House Call

Letter from Charles Dickens to a chimney sweep, March 15, 1864:

Dear Sir,

Since you last swept my study chimney it has developed some peculiar eccentricities. Smoke has indeed proceeded from the cowl that surmounts it, but it has seemingly been undergoing internal agonies of a most distressing nature, and pours forth disastrous volumes of swarthy vapour into the apartment wherein I habitually labour. Although a comforting relief probably to the chimney, this is not altogether convenient to me. If you can send a confidential sub-sweep, with whom the chimney can engage in social intercourse, it might be induced to disclose the cause of the departure from its normal functions.

Faithfully yours,

Charles Dickens

| Literature · Society

The Conscience Fund

During the Civil War, the U.S. Treasury received a check for $1,500 from a private citizen who said he had misappropriated government funds while serving as a quartermaster in the Army. He said he felt guilty.

“Suppose we call this a contribution to the conscience fund and get it announced in the newspapers,” suggested Treasury Secretary Francis Spinner. “Perhaps we will get some more.”

Ever since then, the Treasury has maintained a “conscience fund” to which guilt-ridden citizens can contribute. In its first 20 years, the fund received $250,000; by 1987 it had taken in more than $5.7 million. One Massachusetts man contributed 9 cents for using a damaged stamp on a letter, but in 1950 a single individual sent $139,000.

In order to encourage citizens to contribute, Treasury officials don’t try to identify or punish the donors. Most donations are anonymous, and many letters are from clergy, following up confessions taken at deathbeds.

Many contributions are sent by citizens who have resolved to start anew in life by righting past wrongs, but some are more grudging. In 2004, one donor wrote, “Dear Internal Revenue Service, I have not been able to sleep at night because I cheated on last year’s income tax. Enclosed find a cashier’s check for $1,000. If I still can’t sleep, I’ll send you the balance.”

| Society

The World Backstage

This is charming — an inventory of “all the properties for my Lord Admiral’s men,” taken by theatrical impresario Philip Henslowe on March 10, 1598:

Item: 1 rock, 1 cage, 1 Hell-mouth
Item: 1 tomb of Guido, 1 tomb of Dido, 1 bedstead
Item: 8 lances, 1 pair of stairs for Phaeton
Item: 2 steeples, and 1 chime of bells, and 1 beacon
Item: 1 globe, and 1 golden sceptre; 3 clubs
Item: 2 marchpanes, and the city of Rome
Item: 1 golden fleece; 2 rackets; 1 bay-tree
Item: 1 wooden canopy; old Mahomet’s head
Item: 1 lion skin; 1 bear’s skin; and Phaeton’s limbs, and Phaeton chariot; and Argus’ head
Item: Neptune fork and garland
Item: 8 vizards; Tamburlaine bridle; 1 wooden mattock
Item: Cupid’s bow and quiver; the cloth of the sun and moon
Item: 1 boar’s head and Cerberus’ three heads
Item: 1 caduceus; 2 moss banks, and 1 snake
Item: 2 fans of feathers; Belin Dun’s stable; 1 tree of golden apples; Tantalus’ tree; 9 iron targets
Item: 1 Mercury’s wings; Tasso picture; 1 helmet with dragon; 1 shield with 3 lions; 1 elm bowl
Item: 1 lion; 2 lion heads; 1 great horse with his legs; 1 sackbut
Item: 1 black dog
Item: 1 cauldron for the Jew

Much of what we know about the business of Elizabethan theater comes from a book of accounts that Henslowe kept around the turn of the 17th century. He never mentions Shakespeare directly, but his theaters competed with the Globe.

| Art

The Parent Trap

The founder of Mother’s Day, Anna Jarvis, had no children of her own and decried the commercialization of the holiday.

Jarvis had proposed a national Mother’s Day in 1907, in part to honor her own mother. She promoted the idea with governors, congressmen, editors, and the White House, and in 1914 Woodrow Wilson set aside the second Sunday in May to honor the nation’s mothers. But the holiday was almost immediately co-opted by merchants, a turn that horrified Jarvis. “Confectioners put a white ribbon on a box of candy and advance the price just because it’s Mother’s Day,” she complained in 1924. “There is no connection between candy and this day. It is pure commercialization.”

She tried to stem the tide by legal means, incorporating herself as the Mother’s Day International Association and threatening copyright suits against what she felt were commercial celebrations. She had recommended the wearing of carnations to mark the holiday; when florists raised the price she distributed celluloid buttons instead at her own expense.

She reserved a special bitterness for sons who bought mass-produced cards for their mothers. “A maudlin, insincere printed card or ready-made telegram means nothing except that you’re too lazy to write to the woman who has done more for you than anyone else in the world,” she said. “Any mother would rather have a line of the worst scribble from her son or daughter than any fancy greeting card.”

“The sending of a wire is not sufficient. Write a letter to your mother. No person is too busy to do this.”

It was hopeless. Her spirit never flagged, but her finances began to give way, and in 1943, penniless and almost blind, she was admitted to a Philadelphia hospital. Her friends pledged funds for her support, and she died in a West Chester sanitarium in 1948.

| Society

Black and White

de boer chess problem

By Gerke Luiten De Boer. White to mate in two moves.

