City A contains 20,000 people. One percent of these have one foot only and wear one shoe apiece. Half of the remaining people go barefoot, wearing no shoes at all, and the rest wear two shoes apiece.
In City B, 20 percent of the residents have one foot only and wear one shoe apiece. Of the remainder, half go barefoot and half wear two shoes apiece.
If 20,000 shoes are worn in City B, what is its population?
In desert conditions, helicopter rotors are sometimes surrounded by sparkling rings. When flying sand strikes the abrasion strips on the leading edges of the blades, clouds of eroded titanium particles ignite as they’re exposed to oxygen.
The effect is most visible at night when the aircraft is near the ground, but it’s been observed as high as 1700 feet. It’s named after Benjamin Kopp and Joseph Etchells, two soldiers killed in combat in Afghanistan in July 2009.
Psychologist Abraham S. Luchins discovered a discouraging phenomenon in 1942: When people find a problem-solving strategy that works successfully in multiple trials, they’ll tend to adopt the same strategy even in situations when more efficient solutions are available.
Suppose you’re given water jugs with capacities of 21 units (A), 127 units (B), and 3 units (C) of water. Then you’re asked to use these to measure out 100 units of water. You find that you can do this by filling jug B and using that to fill jug A once and jug C twice, leaving 100 units in jug B. In several similar problems you find that this strategy, B – A – 2C, works.
But then you’re given an “extinction problem” in which this strategy doesn’t work. And in the next problem you’re given jugs of capacity 15, 39, and 3 and asked to measure 18 units of water. The old strategy, B – A – 2C, works here, but there’s a simpler solution: A + C.
In Luchins’ experiments, a control group that had not been primed with the early B – A – 2C successes hit immediately on the A + C solution in the last test. But subjects who did have those early successes tended to revert to the original strategy, reflecting a “mechanized” state of mind that prevented them from seeking more efficient solutions. When Luchins told them “Don’t be blind,” more than half of them found the A + C solution.
The reasons for this are still being studied in different populations and with different types of tasks. Luchins acknowledges that habit can be useful, but notes that when, “instead of the individual mastering the habit, the habit masters the individual — then mechanization is indeed a dangerous thing.”
(Abraham S. Luchins, “Mechanization in Problem Solving: The Effect of Einstellung,” Psychological Monographs 54:6 [1942]: i.)
The flag of Guyana was designed by a college student. In 1960, as that country was emerging from British colonial rule, Whitney Smith, then a 20-year-old undergraduate at Harvard, wrote to independence leader Cheddi Jagan and asked what flag the new country had chosen. Jagan told him no decision had been made and asked him for ideas. Smith designed a flag, got his mother to sew it, and sent it in, and Guyana adopted it, with some slight modifications.
Smith went on to create the journal Flag Bulletin; found the Flag Research Center; design flags for the Saudi Navy, Bonaire, and Aruba; organize the First International Congress of Vexillology (and coin that term); help to found the North American Vexillological Association and the Flag Heritage Association; and write The Flag Book of the United States, Flag Lore of All Nations, and more than 250 flag histories for the Encyclopaedia Britannica.
“I’m a monomaniac, that’s clear,” he told People magazine. “But I’m more fortunate than most people because I have something that infuses my whole life. I relate flags to everything.”
Lime juice is phototoxic — on contact it sensitizes the skin to ultraviolet light, so that exposure to sunlight can then produce redness, itching, burning, and even blisters.
The reaction is called phytophotodermatitis, or margarita photodermatitis. It can also be caused by celery, parsnips, parsley, and figs.
The dome in Vienna’s Jesuit Church isn’t there — artist Andrea Pozzo painted the ceiling of the nave in 1703 to create a convincing illusion when viewed from the right angle.
A stone slab in the floor indicates the ideal spot from which to view it.
janua
n. an introduction to some branch of learning
In Umberto Eco’s Foucault’s Pendulum (1988), two publishers propose a School of Comparative Irrelevance that teaches “useless or impossible courses,” such as Urban Planning for Gypsies, Aztec Equitation, and Potio-section.
