Periander ordered two young men to go out by night along a certain road, to kill the first man they met there, and to bury him.
Then he ordered four more men to find those two and kill them. And he sent an even greater number to murder those four.
Periander then set off down the road himself to wait for them.
In this way he ensured that the location of his grave would never be known.
You are to choose exactly one of two opaque boxes, A and B. A mean demon has put $1,000 in the box he predicted you would not take and nothing in the other. Since you know that the predictions are quite reliable, you can be sure you will pick the wrong box. … [Now suppose] we add a small bonus for taking box B. Some of us are now inclined to say that this modification renders the A option irrational. For it seems that the bonus tips the balance that previously existed between two equally good choices. If taking box A is as rational as taking box B, then the package deal of taking B plus the bonus must be more rational than taking Box A. Yet … if the bonus makes taking B the uniquely rational choice, then you would know that the money was in box A. This knowledge would force you to change your mind in favour of taking box A.
— Roy A. Sorensen, Blindspots, 1988, after Brian Skyrms
Sorensen adds: “Perhaps this reply has some persuasiveness when the bonus is small. But now suppose that the bonus is almost as great as the prize itself, say $900. Wouldn’t it be irrational to forgo a sure $900 by taking box A?”
See Newcomb’s Paradox.
In December 2005, tired of endless credit-card offers, West Hollywood realtor Gary More scrawled NEVER WASTE A TREE across one application and mailed it in.
Chase Visa issued a card to “Never Waste Tree.”
He cut it up.
Apparently vexed by bicycle thieves, Adolph Neubauer had a bright idea in 1899: Crank needles up through the seat when the bike isn’t in use “and thus prevent any one from mounting the bicycle without serious injury.”
He got the patent in 1900. Whether it worked is unknown.
More notable errors in the New York Times:
See also Erratum.
England and Portugal have been allies for 600 years:
It is cordially agreed that if, in time to come, one of the kings or his heir shall need the support of the other, or his help, and in order to get such assistance applies to his ally in lawful manner, the ally shall be bound to give aid and succour to the other, so far as he is able (without any deceit, fraud, or pretence) to the extent required by the danger to his ally’s realms, lands, domains, and subjects; and he shall be firmly bound by these present alliances to do this.
That agreement was signed in 1386. It’s the oldest surviving alliance in the world.
“Cleanliness is almost as bad as godliness.” — Samuel Butler
In June 1836, congressmen Daniel Jenifer of Maryland and Jesse A. Bynum of North Carolina met on the dueling ground in Bladensburg, Md. Jenifer had denounced Andrew Jackson’s party and refused to retract his statement. The two men stood 10 feet apart, both fired six times, and, amazingly, both missed six times. They called it a draw.
In The Field of Honor, his 1883 history of dueling, Benjamin Cummings Truman records a strange contest between Capt. Raoul de Vere and Col. Barbier-Dufai, of Paris. The two agreed to settle a quarrel by entering a coach with daggers in their right hands and with their left arms tied, and fighting while the coach was driven twice around the Place du Carousel. Both died.
Even stranger: A Spaniard and a German both loved the daughter of Maximilian II, but the emperor did not want to risk their lives in a conventional duel. Instead he promised the girl’s hand to whichever man could wrestle his opponent into a bag.
“The two gentlemen expressed their willingness to engage in even so ridiculous a contest for so superior a prize, and fought in the presence of the whole court, the contest lasting more than an hour, the Spaniard finally yielding, having been put fairly into the bag by the German, Baron Eberhard, who took it and its Castilian contents upon his back, and very gallantly laid them at the feet of the young lady, to whom he was married the following day. This is the only duel or tournament of the kind on record.”
See En Garde!
In March 1964, David Threlfall sent a unique request to bookmaker William Hill: “I’d like to bet £10 that a man will set foot on the surface of the moon before the first of January 1970.”
He’d heard President Kennedy’s 1961 address challenging the United States to put a man on the moon by the end of the decade, and “I thought if a bookmaker was prepared to offer reasonable odds it would be a commonsense bet.”
The bookmaker disagreed and put the odds at 1,000 to 1. Threlfall accepted, and the bet was placed on April 10.
As the Apollo program advanced, the odds began to drop, and people began to offer Threlfall thousands of pounds for his betting slip. He held on to it, though, and when Neil Armstrong set foot on the moon in 1969, he received the reward for his forethought — a check for £10,000.
Here’s proof that one leg of a triangle always equals the sum of the other two.
ABC is our triangle. Extend it make a parallelogram, as shown, and divide the parallelogram into a grid. Obviously,
AB + BC = (AG + HJ + KL + MN) + (GH + JK + LM + NC).
Now let the grid grow increasingly fine: Instead of dividing the parallelogram into a 4×4 grid, make it 5×5, then 6×6, and so on. With each iteration, the stairstep figure described above will approximate AC more closely, and yet its total length will always equal AB + BC. Thus, at the limit, AB + BC = AC. Where is the error?
(From Henry Dudeney’s Canterbury Puzzles, via W.W. Rouse Ball’s Mathematical Recreations and Essays, 1892.)