Cadaeic Cadenza

Notes & Commentary



This page discusses some of the finer points in the construction of the short story Cadaeic Cadenza. If for some reason you got here but haven't read the story yet, I highly suggest you read it first.

The primary constraint used in Cadaeic Cadenza is what we call Standard Pilish.  If each word in the story (including section headings, poem titles, everything) is observed, in order, and the number of letters in each word is counted, the following pattern of numbers emerges:

Text:       One / A Poem / A Raven / Midnights so dreary, tired and weary...
No. Lets.:   3    1   4    1   5         9      2    6      5    3    5  ...

Quite obviously, these are precisely the digits of that most famous mathematical constant, the irrational number π (3.1415926535...).

A momentary pause while this sinks in...

The words of Cadaeic Cadenza (again, excepting Section 12) embody the first 3835 decimals of π. The precise encoding rule is this: a word of N letters represents

- the digit N if N<10
- the digit 0 if N=10, and
- two adjacent digits if N>10
    (e.g., a 12-letter word represents the digit '1' followed by '2').

The simplicity and naturalness of this rule mean that it really is useful as a mnemonic device for remembering the digits of π. It is easier (it seems to me) to remember a story than a random sequence of digits, and since it is so easy to mentally translate from the story to digits, it becomes quite possible to rattle off several thousand digits of π using this technique.

The use of Cadaeic Cadenza as a π mnemonic was not, however, the real raison d'etre of this exercise, which instead was to explore the literary possibilities of the extended use of this particular writing constraint.  When it was written, the 3835 digits of Cadaeic Cadenza exceeded the previous world record of 740 digits for a π mnemonic, which was held by the version of The Raven contained in Section One of this very tale (originally composed in July 1995).

But wait, there's more! What about Section 12? As described in the story, since Section 12 is the antepenultimate (one of my favorite English words - it means the one before the next-to-last) section of the tale, it obeys different constraints. The two constraints simultaneously satisfied by Section 12 are:

(1) It is an acrostic. The first letter of each sentence (or line, if a poem) spells the following:

C A D A E I B F E C E ...

which is nothing more than the digits of π represented by the letters of the alphabet (A=1, B=2, C=3, and so on).

(2) It is a lipogram. Section 12 does not contain the letter 'o', the 3rd (or maybe 4th) most common letter in English. The letter 'o' being a circle, this completes the trilogy of constraints all of which are in some way related to the number π.

Finally, there's an "Aha!" hidden inside the lines of Carl Sandburg's poem in Section 13. Note that our narrator, in writing Sandburg's Grass in Section 13, says he is quoting from the antepenultimate chapter of the book he is holding. But Section 13 is not the antepenultimate section of our narrator's tale. So I suppose our narrator had a choice about how to write Section 13, but I think he took the most elegant road: Section 13 is written so that it satisfies the π-digits constraint (since it's not part of the antepenultimate section of this book, and so it must) and it also satisfies the two antepenultimate-section constraints (since it's quoting from the antepenultimate section of the Cambridge Treasury) - it is, in other words, triply-constrained text.

The following sections contain some general remarks about the construction of Cadaeic Cadenza as well as a detailed commentary discussing the additional tricks, jokes, and literary references as well as notes on some of the poetical passages.

Some General Remarks

The π-digits constraint obeyed by Cadaeic Cadenza is not an easy one. It is significantly harder that the famous constraint of not using the letter e, as suggested by the fact that there exist two such novels whereas I have so far only been able to eke out a short story. Of course, with time and labor there is nothing to prevent even longer π works from being constructed.

Part of the challenge in Cadaeic Cadenza was to make it even harder, in the odd-numbered sections, by also attempting to mimic some existing works of poetry. This imposes the additional constraint of trying to follow the story, tone, rhyme scheme, meter, and vocabulary of the poems at hand, in addition to still being a π mnemonic. Of these properties, meter is the most challenging, since the π mnemonic determines the number of letters in each word, which is sometimes at odds with the number of syllables one needs to have (or their accents) in order to obey the meter. The meter in "A Raven" is pretty far off, except in a few stanzas, but in other instances (Jabberwocky, the Rubaiyat stanza, and the final poem in the excerpt from Hamlet in Section 11) it is nearly perfect.

There are at least three reasons why the π constraint is hard:

(1) The obvious one, which is that the length of every word is specified. This often means that much thought has to be put into a single word, since many of the the choices that naturally suggest themselves have the wrong number of letters.

