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Gold Nuggets

The first 10 digits of the golden ratio φ can be rearranged to give the first 10 digits of 1/π:

φ = 1.618033988 …

1/π = .3183098861 …

And the first nine digits of 1/φ can be rearranged to give the first 9 digits of 1/π:

1/φ = .618033988 …

1/π = .318309886 …

http://commons.wikimedia.org/wiki/File:Odom.svg
Image: Wikimedia Commons

In 1983 amateur mathematician George Odom discovered that if points A and B are the midpoints of sides EF and DE of an equilateral triangle, and line AB meets the circumscribing circle at C, then AB/BC = AC/AB = φ. Odom used this fact to construct a pentagon, which H.S.M. Coxeter published in the American Mathematical Monthly with the single word “Behold!”

| Science & Math

Moving Drama

In May 1869, Lewis Carroll and 13-year-old Isabel Seymour traveled together by train from Oxford to Reading, where they parted, he to go on to Guildford and she to Paddington, London. After they had separated, he realized that he had forgotten to give her her ticket. He wrote to her:

My dear Isabel,

I was so sorry to hear from Miss Lloyd of your not being well, and I hope you will not think of writing to me about ‘Alice’ till you are well enough to do so. I only write this on the chance of your being in the humour to read it, or to have it read to you. When you are in that state, I should like you to know the real reason of my having carried off your railway-ticket. … Well, you told me, you know, that it was your first railway-journey alone: naturally that set me thinking, ‘Now what can I do to give her a really exciting adventure?’

Now three plans occurred to me. The first was to wait till the train had started from Reading, and then fire a pistol through your carriage-window, so that the bullet might go near your head and startle you a little. But there were two objections to this plan — one, that I hadn’t got a loaded pistol with me, the other, that the bullet might have gone in at a wrong window, and some people are so stupid, they might not have taken it as a joke.

The second plan was to give you, just as the train left Reading, what should look like a Banbury-cake, but should afterwards turn out to be a rattlesnake. The only objection to this plan was, that they didn’t keep that kind at Reading. They had only common Banbury-cakes, which wouldn’t have done at all.

The third plan was to keep the ticket, so that you might be alarmed when you got to London. Of course I arranged thoroughly with the Guard that the thing was not to be overdone. He was to look a little stern at first, and then gradually to let his expressive features kindle into a smile of benevolence. I was very particular on this point and almost my last words to him were, ‘Are you sure you can manage the benevolence?’ and I made him practice it several times on the platform before I would let him go.

Now you know my whole plan for making your journey a real Adventure. I only hope it succeeded. So, hoping much to hear you are better again, I remain very truly yours,

C.L. Dodgson

| Literature

The Bellamy Salute

http://commons.wikimedia.org/wiki/File:Students_pledging_allegiance_to_the_American_flag_with_the_Bellamy_salute.jpg

When minister Francis Bellamy published the American Pledge of Allegiance in Youth’s Companion in 1892, his colleague James Upham devised a salute to go along with it, snapping the heels together and extending the right arm toward the flag:

At a signal from the Principal the pupils, in ordered ranks, hands to the side, face the Flag. Another signal is given; every pupil gives the flag the military salute — right hand lifted, palm downward, to a line with the forehead and close to it. Standing thus, all repeat together, slowly, ‘I pledge allegiance to my Flag and the Republic for which it stands; one Nation indivisible, with Liberty and Justice for all.’ At the words, ‘to my Flag,’ the right hand is extended gracefully, palm upward, toward the Flag, and remains in this gesture till the end of the affirmation; whereupon all hands immediately drop to the side.

This worked fine until the 1920s, when Italian fascists and then German Nazis adopted similar salutes. Congress delicately changed the American salute to the hand-on-heart gesture in 1942.

| History

The Inman Diaries

When chronic illness confined Boston poet Arthur Crew Inman to a darkened room, he turned inward, scribbling his thoughts and feelings into an enormous diary that eventually filled 155 volumes with 17 million handwritten words — most of them peevish:

A Lithuanian came to read to me. I disliked her at once. She was common. Her voice sounded like an ungreased axle. She spoke with a pronounced accent. She would start to read fairly well, but in short order she would become interested in the book, forget me, let the reading go as it might. I began to ask her questions. She answered in monosyllables. She used gutter slang. Her father, she said, had fled from Poland to escape the Russian term of army service. He had come to America where he had stayed for a while in Elizabeth, New Jersey. After saving some money, he took his family to Amsterdam, New York, and started a dry goods store. The girl had been one of six children. She had not learned to speak English until she was thirteen. She had gone to public school. Now she is studying music at the Boston Conservatory.

