Off-topic matemático total

Thurman

@koan:1aoffu2h:

@Thurman:1aoffu2h:

Ahora mismo, entre los libros de divulgación que he leído con gusto recuerdo "El tao de la física" de Fritjof Capra (uno de los físicos que dio el pistoletazo de salida a la interrelación entre la ciencia occidental y las filosofías orientales), y otro libro suyo, "Sabiduría insólita: conversaciones con personajes notables". También en editorial Kairós, y de varios autores, "Cuestiones cuánticas" y "El paradigma holográfico". Estos dos últimos recogen artículos de físicos y científicos famosos.

Aún recuerdo cuando terminé de leer ese libro. Nunca se me dio bien la fisica y me lo recomendaron tanto que al final cai. El tetris que se montó en mi cabeza fue espectacular. Recomiendo La trama de la vida, tambien de Fritjof Capra que es otro de esos libros que te dejan marcado. De hecho creo que voy a rescatarlos que me habeis puesto los dientes largos.

Cuidado con esas cosas, estáis al límite de caer en la Quantum Quackery. De aquí a ver en el cine chorradas como What the bleep do we know (traducida en españa como Y tu qué sabes?) hay un paso.

En "El paradigma holográfico", por ejemplo, se exponen visiones enfrentadas: Capra defiende la convergencia entre ciencia y mística, y sin embargo Wilber la niega (como he recordado al leer la contraportada). Así que este tipo de libros no siempre son tan parciales; a veces se limitan a reflejar un debate. Supongo que simplifican porque quieren llegar al gran público. Pero de ahí a presentar una serie de argumentos como dogmas de fe hay un abismo.

Además, los pobres mortales ya estamos lo suficientemente espabilados (aunque no especializados) como para saber cuándo intentan vendernos la burra vieja. Se nota mucho cuando cojea de alguna pata o tiene pocos dientes.

De la peli chorra, ni zorra…

Thurman

Ahí os dejo un extracto de la novela sobre Hardy y Ramanujan a los interesados en el tema que sepáis inglés, a modo de improvisado suplemento dominical del foro.

No valen pre-críticas negativas. (Bastante tengo con las 500 páginas que me quedan por delante.) Sólo se admiten elogios al texto original y ánimos al sufrido traductor.

Y si os parece que lo de "sufrido" no está justificado, probad a transcribir en un castellano mínimamente decente lo que entendáis en inglés y ya me contaréis. :mrgreen:
(De todos modos, supongo que empezaré a dar el coñazo con las dudas propiamente matemáticas como dentro de un mes...)

THE INDIAN CLERK - AN EXCERPT
(We gratefully acknowledge David Leavitt and Bloomsbury for the permission to run the following excerpt from The Indian Clerk.)

The letter arrives the last Tuesday in January 1913. At thirty-five, Hardy is a man of habit. Every morning he eats his breakfast, then takes a walk through the Trinity grounds—a solitary walk, during which he kicks at the gravel on the paths as he tries to untangle the details of the proof he's working on. If the weather is fine, he thinks to himself, Dear God, please let it rain, because I don't really want sun pouring through my windows today; I want gloom and shadows so that I can work by lamplight. If the weather is bad, he thinks, Dear God, please don't bring back the sun as it will interfere with my ability to work, which requires gloom and shadow and lamplight.

The weather is fine. After half an hour, he goes back to his rooms, which are good ones, befitting his eminence. Built over one of the archways that lead into New Court, they have mullioned windows through which he can watch the undergraduates passing beneath him on their way to the backs. As always, his gyp has left his letters stacked on the little rosewood table by the front door. Not much of interest today, or so it appears: some bills, a note from his sister, Gertrude, a postcard from his collaborator, Littlewood, with whom he shares the odd habit of communicating almost exclusively by postcard, even though Littlewood lives just on the next court. And then—conspicuous amid this stack of discreet, even tedious correspondence, lumbering and outsize and none too clean, like an immigrant just stepped off the boat after a very long third-class journey—there is the letter. The envelope is brown, and covered with an array of unfamiliar stamps. At first he wonders if it has been misdelivered, but the name written across the front in a precise hand, the sort of hand that would please a schoolmistress, that would please his sister, is his own: G. H. Hardy, Trinity College, Cambridge.

