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.
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.)
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?
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.”
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.)
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.
A study in perspective by University of Hertfordshire psychologist Richard Wiseman:
In early July 1836, three boys searching for rabbits’ burrows near Edinburgh came upon some thin sheets of slate set into the side of a cliff. On removing them, they discovered the entrance to a little cave, where they found 17 tiny coffins containing miniature wooden figures.
According to the Scotsman‘s account later that month, each of the coffins “contained a miniature figure of the human form cut out in wood, the faces in particular being pretty well executed. They were dressed from head to foot in cotton clothes, and decently laid out with a mimic representation of all the funereal trappings which usually form the last habiliments of the dead. The coffins are about three or four inches in length, regularly shaped, and cut out from a single piece of wood, with the exception of the lids, which are nailed down with wire sprigs or common brass pins. The lid and sides of each are profusely studded with ornaments, formed with small pieces of tin, and inserted in the wood with great care and regularity.”
Some accounts say that the coffins had been laid in tiers, the lower appearing decayed and the topmost quite recent, but Edinburgh University historian Allen Simpson believes that all were placed in the niche after 1830, about five years before the boys discovered them.
Who placed them there, and why, remain mysterious. Simpson suggests that they may be an attempt to provide a decent symbolic burial for the victims of murderers William Burke and William Hare, who had sold 17 corpses to local doctor Robert Knox in 1828 for use in anatomy lessons. But 12 of Burke and Hare’s victims were women, and the occupants of the fairy coffins are all dressed as men.
So investigations continue. The eight surviving coffins and their tiny occupants are on display today at the National Museum of Scotland.
In 1872 the British merchant ship Mary Celeste was discovered drifting and apparently abandoned 600 miles off the coast of Portugal. In this episode of the Futility Closet podcast we’ll review this classic mystery of the sea: Why would 10 people flee a well-provisioned, seaworthy ship in fine weather?
We’ll also get an update on the legal rights of apes and puzzle over why a woman would not intervene when her sister is drugged.
Sources for our segment on the Mary Celeste:
Paul Begg, Mary Celeste: The Greatest Mystery of the Sea, 2005.
Charles Edey Fay, Mary Celeste: The Odyssey of an Abandoned Ship, 1942.
J.L. Hornibrook, “The Case of the ‘Mary Celeste': An Ocean Mystery,” Chambers Journal, Sept. 17, 1904.
George M. Walsh, “Chimpanzees Don’t Have The Same Rights As Humans, New York Court Rules,” Associated Press, Dec. 5, 2014.
The opinion from the New York Supreme Court, Appellate Division:
The People of the State of New York ex rel. The Nonhuman Rights Project, Inc., on Behalf of Tommy, Appellant, v. Patrick C. Lavery, Individually and as an Officer of Circle L Trailer Sales, Inc., et al.
“Orangutan in Argentina Zoo Recognised by Court as ‘Non-Human Person’,” Guardian, Dec. 21, 2014.
Coffitivity “recreates the ambient sounds of a cafe to boost your creativity and help you work better.”
This week’s lateral thinking puzzle was submitted by listener Nick Madrid.
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Many thanks to Doug Ross for the music in this episode.
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Russian mathematician Pafnuty Chebyshev devised this puzzling mechanisms in 1888. Turning the crank handle once will send the flywheel through two revolutions in the same direction, or four revolutions in the opposite direction. (A better video is here.)
“What is so unusual in this mechanism is the ability of the linkages to flip from one configuration to the other,” write John Bryant and Chris Sangwin in How Round Is Your Circle? (2011). “In most linkage mechanisms such ambiguity is implicitly, or explicitly, designed out so that only one choice for the mathematical solution can give a physical configuration. … This mechanism is really worth constructing, if only to confound your friends and colleagues.”
For more than 500 million years something has been making hexagonal burrows on the floor of the deep sea. Each network of tiny holes leads to a system of tunnels under the surface. The creature that makes them, known as Paleodictyon nodosum, has never been discovered. It might be a worm or perhaps a protist; the structure might be its means of farming its own food or the remains of a nest for protecting eggs. Fossils have been found in the limestone of Nevada and Mexico, and the burrows even turn up in the drawings of Leonardo da Vinci. But what makes them, and how, remain a mystery.
Somewhat related: When puzzling screw-shaped structures (below) were unearthed in Nebraska in the 1890s they were known as “devil’s corkscrews” and attributed to freshwater sponges or some sort of coiling plant. They were finally recognized as the burrows of prehistoric beavers only when a fossilized specimen, Palaeocastor, was found inside one.
adj. half again as large
adj. not tall
Born in 1915, giant Henry M. Mullins partnered with Tommy Lowe and little Stanley Rosinski to form the vaudeville act Lowe, Hite and Stanley. Of Mullins, who stood 7’6-3/4″ and weighed 280 pounds, doctor Charles D. Humberd said, “It is indeed amazing to watch so vast a personage doing a whirlwind acrobatic act. … He dances, fast and furiously, and engages in a comedy knock-about ‘business’ that would be found strenuous by any trained ‘Physical culturist.’ … He is alert, intelligent, well read, affable and friendly.” The act continued until Rosinski’s death in 1962.
