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Tilt

https://commons.wikimedia.org/wiki/File:Chinese_pythagoras.jpg

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.”

| Science & Math

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.

| Oddities

Podcast Episode 360: Haggard’s Dream

https://commons.wikimedia.org/wiki/File:Henry-Rider-Haggardmw56986.jpg

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 …

| Death · History · Literature · Oddities · Podcast

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.”

| Art · History · Society

All Out

https://commons.wikimedia.org/wiki/File:TaikyokuShogiSente.svg
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.)

| Entertainment

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
| Puzzles

Podcast Episode 357: Scenes From an Earthquake

https://commons.wikimedia.org/wiki/File:Aftermath_of_San_Francisco_earthquake,_1906.jpg

The San Francisco earthquake of 1906 is remembered for its destructive intensity and terrible death toll. But the scale of the disaster can mask some remarkable personal stories. In this week’s episode of the Futility Closet podcast we’ll describe the experiences of some of the survivors, which ranged from the horrific to the surreal.

We’ll also consider a multilingual pun and puzzle over a deadly reptile.

See full show notes …

| History · Podcast

Coincidence

In the 1960s, linguist Robert M.W. Dixon met Albert Bennett, one of the last native speakers of Mbabaram, a vanishing Australian Aboriginal language of north Queensland. “You know what we call ‘dog’?” Bennett said to him. “We call it dog.”

“My heart sank,” Dixon wrote. “He’d pronounced it just like the English word, except that the final g was forcefully released.” He worried that Bennett’s decades of using English had tainted his understanding of Mbabaram.

But Bennett’s assertion was accurate: The Mbabaram word for dog is dúg, which is pronounced nearly identically to the English word, “a one in a million accidental similarity of form and meaning in two unrelated languages,” Dixon wrote.

“It was because this was such an interesting coincidence, that Albert Bennett had thought of it as the first word to give me.”

(Robert M.W. Dixon, Searching for Aboriginal Languages: Memoirs of a Field Worker, 1984.)

| Language

The Billups Neon Crossing Signal

After numerous accidents where the Illinois Central Railroad crossed Highway 7 near Grenada, Mississippi, in the 1930s, inventor Alonzo Billups came up with a one-of-a-kind solution. When a train approached the crossing, motorists were confronted with a lighted skull and crossbones, the glowing words “Stop-DEATH-Stop,” flashing neon arrows indicating the train’s direction, and an air raid siren.

The video here is a simulation; the actual gantry was removed due to a scarcity of neon in the war years. But two photographs survive.

| Death · Oddities · Technology