Oddities

No Vacancy

A seeming paradox by Mitsunobu Matsuyama. Rotating the colored panels about their centers seems to change the area of the square. How is this possible?

Two in One

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

Look at this image closely and you’ll see the features of Albert Einstein.

But look at it from across a room and you’ll see Marilyn Monroe.

It’s a “hybrid image,” created using a technique developed by Aude Oliva of MIT and Philippe Schyns of the University of Glasgow. The image combines the low spatial frequencies of one picture with the high spatial frequencies of another, so that it’s processed differently at different viewing distances.

See their paper for the details, and this gallery for more examples.

Podcast Episode 55: The Dyatlov Pass Incident

https://commons.wikimedia.org/wiki/File:Dyatlov_Pass_incident_02.jpg

On February 1, 1959, something terrifying overtook nine student ski-hikers in the northern Ural Mountains. In this episode of the Futility Closet podcast we’ll recount what is known about the incident at Dyatlov Pass and try to make sense of the hikers’ harrowing final night.

We’ll also hear how Dwight Eisenhower might have delivered the Gettysburg Address and puzzle over why signing her name might entitle a woman to a lavish new home.

Sources for our feature on the Dyatlov Pass incident:

Donnie Eichar, Dead Mountain: The Untold True Story of the Dyatlov Pass Incident, 2013.

“Yuri Yudin,” Daily Telegraph, April 30, 2013, 25.

http://www.ermaktravel.org/Europe/Russia/Cholat-%20Syachil/Kholat%20Syakhl.htm

Here’s the investigators’ description of the hikers’ tent as it was discovered:

“Tent site is located on the Northeastern slope of mountain 1079 (Kholat Syakhl official term) meters at the mouth of river Auspiya. Tent site is located 300 meters from the top of the mountain 1079 with a slope of 30°. Test site consists of a pad, levelled by snow, the bottom of which are contains 8 pairs of skis (for tent support and insulation). Tent is stretched on poles and fixed with ropes. On the bottom of the tent 9 backpacks were discovered with various personal items, jackets, rain coats, 9 pairs of shoes. There were also found men’s pants, and three pairs of boots, warm fur coats, socks, hat, ski caps, utensils, buckets, stove, ax, saw, blankets, food: biscuits in two bags, condensed milk, sugar, concentrates, notebooks, itinerary and many other small items and documents, camera and accessories to a camera. The nature and form of all (…) lesions suggest that they were formed by contact with the canvas inside of the tent with the blade of some weapon (presumably a knife).”

http://www.ermaktravel.org/Europe/Russia/Cholat-%20Syachil/Kholat%20Syakhl.htm

This is the final exposure in hiker Yuri Krivonishchenko’s camera. Possibly the image was exposed on the final night, or possibly weeks afterward, inadvertently, by technicians. Lead investigator Lev Ivanov wrote that the hikers’ cameras gave him “abundant information based on negative density, film speed … and aperture and exposure settings,” but that they did not “answer the main question — what was the reason of escape from the tent.”

Here’s journalist Oliver Jensen’s rendering of the Gettysburg Address in “Eisenhowese.” Jensen provided his original to Dwight Macdonald for his 1961 collection Parodies: An Anthology. “The version below is the original as given me by Jensen, with two or three variations in which The New Republic‘s version [of June 17, 1957] seemed to me to have added a turn of the screw”:

I haven’t checked these figures but 87 years ago, I think it was, a number of individuals organized a governmental set-up here in this country, I believe it covered certain Eastern areas, with this idea they were following up based on a sort of national independence arrangement and the program that every individual is just as good as every other individual. Well, now, of course, we are dealing with this big difference of opinion, civil disturbance you might say, although I don’t like to appear to take sides or name any individuals, and the point is naturally to check up, by actual experience in the field, to see whether any governmental set-up with a basis like the one I was mentioning has any validity and find out whether that dedication by those early individuals will pay off in lasting values and things of that kind.

Well, here we are, at the scene where one of these disturbances between different sides got going. We want to pay our tribute to those loved ones, those departed individuals who made the supreme sacrifice here on the basis of their opinions about how this thing ought to be handled. And I would say this. It is absolutely in order to do this.

