In a Word

n. a prayer or devout wish

An 1898 item in the New York Times notes that William Gladstone once attended a Presbyterian service in Scotland where the minister said, “We pray Thee, Lord, of Thy goodness, to bless the Prime Minister of this great nation, who is now worshipping under this roof in the third pew from the pulpit.” And a Presbyterian minister opening an outdoor event reportedly prayed, “In consequence of the rain, O Lord, and by reason of the regretted absence of the Princess of Lochnagar, caused, doubtless, by the stormy weather, I do not purpose to address Thee at any length.”

Before a battle in the Irish rebellion of 1641, John Leslie, bishop of Clogher, prayed, “O God, for our unworthiness we are not fit to claim Thy help: but if we are bad our enemies are worse, and if Thou seest not meet to help us, we pray Thee help them not, but stand Thou neuter this day, and leave it to the arm of flesh.”

(During the American Civil War, Abraham Lincoln said, “We, on our side, are praying to Him to give us victory, because we believe we are right; but those on the other side pray to Him, look for victory, believing they are right. What must He think of us?”)

In his 1863 history of France, Victor Duruy tells of a soldier named La Hire who sought absolution from a priest during the siege of Montargis in 1427. The priest asked him to confess first, and he said, “I have not time, for I must fall upon the English. But I have done all that a man of war is wont to do.” The chaplain gave him absolution such as it was, and La Hire fell on his knees by the roadside and said, “God, I pray thee that to-day thou wilt do for La Hire that which thou wouldst have La Hire do for thee, if he were God and thou were La Hire.”

Others think the notion of a timeless God, with its perceptual metaphor of God passively perceiving each and every moment of time in a single, unchanging, comprehensive vision, fails to give God the freedom to act in creation, in particular, in the future. Suppose a student receives acceptances from three different universities and is trying to decide which to attend. She prays to God: ‘Lord, at which of the three universities will I have the best overall collegiate experience?’ On the timelessness view, God sees only the choice our petitioner actually makes, not the alternative futures that would have transpired had she chosen to go elsewhere. So how can God answer this prayer?

– W. Jay Wood, God, 2011

“Whatever a man prays for, he prays for a miracle. Every prayer reduces to this: ‘Great God, grant that twice two be not four.’” — Turgenev

See Asking Back.

Self-Replicating Resistors

From Lee Sallows:

self-replicating resistors

In an electrical network, if resistors x and y are placed in series their total resistance is x + y; if they’re placed in parallel it’s 1/(1/x + 1/y).

This offers an intriguing opportunity for self-reference. Each of the networks above contains four resistors with values 1, 2, 3, and 4, and the total resistances of the networks themselves are 1, 2, 3, and 4. So any one of the numbered resistors in these networks can be replaced by one of the networks themselves.

The challenge was posed by Sallows and Stan Wagon as a Macalester College “problem of the week”; these examples were discovered by Brian Trial, an automotive electronics engineer from Ferndale, Mich. Sallows points out that any such solution has a dual that results from changing series connections to parallel, and vice versa, and then replacing all resistors values by their reciprocals.

This leads to a further idea: The two sets of resistors below are “co-replicating” — the four networks on the left can be used to replace the four resistors in any of the networks on the right, and vice versa.

co-replicating resistors

(Thanks, Lee.)

Post Haste

Letter from Lewis Carroll to Winifred Stevens, May 22, 1887:

My dear Winnie,

But you will be getting tired of this long letter: so I will bring it to an end, and sign myself,

Yours affectionately,

C.L. Dodgson

Sleeping Alone

Lori has an icky problem: Worms keep crawling onto her bed. She knows that worms can’t swim, so she puts each leg of the bed into a pail of water, but now the worms crawl up the walls of the room and drop onto her bed from the ceiling. She suspends a large canopy over the bed, but worms drop from the ceiling onto the canopy, creep over its edge to the underside, crawl over the bed, and drop.

Desperate, Lori installs a water-filled gutter around the perimeter of the canopy, but the worms drop from the ceiling onto the outer edge of the gutter, then crawl beneath. (The worms are very determined.) What can Lori do?

Click for solution …

Long Distance

The widespread sail of a ship, rendered concave by a gentle breeze, is also a good collector of sound. It happened once on board a ship sailing along the coast of Brazil, far out of sight of land, that the persons walking on deck, when passing a particular spot, always heard very distinctly the sound of bells, varying as in human rejoicings. All on board came to listen, and were convinced, but the phenomenon was most mysterious. Months afterwards it was ascertained, that at the time of observation the bells of the city of St. Salvador, on the Brazilian coast, had been ringing on the occasion of a festival — their sound, therefore, favoured by a gentle wind, had travelled over perhaps 100 miles of smooth water, and had been brought to a focus by the sail in the particular situation on the deck where it was listened to.

