[Jerome Sankey] challenged Sir William [Petty] to fight with him. Sir William is extremely short-sighted, and being the challengee it belonged to him to nominate place and weapon. He nominates for the place a dark cellar, and the weapon to be a great carpenter’s axe. This turned the knight’s challenge into ridicule, and so it came to nought.
— John Aubrey, Brief Lives, 1697
A train line extends infinitely far east and west. Stations are spaced a mile apart, and midway between each pair of stations is a signal light. There’s one train on the line, and it moves to an adjacent station at the top of each hour. Its choice (east or west) is determined by the engineer, who flips a coin 20 minutes after each hour. If the coin lands heads, the train’s next destination will be the station one mile east. If it lands tails, the train will next go to the station one mile west.
Forty minutes after each hour, one of the infinitely many signal lights will flash. The flash is visible all along the line. The identity of the flashing light is random, and it’s unrelated to the coin toss.
You wake up on this train while it’s stopped at a station. It’s 2:30 p.m., which means the engineer flipped his coin 10 minutes ago. The conductor tells you that the next destination is Willoughby. A map tells you that the Willoughby station is flanked by East Willoughby and West Willoughby, so you must be at one of these two stations, but you don’t know which one. Because these are the only two possibilities and there’s no reason for one to be more likely, you conclude that they’re equally probable.
Before the train departs at 3 p.m., is it possible to guess the outcome of the engineer’s coin toss at 2:20 p.m. with success probability greater than 1/2? El Camino College mathematician Leonard M. Wapner contends that it is. At 2:40 p.m. a signal light will flash. There’s a nonzero probability p that the light that flashes will be one of the two lights adjacent to the Willoughby station. If that happens, it will indicate with certainty the direction of Willoughby (east or west) from your current location. The chance that the flash doesn’t come from one of these two lights is 1 – p, and in that case the chance is 1/2 that it comes from the direction of Willoughby. Overall:
“So,” Wapner writes, “if the light flashes to your east, you would guess that the train will be departing to the east and that the engineer’s coin landed heads. If the light flashes to the west, you would guess that the train will depart to the west and that the engineer’s coin landed tails. You should expect your guess (east/heads or tails/west) to be successful more often than not.”
(He adds, “The Willoughby prediction scheme, though mathematically valid, is far too contrived for it to be achieved in actuality. But there being no mathematical contradictions, the door remains open to variations and applications.”)
(Leonard M. Wapner, “Beyond Chance: Predicting the Unpredictable,” Recreational Mathematics Magazine 12:21 [December 2025], 1-8.)
Cynthia Knight composed this in 1983 — a poem typed entirely on the upper row of a typewriter:
O WOE
(we quote you, poor poet)
We tiptoe up, quiet. You peer out. You opt to write
quite proper poetry
to pour out your pretty repertoire.
We try to woo you to write. You pop out; retire to pout.
Torpor? Terror? Ire? Or worry? We pity you, poor poet.
Put out, you rip your poetry up. Too trite?
We try to pique you.
Were your pep to tire, or your power to rot
We prop you up to retype it.
Or were our top priority to trip you
or were etiquette, piety, or propriety to require you to wire up your typewriter to rewrite it …
O! You write witty quip, pert retort. You titter. You write pure, utter tripe too, I purr.
You err
retype your error
weep
wipe your wet typewriter (your property)
We TOWER o’er you, wee tot — were you TWO?
YOU WORE YOUR TOY TYPEWRITER OUT!
We quit.
(“The Poet’s Corner,” Word Ways 16:2 [May 1983], 87-88.)
In 1943 Buckminster Fuller announced that he’d been getting by on two hours of sleep a day. Each person has a primary and a secondary store of energy, he said; the first is restored quickly and the second takes longer. The trick, then, is to relax as soon as you’ve used up the primary store. Fuller trained himself to take a nap at the first sign of fatigue, which he found happened about every six hours. Taking a half-hour nap at those times left him in “the most vigorous and alert condition I have ever enjoyed,” he said.
“For two years Fuller thus averaged two hours of sleep in 24,” Time reported, adding, “Life-insurance doctors who examined him found him sound as a nut.” Fuller said he’d had to abandon the plan because it conflicted with his coworkers’ schedules. “But he wishes the nation’s ‘key thinkers’ could adopt his schedule; he is convinced it would shorten the war.”