Click for Answer
| Puzzles

Well Done

http://commons.wikimedia.org/wiki/File:Filippo_Palazzi_-_Giovinetta_alla_sorgente_(Napoli).jpg

Using a 7-quart and a 3-quart jug, how can you obtain exactly 5 quarts of water from a well?

That’s a water-fetching puzzle, a familiar task in puzzle books. Most such problems can be solved fairly easily using intuition or trial and error, but in Scripta Mathematica, March 1948, H.D. Grossman describes an ingenious way to generate a solution geometrically.

Let a and b be the sizes of the jugs, in quarts, and c be the number of quarts that we’re seeking. Here, a = 7, b = 3, and c = 5. (a and b must be positive integers, relatively prime, where a is greater than b and their sum is greater than c; otherwise the problem is unsolvable, trivial, or can be reduced to smaller integers.)

Using a field of lattice points (or an actual pegboard), let O be the point (0, 0) and P be the point (b, a) (here, 3, 7). Connect these with OP. Then draw a zigzag line Z to the right of OP, connecting lattice points and staying as close as possible to OP. Now “It may be proved that the horizontal distances from OP to the lattice-points on Z (except O and P) are in some order without repetition 1, 2, 3, …, a + b – 1, if we count each horizontal lattice-unit as the distance a.” In this example, if we take the distance between any two neighboring lattice points as 7, then each of the points on the zigzag line Z will be some unique integer distance horizontally from the diagonal line OP. Find the one whose distance is c (here, 5), the number of quarts that we want to retrieve.

Now we have a map showing how to conduct our pourings. Starting from O and following the zigzag line to C:

  • Each horizontal unit means “Pour the contents of the a-quart jug, if any, into the b-quart jug; then fill the a-quart jug from the well.”
  • Each vertical unit means “Fill the b-quart jug from the a-quart jug; then empty the b-quart jug.”

So, in our example, the map instructs us to:

  • Fill the 7-quart jug.
  • Fill the 3-quart jug twice from the 7-quart jug, each time emptying its contents into the well. This leaves 1 quart in the 7-quart jug.
  • Pour this 1 quart into the 3-quart jug and fill the 7-quart jug again from the well.
  • Fill the remainder of the 3-quart jug (2 quarts) from the 7-quart jug and empty the 3-quart jug. This leaves 5 quarts in the 7-quart jug, which was our goal.

You can find an alternate solution by drawing a second zigzag line to the left of OP. In reading this solution, we swap the roles of a and b given above, so the map tells us to fill the 3-quart jug three times successively and empty it each time into the 7-quart jug (leaving 2 quarts in the 3-quart jug the final time), then empty the 7-quart jug, transfer the remaining 2 quarts to it, and add a final 3 quarts. “There are always exactly two solutions which are in a sense complementary to each other.”

Grossman gives a rigorous algebraic solution in “A Generalization of the Water-Fetching Puzzle,” American Mathematical Monthly 47:6 (June-July 1940), 374-375.

| Puzzles · Science & Math

Sweet and Bubbly

In 2005, archivist George Redmonds discovered something surprising among English birth records of the 14th century: a girl named Diot Coke.

She was born in the West Riding of Yorkshire in 1379. Researchers at Britain’s National Archives believe that her first name is a diminutive of Dionisia and her last name a variation of Cook.

She might have done worse. Popular girls’ names of the time included Godelena, Helwise, Idony, and Avice.

| Language

Clatter Plot

http://commons.wikimedia.org/wiki/File:GenderCircle.png

A puzzle by Lewis Carroll:

Two travelers, starting at the same time, went opposite ways round a circular railway. Trains start each way every 15 minutes, the easterly ones going round in 3 hours, the westerly in 2. How many trains did each meet on the way, not counting trains met at the terminus itself?

Click for Answer
| Puzzles

The Pizza Principle

In 1980, New York patent lawyer Eric Bram correctly predicted that the city’s transit fare would increase. He explained his reasoning to the New York Times: “Since the early ’60s, the price of a slice of pizza has matched, with uncanny precision, the cost of a New York subway ride. Right now, it is impossible for any discerning New Yorker to find a decent slice of pizza for less than 60 cents. The 50-cent fare was doomed.”

He was right. In 1960, the fare was 15 cents, and so was a slice of pizza (a regular slice, mozzarella and tomato sauce, no toppings). In the early 1970s, both rose to 35 cents, and the two continued to rise together. By 2002, pizza had risen to $2 in midtown, while the fare lagged at $1.50; sure enough, the fare rose to $2 the following spring, after eight years without a change.

In 2003 the subway system switched from tokens to MetroCards, finding them more efficient in a digital age. “Who knows if the fundamentals of economics will hold?” Bram asked.

They did. As the price of pizza rose, the fare followed it, rising to $2.25 in 2009 and to $2.50 in 2011. “Don’t ask why,” wrote Clyde Haberman, who tracks all this in the Times. “It simply is so, and has been for decades.”

| Society