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Seis Grados de Separación

- 30 May 2005

Una peculiar cadena de datos

La teoría de los Seis Grados de Separación afirma algo muy simple: cualquier persona del planeta está conectada con cualquier otra, a través de una cadena de conocidos con no más de cinco eslabones o puntos de unión. Quizá muchos han escuchado esta idea, la han visto, o la han visto aplicada a juegos en alguna área, pero el tema se gana su sitio en esta sección: sólo seis niveles nos separan de cualquier persona del planeta. Seis pasos. Seis grados.

Surgida en el siglo XX, la propuesta inicial de esta idea fue hecha en 1929 por el húngaro Frigyes Karinthy, en un relato llamado Chains, cadenas.

En la década de los 50, investigadores del MIT e IBM trataron de demostrar esta teoría de forma matemática (es decir, dado un grupo de N personas, ¿cuál es la probabilidad de que cada miembro de N esté conectado a otro miembro a través de 1, 2,3 … n enlaces). 20 años después, el problema seguía sin soluciones competas o satisfactorias.

En 1967, un sociólogo (Stanley Milgram) desarrolló un experimento (el fenómeno del small-world, el mundo pequeño) con el fin de probar la teoría: al azar, eligió ciudadanos americanos de la región del Centro-Oeste, con el fin de entregar un envío a un desconocido en Massachussets, a miles de kilómetros de distancia. La única información era simple: el nombre, la ubicación genérica (no había direcciones concretas) y la ocupación del destinatario. Con esta información, el objetivo para los que iniciaron la cadena era sencillo: entregar a quien ellos creyeran que podía estar ligado al destinatario, siempre que se cumpliera la condición de tratarse de personas que conocían directamente, y con la idea general de que el primer eslabón sería basado en el hecho de que creyeran que el conocido pudiera estar relacionado, es decir, que tuviera más probabilidades de conectar al destinatario de un modo u otro. Los receptores debían hacer lo mismo, y la cadena seguiría hasta que el destinatario fuera alcanzado.

¿Cuántos pasos se necesitaban? Los participantes pensaban en cientos, los más optimistas en decenas, y muchos creían que era absurdo e imposible. ¿La respuesta? En promedio, se necesitaron entre 5 y 7 intermediarios.

Los resultados (publicados en revistas y en bibliografía científica y psicológica) inspiraron la frase de seis grados de separación, y John Guare, escritor de teatro, popularizó el término con su obra de 1990.

En realidad, los descubrimientos de Milgram no fueron muy fundamentados (el número de paquetes y su muestra de participantes fue muy pequeño para sacara datos válidos o conclusiones, por ejemplo), pero el evento fue innegablemente mediático y una noción cultural relevante en la cultura popular actual. Universidades prestigiosas hicieron juegos, sistemas y demostraciones de los seis grados, basados en este principio, y juegos populares en todo el mundo comenzaron a surgir, muchos de ellos basados en personas conocidas como actores, o gente famosa.

En el 2001, la Universidad de Columbia continuó el experimento de Milgram, usando Internet, y tras pruebas numerosas (casi 50,000 personas enviando el “paquete” a destinatarios de 157 países) se encontró que el número de pasos promedio era… seis. La aplicación de los seis grados es ahora un tema aplicado a cuestiones computacionales, comunicación, circuitos, etc.

Ahora sí, ¿Qué tiene todo esto que ver con el cine?.

En breve, hay dos partes: la primera, una cinta, Six Degrees of Separation, de 1993 (con Will Smith, Stockard Channing, Donald Sutherland), escrita por el mismo John Guare de la obra de teatro del mismo tema; y hay también un segundo nivel, en el que este extremo de relaciones y eslabones se lleva a un caso concreto: Los Seis Grados de Kevin Bacon.

Estos seis grados con Bacon, además de la rima (en inglés) y la broma, hacen uso de la idea general y de un actor concreto, para establecer un criterio de separación entre cualquier actor y Kevin Bacon, buscando el mínimo de pasos posibles.

Un ejemplo: ¿Cuál es el número Bacon de un actor como Elvis Presley? La sorpresa: el Rey tiene un número Bacon de sólo 2. Presley salió en la cinta Change of Habit con Edward Asner, quien sale con Bacon en JFK. Dos eslabones.

¿Lo peculiar? Debido al alto número de cintas en las que Bacon ha participado, y debido que en muchas de ellas es un secundario (¡y uno popular!), las conexiones son muy altas, y muy pocos actores tienen números Bacon altos.

Numéricamente, usando la base de actores de la IMDB (Internet Movie Data Base), muchas pruebas demuestran cosas como que dentro de más de 700,000 actores, sólo 13 necesitan 8 pasos para llegar a él, siendo este “8” el número Bacon más alto. ¡El resto se queda entre 1 y 7!, con un promedio de 2.9 pasos, y con un dato más: sólo 100 actores necesitan 7 u 8 pasos. Si no lo han entendido, es muy simple: ¡No hay actores en esa base de datos que superen el número 8 de eslabones!. Siendo puristas, Fred Ott tiene un número infinito (es decir, no tioene conexión alguna con Bacon), pero la causa es obvia: sólo tiene dos cintas en las que es el único actor, de modo que la cadena no tiene validez, ya que este caso es el extremo y al no haber actores, no puede ni siquiera entrar al juego. Lógicamente, el número Bacon más bajo es el 0, del mismo Bacon, que necesita 0 pasos para ser él mismo.

Lógicamente se pudo haber elegido a otro actor secundario y popular, pero Bacon fue el elegido, y el que carga ahora con el juego completa alrededor suyo, usándolo incluso en publicidad de empresas, en entrevistas, y en varios modos.

Una buena forma de lidiar con el tema.

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5 comentarios para “Seis Grados de Separación”

  1. […] pregunta, por si no es suficiente:: ¿cuál es el número Bacon de la actriz de la […]

    Reply to this comment
  2. neli

    17. Abr, 2011

    Excelente via para la comunicacion

    Reply to this comment
  3. Mono Pancho

    28. Abr, 2012

    Que pasa con el numero Alef y su septima conexion infinitesimal (siguiendo a las matrices logaritmicas de Dirac)?

    Reply to this comment
  4. Lourdes Díaz

    23. May, 2012

    No hay actores en está base de datos que superen el eslabón 8 …. ¿ Es éste el de Bacon?

    Reply to this comment
  5. Soraya Julian

    23. Oct, 2012

    Seria interesante en que se inspiro al sociólogo Stanley Milgram a realizar esta interesante investigacion?

    Por que Los Seis Grados de Kevin Bacon.?

    Reply to this comment

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