Double Entendre

The Exeter Book, an anthology of Anglo-Saxon poetry from the 10th century, contains three riddles that seem shockingly risqué until you see the answers:

I’m a strange creature, for I satisfy women,
a service to the neighbors! No one suffers
at my hands except for my slayer.
I grow very tall, erect in a bed,
I’m hairy underneath. From time to time
a good-looking girl, the doughty daughter
of some churl dares to hold me,
grips my russet skin, robs me of my head
and puts me in the pantry. At once that girl
with plaited hair who has confined me
remembers our meeting. Her eye moistens.

(An onion.)

A strange thing hangs by a man’s thigh,
hidden by a garment. It has a hole
in its head. It is stiff and strong
and its firm bearing reaps a reward.
When the man hitches his clothing high
above his knee, he wants the head
of that hanging thing to poke the old hole
(of fitting length) it has often filled before.

(A key.)

A young man made for the corner where he knew
she was standing; this strapping youth
had come some way — with his own hands
he whipped up her dress, and under her girdle
(as she stood there) thrust something stiff,
worked his will; they both shook.
This fellow quickened: one moment he was
forceful, a first-rate servant, so strenuous
that the next he was knocked up, quite
blown by his exertion. Beneath the girdle
a thing began to grow that upstanding men
often think of, tenderly, and acquire.

(A churn.)

November 21, 2014November 20, 2014 | Literature

Visual Calculus

As a circle rolls along a line, a point on its circumference traces an arch called a cycloid. The arch encloses an area three times that of the circle, a result commonly proven using calculus. Now Armenian mathematician Mamikon Mnatsakanian has devised a “sweeping-tangent theorem” that accomplishes the same proof using intuition:

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

Imagine a tangent to the rolling circle. As the circle rolls, the tangent sweeps out a series of vectors (approximated here using colors). If these vectors are then gathered to a common point while preserving their length and orientation, they form a sort of bouquet whose size and shape turn out to match exactly those of the original circle. Because the enclosing rectangle has four times the area of the rolling circle (2πr × 2r = 4πr²), this shows that the area under the arch has three times the circle’s area.

All this is proven rigorously in Mnatsakanian’s 2012 book New Horizons in Geometry, written with his Caltech colleague Tom Apostol. The two have now collaborated on some 30 papers showing that many surprising and useful results that heretofore had required integration can now be obtained using intuitive methods that can appeal even to a young student.

That’s a welcome outcome for Mnatsakanian, who found himself stranded in the United States when the Armenian government collapsed in 1990. Apostol writes, “When young Mamikon showed his method to Soviet mathematicians they dismissed it out of hand and said ‘It can’t be right. You can’t solve calculus problems that easily.'”

November 21, 2014November 20, 2014 | Science & Math

Constellation

Circling the earth aboard Friendship 7 in 1962, John Glenn had an odd encounter:

The strangest sight of all came with the very first ray of sunrise as I was crossing the Pacific toward the U.S. I was checking the instrument panel and when I looked back out the window I thought for a minute that I must have tumbled upside-down and was looking up at a new field of stars. I checked my instruments to make sure I was right-side-up. Then I looked again. There, spread as far as I could see, were literally thousands of tiny luminous objects that glowed in the black sky like fireflies. I was riding slowly through them, and the sensation was like walking backwards through a pasture where someone had waved a wand and made all the fireflies stop right where they were and glow steadily. They were greenish yellow in color, and they appeared to be about six to 10 feet apart. I seemed to be passing through them at a speed of from three to five miles an hour. They were all around me, and those nearest the capsule would occasionally move across the window as if I had slightly interrupted their flow. On the next pass I turned the capsule around so that I was looking right into the flow, and though I could see far fewer of them in the light of the rising sun, they were still there. Watching them come toward me, I felt certain they were not caused by anything emanating from the capsule. I thought perhaps I’d stumbled into the lost batch of needles the Air Force had tried to set up in orbit for communications purposes. But I could think of no reason why needles should glow like fireflies, nor did they look like needles. As far as I know, the true identity of these particles is still a mystery.

They seem to have been ice crystals, flakes of frost shed by the capsule and illuminated by the sun. Scott Carpenter saw a similar display on the next Mercury mission, Aurora 7, a few months later.

(John Glenn, “If You’re Shook Up, You Shouldn’t Be There,” Life, March 9, 1962.)

