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“Opus 34″

A magic square by Lee Sallows. The 16 pieces progress in area from 1 to 16, and those in each row, column, and long diagonal can be assembled to form the same target shape with area 34.

Science, Fiction

Inspired by Jules Verne’s Twenty Thousand Leagues Under the Sea, marine engineer Simon Lake devoted himself to making a working practical submarine. In 1898, when his company built the first sub to operate successfully in the open sea, Verne sent a congratulatory telegram:

WHILE MY BOOK ‘TWENTY THOUSAND LEAGUES UNDER THE SEA’ IS ENTIRELY A WORK OF IMAGINATION, MY CONVICTION IS THAT ALL I SAID IN IT WILL COME TO PASS. A THOUSAND MILE VOYAGE IN THE BALTIMORE SUBMARINE BOAT IS EVIDENCE OF THIS. THIS CONSPICUOUS SUCCESS OF SUBMARINE NAVIGATION IN THE UNITED STATES WILL PUSH ON UNDER-WATER NAVIGATION ALL OVER THE WORLD. IF SUCH A SUCCESSFUL TEST HAD COME A FEW MONTHS EARLIER IT MIGHT HAVE PLAYED A GREAT PART IN THE WAR JUST CLOSED. THE NEXT GREAT WAR MAY BE LARGELY A CONTEST BETWEEN SUBMARINE BOATS.

Bonus fact: The “20,000 leagues” in Verne’s title refers to the distance of the Nautilus’ voyage, not its depth. The sea is only about 2 miles deep; 20,000 leagues is nearly 70,000 miles.

In a Word

http://commons.wikimedia.org/wiki/File:Otterness_CR022.jpg

immiserization
n. the act of making or becoming progressively more miserable

luctiferous
adj. bringing sorrow, mournful, gloomy

Carry On

Letter to the Times, Feb. 6, 1946:

Sir,

I have just written you a long letter.

On reading it over, I have thrown it into the waste paper basket.

Hoping this will meet with your approval,

I am, Sir,

Your obedient Servant,

A.D. Wintle

Passing Through

http://commons.wikimedia.org/wiki/File:Mystery_airship_SFCall_Nov_19_1896.jpg

November 1896 saw the start of a strange wave of airship sightings across the United States — the San Francisco Call published the image above on Nov. 19, claiming that the craft had passed over eastern Sacramento the previous night, where hundreds had seen “its brilliant searchlight traveling over the city, and who will also swear that they heard the voices of its occupants and distinguished their merry song and laughter.”

In the frenzy that followed, the San Francisco Chronicle published an interview with attorney George D. Collins, who claimed that he represented the airship’s inventor, a wealthy Maine man who had spent 17 years and $100,000 perfecting the craft. “The reports from Sacramento the other night were quite true. It was my client’s ship that inhabitants saw. It started from Oroville, in Butte County, and flew in a straight line for sixty miles directly over Sacramento. After running up and down once or twice over the capital, my friend came on a distance of another seventy miles and landed on a spot on the Oakland side of the bay, where the ship now lies guarded by six men. In another six days several defects will be done away with and it is then his intention to fly right over San Francisco.”

That never happened, and Collins was quickly forgotten, but it’s interesting to note that 10 years earlier, in 1886, inventor Moses Cole had patented a strikingly similar “new and improved aerial vessel” (below). “It consists of two semi-spheroidal balloons,” Scientific American had reported, “between which are situated the cabins for the passengers and crew, these being fitted with windows and surrounded by a circular balcony.” Possibly the Call’s artist had used Cole’s patent for inspiration. Or possibly Collins was telling the truth. Or possibly Martians had adopted Cole’s design as a disguise. We’ll never know.

http://commons.wikimedia.org/wiki/File:Cole_Air_Vessel_1897.jpg

See Just Visiting.

The Suicidal King

Imagine a 1000 x 1000 chessboard on which a white king and 499 black rooks are placed at random such that no rook threatens the king. And suppose the king goes bonkers and wants to kill himself. Can he reach a threatened square in a finite number of moves if Black is trying actively to avoid this?

Click for Answer

Cameo

http://commons.wikimedia.org/wiki/File:Gioacchino_Pagliei_-_The_Naiads,_1881.JPG

The last canto of Dante’s Purgatorio contains this perplexing sentence:

And if perchance
My saying, dark as Themis or as Sphinx,
Fail to persuade thee, (since like them it foils
The intellect with blindness) yet ere long
Events shall be the Naiads, that will solve
This knotty riddle, and no damage light
On flock or field.

When did water nymphs solve the riddle of the Sphinx? It turns out that Dante was relying on a flawed medieval edition of Ovid’s Metamorphoses that rendered Laïades (meaning Oedipus, the son of Laius) as Naïades, or naiads. He believed that water nymphs had ridden their sea monsters across the desert to solve the Sphinx’s riddle.

The version of the story that we know, in which Oedipus solves the riddle, comes from Sophocles’ Oedipus, which, being written in Greek, was unavailable to Dante. And he cast his own version in such exquisite language that it’s now immortal — one classic work misquoting another.

(Thanks, Jim.)

Pi Without Circles

The sum of the squares of the reciprocals of the positive integers is π2/6.

The sum of their fourth powers is π4/90.

The sum of their sixth powers is π6/945.

The area of the region under the Gaussian curve y = e-x2 is the square root of π.

The probability that two integers chosen at random will have no prime factor in common is 6/π2.

The integer 8 can be written as the sum of two squares of integers, m2 + n2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2). The integer 7 can’t be written at all as the sum of such squares. Over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why?

Unquote

http://www.archives.gov

“Mr. Hoover, if you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you and you have to battle with only one of them.” — Calvin Coolidge, to Herbert Hoover

Podcast: Episode 2

As skywatchers prepared for the return of Halley’s comet in 1910, they heard some alarming scientific predictions: Poisonous gases in the comet’s tail might “snuff out all life on the planet,” “leaving the burnt and drenched Earth no other atmosphere than the nitrogen now present in the air.” How should a responsible citizen evaluate a dire prediction by a minority of experts? In this week’s episode of the Futility Closet podcast, we explore the Halley’s hysteria, remember the alarming predictions made for Y2K, and recall a forgotten novella in which Arthur Conan Doyle imagined a dead Earth fumigated by cosmic ether.

We also consider the odd legacy of an Australian prime minister who disappeared in 1967, investigate the role of balloon-borne sheepdogs during the Siege of Paris, learn why Mark Twain’s brother telegraphed the entire Nevada constitution to Washington D.C. in 1864, and offer a chance to win a book in the next Futility Closet Challenge.

You can listen using the player above, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset. The show notes are on the blog, where you can also enter your submissions in this week’s Challenge. Many thanks to Doug Ross for the music in this episode.

Next week we plan to discuss the sad, enigmatic tale of Lillian Alling, an immigrant who grew disenchanted with New York and decided to walk home to Siberia; explore the curious significance of October 4 to Samuel Taylor Coleridge; and offer a new Futility Closet Challenge. If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

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