Rustic Furniture

https://en.wikipedia.org/wiki/File:1857_Seth_Kinman_and_Buchanan_chair.jpeg

In 1856 California hunter Seth Kinman made a unique gift for the new president, James Buchanan — a chair fashioned from horns that elk had shed on his farm. “This winter I killed considerable meat so I thought I would take it easy and set about to make this cheer with a view of sending it on to Washington for Old Buck,” he wrote. “After I got it finished, though, the boys up in our parts thought it enough to travel on; so I thought I would try and go on with it to Washington myself, leaving my mother and four children behind, and started with nothing but my rifle and powder horn. Nobody has yet sot in this cheer, and never shall till after the President.”

He arrived in Washington in May 1857 and presented the chair to Buchanan, who accepted it with great pleasure. “It will serve to remind me of the Californians,” he said. “They are a stamp of men that can be coaxed, but cannot be driven.” As Buchanan tried the chair, Kinman pointed out “that one fork of the antlers at the foot of the chair will make a good boot jack.” (The New York Times observes that this remark was met with “great merriment.”)

Kinman presented another elkhorn chair to Abraham Lincoln, and later a third to Rutherford Hayes. But he topped all of these in 1865 with a “bear chair” that he gave to Andrew Johnson:

https://en.wikipedia.org/wiki/File:CowbodyBearChair.jpg

“This was intended to surpass all his previous efforts, and was made from two grizzly bears captured by Seth,” writes Marshall Anspach in The Lost History of Seth Kinman. “The four legs and claws were those of a huge grizzly and the back and sides ornamented with immense claws. The seat was soft and exceedingly comfortable, but the great feature of the chair was that, by touching a cord, the head of the monster grizzly bear with jaws extended, would dart out in front from under the seat, snapping and gnashing its teeth as natural as life.”

“The chair would appall almost any one with a less firm seat than Andrew Johnson,” noted Frank Leslie’s Illustrated Newspaper, “but, putting looks aside, will, without doubt, make a warm and comfortable seat in the coming cold weather.” Johnson kept it in the White House library.

“A Brief in Rhyme”

From the Ohio Law Reporter: In 1916 a defendant filed this brief in the Court of Common Pleas in Fayette County, Ohio:

The sages of old with reason assumed
The shorter the horse the sooner he’s groomed;
And so with this case and the questions involved,
They’re exceedingly brief and speedily solved.

The plaintiff below was a broker, it seems,
And perhaps being broke, saw a fee in his dreams,
He had from one Ellis a small farm to sell
And likewise, from Strobel, a town-lot as well.

One day on the street by accident strange
He met Mr. Strobel and proposed an exchange.
He also, quite prudently, spoke of the fee
And told Brother Strobel how much it would be.

He stated both principals ought to agree
On the portion each party would pay of said fee.
“Very well,” then said Strobel, “I’ll trade for his farm,
And as for your fee, have not an alarm,

“Go straight and see Ellis, and get him to say
How much of said fee he’ll be willing to pay.”
The broker then started to see Mr. Ellis,
And now his reply Brother Ellis will tell us:

“I’ll pay just $2, and no more,” said he;
“Of the said $16 you charge as your fee.
If Strobel won’t trade upon that I’d as well
Keep my money and let the — trade go — a spell.”

Then the broker returned and reported to Strobel
Who sanctioned the terms in these words grand and noble
“$2 from 16 leaves 14 for me
And this I will pay you, to make up your fee;

“Day-after-tomorrow I’ll pay you a V
And the rest in installments — to this I agree;
Go close up the deal as soon as can be,
The sooner the better for you and for me.”

So the deal was soon closed and the deeds passed, you bet
But that “day-after-tomorrow” has never come yet
And that was the day Strobel promised to pay
That first V installment in such a sure way.

The evidence shows that when Strobel sent
The broker to see Mr. Ellis, he went
And did everything he required that he should
And tried to get Ellis to pay all he could.

And now I submit, Your Honor, to you
In absence of proof to a contrary view,
The law will presume good faith in this case
And order the broker to win in the race.

(signed) W.E. MAYNARD
Washington Court House, Ohio

“Of the result of his effort we are not informed,” reports the journal, “but it no doubt was given ‘careful consideration.'”

