Foregone Conclusions

Here’s the opening of Alice’s Adventures in Wonderland:

Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do; once or twice she had peeped into the book her sister was reading.

Choose any of the first 12 words and tap your way forward in the sentence from that point, tapping one word for each letter. So, for example, if you choose the word Alice, which has five letters, you’d tap was, beginning, to, get, and land on very. Then do the same thing with that word, advancing four letters to land on by. If you keep this up you’ll always arrive at the word sister.

That’s from Martin Gardner; the same trick works with “Twinkle, Twinkle, Little Star,” the opening of the Bible, and countless other texts.

It’s less surprising than it seems — it’s based on a principle called the Kruskal count, proffered originally by Rutgers physicist Martin Kruskal as a card trick. In each case various tributaries merge into a common stream that arrives at a predictable destination. Here’s an analysis (PDF).

February 6, 2016February 5, 2016 | Science & Math

The Dark Side

In a certain chess position, each row and each column contains an odd number of pieces. Prove that the total number of pieces on black squares is an even number.

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As usual in chess, let the bottom left-hand square be black. If we number the rows from the bottom and the columns from the left, then every black square is either in an odd-numbered row or an even-numbered column. That is, all the black squares can be found in rows 1, 3, 5, 7 and columns 2, 4, 6, 8. Let the black squares in rows 1, 3, 5, 7 be marked A and the black squares in columns 2, 4, 6, 8 be marked B, and let the white squares in rows 1, 3, 5, 7 be marked C. Leave the rest of the white squares unmarked. Finally, let a, b, c denote the total number of pieces that sit on squares marked A, B, C, respectively. We want to show that a + b is an even number. Each row contains an odd number of pieces. That means that a + c, the total number of pieces in rows 1, 3, 5, 7, is the sum of four odd numbers, which means it’s even. Likewise, b + c, the total number of pieces in columns 2, 4, 6, 8, is also the sum of four odd numbers and thus even. So (a + c) + (b + c) = a + b + 2c is even, and this implies that a + b is even. (From V. Proizvolov, “Problems Teaching Us How to Think,” Quantum, January-February 2002, via Ross Honsberger’s Mathematical Delights, 2004.)

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February 5, 2016February 14, 2016 | Puzzles

Right of Way

slippers and roosevelt

Theodore Roosevelt’s friend Jacob A. Riis remembers an encounter with Slippers, the White House cat, during a state dinner in 1906:

The dinner was over, and the President, with the wife of a distinguished Ambassador on his arm, led the procession from the state dining-room along the wide corridor to the East Room at the other end of the building, the ambassadors and plenipotentiaries and ministers following, according to their rank in the official world, all chatting happily with their ladies, seeing no cloud on the diplomatic horizon; when all of a sudden the glittering procession came to a halt. There, on the rug, in the exact middle of the corridor, lay Slippers, stretched at full length, and blinking lazily at the fine show which no doubt he thought got up especially to do him honor. The President saw him in time to avoid treading on him, and stopped. His first impulse was to pick Slippers up, but a little shiver of his lady and a half-suppressed exclamation, as he bent over the cat, warned him that she did not like cats, or was afraid, and for a moment he was perplexed. Slippers, perceiving the attention bestowed on him, rolled luxuriously on the rug, purring his delight. No thought of moving out of the path was in his mind.

There was but one other thing to do, and the man who found a way to make peace between Russia and Japan, did it quickly. With an amused bow, as if in apology to the Ambassadress, he escorted her around Slippers, and kept on his way toward the East Room. Whereupon the representatives of Great Britain, and of France, of Germany, and Italy, of all the great empires and of the little kingdoms clear down to the last on the long list, followed suit, paying their respects to Slippers quite as effectually as if the war-ships of their nations had thundered out a salute at an expenditure of powder that would have kept a poor man comfortable for a year, and certainly have scared even a White House cat almost to death.

(From St. Nicholas, January 1908.)

February 4, 2016 | History

Storm Warning

How do you design a burglar alarm for people who can’t hear? Arnold Zukor came up with this solution in 1912 — when the burglar opens a door or window, a system of racks and gears opens a faucet and sprays the occupant through a nozzle mounted over the bed. “Alarm is thus given.”

If you leave your house during the day, you can disable the door alarm and direct the nozzle outside. Then if the window is opened, the flow of water will be visible from a distance, “indicating thereby the entrance of unauthorized persons into the building.”

February 4, 2016February 3, 2016 | Technology

Unquote

Further excerpts from the notebooks of English belletrist Geoffrey Madan (1895-1947):

“Worldly faces never look so worldly as at a funeral.” — George Eliot

Wit is a new and apt relation of ideas: humour, of images.

Use of words “vision” and “supremely” an infallible sign of the uneducated.