(2) π is conjectured to be (and all numerical evidence points to it being) normal, which means that its digits are statistically indistinguishable from a sequence produced by a uniform random digit generator. Since the digit zero is represented by a 10-letter word, this means that the average number of letters in each word of the story must be about 5.5. Why "about"? Because sometimes two adjacent digits (always starting with a "1") are represented by a single word of more than 10 letters. In fact, the average word length in the Cadenza is about 5.67. The point is that this is significantly higher than the average for typical English text, which is around 4.2. This makes writing harder, since one is forced to use longer words, on average, than is typical. It also means that some very valuable words, like "A" and "I" and "the", are available with much less frequency than one would like.

(3) Not only is the average word length high, but each digit is statistically independent. In ordinary English a long word is most likely to be followed by a small word. In "Pilish" (for this is what I call the peculiar language dictated by the digits of π) there are no such second-order dependencies. Even long runs of long words, which never occur in typical English prose, appear and have to be dealt with.

Another self-imposed challenge in constructing the Cadenza was to include every word (more precisely: group of alphanumeric characters) in the π enumeration. For example, the numbered section headings and section titles are part of the mnemonic. This means that each section had to be engineered to stop at just the right spot, so that a word of the right length was available for the next section number. It is rarely if ever apparent that the end of each section was constrained in this way.

Even harder was the self-imposed constraint in Section 11 (the selection from Hamlet). In this play excerpt, the speaker headings and stage directions are also required to fit into the π sequence! I was able to do this while only having to 'cheat' once (using HAML. instead of HAM. on one occasion).

It might be instructive to give a complete 'plan' of the Cadenza. The following outline shows the beginning of each section plus the very end of the story, with the corresponding digits of π in the right-hand column.

Text                                                     Digit #   Pi digits

One / A Poem / A Raven / Midnights so dreary...              0     3.1415926..

Two / Change / My customary bedtime reading book...         735    3629774..

Three / Of Carrolls / Jabwocky / Slithy toves, borogove...  866    5288658..

Four / An Hypothesis / I exhausted Carroll's rewritten ode  994    42019893..

Five / Dreams / Many depths of accustomed workings...      1298    4646208..

Six / Cadaeics / Conundrums, conundrums, conundrums...     1596    38000..

Seven / Prufrock / Let us depart then...                   1974    583264..

Eight / The Readiness / Michaelmas.  Waking up,...         2815    539062..

Nine / O Ruby Yachts / Poetic Muses alongside th' Bough    3124    414665925..

Ten / Clue / Completing poetical perusals,...              3161    34088..

Eleven / William Shakespeare's Tragedy King Claudius...    3424    6712748..

[no Twelve!]

Thirteen / Sandburg's Grass / Caskets piled beneath...     3684    895757..

Finale / The Victor / Though concise, the aforecited lines 3744    63667305..

           ...I end, whispering ad infinitums / THE END            ..1302033
                                                           3834 -----------

The process of "translating" the literary texts (Edgar Allan Poe's The Raven, Lewis Carroll's Jabberwocky, T. S. Eliot's The Love Song of J. Alfred Prufrock, one stanza of Omar Khayyam's Rubaiyat, part of Act V of Shakespeare's Hamlet, and Carl Sandburg's poem Grass) into Pilish is particularly interesting. At first glance it might seem to be primarily a matter of word substitution, thesaurus-style, however this is very rarely the case. As mentioned above, the statistics of the words lengths are so different from typical English that it is usually not possible to match or translate on a word-by-word basis.

There are a few sentences in Cadenza that might be considered straightforward 'translations'. For example, the third line of Prufrock is "Impersonating the sufferers etherising upon pallets", which is more or less a word-by-word paraphrase of T. S. Eliot's original "Like a patient etherised upon a table". Even so, note that I had to change from singular to plural "patients" and "pallets" and the verb form of "etherise" has changed.

