Six by Six

The sestina is an unusual form of poetry: Each of its six stanzas uses the same six line-ending words, rotated according to a set pattern:

https://commons.wikimedia.org/wiki/File:Sestina_system_alt.svg

This intriguingly insistent form has appealed to verse writers since the 12th century. “In a good sestina the poet has six words, six images, six ideas so urgently in his mind that he cannot get away from them,” wrote John Frederick Nims. “He wants to test them in all possible combinations and come to a conclusion about their relationship.”

But the pattern of permutation also intrigues mathematicians. “It is a mathematical property of any permutation of 1, 2, 3, 4, 5, 6 that when it is repeatedly combined with itself, all of the numbers will return to their original positions after six or fewer iterations,” writes Robert Tubbs in Mathematics in Twentieth-Century Literature and Art. “The question is, are there other permutations of 1, 2, 3, 4, 5, 6 that have the property that after six iterations, and not before, all of the numbers will be back in their original positions? The answer is that there are many — there are 120 such permutations. We will probably never know the aesthetic reason poets settled on the above permutation to structure the classical sestina.”

In 1986 the members of the French experimental writers’ workshop Oulipo began to apply group theory to plumb the possibilities of the form, and in 2007 Pacific University mathematician Caleb Emmons offered the ultimate hat trick: A mathematical proof about sestinas written as a sestina:

emmons sestina

Bonus: When not doing math and poetry, Emmons runs the Journal of Universal Rejection, which promises to reject every paper it receives: “Reprobatio certa, hora incerta.”

(Caleb Emmons, “S|{e,s,t,i,n,a}|“, The Mathematical Intelligencer, December 2007.) (Thanks, Robert and Kat.)

| Poems · Science & Math

Oops

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

Robert Barker and Martin Lucas overlooked a crucial not in their Bible published in 1631. Brewer’s Dictionary of Phrase and Fable notes, “The fine of £300 helped to ruin the printer.” Further Bible errata:

  • The “Cannibal Bible,” printed at Amsterdam in 1682, included the sentence “If the latter husband ate her [for hate her], her former husband may not take her again” (Deuteronomy 24:3).
  • In the “Camel’s Bible” of 1823, Genesis 24:61 reads “And Rebekah arose, and her camels [for damsels].”
  • In an edition published in Charles I’s reign, Psalm 14:1 read “The fool hath said in his heart there is a God.” The printers were fined £3,000, and all copies were suppressed.
  • The “Lions Bible” of 1804 contains the phrase “but thy son that shall come forth out of thy lions [for loins]” (Kings 8:19). In Galatians 5:17 it reads “For the flesh lusteth after the Spirit [for against the Spirit].”
  • In the second edition of the Geneva Bible, 1562, Matthew 5:9 reads “Blessed are the placemakers [peacemakers]: for they shall be called the children of God.” (Also, the chapter heading for Luke 21 has “Christ condemneth the poor widow” rather than “commendeth.”)
  • A 1702 edition has David complain that “printers [princes] have persecuted me without a cause.” (Psalm 119:161)
  • In a 1716 Bible first printed in Ireland, John 5:14 read “sin on more” rather than “sin no more.” “The mistake was undiscovered until 8,000 copies had been printed and bound.”
  • The “Affinity Bible” of 1923 contains a table of affinity with the error “A man may not marry his grandmother’s wife.”
  • In the “Standing Fishes Bible” of 1806, Ezekiel 47:10 reads “And it shall come to pass that the fishes [fishers] shall stand upon it.”
  • A Cambridge printing of 1653 reads “know ye not that the unrighteous shall inherit the Kingdom of God?” instead of “shall not inherit.” (I Corinthians 6:9)
  • In the “Wife-Beater’s Bible” of 1549, Edmund Becke inserted a footnote to I Peter 3:7 reading “And if she be not obediente and healpeful unto hym, endevoureth to beate the fere of God into her heade, that thereby she may be compelled to learne her dutye and do it.”

