Current Affairs

Is it possible to sail on a river on a windless day? In Why Cats Land on Their Feet (2012), Mark Levi points out that the answer is yes, at least in principle. If the keel is turned broadly against the current, then this will carry the boat downstream, drawing the sail through the still air. Now the roles of the sail and the keel are reversed: The keel catches the motion of the river, acting as a sail, and the boat follows the course established by the sail, which acts as a keel. “It’s just like regular sailing,” Levi writes, “except upside down.”

That’s from the point of view of an observer on shore. In the boat’s reference frame, the water is still and a wind is blowing upstream. From this perspective the boat is sailing conventionally — the sail is catching the wind and the keel slices through the water.

“This is a neat symmetry,” Levi notes. “The sail and the keel exchange roles, depending on your reference frame! So the sail and the keel have completely equal rights in that respect.”

Braess’ Paradox
Image: Wikimedia Commons

The diagram above represents a road network where T is the number of travelers. The leg from START to A takes T/100 = t minutes to traverse, as does the leg from B to END. The legs from START to B and from A to END each take a constant 45 minutes.

Now suppose that 4000 drivers want to travel from START to END. The northern and the southern routes are equally efficient, so the drivers will split into two groups, and each will arrive at END in 2000/100 + 45 = 65 minutes.

But now suppose that planners, hoping to improve matters, add a shortcut between A and B with a travel time of 0 minutes. Now all the drivers will take the route from START to A, since in the worst case it will take 4000/100 = 40 minutes, rather than the guaranteed 45 minutes taken by the leg from START to B. From A every driver will take the shortcut to B, for the same reason: Even in the worst case, the trip from B to END is 5 minutes faster than the trip from A to END.

As a result, every driver’s trip now takes 4000/100 + 4000/100 = 80 minutes, which is 15 minutes longer than in the original state of affairs. No individual driver has an incentive to change his behavior, since now the two original routes (northern and southern) each take 4000/100 + 45 = 85 minutes. If the 4000 drivers as a body could agree never to use the shortcut, they’d all be better off. But without a way to enforce this, all are stuck with longer commutes.

The principle was discovered by German mathematician Dietrich Braess in 1968. It’s known as Braess’ paradox.

Podcast Episode 96: The Abduction of Edgardo Mortara

On June 23, 1858, the Catholic Church removed 6-year-old Edgardo Mortara from his family in Bologna. The reason they gave was surprising: The Mortaras were Jewish, and Edgardo had been secretly baptized. In this week’s episode of the Futility Closet podcast we’ll tell the story of little Edgardo and learn how his family’s plight shaped the course of Italian history.

We’ll also hear Ben Franklin’s musings on cultural bigotry and puzzle over an unexpected soccer riot.

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.

Sources for our feature on Edgardo Mortara:

David I. Kertzer, The Kidnapping of Edgardo Mortara, 1997.

Bruce A. Boyer and Steven Lubet, “The Kidnapping of Edgardo Mortara: Contemporary Lessons in the Child Welfare Wars,” Villanova Law Review 45 (2000), 245.

Steven Lubet, “Judicial Kidnapping, Then and Now: The Case of Edgardo Mortara,” Northwestern University Law Review 93:3 (Spring 1999), 961.

Donald L. Kinzer, “Review: The American Reaction to the Mortara Case, 1858-1859,” Mississippi Valley Historical Review 44:4 (March 1958), 740-741.

Alexander Stille, “How a Jewish Boy’s Baptism Changed the Shape of Italy: The Notorious Kidnapping of Edgardo Mortara,” Forward, Aug. 1, 1997.

“Pope John Paul Faces Politics of Sainthood,” Associated Press, Sept. 2, 2000.

Ellen Knickmeyer, “Pope Moves Two Toward Sainthood,” Spartanburg [S.C.] Herald-Journal, Sept. 4, 2000.

Garry Wills, “The Vatican Monarchy,” New York Review of Books, Feb. 19, 1998.

