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Number Forms

http://commons.wikimedia.org/wiki/File:Galton_number_form.svg

When thinking of numbers, about 5 percent of the population see them arranged on a sort of mental map. The shape varies from person to person, assuming “all sorts of angles, bends, curves, and zigzags,” in the words of Francis Galton, who described them first in The Visions of Sane Persons (1881). Usually the forms are two-dimensional, but occasionally they twist through space or bear color.

People who have forms report that they remain unchanged throughout life, but having one is such a peculiarly personal experience that “it would seem that a person having even a complicated form might live and die without knowing it, or at least without once fixing his attention upon it or speaking of it to his nearest friends,” wrote philosopher G.T.W. Patrick in 1893. One man told mathematician Underwood Dudley that “when he told his wife about his number form, she looked at him oddly, as if he were unusual, when he thought that she was the peculiar one because she did not have one.”

The phenomenon is poorly understood even today; possibly it arises because of a cross-activation between the parts of the brain that recognize spatial relationships and numbers. Two of Dudley’s students were identical twins; both had forms, but the forms were different. “Although our understanding of how the brain works has advanced since 1880, it probably has not advanced enough to deal with number forms,” he writes. “Another hundred years or so may be needed.”

| Science & Math

Close Quarters

Let’s hope this isn’t true — Francis Joseph Baigent’s History of the Ancient Town and Manor of Basingstoke (1889) records the story of a woman who was buried alive twice. Baigent cites two sources, an undated tract from around 1675 and a book published in 1786, The Uncertainty of the Signs of Death. Mrs. Blunden, the wife of a local malt trader, was “a fat gross woman” who in July 1674 drank so much poppy-water (opium) that she fell into a deep sleep that arrested any apparent breath or pulse. The apothecary declared that he supposed she would never wake, and her husband left for London on business, directing that she be buried on his return. But the woman’s relatives noted that the weather was warm and that the body would not last four days, so they buried her on the following day, a Wednesday. Now the tract reads:

The Friday following toward the evening some of the Scholars of the Town being at play in the Churchyard near her grave, they fancied they heard a kind of hollow voice, as it were under ground, to which laying their ears and listening more attentively they plainly heard somebody say:

Take me out of my Grave,

which words the complaining voice repeated several times, intermixing them with fearful groans and dismal shriekings.

The boys reported this to several people but were dismissed. They returned to the chuchyard on Saturday and heard the voice again, “if not with so distinct yet with a louder accent,” and that afternoon the clerk finally exhumed Mrs. Blunden. “And now surveying her body, they found it most lamentably beaten, which they concluded to proceed from the violence she did herself in that deplorable an astonishment, but upon the most diligent scrutiny they could not apprehend that she had the least breath of life remaining, and therefore they again let her down into the grave, intending on the morrow to send to the Coroner.”

Guards were set to watch the resealed grave, but as the night was wet they abandoned their post, and “on the morrow morning at their return to the grave, they found she had torn off great part of her winding sheet, scratched herself first in several places, and beaten her mouth so long till it was all in gore blood.”

A number of citizens were indicted for their negligence, but a town doctor testified that he had held a mirror to Blunden’s mouth before her burial and could see no sign of breath, so “only the Town had a considerable fine set upon them for their neglect.”

| Death

Side Issue

A conundrum by Russian puzzle maven Boris Kordemsky:

A work train composed of a locomotive and five cars has just stopped at a railway station when word comes that a passenger train is approaching. The smaller train must make way for it to pass through, but the station has only one siding, and this will accommodate only three cars (or an engine and two cars). How can it arrange to let the passenger train through?

Click for Answer
| Puzzles

“The Poet’s Reply”

What’s unusual about this poem, composed by James Rambo for Word Ways, May 1977?

Use fulsome howl or direst word in galling us; toil over a shoddy ode?
Listen, dressed in gyves, tiger, allies fall, ensnared in timeless eras, mentally in agony, essays in gall.
Outwit Hades, ignore verses, you real lover? Come!