Typically, however, the translation process involves recasting a line or sentence in a rather different form while trying to retain as much of the meaning as possible. Of course it's nice to use some of the same words, even if they have to appear in a different place, or, failing that, words of the right tone. For example, the next to last line of the 7th stanza of The Raven is, in the original,

Perched upon a bust of Pallas just above my chamber door

which is turned into

Then sat on Pallas' pallid bust, watching me (I sat not therefore)

The first half of our translated line captures the primary thought of sitting on the bust of Pallas, and even manages to use those words. The "watching me" is an invention, not found in Poe's original, but it seems to fit - after the bird sits, is it not reasonable that it would appear to the narrator to be watching him? The parenthetical "(I sat not therefore)" is inserted in deference to the rhyme scheme but also matches the original reasonably, since the narrator is supposed to remain standing until stanza 12.

The subtle shifts in meaning are often interesting. In Prufrock the original line

Time to turn back and descend the stair


Mornings for mounting stairs

so that descending stairs turns into ascending. In The Raven, stanza 6, line 2, the tapping sound returns with Poe's line

Soon I heard again a tapping somewhat louder than before

which becomes

While intrusive tap did then come thrice - O, so stronger than sounded afore

The bird raps three times instead of once! All because the need for a 6-letter word in the middle of the line suggested the use of "thrice".

In short, the process of writing Pilish is not unlike that involved in translating between two different languages. But yet we're "translating" from English to English! How strange.

Detailed Commentary

In this section each part of Cadaeic Cadenza is discussed in detail, including notes on some of the more fortuitous poetic passages and an explanation of some of the hidden references. This discussion, while somewhat lengthy, is by no means complete. The interested reader is encouraged to sit down with a copy of the Cadenza side-by-size with the literary texts (Edgar Allan Poe's The Raven, Lewis Carroll's Jabberwocky, T. S. Eliot's The Love Song of J. Alfred Prufrock, stanza 12 of the Rubaiyat, Act V of Shakespeare's Hamlet, and Carl Sandburg's Grass) and make his or her own comparisons. Pilish writing is rarely if ever "done", so find the line or phrase you like the least in the Cadenza and try to write it better yourself!

In the following, quotations from the Cadenza are always given in bold text, while other quotations are in italics. The discussion is organized by section.

One / A Poem

Before looking at A Raven in detail, a few general comments on its structure. In Poe's original, each stanza has six lines, with the fifth line being a 'refrain' that's usually very similar to the fourth line. Due to the random nature of π's digits, it's not possible to have two adjacent lines resemble each other very much, so I decided to eliminate the refrain, and be satisfied with five lines in each stanza.

The meter of A Raven is not very good, being sacrificed in order to do a better job of matching the story, tone, rhyme scheme, and vocabulary of Poe's original. In particular, the internal rhymes in the first and third line of each stanza are present, and the rhyme syllable in the other three lines is, as in Poe's version, "-ore". A surprisingly high percentage of the stanzas end in "nevermore", as they should. The story is followed quite closely, certainly at the stanza level, and much of the time even at the line level.

Now, some commentary on individual passages.

Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.

Poe's original first two lines of the poem are

Once upon a midnight dreary, while I pondered weak and weary,
Over many a quaint and curious volume of forgotten lore,

The first line is an example where the meter is completely sacrificed in order to do a nice job of word matching. Four of the six words in the Cadenza version are the same as in Poe (midnight, dreary, and, weary)! Only tired has had to be substituted for weak. Ponder is also present, having been moved from the first line to the second. Volume is present, too, and the second line ends in lore, just like it should.

"Surely" (said silently) "it was the banging, clanging window lattice."

This line (stanza 6, line 3) in the original is

"Surely," said I, "surely that is something at my window lattice;

Note that the first two words and last two words are identical to the original, as well as the quotation structure! The Pilish banging, clanging is intended to evoke Poe's penchant for repeated sounds, as in his poem The Bells.

Then sat on Pallas' pallid bust, watching me (I sat not therefore)

This line (stanza 7, line 4) was discussed earlier, but it's worth pointing out that the nice phrase Pallas' pallid bust is a combination of the original version of this line,

Perched upon a bust of Pallas just above my chamber door

and the second line of stanza 18, which is

On the pallid bust of Pallas just above my chamber door;

Actually maintain a surname, upon Pluvious seashore?

This line (stanza 8, line 4) is an interesting example of word substitution. The original is

Tell me what thy lordly name is on the Night's Plutonian shore!

