“A Dry Quicksand”

In the southwestern corner of the desert of southern Arabia, north of the western end of Hadramaut, and approached from the little village of Sawa, is a very remarkable spot described by Wrede from his visit in 1843, whose description is reproduced in a recent number of the Revue coloniale internationale. There are here, in the waste of yellow sand, several spots covered by a grayish white dust, which swallow up every object thrown into them. One of these spots, described by Wrede, is about two miles long and a little less in breadth. It sinks gradually toward the middle and is apparently due to the work of the wind. Wrede approached it with the greatest care and sounded it with his staff. The edge is stony and falls away suddenly. When the staff was thrust into the fine material beyond the edge, almost no resistance was felt and it was as if the staff had been thrust into water. When it was passed through the fine dust lengthwise the resistance was almost imperceptible. A stone of two pounds weight or more was fastened to a cord sixty fathoms long and thrown in as far as possible. It sank at once and with increasing velocity so that at the end of five minutes the end of the cord had disappeared. The presence of Bedouins prevented any more observations. The natives believe that great treasures are buried here and are watched over by genii who pull down into the depths the unwary treasure-seeker.

— American Meteorological Journal, May 1886

| Oddities

Field Work

baden-powell butterfly

In 1891, Robert Baden-Powell wandered the mountains of Dalmatia with a butterfly net and a sketchbook. If he was accosted by one of the forts in the area, he would show his drawings to the soldiers and explain that he was hunting a particular species, and they would send him on his way.

In fact he was working as an intelligence officer for the British government. “They did not look sufficiently closely into the sketches of butterflies to notice that the delicately drawn veins of the wings were exact representations, in plan, of their own fort, and that the spots on the wings denoted the number and position of guns and their different calibres”:

baden-powell fort

The large dots denote the locations of the fort’s main guns, and the smaller show field artillery and machine-gun emplacements.

“Fortunately for us, we are as a nation considered by the others to be abnormally stupid, therefore easily to be spied upon,” he wrote in his 1915 memoir My Adventures as a Spy. “But it is not always safe to judge entirely by appearances.”

| History

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