Say Red

https://commons.wikimedia.org/wiki/Category:OpenClipart_ornamental_playing_cards

Cornell mathematician Robert Connelly devised this intuition-defying card game. I shuffle a standard deck of 52 cards and deal them out in a row before you, one at a time. At some point before the last card is dealt, you must say the word “red.” If the next card I deal is red, you win $1; if it’s black you lose $1. If you play blind, your chance of winning is 1/2. Can you improve on this by devising a strategy that considers the dealt cards?

Surprisingly, the answer is no. Imagine a deck with two red cards and two black. Now there are six equally likely deals:

RRBB
RBBR
BBRR
RBRB
BRBR
BRRB

By counting, we can see that the chance of success remains 1/2 regardless of whether you call red before the first, second, third, or fourth card.

Trying to outsmart the cards doesn’t help. You might resolve to wait and see the first card: If it’s black you’ll call red immediately, and if it’s red you’ll wait until the fourth card. It’s true that this strategy gives you a 2/3 chance of winning if the first card is black — but if it’s red then it has a 2/3 chance of losing.

Similarly, it would seem that if the first two cards are black then you have a sure thing — the next card must be red. This is true, but it will happen only once in six deals; on the other five deals, calling red at the third card wins only 2/5 of the time — so this strategy has an overall success rate of (1/6 × 1) + (5/6 × 2/5) = 1/2, just like the others. The cards conspire to erase every seeming advantage.

The same principle holds for a 52-card deck, or indeed for any deck. In general, if a deck has r red cards and b black ones, then your chance of winning, by any strategy whatsoever, is r/(b + r). Seeing the cards that have already been dealt, surprisingly, is no advantage.

(Robert Connelly, “Say Red,” Pallbearers Review 9 [1974], 702.)

| Science & Math

Unquote

https://commons.wikimedia.org/wiki/File:Phillip_Roth_-_1973.jpg

“It is only through fiction that facts can be made instructive or even intelligible.” — George Bernard Shaw

“People think that because a novel’s invented, it isn’t true. Exactly the reverse is the case. Biography and memoirs can never be wholly true, since they cannot include every conceivable circumstance of what happened. The novel can do that.” — Anthony Powell

“I write fiction and I’m told it’s autobiography, I write autobiography and I’m told it’s fiction, so since I’m so dim and they’re so smart, let them decide what it is or it isn’t.” — Philip Roth

| Literature · Quotations

The Bird Cage

https://docs.google.com/viewer?url=patentimages.storage.googleapis.com/pdfs/US200358.pdf

In the 1870s baseball catchers played bare-faced, routinely suffering broken noses and teeth; to protect themselves they stood two dozen feet behind the batter, which prevented the pitcher from throwing his best pitches. Finally Fred Winthrop Thayer, captain of Harvard’s team, invented a “Safety-Mask for Base-Ball Players” to minimize the damage.

“It is not an unfrequent occurrence in the game of base-ball for a player to be severely injured in the face by a ball thrown against it,” he wrote in the patent application. “With my face-guard such an accident cannot happen.”

When catcher Jim Tyng first wore Thayer’s mask on April 12, 1877, it was roundly derided. Spectators yelled “Mad dog!” and “Muzzle ’em!”, and opposing players greeted Tyng with “good natured though somewhat derisive pity.” The Portland, Maine, Sunday Telegram wrote, “There is a great deal of beastly humbug in contrivances to protect men from things which do not happen. There is about as much sense in putting a lightning rod on a catcher as there is a mask.”

Catchers finally submitted when sportwriter Henry Chadwick faulted their “moral courage.” “Plucky enough to face the dangerous fire of balls from the swift pitcher,” he wrote, “they tremble before the remarks of the small boys of the crowd of spectators, and prefer to run the risk of broken cheek bones, dislocated jaws, a smashed nose or blackened eyes, than stand the chaff of the fools in the assemblage.”

Today Thayer’s Harvard mask is in the National Baseball Hall of Fame.

| Entertainment · Technology

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:

  • In Myles Coverdale’s 1535 Bible, Psalm 91:5 read “Thou shall not nede to be afrayed for eny bugges by night” (rather than terror).
  • 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