In one edition published in 1944, a broken bit of type in I Peter 3:5 caused own to appear as owl, producing the alarming sentence “For after this manner in the old time the holy women also, who trusted God, adorned themselves, being in subjection to their owl husbands.”

| Literature · Religion

Podcast Episode 53: The Lost Colony

https://books.google.com/books?id=eu1neCSs4RsC&pg=PA254

It’s been called America’s oldest mystery: A group of 100 English colonists vanished from North Carolina’s Roanoke Island shortly after settling there in 1587. But was their disappearance really so mysterious? In this episode of the Futility Closet podcast we’ll trace the history of the “lost colony” and consider what might have happened to the settlers.

We’ll also visit an early steam locomotive in 1830 and puzzle over why writing a letter might prove to be fatal.

See full show notes …

| History · Oddities · Podcast

In a Word

toffs and toughs

fastuous
adj. haughty, arrogant, pretentious, or showy

alabandical
adj. barbarous, uncivilized

floccipend
v. to regard as insignificant or of no account

In 1937 photographer Jimmy Sime caught sight of five boys outside Lord’s Cricket Ground during the annual Eton vs. Harrow match. Peter Wagner and Tim Dyson were Harrow students awaiting a ride to the Wagners’ country home in Surrey, and George Salmon, Jack Catlin, and George Young were working-class boys who had spent the morning at the dentist and hoped to earn some money running errands at Lord’s.

Sime’s photo filled three columns of the News Chronicle‘s front page on July 10 under the headline “Every Picture Tells a Story.” It has been reprinted widely since as an illustration of the British class system, sometimes with the title Toffs and Toughs.

In 1998, journalist Geoffrey Levy tracked down Young and Salmon, then in their 70s, and asked whether they’d resented the Harrow boys. “Nah,” Young said. “We had our lives, they had theirs.” Salmon said, “In those days you accepted what you were and what they were, and got on with it.”

| Language · Society

Three Chess Puzzles

rockwell chess problem

1. By A.F. Rockwell. White to mate in two moves. (Solutions are below.)

2. In 1866 Sam Loyd asked: Suppose you’re playing White against an opponent who’s required to mirror every move you make — if you play 1. Nf3 he must play 1. … Nf6, and so on. Can you design a game in which your eighth move forces your opponent to checkmate you with a nonmirror move?

miles chess problem

3. An endgame study by J.A. Miles. “White to play and draw the game.”

Click for Answer
| Puzzles

Me, a Name I Call Myself

https://commons.wikimedia.org/wiki/File:US_Navy_030513-N-2069B-001_Students_and_faculty_from_both_Akers_and_R.J._Neutra_Elementary_Schools_aboard_the_Naval_Air_Station_Lemoore,_Calif.,_show_their_appreciation_for_the_members_of_the_U.S._military.jpg

It seems a bit arrogant that those of us in the United States refer to ourselves as “Americans” when more than half a billion other people live in the Americas. But what should we call ourselves instead?

“You have properly observed that we can no longer be called Anglo-Americans,” noted Thomas Jefferson in a letter after the Revolution. “That appellation describes now only the inhabitants of Nova Scotia, Canada, &c. I had applied that of Federo Americans to our citizens, as it would not be so decent for us to assume to ourselves the flattering appellation of free Americans.”

What’s a better term? In 1992 Columbia University etymologist Allen Walker Read compiled a list of suggestions that have been made over the years:

  • United Statesards
  • United Statesese
  • Unisians
  • United Statesians
  • Columbards
  • United Statesmen
  • United Statesers
  • Statesmen
  • Staters
  • Unistaters
  • Usarians
  • U.S. men
  • Usonians
  • Usonans
  • Ustatians
  • Uessians
  • Unessians
  • Statesiders
  • Statunitensi
  • United Stateans
  • Unistatians
  • Unitedstatians

Perhaps we’re all counterfeit: In early usage “Americans” applied not to European colonists but to the native Indians whose territory they were invading. John Locke wrote in 1671: “So if you should ask an American how old his son is, i.e., what the length of duration was between his birth and this moment, he would … tell you his son was 30 or 40 moons old as it happened.”