Because he is a few minutes ahead of schedule—he has already read the newspapers at breakfast, checked the Australian cricket scores, shaken his fist at an article glorifying the advent of the automobile—Hardy sits down, opens the envelope, and removes the sheaf of papers that it contains. From some niche in which she has been hiding, Hermione, his white cat, emerges to settle on his lap. He strokes her neck, and she digs her claws into his legs.

"Dear Sir," he reads.

I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years 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 the conventional regular course which is followed in a University course, but I am striking 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."

He skips to the end of the letter—"S. Ramanujan" is the author's name—then goes back and reads the rest. "Startling," he decides, does not begin to describe the claims the youth has made. For instance, he writes: "Very recently I came across a tract by you styled Orders of Infinity in page 36 of which I find a 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." Well, if that's the case, it means that the boy has done what none of the great mathematicians of the past sixty years has managed to do. It means that he's improved on the prime number theorem. Which would be startling.

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. Being inexperienced I would very highly value any advice you give me. Requesting to be excused for the trouble I give you.

The trouble I give you! Hardy shifts Hermione, much to her annoyance, off his lap, then gets up and moves to his windows. Beneath him, two gowned undergraduates stroll arm in arm toward the archway. Watching them, he thinks of asymptotes, values converging as they near a sum they will never reach: a half foot closer, then a quarter foot, then an eighth… One moment he can almost reach out and touch them, the next—whoosh—they're gone, sucked up by infinity. Now there's a divergent series for you. The envelope from India has left a curious smell on his fingers, of soot and what he thinks might be curry. The paper is cheap. In two places the ink has run.

This is not the first time that Hardy had received letters from strangers. For all its remoteness from the ordinary world, pure mathematics holds a mysterious attraction for cranks of all stripes. Some of the men who have written to Hardy are genuine lunatics, claiming to have in their hands formulae pointing to the location of the lost continent of Atlantis, or to have discovered cryptograms in the plays of Shakespeare indicating a Jewish conspiracy to defraud England. Most, though, are merely amateurs whom mathematics has fooled into believing that they have found solutions to the most famous unsolved problems. I have completed the long-sought proof to Goldbach's Conjecture—Goldbach's Conjecture, stating simply that any even number greater than two could be expressed as the sum of two primes. Needless to say I am loath to send my actual proof, lest it fall into the hands of one who might publish it as his own…Experience suggests that this Ramanujan falls into the latter category. Being poor—as if mathematics has ever made anyone rich! I have not given the actual investigations nor the expressions that I get—as if all the dons of Cambridge are waiting with baited breath to receive them!

Nine dense pages of mathematics accompany the letter. Sitting down again, Hardy looks them over. At first glance, the complex array of numbers, letters, and symbols suggests a passing familiarity with, if not a fluency in, the language of his discipline. Yet how strangely the Indian uses that language! What he is reading, Hardy thinks, is the equivalent of English spoken by a foreigner who has taught the tongue to himself.

He looks at the clock. Quarter past nine. He's fifteen minutes off schedule. So he puts the letter aside, answers another letter (this one from his friend Bohr in Copenhagen), reads the latest issue of Cricket, completes all the puzzles on the "Perplexities" page of the Strand (this takes him—he times it—four minutes), works on the draft of a paper he is writing with Littlewood, and at one precisely puts on his blue gown and walks over to Hall for lunch. God, as he hoped, has disregarded his prayer. The sun is glorious today, warming his face even as he must shove his hands into his pockets. (How he loves cold, bright days!) Then he steps inside Hall, and its gloom muffles the sun so thoroughly his eyes don't have time to adjust. Mounted on a platform above the roar of two-hundred undergraduates, watched over by portraits of Byron and Newton and other illustrious old Trinitarians, twenty or so dons sit at the high table, muttering to one another. A smell of soured wine and old meat hovers. There is an empty seat to Bertrand Russell's left, and Hardy takes it, Russell nodding at him in greeting. Then a prayer is read in Latin; benches scrape, waiters pour wine, the undergraduates begin to eat lustily. Littlewood, across the table from him and five places to the left, has become caught up in conversation with Jackson, an elderly classics don—a pity, as Hardy wants to talk with him about the letter. But perhaps it's just as well. Given some time to think, he might realize it's all nonsense, and spare himself coming off as an idiot.

