schnittke gravestone

Composer Alfred Schnittke’s gravestone bears a musical staff with a semibreve rest under a fermata, indicating that the rest should be held as long as desired. It’s marked fff, or fortississimo, meaning that it should be performed very strongly.

Overall it might be interpreted to mean “a decided rest of indefinite length.”


Why do we cultivate friendships? What reason do I have to be a friend to another person, that is, to care about him for his own sake? In order to make the friendship worthwhile, such a reason would have to explain how doing it makes my own life better. But that’s a problem: If I pursue the friendship in order to improve my own life, then I’m not really being a true friend, caring about my friend for his own sake.

University of Newcastle philosopher Joe Mintoff writes, “The problem is that, even though many of us think that being a true friend makes our lives better, paradoxically this thought had better not guide our pursuit of friendship, lest this mean that we are not true friends and that our lives are not made better.” Why, then, do we seek to befriend others?

(Joe Mintoff, “Could an Egoist Be a Friend?,” American Philosophical Quarterly 43:2 [April 2006], 101-118.)

The Two Errand Boys

dudeney errand boys

Another conundrum from Henry Dudeney’s Canterbury Puzzles:

A country baker sent off his boy with a message to the butcher in the next village, and at the same time the butcher sent his boy to the baker. One ran faster than the other, and they were seen to pass at a spot 720 yards from the baker’s shop. Each stopped ten minutes at his destination and then started on the return journey, when it was found that they passed each other at a spot 400 yards from the butcher’s. How far apart are the two tradesmen’s shops? Of course each boy went at a uniform pace throughout.

Click for Answer

Podcast Episode 134: The Christmas Truce

In December 1914 a remarkable thing happened on the Western Front: British and German soldiers stopped fighting and left their trenches to greet one another, exchange souvenirs, bury their dead, and sing carols in the spirit of the holiday season. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Christmas truce, which one participant called “one of the highlights of my life.”

We’ll also remember James Thurber’s Aunt Sarah and puzzle over an anachronistic twin.


In 1898, G.W. Roberts of Birmingham made a full-size piano from 3,776 matchboxes and 5 pounds of glue.

In 1892, 69 men raced 302 miles on stilts, from Bordeaux to Bayonne and Biarritz and back.

Sources for our feature on the Christmas truce:

Terri Blom Crocker, The Christmas Truce: Myth, Memory, and the First World War, 2016.

Stanley Weintraub, Silent Night: The Story of the World War I Christmas Truce, 2001.

Chris Baker, The Truce: The Day the War Stopped, 2014.

Peter Hart, “Christmas Truce,” Military History 31:5 (January 2015), 64-70.

Joe Perry, Christmas in Germany: A Cultural History, 2010.

Ian Herbert, “Muddy Truth of the Christmas Truce Game,” Independent, Dec. 24, 2014.

David Brown, “Remembering a Victory For Human Kindness,” Washington Post, Dec. 25, 2004.

“Alfred Anderson, 109, Last Man From ‘Christmas Truce’ of 1914,” New York Times, Nov. 22, 2005.

“The Christmas Truce, 1914,” The Henry Williamson Society (accessed Dec. 16, 2016).

Mike Dash, “The Story of the WWI Christmas Truce,” Smithsonian, Dec. 23, 2011.

Stephen Moss, “Truce in the Trenches Was Real, But Football Tales Are a Shot in the Dark,” Guardian, Dec. 16, 2014.

Listener mail:

Kirk Ross, The Sky Men: A Parachute Rifle Company’s Story of the Battle of the Bulge and the Jump Across the Rhine, 2004.

A short version of the barrel-of-bricks episode from MythBusters:

Listener Daniel Sterman recommends the original episode, “Barrel of Bricks,” from Oct. 10, 2003.

Wikipedia, “Sandman (Wesley Dodds)” (accessed Dec. 16, 2016).

Wikipedia, “Sala Gang” (accessed Dec. 16, 2016).

This week’s lateral thinking puzzle was suggested by listeners Greg Askins, Stacey Irvine, and Donald Mates. Here are three corroborating links (warning — these spoil the puzzle).

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page 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 Thanks for listening!

New Music

The score for British composer Cornelius Cardew’s Treatise is 193 pages of abstract and geometric shapes. There’s no indication as to how to interpret these, but Cardew suggested that the players work out a plan in advance.


Sylvano Bussotti’s Five Pieces for David Tudor drives conventional notation in the direction of graphics and visual art. “For Bussotti, musical results, whatever they may be, flow directly from the visual,” writes Simon Shaw-Miller in Visible Deeds of Music (2002). “The ear plays no part until the work is performed.”


