In a Word

https://commons.wikimedia.org/wiki/File:1815-regency-proposal-woodcut.gif

agamy
n. absence of marriage; the state or condition of being unmarried

viripotent
adj. (of a woman) physically fit for marriage

affidation
n. sworn confirmation of one’s intent to marry

deuterogamy
n. marriage a second time

Pascal’s Primes

In Pascal’s triangle, each number is the sum of the two immediately above it:

https://commons.wikimedia.org/wiki/File:Pascaltriangle2.PNG

In 1972, Henry Mann and Daniel Shanks found a curious connection between the triangle and prime numbers. Stagger the triangle’s rows so that row n starts at column 2n:

pascal prime table

Now a column number is prime precisely when the numbers in that column are each divisible by their row number. For instance, in the diagram above, column 13 has two entries — 10, which is divisible by 5, and 6, which is divisible by 6 — so 13 is prime. The numbers in column 12 are not all evenly divisible by their row numbers, so 12 is not prime.

“It’s a nifty and surprising result,” writes James Tanton in Mathematics Galore! (2012), “but it is not a formula that allows us to find prime numbers with ease.”

(Henry B. Mann and Daniel Shanks, “A Necessary and Sufficient Condition for Primality, and Its Source,” Journal of Combinatorial Theory, Series A 13:1 [1972], 131-134.)

Podcast Episode 87: A Sleuthing Cabbie, Edward VI’s Homework, and a Self-Aware Crow

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

In this week’s episode of the Futility Closet podcast we’ll share seven oddities from Greg’s research, from Arthur Conan Doyle’s encounter with a perceptive Boston cabbie to a computer’s failed attempts to rewrite Aesop’s fables.

We’ll also hear boxer Gene Tunney’s thoughts on Shakespeare and puzzle over how a man on a park bench can recognize a murder at sea.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Sources for the items in this week’s episode:

Joseph Hatton, “Revelations of an Album,” in The Idler, April 1897.

Charles Dickens mentioned “MOOR EEFFOC” in an abandoned autobiography. Michael Quinion has a bit more at World Wide Words.

Albert Pierce Taylor, Under Hawaiian Skies, 1922.

“John Cazale,” IMDb (accessed 12/23/2015).

Ed Zern reviewed Lady Chatterley’s Lover for Field & Stream in November 1959.

John Strype, Ecclesiastical Memorials, Relating Chiefly to Religion, and the Reformation of It, 1822.

Noel Williams and Patrik Holt, Computers and Writing: Models and Tools, 1989.

Listener mail:

“Yale Students Hear Tunney,” Ottawa Citizen, April 24, 1928.

“Lauds Gene Tunney,” Lewiston [Maine] Daily Sun, July 11, 1929.

This week’s lateral thinking puzzle is from Jed’s List of Situation Puzzles.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

All Aboard

https://books.google.com/books?id=sWhIAAAAYAAJ&pg=PA225

Two more railway oddities. When the local railroad closed its branch, the port of Thames Haven, in southeastern England, devised a trolley driven by the wind. “With a good breeze a speed of from twenty to twenty-five miles an hour can be attained with perfect safety,” reported The Railway Magazine in September 1905. “As can be seen by the photograph, the trolley is an ordinary one, such as are in common use by plate-layers on the railway.”

The second idea is even more dramatic — from Railway World, June 1, 1906:

Despatches from Geneva state that an Austrian engineer, Herr Balderauer, of Salzburg, has been experimenting with much success in the mountains near Salzburg with a novel balloon railway. It consists of a large captive balloon attached to a single steel rail, which in turn is fixed firmly to the side of a steep mountain, whose precipitous slopes no other form of railway could climb without making a series of serpentine detours and passing through tunnels. The balloon remains balanced in the air about ten yards above the rail to which it is attached by a stout wire cable, and it is moved up and down the side of the mountain at the will of the engineer. For an ascent the balloon itself furnishes the lifting force by means of hydrogen; for the descent a large reservoir attached to the balloon is filled with water at the highest station, and serves as ‘ballast.’ Under the balloon is a circular car, seating ten persons. The wire cable from the balloon passes through the floor of the car to a speed regulator underneath, which is controlled by the engineer.

I gather this was actually built, but I haven’t been able to find an image. I’ll keep looking.

12/29/2015 UPDATE: Evidently the balloon system was devised by Salzburg engineers named Balderauer and Brockebusch, who called it the Gebirgsbahn. A reader found this image in Illustrirte Zeitung, Sept. 30, 1897:

https://books.google.com/books?id=SnY5AQAAMAAJ&dq=%22eine%20neue%20gebirgsbahn%22%20ballon%20OR%20ballast&pg=PA448&ci=361%2C30%2C610%2C950&source=bookclip#v=onepage&q&f=true

A “strong rope” connected the balloon to the running gear through a large opening in the “wreath-shaped” passenger car. The water reservoir, which could be filled to different heights according to the expected wind strength, was attached to the running gear, with a mechanism for the operator to release water as needed. The railway had a planned capacity of 1500 kg for passengers and aeronauts, and was to include a hangar for storing the balloon during windstorms, during which the operators planned to suspend service.