(Allen Walker Read, “Derivative Forms From the Name United States,” paper read at the 31st annual Names Institute sponsored by The American Name Society, Baruch College of The City University of New York, May 2, 1992.)

| Language · Society

Summing Up

Artist Thomas Cole took up a grand theme in 1833 — The Course of Empire, a series of five paintings that depict the rise and fall of a civilization. The Savage State shows a prehistoric wilderness in which the only artificial note is a circle of teepees:

https://commons.wikimedia.org/wiki/File:Cole_Thomas_The_Course_of_Empire_The_Savage_State_1836.jpg

The Arcadian or Pastoral State shows the beginning of agriculture, with a primitive temple, farmers, and shepherds:

https://commons.wikimedia.org/wiki/File:Cole_Thomas_The_Course_of_Empire_The_Arcadian_or_Pastoral_State_1836.jpg

The Consummation of Empire shows a thriving city, with an imperial procession crossing a triumphal bridge:

https://commons.wikimedia.org/wiki/File:Cole_Thomas_The_Consummation_The_Course_of_the_Empire_1836.jpg

Destruction shows barbarians sacking the city and nature herself punishing human presumption:

https://commons.wikimedia.org/wiki/File:Cole_Thomas_The_Course_of_Empire_Destruction_1836.jpg

And Desolation shows the return of nature, with trees growing up through the ruins of the city:

https://commons.wikimedia.org/wiki/File:Cole_Thomas_The_Course_of_Empire_Desolation_1836.jpg

Interestingly, all five paintings depict the same scene: In the foreground is a natural port, and in the background is a distinctive mountain precipice. The time of day passes from dawn to dusk.

In 1836 more than 2,000 people attended the paintings’ exhibition at the National Academy of Design, an audience unprecedented in the United States. “The philosophy of my subject is drawn from the history of the past, wherein we see how nations have risen from the savage state to that of power and glory, and then fallen, and become extinct,” Cole had written to his patron Luman Reed. “You will perceive what an arduous task I have set myself; but your approbation will stimulate me to conquer difficulties.”

(Thanks, Cody.)

| Art

Overheard

https://commons.wikimedia.org/wiki/File:SU12III_W%C5%82oc%C5%82awek_(rys).jpg
Image: Wikimedia Commons

A puzzle by Princeton mathematician John Horton Conway:

Last night I sat behind two wizards on a bus, and overheard the following:

A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.

B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?

A: No.

B: Aha! AT LAST I know how old you are!

“This is an incredible puzzle,” writes MIT research affiliate Tanya Khovanova. “This is also an underappreciated puzzle. It is more interesting than it might seem. When someone announces the answer, it is not clear whether they have solved it completely.”

We can start by auditioning various bus numbers. For example, the number of the bus cannot have been 5, because in each possible case the wizard’s age and the number of his children would then uniquely determine their ages — if the wizard is 3 years old and has 3 children, then their ages must be 1, 1, and 3 and he cannot have said “No.” So the bus number cannot be 5.

As we work our way into higher bus numbers this uniqueness disappears, but it’s replaced by another problem — the second wizard must be able to deduce the first wizard’s age despite the ambiguity. For example, if the bus number is 21 and the first wizard tells us that he’s 96 years old and has three children, then it’s true that we can’t work out the children’s ages: They might be 1, 8, and 12 or 2, 3, and 16. But when the wizard informs us of this, we can’t declare triumphantly that at last we know how old he is, because we don’t — he might be 96, but he might also be 240, with children aged 4, 5, and 12 or 3, 8, and 10. So the dialogue above cannot have taken place.

