“Travelling is one Way of lengthening Life, at least in Appearance. It is but a Fortnight since we left London; but the Variety of Scenes we have gone through makes it seem equal to Six Months living in one Place.” — Benjamin Franklin, letter to Mary Stevenson, from Paris, Sept. 14, 1767
First-Sergeant Thomas Innes Woods, of Company B, was killed on May 8th [1864]. The first time that Sergeant Woods was ever known to ask permission to leave his post on march or in battle occurred this day, after the Regiment’s all-night march to reach Spottsylvania ahead of Lee. When it became evident that a battle was imminent, Sergeant Woods asked Captain H.W. Grubbs for a pass to go to the rear. On his declaring that he was not sick, he was advised by the Captain that under the circumstances he could not be excused, and Sergeant Woods resumed his post at the head of the Company. Shortly after, during a halt by the roadside, Sergeant Woods wrote in his diary the following, addressed to his friend, Sergeant James A. McMillen: ‘I am going to fall to-day. If you find my body, I desire you to bury it and mark my grave so that if my friends desire to take it home they can find it. Please read the Ninetieth Psalm at my burial.’ He was killed early in the battle. His body was found by Sergeant McMillen and others of Company B, the diary being found in his pocket. His request for the Ninetieth Psalm to be read at the grave was complied with.
— Charles F. McKenna, ed., Under the Maltese Cross, Antietam to Appomattox: The Loyal Uprising in Western Pennsylvania, 1861-1865: Campaigns 155th Pennsylvania Regiment, 1910
In Pale Fire, Nabokov notes an “absolutely extraordinary, unbelievably elegant” verbal curiosity:
A newspaper account of a Russian tsar’s coronation had, instead of korona (crown), the misprint vorona (crow), and when next day this was apologetically ‘corrected,’ it got misprinted a second time as korova (cow).
“The artistic correlation between the crown-crow-cow series and the Russian korona–vorona–korova series is something that would have, I am sure, enraptured my poet,” he wrote. “I have seen nothing like it on lexical playfields and the odds against the double coincidence defy computation.”
In 1943, fed up with modernist poetry, two Australian servicemen invented a fake poet and submitted a collection of deliberately senseless verses to a Melbourne arts magazine. To their delight, they were accepted and their author hailed as “one of the most remarkable and important poetic figures of this country.” In this week’s episode of the Futility Closet podcast we’ll tell the story of the Ern Malley hoax, its perpetrators, and its surprising legacy in Australian literature.
We’ll also hear a mechanized Radiohead and puzzle over a railroad standstill.
Canada’s “victory nickel,” struck from 1943 to 1945, included a special message to stimulate the war effort: Engraved around the rim were the words WE WIN WHEN WE WORK WILLINGLY in Morse Code.
The coin was reissued in 2005 to commemorate the 60th anniversary of V-E Day.
Princeton mathematician John Horton Conway investigated this curious permutation:
3n ↔ 2n
3n ± 1 ↔ 4n ± 1
It’s a simple set of rules for creating a sequence of numbers. In the words of University of Calgary mathematician Richard Guy, “Forwards: if it divides by 3, take off a third; if it doesn’t, add a third (to the nearest whole number). Backwards: if it’s even, add 50%; if it’s odd, take off a quarter.”
If we start with 1, we get a string of 1s: 1, 1, 1, 1, 1, …
If we start with 2 or 3 we get an alternating sequence: 2, 3, 2, 3, 2, 3, …
If we start with 4 we get a longer cycle that repeats: 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, …
And if we start with 44 we get an even longer repeating cycle: 44, 59, 79, 105, 70, 93, 62, 83, 111, 74, 99, 66, 44, …
But, curiously, these four are the only loops that anyone has found — start with any other number and it appears you can build the sequence indefinitely in either direction without re-encountering the original number. Try starting with 8:
…, 72, 48, 32, 43, 57, 38, 51, 34, 45, 30, 20, 27, 18, 12, 8, 11, 15, 10, 13, 17, 23, 31, 41, 55, 73, 97, …
Paradoxically, the sequence climbs in both directions: Going forward we multiply by 2/3 a third of the time and by roughly 4/3 two-thirds of the time, so on average in three steps we’re multiplying by 32/27. Going backward we multiply by 3/2 half the time and by roughly 3/4 half the time, so on average in two steps we’re multiplying by 9/8. And every even number is preceded by a multiple of three — half the numbers are multiples of three!
What happens to these chains? Will the sequence above ever encounter another 8 and close up to form a loop? What about the sequences based on 14, 40, 64, 80, 82 … ? “Again,” writes Guy, “there are many more questions than answers.”
(Richard K. Guy, “What’s Left?”, Math Horizons 5:4 [April 1998], 5-7; and Richard K. Guy, Unsolved Problems in Number Theory, 2004.)
When Danish naval officer Gustav Holm was exploring the eastern coast of Greenland in 1885, an Inuit named Kunit gave him this three-dimensional wooden map.
The two parts form one whole: The bottom carving represents the coast from Sermiligak to Kangerdlugsuatsiak, and the top is an island offshore. The Inuit would carry these maps in their kayaks to navigate the waters between the two landmasses.
(From David Turnbull, Maps Are Territories, 1989.)
In Sam Peckinpah’s 1977 World War II film Cross of Iron, a soldier hears a rumbling noise, peers out of his trench, and shouts “Tanks! Tanks!”
The French subtitles read, “Merci, merci!”
Where is a sound? If I play a note at the piano, you and I both seem to locate it at the instrument. But we both also know that we perceive the note because the piano sends waves through the air that strike our ears. That would mean that most of our auditory perception is illusion. Is that what we want to say?
Philosopher George Berkeley wrote, “When I hear a coach drive along the streets, immediately I perceive only the sound, but from experience I have had that such a sound is connected with a coach, I am said to hear the coach.” Perhaps the sound lies at our ears, or at our sensation of it, and it’s only our experience of the world that leads us to attribute it to some remote source. But that raises problems of its own. If sound is sensation, then can a sound occur if no one is present to hear it?
Perhaps the answer lies in between: Acoustics tells us that sounds are vibrations transmitted by the air. But vibrations of very high or low pitch aren’t perceptible to human ears. Are these still sounds?
Just an oddity — in Nature, June 5, 1919, Cambridge zoologist John Stanley Gardiner notes that a Fiji harbormaster had informed him of a saltwater crocodile that had landed alive on Rotuma, 260 miles to the north and 600 miles east of the New Hebrides.
“It certainly did not come from Fiji or any lands to the east, as crocodiles do not now exist on them,” Gardiner wrote. “It must indeed have crossed from the west, and covered at least 600 miles of open, landless sea.
“This occurrence is sufficiently remarkable to be placed on permanent record.”