Stripsody, by Bussotti’s friend Cathy Berberian, is composed as a cartoon strip, complete with characters (including Tarzan and Superman) and sound effects at approximate pitch (including oink, zzzzzz, pwuitt, bang, uhu, and kerplunk). The instructions explain, “The score should be performed as if [by] a radio sound man, without any props, who must provide all the sound effects with his voice.” Here’s an example:

See Difficult Music.


In 1834, engineer John Scott Russell was experimenting with boats in Scotland’s Union Canal when he made a strange discovery:

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped — not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.

They’re known today as solitons. He found that such waves can travel over very large distances, at a speed that depends on their size and width and the depth of the water. Remarkably, as shown above, they emerge from a collision unchanged, simply “passing through” one another.

(Thanks, Steve.)

Keyboard Variations

Inspired by Isaac Newton’s theory that the seven notes of the diatonic scale were related to the colors of the spectrum, French mathematician Louis Bertrand Castel in 1725 invented an “ocular harpsichord” outfitted with lanterns so that “the pressing of the keys would bring out the colours with their combinations and their chords; in one word, with all their harmony, which would correspond exactly to that of any kind of music.” Voltaire devoted Chapter 14 of his Eléments de la philosophie de Newton to the the theory and to Castel’s instrument, and Telemann composed several pieces for it.

The Great Stalacpipe Organ in Luray Caverns, Virginia, produces its tones by striking stalactites with rubber mallets. Leland W. Sprinkle spent three years in the 1950s identifying promising stalactites, shaving them to pitch, and wiring solenoids to trigger the mallets. The tones can be heard throughout the cavern even without amplification, but a loudspeaker system is normallly used.

I think I’ve written elsewhere about the Katzenklavier, a thankfully imaginary instrument first described by Athanasius Kircher in 1650. In the words of one writer, “if a key was pressed on the keyboard, the corresponding tail would be pulled hard, and it would produce each time a lamentable meow.”

Allegedly Louis XI of France challenged Abbé de Baigne to do the same thing with pigs to produce a “piganino”:

That brutal monarch, Louis XI of France, is said to have constructed, with the assistance of the Abbé de Baigne, an instrument designated a ‘pig organ,’ for the production of natural sounds. The master of the royal music, having made a very large and varied assortment of swine, embracing specimens of all breeds and ages, these were carefully voiced, and placed in order, according to their several tones and semitones, and so arranged that a key-board communicated with them, severally and individually, by means of rods ending in sharp spikes. In this way a player, by touching any note, could instantly sound a corresponding note in nature, and was enabled to produce at will either natural melody or harmony!

“The result is said to have been striking, but not very grateful to human ears.”

After our civilization has destroyed itself, the Adriatic will still be playing harmonies on the “sea organ” in Zadar, Croatia. Wind and waves interact with a system of polyethylene tubes to produce sound in a resonating cavity. In 2006 architect Nikola Bašic received the European Prize for Urban Public Space for the project, voted the best among 207 candidate projects from across Europe.

12/17/2016 UPDATE: I completely forgot the mouse organ! (Thanks, Gavin.)

The More the Airier?,_1921.png

In 1921 aeronautical engineer Giovanni Caproni designed a 100-seat transatlantic airliner with nine wings. With an empty weight of 14,000 kg, the Caproni Ca.60 Transaereo did tolerably well on its first test flight on Lake Maggiore, but it crashed on the second and never flew again. Caproni said, “So the fruit of years of work, an aircraft that was to form the basis of future aviation, all is lost in a moment. But one must not be shocked if one wants to progress. The path of progress is strewn with suffering.”

Nine wings isn’t even the record — that might belong to the “clever but somewhat dogmatic” Victorian engineer Horatio Phillips, who devised aircraft with up to 200 airfoils, basing them on a multi-vaned marine hydrofoil that he had designed. “But air and water do not behave similarly,” notes James Gilbert in The World’s Worst Aircraft (1976). “Air is compressible, while water, as you will know if you have ever belly-flopped into a swimming pool, hardly is. Multiple vanes lift well in water, poorly if at all in air.” Phillips spent £4,000 and gave up.

Growth Potential

Suppose you’re working on an algebraic expression that involves variables, addition, multiplication, and parentheses. You try repeatedly to expand it using the distributive law. How do you know that the expression won’t continue to expand forever?

For example, expanding

(x + y)(s(u + v) + t)


x(s(u + v) + t) + y(s(u + v) + t),

which has more parentheses than the original expression.

Click for Answer