A puzzle from Eureka, March 1957:
These drawings depict an object as seen from above and from the front. What does it look like when viewed from the side? The object has no curved surfaces, and all hidden edges in such drawings are represented by dotted lines.
In England and France, from the 1500s to the 1700s, the placement of a letter writer’s signature on the page conveyed meaning as to his relationship with the recipient. In his 1568 letter-writing manual Enimie of Idlenesse, William Fulwood writes that the subscription and signature of the letter “must be doone according to the estate of the writer, and the qualitie of the person to whom wee write: For to our superiors wee must write at the right side in the neither end of the paper, saying: By your most humble and obedient sonne, or seruant, &c. Or, yours to commaund, &c. And to our equals we must write towards the middest of the paper, saying: By your faithfull friend for euer, &c. Or, yours assured, &c. To our inferiours wee may write on high at the left hand, saying: By yours, &c.”
In 1601 John Donne married Anne More without the blessing of her father, who was lieutenant of the Tower of London. Donne was incarcerated, and in his letters begging for clemency he crammed his signature into the bottom right-hand corner of the page to signal his self-abasement.
(From Sam Willis and James Daybell, Histories of the Unexpected, 2018.)
There was an artist once, and he painted a picture. Other artists had colours richer and rare, and painted more notable pictures. He painted his with one colour, there was a wonderful red glow on it; and the people went up and down, saying, ‘We like the picture, we like the glow.’
The other artists came and said, ‘Where does he get his colour from?’ They asked him; and he smiled and said, ‘I cannot tell you’; and worked on with his head bent low.
And one went to the far East and bought costly pigments, and made a rare colour and painted, but after a time the picture faded. Another read in the old books, and made a colour rich and rare, but when he had put it on the picture it was dead.
But the artist painted on. Always the work got redder and redder, and the artist grew whiter and whiter. At last one day they found him dead before his picture, and they took him up to bury him. The other men looked about in all the pots and crucibles, but they found nothing they had not.
And when they undressed him to put his grave-clothes on him, they found above his left breast the mark of a wound — it was an old, old wound, that must have been there all his life, for the edges were old and hardened; but Death, who seals all things, had drawn the edges together, and closed it up.
And they buried him. And still the people went about saying, ‘Where did he find his colour from?’ And it came to pass that after a while the artist was forgotten — but his work lived.
— Olive Schreiner, Dreams, 1891
In James Thurber’s 1957 fairytale book The Wonderful O, two pirates, Black and Littlejack, assail the innocent island of Ooroo, seeking hidden treasure. Frustrated with their unsuccessful search, Black issues an edict banning the letter O, which he hates (his mother had once become wedged in an O-shaped porthole; “we couldn’t pull her in and so we had to push her out”). Accordingly the orchestra loses its violins, cellos, and trombones; the villagers must move from cottages to huts; and so on. One laments:
They are swing chas. What is slid? What is left that’s slace? We are begne and webegne. Life is bring and brish. Even schling is flish. Animals in the z are less lacnic than we. Vices are filled with paths and scial intercurse is baths. Let us gird up ur lins like lins and rt the hrrr and ust the afs.
I’ll leave you to read the resolution yourself.
For a more recent fable about an island beset by a letter shortage, see Mark Dunn’s progressively lipogrammatic 2001 novel Ella Minnow Pea. Maybe it’s the same island!
A puzzle from the 1998 Moscow Mathematical Olympiad, via Peter Winkler’s excellent Mathematical Puzzles, 2021:
An anthropologist is surrounded by a circle of natives. Each native either always lies or always tells the truth. The anthropologist asks each native whether the native to his right is a liar or a truth teller. From their answers, she’s able to deduce the fraction of the circle who are liars. What is the fraction?
Death is always on the way, but the fact that you don’t know when it will arrive seems to take away from the finiteness of life. It’s that terrible precision that we hate so much. But because we don’t know, we get to think of life as an inexhaustible well. Yet everything happens only a certain number of times, and a very small number, really. How many more times will you remember a certain afternoon of your childhood, some afternoon that’s so deeply a part of your being that you can’t even conceive of your life without it? Perhaps four or five times more. Perhaps not even that. How many more times will you watch the full moon rise? Perhaps twenty. And yet it all seems limitless.
— Paul Bowles, The Sheltering Sky, 1949
In the 1990s, South Baltimore native Gordon Beard compiled a series of phrasebooks to help bewildered travelers understand his city’s residents:
amblanz — ambulance
bobwar — barbed wire
corter — quarter
flare — flower
goff — golf
har — hire
keerful — careful
mare — mayor
neck store — next door
orning — awning
plooshin — pollution
roolty — royalty
twunny — twenty
varse — virus
warsh — wash
yewmid — humid
John Goodspeed, for 17 years a columnist at the Baltimore Evening Sun, had compiled his own list in the 1960s:
ahrsh — Irish
chowld — child
dayon — down
harrid — Howard
koor — car
larnix — larynx
nass — nice
owen — on
shares — showers
urshter — oyster
Apparently the confusion has persisted for decades. “The life of a Baltimore Army lieutenant may have been saved by Baltimore during the Battle of the Bulge in World War II,” Goodspeed once reported. “Military police suspected him of being a German spy in an American uniform, but an M.P. from Baltimore heard the lieutenant pronounce his home town as ‘Balamer’ and passed him as genuine. Only a native can say it that way.”
University of California psychologist Diana Deutsch discovered this illusion in 1973. Play the file using stereo headphones. If you hear a high tone in one ear and a low tone in the other, decide which ear is hearing the high tone. Then reverse the headphones and play the file again.
“Despite its simplicity, this pattern is almost never heard correctly, and instead produces a number of illusions,” Deutsch writes. Some people hear a single moving tone; some hear silence; some notice no change when the headphones are reversed. Some impressions even seem to vary with the handedness of the subject!
What you’re hearing is simply an octave interval, with the high note played in one ear and the low in the other, the two regularly switching places. Seen on paper it’s remarkably simple, which makes the confusion all the more striking. Deutsch suspects that two different decision mechanisms are being invoked at once — one determines what pitch we hear, and the other determines where it’s coming from. More info here.
Most people would agree that children have special duties to their parents, even once the children have grown up. We might feel an obligation to keep in touch with them, for example, or to care for them in their old age. Where do these duties come from?
Each of these explanations is unsatisfactory, writes Boston University philosopher Simon Keller. “Each tries to assimilate the moral relationship between parent and child to some independently understood conception of duty, but this relationship is different in structure and content from any that we are likely to share with anyone apart from a parent.” So what’s the source of our obligation to our parents?
(Simon Keller, “Four Theories of Filial Duty,” Philosophical Quarterly 56:223 [April 2006], 254-274.)
Philosophy, Art, & Science, an ambigram by typographer John Langdon. It reads the same upside down.
