larger genera in each country would oftener present varieties than the species of the smaller genera; for wherever many closely related species i.
Where many large trees grow, we expect to find saplings. Where many species of a genus have been formed through variation, circumstances have been favourable for variation; and hence we might expect that the circumstances would generally still be favourable to variation. On the other hand, if we look at each species as a special act of creation, there is no apparent reason why more varieties should occur in a group having many species that in one having few.
Boy, that museum was full of glass cases. There were even more upstairs, with deer inside them drinking at water holes, and birds flying south for the winter. The birds nearest you were all stuffed and hung up on wires, and the ones in back were just painted on the wall, but they all looked like they were really flying south, and if you bent your head down and sort of looked at them upside down, they looked in an even bigger hurry to fly south. The best thing, though, in that museum was that everything always stayed right where it was. You could go there a hundred thousand times, and that Eskimo would still be just finished catching those two fish, the birds would still be on their way south, the deers would still be drinking out of that water hole, with their pretty antlers and their pretty, skinny legs, and that squaw with the naked bosom would still be weaving that same blanket.
The only thing that would be different would be you. Not that you'd be so much older or anything. It wouldn't be that, exactly. You'd just be different, that's all. You'd have an overcoat on this time. Or the kid that was your partner in line the last time had got scarlet fever and you'd have a new partner. Or you'd have a substitute taking the class, instead of Miss Aigletinger. Or you'd heard your mother and father having a terrific fight in the bathroom. Or you'd just passed by one of those puddles in the street with gasoline rainbows in them. I mean you'd be different in some way—I can't explain what I mean.
And even if I could, I'm not sure I'd feel like it. I said no, there wouldn't be marvelous places to go to after I went to college and all. It'd be entirely different. We'd have to go downstairs in elevators with suitcases and stuff. We'd have to phone up everybody and tell 'em good-by and send 'em postcards from hotels and all. And I'd be working in some office, making a lot of dough, and riding to work in cabs and Madison Avenue buses, and reading newspapers, and playing bridge all the time, and going to the movies and seeing a lot of stupid shorts and coming attractions and newsreels.
There's always a dumb horse race, and some dame breaking a bottle over a ship, and some chimpanzee riding a goddam bicycle with pants on. It wouldn't be the same at all. You don't see what I mean at all. It was mostly literature, though. They had this course you had to take, Oral Expression.
I was still feeling sort of dizzy or something, and I had a helluva headache all of a sudden. But you could tell he was interested, so I told him a little bit about it. And if the boy digresses at all, you're supposed to yell 'Digression! It just about drove me crazy. That digression business got on my nerves. The trouble with me is, I like it when somebody digresses. It's more interesting and all. I like somebody to stick to the point and all. But I don't like them to stick too much to the point. I guess I don't like it when somebody sticks to the point all the time. The boys that got the best marks in Oral Expression were the ones that stuck to the point all the time—I admit it.
But there was this one boy, Richard Kinsella. He didn't stick to the point too much, and they were always yelling 'Digression! It was terrible, because in the first place, he was a very nervous guy—I mean he was a very nervous guy—and his lips were always shaking whenever it was his time to make a speech, and you could hardly hear him if you were sitting way in the back of the room.
When his lips sort of quit shaking a little bit, though, I liked his speeches better than anybody else's. He practically flunked the course, though, too. He got a D plus because they kept yelling 'Digression! For instance, he made this speech about this farm his father bought in Vermont. They kept yelling 'Digression! Vinson, gave him an F on it because he hadn't told what kind of animals and vegetables and stuff grew on the farm and all. What he did was, Richard Kinsella, he'd start telling you all about that stuff—then all of a sudden he'd start telling you about this letter his mother got from his uncle, and how his uncle got polio and all when he was forty-two years old, and how he wouldn't let anybody come to see him in the hospital because he didn't want anybody to see him with a brace on.
It didn't have much to do with the farm—I admit it—but it was nice. It's nice when somebody tells you about their uncle. Especially when they start out telling you about their father's farm and then all of a sudden get more interested in their uncle. I mean it's dirty to keep yelling 'Digression! It's hard to explain. For one thing, I had this terrific headache all of a sudden. I wished to God old Mrs.
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Antolini would come in with the coffee. That's something that annoys hell out of me—I mean if somebody says the coffee's all ready and it isn't. One short, faintly stuffy, pedagogical question. Don't you think there's a time and place for everything?
Don't you think if someone starts out to tell you about his father's farm, he should stick to his guns, then get around to telling you about his uncle's brace? Or, if his uncle's brace is such a provocative subject, shouldn't he have selected it in the first place as his subject—not the farm? I didn't feel much like thinking and answering and all. I had a headache and I felt lousy. I even had sort of a stomach-ache, if you want to know the truth. I guess he should. I mean I guess he should've picked his uncle as a subject, instead of the farm, if that interested him most.