When we say that the function of the heart is to pump the blood, what do we mean, exactly? Typically an object’s function is something that confers some good or contributes to some goal: In pumping blood my heart keeps me alive; in grasping objects my hands help me manipulate my environment.
But is that right? Suppose someone designs a sewing machine with a self-destruct button. Pressing the button will never have good consequences for anyone, and no one will ever set a goal that’s furthered by blowing up the machine. Still, it seems correct to say that the button’s function is to destroy the machine.
Another example, from Johns Hopkins philosopher Peter Achinstein: “Suppose that a magnificent chair was designed as a throne for the king, i.e., it was designed to seat the king. However, it is actually used by the king’s guards to block a doorway in the palace. Finally, suppose that although the guards attempt to block the doorway by means of that chair they are unsuccessful. The chair is so beautiful that it draws crowds to the palace to view it, and people walk through the doorway all around the chair to gaze at it. But its drawing such crowds does have the beneficial effect of inducing more financial contributions for the upkeep of the palace, although this was not something intended. What is the function of this chair?”
(Peter Achinstein, “Function Statements,” Philosophy of Science, September 1977.)
The following remarkable coincidence will be read with interest: Sometime since it was announced that a man at Titusville, Pennsylvania, committed suicide for the strange reason that he had discovered that he was his own grandfather. Leaving a dying statement explaining this singular circumstance, we will not attempt to unravel it, but give his own explanation of the mixed-up condition of his kinsfolk in his own words. He says, ‘I married a widow who had a grown-up daughter. My father visited our house very often, fell in love with my stepdaughter, and married her. So my father became my son-in law, and my step-daughter my mother, because she was my father’s wife. Some time afterwards, my wife gave birth to a son; he was my father’s brother-in-law, and my uncle, for he was the brother of my step-mother. My father’s wife — i.e. my step-daughter — had also a son; he was, of course, my brother, and in the mean time my grandchild, for he was the son of my daughter. My wife was my grandmother, because she was my mother’s mother. I was my wife’s husband and the grandchild at the same time. And as the husband of a person’s grandmother is his grandfather, I was my own grandfather.’ After this logical conclusion, we are not surprised that the unfortunate man should have taken refuge in oblivion. It was the most married family and the worst mixed that we ever heard of. To unravel such an entangling alliance could not have resulted otherwise than in an aberration of mind and subsequent suicide.
— Littell’s Living Age, May 9, 1868
(Yes, I know about the song!) (Thanks, Dave.)
A bit more on philosophy and time travel: It seems consistent to suppose that a time traveler can affect the past but not change it. Perhaps I will invent a time machine tomorrow and race heroically back to 1865 to save Lincoln from John Wilkes Booth. I might arrive at Ford’s Theater and race up to Lincoln’s box; I might even wrestle dramatically with Booth in the hallway. But we know in advance that I won’t be successful, because history tells us that Booth did shoot Lincoln that night.
This way of looking at it entails no paradoxes, but it does create a problem. If time travel is possible then presumably hundreds of well-intentioned time travelers converged on Lincoln’s box that night, all determined to save the president and all somehow slipping on banana peels at the wrong moment. This is not impossible, but it seems terrifically unlikely — so much so that the very fact of Lincoln’s death seems to imply that time travel is not possible.
But University of Sydney philosopher Nicholas J.J. Smith points out that we don’t quite know this: A time machine may be invented a century from now with a backward range of only 50 years. In that case we have no experience from which to judge these matters. “One cannot conclude from the supposition that local backward time travel would bring with it what we ordinarily regard as improbable coincidences, that such time travel will occur only rarely: for the only reason we regard the events in question as improbable coincidences is that within our experience, they have not occurred very often — and our experience does not (apparently) encompass backward time travel.”
(Nicholas J.J. Smith, “Bananas Enough for Time Travel?”, The British Journal for the Philosophy of Science, September 1997.)
In the 1970 Scientific American article “How Snakes Move,” Carl Gans points out an oddity in a Sherlock Holmes story:
In ‘The Adventure of the Speckled Band’ Sherlock Holmes solves a murder mystery by showing that the victim has been killed by a Russell’s viper that has climbed up a bell rope. What Holmes did not realize was that Russell’s viper is not a constrictor. The snake is therefore incapable of concertina movement and could not have climbed the rope. Either the snake reached its victim some other way or the case remains open.