In a letter to Maud Standen dated Dec. 18, 1877, Lewis Carroll included a puzzle:
[M]y ‘Anagrammatic Sonnet’ will be new to you. Each line has 4 feet, and each foot is an anagram, i. e., the letters of it can be re-arranged so as to make one word. Thus there are 24 anagrams, which will occupy your leisure moments for some time, I hope. Remember, I don’t limit myself to substantives, as some do. I should consider ‘we dishwished’ a fair anagram.
As to the war, try elm. I tried.
The wig cast in, I went to ride.
‘Ring? Yes.’ We rang. ‘Let’s rap.’ We don’t.
‘O shew her wit!’ As yet she won’t.
Saw eel in Rome. Dry one: he’s wet.
I am dry. O forge! Th’rogue! Why a net?
For example, the first foot in the first line, “As to,” can be rearranged to spell OATS. Carroll left no solution, but he did add a parting riddle to which we have the answer:
“To these you may add ‘abcdefgi,’ which makes a compound word — as good a word as ‘summer-house.'” What is it?
tesserarian
adj. pertaining to play
aspernate
v. to scorn
absit
n. a student’s temporary leave of absence
denegate
v. to deny or refuse
In 1873, when the University of Michigan challenged Cornell to the new game of football, Cornell president Andrew D. White declined. He said, “I will not permit thirty men to travel four hundred miles to agitate a bag of wind.”
“Jottings” from the notebooks of Bulgarian novelist Elias Canetti, published as The Human Province (1978):
“Square tables: the self-assurance they give you, as though one were alone in an alliance of four.”
Robert Runcie, Archbishop of Canterbury, cooperated as Humphrey Carpenter prepared his biography, believing that the book wouldn’t be published until after his passing. Eventually he was forced to write,
My dear Humphrey
I have done my best to die before this book is published. It now seems possible that I may not succeed. Since you know that I am not enthusiastic about it you are generous to give me space for a postscript.
Excerpts from the index of Together, Norman Douglas’ 1923 account of his travels in Calabria:
Anna, the old nurse, her passion for idiots and corpses, 39-40, for wolf-stories, 210; gets it hot, 91; shakes chocolate from a tree, 209; not old at all, 210
Ants, unreliable workmen, 120
Beds, local, their discomforts, 3; double, their uses, 218
Brunnenmacher (father) mountaineer, presumably hirsute, 25; (son) mountaineer, indubitably hirsute, 25; his smile and his blasphemies, 25, 26; takes author in hand, 28, 124
Cement, an abomination, 75, 128, 225
Cocoa, an abomination, 10
Cows, explode from over-eating, 204
Dachshund, lady-dog, sets a bad example, 4
Elephant-trap, a disused, 113
Erratic blocks, 176, 185, 186, 230
Falling in love, with a mountain, 30
Grand-aunts, the delight of childhood, 41, 47, 92, 214
Grandfather, maternal, a feudal monster, always spick-and-span, 196; excavates in imagination the Akropolis of Athens, 197; tells Prince Consort how to handle Queen Victoria, 198; sometimes mistaken for an angel, 199; dominates his harem, 200; vicious to the last, 201
Hare, how to shoot, 123; how not to cook, 203
Moralists, their limitations, 84
Ovid, blunders in botany, 83
Poets, should avoid towns, 82; generally born naked, 165; talk nonsense about pomegranates, 202
Theocritus, seldom caught napping, 83
Weisses Kreuz, hotel, its manager worth making love to, 203
Douglas had a penchant for droll indexes. His index for Some Limericks (1928) contains the entry “Spain, project for fertilizing arid tracts of, its ruler disinclined for tête-à-tête diversions”.
From the will of John G—-e, who died at Lambeth around 1772:
Whereas it was my misfortune to be made very uneasy by Elisabeth G—-e, my wife, for many years, from our marriage, by her turbulent behavior; for she was not content with despising my admonitions, but she contrived every method to make me unhappy; she was so perverse in her nature, that she would not be reclaimed, but seemed only to be born to be a plague to me; the strength of Sampson, the knowledge of Homer, the prudence of Augustus, the cunning of Pyrrhus, the patience of Job, the subtilty of Hannibal, and the watchfulness of Hermogenes, could not have been sufficient to subdue her; for no skill or force in the world would make her good; and as we have lived separate and apart from each other eight years, and she having perverted her son to leave and totally abandon me, therefore I give her one shilling only.
From the Annual Register.