“No great country was ever saved by good men, because good men will not go the length that may be necessary.” — Horace Walpole

“Precautions are always blamed. When successful, they are said to be unnecessary.” — Benjamin Jowett

“Some speak and write as if they wanted to say something: others as if they had something to say.” — Archbishop Richard Whately

“A rose has no back.” — Chinese reply if you apologize for turning your back

Reasonable to ask young people to be adventurous, to go to the North Pole, say: but religion asks them to start off, without being sure if there is a North Pole.

Three pieces of earnest advice from the Revd. H.J. Bidder, aged 86, after sitting silent, with a crumpled face, all through dinner, and once loudly asking the man opposite who I was:

1. Never drink claret in an East wind.
2. Take your pleasures singly, one by one.
3. Never sit on a hard chair after drinking port.

February 3, 2016 | Quotations

Grist

A few adventures of Dashiell Hammett, who worked for the Pinkerton Detective Agency before turning to fiction:

“I know a man who once stole a Ferris-wheel.”
“I was once engaged to discharge a woman’s housekeeper.”
“I was once falsely accused of perjury and had to perjure myself to escape arrest.”
“A man whom I was shadowing went out into the country for a walk one Sunday afternoon and lost his bearings completely. I had to direct him back to the city.”
“Three times I have been mistaken for a Prohibition agent, but never had any trouble clearing myself.”
“I know an operative who while looking for pickpockets at the Havre de Grace race track had his wallet stolen. He later became an official in an Eastern detective agency.”
“I know a detective who once attempted to disguise himself thoroughly. The first policeman he met took him into custody.”
“In 1917, in Washington, D.C., I met a young woman who did not remark that my work must be very interesting.”
“The chief of police of a Southern city once gave me a description of a man, complete even to a mole on his neck, but neglected to mention that he had only one arm.”

Interestingly, he notes that “the chief difference between the exceptionally knotty problem confronting the detective of fiction and that facing the real detective is that in the former there is usually a paucity of clues, and in the latter altogether too many.”

(“From the Memoirs of a Private Detective,” The Smart Set, March 1923.)

February 3, 2016February 1, 2016 | Crime · Literature

Lost in Translation

In January 1968, North Korea captured the American spy vessel Pueblo and held 82 crew members captive for 11 months. During the crisis, the North Korean government released the photo above, claiming that the Americans were apologetic and cooperating with their captors.

The Americans managed to send a different message — three of them are extending their middle fingers. They had told the Koreans this was a “Hawaiian good luck sign.”

Commander Lloyd M. Bucher found a way to accomplish the same thing verbally — he wrote the confession “We paean the DPRK [North Korea]. We paean their great leader Kim Il Sung.”

February 2, 2016February 1, 2016 | History · Language

Personal Warmth

Mark Levi notes an interesting coincidence in Why Cats Land on Their Feet (2012): Dividing normal human body temperature (in Celsius) into 100 approximates e:

$\displaystyle \frac{100}{36.8^\circ}\approx e$

“The estimate will be on the low side if you run a fever, or on the high side if you have hypothermia,” Levi writes. “This observation makes the natural logarithm — the one with the base e — seem even more natural.”

February 1, 2016 | Science & Math

Podcast Episode 92: The Forgotten Amendment

In 1982, college sophomore Gregory Watson got a C on a term paper arguing that a long-forgotten constitutional amendment could still be ratified. In this week’s episode of the Futility Closet podcast we’ll follow his 10-year mission to prove his professor wrong and get the amendment added to the Constitution.

We’ll also learn an underhanded way to win a poetry contest and puzzle over how someone can murder a corpse.

See full show notes …

February 1, 2016October 19, 2017 | History · Podcast

Last Wishes

British Army gunner Frank Bracey wrote this letter to his wife in May 1916 and left it to be opened in the event of his death:

Dearest Win

I am writing just a line Win in case of accidents. Just to let you know how I have always loved you Dear. You are the best little girl on God’s earth have I told you before. But I am writing this because I have a feeling that I shall not come back again. I have most of your letters in this box Dear and I wish you to have them and the cards. You may think I am a bit taped writing this dear but I cannot help it. If I do come back dearest you will never see this letter but I have a strong feeling that I shall never see England again. In case I do pop under the earth I want you to be happy and look out for a worthier chap than your Humble, you have been every thing to me Win. I know your love is mine forever dearest but if I do not come back I wish you the best of happiness and a good husband. I know you told me what you would do for yourself if I did not return but Win for the sake of our love I wish you to be brave, it would be hard for you little girl I know, but do nothing of the kind. My last wish is that you marry a good man and to be happy and to think of your Humble now and then. I felt I must write these few lines Win but whatever happens dear just keep a stout heart and think that your Frank did his bit for the women of this little isle. I expect you will think your Humble crazy but I was never saner than I am now.

Frank

He was killed in Pas-de-Calais that August. He is buried at the British military cemetery at Saint-Amand.

January 31, 2016January 30, 2016 | History