Dead Letters

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!

An Observant Anthropologist

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?

Click for Answer


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.”

The Octave Illusion

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.

Filial Duty

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?

  • Certainly my parents have done a great deal for me, so perhaps I owe them a debt. But it seems there’s no way to repay this debt completely, and I seem to owe it regardless of how great (or small) a burden I was to them as a child. (Also my obligation to them seems to vary with my own circumstances, which is not the case with other debts.)
  • Perhaps what I really owe them is an appropriate gratitude for what they’ve done for me. But this doesn’t seem right either — if I help my mother through a difficult time, fundamentally it’s because she wants me there, not to show that I recognize and appreciate what she’s done for me. Also, I seem to feel a duty to her even if I required relatively little sacrifice as a child, which is not normally how we think about gratitude.
  • Maybe my parents and I are friends, and I owe them the duties that come with friendship. But I can’t choose to end our relationship, as I can with friends, and I would never feel an obligation to provide medical care (say) for my friends, as I would for my parents.

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.)

Buttoned Up

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-
Wore orange

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:

  • The superstition of today is the science of yesterday.
  • Providers are often disliked, often despised.
  • I think “waiter” is such a funny word. It is we who wait.
  • It is impossible to persuade a man who does not disagree, but smiles.
  • I’m not lonely before they come. I’m only lonely when they go away.
  • Dangerous people often seem boring.
  • She was astonishingly ugly, one was compelled to look at her.
  • I am an honest man … when treating of the few existing subjects to which honesty is due.
  • Suffering isn’t in proportion to what the sufferer deserves.
  • He exhausted his capacity for conversation when he became an Englishman.

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.