By Alexander Yarosh. The position above was reached in a legal game, except that one piece has been knocked off the board. What was it?
Saving Face
“The Joker,” a picture-preserving geomagic square by Lee Sallows. The 16 pieces can be assembled in varying groups of 4 to produce the same picture in 16 different ways, without rotation or reflection.
The outline need not be a joker — it can take almost any shape.
In a Word
titivil
n. “Name for a devil said to collect fragments of words dropped, skipped, or mumbled in the recitation of divine service, and to carry them to hell, to be registered against the offender.” [OED]
Low Profile
In 2008 L.A. Innes of Jamestown, Saint Helena, auctioned a collection of images taken during the Boer War. This one shows a prisoner standing next to a tortoise on the island. The tortoise was mature at the time of the photograph, which was taken in 1900, and investigators were surprised to find that he’s still alive — “Jonathan” lives on the grounds of the governor’s residence, blind in one eye but still active and mating with other tortoises.
If he was 70 at the time Innes’ photograph was taken, then he’s 184 today — the oldest living reptile on earth.
Small World
I don’t think this was ever built — in 1904 engineer Hiram Stevens Maxim designed an amusement with a rotating parabolic floor “for producing illusionary effects”:
With such a contrivance when persons enter the hollow sphere they will not be able to tell whether it is revolving or standing still and by reason of the parabolic floor, persons near the outer edge would, to the persons standing near the centre, appear to be walking with their heads directed inward. When the sphere revolves some curious phenomena will be obtained in walking outward and inward on such a floor, and the throwing of a ball from the centre outward and vice versa will move in an unexpected direction that will be very puzzling to the people in the sphere.
Fig. 3, below, shows the perspective from the edge of the floor as it rotates. If mirrors were positioned overhead, as in Fig. 4, “people could then be made to appear to be walking all over the inside of the sphere with their heads pointing inward and their feet pointing outward.”
The Just World Phenomenon
In 1966 University of Kentucky social psychologist Melvin Lerner asked 72 undergraduate women to observe a peer working on a learning task. When the learner made an error she appeared to receive a painful electric shock. In describing her suffering, the observers tended to reject and devalue her when they thought they would continue to see her suffer in a later session.
Lerner suggested that we come to terms with the suffering we see around us by deciding that the world is just — that those who are unfortunate somehow deserve their fate, and thus that we can avoid such a fate ourselves. This is reflected in figures of speech such as “You reap what you sow” and “He got what was coming to him.”
“If people did not believe that they could get what they want and avoid what they abhor by performing certain appropriate acts, they would be virtually incapacitated,” Lerner wrote. “If this is true, then the person who sees suffering or misfortune will be motivated to believe that the unfortunate victim in some sense merited his fate.”
(Melvin J. Lerner and Carolyn H. Simmons, “Observer’s reaction to the ‘innocent victim’: Compassion or rejection?”, Journal of Personality and Social Psychology 4(2) [August 1966], 203-210.)
Seeing Double
In 1944, as the Allies were preparing to invade France, British Intelligence sought a way to confuse the Germans as to their plans. They hired Meyrick Clifton James (right), an Australian-born lieutenant in the Army Pay Corps who bore a striking resemblance to Field Marshal Bernard Montgomery, who would be commanding the Allied ground troops during the invasion. David Niven, then a colonel in the Army Film Unit, invited James to London under cover as a journalist, and James set about studying the general’s speech patterns and mannerisms. Then he was conspicuously dispatched, as Monty, to Gibraltar and then to Algiers, watched by avid German spies.
It seemed to work. The plot went through “from start to finish without a hitch,” MI5 reported, “and we knew that the main feature of its story had reached the Germans.” The real Monty led the successful landings at Normandy while James recovered from the ordeal in a safe house in Cairo. “He was under terrible pressure and strain,” reported the wife of an intelligence officer detailed to look after him. “Coming out of that part was very difficult for him.” But he had some consolation: Under army rules, he would receive the equivalent of a general’s pay for every day he had impersonated Monty.
Podcast Episode 16: A Very Popular Sack of Flour
In 1864 Nevada mining merchant Reuel Gridley found a unique way to raise money for wounded Union soldiers: He repeatedly auctioned the same 50-pound sack of flour, raising $250,000 from sympathetic donors across the country.
In this episode of the Futility Closet podcast we’ll discover the origins of Gridley’s floury odyssey. We’ll also hear H.L. Mencken’s translation of the Declaration of Independence into American English and try to figure out where tourism increases the price of electricity.
Unquote
“If Bacon wrote Shakespeare, who wrote Bacon?” — George Lyman Kittredge
Two-Toned
A problem from the 2004 Moscow Mathematical Olympiad:
An arithmetic progression consists of integers. The sum of its first n terms is a power of two. Prove that n is also a power of two.