Although the Trinity menu is written in French, the food is decidedly English: poached turbot, followed by a cutlet, turnips and cauliflower, and some sort of sponge cake in a glutinous sauce. Hardy eats little of it. He has very strong opinions about food, of which the strongest is a detestation of roast mutton that dates back to his days at Winchester, when it seemed that there was never anything else on the menu. And turbot, in his opinion, is the roast mutton of the fish world.

Russell seems to have no problem with the turbot. Although they are good friends, they don't much like each other—a condition of friendship Hardy finds to be much more usual than is usually supposed. For the first few years that he knew him, Russell wore a bushy mustache that, as Littlewood noted, lent to his face a deceptively dim and mild expression. Then he shaved it off, and his face, as it were, caught up with his personality. Now thick brows, darker than the hair on his head, shade eyes that are at once intensely focused and remote. The mouth is sharp and slightly dangerous looking, as if it might bite. Women adore him—in addition to a wife he has a clutch of mistresses—which surprises Hardy, as another of Russell's distinctive features is acute halitosis. The breadth of his intellect and its vigor—his determination not merely to be the greatest logician of his time, but to diagnose human nature, to write philosophy, to enter into politics—impresses and also irritates Hardy, for the voraciousness of such a mind can sometimes look like capriciousness. For instance, in addition to the third volume of his mammoth Principia Mathematica, he has just published a monograph entitled The Problems of Philosophy. And yet tonight it is neither the principles of mathematics nor the problems of philosophy of which he is speaking. Instead he is amusing himself (and not amusing Hardy) by laying out—complete with diagrams sketched on a pad—his translation into logical symbolism of the Deceased Wife's Sister Act, which legalizes the marriage of a widower to his wife's sister; Hardy all the while keeping his face averted so as not to have to take in Russell's acrid breath. When Russell finishes (at last!), Hardy changes the subject to cricket: off-spinners and short legs, hooking mechanisms, the injudicious strategies that, in his opinion, cost Oxford its last game against Cambridge. Russell, as bored by cricket as Hardy is by the Deceased Wife's Sister Act, helps himself to another cutlet. He asks if there are any new players for the university whom Hardy admires, and Hardy mentions an Indian, Chatterjee of Corpus Christi. The summer before, Hardy watched him play in the freshman's match and thought him very good. (Also very handsome—though he does not say this.) Russell eats his gateau avec crème anglaise. It is a considerable relief when at long last the proctor utters the final grace, freeing Hardy to escape logical symbolism and walk over to Grange Road for his daily game of indoor tennis. As it happens, his partner this afternoon is a geneticist called Punnett, with whom he also sometimes plays cricket. And what does Punnett think of Chatterjee? he asks. "Perfectly fine," Punnett says. "They take their cricket seriously over there, you know. When I was in Calcutta, I spent hours on the maidan. We'd watch the young men play and eat the strangest stuff—a sort of puffed rice with a sticky sauce poured over it."

Recollections of Calcutta distract Punnett, and Hardy beats him easily. They shake hands, and he returns to his rooms, wondering whether it's Chatterjee's playing or his handsomeness—a very European handsomeness that the contrasting dark skin only renders all the more unexpected—that has really drawn his attention. Meanwhile Hermione is yowling. The bedder has forgotten to feed her. He mixes tinned sardines, cold boiled rice, and milk in her dish, while she rubs her cheek against his leg. Glancing at the little rosewood table, he sees that the gyp has delivered another postcard from Littlewood, which he ignores as he did the last, not because he doesn't care to read it, but because one of the tenets that governs their partnership is that neither should ever feel obliged to postpone more pressing matters in order to answer the other's correspondence. By adhering to this rule, and others like it, they have established one of the only successful collaborations in the history of their solitary discipline, leading Bohr to quip, "Today, England can boast three great mathematicians: Hardy, Littlewood, and Hardy-Littlewood."

