Math and Poetry

In 1972 the Belgian mathematician Edouard Zeckendorf established Zeckendorf’s theorem: that every positive integer can be represented as the sum of non-consecutive Fibonacci numbers in one and only one way.

In 1979 French poet Paul Braffort celebrated this with a series of 20 poems, My Hypertropes. Each of the 20 poems in the series is informed by the foregoing poems that make up its Zeckendorff sum. For example, the Zeckendorff representation of 12 is 8 + 3 + 1, so poem 12 in Braffort’s sequence shares some characters or images with each of these poems. This forced Braffort to build scenarios that would permit these relations as he wrote the poems.

Each of the numbers 1, 2, 3, 5, 8, and 13 is its own Zeckendorff representation, so Braffort related each of these to its two foregoing Fibonacci numbers (e.g., 8 = 3 + 5). This means that only the first poem, “The Preallable Explanation (or The Rhyme’s Reason),” is not influenced by any of the others. Here is that first poem, as translated by Amaranth Borsuk and Gabriela Jaurequi:

This is my work, this is my study,
like Jarry, Cyrano puffy,

to split hairs on Rimbaud
and on willies find booboos.

If it was fair or if it snowed
in Lhassa Emma Sophie Bo-

vary widow of slow carnac
gave herself to the god of wack.

Leibnitz, saying: “Verse …” What an ac-
tor for this superb “Vers …”. Oh “nach”!

He aims, Emma, the apoplexy
of those drunk on galaxy.

At the club of “spinach” kings (nay,
Bach never went there, Banach yea!)

Leibnitz — his graph ibo: not six
mus, three nus, one phi, bona xi —

haunts without profit Bonn: “Ach! Gee
if I were great Fibonacci!!! …”

Now, for example, Poem 12, “MODELS (for Petrovich’s Band),” is an alexandrine with two six-line stanzas. The Zeckendorff representation of 12 is 1 + 3 + 8, so in each stanza of Poem 12 the first line is influenced by Poem 1, the third by Poem 3, and the sixth by Poem 8, each drawing on specific lines in the source poem. The first line in the sixth couplet of Poem 1, “He aims, Emma, the apoplexy,” informs the first line of Poem 12, “For a sweet word from Emma: a word for model”; the second line of the sixth couplet from Poem 1, “of those drunk on galaxy,” informs the first line of the second stanza in Poem 12, “Our galaxies have already packed their valise”; the phrase “when I saw you / weave a letter to Elise” in Poem 3 becomes “they say from this time forth five letters to Elise” in Poem 12; and the couplet “And Muses who compose / They’re a troop they’re tropes” in Poem 8 becomes “Tragic tropes: Leonardo is Fibonacci.”

“Thus, Braffort’s collection of poems, My Hypertropes, has an internal structure provided by a mathematical theorem,” writes Robert Tubbs in Mathematics in Twentieth-Century Literature and Art (2014). “The structure does not entirely determine these poems, but it does provide connections between the poems that might not be there otherwise.”

This

This is not very interesting
But if
You have read this far already
You will
Probably
Read as far as this:
And still
Not really accomplishing
Anything at all

You might
Even read on
Which brings you to
The line you are reading now
And after all that you are still
Probably dumb enough to keep
Right on making
A dope of yourself
By reading
As far down
The page as this.

— Anonymous, Princeton Tiger, 1949

Circle Ode

https://archive.org/details/jstor-25228707

This love lyric was written by Shahin Ghiray (c. 1747-1787), the last sultan of the independent Crimea before its conquest by the Russians. It’s written in Turkish but in the Persian letter style of Arabic. The reader starts at the central letter and reads upward, which leads him into a series of arcs around the circle. Each arc forms a diptych that begins and ends with the central letter, and each line in the diptych intersects its neighbor so that they share a word.