But if you look at the over-all picture of this, we can’t pay any tribute — we can’t sanctify this area, you might say — we can’t hallow according to whatever individual creeds or faiths or sort of religious outlooks are involved like I said about this particular area. It was those individuals themselves, including the enlisted men, very brave individuals, who have given this religious character to the area. The way I see it, the rest of the world will not remember any statements issued here but it will never forget how these men put their shoulders to the wheel and carried this idea down the fairway.

Now frankly, our job, the living individuals’ job here, is to pick up the burden and sink the putt they made these big efforts here for. It is our job to get on with the assignment — and from these deceased fine individuals to take extra inspiration, you could call it, for the same theories about the set-up for which they made such a big contribution. We have to make up our minds right here and now, as I see it, that they didn’t put out all that blood, perspiration and — well — that they didn’t just make a dry run here, and that all of us here, under God, that is, the God of our choice, shall beef up this idea about freedom and liberty and those kind of arrangements, and that government of all individuals, by all individuals and for the individuals, shall not pass out of the world-picture.

This week’s lateral thinking puzzle was submitted by listener Tyler St. Clare (conceived by his friend Matt Moore).

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter. Thanks for listening!

Podcast Episode 53: The Lost Colony

https://books.google.com/books?id=eu1neCSs4RsC&pg=PA254

It’s been called America’s oldest mystery: A group of 100 English colonists vanished from North Carolina’s Roanoke Island shortly after settling there in 1587. But was their disappearance really so mysterious? In this episode of the Futility Closet podcast we’ll trace the history of the “lost colony” and consider what might have happened to the settlers.

We’ll also visit an early steam locomotive in 1830 and puzzle over why writing a letter might prove to be fatal.

Sources for our feature on the lost colony at Roanoke:

James Horn, A Kingdom Strange: The Brief and Tragic History of the Lost Colony of Roanoke, 2011.

Karen Ordahl Kupperman, Roanoke: The Abandoned Colony, 2007.

Giles Milton, Big Chief Elizabeth: The Adventures and Fate of the First English Colonists in America, 2011.

Lee Miller, Roanoke: Solving the Mystery of the Lost Colony, 2013.

http://commons.wikimedia.org/wiki/File:First_passenger_railway_1830.jpg

Fanny Kemble wrote of her encounter with an early locomotive in a letter dated Aug. 26, 1830 (“A common sheet of paper is enough for love, but a foolscap extra can alone contain a railroad and my ecstasies”). It appears in her 1878 memoir Records of a Girlhood.

She sat alongside engineer George Stephenson, who explained his great project and with whom she fell “horribly in love.” At one point on their 15-mile journey they passed through a rocky defile:

You can’t imagine how strange it seemed to be journeying on thus, without any visible cause of progress other than the magical machine, with its flying white breath and rhythmical, unvarying pace, between these rocky walls, which are already clothed with moss and ferns and grasses; and when I reflected that these great masses of stone had been cut asunder to allow our passage thus far below the surface of the earth, I felt as if no fairy tale was ever half so wonderful as what I saw.

This week’s lateral thinking puzzle was contributed by listener Blaine, who sent this corroborating link (warning — this spoils the puzzle).

This episode is sponsored by our patrons and by The Great Courses — go to http://www.thegreatcourses.com/closet to order from eight of their best-selling courses at up to 80 percent off the original price.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter. Thanks for listening!

Podcast Episode 52: Moving Day in New York

https://commons.wikimedia.org/wiki/File:Goethe_1791.jpg

For centuries, May 1 brought chaos to New York, as most tenants had to move on the same day, clogging the streets with harried people and all their belongings. In this episode of the Futility Closet podcast we’ll review the colorful history of “Moving Day” and wonder how it lasted through two centuries.

We’ll also recount some surprising escapes from sinking ships and puzzle over a burglar’s ingenuity.

Sources for our feature on Moving Day, New York City’s historic custom of changing residence on May 1:

Kenneth A. Scherzer, The Unbounded Community: Neighborhood Life and Social Structure in New York City, 1830-1875, 1992.

Elizabeth Blackmar, Manhattan for Rent, 1785-1850, 1991.

William Shepard Walsh, Curiosities of Popular Customs … Illustrated, 1897.

“Expressmen and Cartmen’s Charges — The Laws Relative Thereto,” New York Times, April 14, 1870.

“Rich Are Homeless This Moving Day,” New York Times, Oct. 1, 1919.

