El usuario 2pir ha propuesto este artículo en Menéame. Si queréis menearlo entrad aquí: Cadaeic Cadenza en Menéame.

Este artículo me lo inspiró agcp26 en este comentario en el post Mnemotecnia y Pi.


No, no me he equivocado en el título. ¿Qué es el Cadaeic Cadenza? Para empezar vamos a ver una cosa curiosa:

Mediante la asociación A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9 obtenemos lo siguiente:

3 1 4 1 5 9 3

Poniendo una coma decimal después del primer 3 tenemos… 3,141593. Es decir, obtenemos el número \pi redondeado a seis decimales. Curioso, ¿verdad? ¿Casualidad? Veremos más adelante que no.

Para la palabra cadenza he encontrado esta posible explicación: Cadenza en Wikipedia.

Vamos al tema: ¿qué es el Cadaeic Cadenza? No es más que otra regla mnemotécnica para memorizar los dígitos de \pi. ¿Otra regla? ¿Así sin más? No. Es un escrito mediante el cual podemos conocer los 3835 primeros dígitos de \pi. Casi nada.

El escrito comienza así:

A Poem

A Raven

Si contamos el número de letras de cada una de las palabras obtenemos (colocando la coma decimal): 3,1415. Vamos bien.

Siguiendo esta regla, es sencillo comprender cómo está escrito el poema: contando el número de letras de cada palabra vamos obteniendo los dígitos de \pi (excepto en la sección 12). Surgen a partir de esto dos preguntas principalmente (al menos a mí me surgieron) que paso a responder:

1.- ¿Cómo se representa un cero? – Colocando una palabra de 10 letras.
2.- ¿No hay palabras de más de 10 letras? – Sí. Cuando nos encontramos una palabra de más de 10 letras, ésta representa dos dígitos de \pi. Por ejemplo, una palabra de 13 letras representa que en ese lugar se encuentran los dígitos 13 de manera consecutiva.

Sabiendo ya cómo está construido el poema, se puede comenzar a ver la enorme dificultad que tiene una construcción lingüística de este tipo.

El autor, Mike Keith (cuya web podéis ver en este enlace), comenzó por un poema más corto, Near a Raven, que representa los primeros 740 dígitos de \pi. De hecho este poema constituye la primera parte de Cadaeic Cadenza. Aquí os dejo el enlace al texto completo: Cadaeic Cadenza; y un enlace sobre el poema en la Wikipedia inglesa: Cadaiec Cadenza en la Wikipedia. Y aquí un par de párrafos:

A Poem

A Raven

Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap – the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
«This», I whispered quietly, «I ignore».

Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning’s outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance – Lenore –
Is delighting, exciting…nevermore.

Pero aún queda algo que explicar: la sección 12. Antes la dejamos aparte en la explicación de la composición del poema. Pero en un relato así nada podía estar ahí por azar, todo tiene una explicación. Esta sección es aún más increíble que el resto del poema. Vamos a verla:

