Which of the two shaded areas is larger, the central disc or the outer ring?
Surprisingly, they’re equal. Each of the concentric circles has a radius 1 unit larger than the last. So the area of the central disc is π × 32 square units, and the area of the outer ring is π × 52 – π × 42 = π × 32 square units. So the two areas are the same.
A brewery stored its beer in a cellar some distance from the bottling plant. The cellar was cooled by pipes that circulated a saline solution from a central cooling unit. The main pipe that connected this cooling unit and the cellar happened to pass near the cellar of a retailer.
The brewery’s owner eventually discovered that the retailer was using the saline solution to cool his own cellar. He sued the retailer for theft, but the judge ruled, “In accordance with Article 242 of the Criminal Code, theft is the unlawful appropriation of commodities belonging to another party. In the present case no theft has been committed, since the saline solution was not misappropriated; rather, it was returned in its entirety to the brewery’s main pipe.”
The brewery owner appealed the case, arguing, “The issue is not the theft of saline solution but the theft of energy. If the saline solution is used to cool the defendant’s cellar in addition to my own, I have to pay more for electricity to operate the central cooling unit.”
The court of appeals ruled: “The saline solution acquires heat from the retailer’s cellar; therefore, energy belonging to the brewery is not being stolen. On the contrary, the brewery is receiving gratuitous energy from the retailer.”
This story appeared in a German scientific monograph, “Questions of Thermodynamical Analysis,” by P. Grassman. In propounding it in May 1990, Quantum added, “We all agree the judge was wrong, but not everyone can correctly explain his error. Can you?”
Letters to the Sydney Morning Herald during the planning of the Sydney Opera House:
“Faced with the nightmare illustrated in your columns, some 25th century Bluebeard’s lair, its ominous vanes pointed skywards apparently only for the purpose of discharging guided missiles or some latter-day nuclear Evil Eye, words fail.”
— W.H. Peters, Sydney, Jan. 31, 1957
“To me, the winning design suggests some gargantuan monster which may have wandered over the land millions of years ago. It certainly is right out of place beside the dignity of the Harbour Bridge.”
— M. Rathbone, Kensington, Jan. 31, 1957
“This whale of a monument to the clever ugliness of ‘modern’ art will be a constant eyesore. Its over-finished roof with many curved surfaces all covered with white tiles will be a glaring monstrosity. Could not the suffering which it will cause be more equitably distributed by constructing the fins in such a way that they will act as giant megaphones and thus keep residents on the north supplied with the dying screams of melodramatic sopranos?”
— J.R.L. Johnstone Beecroft, Feb. 1, 1957
“With all respects to so-called modern art, I feel that the design is completely unbefitting our foreshores. Perhaps the judges had in mind the installation of a Big Dipper on the peak of the roof to help the opera company balance its budget.”
— Jack Zuber, Kingsgrove, Feb. 1, 1957
In 2003 Danish architect Jørn Utzon received the Pritzker Architecture Prize, architecture’s highest honour. The citation read, “There is no doubt that the Sydney Opera House is his masterpiece. It is one of the great iconic buildings of the 20th century, an image of great beauty that has become known throughout the world — a symbol for not only a city, but a whole country and continent.”
Peculiarly British limericks:
There was a young fellow of Beaulieu,
Who loved a fair maiden most treaulieu.
He said, “Do be mine,”
And she didn’t decline,
So the wedding was solemnized deaulieu.
There was a young maid of Aberystwyth,
Who took corn to the mill to make grystwyth,
The miller, named Jack,
With a pat on her back,
Pressed his own to the lips that she kystwyth.
There was a mechalnwick of Alnwick,
Whose opinions were anti-Germalnwick;
So when war had begun,
He went off with a gun
The proportions of which were Titalnwick.
There was a young lady of Slough,
Who went for a ride on a cough.
The brute pitched her off
When she started to coff;
She ne’er rides on such animals nough. (Langford Reed)
A bald-headed judge called Beauclerk
Fell in love with a maiden seau ferk
Residing at Bicester,
Who said when he kicester,
“I won’t wed a man without herk.”