Poet Dick Higgins writes, “When I asked a Persian student to read this for me, the sound, with its opening alliterations, was as much a tour de force as the visual aspect.” Unfortunately it’s hard to reflect all this in English; J.W. Redhouse attempted this translation in the Journal of the Royal Asiatic Society in 1861:

Let but my beloved come and take up her abode in the mansion of her lover, and shall not thy beautiful face cause his eyes to sparkle with delight!
Or, would she but attack my rival with her glances, sharp-pointed as daggers, and, piercing his breast, cause him to moan, as a flute is pierced ere it emit its sighing notes.
Turn not away, my beauty; nor flee from me, who am a prey to grief; deem it not fitting that I be consumed with the fire of my love for thee.
If the grace of God favour one of His servants, that man, from a state of utter destitution, may become the monarch of the world.
Tears flow from my eyes by reason of their desire to reach thee; for the sun of thy countenance, by an ordinance of the Almighty power, attracts to itself the moisture of the dew-drops.
If thou art wise, erect an inn on the road of self-negation; so that the pilgrims of holy love may make thereof their halting-place.
O proud and noble mistress of mine! with the eyebrows and glances that thou possessest, what need of bow or arrow wherewith to slay thy lover?
Is it that thou hast loosed thy tresses and veiled therewith the sun of thy countenance? Or is it that the moon has become eclipsed in the sign of Scorpio?
I am perfectly willing that my beloved should pierce my heart; only let that beauty deem me worthy of her favour.
Write, O pen! that I am a candidate for the flames, even as a salamander; declare it to be so, if that queen of beauty will it.
Is it the silvery lustre of the moon that has diffused brightness over the face of nature; or is it the sun of thy countenance that has illumined the world?
If any disputant should cavil, and deny the existence of thy beauty, would not thy adorer, hovering as a mote in its rays, suffice to convince the fool, if he had but common sense?
It is true that lovers do unremittingly dedicate their talents to the praise of their mistresses; but has thy turn yet come, Shahin-Ghiray, so to offer thy tribute of laudation?

Misc

A fragment from Robert Frost’s notebook on “Democracy”:

Cancellation Club. A mens club for rendering womens vote ineffective by voting the other way. One woman said No matter if her vote was offset. She only voted to assert herself — not to win elections.

A word-level palindrome by Allan Miller (from Mad Amadeus Sued a Madam):

MAYBE GOD CAN KNOW ALL WE DO; WE ALL KNOW, CAN GOD? MAYBE …

“I read the Tchechov aloud. I had read one of the stories myself and it seemed to me nothing. But read aloud, it was a masterpiece. How was that?” — Katherine Mansfield, journal, 1922

Dryden’s epitaph on his wife:

Here lies my wife, here let her lie;
Now she’s at rest, and so am I.

(Thanks, Bob.)

Death Poems

https://commons.wikimedia.org/wiki/File:Akashi_Gidayu_writing_his_death_poem_before_committing_Seppuku.jpg

In Japanese culture it is traditional to write a “farewell poem to life,” or jisei, as death approaches. Zen monk Kozan Ichikyo wrote this verse on the morning of his death in 1360:

Empty-handed I entered the world
Barefoot I leave it.
My coming, my going —
Two simple happenings
That got entangled.

And monk Mumon Gensen wrote this in 1390:

Life is like a cloud of mist
Emerging from a mountain cave
And death
A floating moon
In its celestial course.
If you think too much
About the meaning they may have
You’ll be bound forever
Like an ass to a stake.

On March 17, 1945, Gen. Tadamichi Kuribayashi sent a letter to Imperial headquarters apologizing for ceding Iwo Jima to American forces. He closed with a death poem:

Unable to complete this heavy task for our country
Arrows and bullets all spent, so sad we fall.
But unless I smite the enemy,
My body cannot rot in the field.
Yea, I shall be born again seven times
And grasp the sword in my hand.
When ugly weeds cover this island,
My sole thought shall be the Imperial Land.

His body could not be identified later — it appears that prior to the final battle he removed his officer’s insignia in order to fight among his men as an ordinary soldier.

Two Poems for Middle Age

Mezzo Cammin

Half of my life is gone, and I have let
The years slip from me and have not fulfilled
The aspiration of my youth, to build
Some tower of song with lofty parapet.
Not indolence, nor pleasure, nor the fret
Of restless passions that would not be stilled,
But sorrow, and a care that almost killed,
Kept me from what I may accomplish yet;
Though, half-way up the hill, I see the Past
Lying beneath me with its sounds and sights,–
A city in the twilight dim and vast,
With smoking roofs, soft bells, and gleaming lights,–
And hear above me on the autumnal blast
The cataract of Death far thundering from the heights.