Harvard professor Daniel Aaron, who edited the diaries for publication in 1985, called them “surely one of the fullest and largest diaries ever kept by any American.” Inman would have agreed with him. “I trust to do in nonfiction what Balzac did in fiction,” he said. Perhaps he succeeded — the diaries were turned into an opera in 2007, and a film version starring John Hurt is in development.

| Literature

Honorable Prisoners

After John II of France was captured by the English in 1356, he paid 1 million gold crowns for his ransom and promised to pay 2 million more. As a guarantee he offered his son Louis as a hostage. When word came that Louis had escaped, John voluntarily returned to captivity in England, citing reasons of “good faith and honor.” He died there in 1364.

In 1916, after two years in a German prisoner-of-war camp, British Army captain Robert Campbell received word that his mother was dying of cancer. He wrote to Kaiser Wilhelm II asking permission to visit her, and was given two weeks’ leave on condition that he return afterward. Campbell went to England, spent a week with his dying mother, then returned to confinement in Germany, where he remained until the war ended.

“Captain Campbell was an officer, and he made a promise on his honor to go back,” said historian Richard Van Emden, who uncovered the episode while researching his book Meeting the Enemy. “Had he not turned up there would not have been any retribution on any other prisoners. What I think is more amazing is that the British Army let him go back to Germany.”

| History

Harm’s Way

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On Sept. 9, 1900, the day after a strong storm made landfall on the Texas coast, the U.S. Weather Bureau wired Western Union, Do you hear anything about Galveston?

The first response was We have been absolutely unable to hear a word from Galveston since 4 p.m. yesterday …. But then:

First news from Galveston just received by train which could get no closer to the bay shore than six miles, where Prairie was strewn with debris and dead bodies. About two hundred corpses counted from train. Large Steamship stranded two miles inland. Nothing could be seen of Galveston. Loss of life and property undoubtedly most appalling.

The storm had put the entire city under 8 to 15 feet of water and lashed it with winds reaching 145 mph. With 8,000 dead, it remains the deadliest natural disaster in U.S. history. Following is the only account known to have been written while the storm was taking place — it’s an unsigned letter by a woman, probably a nurse, who was employed at the John Sealy Hospital:

A.M.
It does not require a great stretch of imagination to imagine this structure a shaky old boat out at sea. The whole thing rocking like a reef, surrounded by water, said water growing closer, ever closer. Have my hands full quieting nervous, hysterical women.

12-noon.
Things beginning to look serious. Water up to the first floor in the house, all over the basement of the hospital. Cornices, roofs window lights blinds flying in all directions.

The scenes about here are distressing. Everything washed away. Poor people trying, vainly to save their bedding, & clothing. Methinks the poor nurses will be trying to save their beds in short order. Now flames in the distance. It is all a grand, fine sight. Our beautiful Bay, a raging torrent.

3 p.m.
Am beginning to feel a weakening desire for something ‘to cling to.’ Should feel more comfortable in the embrace of your arms. You hold yourself in readiness to come to us? Should occasion demand? Darkness is overwhelming us, to add to the horror. Dearest — I — reach out my hand to you. My heart — my soul.

That’s all we have — we don’t know who wrote the letter, or whether she survived the storm (the hospital remained standing).

According to some survivors, we’re lucky to have any accounts at all. “One hour more of that wind would have killed every person on the island,” wrote Walker W. Davis, a salesman who waited out the storm in the Tremont Hotel.

Margaret Rowan Bettencourt, who was 9 years old at the time, remembered that the East End, where her grandmother’s house was located, was largely reduced to splinters. “They never would’ve found her place, but my aunt had a ‘polly’ [parrot] that was up in the attic and the attic didn’t go to pieces. It just sat on the top of the house and the next morning the polly was hollering ‘Pretty Polly. Pretty Polly.’ That’s how they found where they lived.”

| History

Roots

In the old times these isles lay there as they do now, with the wild sea round them. The men who had their homes there knew naught of the rest of the world and none knew of them. The storms of years beat on the high white cliffs, and the wild beasts had their lairs in the woods, and the birds built in trees or reeds with no one to fright them. A large part of the land was in woods and swamps. There were no roads, no streets, not a bridge or a house to be seen. The homes of these wild tribes were mere huts with roofs of straw. They hid them in thick woods, and made a ditch round them and a low wall of mud or the trunks of trees. They ate the flesh of their flocks for food, for they did not know how to raise corn or wheat. They knew how to weave the reeds that grew in their swamps, and they could make a coarse kind of cloth, and a rude sort of ware out of the clay of the earth. From their rush work they made boats, and put the skins of beasts on them to make them tight and strong. They had swords made from tin and a red ore. But these swords were of a queer shape and so soft that they could be bent with a hard blow.