Through the Looking-Glass

In 2015, to celebrate the 150th anniversary of the publication of Alice’s Adventures in Wonderland, master sculptor Karen Mortillaro created 12 new sculptures, one for each chapter in Lewis Carroll’s masterpiece. Each takes the form of a table topped with an S-cylindrical mirror, with a bronze sculpture on either side. The sculpture that stands before the mirror is anamorphic, so that the curved mirror’s reflection “undistorts” it, giving it meaning:

http://rmm.ludus-opuscula.org/PDF_Files/Mortillaro_AnamorphicSculpture_49_61(4_2015)_low.pdf

“The S-cylindrical mirror is ideal for this project because it allows for the figures on one side of the mirror to be sculpted realistically, while those on the opposite side of the mirror are distorted and unrecognizable,” Mortillaro writes. “The mirror is symbolic of the parallel worlds that Alice might have experienced in her dream state; the world of reality is on one side of the mirror; and the world of illusion is on the mirror’s opposite side.”

Mortillaro’s article appears in the September 2015 issue of Recreational Mathematics Magazine.

Podcast Episode 141: Abducted by Indians, a Captive of Whites

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

In 1836, Indians abducted a 9-year-old girl from her home in East Texas. She made a new life among the Comanche, with a husband and three children. Then, after 24 years, the whites abducted her back again. In this week’s episode of the Futility Closet podcast we’ll tell the story of Cynthia Ann Parker, caught up in a war between two societies.

We’ll also analyze a forger’s motives and puzzle over why a crowd won’t help a dying woman.

Intro:

Mathematician Ernst Straus invented a shape in which a ball might bounce forever without finding a hole.

In 1874 a Massachusetts composer set the American constitution to music.

Sources for our feature on Cynthia Ann Parker:

Margaret Schmidt Hacker, Cynthia Ann Parker: The Life and the Legend, 1990.

Jack K. Selden, Return: The Parker Story, 2006.

Jan Reid, “One Who Was Found: The Legend of Cynthia Ann Parker,” in Michael L. Collins, ed., Tales of Texoma, 2005.

Jo Ella Powell Exley, Frontier Blood, 2001.

Jack C. Ramsay Jr., Sunshine on the Prairie, 1990.

George U. Hubbard, The Humor and Drama of Early Texas, 2003.

Richard Selcer, “The Robe,” Wild West 28:5 (February 2016), 60-64.

Glen Sample Ely, “Myth, Memory, and Massacre: The Pease River Capture of Cynthia Ann Parker [review],” Southwestern Historical Quarterly 115:1 (July 2011), 91-92.

Gregory Michno, “Nocona’s Raid and Cynthia Ann’s Recapture,” Wild West 23:2 (August 2010), 36-43.

Paul H. Carlson and Tom Crum, “The ‘Battle’ at Pease River and the Question of Reliable Sources in the Recapture of Cynthia Ann Parker,” Southwestern Historical Quarterly 113:1 (July 2009), 32-52.

Anne Dingus, “Cynthia Ann and Quanah Parker,” Texas Monthly 27:5 (May 1999), 226.

“Cynthia Ann Seized History,” Southern Living 25:3 (March 5, 1990), 61.

Lawrence T. Jones III, “Cynthia Ann Parker and Pease Ross: The Forgotten Photographs,” Southwestern Historical Quarterly 93:3 (January 1990), 379-384.

Rupert N. Richardson, “The Death of Nocona and the Recovery of Cynthia Ann Parker,” Southwestern Historical Quarterly 46:1 (July 1942), 15-21.

Listener mail:

Donald MacGillivray, “When Is a Fake Not a Fake? When It’s a Genuine Forgery,” Guardian, July 1, 2005.

Noah Charney, “Why So Many Art Forgers Want to Get Caught,” Atlantic, Dec. 22, 2014.

Jonathon Keats, “Masterpieces for Everyone? The Case of the Socialist Art Forger Tom Keating,” Forbes, Dec. 13, 2012.

This week’s lateral thinking puzzle was contributed by listener Paul Sophocleous, who sent this corroborating link (warning — this spoils the puzzle).

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

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation on the Support Us page of the Futility Closet website.

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!

