Cross Purposes

ferland crossword grid

The daily New York Times crossword puzzle fills a grid measuring 15×15. The smallest number of clues ever published in a Times puzzle is 52 (on Jan. 21, 2005), and the largest is 86 (on Dec. 23, 2008).

This set Bloomsburg University mathematician Kevin Ferland wondering: What are the theoretical limits? What are the shortest and longest clue lists that can inform a standard 15×15 crossword grid, using the standard structure rules (connectivity, symmetry, and 3-letter words minimum)?

The shortest is straightforward: A blank grid with no black squares will be filled with 30 15-letter words, 15 across and 15 down.

The longest is harder to determine, but after working out a nine-page proof Ferland found that the answer is 96: The largest number of clues that a Times-style crossword will admit is 96, using a grid such as the one above.

In honor of this result, he composed a puzzle using this grid — it appears in the June-July 2014 issue of the American Mathematical Monthly.

(Kevin K. Ferland, “Record Crossword Puzzles,” American Mathematical Monthly 121:6 [June-July 2014], 534-536.)

Palinmorses

Morse code palindromes, contributed by reader Dave Lawrence:

ANNEXING ·- -· -· · -··- ·· -· --·
BEEFIEST -··· · · ··-· ·· · ··· -
DEFOREST -·· · ··-· --- ·-· · ··· -
ESTHETES · ··· - ···· · - · ···
FINAGLED ··-· ·· -· ·- --· ·-·· · -··
HEARTIES ···· · ·- ·-· - ·· · ···
HECTARES ···· · -·-· - ·- ·-· · ···
INDEBTED ·· -· -·· · -··· - · -··
INTERNAL ·· -· - · ·-· -· ·- ·-··
INTUITED ·· -· - ··- ·· - · -··
RECENTER ·-· · -·-· · -· - · ·-·
SATIATES ··· ·- - ·· ·- - · ···
SEVENTHS ··· · ···- · -· - ···· ···
SHEEPISH ··· ···· · · ·--· ·· ··· ····
SOPRANOS ··· --- ·--· ·-· ·- -· --- ···
SUBHEADS ··· ··- -··· ···· · ·- -·· ···
WAVERING ·-- ·- ···- · ·-· ·· -· --·
WRECKING ·-- ·-· · -.-· -.- ·· -· --·
ANTICKING ·- -· - ·· -·-· -·- ·· -· --·
FOOTSTOOL ··-· --- --- - ··· - --- --- ·-··
FRESHENED ··-· ·-· · ··· ···· · -· · -··
INCIDENCE ·· -· -·-· ·· -·· · -· -·-· ·
SATURATES ··· ·- - ··- ·-· ·- - · ···
SIDELINES ··· ·· -·· · ·-·· ·· -· · ···
INITIALLED ·· -· ·· - ·· ·- ·-·· ·-·· · -··
INTERSTICE ·· -· - · ·-· ··· - ·· -·-· ·
RESEARCHER ·-· · ··· · ·- ·-· -·-· ···· · ·-·
WINTERTIME ·-- ·· -· - · ·-· - ·· -- ·
ANTIQUATING ·- -· - ·· --·- ··- ·- - ·· -· --·
INTERPRETED ·· -· - · ·-· ·--· ·-· · - · -··
PROTECTORATE ·--· ·-· --- - · -·-· - --- ·-· ·- - ·
INTRANSIGENCE ·· -· - ·-· ·- -· ··· ·· --· · -· -·-· ·

He notes that, perhaps fittingly, the word with the longest run of dots is OBSESSIVE, with 18: --- -··· ··· · ··· ··· ·· ···- ·

Oops

In 1945, the Arkansas legislature passed “An Act to Authorize and Permit Cities of First and Second Class and Incorporated Towns to Vacate Public Streets and Alleys in the Public Interest.” That seems boring enough. But § 8 read as follows:

“All laws and parts of laws, and particularly Act 311 of the Acts of 1941, are hereby repealed.”

With the stroke of a pen they had repealed every law in Arkansas. The state supreme court cleared its throat and ventured an improvement:

“No doubt the legislature meant to repeal all laws in conflict with that act, and, by error of the author or the typist, left out the usual words ‘in conflict herewith,’ which we will imply by necessary construction.”

(Act 17 of 1945 [repl. 1980; now Ark. Stat. § 14-301-301], cited in Antonin Scalia and Bryan Garner, Reading Law, 2012.)

