New Markets
Yale economist Paul Krugman published a curious paper in 2010: “The Theory of Interstellar Trade”:
This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: how should interest charges on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. A solution is derived from economic theory, and two useless but true theorems are proved.
He added, “While the subject of this paper is silly, the analysis actually does make sense. This paper, then, is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics.”
(Paul Krugman, “The Theory of Interstellar Trade,” Economic Inquiry 48:4 [October 2010], 1119-1123. See The Telltale Mart.)
Comment
Preparing a time capsule in 1939, the Westinghouse Electric & Manufacturing Company asked Albert Einstein to compose a message for the people of AD 6939. He sent this:
Our time is rich in inventive minds, the inventions of which could facilitate our lives considerably. We are crossing the seas by power and utilize power also in order to relieve humanity from all tiring muscular work. We have learned to fly and we are able to send messages and news without any difficulty over the entire world through electric waves.
However, the production and distribution of commodities is entirely unorganized so that everybody must live in fear of being eliminated from the economic cycle, in this way suffering for the want of everything. Furthermore, people living in different countries kill each other at irregular time intervals, so that also for this reason any one who thinks about the future must live in fear and terror. This is due to the fact that the intelligence & character of the masses are incomparably lower than the intelligence and character of the few who produce some thing valuable for the community.
I trust that posterity will read these statements with a feeling of proud and justified superiority.
The message was recorded on microfilm and resides 50 feet below Flushing Meadows–Corona Park in New York City.
Nonsense Cookery
Edward Lear’s recipe for amblongus pie, 1872:
Take 4 pounds (say 4 1-2 pounds) of fresh Amblongusses, and put them in a small pipkin.
Cover them with water, and boil them for 8 hours incessantly; after which add 2 pints of new milk, and proceed to boil for 4 hours more.
When you have ascertained that the Amblongusses are quite soft, take them out, and place them in a wide pan, taking care to shake them well previously.
Grate some nutmeg over the surface, and cover them carefully with powdered gingerbread, curry-powder, and a sufficient quantity of Cayenne pepper.
Remove the pan into the next room, and place it on the floor. Bring it back again, and let it simmer for three-quarters of an hour. Shake the pan violently till all the Amblongusses have become of a pale purple colour.
Then, having prepared the paste, insert the whole carefully; adding at the same time a small pigeon, 2 slices of beef, 4 cauliflowers, and any number of oysters.
Watch patiently till the crust begins to rise, and add a pinch of salt from time to time.
Serve up in a clean dish, and throw the whole out of window as fast as possible.
Crash Course
What is this? It’s the history of 800 successive unsteered bicycles, each traveling from left to right until it falls over. Caltech computer scientist Matthew Cook modeled the behavior in 2004, hoping to learn how we balance, steer, and correct our paths on two wheels. He found that just two artificial neurons were enough to control a bicycle competently — the system even learned to thread a series of waypoints:
(Matthew Cook, “It Takes Two Neurons to Ride a Bicycle,” Demonstration at NIPS 4, 2004.) (Thanks, Dan.)
“Stock-Breeding”
From John Scott, The Puzzle King, 1899:
“A farmer, being asked what number of animals he kept, answered: ‘They’re all horses but two, all sheep but two, and all pigs but two.’ How many had he?”
Enterprise
Filmmaker Melton Barker started a novel business in the 1930s: He traveled across the United States, shooting a film in each town using local talent. The residents would gladly pay a fee to see themselves immortalized in a two-reel short, and their support financed the production and Barker’s livelihood until he could reach the next town.
He shot the same film, The Kidnappers Foil, 300 times over 40 years, using the same script and largely the same shots. A young girl named Betty Davis is kidnapped on her birthday, and the town’s children organize a search for her. The finished film, 15 to 20 minutes long, would be screened at local theaters. (The example above was shot in Fayetteville, Arkansas, in February 1937.)
Most of these films have been lost, but the project as a whole was added to the National Film Registry in 2012. The Texas Archive of the Moving Image has a collection of surviving films.
(Thanks, Kevin.)
A Self-Descriptive Crossword Puzzle
From Lee Sallows:
Can you complete the ‘self-descriptive crossword puzzle’ at left below? As in the solution to a similar puzzle seen at right, each of its 13 entries, 6 horizontal, 7 vertical, consists of an English number name folowed by a space followed by a distinct letter. The number preceding each letter describes the total number of occurrences of the letter in the completed puzzle. Hence, in the example, E occurs thirteen times, G only once, and so on, as readers can check. Note that the self-description is complete; every distinct letter is counted.
Though far from easy, the self-descriptive property of the crossword enables its solution to be inferred from its empty grid using reasoning based on orthography only.
Inspiration
Edgar Allan Poe’s tale “The Cask of Amontillado” is regarded today as a testament to his imagination, but in fact it was inspired by a feud with a literary rival. Poe and Thomas Dunn English had been friends, but they had a falling-out that descended into a fistfight in which Poe claimed to administer “a flogging which he will remember to the day of his death.” Thereafter the two caricatured one another in their writings — Poe even successfully sued English’s editors at the New York Mirror for libel in 1846.
In English’s novel 1844, the character Marmaduke Hammerhead is a veiled dig at Poe — he’s a liar and drunkard who is said to be the author of “The Black Crow” and uses phrases such as “Nevermore” and “lost Lenore.” It was in response to this novel that Poe wrote “The Cask of Amontillado” — the story mentions a secret society, a signal of distress, and a particular coat of arms because they all figured in English’s book. The very setting of Poe’s story derives from a scene in English’s novel that takes place in a subterranean vault.
But these associations have now been forgotten, and Poe’s story is remembered as a tale of the fantastic.
Insight
One other interesting item from Paul Halmos’ Problems for Mathematicians, Young and Old (1991): Pick a point in the first quadrant and draw a downward-sloping line through it. This line makes a triangle with the coordinate axes. At what angle should we set the line to minimize the area of the triangle?
This problem yields to calculus, but there’s a simple geometric solution. Reflect the axes through the point to make a box:
Now as we swivel our line through the point, it defines two triangles, one against each set of axes. The area of the combined triangles is equal to or greater than the area of the box. So, intuitively, it reaches a minimum just as the swiveling line becomes a diagonal of the box. That’s the answer.