Caliban’s Will

A curious logic problem by Cambridge mathematician Max Newman, published in Hubert Phillips’ New Statesman puzzle column in 1933:

When Caliban’s will was opened it was found to contain the following clause:

‘I leave ten of my books to each of Low, Y.Y., and ‘Critic,’ who are to choose in a certain order:

  1. No person who has seen me in a green tie is to choose before Low.
  2. If Y.Y. was not in Oxford in 1920 the first chooser never lent me an umbrella.
  3. If Y.Y. or ‘Critic’ has second choice, ‘Critic’ comes before the one who first fell in love.’

Unfortunately, Low, Y.Y., and ‘Critic’ could not remember any of the relevant facts; but the family solicitor pointed out that, assuming the problem to be properly constructed (i.e., assuming it to contain no statement superfluous to its solution) the relevant data and order could be inferred. What was the prescribed order of choosing?

Click for Answer

Dancing the Slaves

After the morning meal came a joyless ceremony called ‘dancing the slaves.’ ‘Those men who were in irons,’ says Dr. Thomas Trotter, surgeon of the Brookes in 1783, ‘were ordered to stand up and make what motions they could, leaving a passage for such as were out of irons to dance around the deck.’ Dancing was prescribed as a therapeutic measure, a specific against suicidal melancholy, and also against scurvy — although in the latter case it was a useless torture for men with swollen limbs. While sailors paraded the deck, each with a cat-o’-nine-tails in his right hand, the men slaves ‘jumped in their irons’ until their ankles were bleeding flesh. One sailor told Parliament, ‘I was employed to dance the men, while another person danced the women.’ Music was provided by a slave thumping on a broken drum or an upturned kettle, or by an African banjo, if there was one aboard, or perhaps by a sailor with a bagpipe or a fiddle. Slaving captains sometimes advertised for ‘a person that can play on the Bagpipes, for a Guinea ship.’ The slaves were also told to sing. Said Dr. Claxton after his voyage in the Young Hero, ‘They sing, but not for their amusement. The captain ordered them to sing, and they sang songs of sorrow. Their sickness, fear of being beaten, their hunger, and the memory of their country, &c., are the usual subjects.’

— Daniel P. Mannix and Malcolm Cowley, Black Cargoes: A History of the Atlantic Slave Trade, 1518-1865, 1962

Planned Forgiveness

My neighbor has been stealing my newspaper. And when I confront him, he apologizes with a sarcastic, condescending air, as if to say that he’s surprised I can read at all. I find it impossible to forgive him, but then I learn that he’s about to lose his job. He’s an aging executive with a large family to support, and I’m sure that this misfortune will soften his scorn and make him more sincerely apologetic. I decide to forgive him when all this happens.

This seems odd — if I’m sure that he’ll lose his job and express real contrition for stealing the paper, why do I have wait for this to happen? Why can’t I forgive him now?

Another twist: I learn that I (and only I) can save his job. This would amount to doing him a large favor, so I feel justified in withholding my help until I’ve forgiven him. But is this fair? Can I refuse to help him until I get a sincere apology, knowing that this will happen only after he loses his job?

Xanthippe is angry that Socrates is late, but she knows that he’ll apologize when she starts making dinner. Knowing this, can’t she skip the dinner and just forgive him? “In other words,” asks Tennessee State University philosopher James Montmarquet, “knowing that he would apologize, may she not still forgive him — having elected, for quite good reasons, not to allow conditions apt for his apology even to take place?”

(James Montmarquet, “Planned Forgiveness,” American Philosophical Quarterly 44:3 [July 2007], 285-296.)

“An Elevation Puzzle”

This does my head in — it’s a puzzle from the October 1958 issue of Eureka, the journal of the Cambridge University Mathematical Society:

“Below are shown the front elevation and plan of a mathematical figure. What is the side elevation?”
Image: Eureka

The terms (I believe) refer to multiview orthographic projection, the illustration technique used in architectural drawings: The front elevation is the view looking squarely at the “front” of the object, and the plan view looks down from above. What is the side view?

Click for Answer

“Auld Saws Speak Truth”

Scottish proverbs:

  • The shortest road’s the nearest.
  • The less wit a man has the less he kens the want o’t.
  • The gude dog doesna aye get the best bane.
  • Sorrow an’ ill weather come unca’d.
  • Silence and thought hurt nae man.
  • Self praise is nae honour.
  • Every bird thinks its ain nest best.
  • He that keeks through a keyhole may see what will vex him.
  • There’s naething mair precious than time.
  • He that lends money to a friend has a double loss.
  • Haste and anger hinder gude counsel.
  • Friends ‘gree best at a distance.
  • Weel done, soon done.
  • Be a friend to yoursel’ and ithers will.
  • A wise man wavers, a fool is fixed.
  • The langest day has an end.

