The Napkin Folding Problem

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Image: Wikimedia Commons

Is it possible to fold a square napkin so that its perimeter increases? This beautifully simple question has attracted sustained attention since Soviet mathematician Vladimir Arnold first posed it in 1956. If each fold must include all layers, then the answer is no: The perimeter of a folded unit square will never exceed 4. In 1997 American physicist Robert J. Lang showed that the perimeter can be increased if certain sophisticated origami techniques are permitted, but in Lang’s solution the panels and folds don’t remain strictly rigid during intermediate steps. It wasn’t until 2004 that A. Tarasov managed to show that the task can be accomplished within the constraints of “rigid origami.” This satisfies the original problem, but some variants of the challenge remain unresolved within the complex world of paper folding.

| Science & Math

Tenterhooks

[Samuel] Rogers met Lord Dudley at one of the foreign watering-places, and began in his vain way, ‘What a terrible thing it is how one’s fame pursues one, and that one can never get away from one’s own identity! Now I sat by a lady the other night, and she began, ‘I feel sure you must be Mr. Rogers.’ — ‘And were you?’ said Lord Dudley.

— Augustus Hare, The Story of My Life, 1896

| Society

Rough Crossing

Notable expressions of dismay made by Panurge during a tempest at sea in Gargantua and Pantagruel:

Ughughbubbubughsh!
Augkukshw!
Bgshwogrbuh!
Abubububugh!
Bububbububbubu! boo-hoo-hoo-hoo!
Ubbubbughschwug!
Ubbubbugshwuplk!
ubbubbubbughshw
bubbubughshwtzrkagh!
Alas, alas! ubbubbubbugh! bobobobobo! bubububuss!
Ubbubbughsh! Grrrshwappughbrdub!
Bubububbugh! boo-hoo-hoo!
Ubbubbubbugh! Grrwh! Upchksvomitchbg!
Ububbubgrshlouwhftrz!
Ubbubbububugh! ugg! ugg!
Ubbubbubbugh! Boo-hoo-hoo!

“My personal favorite, however, is the incredible-sounding ‘Wagh, a-grups-grrshwahw!’,” writes wordplay enthusiast Trip Payne. “Aside from its logological interest (eight consecutive consonants, albeit divided by a hyphen), the word simply does not sound anything like a wail could possibly sound. The ingenuity of Panurge to come up with such a fresh-sounding, imaginative exclamation — particularly under such pressure — is awe-inspiring.” (All these expressions are from Jacques Leclercq’s 1936 translation.)

(Trip Payne, “‘Alas, Alack!’ Revisited,” Word Ways 22:1 [February 1989], 34-35.)

| Language · Literature

Branch Manager

A puzzle from The Book of the Thousand Nights and One Night:

“Solve the following problem if you can: a flock of pigeons alighted upon a tree, some perching upon the upper branches and some upon the lower; those upon the upper branches said to those upon the lower: ‘If one of you flies up to us our number will be double yours; if one of us flies down to you, our numbers will be equal.'”

How large was the flock?

Click for Answer
| Puzzles

A Long Sleep

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Image: Wikimedia Commons

In 1999, archaeologists made a stunning find near the summit of a stratovolcano on the Argentina–Chile border. Three Inca children, sacrificed in a religious ritual 500 years earlier, had been preserved immaculately in the small chamber in which they had been left to die. Due to the dryness and low temperature of the mountainside, the bodies had frozen before they could dehydrate, making them “the best-preserved Inca mummies ever found.” Even the hairs on their arms were intact; one of the hearts still contained frozen blood.

Known as the Children of Llullaillaco, they’re on display today at the Museum of High Altitude Archaeology in Salta.

| Death · History · Science & Math

Overheard

In 1957, a runaway cow in Guildford knocked down a man on a pedestrian crossing. At trial, the defendant’s counsel argued that the owner of a tame animal was not liable for damage it did that was “foreign to its species.” Since a cow was undoubtedly tame, he would seek to prove that “the cow attacked the plaintiff; if that were so, there was no liability.” This was followed by a memorable exchange:

His Lordship: Is one to abandon every vestige of common sense in approaching this matter?

Counsel: Yes, my Lord.

The hearing was adjourned, and the court eventually decided for the defendant.

| Society

Urban Renewal

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Image: Wikimedia Commons

In 2007, during a construction project at 39 Avenue George V in Paris, artist Pierre Delavie draped the site in a scaffolding tarpaulin of 2,500 square meters printed with a distorted image of the site’s former structure. Crows and cornices of polystyrene were even added to complete the effect. When the work was finished, pieces of the trompe-l’œil drapery were sold at auction.

More photos.

| Art

Unquote

“Tradition means giving votes to the most obscure of all classes — our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who merely happen to be walking around.” — G.K. Chesterton

| Quotations · Society

A Pirate’s Credo

Cruising off Rhode Island in 1717, pirate Samuel Bellamy plundered a Boston sloop and granted his crew’s wish to sink her. Before putting the captain ashore, Bellamy told him:

I am sorry they won’t let you have your sloop again, for I scorn to do any one a mischief, when it is not to my advantage; damn the sloop, we must sink her, and she might be of use to you. Though you are a sneaking puppy, and so are all those who will submit to be governed by laws which rich men have made for their own security; for the cowardly whelps have not the courage otherwise to defend what they get by knavery; but damn ye altogether: damn them for a pack of crafty rascals, and you, who serve them, for a parcel of hen-hearted numbskulls. They vilify us, the scoundrels do, when there is only this difference, they rob the poor under the cover of law, forsooth, and we plunder the rich under the protection of our own courage. Had you not better make then one of us, than sneak after these villains for employment?

The captain replied that his conscience forbade him to break the laws of God or man. Bellamy returned, “You are a devilish conscience rascal! I am a free prince, and I have as much authority to make war on the whole world as he who has a hundred sail of ships at sea and an army of 100,000 men in the field; and this my conscience tells me! But there is no arguing with such snivelling puppies, who allow superiors to kick them about deck at pleasure.”

(From Charles Johnson, A General History of the Robberies and Murders of the Most Notorious Pyrates, 1724.)

| Crime · Society