“Rain Adds to Gloom of City Moving Day,” New York Times, Oct. 2, 1919.

“May 1 Moving Rush a Thing of the Past,” New York Times, May 2, 1922.

In 1890 the New York Times published a list of the maximum prices that city ordinances permitted cartmen to charge:

http://www.baruch.cuny.edu/library/alumni/online_exhibits/digital/2007/moving_day/images/015_lg.gif

Sources for our feature on oddities in maritime disasters:

“Andrea Doria Tragedy Recalled by the Survivors,” Associated Press, July 24, 1981.

“A Remarkable Maritime Disaster,” Scientific American, Nov. 24, 1888.

“A Remarkable Collision,” New Zealand Herald, July 26, 1884.

This week’s lateral thinking puzzle was contributed by listener Ken Murphy.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter. Thanks for listening!

Boom Town

https://books.google.com/books?id=A7pZAAAAYAAJ&pg=PA3

In the summer of 1903, the United States Cartridge Company of Tewksbury, Mass., noticed a stain on the floor of its gunpowder magazine. Apparently the dynamite magazine next door had been leaking nitroglycerine. The company asked the dynamite’s owner, American Powder Mills, to attend to the matter, and on July 29 Cartridge’s powder was loaded onto three wagons and moved a few hundred feet away, and an unlucky foreman named Goodwin entered the building, poured a solution on the stain, and began to sweep it with a broom. The spot began to smoke.

The ensuing blast killed 20 people and flattened a score of houses. “Buildings were shaken and windows broken in hundreds of places within a radius of fifteen miles,” reported New England Magazine. “People as far away as Dedham on the south and the mid-New Hampshire towns on the north, felt the shock and guessed at reckless blasts or earthquakes.”

It appears that the fire had caused the dynamite magazine to explode, which set off the three wagons of gunpowder, which set off a third magazine, leased by the Dupont Powder Company. “The ruin caused by the accident was appalling in its perfection,” notes the report. “Three acres of ground were entirely laid waste, the trees and bushes in a considerable radius being torn and blasted as by a breath from a huge furnace.”

The magazines had been built 30 years earlier, when the area had been remote, and the town had grown up around them. “The only safe assumption is that sooner or later every magazine is bound to explode, and must therefore be kept a safe distance from dwelling houses and other buildings.”

(Thanks, Meredith.)

Podcast Episode 51: Poet Doppelgängers

https://commons.wikimedia.org/wiki/File:Goethe_1791.jpg

In this week’s episode of the Futility Closet podcast we’ll look at the strange phenomenon of poet doppelgängers — at least five notable poets have been seen by witnesses when their physical bodies were elsewhere. We’ll also share our readers’ research on Cervino, the Matterhorn-climbing pussycat, and puzzle over why a man traveling internationally would not be asked for his passport.

Sources for our feature on poet doppelgängers:

John Oxenford, trans., The Autobiography of Wolfgang von Goethe, 1969.

G. Wilson Knight, Byron and Shakespeare, 2002.

Julian Marshall, The Life & Letters of Mary Wollstonecraft Shelley, 1889.

Jon Stallworthy, Wilfred Owen, 2013.

W.E. Woodward, The Gift of Life, 1947.

The stories are recounted in the corresponding posts on Futility Closet: Goethe, Byron, Shelley, Owen, Powys.

Listener mail:

Little House of Cats has a photo of Cervino, the (purported) Matterhorn-scaling kitty cat of 1950.

The Daily Mail has photos of Millie, Utah mountaineer Craig Armstrong’s rock-climbing cat. More at Back Country.

Further data on cat rambles:

BBC News, “Secret Life of the Cat: What Do Our Feline Companions Get Up To?”, June 12, 2013 (accessed March 26, 2015).

National Geographic, “Watch: How Far Do Your Cats Roam?”, Aug. 8, 2014 (accessed March 26, 2015).

This week’s lateral thinking puzzles are from Kyle Hendrickson’s 1998 book Mental Fitness Puzzles.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter. Thanks for listening!

Duty Calls

https://commons.wikimedia.org/wiki/File:Portrait_of_Gilbert_Parker.jpg

In May 1905 British MP Sir Gilbert Parker insisted that he had seen the astral body of Sir Crane Rasch in the House of Commons while Rasch was ill at home.