‘Potio-section, as everybody knows, of course, is the art of slicing soup. No, no,’ he said to Diotallevi. ‘It’s not a department, it’s a subject, like Mechanical Avunculogratulation or Pylocatabasis. They all fall under the heading of Tetrapyloctomy.’
‘What’s tetra …?’ I asked.
‘The art of splitting a hair four ways. This is the department of useless techniques. Mechanical Avunculogratulation, for example, is how to build machines for greeting uncles. We’re not sure, though, if Pylocatabasis belongs, since it’s the art of being saved by a hair. Somehow that doesn’t seem completely useless.’
Overall, the school’s aim is “to turn out scholars capable of endlessly increasing the number of unnecessary subjects.” “The Tetrapyloctomy department has a preparatory function; its purpose is to inculcate a sense of irrelevance. Another important department is Adynata, or Impossibilia. Like Urban Planning for Gypsies. The essence of the discipline is the comprehension of the underlying reasons for a thing’s absurdity. We have courses in Morse syntax, the history of antarctic agriculture, the history of Easter Island painting, contemporary Sumerian literature, Montessori grading, Assyrio-Babylonian philately, the technology of the wheel in pre-Columbian empires, and the phonetics of the silent film.”
(Thanks, Macari.)
Financial publisher Gilbert Kaplan fell so in love with Mahler’s second symphony that he bought the manuscript, paid musicians to teach him to conduct it, rented Avery Fisher Hall, and led the American Symphony and the Westminster Symphonic Choir through a performance of his own in 1982.
The orchestra had requested that no reviews be published, but the Village Voice published one anyway — and it was favorable. So Kaplan conducted the symphony another 100 times throughout his life and recorded it twice, with the London Symphony Orchestra and the Vienna Philharmonic. Opinions were mixed, but he did receive some discerning praise. Of a 2008 performance with the New York Philharmonic, Steve Smith wrote in the New York Times:
That Mr. Kaplan is no professional conductor was immediately apparent. Square-shouldered and stiff, he indulged in no flamboyant gymnastics. He conducted from memory, beating time proficiently and providing cues as needed. Only in a few passages, like the pages of heavenly bliss just before the first movement’s tempo-sostenuto conclusion, did a curl of the lip suggest that he was swept up in his work. His efforts were evident throughout a performance of sharp definition and shattering power. From the acute punch of the opening notes, every detail of this huge, complex score came through with unusual clarity and impeccable balance. Every gesture had purpose and impact, and the performance as a whole had an inexorable sweep. … It seems likely that no one is better equipped to reveal the impact of precisely what Mahler put on the page.
But trombonist David Finlayson called the same performance a “woefully sad farce,” and Kaplan wasn’t asked back. “I don’t think anyone will confuse me with Lorin Maazel when it comes to technique,” he said, “and I may need to speak more than somebody who is more skillful, like Lorin, but I do get the results I want, and I did get the results I wanted that night. If some people are displeased, I can’t help it.”
In August 1947 a British South American Airways airliner en route from Buenos Aires to Santiago crashed into Mount Tupungato in the Argentine Andes. The wreckage wasn’t located for 50 years, but it’s believed today that, hindered by the jet stream, the pilots had started their descent before they’d cleared the mountaintops and crashed into Tupungato.
The last Morse code message received by the Santiago airport was “ETA SANTIAGO 17.45 HRS STENDEC.” The operator didn’t recognize the last word and asked that it be sent again. The flight transmitted STENDEC twice more and then was lost. The meaning of that last transmission is unknown — despite much speculation, it’s never been definitively explained.
A dominant male long-tailed manakin acquires a team of subordinate males to help him woo females. “It’s the only example of cooperative male-male displays ever discovered in the entire animal kingdom,” writes Noah Strycker in The Thing With Feathers.
It’s common for male animals to cooperate to impress females, but typically each of those males is hoping to mate. Among manakins the eldest male gets this right, and the others defer until they succeed him.
Strycker writes, “A pair of male long-tailed manakins may work together like this for five years, building up their jungle reputation as hot dancers, before the alpha male dies and the backup singer takes his place with a new apprentice.”
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