But what I mean is, lots of time you don't know what interests you most till you start talking about something that doesn't interest you most. I mean you can't help it sometimes. What I think is, you're supposed to leave somebody alone if he's at least being interesting and he's getting all excited about something. I like it when somebody gets excited about something. You just didn't know this teacher, Mr. He could drive you crazy sometimes, him and the goddam class. I mean he'd keep telling you to unify and simplify all the time.
Some things you just can't do that to. I mean you can't hardly ever simplify and unify something just because somebody wants you to. You didn't know this guy, Mr. I mean he was very intelligent and all, but you could tell he didn't have too much brains. The mark of the immature man is that he wants to die nobly for a cause, while the mark of the mature man is that he wants to live humbly for one.
I am a technological activist. I have a political agenda. I am in favor of basic human rights: I further my goals with technology. I build systems to disseminate information, commit digital piracy, synthesize drugs, maintain untrusted contacts, purchase anonymously, and secure machines and homes.
I release my code and writings freely, and publish all of my ideas early to make them unpatentable. Technology is not a panacea. I refuse to work on technology to track users, analyze usage patterns, watermark information, censor, detect drug use, or eavesdrop. Despite my emphasis on technology, I do not view laws as inherently evil. My goals are political ones, even if my techniques are not. The only way to fundamentally succeed is by changing existing laws.
If I rejected all help from the political arena I would inevitably fail. Bram Cohen, creador de BitTorrent, en su sitio web en I saw one once. It had died and fallen to earth. It was light blue. Its wings were transparent. The color of the sky. But those little birds don't have any legs and they live their whole lives on the wing and they sleep on the wind. They sleep on the wind and never light on this earth but one time. I'm going to take a wild guess and say that Mr. Fourier reproaches us, me and Abel, for not having chosen to study heat conduction.
It is true that Fourier was of the opinion that the principal object of mathematics is public use and the explanation of natural phenomena; but a philosopher like him ought to have known that the sole object of science is the honor of the human spirit, and that onthis view a problem in numbers is worth as much as a problem of the system of the world.
Carl Gustav Jacob Jacobi, en una carta a Legendre, fechada el 2 de julio de Citado por Detlef Laugwitz en Bernhard Riemann, — Turning Points in the Conception of Mathematics. Only Dirichlet, Not I, not Cauchy, not Gauss, knows what a perfectly rigurous proof is, but we learn it only from him.
When Gauss says he has proved something, I think it is very likely; when Cauchy says it, it is a fifty-fifty bet; when Dirichlet says it, it is certain ; I prefer not to go into these delicate matters. Citado por Detlef Laugwitz, Bernhard Riemann, — The paper submitted by Herr Riemann is a concise testimony to its author's thorough and penetrating studies of the area to which the subject treated therein belongs; it is a diligent and ambitious, truly mathematical spirit of investigation, and of praiseworthy and fertile independence.
The report is prudent and concise, and in places even elegant; nevertheless, most readers might well wish for even greater transparency of arrangement in some of the parts. Taken in its entirety, it is a solid and valuable work which not only meets the requirements usually set for test papers for the attainment of the doctorate but exceeds them by far.
Der Vortrag ist umsichtig und concis, theilweise selbst elegant: To judge what one must do to obtain a good or avoid an evil, it is necessary to consider not only the good and the evil in itself, but also the probability that it happens or does not happen; and to view geometrically the proportion that all these things have together. Arnauld, The Art of Thinking , Le sel et le fer, Cassini: Death, be not proud, though some have called thee Mighty and dreadful, for thou art not so; For those whom thou think'st thou dost overthrow, Die not, poor Death, nor yet canst thou kill me.
From rest and sleep, which but thy pictures be, Much pleasure; then from thee much more must flow, And soonest our best men with thee do go, Rest of their bones, and soul's delivery. Thou art slave to fate, chance, kings, and desperate men, And dost with poison, war, and sickness dwell; And poppy or charms can make us sleep as well And better than thy stroke; why swell'st thou then?
One short sleep past, we wake eternally, And death shall be no more; Death, thou shalt die. I know of no better tactic than the illustration of exciting principles by well-chosen particulars. Hugo Franco, diputado nacional. Entero y con fibra, pero un yogur. Aunque la suma de yogures ateste la heladera, cada uno de ellos no deja de ser una casa de juguete, un ecosistema balanceado, un mundito sin grandes ecos y sin grandes amenazas. Somos tantos que a veces creemos que el yogur es grande, pero es chiquito.
