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Saying Nothing

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

| Art · Literature

The Froggy Problem

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?

  1. When the day is fine, I tell Froggy “You’re quite the dandy, old chap!”
  2. Whenever I let Froggy forget that 10 pounds he owes me, and he begins to strut about like a peacock, his mother declares “He shall not go out a-wooing!”
  3. Now that Froggy’s hair is out of curl, he has put away his gorgeous waistcoat.
  4. Whenever I go out on the roof to enjoy a quiet cigar, I’m sure to discover that my purse is empty.
  5. When my tailor calls with his little bill, and I remind Froggy of that 10 pounds he owes me, he does not grin like a hyena.
  6. When it is very hot, the thermometer is high.
  7. When the day is fine, and I’m not in the humor for a cigar, and Froggy is grinning like a hyena, I never venture to hint that he’s quite the dandy.
  8. When my tailor calls with his little bill and finds me with an empty pocket, I remind Froggy of that 10 pounds he owes me.
  9. My railway shares are going up like anything!
  10. When my purse is empty, and when, noticing that Froggy has got his gorgeous waistcoat on, I venture to remind him of that 10 pounds he owes me, things are apt to get rather warm.
  11. Now that it looks like rain, and Froggy is grinning like a hyena, I can do without my cigar.
  12. When the thermometer is high, you need not trouble yourself to take an umbrella.
  13. When Froggy has his gorgeous waistcoat on, but is not strutting about like a peacock, I betake myself to a quiet cigar.
  14. When I tell Froggy that he’s quite a dandy, he grins like a hyena.
  15. When my purse is tolerably full, and Froggy’s hair is one mass of curls, and when he is not strutting about like a peacock, I go out on the roof.
  16. When my railways shares are going up, and when it’s chilly and looks like rain, I have a quiet cigar.
  17. When Froggy’s mother lets him go a-wooing, he seems nearly mad with joy, and puts on a waistcoat that is gorgeous beyond words.
  18. When it is going to rain, and I am having a quiet cigar, and Froggy is not intending to go a-wooing, you had better take an umbrella.
  19. When my railway shares are going up, and Froggy seems nearly mad with joy, that is the time my tailor always chooses for calling with his little bill.
  20. When the day is cool and the thermometer low, and I say nothing to Froggy about his being quite the dandy, and there’s not the ghost of a grin on his face, I haven’t the heart for my cigar!

Unfortunately, Carroll died before he was able to publish the solution — but he warned that it contains “a beautiful ‘trap.'”

| Puzzles

Misc

  • What time is it at the North Pole?
  • The shortest three-syllable word in English is W.
  • After the revolution, the French frigate Carmagnole used a guillotine as its figurehead.
  • 823502 + 381252 = 8235038125
  • PRICES: CRIPES!
  • “Conceal a flaw, and the world will imagine the worst.” — Martial

When Montenegro declared independence from Yugoslavia, its top-level domain changed from .yu to .me.

| History · Language · Quotations · Science & Math · Technology

“Apex”

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

| Poems

Some “Odd” Theorems

http://commons.wikimedia.org/wiki/File:One-seventh_area_triangle.svg

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.

2/5 semicircle theorem

A square inscribed in a semicircle has 2/5 the area of a square inscribed in a circle of the same radius.

1/5 square theorem

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”:

1/5 square theorem - proof

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.

| Science & Math

Books

book cover

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.

Available now on Amazon!

Futility Closet 2

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.

Buy it now on Amazon!

The Little Man

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?

durer peasants memorial

| Art · History · Society

Gold Nuggets

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 …

http://commons.wikimedia.org/wiki/File:Odom.svg
Image: Wikimedia Commons

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!”

| Science & Math

Moving Drama

In May 1869, Lewis Carroll and 13-year-old Isabel Seymour traveled together by train from Oxford to Reading, where they parted, he to go on to Guildford and she to Paddington, London. After they had separated, he realized that he had forgotten to give her her ticket. He wrote to her:

My dear Isabel,

I was so sorry to hear from Miss Lloyd of your not being well, and I hope you will not think of writing to me about ‘Alice’ till you are well enough to do so. I only write this on the chance of your being in the humour to read it, or to have it read to you. When you are in that state, I should like you to know the real reason of my having carried off your railway-ticket. … Well, you told me, you know, that it was your first railway-journey alone: naturally that set me thinking, ‘Now what can I do to give her a really exciting adventure?’

Now three plans occurred to me. The first was to wait till the train had started from Reading, and then fire a pistol through your carriage-window, so that the bullet might go near your head and startle you a little. But there were two objections to this plan — one, that I hadn’t got a loaded pistol with me, the other, that the bullet might have gone in at a wrong window, and some people are so stupid, they might not have taken it as a joke.

The second plan was to give you, just as the train left Reading, what should look like a Banbury-cake, but should afterwards turn out to be a rattlesnake. The only objection to this plan was, that they didn’t keep that kind at Reading. They had only common Banbury-cakes, which wouldn’t have done at all.

The third plan was to keep the ticket, so that you might be alarmed when you got to London. Of course I arranged thoroughly with the Guard that the thing was not to be overdone. He was to look a little stern at first, and then gradually to let his expressive features kindle into a smile of benevolence. I was very particular on this point and almost my last words to him were, ‘Are you sure you can manage the benevolence?’ and I made him practice it several times on the platform before I would let him go.

Now you know my whole plan for making your journey a real Adventure. I only hope it succeeded. So, hoping much to hear you are better again, I remain very truly yours,

C.L. Dodgson

| Literature

The Bellamy Salute

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

When minister Francis Bellamy published the American Pledge of Allegiance in Youth’s Companion in 1892, his colleague James Upham devised a salute to go along with it, snapping the heels together and extending the right arm toward the flag:

At a signal from the Principal the pupils, in ordered ranks, hands to the side, face the Flag. Another signal is given; every pupil gives the flag the military salute — right hand lifted, palm downward, to a line with the forehead and close to it. Standing thus, all repeat together, slowly, ‘I pledge allegiance to my Flag and the Republic for which it stands; one Nation indivisible, with Liberty and Justice for all.’ At the words, ‘to my Flag,’ the right hand is extended gracefully, palm upward, toward the Flag, and remains in this gesture till the end of the affirmation; whereupon all hands immediately drop to the side.

This worked fine until the 1920s, when Italian fascists and then German Nazis adopted similar salutes. Congress delicately changed the American salute to the hand-on-heart gesture in 1942.

| History