Useful somehow, Lord, I rest, wording all in gusto I love.
Rash odd yodel is tendresse; dingy vestige rallies fallen snared.
In time, lesser as men tally, I nag on — yes, say, sing all out — with a design.
O reverses, you’re all overcome!

The two stanzas are spelled identically.

| Language

Mouse Call

Letter from E.B. White to Harper & Brothers editor Eugene Saxton, March 1, 1939:

Herewith an unfinished MS of a book called Stuart Little. It would seem to be for children, but I’m not fussy who reads it. You said you wanted to look at this, so I am presenting it thus in its incomplete state. There are about ten or twelve thousand words so far, roughly.

You will be shocked and grieved to discover that the principal character in the story has somewhat the attributes and appearance of a mouse. This does not mean that I am either challenging or denying Mr. Disney’s genius. At the risk of seeming a very whimsical fellow indeed, I will have to break down and confess to you that Stuart Little appeared to me in a dream, all complete, with his hat, his cane, and his brisk manner. Since he was the only fictional figure ever to honor and disturb my sleep, I was deeply touched, and felt that I was not free to change him into a grasshopper or a wallaby. Luckily he bears no resemblance, either physically or temperamentally, to Mickey. I guess that’s a break for all of us.

Saxton pressed for a fall publication, but Stuart Little wouldn’t appear until 1945. “I pull back like a mule at the slightest goading,” White said.

| Literature

Thoughtful

A jester being on his death-bed, one of his companions begged when he got to the other world, he would put in a good word for him. ‘I may perhaps forget,’ said he; ‘tie a string about my finger.’

— The Laughing Philosopher, 1825

| Death · Humor

Adrift

http://commons.wikimedia.org/wiki/File:Raft_of_M%C3%A9duse-Alexandre_Corr%C3%A9ard-IMG_4788-cropped.JPG

En route to Senegal in 1816, the French frigate Méduse ran aground on a reef. The six boats were quickly filled, so those who remained lashed together a raft from topmasts, yards, and planks, and 147 people crowded onto a space 65 feet long and 23 wide, hoping to be towed to the African coast 50 miles away. (Seventeen crew and passengers remained aboard the Méduse.)

The raft sank 3 feet under their combined weight, and the tow line quickly parted. Rather than try to rescue them, the boats sailed on to the Senegalese capital. On the first night, 20 men drowned. On the second, some soldiers broke open a cask of wine and mutinied; in the ensuing melee, at least 60 were killed. By the following afternoon, the 67 who remained were gnawing sword belts to reduce their hunger. Eventually they descended on a corpse embedded among the logs of the raft. “We shudder with horror on finding ourselves under the necessity of recording that which we put into practice,” one wrote later.

On the fourth day, 48 remained, and that night a second mutiny killed 18 more. By the seventh day their numbers had dropped to 27 and they decided that their provisions would support only 15, so the 12 weakest were thrown to the sharks. The last 15 survived for 13 miserable days, living on garlic cloves, a lemon, and occasionally a flying fish. They were finally spotted by the brig Argus, a moment immortalized by Théodore Géricault (below).

Of the 17 who had remained aboard the Méduse, three survived. One told his story to a survivor of the raft journey, who wrote, “They lived in separate corners of the wreck, which they never quitted but to look for food, and this latterly consisted only of tallow and a little bacon. If, on these occasions, they accidentally met, they used to run at each other with drawn knives.”

For all this, the captain of the Méduse was imprisoned for only three years, an occasion for lasting controversy in French politics. “It is more difficult to escape from the injustice of man,” wrote one commentator, “than the fury of the sea.”

http://commons.wikimedia.org/wiki/File:Theodore_Gericault_Raft_of_the_Medusa-1.jpg

| History

Falling Angels

A fearful accident happened on Friday last at the Madeleine church, Bruges. One of the priests, while performing mass, was suddenly struck to the ground by the falling on his forehead of the marble head of an infant Jesus, which had become detached from its body. Fracture of the skull and a severe wound were the consequence to the unhappy clergyman, who, after lingering in great agony, died yesterday.