Estamos acostumbrados, por ejemplo, a algunos sobreentendidos, como si lo que uno da por hecho fuera ley, y es que, efectivamente, es la ley del yogur. Si lo hubiese conocido, por ejemplo, en un video club de cine de autor, las cosas seguro hubiesen tomado un rumbo diferente. Afuera del yogur hay muchas cosas. When you create counterfeit marriages and put them into the law, you're undermining society's most important safeguard against tyranny.
Citado por Tim Grieve, Bush's war over gay marriage , en Salon. Before returning to Rabelais, let's consider two hanging wires of equal cross section. This latter sentence, I'm sure, has never before appeared in print. One collection of coincidences too unlikely to be dismissed in this way is provided by the case of the proverbial monkey accidentally typing out Shakespeare's Hamlet.
This number is infinitesimal—zero, for all practical purposes. If they want to, they shouldn't waste their time trying to peck one out accidentally but should instead evolve into something that has a better chance of writing Hamlet. Incidentally, why is the question never put as follows: What is the probability that Shakespeare, by randomly flexing his muscles, might accidentally have found himself swinging through the trees like a monkey?
That said, objections to being identified for special purposes by number social secutiry, credir cards, etc. If anything, a number in these contexts inhances individuality; no two people have the same credit-card number, for example, whereas many have similar names or personality traits or socioeconomic profiles.
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I personally use my middle name—John Allen Paulos—to keep the masses from confusing me with the Pope. Fragmento de una entrevista realizada por Marie-Monique Robin durante marxo del para su libro Escuadrones de la muerte. Les dije, pongamos un ejemplo: Yo creo que su poder se detiene en el momento en que este hombre pierde el conocimiento Examining what the Bible has to say about life in the last days, Laurie explores topics such as: When I reached intellectual maturity, and began to ask myself whether I was an atheist, a theist, or a pantheist; a materialist or an idealist; a Christian or a freethinker, I found that the more I learned and reflected, the less ready was the answer; until at last I came to the conclusion that I had neither art nor part with any of these denominations, except the last.
The one thing in which most of these good people were agreed was the one thing in which I differed from them. They were quite sure that they had attained a certain "gnosis" -- had more or less successfully solved the problem of existence; while I was quite sure I had not, and had a pretty strong conviction that the problem was insoluble. And, with Hume and Kant on my side, I could not think myself presumptuous in holding fast by that opinion.
So I took thought, and invented what I conceived to be the appropriate title of "agnostic". It came into my head as suggestively antithetic to the "gnostic" of Church history, who professed to know so much about the very things of which I was ignorant; and I took the earliest opportunity of parading it at our Society, to show that I, too, had a tail, like the other foxes. A remedy for masturbation which is almost always successful in small boys is circumcision. The operation should be performed by a surgeon without administering an anesthetic, as the brief pain attending the operation will have a salutary effect upon the mind, especially if it be connected with the idea of punishment.
In females, the author has found the application of pure carbolic acid to the clitoris an excellent means of allaying the abnormal excitement. El universo ilimitado me agobia con su infalible e impecable don de esparcimiento. Estoy convencido de que todos los hegelianos no son fatuos, pero presiento que todos los fatuos, convenientemente tratados, tienen que terminar por hacerse hegelianos. Parece demasiado abotonado, demasiado encorbatado, demasiado impecablemente rasurado para hablar del vasto e inconsciente Cosmos de pausado aliento con sus terribles abismos y sus mareas ignotas.
William James, en Essays in Radical Empiricisms , Originalmente, en Skeptical Essays , Londres: Contra el incesto entre hermanos hay un argumento muy curioso: Uno de ellos, a primera vista, presenta grandes dificultades. Con este confortable pensamiento podemos terminar nuestro compendio de la Summa contra gentiles. Tome dos bastones en forma de cayado. Una de ellas era: Mi abandono de anteriores creencias no fue nunca completo, sin embargo. Ahora no tengo tales ideas. Originalmente, en My Philosophical Development , Londres: Somos nosotras las que decimos que tenemos los huevos llenos, que hay que tener huevos de oro para animarse a algo y etc.
Bue, nosotras, chicas fuertes, de este tiempo, poderosas. We feel that in proving correctness of programs it is important to make checks explicit. We may decide not to do them, but this must be a decision, not an omission. Biblioteca Borges, Alianza, Menard, en cambio, escribe:. La historia, madre de la verdad; la idea es asombrosa. Spend some time every day learning something new that is disjoint from the problem on which you are currently working remember that this disjointness may be temporary , and read the masters.
You know, for a mathematician, he did not have enough imagination. But he has become a poet and now he is fine. He who seeks for methods without having a definite problem in mind seeks for the most part in vain. Davis y Reuben Hersh. There are 10 11 stars in the galaxy.
