Nocturne

http://www.gutenberg.org/files/11483/11483-h/11483-h.htm

Here’s an oddity: In 1882 Lewis Carroll collaborated on a song with the dreaming imagination of his friend the Rev. C.E. Hutchinson of Chichester. Hutchinson had told Carroll of a strange dream he’d had:

I found myself seated, with many others, in darkness, in a large amphitheatre. Deep stillness prevailed. A kind of hushed expectancy was upon us. We sat awaiting I know not what. Before us hung a vast and dark curtain, and between it and us was a kind of stage. Suddenly an intense wish seized me to look upon the forms of some of the heroes of past days. I cannot say whom in particular I longed to behold, but, even as I wished, a faint light flickered over the stage, and I was aware of a silent procession of figures moving from right to left across the platform in front of me. As each figure approached the left-hand corner it turned and gazed at me, and I knew (by what means I cannot say) its name. One only I recall — Saint George; the light shone with a peculiar blueish lustre on his shield and helmet as he turned and slowly faced me. The figures were shadowy, and floated like mist before me; as each one disappeared an invisible choir behind the curtain sang the ‘Dream music.’ I awoke with the melody ringing in my ears, and the words of the last line complete — ‘I see the shadows falling, and slowly pass away.’ The rest I could not recall.

He played the melody for Carroll, who wrote a suitable lyric of five verses. Hutchinson disclaimed writing the music, but if he didn’t … who did?

(From Stuart Dodgson Collingwood, Life and Letters of Lewis Carroll, 1898.)

11/24/2021 UPDATE: Reader Paul Sophocleous provided this MIDI file of the published music. (Thanks, Paul.)

Podcast Episode 363: The Lambeth Poisoner

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In 1891, a mysterious figure appeared on the streets of London, dispensing pills to poor young women who then died in agony. Suspicion came to center on a Scottish-Canadian doctor with a dark past in North America. In this week’s episode of the Futility Closet podcast we’ll describe the career of the Lambeth Poisoner, whose victims remain uncounted.

We’ll also consider a Hungarian Jules Verne and puzzle over an ambiguous sentence.

See full show notes …

Noc

In 1984, a diver was working in the beluga whale enclosure at San Diego’s National Marine Mammal Foundation when someone shouted “Out, out, out!” On emerging, the diver asked who had told him to exit the tank, and it turned out that the speaker was the whale itself, Noc, who had lived at the facility since his capture in 1977.

Noc’s keepers had previously heard strange sounds coming from the whale and dolphin enclosure that seemed to resemble people talking in the distance, their words just beyond the limit of comprehension. “We were sceptical at first,” neurobiologist Sam Ridgway told New Scientist. “They were definitely unlike usual sounds for a [beluga], and similar to human voices in rhythm and acoustic spectrum.”

The researchers concluded that he was indeed mimicking human speech, though Noc used his nasal tract to produce sounds, rather than a larynx, as humans do. They had only a short window in which to study the behavior: After four years Noc stopped, either because he’d reached maturity or because he’d lost interest.

Hall’s Marriage Theorem

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Suppose we have a group of n men and n women. Each of the women can find some subset of the men whom she would be happy to marry. And each of the men would be happy with any woman who will have him. Is it always possible to pair everyone off into happy marriages?

Clearly this won’t work if, for example, two of the women have their hearts set on the same man and won’t be happy with anyone else. In general, for any subset of the women, we need to be sure that they can reconcile their preferences so that each of them finds a mate.

Surprisingly, though, that’s all that’s required. So long as every subset of women can collectively express interest in a group of men at least as numerous as their own, it will always be possible to marry off the whole group into happy couples.

The theorem was proved by English mathematician Philip Hall in 1935. Another application of the same principle: Shuffle an ordinary deck of 52 playing cards and deal it into 13 piles of 4 cards each. Now it’s always possible to assemble a run of 13 cards, ace through king, by drawing one card from each pile.

Tilt

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As early as the 1st century B.C., the Chinese text Zhou Bi Suan Jing reflected the reasoning of the Pythagorean theorem, showing how to find the hypotenuse of the 3-4-5 triangle. Arrange four 3×4 rectangles around a unit square, as shown, producing a 7×7 square. The diagonals of the four rectangles produce a tilted square. Now, the area of the 7×7 square is 49, and the area of one right triangle with legs 3 and 4 is 6. So the area of the tilted square is 49 – (4 × 6), or 25. This shows that the hypotenuse of each of the right triangles is 5.