November 20, 2014November 19, 2014 | Oddities

The Peace Arch

The border between the United States and Canada blurs a bit between Blaine, Wash., and Surrey, B.C. There stands the Peace Arch, a 20-meter monument to amity between the two nations commissioned by railroad executive Sam Hill in 1921.

The arch stands precisely on the border, at the center of an international park: Citizens of either nation can pass without passport or visa into the other nation’s territory, provided they don’t stray beyond a dedicated area.

The U.S. side of the arch bears the inscription “Children of a common mother,” and the Canadian side reads “Brethren dwelling together in unity.” An iron gate stands open on either side, and an inscription above reads “May these gates never be closed.”

November 20, 2014November 19, 2014 | Oddities

Hesiod’s Anvil

How far off is heaven? In the Theogony Hesiod gives us a clue:

For a brazen anvil falling down from heaven nine nights and days would reach the earth upon the tenth; and again, a brazen anvil falling from earth nine nights and days would reach Tartarus upon the tenth.

How far can an anvil fall in nine days? Galileo, who taught that “the distances measured by the falling body increase according to the squares of the time,” would have determined that the anvil starts 2.96 × 10⁹ km from earth, a distance greater than that between the sun and Uranus.

But Galileo’s calculation assumes that gravitational force is independent of the object’s distance from the earth. If we assume instead that it varies inversely with the square of the distance between mass centers (and if we ignore all masses except those of the earth and the anvil, and assume that the anvil falls in a straight line), King College mathematician Andrew Simoson calculates that Galileo’s anvil wouldn’t reach us for

hesiod's anvil calculation

Instead, under this new assumption, to reach us in nine days an anvil would start 5.81 × 10⁵ km away — about one and a half times the distance between the earth and the moon.

(Andrew J. Simoson, Hesiod’s Anvil, 2007.)

November 19, 2014November 18, 2014 | Science & Math

Reflection

“Sir Winston Churchill once told me of a reply made by the Duke of Wellington, in his last years, when a friend asked him: ‘If you had your life over again, is there any way in which you could have done better?’ The old Duke replied: ‘Yes, I should have given more praise.'” — Bernard Montgomery, A History of Warfare, 1968

November 19, 2014November 18, 2014 | History · Society

Noted

Further excerpts from the notebooks of English belletrist Geoffrey Madan (1895-1947):

Two psychiatrists meeting: “You’re pretty well, how am I?”

Children: unable to understand the concept of uncertainty.

1. Every subject of the Crown is entitled to make pickles.
2. Every man must bear the name of his father.

— Sir John Markham, Chief Justice, 1465

Pedantry is greater accuracy than the case requires.

“Drink … prevents you seeing yourself as others see you.” — Desmond MacCarthy

Safe remarks:

1. To inaudible remark: “That’s just what I’ve been wondering all the evening.”
2. “I can never remember how you spell your name.” (But G.M. Young quoted the man who wearily replied, “Still J-O-N-E-S.”)

“So they went forth both, and the young man’s dog with them.” — Tobit 5:16: the only mention in the Bible of a pet animal

The dust of exploded beliefs may make a fine sunset.

See Observations and More Madan.

November 18, 2014November 17, 2014 | Literature

Full Circle

https://commons.wikimedia.org/wiki/File:Portsmouth_Memorial_Bridge_01.jpg — Image: Wikimedia Commons

For 88 years the Memorial Bridge carried traffic across the Piscataqua River between Portsmouth, N.H., and Kittery, Maine.

At its opening in 1923, 5-year-old Eileen Foley cut the ribbon.

In 2011, Foley, now 93, tied a ribbon at the closing ceremony.

In the interval she had served several terms as mayor of Portsmouth. “Thank you very much for this afternoon,” she said. “I will never forget it.”

(Thanks, Zach.)

November 18, 2014November 17, 2014 | Oddities

Podcast Episode 34: Spring-Heeled Jack — A Victorian Supervillain

Between 1837 and 1904, rumors spread of a strange bounding devil who haunted southern England, breathing blue flames and menacing his victims with steel talons. In the latest Futility Closet podcast we review the career of Spring-Heeled Jack and speculate about his origins.

We also recount Alexander Graham Bell’s efforts to help the wounded James Garfield before his doctors’ treatments could kill him and puzzle over why a police manual gives instructions in a language that none of the officers speak.

See full show notes …

November 17, 2014October 28, 2017 | Podcast