## Stamps and Math

Lee Sallows tells me that the postal system of Macau is releasing a new series of stamps based on magic squares. The full set will touch on everything from the Roman SATOR square to Dürer’s Melencolia. Details are here.

Charmingly, the values of the stamps will be 1, 2, …, 9 Macau patacas, so that the sheet of the nine stamps will itself form a classic Lo Shu magic square. Lee’s contribution, above, is a Nasik 2D geomagic square of order 3 — not only are all the rows and columns magic, but so are all six diagonals, including the four “broken” diagonals.

Somewhat related: In 2000 Finland issued seven stamps in classic tangram shapes, featuring images of science and education. (One of the small triangles, barely visible here, is a Sierpinski gasket.) Only three of the seven shapes are denominated postage, but I should think the temptation is overwhelming to arrange all seven on an envelope in the shape of a little man or a fish or something. I wonder what the post office makes of that.

## Appalling Slave Punishments

From A Narrative of the Adventures and Escape of Moses Roper, From American Slavery, 1848:

“A large farmer, Colonel McQuiller in Cashaw county, South Carolina, was in the habit of driving nails into a hogshead so as to leave the point of the nail just protruding in the inside of the cask; into this, he used to put his slaves for punishment, and roll them down a very long and steep hill. I have heard from several slaves, (though I had no means of ascertaining the truth of this statement,) that in this way he had killed six or seven of his slaves.”

Roper himself escaped from slavery at least 16 times throughout the American South, most often from the prolifically sadistic South Carolina cotton planter J. Gooch. Examples:

“Mr. Gooch had gone to church, several miles from his house. When he came back, the first thing he did was to pour some tar upon my head, then rubbed it all over my face, took a torch with pitch on, and set it on fire; he put it out before it did me very great injury, but the pain which I endured was most excruciating, nearly all my hair having been burnt off.”

“This instrument he used to prevent the negroes running away, being a very ponderous machine, several feet in height, and the cross pieces being two feet four, and six feet in length. This custom is generally adopted among the slave-holders in South Carolina, and other slave States. One morning, about an hour before day break, I was going on an errand for my master; having proceeded about a quarter of a mile, I came up to a man named King, (Mr. Sumlin’s overseer,) who had caught a young girl that had run away with the above machine on her. She had proceeded four miles from her station, with the intention of getting into the hands of a more humane master. She came up with this overseer nearly dead, and could get no farther; he immediately secured her, and took her back to her master, a Mr. Johnson.”

“This is a machine used for packing and pressing cotton. By it he hung me up by the hands at letter a, a horse, and at times, a man moving round the screw e, and carrying it up and down, and pressing the block c into a box d, into which the cotton is put. At this time he hung me up for a quarter of an hour. I was carried up ten feet from the ground, when Mr. Gooch asked me if I was tired? He then let me rest for five minutes, then carried me round again, after which, he let me down and put me into the box d, and shut me down in it for about ten minutes.”

“To one of his female slaves he had given a doze of castor oil and salts together, as much as she could take; he then got a box, about six feet by two and a half, and one and a half feet deep; he put this slave under the box, and made the men fetch as many logs as they could get; and put them on the top of it; under this she was made to stay all night.”

Roper finally escaped to the North in 1834 and moved to England, where he published the book and toured making abolitionist speeches. He died in 1891.

## Two Lucky Escapes

In 1848, railroad construction foreman Phineas Gage was blasting rock near Cavendish, Vt., when an explosion sent a 13-pound tamping iron through his cheek and out the top of his head. Remarkably, he survived: Doctor Edward H. Williams found him sitting in a chair outside his lodgings 30 minutes later, saying, “Doctor, here is business enough for you.” It appears that the rod had destroyed much of his left frontal lobe but left the rest of his brain intact — he lived for another 12 years and has survived ever after in psychology textbooks.