In Mathematics and the Aesthetic (2007), Nathalie Sinclair writes, “The Chinese diagram … is the same as one given by the twelfth-century Indian scholar Bhaskara, whose one-word injunction Behold! recorded his sense of awe.”

Enduring Advice

https://www.flickr.com/photos/d4vidbruce/2793646631/
Image: Flickr

During the Great Depression, Babson College founder Roger Babson commissioned unemployed stonecutters to carve inspiring inscriptions on 25 boulders in Dogtown, an abandoned settlement in Gloucester, Massachusetts:

  • COURAGE
  • IDEAS
  • HELP MOTHER
  • KINDNESS
  • LOYALTY
  • IF WORK STOPS, VALUES DECAY
  • BE ON TIME
  • GET A JOB
  • INDUSTRY
  • INITIATIVE
  • INTEGRITY
  • KEEP OUT OF DEBT
  • SAVE
  • SPIRITUAL POWER
  • STUDY
  • TRUTH
  • WORK
  • BE CLEAN
  • BE TRUE
  • PROSPERITY FOLLOWS SERVICE
  • USE YOUR HEAD
  • IDEALS
  • INTELLIGENCE
  • NEVER TRY/NEVER WIN

Babson did some of the work himself. “Another thing I have been doing, which I hope will be carried on after my death, is the carving of mottoes on the boulders at Dogtown, Gloucester, Massachusetts,” he wrote in 1935. “My family says that I am defacing the boulders and disgracing the family with these inscriptions, but the work gives me a lot of satisfaction, fresh air, exercise and sunshine. I am really trying to write a simple book with words carved in stone instead of printed paper. Besides, when on Dogtown common, I revert to a boyhood which I once enjoyed when driving cows there many years ago.”

The boulders are extant today and can be visited on a hiking trail.

Podcast Episode 360: Haggard’s Dream

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In 1904, adventure novelist H. Rider Haggard awoke from a dream with the conviction that his daughter’s dog was dying. He dismissed the impression as a nightmare, but the events that followed seemed to give it a grim significance. In this week’s episode of the Futility Closet podcast we’ll describe Haggard’s strange experience, which briefly made headlines around the world.

We’ll also consider Alexa’s expectations and puzzle over a college’s name change.

See full show notes …

Progress

https://pixabay.com/photos/australia-sydney-city-port-4338882/

Letters to the Sydney Morning Herald during the planning of the Sydney Opera House:

“Faced with the nightmare illustrated in your columns, some 25th century Bluebeard’s lair, its ominous vanes pointed skywards apparently only for the purpose of discharging guided missiles or some latter-day nuclear Evil Eye, words fail.”

— W.H. Peters, Sydney, Jan. 31, 1957

“To me, the winning design suggests some gargantuan monster which may have wandered over the land millions of years ago. It certainly is right out of place beside the dignity of the Harbour Bridge.”

— M. Rathbone, Kensington, Jan. 31, 1957

“This whale of a monument to the clever ugliness of ‘modern’ art will be a constant eyesore. Its over-finished roof with many curved surfaces all covered with white tiles will be a glaring monstrosity. Could not the suffering which it will cause be more equitably distributed by constructing the fins in such a way that they will act as giant megaphones and thus keep residents on the north supplied with the dying screams of melodramatic sopranos?”

— J.R.L. Johnstone Beecroft, Feb. 1, 1957

“With all respects to so-called modern art, I feel that the design is completely unbefitting our foreshores. Perhaps the judges had in mind the installation of a Big Dipper on the peak of the roof to help the opera company balance its budget.”

— Jack Zuber, Kingsgrove, Feb. 1, 1957

In 2003 Danish architect Jørn Utzon received the Pritzker Architecture Prize, architecture’s highest honour. The citation read, “There is no doubt that the Sydney Opera House is his masterpiece. It is one of the great iconic buildings of the 20th century, an image of great beauty that has become known throughout the world — a symbol for not only a city, but a whole country and continent.”

All Out

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Image: Wikimedia Commons

Played by Japanese priests in the 16th century, taikyoku shogi may be the largest variant of chess ever devised. Each player deploys 402 pieces of 209 types on a board of 1,296 squares to try to capture his opponent’s king(s) and prince(s).

It’s not clear precisely how it was played, but Wikipedia takes more than 10,000 words to describe one likely set of rules.

(Thanks, Alejandro.)

Made to Order

Arrange the digits 0-9 into a 10-digit number such that the leftmost n digits comprise a number divisible by n. For example, if the number is ABCDEFGHIJ, the number ABC must be divisible by 3, ABCDE must be divisible by 5, and so on.

Click for Answer