Sir Arthur Hayter supported him: “I beg to say that I not only saw Sir Carne Rasch myself sitting below the gangway but I called him to the attention of Sir Henry Campbell-Bannerman, with whom I was talking on the front opposition bench, saying I wondered why all the papers had inserted notices of Sir Carne’s illness while he was sitting opposite, apparently quite well. Sir Henry replied that he hoped his illness was not catching.”

Rasch declared later that he had never left his room.

“It seems that this is not the first instance of the sort that has occurred in the House,” noted the New York Sun. “In 1897 Mr. O’Connor, an Irish member, went to Ireland to be present at the deathbed of one of his parents. Swift McNeill saw his wraith in his usual seat on the third opposition bench. It was also seen from the press gallery.”

Animal Spirits

Football fans found an unlikely oracle during the 2008 European championship: an octopus named Paul. Before each match his keepers at the Sea Life Centre in Oberhausen, Germany, would lower two boxes of food into his tank, each bearing the flag of an upcoming competitor. Surprisingly, Paul correctly chose the winner in four of Germany’s six games.

When some observers expressed skepticism, Paul went on to pick the winners of all seven of Germany’s World Cup games in 2010, as well as the final between Spain and the Netherlands, giving him an overall success rate of 85 percent.

Competitors sprang up around the world, including a Singaporean parakeet, a German parrot, and a saltwater crocodile named Dirty Harry, who predicted the result of Australia’s general election by snatching a chicken carcass dangling beneath a caricature of Prime Minister Julia Gillard. Maybe we should quit while we’re ahead.

(Thanks, Lauren.)

Chinese Magic Mirrors

During China’s Han dynasty, artisans began casting solid bronze mirrors with a perplexing property. The front of each mirror was a polished, reflective surface, and the back featured a design that had been cast into the bronze. But if light were cast from the mirrored side onto a wall, the design would appear there as if by magic.

The mirrors first came to the attention of the West in the early 19th century, and their secret eluded investigators for 100 years until British physicist William Bragg worked it out in 1932. Each mirror had been cast flat with the design on the reverse side, giving the disk a varying thickness. As the front was polished to produce a convex mirror, the thinner parts of the disk bulged outward slightly. These imperfections are invisible to direct inspection; as Bragg wrote, “Only the magnifying effect of reflection makes them plain.”

Joseph Needham, the historian of ancient Chinese science, calls this “the first step on the road to knowledge about the minute structure of metal surfaces.”

Podcast Episode 49: Can a Kitten Climb the Matterhorn?


In 1950 newspapers around the world reported that a 10-month-old kitten had climbed the Matterhorn, one of the highest peaks in Europe. In this week’s episode of the Futility Closet podcast we’ll wonder whether even a very determined kitty could accomplish such a feat.

We’ll also marvel at a striking demonstration of dolphin intelligence and puzzle over a perplexed mechanic.

My own original post about Matt, the kitten who climbed the Matterhorn, appeared on Dec. 17, 2011. Reader Stephen Wilson directed me to this page, which rehearses the original London Times story (from Sept. 7, 1950) and adds a confirming account from a Times reader that appeared on Sept. 10, 1975.

Further sources:

“A Cat Climbs the Matterhorn,” Miami News, Oct. 19, 1950 (reprinting an editorial, I think, from the San Francisco Chronicle).

“Cat-Climbing on the Matterhorn,” Sydney Morning Herald, Sept. 9, 1950.

“Mere Kitten Conquers Matterhorn,” Spokane Daily Chronicle, Sept. 7, 1950.

Here’s a photo of the Solvay hut at 12,556 feet, where the kitten reportedly spent the first night of its three-day climb:

Sources for our feature on porpoise trainer Karen Pryor:

Karen Pryor, Lads Before the Wind, 1975.

Thomas White, In Defense of Dolphins: The New Moral Frontier, 2008.

This week’s lateral thinking puzzle was submitted by listener David White.

This episode is sponsored by our patrons and by The Great Courses — go to http://www.thegreatcourses.com/closet to order from eight of their best-selling courses at up to 80 percent off the original price.

Also by Loot Crate — go to http://www.lootcrate.com/CLOSET and enter code CLOSET to save $3 on any new subscription.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter. Thanks for listening!