— Helen W. Pierson, History of England in Words of One Syllable, 1884

| History · Language

Quick Thinking

commons.wikimedia.org/wiki/File:Straßenkämpfe_in_Rouen_1859.jpg

During one of the many nineteenth-century riots in Paris the commander of an army detachment received orders to clear a city square by firing at the canaille (rabble). He commanded his soldiers to take up firing positions, their rifles leveled at the crowd, and as a ghastly silence descended he drew his sword and shouted at the top of his lungs: ‘Mesdames, m’sieurs, I have orders to fire at the canaille. But as I see a great number of honest, respectable citizens before me, I request that they leave so that I can safely shoot the canaille.’ The square was empty in a few minutes.

— American psychiatrist Paul Watzlawick, Change: Principles of Problem Formation and Problem Resolution, 1974

| Society

The Cursing Stone

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Image: Flickr

In 1525, fed up with robbers and highwaymen on the Anglo-Scottish border, Archbishop of Glasgow Gavin Dunbar composed a monumentally comprehensive curse against them:

I curse their head and all the hairs of their head; I curse their face, their brain, their mouth, their nose, their tongue, their teeth, their forehead, their shoulders, their breast, their heart, their stomach, their back, their womb, their arms, their legs, their hands, their feet, and every part of their body, from the top of their head to the soles of their feet, before and behind, within and without.

I curse them going and I curse them riding; I curse them standing and I curse them sitting; I curse them eating and I curse them drinking; I curse them rising, and I curse them lying; I curse them at home, I curse them away from home; I curse them within the house, I curse them outside of the house; I curse their wives, their children, and their servants who participate in their deeds; their crops, their cattle, their wool, their sheep, their horses, their swine, their geese, their hens, and all their livestock; their halls, their chambers, their kitchens, their stanchions, their barns, their cowsheds, their barnyards, their cabbage patches, their plows, their harrows, and the goods and houses that are necessary for their sustenance and welfare.

May all the malevolent wishes and curses ever known, since the beginning of the world, to this hour, light on them. May the malediction of God, that fell upon Lucifer and all his fellows, that cast them from the high Heaven to the deep hell, light upon them.

May the fire and the sword that stopped Adam from the gates of Paradise, stop them from the glory of Heaven, until they forebear, and make amends.

May the evil that fell upon cursed Cain, when he slew his brother Abel, needlessly, fall on them for the needless slaughter that they commit daily.

May the malediction that fell upon all the world, man and beast, and all that ever took life, when all were drowned by the flood of Noah, except Noah and his ark, fall upon them and drown them, man and beast, and make this realm free of them, for their wicked sins.

May the thunder and lightning which rained down upon Sodom and Gomorrah and all the lands surrounding them, and burned them for their vile sins, rain down upon them and burn them for their open sins.

May the evil and confusion that fell on the Gigantis for their opression and pride in building the Tower of Babylon, confound them and all their works, for their open callous disregard and oppression.

May all the plagues that fell upon Pharaoh and his people of Egypt, their lands, crops and cattle, fall upon them, their equipment, their places, their lands, their crops and livestock.

May the waters of the Tweed and other waters which they use, drown them, as the Red Sea drowned King Pharaoh and the people of Egypt, preserving God’s people of Israel.

May the earth open, split and cleave, and swallow them straight to hell, as it swallowed cursed Dathan and Abiron, who disobeyed Moses and the command of God.

May the wild fire that reduced Thore and his followers to two-hundred-fifty in number, and others from 14,000 to 7,000 at anys, usurping against Moses and Aaron, servants of God, suddenly burn and consume them daily, for opposing the commands of God and Holy Church.

May the malediction that suddenly fell upon fair Absalom, riding through the wood against his father, King David, when the branches of a tree knocked him from his horse and hanged him by the hair, fall upon these untrue Scotsmen and hang them the same way, that all the world may see.