— Times, May 3, 1847

An extraordinary and fatal accident happened this morning in the Roman Catholic parish church of Kildare. As the Very Rev. Dr. J.B. Kavanagh, P.P., was standing in front of the altar with his hand on the chalice to raise it at the close of 7 o’clock mass, and was about to descend the altar steps to recite the Rosary and Litany of the blessed Virgin, the marble figure of a cherub over the altar fell down and struck him with great force on the head. He fell back heavily, murmured the words ‘My God’ twice, and then became insensible. A cry of horror and anguish was raised by the congregation who witnessed the accident. Some persons rushed forward to lift him up, while others ran for medical help. Drs. Watson, Dillon and Chaplin were soon in attendance, and Dr. Kavanagh having been raised from the floor was placed on a stretcher and carried into the adjoining convent, where, having never recovered consciousness, he died soon afterwards.

— Times, Oct. 6, 1886

| Oddities

Bad Starts

The popular Bulwer–Lytton Fiction Contest challenges entrants to compose “the opening sentence to the worst of all possible novels”:

As an ornithologist, George was fascinated by the fact that urine and feces mix in birds’ rectums to form a unified, homogeneous slurry that is expelled through defecation, although eying Greta’s face, and sensing the reaction of the congregation, he immediately realized he should have used a different analogy to describe their relationship in his wedding vows.

Less well known is the Lyttle Lytton Contest, which requires that the sentences be short. Winners:

2012 – “Agent Jeffrey’s trained eyes rolled carefully around the room, taking in the sights and sounds.” (Davian Aw)
2011 – “The red hot sun rose in the cold blue sky.” (Judy Dean)
2010 – “‘I shouldn’t be saying this, but I think I’ll love you always, baby, always,’ Adam cried into the email.” (Shexmus Amed)
2009 – “The mighty frigate Indestructible rounded the Horn of Africa and lurched east’ard.” (Pete Wirtala)
2008 – “Because they had not repented, the angel stabbed the unrepentant couple thirteen times, with its sword.” (Graham Swanson)
2007 – “It clawed its way out of Katie, bit through the cord and started clearing.” (Gunther Schmidl)
2006 – “This is the cipher key for all that follows: |||||| || |!” (P. Scott Hamilton)
2005 – “John, surfing, said to his mother, surfing beside him, ‘How do you like surfing?'” (Eric Davis)
2004 – “This is the story of your mom’s life.” (Rachel Lambert)
2003 – “For centuries, man had watched the clouds; now, they were watching him.” (Stephen Sachs)
2002 – “The pain wouldn’t stop, and Vern still had three cats left.” (Andrew Davis)
2001 – “Turning, I mentally digested all of what you, the reader, are about to find out heartbreakingly.” (Top Changwatchai)

Another favorite, offered by Jonathan Blum in a 2007 freeform contest: “Scaling Everest was, by far, the most amazing and transformative experience of my life. Unfortunately, this is a thesis on context-free grammars.”

| Literature

Gray Area

http://commons.wikimedia.org/wiki/File:Karel_Dujardin_-_Italian_Landscape_with_Herdsman_and_a_Piebald_Horse_WGA.jpg

A legal conundrum from Jonathan Swift and Alexander Pope’s Memoirs of Martinus Scriblerus (1741): Sir John Swale bequeaths to Matthew Stradling “all my black and white Horses.” Sir John has six black, six white, and six pied horses. Should Stradling get the pied ones?

On the one hand, “Whatever is Black and White, is Pyed, and whatever is Pyed is Black and White; ergo, Black and White is Pyed, and, vice versa, Pyed is Black and White.”

On the other, “A pyed Horse is not a white Horse, neither is a pyed a black Horse; how then can pyed Horses come under the Words of black and white Horses?”

Perhaps this will help — a proof that all horses are the same color, condensed from Joel E. Cohen, “On the Nature of Mathematical Proofs,” Opus, May 1961, from A Random Walk in Science:

It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have each been shown to be the same color. It follows then that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour.

| Language · Science & Math