Due to the word lengths available, I had to use surname instead of name and seashore instead of shore - all quite reasonable. But what about Plutonian? After some thought, I came up with Pluvious. It starts with 'Plu', just like Plutonian. It's a real word that means "rainy" - a rather fitting connotation for the mood of this poem. Even more obscurely, it might suggest Pluviose, the fifth month of the French Revolutionary calendar. Unfortunately, Pluviose isn't December (the month in which The Raven takes place), but it's January/February, which is close! Pluviose also derived from the same root as pluvious (being a rainy month), and it would be capitalized, thus providing some justification for my capitalization of Pluvious.

"Wretch," (addressing blackbird only) "fly swiftly - emancipate me!"

The interesting thing here is the use of the word blackbird (also used once more later in the poem). Though not strictly correct, I guess (a raven is a black bird, not a blackbird), it's a nod of the head to George Perec's great novel of constraints La Disparition which is written without using the letter 'e'. In the course of the novel six famous literary passages are 'translated' into e-less writing. In the English translation of the novel, A Void, by Gilbert Adair, one of the six poems is The Raven. Of course this title couldn't be used since it contains the letter 'e'. The title of Adair's English e-less Raven is (wait for it...) Black Bird!

Allanpoe, E.

Another example of Pilish transmutation. For consistency, note that the first sentence of Section 2 also refers to him as 'Allanpoe'. This is a general principle I tried to follow - if a name or title or something has to be mutated in some way, at least try to be consistent to the mutation in other places in the story. A good example of this occurs in Section 11.

Two / Change

Although short, this section contains perhaps the most famous, and interesting from a Pilish point of view, portion of the number π.

(the echo 'nevermore nevermore nevermore nevermore nevermore nevermore' survives, for example)

This lovely reference back to A Raven is made possible by the digits of π starting at decimal 762, which are, surprisingly:

. . .9 9 9 9 9 9 . . .

This is, of course, the famous Feynman point, so called because Richard Feynman once said that he would like to memorize π up to decimal 768 just so he could recite it, ending with the six 9's, and then say 'and so on'. (A great idea, but I'm afraid not, realistically, a good party trick, as I know few people who would sit through 768 digits just to get to the punch line...)

The next digit after the 9's is an 8, so there are actually seven long words in a row, something that's very rare in ordinary English. Still, the handy 'nevermore' makes it quite easy to fit into the story. Amazingly, this is not the set of six (or seven) consecutive words in the Cadenza with the largest sum of word lengths. That distinction belongs to a portion of Section 7 (which see).

Sighting no Raven but The Dark Bird,...

There are a few subtle points about the effects of Surta's literary mutation here. If every book were suddenly turned into Pilish, then two different books containing The Raven would, almost certainly, contain two very different versions of The Raven with different titles. Why? Because they would appear at different places in the book, and therefore be required to use different digits of π.

But that's not all! Our hero is reporting about his find in Pilish also. So, we actually don't know the title of the poem he sighted. It was surely not The Raven or even A Raven, but probably not The Dark Bird either. One can only assume that he used Pilish cleverly so that The Dark Bird is an approximation to the title he actually saw.

For the same reason, the poems inserted by our narrator into his story had to be rewritten by him in Pilish, even though they were in Pilish already in whatever book he was reading. An interesting concept that I have not yet tried - translating from Pilish to Pilish! One assumes that he was aided by his memory of the original poems.

Three / Of Carrolls

This poem, a Pilish version of Lewis Carroll's Jabberwocky, works our rather nicely in Pilish. Except for the first couple lines the meter of the poem is nearly perfect, not to mention the vocabulary, story, and rhyme scheme. One major concession, however, was that instead of an A B A B rhyme scheme I used A B C B. Eliminating the need for one pair of rhymes helps considerably, while the more forceful pair is still retained.

One reason, I think, that this poem was easier was because of its neologisms. Whenever I got totally in a bind I was able to make up a Jabberwocky-sounding word to get me out of it. There aren't a lot of these - overuse of this liberty would be considered cheating - but just enough to make the poem work.

The shortened title is, of course, due to the need for an 8-letter word (and the fact that the real title is 11 letters, which requires two particular consecutive digits (1,1), which were nowhere to be found).

"Beware a scrunch, a scratch, stepson!
  Beware Jubjub, withstand a word!
Respect the Jabberwock and dread
    Manxomian songbird!"

This is the second stanza - compare with the original

"Beware the Jabberwock, my son!
  The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
    The frumious Bandersnatch!"