But notice that if we increase the bus number by 1, to 22, then all the math above will still work if we give the wizard an extra 1-year-old child: He might now be 96 years old with four children ages 1, 1, 8, and 12 or 1, 2, 3, and 16; or he might be 240 with four children ages 1, 4, 5, and 12 or 1, 3, 8, and 10. The number of children increases by 1, the sum of their ages increases by 1, and the product remains the same. So if bus number b produces two possible ages for Wizard A, then so will bus number b + 1 — which means that we don’t have to check any bus numbers larger than 21.

This limits the problem to a manageable size, and it turns out that the bus number is 12 and Wizard A is 48 — that’s the only age for which the bus number and the number of children do not uniquely determine the children’s ages (they might be 2, 2, 2, and 6 or 1, 3, 4, and 4).

(Tanya Khovanova, “Conway’s Wizards,” The Mathematical Intelligencer, December 2013.)

Two similar puzzles: A Curious Conversation and A Curious Exchange.

| Puzzles · Science & Math

Head Trauma

Unfortunate newspaper headlines, collected by Robert Goralski for Press Follies, 1983:

TOWN OKS ANIMAL RULE (Asheville Citizen)
TRAVIS MAN DIES AFTER ALTERATION (Sacramento Bee)
INDIAN OCEAN TALKS (The Plain Dealer)
JUVENILE COURT TO TRY SHOOTING DEFENDANT (Deseret News)
TRAIN ROLLS 0 MILES WITH NO ONE ABOARD (New York Times)
LAWMEN FROM MEXICO BARBECUE GUESTS (San Benito [Texas] News)
FLIES TO RECEIVE NOBEL PRIZE (New York Times)
CARTER TICKS OFF BLACK HELP (San Francisco Examiner)
MAULING BY BEAR LEAVES WOMAN GRATEFUL FOR LIFE (Herald-Dispatch, Huntington, W.Va.)
SILENT TEAMSTER GETS CRUEL PUNISHMENT: LAWYER (The Home News, Brunswick, N.J.)
MANCHESTER MAN BURSTS, HALTS TRAFFIC (Hartford Times)
SKELETON TIED TO MISSING DIPLOMAT (Philadelphia Evening Bulletin)
POET DOESN’T WANT AUDIENCE OF ILLERATES (Raleigh Times)
GLASS EYE IS NO HELP IN IDENTIFYING CORPSE (Deseret News)
FORMER MAN DIES IN CALIFORNIA (Freemont County [Calif.] Chronicle News)
MATH IMPROVEMENT INDICATES LEARNING IS TIED TO TEACHING (New York Times)
PAIR CHARGED WITH BATTERY (Denver Post)
TUNA RECALLED AFTER DEATH (Chicago Daily News)
TWO CONVICTS EVADE NOOSE; JURY HUNG (Oakland Tribune)
JERK INJURES NECK, WINS AWARD (Buffalo News)
TEACHERS’ HEAD GOES OFF TO JAIL (Sarasota Herald-Tribune)
SIX SENTENCED TO LIFE IN CLARKSVILLE (Nashville Banner)
POPE LAUNCHES TALKS TO END LONG DIVISION (Pomono Progress Bulletin)
A GRATEFUL NATION BURIES SAM RAYBURN (New York Herald Tribune)
SHOUTING MATCH ENDS TEACHER’S HEARING (Newsday)
DOCTOR TESTIFIES IN HORSE SUIT (Waterbury Republican)

Some are inspired: When the New York Times reported that a mansion-hunting Aristotle Onassis had visited Buster Keaton’s former estate, it chose the headline ARISTOTLE CONTEMPLATING THE HOME OF BUSTER.

| Language

Podcast Episode 52: Moving Day in New York

https://commons.wikimedia.org/wiki/File:Goethe_1791.jpg

For centuries, May 1 brought chaos to New York, as most tenants had to move on the same day, clogging the streets with harried people and all their belongings. In this episode of the Futility Closet podcast we’ll review the colorful history of “Moving Day” and wonder how it lasted through two centuries.

We’ll also recount some surprising escapes from sinking ships and puzzle over a burglar’s ingenuity.

See full show notes …

| History · Oddities · Podcast