— Longfellow

To the Natural World: At 37

Exquisite world, powerful, joyous, splendid,
Where, almost when we learn to live, our life is ended,
Where, when we gather our trophy errors in,
And face the array and cannot again begin
To make another life less fatal, less
Like a poor travesty of some greatness,
World, you rebuke us calmly, ceaselessly,
With mute round of rising sun and mimicking sea,
With flood and ebb and taciturn refrain
In round diurnal rings, waxing to wane.
Our mortal life runs through you its swift line
Closing no circle, marking its scratch design,
Fusiform, the spindle, this is its mortal shape;­–
O lovely world, midway in large landscape
I pause, look forward. Weakness with wisdom lie
Ahead with nodding age; error and energy
Behind, dim in regret and chaos where
I left my early self and got the despair
That seizes all who see how folly gone
Is their sweet youth with darkness sudden on.
World deign, for one moment, O deign to culminate
One wave in me; O in me consummate
Your surge with all beholding happy power.
So, overlapping once, here in the midway hour,
Let me watch outward splendor solemnly for
Life’s brief in all this bigness, O sun’s calm, O
Sea’s roar.

— Genevieve Taggard

“The Sons of Our Sons”

https://commons.wikimedia.org/wiki/File:Capture_of_Carency_aftermath_1915_1.jpg

In 1919 Russian author Ilya Ehrenburg wrote a message to posterity:

The sons of our sons will marvel,
Paging the textbook:
“1914 … 1917 … 1919 …
How did they live? The poor devils!”
Children of a new age will read of battles,
Will learn the names of orators and generals,
The numbers of the killed,
And the dates.

They will not know how sweetly roses smelled above the trenches,
How martins chirped blithely between the cannon salvos,
How beautiful in those years was
Life.

Never, never did the sun laugh so brightly
As above a sacked town,
When people, crawling out of their cellars,
Wondered: is there still a sun?
Violent speeches thundered,
Strong armies perished,

But the soldiers learned what the scent of snowdrops is like
An hour before the attack.
People were led at dawn to be shot …
But they alone learned what an April morning can be.
The cupolas gleamed in the slanting rays,
And the wind pleaded: Wait! A minute! Another minute!
Kissing, they could not tear themselves from the mournful mouth,
And they could not unclasp the hands so tightly joined.
Love meant: I shall die! I shall die!
Love meant: Burn, fire, in the wind!
Love meant: O where are you, where?

They love as people can love only here, upon this rebellious and
tender star.

In those years there were no orchards golden with fruit,
But only fleeting bloom, only a doomed May.
In those years there was no calling: “So long!”
But only a brief, reverberant “Farewell!”
Read about us and marvel!
You did not live in our time — be sorry!
We were guests of the earth for one evening only.
We loved, we destroyed, we lived in the hour of our death.
But overhead stood the eternal stars,
And under them we begot you.

In your eyes our longing still burns,
In your words our revolt reverberates yet
Far into the night, and into the ages, the ages, we have scattered
The sparks of our extinguished life.

“De Sancta Cruce”

https://archive.org/details/monumen01gese

The English scholar Alcuin devised this remarkable acrostic poem in the ninth century. The text can be read in conventional lines of Latin, and additional phrases are embedded in a symmetrical arrangement of lines that represent the cross inscribed upon the world:

Horizontal, top and bottom:

Crux decus es mundi Iessu de sanguine sancta (“Cross, you are the glory of the world, in Jesus’ blood sanctified”)

Suscipe sic talem rubicumdam celsa coronam (“Accept, exalted cross, from me this scarlet crown”)

Vertical, left and right:

Crux pia vera salus partes in quatuor orbis (“Pious cross, true salvation in the four corners of the world”)

Alma teneto tuam Christo dominane coronam (“Beneficent, take your crown, Christ being the Lord”)

The cross:

Rector in orbe tuis sanavit saecla sigillis (“The ruler of the world saved generations by your sign”)

Surge lavanda tuae sunt saecula fonte fidei (“Rise, the world is cleansed in the font of faith”)

The diamond, representing the world (whose four corners are referenced in the vertical line on the left):

Salve sancta rubens, fregisti vincula mundi (“Hail holy scarlet, you have shattered the world’s shackles”)

