Young telegraph operator Joseph Orton Kerbey was enlisted as a spy for the federal forces during the Civil War. In 1861, laid up in a sick bed in Richmond, he needed a way to communicate his latest discoveries to his friends in the north. The message would have to appear innocent and contain the key to its own decipherment. Here’s what he sent:
He directed it, not to his father’s name and address, but to a friend in the telegraph office at Annapolis. What was the hidden message?
In 1990, Spanish philosopher Jon Perez Laraudogoitia submitted an article to Mind entitled “This Article Should Not Be Rejected by Mind.” In it, he argued:
They published it. “This is, I believe, the first article in the whole history of philosophy the content of which is concerned exclusively with its own self, or, in other words, which is totally self-referential,” Laraudogoitia wrote. “The reason why it is published is because in it there is a proof that it should not be rejected and that is all.”
In a historic passage Mallarmé describes the terror, the sense of sterility, that the poet experiences when he sits down to his desk, confronts the sheet of paper on which his poem is supposed to be composed, and no words come to him. But we might ask, why could not Mallarmé, after an interval of time, have simply got up from his chair and produced the blank sheet of paper as the poem that he sat down to write? Indeed, in support of this, could one imagine anything that was more expressive of, or would be held to exhibit more precisely the poet’s feelings of inner devastation than the virginal paper?
— Richard Wollheim, “Minimal Art,” in Minimal Art, ed. Gregory Battcock, 1968
Speaking of Lewis Carroll — and further to Wednesday’s logic exercise — here’s the king of all Carroll’s logic problems. What’s the strongest conclusion that can be drawn from these premises?
Unfortunately, Carroll died before he was able to publish the solution — but he warned that it contains “a beautiful ‘trap.'”
When Montenegro declared independence from Yugoslavia, its top-level domain changed from .yu to .me.
The lion tamers wrestle with the lions in a cage,
With but a fragile whip they dare their charges’ feral rage.
They put their heads in tigers’ mouths and do not flinch a grain,
But … they never tried to take a cat five hundred miles to Maine.
You hunters who bring back alive from Afric’s roaring shore
The nilghai and the elephant, the rhino and the boar;
Who load them on a steamer and evince no sign of strain —
Let’s see you drive a cat five hundred miles to Maine.
Go cope with your rhinoceros bare-handed and alone,
Or kick a famished grizzly if for harmless fun you hone,
Or aggravate a timber wolf with pokings of a cane,
But do NOT try to drive a cat five hundred mile to Maine.
There is no word, there is no tongue, there is no ink to tell
One tenth of what one cat can raise of concentrated hell,
When after two hours’ driving to mistaken qualms you yield
And take poor puss to stretch her limbs in some adjacent field.
And if you’ve done the things set forth in stanzas two and three,
You stand a chance, when Krazy from the leash has wriggled free
(Provided you are clad in steel with hat and gloves to match),
To get her back into the car without a bite or scratch.
Ye lion tamers, naturalists, and big-game hunters eke,
When I’m around be chary of your tendency to speak.
To hear you boast your petty deeds gives me a shooting pain
For I have driven Krazy — phew! — five hundred miles to Maine!
— Baron Ireland
Draw any triangle and divide each leg into three equal segments. Connect each vertex to one of the trisection points on the opposite leg, as shown, and the triangle formed in the center will have 1/7 the area of the original triangle.
A square inscribed in a semicircle has 2/5 the area of a square inscribed in a circle of the same radius.
Draw a square and connect each vertex to the midpoint of an opposite side, as shown. The square formed in the center will have 1/5 the area of the original square.
A “proof without words”:
Trisect each side of a triangle and join each vertex to the opposite trisection points. Then write a hexagram in the hexagon in the center. The area of the hexagram is 7/100 the area of the original triangle.
Futility Closet: An Idler’s Miscellany of Compendious Amusements collects some of my favorite finds in a career of dedicated curiosity-seeking: lawyers struck by lightning, wills in chili recipes, a lost manuscript by Jules Verne, dreams predicting horse race winners, softball at the North Pole, physicist pussycats, 5-year-olds in the mail, camels in Texas, balloons in the arctic, a lawsuit against Satan, starlings amok, backward shoes, revolving squirrels, Dutch Schultz’s last words, Alaskan mirages, armored baby carriages, pig trials, rivergoing pussycats, a scheme to steal the Mona Lisa, and hundreds more.
Plus a selection of the curious words, odd inventions, and quotations that are regular features on the site, as well as 24 favorite puzzles and a preface explaining how Futility Closet came to be and how I come up with this stuff.
Another helping of Futility Closet’s best — hundreds of entertaining oddities in history, literature, language, art, philosophy, and mathematics, the perfect gift for people who are impossible to buy gifts for.
Futility Closet 2: A Second Trove of Intriguing Tidbits contains hundreds of hand-picked favorites from the site’s burgeoning archive of the marvelous, the diverting, and the strange: joyous dogs, soul-stirring Frenchmen, runaway balloons, U-turning communists, manful hummingbirds, recalcitrant Ws, intractable biplanes, hairless trombonists, abusive New Zealanders, unreconstituted cannibals, mysterious blimps, thrice-conscripted Koreans, imaginary golf courses, irate Thackerays, and hundreds more. Plus the amusing inventions, curious words, and beguiling puzzles that regularly entertain millions of website visitors and podcast listeners.
In 1525, more than 100,000 German peasants demanded an end to serfdom and were massacred by the well-organized armies of the ruling class. After observing the ornate memorials with which the aristocrats congratulated themselves, Albrecht Dürer proposed a similarly baroque monument to the slain peasants:
Place a quadrangular stone block measuring ten feet in width and four feet in height on a quadrangular stone slab which measures twenty feet in length and one foot in height. On the four corners of the ledge place tied-up cows, sheep, pigs, etc. But on the four corners of the stone block place four baskets, filled with butter, eggs, onions, and herbs, or whatever you like. In the centre of this stone block place a second one, measuring seven feet in length and one foot in height. On top of this second block place a strong chest four feet high, measuring six and a half feet wide at the bottom and four feet wide at the top. Then place a kettle upside down on top of the chest. The kettle’s diameter should be four and a half feet at the rim and three feet at its bottom. Surmount the kettle with a cheese bowl which is half a foot high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and has a diameter of a foot and a half at the bottom, and of only a foot at the top. Its spout should protrude beyond this. On the top of the butter keg, place a well-formed milk jug, two and a half feet high, and with a diameter which is one foot at its bulge, half a foot at its top, and is wider at its bottom. Into this jug put four rods branching into forks on top and extending five and a half feet in height, so that the rods will protrude by half a foot, and then hang peasants’ tool on it – like hoes, pitchforks, flails, etc. The rods are to be surmounted by a chicken basket, topped by a lard tub upon which sits an afflicted peasant with a sword stuck into his back.
What would that look like?
The first 10 digits of the golden ratio φ can be rearranged to give the first 10 digits of 1/π:
φ = 1.618033988 …
1/π = .3183098861 …
And the first nine digits of 1/φ can be rearranged to give the first 9 digits of 1/π:
1/φ = .618033988 …
1/π = .318309886 …
In 1983 amateur mathematician George Odom discovered that if points A and B are the midpoints of sides EF and DE of an equilateral triangle, and line AB meets the circumscribing circle at C, then AB/BC = AC/AB = φ. Odom used this fact to construct a pentagon, which H.S.M. Coxeter published in the American Mathematical Monthly with the single word “Behold!”