Time Passages

http://commons.wikimedia.org/wiki/File:Sc%C3%A8ne_de_rue_parisienne_par_Frank_Boggs.jpg

In ordinary life we shift frequently between observing the world before us and summoning impressions from memory. Reproducing this experience in fiction can require an immense sophistication of the reader. In Narrative Discourse: An Essay in Method (1983), Gérard Genette examines a passage from Proust’s Jean Santeuil in which Jean finds the hotel in which lives Marie Kossichef, whom he once loved, and compares his impressions with those that he once thought he would experience today:

“Sometimes passing in front of the hotel he remembered the rainy days when he used to bring his nursemaid that far, on a pilgrimage. But he remembered them without the melancholy that he then thought he would surely someday savor on feeling that he no longer loved her. For this melancholy, projected in anticipation prior to the indifference that lay ahead, came from his love. And this love existed no more.”

Understanding this one paragraph requires shifting our focus between the present and the past nine times. If we designate the sections by consecutive letters, and if 1 is “once” and 2 is “now,” then A goes in position 2 (“Sometimes passing in front of the hotel he remembered”), B goes in position 1 (“the rainy days when he used to bring his nursemaid that far, on a pilgrimage”), C in 2 (“But he remembered them without”), D in 1 (“the melancholy that he then thought”), E in 2 (“he would surely some day savor on feeling that he no longer loved her”), F in 1 (“For this melancholy, projected in anticipation”), G in 2 (“prior to the indifference that lay ahead”), H in 1 (“came from his love”), and I in 2 (“And his love existed no more”).

This produces a perfect zigzag: A2-B1-C2-D1-E2-F1-G2-H1-I2. And defining the relationships among the elements reveals even more complexity:

If we take section A as the narrative starting point, and therefore as being in an autonomous position, we can obviously define section B as retrospective, and this retrospection we may call subjective in the sense that it is adopted by the character himself, with the narrative doing no more than reporting his present thoughts (‘he remembered …’); B is thus temporally subordinate to A: it is defined as retrospective in relation to A. C continues with a simple return to the initial position without subordination. D is again retrospective, but this time the retrospection is adopted directly by the text: apparently it is the narrator who mentions the absence of melancholy, even if this absence is noticed by the hero. E brings us back to the present, but in a totally different way from C, for this time the present is envisaged as emerging from the past and ‘from the point of view’ of that past: it is not a simple return to the present but an anticipation (subjective, obviously) of the present from within the past; E is thus subordinated to D as D is to C, whereas C, like A, was autonomous. F brings us again to position 1 (the past), on a higher level than anticipation E: simple return again, but return to 1, that is, to a subordinate position. G is again an anticipation, but this time an objective one, for the Jean of the earlier time foresaw the end that was to come to his love precisely as, not indifference, but melancholy at loss of love. H, like F, is a simple return to 1. I, finally, is (like C), a simple return to 2, that is, to the starting point.

All in a passage of 71 words! And Genette points out in passing that a first reading is made even more difficult because of the apparently systematic way in which Proust eliminates simple temporal indicators such as once and now, “so that the reader must supply them himself in order to know here he is.”

Fascinating Rhythm

The theme music for the British television series Inspector Morse starts with a motif based on the Morse code for the word Morse:

-- --- ·-· ··· ·

“It was just a little in-joke,” composer Barrington Pheloung told Essex Life & Countryside in 2001. “I put his name at the beginning and then it recurred all the way through.”

Encouraged, he carried the idea into subsequent episodes. “Sometimes I got a bit cheeky and spelled out the killer’s name in the episode. In the episode ‘WHOK,’ which was a bit of an enigma, the culprit was called Earle. So he got plastered all over the orchestra.” When viewers caught on to this, occasionally he’d insert another character’s name to fool them.

And sometimes he’d give them the slip entirely. When the episode aired in which the detective was due to reveal his first name, 20 million people tuned in to listen for clues in the music, and a national newspaper enlisted the Royal College of Signalling to decipher the notes. They found nothing. (The inspector’s name is Endeavour.)

(Thanks, Dave.)