The stanza starts with the right word - beware - and it mentions both the Jabberwock and the Jubjub. (Sadly, the Bandersnatch is nowhere to be seen!) Manxomian is stolen from the next stanza of Carroll's original, which refers to the manxome foe. The first line of our version, with scrunch and scratch, is intended to be reminscent of the bite and catch in line 2 of the original. Finally, note another mild shift in meaning: the son turns into a stepson!

In closing, recall that in Carroll's original poem the last stanza is identical to the first. This is impossible in Pilish, but a comparison of our first and last stanza shows that they are at least somewhat similar (both containing borogove, slithy, toves, mimsy, and gimble). I was, however, forced to mutate tove into trove the second time.

Four / An Hypothesis

I exhausted Carroll's rewritten ode, Jabwocky,...

Note the consistency with the name of the poem in the previous section.

A few schemata involving linguistical play

The list of definitions was an interesting challenge in Pilish writing. Two of the definitions (palindrome and pun) even contain examples.

Turning to "Poetry, Anderson", thus emerged...

A reference to Jon Anderson and his musical group Yes. See the next section for more details.

Five / Dreams

This section is a homage to the British progresive-rock band Yes. The title, Dreams, sounds rather Yes-like, and is also a reference to the fact that our narrator (seemingly, though the story does not say this explicitly) is going to sleep. Perhaps he dreams the lyrics?

Unlike the other odd-numbered sections, the poetry in this section is not intended to duplicate an actual work, but rather to evoke the spirit of Yes's stream-of-consciousness style of lyrics, such as epitomized by the opening and closing sections of The Revealing Science of God from Tales from Topographic Oceans; lyrics such as:

Dawn of thought
   Transferred through moments
Of days under searching Earch
   Revealing corridors of time
Provoking memories, disjointed but with purpose
   Craving penetrations offer links with the self
Instructors sharp and tender love
   As we took to the air
A picture of distance

At the end of this section we find

To stories wonderous

Made possible by the lovely digit sequence 7777, the repeated awakens has a double meaning: (1) Our narrator is awakening from his sleep, and (2) It's a nod to the quintessential Yes song Awaken. Similarly, stories wonderous is a reference to their song Wonderous Stories. Note that throughout this section British spelling is used consistently (as it should be), which makes a difference when it comes to word lengths.

Six / Cadaeics

"I'm a Cadaeic!"
"I'm a Cadaeic! I'm a real Cadaeic!", shouted an old woman.

This bit of nifty dialogue is made possible by a rare sequence of digits containing three 217's:

217 3 217 21(4)7

Deplorably, he - Surta - . . .

Surta spelled backwards is Atrus, the hero of the CD-ROM game and novel Myst. It's spelled backwards because of the reflexive nature of our story as compared to Myst. In Myst, a man makes changes in worlds by writing in books. In our Cadenza, a man makes changes in books by acting in the world. See?

Seven / Prufrock

This is the longest section (841 decimals) of the Cadenza, a Pilish version of T. S. Eliot's The Love Song of J. Alfred Prufrock. Although there is a good deal of rhythm in the original, there is also a free-verse feel, so I felt justified in not worrying overmuch about the meter. Indeed, in the middle section I also play fast and loose with the rhyme scheme. However, the first and last sections do a fair job with both meter and rhyme.

The original begins with a six-line quotation in Italian from The Inferno. This is omitted in the Pilish version.

Let us depart then,
While eventide's withering skies threaten,
Impersonating the sufferers etherising upon pallets;

These are the first three lines of the poem. The original is:

Let us go then, you and I,
While the evening is spread out against the sky
Like a patient etherised upon a table;

The Pilish version begins with Let us, just like it should. Line 2 is somewhat different, but at least says something about the sky. It has been said that line 3 of this poem (especially the word etherised) singlehandedly ushered in the era of 20th-century poetry, so I obviously felt the need to preserve the word etherised as closely as possible. Finally, note that lines one and two rhyme, as in the original.

To an affair th' matricarchs sadly go
To talk touching MicAngelo.

Two of the more famous lines in the poem, which in the original are

In the room the women come and go
Talking of Michelangelo.

Given the constraints of Pilish, this is a pretty nice match. Both lines end with the right word, and talk is also present in the second line. The transmutation of Michelangelo is typical Pilish.

And, deeming that March night too remarkably quiet,
Stealithily curled womblike in quiescence, and fell perfectly asleep.