In 1978, Russian physicist Anatoli Bugorski suffered a high-tech version of the same accident — he was checking a piece of equipment when the safety mechanisms failed and he put his head in the path of a proton beam, which burned through his face and brain, passing out the back of his head. Doctors expected him to die, but he recovered and even completed his doctorate. The left half of his face was paralyzed and he lost hearing in his left ear, but he’s still alive today.

(Thanks, Pål.)

## “The Sons of Our Sons”

In 1919 Russian author Ilya Ehrenburg wrote a message to posterity:

The sons of our sons will marvel,
Paging the textbook:
“1914 … 1917 … 1919 …
How did they live? The poor devils!”
Children of a new age will read of battles,
Will learn the names of orators and generals,
The numbers of the killed,
And the dates.

They will not know how sweetly roses smelled above the trenches,
How martins chirped blithely between the cannon salvos,
How beautiful in those years was
Life.

Never, never did the sun laugh so brightly
As above a sacked town,
When people, crawling out of their cellars,
Wondered: is there still a sun?
Violent speeches thundered,
Strong armies perished,

But the soldiers learned what the scent of snowdrops is like
An hour before the attack.
People were led at dawn to be shot …
But they alone learned what an April morning can be.
The cupolas gleamed in the slanting rays,
And the wind pleaded: Wait! A minute! Another minute!
Kissing, they could not tear themselves from the mournful mouth,
And they could not unclasp the hands so tightly joined.
Love meant: I shall die! I shall die!
Love meant: Burn, fire, in the wind!
Love meant: O where are you, where?

They love as people can love only here, upon this rebellious and
tender star.

In those years there were no orchards golden with fruit,
But only fleeting bloom, only a doomed May.
In those years there was no calling: “So long!”
But only a brief, reverberant “Farewell!”
You did not live in our time — be sorry!
We were guests of the earth for one evening only.
We loved, we destroyed, we lived in the hour of our death.
But overhead stood the eternal stars,
And under them we begot you.

In your eyes our longing still burns,
In your words our revolt reverberates yet
Far into the night, and into the ages, the ages, we have scattered
The sparks of our extinguished life.

## Double Jeopardy

On Jan. 30, 1835, as Andrew Jackson was departing a U.S. representative’s funeral service at the Capitol, troubled English house painter Richard Lawrence confronted him, drew a pistol from his pocket, pointed it at Jackson’s heart, and pulled the trigger.

“The explosion of the cap was so loud that many persons thought the pistol had fired,” said Sen. Thomas Benton, who heard it from the foot of the steps. It hadn’t — only the cap had exploded.

Realizing the misfire, Lawrence dropped the pistol and drew another of the same make and design from his pocket. He cocked it, aimed it at Jackson’s heart, and pulled the trigger. A second shot reverberated through the rotunda, but again only the cap had exploded. The crowd subdued Lawrence, who was later found to be insane.

The sergeant-at-arms at the Capitol recovered both pistols and found that they had been properly loaded. Meriwether Lewis Randolph found that they had contained “powder of the best quality, & the balls rammed tight,” but “the percussion caps exploded without igniting the powder.” Jack Donelson recapped the pistols and tested them to see if they would fire, and they did, perfectly.

An expert on small arms estimated the odds of two successive misfires of perfectly loaded pistols with high-quality powder at about 125,000 to 1. Benton wrote, “The circumstance made a deep impression upon the public feeling and irresistibly carried many mind to the belief in a superintending Providence, manifested in the extraordinary case of two pistols in succession — so well loaded, so coolly handled, and which afterwards fired with such readiness, force, and precision — missing fire, each in its turn, when leveled eight feet at the President’s heart.”

