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.”

Knights and Scoundrels

A problem from the 1994 Italian Mathematical Olympiad:

Every inhabitant on the island of knights and scoundrels is either a knight (who always tells the truth) or a scoundrel (who always lies). A visiting journalist interviews each inhabitant exactly once and gets the following answers:

A1: On this island there is at least one scoundrel.
A2: On this island there are at least two scoundrels.

An-1: On this island there are at least n – 1 scoundrels.
An: On this island everyone is a scoundrel.

Can the journalist decide whether the knights outnumber the scoundrels?

Click for Answer

Ersatz English

The lyrics in Italian singer Adriano Celentano’s 1972 single “Prisencolinensinainciusol” sound like American English, but they’re gibberish.

“Ever since I started singing, I was very influenced by American music and everything Americans did,” he told NPR in 2014. “So at a certain point, because I like American slang — which, for a singer, is much easier to sing than Italian — I thought that I would write a song which would only have as its theme the inability to communicate. And to do this, I had to write a song where the lyrics didn’t mean anything.”

It reached number 4 on the Belgian charts in 1973.

Cutting Up

http://commons.wikimedia.org/wiki/File:Japanese_theorem_green.svg
Image: Wikimedia Commons

Choose any number of points on a circle and connect them to form a polygon.

This polygon can be carved into triangles in any number of ways by connecting its vertices.

No matter how this is done, the sum of the radii of the triangles’ inscribed circles is constant.

This is an example of a Sangaku (literally, “mathematical tablet”), a class of geometry theorems that were originally written on wooden tablets and hung as offerings on Buddhist temples and Shinto shrines during Japan’s Edo period (1603-1867). This one dates from about 1800.

In a Word

http://commons.wikimedia.org/wiki/File:Jacob_J_Lew_Signature.svg

chirography
n. one’s own handwriting or autograph; a style or character of writing

What is this? It’s the signature of Treasury Secretary Jack Lew. When Lew was nominated for the post in January 2013, it threatened to appear on all U.S. paper currency for the duration of his tenure.

Barack Obama said, “Jack assures me that he is going to work to make at least one letter legible in order not to debase our currency, should he be confirmed as secretary of the Treasury.” He did so — the current signature is below.

Lew’s predecessor, Timothy Geithner, had a similarly incomprehensible signature and produced a more legible version for the currency. “I took handwriting in the third grade in New Delhi, India,” he said, “so I probably did not get the best instruction on handwriting.”

http://commons.wikimedia.org/wiki/File:Jacob_Lew_new_money_signature.png

“A Bit of Spanish”

2015-01-07-a-bit-of-spanish

This pleasing cryptarithm, by Bob High, appears in the September/October 2014 issue of MIT Technology Review. If each letter stands for a digit, what arithmetic sum is enciphered here?

Click for Answer

You Are Here

Metaphors for life:

“A theater in which the worst people often have the best seats.” — Aristonymus

“A hospital in which every patient is possessed by the desire to change his bed.” — Charles Baudelaire

“A maze in which we take the wrong turning before we have learned to walk.” — Cyril Connolly

“A garish, unrestful hotel.” — Joseph Conrad

“Like eating artichokes — you’ve got to go through so much to get so little.” — Tad Dorgan

“For most men … a search for the proper manila envelope in which to get themselves filed.” — Clifton Fadiman

“A library owned by an author. In it are a few books which he wrote himself, but most of them were written for him.” — Harry Emerson Fosdick

“An onion, and one peels it crying.” — French proverb

“The only riddle that we shrink from giving up.” — W.S. Gilbert

“Life is something like this trumpet. If you don’t put anything in it, you don’t get anything out.” — W.C. Handy

“A succession of frontispieces. The way to be satisfied is never to look back.” — William Hazlitt

“A long headache in a noisy street.” — John Masefield

“A foreign language: all men mispronounce it.” — Christopher Morley

“A party: one arrives long after it’s started, and one’s going to leave long before it’s over.” — Robert Morley

The Edinburgh Fairy Coffins

http://commons.wikimedia.org/wiki/File:Arthur%27s_Seat_coffins.jpg
Image: Wikimedia Commons

In early July 1836, three boys searching for rabbits’ burrows near Edinburgh came upon some thin sheets of slate set into the side of a cliff. On removing them, they discovered the entrance to a little cave, where they found 17 tiny coffins containing miniature wooden figures.

According to the Scotsman‘s account later that month, each of the coffins “contained a miniature figure of the human form cut out in wood, the faces in particular being pretty well executed. They were dressed from head to foot in cotton clothes, and decently laid out with a mimic representation of all the funereal trappings which usually form the last habiliments of the dead. The coffins are about three or four inches in length, regularly shaped, and cut out from a single piece of wood, with the exception of the lids, which are nailed down with wire sprigs or common brass pins. The lid and sides of each are profusely studded with ornaments, formed with small pieces of tin, and inserted in the wood with great care and regularity.”

Some accounts say that the coffins had been laid in tiers, the lower appearing decayed and the topmost quite recent, but Edinburgh University historian Allen Simpson believes that all were placed in the niche after 1830, about five years before the boys discovered them.

Who placed them there, and why, remain mysterious. Simpson suggests that they may be an attempt to provide a decent symbolic burial for the victims of murderers William Burke and William Hare, who had sold 17 corpses to local doctor Robert Knox in 1828 for use in anatomy lessons. But 12 of Burke and Hare’s victims were women, and the occupants of the fairy coffins are all dressed as men.

So investigations continue. The eight surviving coffins and their tiny occupants are on display today at the National Museum of Scotland.