Close Call

From reader Isaac Lubow:

In 2008 a Learjet operated by Kalitta Air was en route from Manassas, Va., to Ypsilanti, Mich., when the air traffic controller noted that the pilot’s microphone button was being pressed continuously. When he contacted the plane, the pilot told him in slow, slurred words, over the sound of audible alarms, that he was unable to maintain altitude, speed, or heading but that everything else was “A-OK.”

Euphoria is a sign of hypoxia. With the help of the pilot of a nearby aircraft, the controllers were able to understand that the Learjet had become depressurized. It turned out that the first officer had been completely unconscious, and his flailing arm had both disengaged the autopilot and keyed the microphone. The open microphone had alerted the controllers, and the need to hand-fly the plane had kept the pilot conscious and able to respond to their commands.

The pilot managed to descend from 32,000 feet to 11,000, where the crew recovered, and the plane landed safely at Detroit’s Willow Run Airport. Controllers Jay McCombs and Stephanie Bevins were awarded the Archie League Medal of Safety, and the episode is now used as a classroom teaching aid at the Civil Aerospace Medical Institute in Oklahoma City.

(From Fear of Landing. Thanks, Isaac.)

Picket Fences

https://commons.wikimedia.org/wiki/File:First_six_triangular_numbers.svg
Image: Wikimedia Commons

A triangular number is one that counts the number of objects in an equilateral triangle, as above:

1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21

Some of these numbers are palindromes, numbers that read the same backward and forward. A few examples are 55, 66, 171, 595, and 666. In 1973, Charles Trigg found that of the triangular numbers less than 151340, 27 are palindromes.

But interestingly, every string of 1s:

1
11
111
1111
11111

… is a palindromic triangular number in base nine. For example:

119 = 9 + 1 = 10
1119 = 92 + 9 + 1 = 91
11119 = 93 + 92 + 9 + 1 = 820
111119 = 94 + 93 + 92 + 9 + 1 = 7381

The pattern continues — all these numbers are triangular.

02/12/2017 UPDATE: Reader Jacob Bandes-Storch sent a visual proof:

“Given a number n in base 9, if we tack a 1 on the right, the resulting number is 9*n + 1. (By shifting over one place to the left, each digit becomes nine times its original value, and then we add 1 in the ones place.) So given a triangular number, there’s probably a way of sticking together 9 copies of it with a single additional unit to form a new triangle. Sure enough:”

bandes-storch proof 1

bandes-storch proof 2

R.I.P. Raymond Smullyan, 1919–2017

Philosopher and logician Raymond Smullyan passed away on Monday. He was 97.

From my notes, here’s a paradox he offered at a Copenhagen self-reference conference in 2002:

Have you heard of the LAA computing company? Do you know what LAA stands for? It stands for ‘lacking an acronym.’

Actually, the above acronym is not paradoxical; it is simply false. I thought of the following variant which is paradoxical — it is the LACA company. Here LACA stands for ‘lacking a correct acronym.’ Assuming that the company has no other acronym, that acronym is easily seen to be true if and only if it is false.

Small World

paramount shooting locations 1927

In 1927, Chicago investment bank Halsey, Stuart & Co. published a prospectus inviting its clients to consider investing in the burgeoning motion picture business. Among the illustrations was this Paramount Studios map of international shooting locations in California.

“It was not mere chance that established the motion picture industry in Southern California,” notes the booklet. “The actual localization of production there came through a process of pure competitive selection in which the geographical advantages favorable to producers in that region literally forced competing directors and their companies to come to California — and Hollywood.

“The advantages of dependable sunshine, permitting outdoor production without delays, and of great variety in scenery at close range (the ocean on one side, the deserts, mountains, and forests in other directions), so that the sequence of almost any picture can be suitably filmed with but little cost for travel — all have militated to established Hollywood as the center of the motion picture world.”

(“The Motion Picture Industry as a Basis for Bond Financing,” reprinted in Tino Balio, ed., The American Film Industry, 1985.)

The Windmill Algorithm

http://szimmetria-airtemmizs.tumblr.com/post/156030216713/windmill-algorithm-notice-that-the-number-of-the

Suppose we have a finite set of points in the plane, no three of which are collinear. A line drawn through one of them pivots around that point until it encounters another point, when it adopts that point as the new pivot. Call this line a “windmill”; it continues indefinitely, always rotating in the same direction. Show that we can choose an initial point and line so that the resulting windmill uses each point as a pivot infinitely many times.

Click for Answer