That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers. No es el summum de la espiritualidad, pero es la base. Tzvi Grunblatt, rabino, director del Movimiento Jabad Lubavitch.
De una entrevista aparecida en El Observador, Perfil. Why was this circle of ideas, and not another, so interesting to me? Robin Hartshorne once asked me very earnestly what motivated me to work on a particular problem. But to attribute all of our choices to this hope is reductionist, as silly as attributing all of the choice of a marriage partner to sexual attraction. As with love and marriage, its usually more interesting to tell stories.
David Eisenbud, Syzygies, degrees, and choices from a life in mathematics. Von Neumann says somewhere that the real use of computers in mathematics will be to improve the intuition of mathematicians. I would add that the data produced by computation frequently lead to conjectures and often to strong convictions about them! This inductive method of discovering mathematical theorems provides a nice complement to the deductive method, which might somewhat uncharitably be described as piling theorems one already knows on top of each other to guess and make a new theorem.
The inductive method often leads to conjectures that are trivial, or merely uninteresting, and sometimes to conjectures that are very hard because they come without a pedigree of the reasons for believing in them. But sometimes it leads to conjectures having a kind of freshness and originality that may be harder to achieve with the deductive method. Perhaps the ease and tradition of inductive work is the reason number theory has so many more wonderful—and difficult—conjectures than other fields of mathematics. I think many of these other fields are gaining, as computer experiments become easier and more popular.
Unfortunately, I must say that I am very dissatisfied with it. It is very important and also correct, so on that count I have no reproach. The reproach relates rather to the proof of his fundamental theorem, which does not meet even the most moderate expectations which one has for mathematical proofs. It is by no means enough that the author makes the matter clear to himself, rather one wishes that he construct the proof according to definite rules. With this he cannot teach anyone; I can only learn that which is made as clear to me as the rules of one times one He counts on the importance and correctness to suffice.
This may hold for the first discovery but for a detailed Annalen paper it is not enough. Citado por Yuri Tschinkel, en Bull. It is the snobbishness of the young to suppose that a theorem is trivial because the proof is trivial. We used to think that if we knew one, we knew two, because one and one are two. I hope that posterity will judge me kindly, not only as to the things which I have explained, but also as to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
I have yet to see any problem which, when you looked at it in the right way, did not become still more complicated. Natural science does no simply describe and explain nature; it is part of the interplay between nature and ourselves: It behoves us always to remember that in physics it has taken great men to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows of a cup. One had to be Newton to notice that the moon is falling, when everyone sees that it does not fall.
One of the duties of the mathematician in acting as an adviser to scientists [ The whole question of imagination in science is often misunderstood by people in other disciplines They often overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know.
The problem of creating something which is new, but which is consistent with everything which has been seen before, is one of extreme difficulty. If the human brain was so simple that we could understand it, them we would be so simple that we could not. Series in Computational Mathematics 6 , Springer Verlag, When a new particle or new fact is discovered, I notice that all the theorists do one of two things: Elementary Particles, 2 , p.
Nussenzuerg, Causality and Dispersion relations. Mathematics in Science and Engineering 95 , Academic Press, In order to learn, we must make mistakes, and the most fruitful mistake which nature could have implanted in us would be the assumption of even greater simplicities than we are likely to meet in this bewildering world of ours.
To probe a hole we first use a straight stick to see how far it takes us. To probe the visible world we use the assumption that things are simple until they prove otherwise. Jamais de la vie. La science ne s'apprend pas: Schidt, Hommes de Science: Nothing of value is free. It is very easy, Mr. For the development of a general theory, it is an unhappy accident that only one honeycomb is regular, and olny one quasi-regular.
We have not succeeded in answering all out problems. The answers we have found only serve to raise a whole set of new questions. In some ways, we feel we are as confused as ever, but we believe we are confused on a higher level and about more important things. Philosophy is written in this grand book, the universe, which stands continually open to our gaze.
But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a word of it; without these one wanders about in a dark labyrinth. Friedrichs once told me of a chance encounter with Heisenberg in the sixties. He took the opportunity to express to Heisenberg the profound gratitude of mathematicians for his having created a subject that has led to so much beautiful mathematics.
Heisenberg allowed that this was so; Friedrichs then added that mathematics has, to some extent, repaid this debt. Heisenberg was noncommittal, so Friedrichs pointed out that it was a mathematician, von Neumann, who clarified the difference between a selfadjoint operator and one that was merely symmetric. Lax, Mathematics and Physics. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes.
But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.
It's impossible to compute things which don't exist. It's difficult to compute things which almost don't exist. Cleve Moler, en un mensaje a sci.