Larghissimo

John Cage indicated that his 1987 piece Organ2/ASLSP should be played “as slow as possible,” but he declined to say how slow that is. Because a pipe organ can be rebuilt piecemeal as it plays, in principle there’s no limit to how long a performance can last.

In 1997 a conference of musicians and philosophers decided to take Cage’s instruction seriously and arranged a performance that would last 639 years. Fed by a bellows, a custom-built organ in the St. Burchardi church in Halberstadt, Germany, has been playing the piece since Sept. 5, 2001; it began with a contemplative 17-month pause, then played the first chord (A4-C5-F#5) for two years. Since then it’s got through only 12 changes; the next won’t occur until Sept. 5, 2020.

This will go on for another 620 years, ending on September 5, 2640. By that time someone somewhere will probably be playing it even more slowly.

Huffman’s Pyramid

huffman's pyramid

Here’s a subtly impossible figure devised by UC-Santa Cruz computer scientist David Huffman. If it’s a three-sided pyramid, then its edges define the intersections of three planes and should meet in a single point. But they don’t:

huffman's pyramid impossibility

This is intriguing because the figure doesn’t immediately look impossible. In Vagueness and Contradiction, philosopher Roy Sorensen writes, “The impossibility of an appearance is sometimes concealed without overloading our critical capacities.”

Possibly this is because we sense that other solutions are possible that can reconcile the error. Zenon Kulpa points out that the pyramid becomes intelligible if we imagine that the farther side hides a fourth edge, giving the figure four sides rather than three. He describes two families of such solutions in “Are Impossible Figures Possible?”, Signal Processing, May 1983.

Podcast Episode 48: The Shark Arm Affair

http://commons.wikimedia.org/wiki/Image:Tiger_shark.png

In 1935 a shark in an Australian aquarium vomited up a human forearm, a bizarre turn of events that sparked a confused murder investigation. This week’s episode of the Futility Closet podcast presents two cases in which a shark supplied key evidence of a human crime.

We’ll also learn about the Paris Herald’s obsession with centigrade temperature, revisit the scary travel writings of Victorian children’s author Favell Lee Mortimer, and puzzle over an unavenged killing at a sporting event.

Sources for our feature on the shark arm affair:

Andrew Tink, Australia 1901-2001: A Narrative History, 2014.

Dictionary of Sydney, “Shark Arm murder 1935,” accessed March 5, 2015.

“Arm-Eating Shark Bares Weird Killing,” Pittsburgh Press, July 9, 1935.

“Shark Gives Up Clue to Murder,” Milwaukee Journal, July 9, 1935.

“‘Shark Arm’ Murder Mystery Still Baffles Australian Police,” Toledo Blade, Dec. 14, 1952.

The 1799 episode of the Nancy’s forged papers appears in (of all places!) Allan McLane Hamilton’s 1910 biography The Intimate Life of Alexander Hamilton (Hamilton appeared for the United Insurance Company in the case). It’s confirmed in Xavier Maniguet’s 2007 book The Jaws of Death: Sharks as Predator, Man as Prey. Apparently both the “shark papers” and the shark’s jaws were put on public display afterward and are now in the keeping of the Institute of Jamaica; I gather the case made a sensation at the time but has largely been forgotten.

Sources for our feature on James Gordon Bennett and the “Old Philadelphia Lady”:

The International New York Times, “Oct. 5, 1947: Old Philadelphia Lady Said It 6,718 Times,” Oct. 14, 2013.

James B. Townsend, “J.Gordon Bennett, Editor by Cable,” New York Times, May 19, 1918.

Mark Tungate, Media Monoliths, 2005.

This week’s lateral thinking puzzle was submitted by listener Lily Geller, who sent this corroborating link (warning — this spoils the puzzle!).

This episode is sponsored by our patrons and by Loot Crate — go to http://www.lootcrate.com/CLOSET and enter code CLOSET to save $3 on any new subscription.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. And you can finally follow us on Facebook and Twitter.

Thanks for listening!

Getting Personal

https://www.flickr.com/photos/denverjeffrey/2502522077/

Image: Flickr

Avon, Colorado, has a bridge called Bob. The four-lane, 150-foot span, built in 1992, connects Avon with the Beaver Creek ski resort across the Eagle River. The town council held a naming contest and received 85 suggestions, including Avon Crossing and Del Mayre Bridge. It was 32-year-old construction worker Louie Sullivan who said, “Oh, heck, just name it Bob,” a suggestion that set city manager Bill James “laughing so hard he had to leave the room.”

