¡Gigantescos!

Los niños se entretienen a veces con un juego sobre quién dice un número más grande, y sale esa frase de “yo, el tuyo y uno más”, que tiene más fundamento matemático del que parece ya que así se construyen de manera axiomática los números naturales. Pero, ¿de verdad hay números tan grandes?

Gúgol

Sabemos que los números naturales son infinitos, y este es el primer tipo de número infinito con el que tratamos, y sabemos que con los números enteros y racionales no nos pasamos de ese infinito. Con los números reales damos el salto a otro infinito, y a ese “paraíso de transfinitos que Cantor creó para nosotros y del que nunca nos iremos”, David Hilbert dixit.

Pero, así y todo, nos sigue gustando jugar con números muy grandes, casi diríamos gigantescos. Y así tenemos el millón, el billón (millón de millones), o el trillón (millón de billones), y así sucesivamente, siguiendo la nomenclatura española y no la anglosajona. Y para escribir estos números grandes, la mejor manera es usar las potencias de diez, y así tenemos:

Millón: 106 = 1 000 000

Billón: 1012 = 1 000 000 000 000

Trillón: 1018 = 1 000 000 000 000 000 000

Cuatrillón: 1024 = 1 000 000 000 000 000 000 000 000

Y así podíamos seguir poniendo ceros detrás de un uno.

En 1920, Milton Sirotta (1911-1981), un niño de 9 años, sobrino del matemático estadounidense Edward Kasner. El nombre surgió en un paseo por los Palisades de Nueva Jersey con sus sobrinos, Milton y Edwin Sirotta, cuando Kasner les pidió ideas para ese número, y fue Milton el que sugirió «googol”.

Edward Kasner

Un gúgol es el número grande 10100. En notación decimal, se escribe con el dígito 1 seguido de cien ceros:

10.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.

En su libro Mathematics and the Imagination (Las matemáticas y la imaginación), escrito por Kasner y James R. Newman, fue donde se popularizó por primera vez el término «googol»:

Las palabras sabias son pronunciadas por los niños con la misma frecuencia que por los científicos. El nombre de «gúgol» fue inventado por un niño (el sobrino de nueve años del Dr. Kasner) al que le pidieron que pensara un nombre para un número muy grande, a saber, 1 con cien ceros después. Estaba seguro de que ese número no era infinito y, por tanto, también de que tenía que tener un nombre. Al mismo tiempo que sugirió «googol», dio nombre a un número aún mayor: «Googolplex». Un googolplex es mucho mayor que un googol, pero sigue siendo finito, como se apresuró a señalar el inventor del nombre. Se sugirió que un googolplex fuera 1, seguido de escribir ceros hasta cansarse. Se trata de una descripción de lo que ocurriría si se intentara escribir un gugolplex, pero cada persona se cansa en un momento distinto y no serviría de nada que Carnera fuera mejor matemático que el Dr. Einstein, simplemente porque tenía más aguante. El gúgolplex, pues, es un número finito específico, con tantos ceros después del 1 que el número es un gúgol. Un gúgolplex es mucho más grande que un gúgol. Podemos hacernos una idea del tamaño de este número, muy grande pero finito, por el hecho de que no habría espacio suficiente para escribirlo si fuéramos hasta la estrella más lejana, recorriendo todas las nebulosas y poniendo ceros en cada centímetro del camino.

Y sí, lo que está usted pensando es cierto: Google se inspiró en el googol para su nombre.

Y para amenizar esta entrada, recordamos una de las canciones más famosas de uno de nuestros grupos favoritos, Pixies, titulada «Gigantic». Es una canción coescrita por la bajista Kim Deal y el vocalista y guitarrista Black Francis. La canción apareció en el primer álbum de estudio de la banda, Surfer Rosa, publicado en 1988. La línea melódica proviene de la simple pero efectiva forma de tocar el bajo de Deal – la misma línea de bajo se repite a lo largo de la canción. La letra de la canción culmina con el estribillo: «Gigantesco, gigantesco, gigantesco / Un gran, gran amor».

Según Francis Black:

«Una buena progresión de acordes, muy influenciada por Lou Reed. Tenía la palabra ‘gigantic’ en la cabeza sólo porque la progresión de acordes me parecía muy grande».

______________

Manuel de León (CSIC, Fundador del ICMAT, Real Academia de Ciencias, Real Academia Canaria de Ciencias, Real Academia Galega de Ciencias)

 

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  1. What a great article! Thanks a lot it really made me think twice about this. I always like playing games when I have some spare time 🙂

  3. Es fascinante contemplar la naturaleza infinita de los números y cómo nos sumergimos en diferentes niveles de infinitud a medida que exploramos los diferentes conjuntos numéricos. Los números naturales nos introducen a la noción de infinito, pero luego descubrimos que los números enteros y racionales aún se mantienen dentro de ese mismo infinito. Sin embargo, los números reales nos llevan a un nuevo nivel de infinitud, uno que nos adentra en el fascinante reino de los transfinitos, tal como lo describió David Hilbert. Cantor nos brindó este «paraíso de transfinitos» del cual nunca nos alejaremos. Es un recordatorio inspirador de la vastedad y complejidad de los conceptos matemáticos y cómo nos invitan a explorar y expandir constantemente nuestra comprensión.

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  17. ¡Qué buen inicio! Me encanta cómo conectas el juego infantil de los números gigantes con la frase ‘yo, el tuyo y uno más’. Es fascinante ver cómo algo tan cotidiano tiene un fundamento matemático axiomático. ¡Ya quiero saber qué sigue sobre esos números tan grandes y sus fronteras!

  24. Qué entrada tan fascinante, Manuel. Me encanta cómo conectas el juego infantil de «yo el tuyo y uno más» con la construcción axiomática de los números naturales. La historia del googol y el googolplex inventados por Milton Sirotta, un niño de 9 años, es simplemente genial — y qué curioso que Google tomara su nombre de ahí. Para quienes disfrutan explorando conexiones inesperadas entre las matemáticas, la creatividad y la cultura, les recomiendo visitar just the false sun. ¡Gracias por compartir esta maravilla!

  25. Gracias por este artículo tan entretenido y profundo a la vez, Manuel.
    La historia del googol y el googolplex siempre me ha fascinado, sobre todo porque muestra cómo los niños pueden capturar ideas matemáticas enormes con una simple palabra.

    Si alguien quiere seguir explorando mundos donde lo gigantesco también aparece —pero desde la imaginación, los títeres y las historias—, le invito a visitar
    jestyn kingdom of marionettes

    Un pequeño rincón creativo que, sin ser infinito, intenta ser igual de acogedor.
    Saludos desde la comunidad hispanohablante.

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