The inventors took a “small-scale proof-of-concept trip” in 1896, which they deemed “quite satisfactory,” and construction was scheduled for the following spring. In August 1901 New Zealand’s Feilding Star reported that “Not a single accident has occurred during three months of experiments, and the system is without any danger,” but we don’t find any mention of it after that.

(Thanks, Derek and Stephan.)

Buzz Off

https://patents.google.com/patent/US144792A/en

Mosquito nets will keep insects off you during sleeping hours, but you’re left to fend for yourself during the day. Boston inventor Thomas Prentiss offered this improvement in 1873, so you can get some exercise in fly-plagued regions and ward off sunstroke as well:

This, my invention, consists in an umbrella, sun-shade, or similar article covered with suitable gauze or netting. To the lower edge of the sun-shade, umbrella, &c., is secured a similar netting of ample dimensions, so that one or more persons can be protected under it. The height of the netting may be made so that the lower edge thereof shall reach the ground when the person who carries it is standing.

The handle can be placed in a socket in a chair or settee, or you can stroll around with it. And the whole thing folds up like an umbrella when you’re not using it. The hat, I suppose, is optional.

Lofty Sentiments

https://books.google.com/books?id=K2XVAAAAMAAJ&pg=PA144

The first marriage ever celebrated in a balloon was held on Oct. 19, 1874, between Mary Elizabeth Walsh and Charles M. Colton, two performers in P.T. Barnum’s Roman Hippodrome in Cincinnati. Fifty thousand people watched as the “monster balloon” P.T. Barnum, trimmed with flags and flowers and “full almost to bursting with the best of gas,” carried the wedding party a mile above Lincoln Park, where minister Howard Jeffries performed the ceremony and made the following remarks:

Marriage is not an earthly but a heavenly institution, belonging to the higher realms of life, and as such is it revered by the enlightened; the greater the enlightenment of any country or community the greater the respect it accords marriage; as an institution above those of the world, merely, it is, then, most fitting that its solemnization should be celebrated far above the earth.

May you, whose life-destinies have been joined together at this altitude, be always lifted above the adversities of life. Hence you look down upon the multitudes below, who appear as pigmies from your elevation, and you see that the sun is fast going down upon them; shadows lengthen and darkness will quickly enwrap them. Upon you the sun shines with greater brilliancy than we have seen it at any time to-day; so may it be in life, and you be exempt from shadows and darkness, though you see them fall upon others. As you here serenely float above the hills, the rocks and the roughness below, so may your united destinies bear you above the rugged places of life; may you have no hills of sorrow to scale, no valley of adversity to pass through, no rock of passion to stumble upon, no treacherous ditch of contention to fall into.

Soon we shall all descend to earth, as we must shortly all go down to the grave. As upon leaving this vessel you two will pass forward in company while you live, so, when you have both crossed to ‘that bourn from whence no traveler returns,’ may your united souls in company explore the glorious paradise of God’s redeemed.

He left them with this certificate:

https://books.google.com/books?id=K2XVAAAAMAAJ&pg=PA144

(From History of Donaldson’s Balloon Ascensions, 1875.)

The Keyhole

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Draw circles C1 and C2 with the common chord PQ. Now choose a point A on the arc of C1 that’s outside of C2 and project it through P to B and through Q to C.

Surprisingly, the length of BC remains the same no matter where A is chosen on its arc of C1.

A Southern Education

Sentence completion exercises from Levi Branson’s First Book in Composition, 1863:

_______ is a Confederate State.

Gen. _______ reduced Fort Sumter.

South Carolina is the greatest _______ country in the Confederate States.

Louisiana raises more _______ than any other State in the Confederacy.

Abraham Lincoln led _______ people into war.

Jefferson Davis defended _______ country bravely, and deserves great applause for _______ patriotism.

General Stuart _______ started in pursuit; he _______ overtook the enemy, _______ led on the attack in person, and gained a complete victory.

General Lee defeated the Yankees, _______ his army was much smaller _______ theirs.

I saw the Confederate flag _______ from the City Hall.

From Marinda Branson Moore’s Dixie Speller, 1864:

It makes us sad to hear the booming of cannon in time of war. We think of our dear friends who are in the army, and fear they may be killed.

War is a sad thing, and those who bring it about will have much to answer for.

Some people lay all the blame at the door of the rulers of the nation. In some countries this is true, but in our country it is not so. The people elect their own rulers, and they should not choose bad men. If the rulers in the United States had been good Christian men, the present war would not have come upon us.

The people sent bad men to Congress, and they were not willing to make just laws, but were selfish, and made laws to suit themselves.

The Bible says “When the wicked bear rule the nation mourneth, but when the righteous are in authority, the people rejoice.”

People often do wrong, and when trouble comes upon them, they say God sent it.

God has made good laws for man, and if we do right we will be happy; but sin will always bring trouble.

Let every boy learn this lesson, and when he is a man, let him not vote for a bad man to fill an office of trust. — Then the men who wish to be in office will strive to be good, and the nation will be happy.