– Neil Arnott, Elements of Physics, 1829

Going Places

German engineer Robert Michael patented this “curved shoe” in 1905. It’s intended to increase the length of each stride “to serve for the quick forward movement of people in walking.”

It also beats bicycles because it won’t sink into rough ground. “The user can in walking use a stick as in walking with snow shoes.”

Free Range

Description of the facts underlying an 1828 action against John Ramage, a Liverpool man accused of “omitting to take proper care of a cow”:

The circumstances of the case were of a somewhat singular nature. It appeared, from the evidence, that, about six o’clock in the evening of the 8th of July last, a cow was found wandering in Tithebarn-street in a very disorderly manner, to the terror of the lieges, several of whom it had thrown down, and, for this conduct, it had been seized and dragged to the pound kept by the defendant. Here the restive animal determined on making her escape, and, ascending a flight of six stone steps, she proceeded along a passage, and, breaking open a door, found herself in a room where Mrs. Ramage and her family were taking tea. The company ran screaming from the room, leaving her to the uninterrupted enjoyment of the bohea, and buttered toast. The cow immediately commenced operations on the good things before her, but from natural awkwardness, overthrew table and tea-service, and, after doing some other mischief, bolted through a door opposite the one at which she had entered the room, and down five steps into a yard, where egress was stopped; and, before she could retrace her steps, Mr. Ramage and his assistants took her into custody, and conveyed her to her original place of durance.

The next morning, Mr. Ramage, on visiting the yard, found that his prisoner had again escaped, and he immediately made a search for her. She had climbed a heap of stones, lying in one corner of the yard, to a wall about twelve feet from the ground, along which she had walked (though the wall was but one brick and a half thick) a distance of sixteen feet, and climbed somewhat higher to the top of a shed; this she had walked over, and again elevated herself by gaining the top of a building used as a filecutter’s shop. Not being sufficiently acquainted with that part, she at once pushed one of her feet through the sky-light, to the inexpressible horror of Mr. Rockett, the file-cutter, who was at work below. Having extricated her foot, she again ascended, and walked along the roof of a warehouse, the height of an ordinary three-story house. This roof proved to be too weak to support the weight of the animal, and she fell through upon a pile of bags of cotton, and rolled to the floor, where her journeyings ended, for she was found in this room, lying on her side, very materially injured. … After some deliberation, the jury returned a verdict for the plaintiff, damages 2l. 2s., subject to a point reserved for decision as to the jurisdiction of the court to try the cause.

Liverpool Courier, reprinted in Annual Register, October 1828

Operation Fantasia

In 1943, seeking to use psychological warfare to prevail in its efforts against the Japanese, the U.S. Office of Strategic Services hit on a strange plan. Noting that Shintoists might view the image of an illuminated fox as a harbinger of bad times, the agency’s experts suggested that “under extremely trying conditions” the Japanese “would be adversely affected by what they might consider an evil omen” and succumb to “fear, terror, and despair.”

How does one make a glowing fox? Planners started by experimenting with fox-shaped balloons covered in luminous paint and dangled by fishing line, but by the end of 1944 they’d shelved that idea and begun spraying live foxes with luminous paint, hoping to release them across the “entire field of combat,” calling this America’s “most potent” psychological tool against the Japanese.

The operation would begin by distributing pamphlets warning of impending evil and patterned after those of Japanese soothsayers. These would be airdropped and also spread by field operatives who would blow special reed whistles to simulate a fox-like “cry of the damned” and use powders and pastes to spread “fox odors.” The OSS also enlisted Japanese collaborators to “simulate persons possessed of the Fox spirit.”

To test the plan, the agency actually released 30 foxes in Central Park that “were painted with a radiant chemical which glowed in the dark.” As a result, according to one report, “Horrified citizens, shocked by the sudden sight of the leaping ghostlike animals, fled from the dark recesses of the park with the ‘screaming jeemies.’”

Heartened at this result, the planners set about procuring as many foxes as possible from China and Australia in anticipation of an Allied invasion of Japan. Only the war’s sudden conclusion, with the dropping of the atomic bomb, stopped the operation from going forward.

“Still, the development of their idea demonstrates how Americans during the war perceived the psychology of their Asian foe in a far different way than they saw their enemies in Europe,” writes Robert Kodosky in Psychological Operations American Style (2007). “Based on their notions of Japan’s primitive state, Americans produced plans like ‘Operation Fantasia’ for use against Japanese that stood as much more absurd than any European campaign they proved willing to consider.”

(Thanks, Meaghan.)


“They are ill discoverers that think there is no land, when they can see nothing but sea.” — Francis Bacon

The Simson Line

Draw any triangle ABC and pick any point P on its circumcircle.

The closest points to P on lines AB, BC, and AC will be collinear.

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