As for the letter, it sits where he had left it, on the table next to his battered rattan reading chair. Hardy picks it up. Is he wasting his time? Better, perhaps, just to toss it in the fire. No doubt others have done so. His is probably just one name on a list, possibly alphabetical, of famous British mathematicians to whom the Indian has sent the letter, one after the other. And if the others tossed the letter in the fire, why shouldn't he? He's a busy man. G. H. Hardy hardly (Hardy hardly) has time to examine the jottings of an obscure Indian clerk…as he finds himself doing now, rather against his will. Or so it feels.

Thurman

Puesto que el foro no va muy bien y me ha repetido el extracto anterior, aprovecho para colgar este cuadro de Varo que precisamente se titula Ciencia inútil o el alquimista. Sirva de ejemplo de la ciencia como fuente de inspiración de otras artes.

alrom

Ostras Thurman, no sólo has de zamparte los términos matemáticos, también te has de enfrentar al slang de Cambridge que se las trae… Vaya una te ha caído, exige paga extra

Thurman

Encima no me ha caído, alrom, la pedí, que todavía tiene más delito.

Pero, bueno, juega a mi favor que estudié en Cambridge una temporada. La verdad es que me apetecía volver aunque sólo fuera con la imaginación.

Marniello

Hete aquí una movida divertida y bizarra. Está en català, lamento no tener ganas de traducir 15 lineas, pero creo que más o menos, se puede entender:

Potser us en recordeu del Número de Bacon, que se li assigna a un actor o actriu en funció de la distància respecte l'actor nord-americà Kevin Bacon a una xarxa on el criteri relacional és haver actuat a la mateixa pel·lícula que algú altre. Així, Kevin Bacon tindria un número de Bacon 0 i Lori Singer, que surt amb ell a Footloose, tindria un 1. Algú que hagi compartit staff amb Lori Singer però no amb Bacon tindria un 2, i així succesivament… És la cosa aquella de les sis passes de separació... (Aquí teniu un cercador del número de Bacon a partir de la base de dades de IMDB http://oracleofbacon.org/)
Sembla que hi ha un altre índex anomenat el Número d'Erdös, que marca la distància respecte aquest matemàtic hongarès i el criteri relacional és senzillament haver signat a mitges un article científic.
Com comprendreu hi ha MOLT POQUETA gent que tingui un Número de Bacon-Erdös, és a dir que pertanyi a les dues xarxes alhora...
Doncs resulta, i aquí ve el detall freak, que la persona amb un número Bacon-Erdös més baix (6!!! = Bacon 2 + Erdös 4) és ni més ni menys que l'actriu Danica McKellar, més coneguda com a Winnie Cooper, la novieta morena i mona del xaval d'Aquellos Maravillosos Años.
Tócate los huevos.

Disperso

Fascinante.

hiperion

Joer, número de Erdös 4… no está mal :shock:

Como anécdota, es curiosa la que aparece en la wikipedia:

Bill Tozier, a researcher with an Erdős number of 4, offered the chance for collaboration to attain an Erdős number of 5 in an auction on eBay. The final bid was $1,031, though apparently the winning bidder had no intention to pay[12]. The winner (who already had an Erdős number of 3) considered it a "mockery", and said "papers have to be worked and earned, not sold, auctioned or bought".

Y sobre la Winnie, parece que ha sacado un libro de mates (aparte de tener un teorema con su nombre, teorema Chayes-McKellar-Winn)…

Cosas veredes, amigo Sancho…

Chucho

Andrés Pajares y Alfredo Lando tienen un Bacon index de 3… me parece soprendente...

last chance

me encantan los últimos posts de este hilo. una historia digna de una novela de Paul Auster

gRR

¿Y esta mujer por qué tiene un número de Erdős de 4? ¿El teorema este que mencionas, Hiperion, no será de ella, no?

