The names of the 48 contiguous United States fall neatly into the two halves of the alphabet:
16 start with A-L, 16 with M-N, and 16 with O-Z.
Square Dance
From the 2001 Moscow Mathematical Olympiad:
Two stones, one black and one white, are placed on a chessboard. A move consists of moving one stone up, down, left, or right. The two stones may not occupy the same square. Does a sequence of moves exist that will produce every possible arrangement of the stones, each occurring exactly once?
Figure and Ground
The tradition of flying a flag at half-staff began when a symbolic space was left at the top of the staff for the “invisible flag of death,” signifying death’s dominion over earthly affairs.
A riderless horse accompanies the funeral procession of U.S. military officers. The horse above, Black Jack, accompanied more than 1,000 such processions, including those for John F. Kennedy, Herbert Hoover, Lyndon Johnson, and Douglas MacArthur.
When Russian ballerina Anna Pavlova died in 1931, her next show went on as scheduled, with a spotlight circling an empty stage.
Unquote
“In like manner, if I let myself believe anything on insufficient evidence, there may be no great harm done by the mere belief; it may be true after all, or I may never have occasion to exhibit it in outward acts. But I cannot help doing this great wrong towards Man, that I make myself credulous. The danger to society is not merely that it should believe wrong things, though that is great enough; but that it should become credulous, and lose the habit of testing things and inquiring into them; for then it must sink back into savagery.” — William Kingdon Clifford
(He distilled this into a credo: “It is wrong always, everywhere, and for any one, to believe anything upon insufficient evidence.”)
The Puzzle of the Self-Torturer
You’re fitted with a watch that imparts an electric current to your skin in increments too small to distinguish. Initially it’s set to 0 (off), and the settings run up to 1000. At the start of each week you’re allowed a period of experimentation to compare various settings, and then the watch is returned to its last setting. Then you have the option to increase the setting by 1; if you do this, you get $10,000. You may never reduce the setting.
What should you do? On the first day your experimentation shows you that the highest setting is completely intolerable; at that setting you’d pay any amount of money to get rid of the watch. But on this first week your decision is simply whether to advance from 0 to 1, getting $10,000 for accepting an imperceptible amount of pain. That seems attractive.
The trouble seems to be that your evaluations are “transitive” only at a large scale. If you prefer 0 to 500 and 500 to 1000, then it’s valid to conclude that you’ll prefer 0 to 1000. But if you prefer 51 to 4 (because of the financial reward) and 103 to 51, can we conclude that you’ll prefer 103 to 4? Not necessarily.
Unfortunately for all of us, this describes a lot of life. “The self-torturer is not alone in his predicament,” writes philosopher Warren S. Quinn, who proposed this puzzle in 1990. “Most of us are like him in one way or another. We like to eat but also care about our appearance. Just one more bite will give us pleasure and won’t make us look fatter; but very many bites will. And there may be similar connections between puffs of pleasant smoking and lung cancer, or between pleasurable moments of idleness and wasted lives.” What’s the best course?
(Warren S. Quinn, “The Puzzle of the Self-Torturer,” Philosophical Studies, May 1990)
Open and Shut
A poser by Cyril Pearson, puzzle editor for the London Evening Standard at the turn of the 20th century:
Upon the shutters of a barber’s shop the legend above was painted in bold letters. One evening about 8:30, when it was blowing great guns, quite a crowd gathered round the window, and seemed to be enjoying some excellent joke. What was amusing them when the shutter blew open?
Weird Verse
H.P. Lovecraft’s cosmic horror tales describe a world that’s literally beyond human understanding — his characters glimpse a universe ruled by monstrous gods whose very aspect imperils our sanity.
For his 2011 experimental poem Cthulhu on Lesbos, David Jalajel reflected this by taking phrases from Lovecraft’s 1928 story “The Call of Cthulhu” and arranging them into Sapphic stanzas without regard to conventional syntax:
Dark to visit faithful But Great had ever
Old The carven idol was great Cthulhu,
None might say or others were like the old but
Things were by word of
Mouth. The chanted secret — was never spoken
Only whispered. chant “In his house at R’lyeh
Dead Cthulhu waits of the found be hanged, and
Rest were committed
It ends, fittingly, on a fearsome but enigmatic note:
Prance and slay around in by sinking black else
World by now be screaming with fright and frenzy.
Knows the end? has risen may sink, and sunk may
Rise. and in deep, and
Babel on Olympus
In 1996, MIT philosopher George Boolos published this puzzle by Raymond Smullyan in The Harvard Review of Philosophy, calling it “the hardest logical puzzle ever”:
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.
Boolos made three clarifying points:
- It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
- What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
- Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
What’s the solution?
“The Wayfarer”
The wayfarer,
Perceiving the pathway to truth,
Was struck with astonishment.
It was thickly overgrown with weeds.
“Ha,” he said,
“I see that none has passed here
In a long time.”
Later he saw that each weed
Was a singular knife.
“Well,” he mumbled at last,
“Doubtless there are other roads.”
— Stephen Crane
Kid Lit
In 1967 Luis d’Antin Van Rooten published Mots D’Heures: Gousses, Rames, a collection of French poems that make little sense until you read them aloud:
Oh, les mots d’heureux bardes
Où en toutes heures que partent.
Tous guetteurs pour dock à Beaune.
Besoin gigot d’air
De que paroisse paire.
Et ne pour dock, pet-de-nonne.
Et qui rit des curés d’Oc?
De Meuse raines, houp! de cloques.
De quelles loques ce turque coin.
Et ne d’ânes ni rennes,
Écuries des curés d’Oc.
In 1980 Ormonde de Kay met this with N’Heures Souris Rames:
Très bel aï n’ de maïs
Si à Oudh héronne.
Des Halles Roi Naphte de phare mer soif
Chicot taffetas tel suite de carvi naïf.
Didier voyou si sachée saille t’ignore l’aï
Fesse très bel aï n’ de maïs.
Rabais dab dab
Trille, ménine, taupe.
Hindou d’yeux tines, que débit?
Débouchoir du bécarre
De canne d’élastique maigre.
Trop d’émaux, nefs alterés.
And in 1981 John Hulme expanded into German with Mörder Guss Reims:
Schach an Schill! Wend’ ab die Hilde —
Fesch Appel, oh Worte!
Schachfell Daunen, Brockensgrauen,
Und Schill Keim Tuümpel in Naphtha.
Pater keck, Pater keck, Bechers Mann.
Bigamie er keck es Festeschuh kann.
Batet und Brikett und Marktwitwe Tie
Und Butter, Tinte offen fort Omi Anämie.
Um die Dumm’ die Saturn Aval;
Um die Dumm’ die Ader Grät’ fahl.
Alter ging’s Ohr säss und Alter ging’s mähen.
Kuh denn “putt” um Dieter Gitter er gähn.
“In this lively allegorical poem a foolish Greek maiden becomes embroiled with the supernatural and is rescued in the nick of time from a fate worse than immortality by being turned into a cow.”
See also “It Means Just What I Choose It to Mean” and Read It Aloud.
(I think de Kay is the same fellow who proposed the theory of continental drip — a very playful man!)