May the malediction that fell upon Nebuchadnezzar’s lieutenant, Holofernes, making war and savagery upon true Christian men; the malediction that fell upon Judas, Pilate, Herod, and the Jews that crucified Our Lord; and all the plagues and troubles that fell on the city of Jerusalem therefore, and upon Simon Magus for his treachery, bloody Nero, Ditius Magcensius, Olibrius, Julianus Apostita and the rest of the cruel tyrants who slew and murdered Christ’s holy servants, fall upon them for their cruel tyranny and murder of Christian people.

And may all the vengeance that ever was taken since the world began, for open sins, and all the plagues and pestilence that ever fell on man or beast, fall on them for their openly evil ways, senseless slaughter and shedding of innocent blood.

I sever and part them from the church of God, and deliver them immediately to the devil of hell, as the Apostle Paul delivered Corinth.

I bar the entrance of all places they come to, for divine service and ministration of the sacraments of holy church, except the sacrament of infant baptism, only; and I forbid all churchmen to hear their confession or to absolve them of their sins, until they are first humbled by this curse.

I forbid all Christian men or women to have any company with them, eating, drinking, speaking, praying, lying, going, standing, or in any other deed-doing, under the pain of deadly sin.

I discharge all bonds, acts, contracts, oaths, made to them by any persons, out of loyalty, kindness, or personal duty, so long as they sustain this cursing, by which no man will be bound to them, and this will be binding on all men.

I take from them, and cast down all the good deeds that ever they did, or shall do, until they rise from this cursing.

I declare them excluded from all matins, masses, evening prayers, funerals or other prayers, on book or bead; of all pigrimages and alms deeds done, or to be done in holy church or be Christian people, while this curse is in effect.

And, finally, I condemn them perpetually to the deep pit of hell, there to remain with Lucifer and all his fellows, and their bodies to the gallows of Burrow moor, first to be hanged, then ripped and torn by dogs, swine, and other wild beasts, abominable to all the world.

And their candle goes from your sight, as may their souls go from the face of God, and their good reputation from the world, until they forebear their open sins, aforesaid, and rise from this terrible cursing and make satisfaction and penance.

As part of Carlisle’s millennium celebrations in 2001, local artist Gordon Young carved 383 words of the curse into a granite boulder. Since then, local livestock herds have been wiped out by foot-and-mouth disease, a devastating flood has struck the city, factories have closed, and the Carlisle United soccer team dropped a league. Jim Tootle, a local councillor who blamed these misfortunes on the revived curse, himself died suddenly in 2011.

“It is a powerful work of art but it is certainly not part of the occult,” Young insisted. “If I thought my sculpture would have affected one Carlisle United result, I would have smashed it myself years ago.”

(Thanks, NMN.)

| History · Oddities

Memoria Technica

By reducing each chapter of the Bible to a single line and presenting these lines in rhyming quatrains, the Juvenile Bible of 1804 condenses the Old and New Testaments into 69 memorizable pages. By learning a simple system, one can then cite any chapter of the Bible from memory. Here are the first three stanzas of Genesis:

1 All things created, Moses writes,
2 And Paradise displays;
3 Tells Adam’s fall, which ruin’d all:
4 Cain righteous Abel slays.

5 Before the flood man’s life was long:
6 Noah the ark doth frame:
7 The world is drown’d, eight favour found,
8 Out of the ark they came.

9 Cov’nant of rain-bow; Noah drunk,
10 His offspring is increast;
11 They Babel rear, confounded are.
12 Abram is call’d and blest.

To aid in memorization, the stanzas begin with successive letters of the alphabet, so a stanza that starts with A always marks the first chapter of a book, B the 5th, C the 9th, and so on. Once we’ve memorized the stanzas above, we can always name the chapter in Genesis in which the Tower of Babel is described: It’s the third line of the stanza beginning with C, so it’s chapter 11. Conversely, if we’re asked to name the subject of any given chapter, we can produce the answer using the same system.

“This novel and curious arrangement will, it is presumed, gratify the taste of young readers, and not only give them a relish for the Sacred Volume, but even assist their memories when duly acquainted with it,” writes the anonymous author. To his credit, he adds, “No portion of it should ever be allotted as a Task; the Author of this Work being well convinced, it is owing to the modern and impious mode of Education, compelling Children to learn Collects, chapters in the Bible, Hymns, &c. as occasional Exercises, and frequently by way of Punishment that the Word of God is not heard and read with that satisfaction it always should be.”

| Literature · Religion