Por cierto Chucho, que a mí me sorprendría más que Landa o Pajares tuvieran un número de Erdős de 3. Heh.

Pekh

@Chucho:2wtrd8fg:

Andrés Pajares y Alfredo Lando tienen un Bacon index de 3… me parece soprendente...

Y Sara Montiel y Carmen Sevilla un 2

Disperso

Pero estas son como muy cercanas.

Jesús Puente y John ford también tienen 2.

Marniello

Uno de mis amigos tiene un 3. Y no, no es ningún famosete, es un pringado. Simplemente salió como quasiextra en Las Maletas de Tulse Luper.

koan

Estais muy enfermos. Hace como 6 años que me llegó el famoso mail con lo del oraculo de Bacon. Entre mis colegas y yo probamos determinados nombres, incluidos los de algunos colegas que han trabajado en el medio con papeles mas bien pequeños por aquello de hacer la coña y tal. Pero esto de probar a
¿¿¿¿¿¿¿¿¿¡¡¡¡¡¡¡¡¡JESUS PUENTE!!!!?????????????

Pues eso, estais muy enfermos

Trinxo

Anita la biologa tiene un numero 3 de Bacon ese, lo que me parece fatal es que el gran Bertín Osborne no tenga parentesco con el Bacon.

hiperion

Volviendo a Winnie, la chica colaboró con un profesor suyo , Lincoln Chayes , y un compañero de universidad en un artículo (en el que aparece el teorema) del año 98, Percolation and Gibbs states multiplicity for ferromagnetic Ashkin–Teller models on Z2 (disponible en http://www.danicamckellar.com/math/percolation.pdf), cuando todavía estaba estudiando, parece. El tal Chayes colaboró con otro menda. R. Kotecky, en 1995, y este Kotecky con un tal D.Preiss en 1986, y este último colaboró con Erdös en 1976.

¿De qué va el artículo de la Winnie? No tengo ni pajolera idea. En un comentario perdido por internet dicen esto:

_Si sois matemáticos, claro que este artículo se sale de vuestros conocimientos. Se trata de mecánica estadística pura, asociada a fenómenos de percolación y ferromagnetismo.

El modelo de Ashkin-Teller es una generalización del famoso modelo de Ising. Este último consiste en una serie de, pongamos, núcleos atómicos o partículas ordenadas en una cuadrícula, que tiene dos estados posibles del “espín”. La interacción entre dos partículas próximas con el mismo espín tiene un valor, y otro distinto si los espines son diferentes. Con esas premisas, se estudian los fenómenos macroscópicos que esta serie de núcleos o partículas darían lugar. El modelo de Ashkin-Teller introduce cuatro estados de espín y puede, más o menos, asociarse a dos “capas” o rejillas de elementos similares a modelos elementales de Ising.

Estos modelos tienen interés, por ejemplo, en física del estado sólido, ya que permiten emular el comportamiento magnético de determinados materiales.

Muy bien por Danica si se ha metido en estos berenjenales, porque no es una parte de la física matemática sencilla._

Pos fale. Más curiosidades: Natalie Portman tiene un número de Erdös-Bacon de 7 (de Erdös, 5), igual que Mayim Bialik (la Blossom).

gRR

Famosísimo el modelo de Ising, por supuesto :lol:

...pues no me importaría nada tener un número de Portman igual a 1. O inferior si se pudiere :oops:

Thurman

Ya que estáis con los cálculos estos, igual os hace gracia esta página donde te averiguan por ordenador tu porcentaje de parecido físico con los famosos:

http://www.myheritage.es/collage-celebridades

wolfcatala

@gRR!!:3rm27xju:

Famosísimo el modelo de Ising, por supuesto

No te rías gRR!! que sí que es muy famoso el modelo de Ising. Lo he estudiado incluso yo en la carrera. Y, en efecto, a partir de él se derivan muchos otros. Vamos, que ha dado de comer a mucha gente. Pero tiene más de física que de matemáticas, quizás por eso al que ha escrito eso le ha parecido chungo, pero no lo es tanto. Estoy flipando con todo esto. Portman y la Blossom también? Este hilo es genial. Keep it up!