We want to build a road between two cities, A and B, that are separated by a river. We can build a bridge, but it must be perpendicular to the river’s banks, as shown. Where along the river’s length should we place the bridge if we want to minimize the total length of the road?
The closing days of World War II witnessed a bizarre battle with some unlikely allies: American and German soldiers joined forces to rescue a group of French prisoners from a medieval castle in the Austrian Alps. In this week’s episode of the Futility Closet podcast we’ll follow the Battle for Castle Itter, the only time that Allies and Germans fought together in the war.
We’ll also dodge another raft of aerial bombs and puzzle over a bottled pear.
Hatebeak (above) is a death metal band fronted by a Congo African grey parrot named Waldo. To date they’ve released four albums, Beak of Putrefaction, Bird Seeds of Vengeance, The Thing That Should Not Beak, and Number of the Beak.
Bird Seeds of Vengeance was made with Caninus, a deathgrind band led by two pitbull terriers, Basil and Budgie. Unfortunately Basil died in 2011, and founding member Budgie died earlier this year, so the band has now retired.
“We are all lucky to have had her in our orbit for as long as we did,” the surviving members wrote after Budgie’s death. “She touched many lives, licked many faces, pushed many people out of beds, stole many slices of pizza, ate many soundguy burritos and, most importantly, inspired many to adopt from shelters instead of buying from pet shops or online breeders.”
G.K. Chesterton stood 6 foot 4 and weighed 286 pounds.
During the First World War a lady in London asked why he was not out at the front.
He said, “If you go round to the side, you will see that I am.”
From T.R. Dawson, a logic problem posing as a chess puzzle. If pinned men do not check, how can White mate in two moves?
Here’s how the Union enciphered its messages during the Civil War. Abraham Lincoln sent this dispatch on June 1, 1863:
GUARD ADAM THEM THEY AT WAYLAND BROWN FOR KISSING VENUS CORRESPONDENTS AT NEPTUNE ARE OFF NELLY TURNING UP CAN GET WHY DETAINED TRIBUNE AND TIMES RICHARDSON THE ARE ASCERTAIN AND YOU FILLS BELLY THIS IF DETAINED PLEASE ODOR OF LUDLOW COMMISSIONER
The first word, GUARD, indicates the size of a containing rectangle and the paths on which the words must be laid out to decipher the message. In this case, they’ll go up the first column, down the second, up the fifth, down the fourth, and up the third. Also, just to confuse the Confederates, every eighth word after GUARD is a null and should be discarded. So we get:
FOR VENUS LUDLOW RICHARDSON AND BROWN CORRESPONDENTS OF THE TRIBUNE WAYLAND AT ODOR ARE DETAINED AT NEPTUNE PLEASE ASCERTAIN WHY THEY ARE DETAINED AND GET THEM OFF IF YOU CAN ADAM NELLY THIS FILLS UP
The last steps are to remove THIS FILLS UP, which is only there to fill out the block, and to replace a few code words:
VENUS = colonel
WAYLAND = captured
ODOR = Vicksburg
NEPTUNE = Richmond
ADAM = President of the United States
NELLY = 4:30 p.m.
That gives us the final message:
For Colonel Ludlow,
Richardson and Brown, correspondents of the Tribune, captured at Vicksburg, are detained at Richmond. Please ascertain why they are detained and get them off if you can.
The President, 4:30 p.m.
This system was such a valuable source of breaking news that Lincoln often visited the military telegraph office in the War Department, next to the White House, and would chat with the operators there. One of them, David Homer Bates, who was only 18 when the war started, remembered, “Outside the members of his cabinet and his private secretaries, none were brought into closer or more confidential relations with Lincoln than the cipher-operators, … for during the Civil War the President spent more of his waking hours in the War Department telegraph office than in any other place, except the White House. … His tall, homely form could be seen crossing the well-shaded lawn between the White House and the War Department day after day with unvaried regularity.”
(From David Kahn, The Codebreakers, 1996.)
“Those praised in a book take that praise, and more, as their due. What you meant as a gift is accepted as an obligation. In a second printing of one of his books, a writer listed the misprints in the first. Among them was the dedication.” — Baltasar Gracián
Between 1937 and 1939, Nazi Germany built a colossal beach resort on the island of Rügen in the Baltic Sea. Its scale was enormous: Meant to host 20,000 holiday-makers at a time in shifts of 10 days, the six-story edifice of 10,000 double rooms stretches for 4.5 kilometers, requiring almost an hour to walk its length. At the end of the war seven of a planned eight blocks and part of a main square had been completed. Since then it’s housed small-scale projects, including a youth and a family hostel, a skating hall, a theatre, workshops, museums, art galleries, secondhand shops, and a disco. Today five of the blocks have been developed as apartments and a new hostel, while the remaining three lie in ruins.
Until four years ago, fully 1 percent of Greenland’s population was housed in a single building, Blok P. Erected in the 1960s, it was five stories high and stretched 200 meters, the largest construction project in the Kingdom of Denmark, with one end boasting the world’s largest flag of Greenland. But its poor design made the building a difficult and depressing home for its residents, and it was demolished in 2012.
Before the Turkish invasion of Cyprus in 1974, the tourist district of Varosha was the nation’s premier vacation destination, with high-rise hotels, shopping centers, restaurants, and nightclubs. With the invasion, the entire population of 39,000 fled, leaving behind an opulent ghost town. Since then it’s been fenced off, accessible only by the Turkish military and United Nations personnel. Negotiations continue, but after 40 years of mounting disrepair it’s not clear how much of it might still be salvaged.
(Thanks, Matthias and Steve.)
Tom has a crystal ball that shows him the future. One day it shows him a bomb going off in the city. He alerts the authorities, who disable the bomb, saving millions of people. Tom is glad, but he wonders: How can this outcome be logically consistent with the future that the crystal ball had shown him? In that future he saw millions of people die, but in this future they’re still alive. He realizes that when he contacted the authorities the timeline must have split in two. In the original timeline, the bomb went off just as the crystal ball had foretold, and the city’s population did die. But in this new timeline, the authorities defused the bomb and everyone lived.
This understanding seems to explain what has happened, but it leaves a worrying subjective question. If there are two timelines then there are two Toms, both sharing the same history and presumably each realizing that two instances of his identity now exist. “We are familiar with physical things splitting into two, and can accept in principle that they could even be duplicated,” writes Western University philosopher John L. Bell. “But it is extremely difficult to make sense of the idea that an individual consciousness can be so split.”
The doomed Tom might ask himself, “Why am I the doomed Tom?” Objectively the answer is that he’s the Tom who failed to alert the authorities to the coming catastrophe. “But from a subjective point of view he can ask: why was I the Tom who failed to act? Why couldn’t I have been the saved Tom? There seems to be no satisfactory answer to this question.”
In his Philosophy of Mathematics and Natural Science, mathematician Hermann Weyl notes that Leibniz thought he had resolved the tension between freedom and predestination by letting God consider the infinite number of possible universes and assign existence to one of them. “This solution may objectively be sufficient,” Weyl wrote, “but it is shattered by the desperate outcry of Judas, ‘Why did I have to be Judas?'”
(From Oppositions and Paradoxes, 2016.)