Another interesting case of Pilish mutation. In the original, these lines are

And seeing that it was a soft October night,
Curled once about the house, and fell asleep.

Suddenly it's March instead of October! Such are the vagaries of Pilish. In the second line, note the incorporation of curled and fell asleep.

Sit stuck, wriggling, alongside baroque designs.
Altogether hopelessly extinguished, wherefore should I assume?

The set of consecutive words from wriggling to wherefore, with word lengths

. . .9 9 7 7 10 10 12 9 . . .

is the set of six (and also seven and eight) consecutive words with the largest sum of word lengths in the entire Cadenza. The sequence (9 7 7 10 10 12) beats the Feynman point (9 9 9 9 9 9) by one. Of course, I need not have chosen to represent the pair of digits (1,2) by a 12-letter word, but since I did, there we are. Luckily this long sequence of long words is split between the end of one line and beginning of another, so that both still wind up sounding reasonable.

Oh, I can envision being as an empty claw
Scuttling violently about seas' silent floors.

Another nice match to the original, which is

I should have been a pair of ragged claws
Scuttling across the floors of silent seas.

Empty in line 1 has a nice connotation, given the overall emotion of the poem. In the second line, four of the six words exactly match the original! Note the reordering of the last three words in order to make this possible.

I, too, am not William Shakspar's Hamlet - this I know, above a doubt.
Am one related lord, posing on the side
For acting very small acts or starting small episodes,
Most easy tool, Prince's attentive slave,
Am always ready, obedient, useful,
Politic, cautious, of a meticulous frame;

Compare these lines with the original, which is:

No! I am not Prince Hamlet, nor was meant to be;
Am an attendant lord, one that will do
To swell a progress, start a scene or two,
Advise the prince; no doubt, an easy tool
Deferential, glad to be of use,
Politic, cautious, and meticulous;

The phrase William Shakspar's Hamlet has a hidden meaning. In Gilbert Adair's translation of George Perec's e-less novel La Disparition, William Shakespeare is always referred to as William Shakspar, that which is obtained by deleting the e's in Shakespeare's name. Since I am an admirer of Perec/Adair's work, and took some inspiration from it, the opportunity to insert 'William Shakspar' into this sentence (followed by Hamlet, no less!) seemed quite appropriate.

Eight / The Readiness

Thence appeared, transmuted, one quatrain that that eminent Persian - the tent-maker Omar - fashioned (as translated by Edward FitzGerald), hence:

A nice long sentence, incorporating the word quatrain (by which name the stanzas of the Rubaiyat are always known), Khayyam's name Omar, the fact that he was a Persian and a tent-maker, and the fact that the translation of the Rubaiyat that everyone knows was done by Edward FitzGerald.

Nine / O Ruby Yachts

Ah, finally, the Rocky & Bullwinkle reference! Surely you recall the episode in which the object of their (not to mention Boris and Natasha's) attention was a small jewel-encrusted boat, which turned out to be The Ruby Yacht of Omar Khayyam?!

This section contains the most famous of the 101 stanzas of the Rubaiyat. Our version is:

Poetic Muses alongside th' Bough
An oversupply o' Wine, possessed somehow
  Thou with me treading Eden's Wilderness
Through all it seems a Paradise enough!

as compared to the original

A Book of Verses underneath the Bough,
A Jug of Wine, a Loaf of Bread--and Thou
  Beside me singing in the Wilderness
Oh, Wilderness were paradise enow!

Another relatively satisfying translation, with almost perfect meter and rhyme (note that in the Pilish version, enough is to be pronounced the way FitzGerald spelled his: enow). At least one major word in each line (Bough, Wine, Wilderness, Paradise) survives, and the last two words of the stanza match.

[Stanza twelve;
Translator: FitzGerald, Ed A.
3rd ed., 1872]

OK, I admit it, I made up a middle initial for Edward FitzGerald! He must have had one, though...I just need to find out what it really was.

This stanza is indeed, as it says here, stanza twelve in FitzGerald's third edition. (The stanzas were not numbered the same in all editions.) The '1872' is the only instance in the entire Cadenza of a numeric string. Being four characters long, it of course represents the digit '4'. Similarly, '3rd' represents the digit 3 (not because it contains a 3, but because it's three characters long!).