Signa valete novis reserata salutibus orbi (“Wonders are manifest, revealed anew to the world in saving works”)

A translation of the full text:

Cross, you are the glory of the world, in Jesus’ blood sanctified.
God the king from the cross conveyed heaven’s judgment.
A victor he reigns, destroying evil and conquering the enemy,
Christ the great sacrifice nailed on the cross for us.
The shepherd by dying redeemed his sheep with his healing right hand.
Glorious, holy salvation from the venerable tree,
he seized the prize, shrugging off the ties of flesh.
Though in bonds the highest king freed us, and he himself
giving his life to the cross triumphed over death,
The kingdom of heaven gaped when the world’s enemy was destroyed.
The sign will be more manifest and all good people will wear it,
praising it with all strength; let all discern more profoundly
so that they may see how many his holy passion frees
from eternal sorrow, and see one thrown down by time
to heal those oppressed by the enemy’s torments; there
may the highest and true Joseph now be our salvation,
who suffered high upon the cross such that error can’t seduce
and poison men and drag them from the light of faith.
The ruler of the world saved generations by your sign.
You, my life, my salvation! For you alone my voice composes hymns,
and shall always sing the highest songs, clear and plain
with the plectrum; for David famous for his song
proves that it is proper for us to testify holiness continually
in elaborate style — accept that which I have just begun, O Christ supernal,
true salvation, great sufferer, you sacred and holy light. Now
the secular nations sing the beneficent sign of the cross,
all the earth trembles and in one accord proclaims
the fame of the cross. In prayer it reveals its inmost heart.
Now hear, vain men, confounded in evil:
The almighty shines forth. May blessed faith fill your hearts
and the serpent not drive them back to their old ways.
The highest and most faithful redeemer has restored us
to his kingdom, and has conquered by this sign the obdurate one,
toppling warlike Satan from the place he hazarded to rule.
Glorious cross, the world should loose its prayers to you.
Accept, exalted cross, from me this scarlet crown.

(From Monumenta Germaniae Historica, part one, 1880, and Jay Hopler and Kimberly Johnson, eds., Before the Door of God: An Anthology of Devotional Poetry, 2013. Thanks, Brandon.)

A Poetic Puzzle

On Oct. 25, 1875, Lewis Carroll sent this verse to Mrs. J. Chataway, mother of one of his child-friends, Gertrude. “They embody, as you will see, some of my recollections of pleasant days at Sandown”:

Girt with a boyish garb for boyish task,
Eager she wields her spade — yet loves as well
Rest on a friendly knee, the tale to ask
That he delights to tell.

Rude spirits of the seething outer strife,
Unmeet to read her pure and simple spright,
Deem, if you list, such hours a waste of life,
Empty of all delight!

Chat on, sweet maid, and rescue from annoy
Hearts that by wiser talk are unbeguiled!
Ah, happy he who owns that tenderest joy,
The heart-love of a child!

Away, fond thoughts, and vex my soul no more!
Work claims my wakeful nights, my busy days:
Albeit bright memories of that sunlit shore
Yet haunt my dreaming gaze!

He asked her leave to have it published. The child in the verse is not named — why should he feel obliged to ask permission?

Click for Answer

Of Thee I Sing

The editors of the Journal of Organic Chemistry received a novel submission in 1970 — Brown University chemists J.F. Bunnett and Francis Kearsley wrote their paper “Comparative Mobility of Halogens in Reactions of Dihalobenzenes With Potassium Amide in Ammonia” in blank verse:

Reactions of potassium amide
With halobenzenes in ammonia
Via benzyne intermediates occur.
Bergstrom and associates did report,
Based on two-component competition runs,
Bromobenzene the fastest to react,
By iodobenzene closely followed,
The chloro compound lagging far behind,
And flurobenzene to be quite inert
At reflux (-33°).

This goes on for three pages. The journal published it with a note: “Although we are open to new styles and formats for scientific publication, we must admit to surprise upon receiving this paper. However, we find the paper to be novel in its chemistry, and readable in its verse. Because of the somewhat increased space requirements and possible difficulty to some of our nonpoetically inclined readers, manuscripts in this format face an uncertain future in this office.”

(Thanks, Bob.)