Oddities

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

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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

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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

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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

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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

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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.

“Assumptions”

A study in perspective by University of Hertfordshire psychologist Richard Wiseman:

(Thanks, Paul.)

The Edinburgh Fairy Coffins

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.

Podcast Episode 40: The Mary Celeste: A Great Sea Mystery

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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.

Listener mail:

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.

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. Thanks for listening!

Chebyshev’s Paradoxical Mechanism

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.”

(Thanks, Dre.)

Nobody Home

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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.

http://commons.wikimedia.org/wiki/File:Daemonelix_burrows,_Agate_Fossil_Beds.jpg

(Thanks, Paul.)

In a Word

sesquialteral
adj. half again as large

improcerous
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.

Function Statements

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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.)

“A Man His Own Grandfather”

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.)

Time and Chance

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.)