See This Sceptred Isle and Sound Rhymes.
surbate
v. to make one’s feet sore
There’s a little old fellow and he has a little paintpot,
And a paucity of brushes is something that he ain’t got,
And when he sees a road sign, the road sign he betters,
And expresses of himself by eliminating letters.
Thus THROUGH ROAD
Becomes ROUGH ROAD
And CURVES DANGEROUS
Is transformed to CURVES ANGER US
And 24-HOUR SERVICE
Turns into 24-HOUR VICE
And MEN AT WORK IN ENTRANCE
Is reduced to MEN AT WORK IN TRANCE
An SLOW DOWN BRIDGE ONE WAY
Is triumphantly condensed to
LOW DOWN BRIDE ON WAY
But the old fellow feels a slight dissatisfaction
With the uninspiring process of pure subtraction.
The evidence would indicate he’s taken as his mission
The improvement of the road signs by the process of addition.
Thus TRAFFIC LIGHT AHEAD
Becomes TRAFFIC SLIGHT AHEAD
And GAS AND OIL
Is improved to GASP AND BOIL
And simple REST ROOMS
Appear as QUEEREST ROOMS
And UNDERPASS ONE WAY
Emerges as UNDERPASS GONE AWAY
And (perhaps his masterpiece)
RIGHT
EAST BOUND
TUNNEL
Is elaborated to
FRIGHTENED
BEASTS ABOUND
IN TUNNEL
Thus we see the critical mood
Becomes the creative attitude.
— Morris Bishop
In 1945, a U.S. Army transport plane crashed in New Guinea, leaving three survivors marooned in the island’s mountainous interior. Injured, starving, and exhausted, the group seemed beyond the hope of rescue. In this week’s episode of the Futility Closet podcast we’ll describe the plight of the stranded survivors and the remarkable plan to save them.
We’ll also reflect on synthetic fingerprints and puzzle over a suspicious notebook.
Designed in Belgium in 1860, the Apache centerfire revolver attracted a following in the French underworld because it combined three weapons in one: a single-action six-shot revolver, a dual-edged bayonet, and a set of brass knuckles that doubles as the revolver’s grip. The knife and the knuckle duster fold inward, so the whole apparatus can fit easily into a pocket or bag.
Without sights, trigger guard, or safety, the gun is tricky to operate, but then you probably won’t want it for long-range shootouts. “It was designed for self-defence and to be used at very close quarters,” said Charles Hartley, who auctioned off one of the few specimens in 2014. “There is no barrel to the gun so the user would have had to have had it pressed up against someone’s chest.”
Though its pinfire bullets are now obsolete, the weapon’s novelty still attracts collectors — another Apache, auctioned in 2013, drew $2,850.
(Thanks, Carlos.)
Suppose there are an infinite number of Grim Reapers. Each has an appointed time to kill Fred if it finds him alive.
The last Grim Reaper (call it #1) is appointed to do this exactly one minute after noon. The next-to-last (#2) is appointed to do it one half minute after noon. And so on: If it finds him alive, Reaper n will kill Fred exactly 1/2(n-1) minutes after noon.
Thus there is no first Reaper. For any given Reaper, there are infinitely many others who precede it by moments.
Whatever happens, we know that Fred can’t survive this ordeal — to go on with his life he must still be alive at 12:01, and we know for certain that if he lives that long then Reaper #1 will kill him. But in order to survive to 12:01 he must still be alive at 30 seconds after 12 — and at that time Reaper #2 will kill him. And so on. It appears that no Reaper will ever get the chance to kill Fred, because each is preceded by another who will rob him of the opportunity.
So it’s impossible that Fred survives, but it’s also impossible that any Reaper kills him. Must we say that he dies for certain but of no cause?
(From José Benardete’s Infinity: An Essay in Metaphysics, 1964.)
“No thoroughly occupied man was ever yet very miserable.” — Letitia Elizabeth Landon