Ten / Clue

Accurately-reproduced picture of the Woolsthorp Manor House (Grantham, England)

One of the more oblique references in the Cadenza - this is where Isaac Newton was born and where he lived during his invention of the calculus. The calculus and Newton's formulas for π produced one of the great leaps forward in the calculation of π's digits.

Eleven / William Shakespeare's tragedy King Claudius

The appearance of three particular consecutive digits (7,1,2) means that I could fully spell out William Shakespeare's name. King Claudius is another example of Pilish transmutation. I wanted to say Hamlet or perhaps Prince Hamlet, but this wasn't possible. So, I simply used another main character in the play, Hamlet's father King Claudius, to title the play!

As mentioned in the 'General Remarks' section, the speaker headings and stage directions also fit into the pattern required by the digits of π. Each line in Section 11 is simply read from left to right with each alphabetic string encountered taken in order. A neat trick is found in the two lines:

HAM.  Behold,                       [Thrusting skullbone heavenward.]
wretched Yorick! Truly, Horaitio, truly I adored him...

In the original, this is

HAM.  Let me see. [Takes the skull.] Alas, poor Yorick! I knew him, Horatio.

By inserting the stage direction in an odd place, after the 'Behold', I was able to make Behold, wretched Yorick!, a reasonable simulation of Alas, poor Yorick!

Another strange trick is used in Section 11: the name Horatio is consistently misspelled as Horaitio. Doing this makes a huge improvement in the whole section, as can be seen by examining the four places where his name appears.

Originally, Caesar dies. In subsequent time, Caesar resides under th' earth. Thereupon, celebrated Caesar's decomposed.

Another interesting twist. The original is

Alexander died, Alexander was buried, Alexander returneth into dust.

The Cadenza version follows the meaning quite closely, except that Caesar has been substituted for Alexander! This change is quite fitting since Caesar is the subject (even in the original) of the four-line poem that Hamlet is about to recite.

A Caesar now becomes a sediment
Henceforth to toughen graveyard's fundament;
Although a sovereign overrules with ire,
Henceforth, heartless, resembles th' ashy mire!


The original of this is:

Imperious Caesar, dead and turn'd to clay
Might stop a hole to keep the wind away.
O, that the earth which kept the world in awe
Should patch a wall t'expel the winter's flaw!

The meter and rhyme scheme of the Cadenza version is perfect - not an easy task given the word lengths that have to be used. In order to satisfy the meter, a large number of long (8, 9, or 10 letters) words with only two syllables were required: henceforth, graveyard's, although, sovereign, heartless. Even with this difficulty the meaning is still preserved reasonably well.

The stage direction is somewhat of a cheat. Indeed there is such a stage direction present in the original, but it does not occur until 6 lines later.

Twelve / The Meeting

This being the antepenultimate section, it is not written in Pilish but rather using the two antepenultimate-section constraints: (1) No letter o's, and (2) The initial letters of each sentence 'spell' the digits of π, using A=1, B=2, and so on. Specifically, the initial letters of the 66 sentences in this section are:


which are, indeed, the first 66 decimals of π.

The other noteworthy little reference is:

B'Gah's skull!

since BGAH = 2.718, or e, arguably the second most famous transcendental constant.

Thirteen / Sandburg's Grass

As described earlier in these notes, this section of the Cadenza satisfies all three constraints simultaneously:

- It does not contain the letter 'o'.
- Its lines' initial letters are CADAEIBFECE, which spell 3.1415926535.
- The word lengths continue to follow the pattern dictated by the digits of
π starting at digit 3684.

Despite these very restrictive constraints, it does a reasonable job of simulating Carl Sandburg's original. A few points to note:

Caskets piled beneath Austerlitzes, Dresdens

The original is

Pile the bodies high at Austerlitz and Waterloo

so that the direction of piling has been reversed. Note that Waterloo is 8 letters, so it would have fit the last word in the Pilish version, but it contains the letter 'o' and therefore could not be used. (Besides, it's more consistent with Austerlitzes to use a plural.) Austerlitzes is made possible by the fortuitous digit pair (1,2).

There are three lines in Sandburg's poem that list battles. Line 1 has battles from the Napoleonic Wars, line 4 from the American Civil War, and line 5 from World War I. This feature is still present in the Cadenza version, even though some of the battle names are changed.

Finale / The Victor

I end, whispering ad infinitums. THE END

Since the digits of π go on forever, is it not fitting to end with ad infinitums? This section is engineered to stop just before a double-3 in π, so that the final words can be THE END.

