Quickie

University of Strathclyde mathematician Adam McBride recalls that in his student days a particular teacher used to present a weekly puzzle. One of these baffled him:

Find positive integers a, b, and c, all different, such that a3 + b3 = c4.

“The previous puzzles had been relatively easy but this one had me stumped,” he wrote later. He created three columns headed a3, b3, and c4 and spent hours looking for a sum that would work. On the night before the deadline, he found one: 703 + 1053 = 354.

“This shows how sad a person I was! However, I then realised also how stupid I had been. I had totally missed the necessary insight.” What was it?

Click for Answer
| Puzzles

A New Line

https://commons.wikimedia.org/wiki/File:Thomas_Stearns_Eliot_by_Lady_Ottoline_Morrell_(1934).jpg

In 1948, as T.S. Eliot was departing for Stockholm to accept the Nobel Prize, a reporter asked which of his books had occasioned the honor.

Eliot said, “I believe it’s given for the entire corpus.”

The reporter said, “And when did you publish that?”

Eliot later said, “It really might make a good title for a mystery — The Entire Corpus.”

| Literature

All Relative

1. A puzzle from J.A.H. Hunter’s Fun With Figures, 1956:

Tom and Tim are brothers; their combined ages make up seventeen years. When Tom was as old as Tim was when Tim was twice as old as Tom was when Tom was fifteen years younger than Tim will be when Tim is twice his present age, Tom was two years younger than Tim was when Tim was three years older than Tom was when Tom was a third as old as Tim was when Tim was a year older than Tom was seven years ago. So how old is Tim?

2. Another, by Sam Loyd:

“How fast those children grow!” remarked Grandpa. “Tommy is now twice as old as Maggie was when Tommy was six years older than Maggie is now, and when Maggie is six years older than Tommy is now their combined ages will equal their mother’s age then, although she is now but forty-six.” How old is Maggie?

3. According to Wirt Howe’s New York at the Turn of the Century, 1899-1916, this question inspired an ongoing national debate when it appeared in the New York Press in 1903:

Brooklyn, October 12

Dear Tip:

Mary is 24 years old. She is twice as old as Anne was when she was as old as Anne is now. How old is Anne now? A says the answer is 16; B says 12. Which is correct?

John Mahon

Click for Answer
| Puzzles

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:

  • 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