Sullivan said he was surprised at the town’s vote; previously he had considered Avon a bit stuffy. “It raises my faith in their sense of humor,” he said.

Young Riders

http://commons.wikimedia.org/wiki/File:Abernathy_3641566828_cfa488c790_o.jpg

Sons of Jack “Catch-‘Em-Alive” Abernathy, the youngest U.S. Marshal in history, Louis and Temple Abernathy inherited their father’s self-reliance: In 1910, when they were 10 and 6 years old, they rode on horseback from their Oklahoma ranch to Manhattan to greet Theodore Roosevelt as he returned from Africa. After riding behind Roosevelt’s car in a ticker-tape parade, they drove home in a new car.

The following year, apparently bored, they accepted a $10,000 challenge to ride on horseback from New York to San Francisco in 60 days or less, never eating or sleeping indoors. They missed the deadline by two days but still established a speed record. And in 1913 they rode by motorcycle from Oklahoma to New York City.

The two went on to successful careers in law and oil. “Teach a boy self-reliance from the moment he tumbles out of the cradle, make him keep his traces taut and work well forward in his collar, and 99 times out of a hundred his independence will assert itself before he is 2 years old,” their father told a newspaper after their first trip. “That’s my rule, and if you don’t think I’ve taken the right tack talk to my boys for five minutes and they’ll convince you that they are men in principles even if they are babies in years. God bless ’em.”

The Pythagoras Paradox

http://commons.wikimedia.org/wiki/Category:Mathematical_paradoxes#mediaviewer/File:Pythagoras_paradox.png

Draw a right triangle whose legs a and b each measure 1. Draw d and e to complete a unit square. Clearly d + e = 2.

Now if we cut a “step” into the square as shown, then f + h = 1 and g + i = 1, so the total length of the “staircase” is still 2. Cut still finer steps and j + k + l + m + n + o + p + q is likewise 2.

And so on: The more finely we cut the steps, the more closely their shape approximates that of the original triangle’s diagonal. Yet the total length of the stairstep shape remains 2, the sum of its horizontal and vertical elements. At the limit, then, it would seem that c must measure 2 … but we know that the length of a unit square’s diagonal is the square root of 2. Where is the error?

(Thanks, Alex.)

Mixed Greens

http://commons.wikimedia.org/wiki/File:San_Francisco_Earthquake_of_1906,_After_the_earthquake_-_NARA_-_522948.tif

Professor Starr Jordan, President of Leland Stanford University, told of a case where nature had juggled with real estate during the San Francisco earthquake. An earthquake crack had passed directly in front of three cottages, and moved the rose-garden from the middle cottage to the furthest one, and the raspberry patch from the near cottage exactly opposite the middle one. History does not relate how the law decided who owned the roses and the raspberries after their rearrangement.

— M.E. David, Professor David: The Life of Sir Edgeworth David, 1937

Sea Music

The lovely Irish folk tune Port na bPúcaí (“The Music of the Fairies”) had mystical beginnings — it’s said that the people of the Blasket Islands heard ethereal music and wrote an air to match it, hoping to placate unhappy spirits. Seamus Heaney’s poem “The Given Note” tells of a fiddler who took the song “out of wind off mid-Atlantic”:

Strange noises were heard
By others who followed, bits of a tune
Coming in on loud weather
Though nothing like melody.

Recent research suggests that, rather than fairies, the islanders may have been hearing the songs of whales transmitted through the canvas hulls of their fishing boats. Humpback whales pass through Irish waters each winter as they migrate south from the North Atlantic, and their songs seem to resemble the folk tune.

Ronan Browne, who plays the air above on Irish pipes, writes, “In the mid 1990s I went rooting through some cassettes of whale song and there in the middle of the Orca (Killer Whale) section I heard the opening notes of Port na bPúcaí!”

No one can say for certain whether the one inspired the other, of course, but if it didn’t it’s certainly a pleasing coincidence.

(Thanks, James.)