3835 Digits of Pi

For those who like to "play along at home", here are the 3835 digits of π embodied in Cadaeic Cadenza. Digits are numbered starting from zero, so the numbers in the right column denote how many of digits after the decimal point the right-most digit in that row is.

14159265358979323846264338327950288419716939937510                 50
58209749445923078164062862089986280348253421170679                100
82148086513282306647093844609550582231725359408128                150
48111745028410270193852110555964462294895493038196                200
44288109756659334461284756482337867831652712019091                250
45648566923460348610454326648213393607260249141273                300
72458700660631558817488152092096282925409171536436                350
78925903600113305305488204665213841469519415116094                400
33057270365759591953092186117381932611793105118548                450
07446237996274956735188575272489122793818301194912                500
98336733624406566430860213949463952247371907021798                550
60943702770539217176293176752384674818467669405132                600
00056812714526356082778577134275778960917363717872                650
14684409012249534301465495853710507922796892589235                700
42019956112129021960864034418159813629774771309960                750
51870721134999999837297804995105973173281609631859                800
50244594553469083026425223082533446850352619311881                850
71010003137838752886587533208381420617177669147303                900
59825349042875546873115956286388235378759375195778                950
18577805321712268066130019278766111959092164201989               1000
38095257201065485863278865936153381827968230301952               1050
03530185296899577362259941389124972177528347913151               1100
55748572424541506959508295331168617278558890750983               1150
81754637464939319255060400927701671139009848824012               1200
85836160356370766010471018194295559619894676783744               1250
94482553797747268471040475346462080466842590694912               1300
93313677028989152104752162056966024058038150193511               1350
25338243003558764024749647326391419927260426992279               1400
67823547816360093417216412199245863150302861829745               1450
55706749838505494588586926995690927210797509302955               1500
32116534498720275596023648066549911988183479775356               1550
63698074265425278625518184175746728909777727938000               1600
81647060016145249192173217214772350141441973568548               1650
16136115735255213347574184946843852332390739414333               1700
45477624168625189835694855620992192221842725502542               1750
56887671790494601653466804988627232791786085784383               1800
82796797668145410095388378636095068006422512520511               1850
73929848960841284886269456042419652850222106611863               1900
06744278622039194945047123713786960956364371917287               1950
46776465757396241389086583264599581339047802759009               2000
94657640789512694683983525957098258226205224894077               2050
26719478268482601476990902640136394437455305068203               2100
49625245174939965143142980919065925093722169646151               2150
57098583874105978859597729754989301617539284681382               2200
68683868942774155991855925245953959431049972524680               2250
84598727364469584865383673622262609912460805124388               2300
43904512441365497627807977156914359977001296160894               2350
41694868555848406353422072225828488648158456028506               2400
01684273945226746767889525213852254995466672782398               2450
64565961163548862305774564980355936345681743241125               2500
15076069479451096596094025228879710893145669136867               2550
22874894056010150330861792868092087476091782493858               2600
90097149096759852613655497818931297848216829989487               2650
22658804857564014270477555132379641451523746234364               2700
54285844479526586782105114135473573952311342716610               2750
21359695362314429524849371871101457654035902799344               2800
03742007310578539062198387447808478489683321445713               2850
86875194350643021845319104848100537061468067491927               2900
81911979399520614196634287544406437451237181921799               2950
98391015919561814675142691239748940907186494231961               3000
56794520809514655022523160388193014209376213785595               3050
66389377870830390697920773467221825625996615014215               3100
03068038447734549202605414665925201497442850732518               3150
66600213243408819071048633173464965145390579626856               3200
10055081066587969981635747363840525714591028970641               3250
40110971206280439039759515677157700420337869936007               3300
23055876317635942187312514712053292819182618612586               3350
73215791984148488291644706095752706957220917567116               3400
72291098169091528017350671274858322287183520935396               3450
57251210835791513698820914442100675103346711031412               3500
67111369908658516398315019701651511685171437657618               3550
35155650884909989859982387345528331635507647918535               3600
89322618548963213293308985706420467525907091548141               3650
65498594616371802709819943099244889575712828905923               3700
23326097299712084433573265489382391193259746366730               3750
58360414281388303203824903758985243744170291327656               3800
1809377344403070746921120191302033                               3834