This is indeed perplexing. If it’s not a fact that vipers can climb ropes, then how did Holmes solve the case? If vipers can climb ropes in Holmes’ world but not in ours, then how can we follow his reasoning in other matters? What other features of Holmes’ world differ from ours?
One way out: “The story never quite says that Holmes was right that the snake climbed the rope,” notes philosopher David Lewis. So perhaps the snake did reach its victim in some other way and Holmes was simply wrong.
(David Lewis, “Truth in Fiction,” American Philosophical Quarterly, January 1978.)
On Feb. 19, 1916, as workers were digging a new subway line under the East River toward Brooklyn Heights, a burst of compressed air blew 28-year-old Marshall Mabey up through 12 feet of river bed, through the river, and 25 feet into the air atop a geyser of water. Impossibly, he was not seriously injured. From the New York Times:
‘The first thing that told me something was wrong,’ he related yesterday, ‘was when I saw an opening in the earth ahead of the shield which was used to protect the tunnel as we went along. The hole was then about eighteen inches in size. Frank Driver, my partner, and I grabbed hold of a big plank and threw it at the hole to stop it up. I found that the air pressure was pushing me toward the hole, and I tried to save myself by grabbing the air pipes. I missed them, and then I felt myself being pushed into the hole.
‘As I struck the mud it felt as if something was squeezing me tighter than I had ever been squeezed. I was smothered and I guess I lost consciousness. They tell me I was thrown about twenty-five feet above the water when I came out, but I don’t remember that.
‘I am a good swimmer and I kept my mouth shut and came up to the surface. I had on my big rubber boots and they bothered me but I managed somehow to keep my head above the surface. My left leg was numb but I could move it. Finally men on a pier threw me a rope and I held on until I was taken out of the water.’
He said he hoped to return to work within a day or two. “Of course I know that Marshall is in danger every time he goes to work,” said his wife, “but all work is dangerous and my husband is as careful as he can be. His job is a good one and I am glad he has it.”
For most of the 20th century, a man in black appeared each year at the grave of Edgar Allan Poe. In the predawn hours of January 19, he would drink a toast with French cognac and leave behind three roses in a distinctive arrangement. No one knows who he was or why he did this. In this episode of the Futility Closet podcast we review the history of the “Poe Toaster” and his long association with the great poet’s memorial.
We’ll also consider whether Winnie-the-Pooh should be placed on Ritalin and puzzle over why a man would shoot an unoffending monk.
Sources for our segment on the Poe Toaster:
“Mystery Man’s Annual Visit to Poe Grave,” China Daily, Jan. 20, 2008.
“Poe Toaster Remains a Mystery,” WBAL Radio, Jan. 19, 2013.
“‘Toaster’ Rejects French Cognac at Poe’s grave,” Washington Times, Jan. 19, 2004.
Sarah Brumfield, “Poe Fans Call an End to ‘Toaster’ Tradition,” AP News, Jan. 19, 2012.
Liz F. Kay, “Poe Toaster Tribute Is ‘Nevermore’,” Baltimore Sun, Jan. 19, 2010.
Michael Madden, “Yes, Virginia, There Is a Poe Toaster,” Baltimore Sun, Jan. 26, 2011.
Mary Carole McCauley, “Poe Museum Could Reopen in Fall,” Baltimore Sun, Jan. 20, 2013.
Ben Nuckols and Joseph White, “Edgar Allan Poe’s Mysterious Birthday Visitor Doesn’t Show This Year,” Huffington Post, March 21, 2010 (accessed Dec. 1, 2014).
Here’s the only known photo of the toaster, taken at his 1990 apparition and published in the July 1990 issue of Life magazine:
The psychiatric diagnoses of Winnie-the-Pooh and his friends appear in Sarah E. Shea, Kevin Gordon, Ann Hawkins, Janet Kawchuk, and Donna Smith, “Pathology in the Hundred Acre Wood: A Neurodevelopmental Perspective on A.A. Milne,” Canadian Medical Association Journal, Dec. 12, 2000.
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Many thanks to Doug Ross for the music in this episode.
If you have any questions or comments you can reach us at email@example.com. Thanks for listening!
In A Thing or Two About Music (1972), Nicolas Slonimsky describes a series of “puzzle minuets” composed by 18th-century harpsichordist Johann Schobert:
Schobert is not a misprint for Schubert. He was an estimable Silesian-born musician who settled in Paris in 1760 and wrote many compositions in the elegant style of the time. Mozart knew his music well and was even influenced by his easy grace in writing piano pieces. Schobert was something of a musical scientist. Among his compositions is a page entitled, ‘A Curious Musical Piece Which Can Be Played on the Piano, on the Violin, and on the Bass, and at that in Different Ways.’ This page contained five minuets, one of which could be played upside down without any change, one which would result in a new piece when turned upside down, and one which would furnish a continuation upside down. Two could be played on the violin and on the bass by assigning the treble clef right side up and the bass clef upside down.
