• Matemáticos reconocidos poco conocidos

    Karl Weierstraß
    (1815 - 1897)

    Maestro de Cantor, Runge,  Schwarz  y de toda una generación de matemáticos alemanes, Weierstrass es el responsable de uno de los métodos más efectivos en Cálculo: el método épsilon (nombrado así pues su notación utiliza la letra griega ε). Gracias a este método se pudieron probar varios teoremas fundamentales para el fundamento de la matemática infinitesimal lo que a la postre permitió varios de los desarrollos tecnológicos de la actualidad.

    Nacido en Ostenfelde, Westphalia (ahora parte de Alemania) , en 1828, al establecerse su familia en Paderborn, ingresó al Gimnasio Católico (institución equivalente a la educación media superior) y paso mucho de su tiempo leyendo el Journal of Pure and Applied Mathematics,  que era la revista matemática líder en Europa.  

    Mientras era profesor en el Instituto Industrial de Berlín, Weierstrass desarrollo una de las más grandes ideas matemáticas hasta el momento.  En su “Introducción al Análisis” druante los años 1859-1860, dio al mundo una rigurosa metodología para que los matemáticos trabajaran con la noción de secuencias infinitas o series que alcanzaban un límite. 

    Hasta ese momento, mucho del desarrollo del cálculo Newtoniano se basaba en ideas, nociones que se sabían verdad pero no se habían demostrado rigurosamente. El concepto de “límite infinito” aplicado a variables fijas, como en la expresión “n tiende a infinito” no se sabía realmente su significado formal.  El método épsilon resolvió esto.

    Weierstrass razonó: En lugar de que el límite estuviera definido para n como el proceso de alcanzar el infinito, por qué no definimos una secuencia infinita que tenga un límite si para cualquier épsilon  ε, siempre puedes encontrar un entero n tal que para todos los enteros m>=n, el emésimo término de la secuencia siempre estuviera a ε del límite.

    Entre los conceptos que gracias al método épsilon se pudieron formalizar se encuentran:
    + El concepto de continuidad , pieza clave para el desarrollo de la ciencia
    + El teorema de Weierstraß que trata sobre máximos y mínimos locales, y
    + Teorema de Bolzano-Weierstrass , otra pieza fundamental en la construcción de los ladrillos fundamentales del cálculo: los números Reales.

    Mucho le debe la humanidad a este gigante Alemán de las matemáticas.

  • El ser humano frente a la adversidad: Alter hours



    Si Taxi Driver constituía un alucinante viaje al corazón de la angustia, a una noche desolada, deshumanizada, violenta y salvaje como metáfora del atormentado interior del ser humano alienado y perdido en la inmensidad de una sociedad decadente y opresiva, After hours, traducida estúpidamente en España como Jo, ¡qué noche!, película dirigida por Martin Scorsese en 1985, es una especie de emulación en apariencia (pero sólo en apariencia) amable, también con Nueva York como marco, de ese mismo y desigual enfrentamiento entre el hombre con aspiraciones de bienestar y felicidad y un contexto colectivo que lo reduce a mera estadística, que lo ningunea, coarta, utiliza y pervierte, que le hace perder sus puntos de referencia y su lugar con respecto a sus semejantes.

    Griffin Dunne (también productor de la película, que consiguió imponerse como intérprete por delante de Robert De Niro, para quien estaba pensado el papel en lo que, si volvemos a pensar en la anterior película de Scorsese, hubiera constituido un irónico guiño al público y a la propia carrera del director), inolvidable en esta película por su magistral encarnación y caracterización de lo que comúnmente llamaríamos un “pringao”, es Paul Hackett, un discreto y anónimo empleado de una multinacional de la informática dedicado a cuestiones de programación. Es un hombre solitario: la enorme oficina, en la que prácticamente no tiene relación con ninguna de las decenas y cientos de personas con las que se cruza diariamente, exceptuando a aquellos a los que tiene que adiestrar en los instrumentos de su trabajo, gente a la que no volverá a ver ni a hablar, es una metáfora de su propia vida. Largas jornadas de trabajo, desplazamientos interminables de punta a punta de la ciudad, horas y horas sin hablar con nadie, concentrado en el cajón en el que trabaja sin dirigirle la palabra a cualquiera de las personas que, no obstante, lo rodean constantemente, triste soledad compartida con una cena rápida y el televisor cada noche al regreso a casa… Una perspectiva de vida que amenaza con prolongarse sine die y para la que parece no encontrar alternativa. El actual y prolongado insomnio que padece no ayuda a mitigar los efectos de la soledad forzosa en la que se encuentra, y las salidas nocturnas a horas intempestivas para cenar o tomar café en alguno de los locales próximos a su casa no le sirven de consuelo ni de remedio. Al menos hasta que, una noche cualquiera, una joven atractiva (Rosanna Arquette, sutilmente perturbadora), se interesa por el libro que está leyendo mientras su café se enfría (de Henry Miller, para más señas), traban conversación, y le da su teléfono. Paul, acostumbrado a encerrarse en sí mismo, a vivir de espaldas a una sociedad que suele darle pescozones cada vez que es capaz de asomar la cabeza fuera de su armadura, se retrae todo lo que puede, pero finalmente marca el número… y su vida cambia. Por lo menos, durante una noche: su llamada de teléfono le abre la puerta a un mundo de extrañas circunstancias encadenadas, una especie de apoteosis del mal fario, de casualidad adversa, de azar tramposo que se ensaña, se recrea en el destino de Paul haciéndole vivir una continua sucesión de fenómenos absurdos, inexplicables, retorcidamente ilógicos, en el peor barrio de Nueva York, un microcosmos nocturno vestido de cuero y poblado por islotes, por territorios humanos a la deriva, una fauna de lo más variopinto que incluye sombríos artistas amantes del sadomasoquismo, camareras desquiciadas, desvalijadores de pisos, porteros de discoteca, almas solitarias que beben sus copas en un rincón oscuro, contorsionistas de la música disco y demás criaturas de la noche que transitan por camuflados locales nocturnos abiertos hasta el amanecer y tan vacíos como la propia vida de quienes se encargan de mantener el neón encendido.