And “There’s naething sae gude on this side o’ time but it micht hae been better.”

(From Colin S.K. Walker, Scottish Proverbs, 2000.)

Nice Try

In 2021 Denmark’s Kunsten Museum of Modern Art engaged artist Jens Haaning to recreate two of his earlier works, An Average Austrian Year Income and An Average Danish Annual Income. Those pieces had presented framed piles of kroner and euro bills to represent the sums indicated in their titles, so the museum gave Haaning 532,549 kroner for the purpose.

Instead, he delivered two framed blank canvases. The title of this new work, he said, was Take the Money and Run.

“This is only a piece of art if I don’t return the money,” he told the New York Times. “I believe that I have created a good and relevant piece of artwork, which could be hung on the wall.”

It didn’t work out that way — on Sept. 18, a Copenhagen court ruled that he must return the money.

Haaning acknowledged that he hadn’t fulfilled the commission, but “I completed something else,” he argued. “You’re asked to show a 10- and a 12-year-old work, and suddenly you have a better concept.”

(Thanks, Sharon.)


In a certain fair island, for commerce renown’d,
Whose fleets sailed in every sea,
A set of fanatics, men say, there was found,
Who set up an island and worship around,
And called it by name Elessdé.

Many heads had the monster, and tails not a few,
Of divers rare metals was he;
And temples they built him right goodly to view,
Where oft they would meet, and, like idolists true,
Pay their vows to the great Elessdé.

Moreover, at times would their frenzy attain
(‘Twas nought less) to so high a degree,
That his soul-blinded votaries did not complain,
But e’en laid down their lives his false favour to gain–
So great was thy power, Elessdé.

As for morals, this somewhat unscrupulous race
Were lax enough, ‘twixt you and me;
Men would poison their friends with professional grace,
And of the fell deed leave behind ne’er a trace,
For the sake of the fiend, Elessdé.

Then forgery flourished, and rampant and rife
Was each form of diablerie;
While the midnight assassin, with mallet and knife,
Would steal on his victim and rob him of life,
And all for thy love, Elessdé.

There were giants of crime on the earth in that day,
The like of which we may not see:
Although, peradventure, some sceptic will say
There be those even now who acknowledge the sway
Of the god of the world — £ s. d.

(That is, pounds, shillings, and pence, the pre-decimal currencies of the British Isles.)

From William T. Dobson, Poetical Ingenuities and Eccentricities, 1882.

Roll Call

More than 500 of the commanders in the American Civil War were West Point graduates, and all but a handful of these studied under the same military theorist, Dennis Hart Mahan, whose course “Engineering and the Science of War” applied the lesson of Napoleon’s campaigns — that the key to success was rapid maneuver to concentrate one’s forces at a critical point of weakness in the enemy position. (Of Grant’s encirclement of Vicksburg, Mahan said, “European warfare can produce nothing equal to it since the 1st Napoleon.”)

In addition to Grant, Mahan’s pupils included William Tecumseh Sherman, George Meade, George B. McClellan, Henry Halleck, George Henry Thomas, John Sedgwick, Ambrose Burnside, Joseph Hooker, and Philip Sheridan among the Union forces and Robert E. Lee, Jefferson Davis, Stonewall Jackson, James Longstreet, Albert Sidney Johnston, P.G.T. Beauregard, John Bell Hood, Richard S. Ewell, J.E.B. Stewart, and William J. Hardee in the Confederacy. Historian James Robertson called him “the guru of the generals.”

(James Robertson, The Untold Civil War, 2011.)


The “Swiss family Robinson” is not named Robinson. The title of Johann David Wyss’s 1812 novel shows the enormous influence of Daniel Defoe’s Robinson Crusoe even a century after its publication; the 18th century was filled with “Robinsonades” in German, Dutch, French, Danish, Swiss, Swedish, and Italian:

Teutsche Robinson, 1722
Americanische Robinson, 1724
Nordische Robinson, 1741
Hollandsche Robinson, 1743
Dänische Robinson, 1750
Walchersche Robinson, 1752
Maldivschen Philosophen Robine, 1753
Oude en Jongen Robinson, 1753
Isländische Robinson, 1755
Hartz-Robinson, 1755
Robinson vom Berge Libonon, 1755
Haagsche Robinson, 1758
Robertson [sic] aux terres australes, 1766
Steyerische Robinson, 1791
Böhmische Robinson, 1796

Wyss’s marooned Swiss family is nameless.

(Gary Dexter, Why Not Catch-21?, 2007.)