Several spherical planets of equal size are floating in space. The surface of each planet includes a region that is invisible from the other planets. Prove that the sum of these regions is equal to the surface area of one planet.
Language Arts
Johann David Steingruber fulfilled his literary ambitions on a drafting table — his Architectural Alphabet (1773) renders each letter of the alphabet as the floor plan of a palace.
Antonio Basoli’s Alfabeto Pittorico (1839) presents the letters as architectural drawings:
Perhaps next we can actually build them.
Unquote
“It is the law of life that if you are kind to someone you feel happy. If you are cruel you are unhappy. And if you hurt someone, you will be hurt back.” — Cary Grant
“When I do good, I feel good. When I do bad, I feel bad. That’s my religion.” — Abraham Lincoln
“It all comes to this: the simplest way to be happy is to do good.” — Helen Keller
Agitato
A fight with a piano that came near proving disastrous to the greatest of pianists, occurred on shipboard wile Paderewski was on his way to New York a short time ago. Paderewski in his state room had a small upright piano on which to practice. It was fastened to the floor by means of bolts. On the opposite side of the room was the bed. In a heavy storm the piano was loosened by the rolling of the vessel. Straight it made for the pianist and crashed into his bed, nearly pinning him to the wall. Paderewski on reaching the floor rushed to the opposite side of the room. Instantly the piano followed, coming at him with great force. He dodged it, but it came at him again, being hurled about in the room by the rolling of the boat. The pianist tried to get out the door, but could not loosen the bolt and he was thus hemmed in with the tumbling piano which threatened to crush him to death at every second. There was nothing to do but wrestle with the instrument. He grasped it as it came toward him again and after lengthy struggle in which he was nearly exhausted, succeeded in binding it to the wall.
— Popular Mechanics, 1902
Overtime
As a boy in Romania, György Ligeti had been enchanted with the story about a widow who lives in a house full of clocks. “Nobody comes, maybe for a hundred years,” he said. “Nothing happens. So there is a combination of movement, which is machine-like, and absolutely nothing … a timelessness … no beginning and no end.”
When he became a composer, Ligeti set out to capture this feeling with Poème symphonique for 100 metronomes. At a conductor’s signal, each of 10 players winds up 10 metronomes; after an interval, the conductor gives a second signal, at which the players set the metronomes running, each at a unique tempo, and the performers leave the stage.
As soon as some of the metronomes have run down, changing rhythmic patterns emerge, depending on the density of the ticking, until, at the end, there is only one, slowly ticking metronome left, whose rhythm is then regular. The homogeneous disorder of the beginning is called ‘maximal entropy’ in the jargon of information theory (and in thermodynamics). The irregular grid structures gradually emerge, and the entropy is reduced since previously unpredictable ordered patterns grow out of the opening uniformity. When only a single metronome is left ticking in a completely predictable manner, then the entropy is maximal again — or so the theory goes.
All this went right over the heads of the Holland audience for whom the piece debuted in 1963. “The last tick of the last metronome was followed by an oppressive silence,” Ligeti remembered. “Then there were menacing cries of protest,” and a planned television performance was canceled. Undaunted, Ligeti later altered the performance so that the metronomes were already running when the audience entered the concert hall, “so that the piece truly runs like a machine: metronomes and audience are confronted with each other without any human mediation.” “Radicalism and petit-bourgeois attitudes are not so far from one another,” he wrote. “Both wear the blinkers of the narrow-minded.”
Strategy
When Franklin was negotiating in Paris, he sometimes went into a café to play at chess. A crowd usually assembled, of course to see the man rather than the play. Upon one occasion, Franklin lost in the middle of the game, when composedly taking the king from the board, he put him into his pocket, and continued to move. The antagonist looked up. The face of Franklin was so grave, and his gesture so much in earnest, that he began with an expostulatory, ‘Sir.’ ‘Yes, Sir, continue,’ said Franklin, ‘and we shall soon see that the party without a king will win the game.’
— From a letter by Frances Wright to Jeremy Bentham, relaying an anecdote from Lafayette, Sept. 12, 1821
Bad Behavior
You and I drive from Los Angeles to Las Vegas in separate cars. We depart simultaneously, and you stay always ahead of me, dutifully driving the speed limit throughout the trip. Nonetheless I get ticketed for speeding. How?
The Parity Paradox
Consider a finite list of n statements:
S1: At least one of statements S1-Sn is false.
S2: At least two of statements S1-Sn is false.
…
Sn-1: At least n-1 of statements S1-Sn is false.
Sn: At least n of statements S1-Sn is false.
Is this a paradox? It depends: The statements form a self-consistent system if n is even, but not if it’s odd.
From Roy T. Cook’s new book Paradoxes — which is dedicated in part to “anyone whom I don’t discuss in this book.”
Patron Ain’t
Franz Bibfeldt is unusual among theologians — he doesn’t exist. In 1947, divinity student Robert Clausen invented the name for a fictitious footnote in a term paper at Concordia Seminary in St. Louis, and his classmate Martin Marty then wrote a review of Bibfeldt’s book The Relieved Paradox in the seminary magazine. The book was imaginary, but the conspirators arranged for it to be cataloged at the school library and always checked out.
When the hoax was discovered, the perpetrators were reprimanded and Marty was sent to Chicago, where he eventually rose to become a dean at the University of Chicago divinity school. So, Marty said, “Bibfeldt had more influence on me than any other theologian.”
Under Marty’s influence, Bibfeldt grew into an invisible mainstay at the school. A display case in the entry hall was filled with signed photographs of mayor Richard Daley, Spiro Agnew, Illinois senator Charles Percy, former Georgia governor Lester Maddox, and the 1971 Playmate of the Year, all inscribed to Bibfeldt, and an annual symposium featuring bratwurst and beer was held each year on the Wednesday closest to April Fool’s Day. Graduates eventually spread Bibfeldt’s gospel elsewhere — he’s noted in the Oxford Encyclopedia of the Reformation; a session at the American Association of Religions meeting in 1988 was devoted to Bibfeldt; and in 1994 the evangelical satire magazine The Wittenberg Door named him theologian of the year.
Bibfeldt himself is characteristically modest — reportedly he has given only one interview, and that to Howard Hughes — but his acts are famous:
- He adapted the Sermon on the Mount for American audiences, writing, “Blessed are the happy who have everything, because they won’t need to be comforted” and “Blessed are the impeccably dressed, because they will look nice when they see God.”
- He responded sharply to Kierkegaard’s Either/Or with a treatise titled Both/And, followed by the conciliatory Either/Or and/or Both/And.
- Other publications include A Pragmatist’s Paraphrase of Selected Sayings of Jesus, The Boys of Sumer: Akkadian Origins of the National Pastime, I Hear What You’re Saying, But I Just Don’t Care: Thoughts on Pastoral Counseling, Luther on Vacation: From Worms to Cancun, and The Wealth of King Solomon: A Hebrew Scripture Prefigurement of Sports Contracts.
- “It is more difficult for a rich man to enter the Kingdom of Heaven than for a camel to pass through the eye of a needle,” he wrote. “Yet, with genetic engineering, we can now breed very small camels.”
“We use him very mildly, gently, to satirize the whole theological system,” Marty said. “There’s really no malice in it.”