UPDATE: In the same spirit, the theme to the 1970s British sitcom Some Mothers Do ‘Ave ‘Em (below) spells out the series’ title in Morse code (minus the apostrophes). (Thanks, Nick.)

https://www.youtube.com/watch?v=ICnl_7u0sp8

Punctual

Ernest Hemingway published this “blank verse” in his high school literary magazine in 1916:

hemingway blank verse

Get it? David Morice followed up with this “punctuation poem” in Word Ways in February 2012:

% , & —
+ . ? /
” :
% ;
+ $ [ \

It’s a limerick:

Percent comma ampersand dash
Plus period question mark slash
Quotation mark colon
Percent semicolon
Plus dollar sign bracket backslash

(Thanks, Volodymyr.)

DO IT NOW

http://commons.wikimedia.org/wiki/File:Karikatur_von_Arnold_Schwarzenegger.jpg
Image: Wikimedia Commons

ArnoldC, a language devised by Finnish computer programmer Lauri Hartikka, assigns programming functions to catch phrases from Arnold Schwarzenegger movies. Some keywords:

False: I LIED

True: NO PROBLEMO

If: BECAUSE I’M GOING TO SAY PLEASE

Else: BULLSHIT

EndIf: YOU HAVE NO RESPECT FOR LOGIC

While: STICK AROUND

EndWhile: CHILL

MultiplicationOperator: YOU’RE FIRED

DivisionOperator: HE HAD TO SPLIT

EqualTo: YOU ARE NOT YOU YOU ARE ME

GreaterThan: LET OFF SOME STEAM BENNET

Or: CONSIDER THAT A DIVORCE

And: KNOCK KNOCK

DeclareMethod: LISTEN TO ME VERY CAREFULLY

MethodArguments: I NEED YOUR CLOTHES YOUR BOOTS AND YOUR MOTORCYCLE

Return: I’LL BE BACK

EndMethodDeclaration: HASTA LA VISTA, BABY

AssignVariableFromMethodCall: GET YOUR ASS TO MARS

ReadInteger: I WANT TO ASK YOU A BUNCH OF QUESTIONS AND I WANT TO HAVE THEM ANSWERED IMMEDIATELY

AssignVariable: GET TO THE CHOPPER

SetValue: HERE IS MY INVITATION

EndAssignVariable: ENOUGH TALK

ParseError: WHAT THE FUCK DID I DO WRONG

This program prints the string “hello world”:

IT'S SHOWTIME
TALK TO THE HAND "hello world"
YOU HAVE BEEN TERMINATED

More on GitHub.

The Hidden Psalm

The final movement on John Coltrane’s 1965 album A Love Supreme is a “musical narration” of a devotional poem that Coltrane included in the album’s liner notes — he put the handwritten poem on a music stand and “played” it as if it were music.

“Coltrane’s hushed delivery sounds deliberately speechlike,” write Ashley Kahn in his 2003 history of the album. “He hangs on to the ends of phrases, repeats them as if for emphasis. He is in fact ‘reading’ through his horn.”

The hidden psalm was marked by New York musicians for decades before Rutgers University musicologist Lewis Porter presented a formal analysis to the American Musicological Society in 1980. “You will find that he plays right to the final ‘Amen’ and then finishes,” he writes in his 1997 biography of the saxophonist. “There are no extra notes up to that point. You will have to make a few adjustments in the poem, however: Near the beginning where it reads, ‘Help us resolve our fears and weaknesses,’ he skips the next line, goes on to ‘In you all things are possible,’ then plays ‘Thank you God’ … towards the end he leaves out ‘I have seen God.'”

“I think music can make the world better and, if I’m qualified, I want to do it,” Coltrane had said. “I’d like to point out to people the divine in a musical language that transcends words. I want to speak to their souls.”

(Thanks, Jeff.)

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.”

A Second Paradox of Blackmail

We covered one paradox regarding blackmail in 2010: If it’s legal for me to reveal your secret, and it’s legal for me to ask you for money, why is it illegal for me to demand payment to keep your secret? In the words of Northwestern University law professor James Lindgren, “Why do two rights make a wrong?”

Here’s a second paradox: If you had initiated the same transaction — if you had offered to pay me for my silence, and I’d agreed — then we’d have the same outcome, but this time it’s legal. “It is considered paradoxical that the sale of secrecy is legal if it takes the form of a bribe, yet is illegal where the sale of secrecy takes the form of blackmail,” writes Loyola University economist Walter Block. “Why should the legality of a sale of secrecy depend entirely upon who initiates the transaction? Why is bribery legal but blackmail not?”

(Walter Block et al., “The Second Paradox of Blackmail,” Business Ethics Quarterly, July 2000.)