    Inquietante, absorbente, fascinante y también arriesgada aventura urbana en la que el protagonista se ve inmerso de manera imprevisible, la película representa, con la metáfora minimalista del viaje constante a través de las calles desiertas, los locales vacíos y los apartamentos despoblados de un barrio cualquiera, una introspección al interior de cada individuo y al planteamiento de cuestiones acerca de nuestro lugar en la sociedad, lo que significamos para los demás y el forzoso anonimato al que somos conducidos, convertidos en cifras asépticas, en una sociedad moderna que ha perdido el trato y contacto humanos como vehículo de relación y de enriquecimiento vital y personal. Todos los personajes de la película vacilan, dudan, se equivocan, luchan denodada, desesperadamente, por tender puentes de comunicación hacia los demás (como grita Paul en un momento del metraje: “¡yo sólo quería salir con una chica a tomar una copa, pasar un buen rato”), y es la incomprensión, la falta de entendimiento e incluso el estallido de la violencia y el odio irracionales el único resultado de este empeño profundamente humano y destinado al fracaso absoluto (metáfora visual y narrativa de incalculable valor es la de Dunne introducido en una de esas esculturas tamaño natural elaborada con yeso y recubiertas de papel de periódico).

    Este enloquecido periplo de Hackett a través de un planisferio de soledades compartidas no deriva como en otros trabajos de Scorsese en una orgía de violencia y sangre, sino que la visión quiere ser más esperanzada: Paul, a pesar de todo, encuentra ayuda en medio del cataclismo de absurdos en el que se ha metido, una mano tendida que, aunque sea de casualidad a través de un memorable final que todavía contribuye más si cabe, como otro absurdo esta vez dirigido al público, a cerrar el amplio catálogo de rocambolescas vivencias nocturnas del protagonista, le pone de nuevo en la senda correcta, la simple, monótona, aburrida vida diaria de la que no cabe intentar salir sin exponerse a una vorágine de imprevistos que caen como rayos y centellas sobre el pobre insensato que ha osado intentar romper el equilibrio metódicamente dispuesto sobre el que se ha diseñado nuestra vida de máquinas del siglo XX (o ya XXI). Así que Paul vuelve, o mejor dicho, le hacen volver, a su vida gris y triste, pero al menos ha conseguido una leve brizna de calor humano en forma de abrazo que le haga recobrar la esperanza en el género humano, de que en este mundo de cemento y vidrio todavía pervive algo de humanidad, justo antes de que su ordenador, como cada mañana, y siempre porque a alguien se le ocurrió programarlo así, le suelte de sopetón su metálico, frío y burocrático “Buenos días, Paul. ¿Cómo estás hoy?”.
    Bellamente rodada, retrato preciosista y meticuloso de la noche neoyorquina y de sus habitantes, la película combina una estética sombría y decadente, llena de espacios vacíos, despoblados, excelentemente sugerida por planos generales de espacios abiertos por los que pulula un único personaje solitario, o de rincones coquetos en los que un ser olvidado busca la compañía de un instante, con un tono ligero salpicado de fenomenales momentos de comedia basada en los malos entendidos y en desesperantes casualidades que complican a cada minuto el regreso de Paul a casa para protegerse en el aburrimiento de su insombio bajo las sábanas. Junto a Dunne y Arquette, rostros habituales del cine y la televisión americanas (Linda Fiorentino, mucho antes de convertirse en femme fatale oficial de los noventa, Bronson Pinchot, John Heard, Teri Garr, Cheech Marin, antes de ingresar en el grupo de Robert Rodriguez, o el propio Scorsese en un cameo discotequero) recrean de manera efectiva cada uno de esos universos humanos solitarios y un tanto desequilibrados que se cruzan con Paul en su singladura nocturna, un viaje que viene acompañado de imágenes tan sugerentes (maravillosa Arquette en la intimidad de su dormitorio) como inquietantes aderezadas con la ya proverbial excelente utilización de la música (desde piezas clásicas hasta incluso una guitarra flamenca ilustrando el demencial y memorable trayecto en taxi, billete volando por la ventanilla incluido, de Dunne hacia lo que él cree que es su cita de amor; trayecto de ida y vuelta, como se ve más tarde…) por parte de Scorsese.

    En suma, una divertida, inquietante e intrigante parábola de la soledad del ser humano en la sociedad actual que, además de hacernos reír (y no poco) y mantenernos en vilo ante el incierto y amenazado destino del protagonista, no obstante, intenta rebuscar la persona que llevamos dentro como única vía para impedir la subsunción de la especie en este ecosistema de consumismo, deshumanización y cúmulo de absurdos vitales que llamamos sociedad, democracia o economía de mercado en el que nos vemos reducidos a números que sólo se consideran en términos de rentabilidad, en el que nos enfrentamos solos a la adversidad, en el que enfermamos de un mal llamado soledad.

    Imagen tomada de Internet.

    Aragón, España.
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