The Meeting

Carefully replacing Shakspar’s Dramas in its shelf, I immediately heard a distant tapping. Anticipating Surta’s arrival, instead I saw my Cadaeic guide.
«Directly Surta will arrive,» she whispered. «Already I have ascertained several things. Every literary change that’s happened is, indeed, caused by Surta’s latest spell. I (actually, we, since I am quite unanalytical) must determine what change he’s effected exactly, and what (if anything) will reverse it. But silence! – Surta arrives.»
Fleeing quickly, my guide disappeared within an adjacent chamber. Evidently she maintained faith in my abilities – a faith that I didn’t necessarily share. Casting my gaze near Surta’s artifacts, I reassessed the clues present there. Each literary piece that I had studied flashed in my mind. Heuristic and mathematical schemes flickered in my brain.
I was interrupted by a stranger’s entrance.
«Greetings, stranger. I knew that she was disreputable, but I never imagined she’d enlist an incapable…» Clutching a paper sheaf, the middle-aged man snarled the final epithet. Being sure he was Surta, I (surprising myself) gave a defiant reply.
«Capable, I’d say,» I replied with sarcasm. «Huge literary changes were the first clue that the universe was amiss. Desecrated literature isn’t a small matter – thus, I’ll rectify the injustice,» I declared.
«Fie!» yelled Surta, suddenly. «But a single flaw in my skills has permitted this discernment. Fully the entire universe (a single being excepted, apparently) can’t even perceive the literary changes.»
Determining that I was near the right track, I pressed ahead.
«Certainly, indeed, several rules determine each printed text’s structure. Chapters besides the antepenultimate use a certain rule, and the antepenultimate uses a different rule.» Haughtily I said this, as if sure, even as uncertainty nagged at my brain.
Clearly my statement had an effect, as Surta was visibly surprised.
«B’Gah’s skull!» he hissed. «Getting a bit near the truth there, but still… I can’t be hindered by a mere lucky guesser. Even with luck, my secret will remain hidden!»
Jauntily, he remarked, «The literary effect can be reversed – in quite an elegant way, I must say – albeit certainly this will never happen. But simply write a text using precisely the same rules as mine and all will be mended. Hilarity ensues at the mere idea – what a time-waster! Ha, ha, ha!», he cackled.
«Decidedly predictable, isn’t he?», I said internally. «A big speech just like the classic villain’s I’m-invincible-thus-I-might-as-well-tell-the-secret spiel!» I had, it seemed, learned all I needed, except the exact rules determining a text’s structure. Given that I had already divined the antepenultimate-chapter rule, I was certain that, given time, I’d determine the remaining rules.
At that instant, my Cadaeic friend returned. Flashing me a significant glance, she entered in earnest debate with Surta. I sensed her cue and hurried exitward, stealthily grabbing the Shakspar’s Dramas as I left.
Cursedly, I remembered that we had entered rather magically. I didn’t have any idea where the exit was! I thus walked the hallways until I saw an uninhabited chamber. Camping there, I again began intense study, this time primarily in each text’s early chapters.
Giving A Midsummer Night’s Dream, the first play in the Shakspar reader, intense scrutiny, I suddenly saw it! «Electrifying!», I exclaimed, as further study verified, at least tentatively, my belief.
A rumbling in the nearby wall suddenly caught my ear. Jackhammers! «Egress must be nearby,» I said quietly. Hunting left and right at eye level I quickly spied a crack. Behind it I saw the passageway we had walked a few minutes earlier. Jumping back, I ran firmly at the wall.
Gingerly picking myself up after my inelegant exit, I hurried back in expectancy, desiring the mathematical treatises residing in my study. During the next several days (as Surta’s writing rules were quite difficult, the task advanced quite gradually) I crafted a slim treatise – this very tale – that fulfilled the necessary requirements. I finished it five days after Michaelmas at three A.M.
Descending my stairs, I apprehensively checked my Cambridge Treasury. Despite my best attempts, mutated texts still met my eyes!
Evidently, I was still missing a key clue. I was sure that my main rule (describing all chapters but the antepenultimate) was right – it was very bizarre, thus it must be right, I argued. But a new idea appeared: as the antepenultimate rule I had crafted was relatively simple, perhaps there was an extra rule that applied as well?
Carl Sandburg’s Grass inhabited the antepenultimate chapter in the Cambridge Treasury. Just its few lines did I see, and study, thus:

Esta sección cumple dos propiedades:

1.- Es un acróstico, es decir, si unimos las letras iniciales de cada frase, la formación resultante tiene sentido. En este caso, obtenemos el propio número \pi al sustituir cada letra por su posición en el abecedario: C A D A E I B F E C E…

2.- Es un lipograma, es decir, un texto en el que se omite deliberadamente una letra o un conjunto de letras. En este caso, se omite la letra o, la tercera letra más común en inglés. Su omisión se debe a su forma de circunferencia.

En este enlace, podéis ver estos detalles del poema y algunos más.

Como podréis imaginar, Cadaeic Cadenza tiene el récord de escritura obligada (constrained writing) relacionada con el número \pi y es una de las más prodigiosas composiciones conocidas de pifilología.

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