## Page Turners

“Sorts of readers,” categorized for you by Samuel Taylor Coleridge:

1. Spunges that suck up every thing and, when pressed give it out in the same state, only perhaps somewhat dirtier — . 2. Sand Glasses — or rather the upper Half of the Sand Glass, which in a brief hour assuredly lets out what it has received — & whose reading is only a profitless measurement and dozeing away of Time — . 3. Straining Bags, who get rid of whatever is good & pure, and retain the Dregs. — and this Straining-bag class is again subivided into Species of the Sensual, who retain evil for the gratification of their own base Imaginations, & the calumnious, who judge only by defects, & to whose envy a beauty is an eye-sore, a fervent praise respecting another a near-grievance, and the more virulent in its action because the miserable man does not dare confess the Truth to his own Heart — . 4. and lastly, the Great-Moguls Diamond Sieves — which is perhaps going farther for a Simile than its superior Dignity can repay, inasmuch as a common Cullender would have been equally symbolic/ but imperial or culinary, these are the only good & I fear the least numerous, who assuredly retain the good, while the superfluous or impure passes away and leaves no trace.

(From his 1808 Lectures on Principles of Poetry.)

## Stretch Goals

Two circles intersect. A line AC is drawn through one of the intersection points, B. AC can pivot around point B — what position will maximize its length?

## In a Word

consenescence
n. the growing old together

## The Twelve-Angled Stone

Midway along the northwestern face of a monumental Inca building at 410 Calle Hatunrumiyoc in Cusco is a large irregular block of stone worked by a master mason in the era before Columbus. Fitted into place without mortar despite its complex shape, the “twelve-angled stone” has become a hallmark of Inca craftsmanship.

“Just as individual blocks were prepared, so too were the adjoining stones already set in the wall,” notes Southern Methodist University art historian Adam Herring. “In order to receive a new block, bedding planes were carved into those stones below or to the side of the block to be added. This is how the Twelve-Angled Stone took on its busy upper outline; the upper portions of the block were recarved several times over as five blocks — set in a left to right sequence — were fitted along the course above. Other blocks in the wall were similarly shaped, then reshaped as new blocks were added to the masonry mass. As stones of irregular size and degree of finish were inserted into the mural fabric with fastidious technical consistency, the wall went up as tectonic sculpture.”

Pablo Neruda remarked on the “rocky petals” that distinguish this style of architecture; Che Guevara called it “an enigma in stone.” The mason who left this hallmark was a master of this craft, but his identity is unknown.

(Adam Herring, “Shimmering Foundation: The Twelve-Angled Stone of Inca Cusco,” Critical Inquiry, Autumn 2010.)

## The Imaginary Prisons

Italian artist Giovanni Piranesi spent his days making etchings of Roman ruins, but in 1745 he turned out a series of much darker visions, which he called Le Carceri d’Invenzione. “Vaults of colossal proportions from which hang extinguished lanterns, openings closed by bars, spiral staircases and suspended passageways which lead nowhere, immense gallows and wheels, ropes strung on pulleys evoking strange tortures,” writes Roseline Bacou in her collection of the artist’s etchings and drawings, “all these are the visible elements of a closed and nocturnal world.” Thomas De Quincey wrote:

Many years ago, when I was looking over Piranesi’s Antiquities of Rome, Mr. Coleridge, who was standing by, described to me a set of plates by that artist … which record the scenery of his own visions during the delirium of a fever: some of them … representing vast Gothic halls, on the floor of which stood all sorts of engines and machinery, wheels, cables, pulleys, levers, catapults, etc., etc., expressive of enormous power put forth, and resistance overcome. Creeping along the sides of the walls, you perceived a staircase; and upon it, groping his way upwards, was Piranesi himself: follow the stairs a little further, and you perceive it come to a sudden abrupt termination, without any balustrade, and allowing no step onwards to him.

The full collection is here. Aldous Huxley read into the prints “things existing in the physical and metaphysical depths of human souls — to acedia and confusion, to nightmare angst, to incomprehension and to panic bewilderment.” In reworking the prints Piranesi came to relate them to early Rome: One column in the vaults bears the inscription AD TERROREM INCRESCENTIS AVDACIAE, a quotation from Livy’s History of Rome in which the early king Ancus Marcius responds to a loss of values among his people by establishing a prison in the center of the city, “to terrify the growing audacity.” But the initial series were pure fantasy, and their inspiration is unknown.