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.
Divide a pile of 14 buttons into two smaller piles, say of 9 and 5 buttons. Then write on a piece of paper: 9 × 5 = 45. Divide the pile of 9 into two smaller piles, say of 6 and 3, and write 6 × 3 = 18 on the paper. Keeping doing this, splitting each pile into two and recording the pair of numbers you get, until you have 14 separate piles of one button each. An example might run like this:
9 × 5 = 45
6 × 3 = 18
1 × 4 = 4
4 × 2 = 8
2 × 1 = 2
2 × 2 = 4
3 × 1 = 3
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1
1 × 2 = 2
1 × 1 = 1
No matter how you proceed, if you start with a pile of 14 buttons, the products in the right column will always sum to 91.
(James Tanton, “A Dozen Questions About Pile Splitting,” Math Horizons 12:1 [September 2004], 28-31.)
Rhymes for unrhymable words, by Willard R. Espy:
It is unth-
inkable to find
A rhyme for month
Except this special kind.
The four eng-
ineers
Wore orange
Brassieres.
Love’s lost its glow?
No need to lie; j-
ust tell me “go!”
And I’ll oblige.
(From his entertaining rhyming dictionary.)
Striking excerpts from the writings of Scottish novelist Muriel Spark, from Penelope Jardine’s 2018 collection A Good Comb:
Jardine’s title comes from the observation “It calms you down, a good comb,” remarked by an unnamed character in Spark’s 1960 novel The Ballad of Peckham Rye.
Memorable excerpts from student geology examinations, from W.D. Ian Rolfe’s 1980 collection Geological Howlers:
“A dinosaur is an extinct animal still found in Australia,” one student contended. “It was sometimes so large that its feet are found in the Precambrian and its head in the Silurian because it was too big to lie down where it died.”