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.)

Truth in Fiction

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.)

Express

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.”

Podcast Episode 37: Edgar Allan Poe’s Graveyard Visitor

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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:

poe toaster

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.

Many thanks to Harry’s for supporting this week’s episode. Enter coupon code CLOSETHOLIDAY and get $5 off a Winter Winston set at Harrys.com.

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.

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!

Invertible Minuets

schobert puzzle minuets

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.