The full page is here. I haven’t tried playing it.
French aristocrat François Racine de Monville added a striking summer house to his estate in 1785 — it was designed to resemble the ruined column of an imaginary gigantic temple:
The “colonne brisée” contained four stories of oval rooms connected by a spiral staircase hung with rare plants under a skylight. It was admired by Benjamin Franklin, and it inspired Thomas Jefferson in his own architectural work. (“How grand the idea excited by the remains of such a column!” he wrote to Maria Cosway.) It had fallen into disrepair by the 1950s, but it was renovated and reopened to the public in 2009.
In 1968, American Hugo Vihlen sailed from Casablanca to Florida in a boat 5 feet 11 inches long.
In 1992, Englishman Tom McNally sailed from Portugal to Fort Lauderdale in a boat 5 feet 4.5 inches long.
In 1993 Vihlen reclaimed the record by sailing from Newfoundland to Falmouth in a boat 5 feet 4 inches long.
“Tom McNally made plans to fight back with a minuscule three-foot, eleven-inch boat, and when Vihlen later heard about that he announced his intention to build a three-foot, eight-inch aluminum boat,” writes William Longyard in A Speck on the Sea (2003). “The battle would continue between these two friends and rivals.”
French writer Paul Fournel’s 1990 novel Suburbia begins conventionally enough:
Table of Contents
A Word from the Publisher vi
Foreword by Marguerite Duras vii
An Introductory Note by the Author viii
Afterword by François Caradec 215
Supplement for Use in Schools 217
And the “Word from the Publisher” promises that “the quality of this little novel, now that passions have subsided, has emerged ever more forcefully.” But the first page is blank except for four footnotes:
1. In French in the original.
2. Concerning the definition of suburb, see the epigraph et seq.
3. What intention on the author’s part does this brutal opening suggest?
4. Local judge.
The same thing happens on the second page:
1. Notice how Norbert comes crashing onto the scene.
2. This passage is a mixture of backslang and immigrant jargon. Transpose into normal English.
4. Obscene gesture.
And so on — except for footnotes, all the pages in Suburbia are blank. “In Suburbia Fournel was not attempting to give some postmodernist exploration of the nature of literature,” explains Robert Tubbs in Mathematics in Twentieth-Century Literature and Art (2014). “Suburbia, instead, was written according to the lipogrammatic constraint that it contain no letters or symbols. This constraint force Fournel to write a textless narrative. Because of the footnotes on each page, it has content — it is not an empty text; it is simply a textless text, a text that just happens not to contain any words.”
Martin Scorsese’s film Hugo was inspired by a real event. In 1928 Philadelphia’s Franklin Institute received the remains of an 18th-century brass automaton that had been damaged in a fire. It had been donated by the descendants of wealthy manufacturer John Penn Brock; they knew it had been acquired in France and supposed it to be the work of the German inventor Johann Nepomuk Maelzel, famed for his metronome.
The institute’s machinist set about restoring the machine and discovered that its mechanism used an ingenious system of cams to store almost 300 kilobits of information. When he had finished his work, he placed a pen in its hand and watched it draw four strikingly elaborate illustrations and write three poems (click to enlarge):
The final poem contained a surprise — in its border the machine wrote Ecrit par L’Automate de Maillardet, “written by the automaton of Maillardet.” The automaton’s creator was not Johann Maelzel but the Swiss mechanician Henri Maillardet — and this fact had been remembered only because he had taught the machine to write his name.
Subsequent research showed that Maillardet had created the automaton in the 1700s and exhibited it throughout Europe and Russia. How it came to America is not known. It’s on display today at the Franklin Institute, which demonstrates its talents publicly several times a year.
The epilogue of The Time Machine contains this strange passage:
One cannot choose but wonder. Will he ever return? It may be that he swept back into the past, and fell among the blood-drinking, hairy savages of the Age of Unpolished Stone; into the abysses of the Cretaceous Sea; or among the grotesque saurians, the huge reptilian brutes of the Jurassic times. He may even now — if I may use the phrase — be wandering on some plesiosaurus-haunted Oolitic coral reef, or beside the lonely saline lakes of the Triassic Age.
What indeed can “now” mean in this context? If the Time Traveller’s life ended on a prehistoric beach, argues philosopher Donald C. Williams, then surely this became an established fact on the day that it happened. If the concept of time is to have any coherence, then history is a tapestry that is eternal and unchanging; to say that it can be changed “at” some future moment seems to be a flat contradiction. “At” where?
“Time travel,” Williams writes, “is analyzable either as the banality that at each different moment we occupy a different moment from the one we occupied before, or the contradiction that at each different moment we occupy a different moment from the one which we are then occupying — that five minutes from now, for example, I may be a hundred years from now.”
(Donald C. Williams, “The Myth of Passage,” Journal of Philosophy, July 1951.)