A Late Contribution

A ghost co-authored a mathematics paper in 1990. When Pierre Cartier edited a Festschrift in honor of Alexander Grothendieck’s 60th birthday, Robert Thomas contributed an article that was co-signed by his recently deceased friend Thomas Trobaugh. He explained:

The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom’s simulacrum remarked, ‘The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf.’ Awaking with a start, I knew this idea had to be wrong, since some perfect complexes have a non-vanishing K0 obstruction to extension. I had worked on this problem for 3 years, and saw this approach to be hopeless. But Tom’s simulacrum had been so insistent, I knew he wouldn’t let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor.

Thomason himself died suddenly five years later of diabetic shock, at age 43. Perhaps the two are working again together somewhere.

(Robert Thomason and Thomas Trobaugh, “Higher Algebraic K-Theory of Schemes and of Derived Categories,” in P. Cartier et al., eds., The Grothendieck Festschrift Volume III, 1990.)

The Coin Paradox

In the top figure, one coin rolls around another coin of equal size.

In the bottom figure, the same coin rolls along a straight line.

In each case the rolling coin has made one complete rotation. But the red arc at the top is half the length of the red line at the bottom. Why?

Round and Round

Army ants are blind; they follow the pheromone tracks left by other ants. This leaves them vulnerable to forming an “ant mill,” in which a group of ants inadvertently form a continuously rotating circle, each ant following the ones ahead and leading the ones behind. Once this happens there’s no way to break the cycle; the ants will march until they die of exhaustion.

American naturalist William Beebe once came upon a mill 365 meters in circumference, a narrow lane looping senselessly through the jungle of British Guiana. “It was a strong column, six lines wide in many places, and the ants fully believed that they were on their way to a new home, for most were carrying eggs or larvae, although many had food, including the larvae of the Painted Nest Wasplets,” he wrote in his 1921 book Edge of the Jungle. “For an hour at noon during heavy rain, the column weakened and almost disappeared, but when the sun returned, the lines rejoined, and the revolution of the vicious circle continued.”

He calculated that each ant would require 2.5 hours to make one circuit. “All the afternoon the insane circle revolved; at midnight the hosts were still moving, the second morning many had weakened and dropped their burdens, and the general pace had very appreciably slackened. But still the blind grip of instinct held them. On, on, on they must go! Always before in their nomadic life there had been a goal — a sanctuary of hollow tree, snug heart of bamboos — surely this terrible grind must end somehow. In this crisis, even the Spirit of the Army was helpless. Along the normal paths of Eciton life he could inspire endless enthusiasm, illimitable energy, but here his material units were bound upon the wheel of their perfection of instinct. Through sun and cloud, day and night, hour after hour there was found no Eciton with individual initiative enough to turn aside an ant’s breadth from the circle which he had traversed perhaps fifteen times: the masters of the jungle had become their own mental prey.”

The Paradox of the Muddy Children

Three children return home after playing outside, and their father tells them that at least one of them has a muddy face. He repeats the phrase “Step forward if you have a muddy face” until all and only the children with muddy faces have stepped forward.

If there’s only one child with a muddy face, then she’ll step forward immediately — she can see that no other children have muddy faces, so her father must be talking about her. Each of the other children will see her muddy face and stand fast, since they have no way of knowing whether their own faces are muddy.

If there are two children with muddy faces, then no one will step forward after the first request, since each might think the father is addressing the other one. But when no one steps forward after the first request, each will realize that there must be two children with muddy faces, and that she herself must be one of them. So both will step forward after the second request, and the rest will stand fast.

A pattern emerges: If there are n children with muddy faces, then n will step forward after the nth request.

But now imagine a scenario in which more than one of the children has a muddy face, but the father does not tell them that at least one of them has a muddy face. Now no one steps forward after the first request, for the same reason as before. But no one steps forward at the second request either, because the fact that no one stepped forward after the first request no longer means that there is more than one child with a muddy face.

This is perplexing. In the second scenario all the children can see that at least one of them has a muddy face, so it seems needless for the father to tell them so. But without his statement the argument never gets going; despite his repeated requests, no child will ever step forward. What’s missing?

(From Michael Clark, Paradoxes From A to Z, 2007.)

Home Cooking

http://commons.wikimedia.org/wiki/File:Map_of_USA_showing_unlabeled_state_boundaries.png

The map of the continental United States contains an elf making chicken.

He’s known as Mimal, after the states that make him up: Minnesota (hat), Iowa (head), Missouri (shirt), Arkansas (pants), and Louisiana (boots).

Fittingly, the chicken is Kentucky and the tin pan is Tennessee.