The Angel Problem

https://commons.wikimedia.org/wiki/File:Angel_problem.svg
Image: Wikimedia Commons

An angel stands on an infinite chessboard. On each turn she can move at most 3 king’s moves from her current position. Play then passes to a devil, who can eat any square on the board. The angel can’t land on an eaten square, but she can fly over it, as angels have wings. (In the diagram above, the angel starts at the origin of the grid and, since she’s limited to 3 king’s moves, can’t pass beyond the blue dotted boundary on her next turn.)

The devil wins if he can strand the angel by surrounding her with a “moat” 3 squares wide. The angel wins if she can continue to move forever. Who will succeed?

John Conway, who posed this question in 1982, offered $100 for a winning strategy for an angel of sufficiently high “power” (3 moves may not be enough; in fact a 1-power angel, an actual chess king, will lose). He also offered $1000 for a strategy that will enable a devil to win against an angel of any power.

It’s not immediately clear what strategy can save the angel. If she simply flees from nearby eaten squares, the devil can build a giant horseshoe and drive her into it. If she sprints in a single direction, the devil can build an impenetrable wall to stop her.

In fact it wasn’t until 2006 that András Máthé and Oddvar Kloster both showed that the angel has a winning strategy. In some variants, in higher dimensions, it’s still not certain she can survive.

(John H. Conway, “The Angel Problem,” in Richard J. Nowakowski, ed., Games of No Chance, 1996.)

While You Wait

https://commons.wikimedia.org/wiki/File:Grand_tour_guide_to_the_Yellowstone_National_Park_-_a_manual_for_tourists,_being_a_description_of_the_Mammoth_hot_springs,_the_geyser_basins,_the_cataracts,_the_ca%C3%B1ons,_and_other_features_of_the_new_(14761103635).jpg

Old Faithful is sometimes degraded by being made a laundry. Garments placed in the crater during quiescence are ejected thoroughly washed when the eruption takes place. Gen. Sheridan’s men, in 1882, found that linen and cotton fabrics were uninjured by the action of the water, but woolen clothes were torn to shreds.

— William C. Riley, Official Guide to the Yellowstone National Park, 1889

Safe!

https://patents.google.com/patent/US171038A/en

How can an umpire be sure a runner has reached first base? In 1875 inventor John O’Neill suggested fitting it with a bell to “indicate clearly and positively, without chance of error, the exact moment when the base is touched by the runner.”

The trouble is that the “enunciating base” will also sound when the first baseman steps on it. Ten years later William Williams suggested an electric bell, which could be heard more clearly by a single umpire behind home plate, but it faced the same objection. Both were forgotten.

Perspective

https://commons.wikimedia.org/wiki/File:Markus_Raetz_Geneve_Oui.jpg

Artist Markus Raetz erected this sign on the Rue du Rhône (at Place de la Fusterie) in downtown Geneva. What it says depends on where you stand.

Here’s a similar idea exhibited in a gallery:

Vinkensport

Each year, thousands of people take up seats along the streets of Flanders. Before each of them is a wooden box, and in each box is a single male finch. At a timekeeper’s signal, the observers begin to count the birds’ calls, making tally marks on long wooden sticks. After one hour, the bird that has sung the most calls is recognized as the winner.

This is vinkensport, a tradition in Flemish culture for more than 400 years. It was started by merchants in 1596, and as of 2007 an estimated 13,000 vinkeniers were still breeding 10,000 birds each year.

The sport’s popularity is growing, but like any sport it’s subject to cheating: When one finch produced 1,278 susk-e-wiets in an hour, its owner was accused of doping it with testosterone. Another competitor attracted suspicion when his box emitted exactly 725 calls in each of two matches; when a judge ordered the box opened, he discovered a mini-CD player inside.

Departing the Club

https://commons.wikimedia.org/wiki/File:Interior_of_the_Athen%C3%A6um_Club,_London-11297527785.jpg

At London’s prestigious Atheneum a venerable retainer reported to the club manager that member Prestwick was asleep in his favorite wing chair with a copy of The Times folded across his face. ‘What’s so unusual about that?’ asked the manager. ‘Member Prestwick has always slept in that chair with The Times folded across his face.’

‘I know, sir,’ replied the retainer, ‘but it’s yesterday’s Times.’

— Louis Kronenberger, The Cutting Edge, 1970

Return to Sender

This just caught my eye: Competitive boomerang throwers participate in a number of events: distance, accuracy, trick catches, and so on. One of the most popular of these is maximum time aloft, in which the goal is to keep the boomerang in the air as long as possible with a single throw.

Unbelievably, the record here is 17 minutes and 6 seconds, set by John Gorski of Avon, Ohio, in 1993. At the time a respectable flight might last 30 to 40 seconds, but Gorski’s boomerang hit a thermal that carried it upward an estimated 200 meters, where it hovered for several minutes over the Olentangy River. It drifted south for 225 meters, then headed north again, descending to find Gorski, who managed to catch it 40 meters from where he’d thrown it.

“I couldn’t believe I’d got it back,” Gorski said later. “I thought, ‘I’m never going to see this boomerang again,’ but then it stopped drifting and just hung there.”

Tournament director Chet Snouffer called it “an unbelievable, once-in-a-lifetime experience — he caught the perfect wave and surfed it right into the record books.”

Misc

  • Conceptual artist Joseph Beuys accepted responsibility for any snow that fell in Düsseldorf February 15-20, 1969.
  • Any three of the numbers {1, 22, 41, 58} add up to a perfect square.
  • Nebraska is triply landlocked — a resident must cross three states to reach an ocean, gulf, or bay.
  • The only temperature represented as a prime number in both Celsius and Fahrenheit is 5°C (41°F).
  • “A person reveals his character by nothing so clearly as the joke he resents.” — Georg Christoph Lichtenberg

“I was tossing around the names of various wars in which both the opponents appear: Spanish-American, Franco-Prussian, Sino-English, Russo-Japanese, Arab-Israeli, Judeo-Roman, Anglo-Norman, and Greco-Roman. Is it a quirk of historians or merely a coincidence that the opponent named first was always the loser? It would appear that a country about to embark on war would do well to see that the war is named before the fighting starts, with the enemy named first!” — David L. Silverman

Lost Treasure

https://commons.wikimedia.org/wiki/File:Treasure_Island_Map_over_Treasure_Island.png

Robert Louis Stevenson’s original map of Treasure Island was lost during publication. He sent it to his editor and was “aghast” to learn that it was never received. “I had written it up to the map,” he wrote — most of the novel’s plot had been inspired by the picturesque map he had dreamed up at the start. Now he had to redraw it working backward, inferring the island’s layout from the descriptions in the text.

It is one thing to draw a map at random, set a scale in one corner of it at a venture, and write up a story to the measurements. It is quite another to have to examine a whole book, make an inventory of all the allusions contained in it, and with a pair of compasses, painfully design a map to suit the data. I did it; and the map was drawn again in my father’s office, with embellishments of blowing whales and sailing ships, and my father himself brought into service a knack he had of various writing, and elaborately FORGED the signature of Captain Flint, and the sailing directions of Billy Bones. But somehow it was never Treasure Island to me.

“It is, perhaps, not often that a map figures so largely in a tale, yet it is always important,” Stevenson wrote. “Even with imaginary places, [the author] will do well in the beginning to provide a map; as he studies it, relations will appear that he had not thought upon; he will discover obvious, though unsuspected, short-cuts and footprints for his messengers; and even when a map is not all the plot, as it was in Treasure Island, it will be found to be a mine of suggestion.”

(From Stevenson’s “My First Book: ‘Treasure Island,'” first published in the Idler, August 1894.)