Garry Wills, “Popes Making Popes Saints,” New York Review of Books, July 9, 2013.

Justin Kroll, “Steven Spielberg Boards Religious Drama ‘Edgardo Mortara’,” Variety, April 17, 2014.

Ben Franklin’s “Remarks Concerning the Savages of North-America” was published in 1784 by Franklin’s Passy Press in France.

This week’s lateral thinking puzzle was contributed by listener Tommy Honton, who sent these corroborating links (warning: these spoil the puzzle).

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

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!

Late Service

The U.S. Department of Veterans Affairs is still paying a pension earned by a Civil War soldier.

Union infantryman Mose Triplett was 19 at the war’s end in 1865. In the 1920s he married a woman nearly 50 years his junior, and they had a daughter, Irene, in 1930, when Mose was 83 and his wife was 34.

Irene Triplett, now 85 years old and the last child of any Civil War veteran still on the VA benefits rolls, lives today in a nursing home in Wilkesboro, N.C. She collects $73.13 each month through the pension her father earned for her in 1865.

(Thanks, Tom.)


Ordered to blockade Martinique in 1803, Commodore Sir Samuel Hood covered an island with guns and declared it a sloop-of-war. Perched 175 meters above the sea, the guns denied all entrance to Fort-de-France, the island’s main port, for 17 months.

The British Royal Navy still regards “HMS Diamond Rock” as being in commission — when passing the island, personnel on Royal Navy ships stand at attention and salute the rock.

Since that time, a naval establishment on land has been referred to as a “stone frigate.”

Other Business

In 1985, as the U.S. Senate was considering whether to declare the rose America’s national flower, Sen. Howell Heflin (D-Ala.) read out a seven-verse poem in support of the measure:

Marigolds and dogwood,
Camellias and more,
All flowers are beautiful
And made to adore.

But today there are deficits,
And farm bills and trade,
Aren’t these the subjects
On which decisions should be made?

Still, if on a nation’s flower
A few moments we spend,
We might be refreshed and
Come down to Earth again.

Besides, to select a flower
As America’s might not be bad,
Because I sure don’t want
To make the garden clubs mad.

But all flowers are delicate.
Each can refresh and amuse,
And that is the reason
I feel no flower should lose.

Still the rose is universal,
Its support has a strong voice,
So there should be no question
That the rose is the choice.

So let us raise our voice and
Proclaim with all our power
That the rose is more than beautiful —
It is “America’s Flower.”

Sen. Bennett Johnston (D-La.), who sponsored the joint resolution, replied in kind:

Roses are red,
Violets are blue,
Heflin should be
A co-sponsor of this bill too.

Ronald Reagan signed the measure into law the following year.

(Thanks, Sam.)

Rise and Shine

In 1919 John D. Humphrey patented an alarm clock designed “to impart a blow to an individual.”

There’s no bell. At the appointed hour, the clock drops a rubber ball onto your face to awaken you “without unnecessary shock.”

Humphrey intended it chiefly for the deaf. He described it as “simple in construction and positive and certain in action.”


“To the memory of Miss Emily Kay, cousin to Miss Ellen Gee, of Kew, who died lately at Ewell, and was buried in Essex.”

Sad nymphs of U L, U have much to cry for,
Sweet M L E K U never more shall C!
O S X maids! come hither and D 0,
With tearful I, this M T L E G.

Without X S she did X L alway,
Ah me! it truly vexes 1 2 C
How soon so D R a creature may D K,
And only leave behind X U V E!

Whate’er 1 0 to do she did discharge,
So that an N M E it might N D R:
Then why an S A write? — then why N
Or with my briny tears B D U her B R?

When her Piano-40 she did press,
Such heavenly sounds did M N 8, that she
Knowing her Q, soon 1 U 2 confess
Her X L N C in an X T C.

Her hair was soft as silk, not Y R E,
It gave no Q, nor yet 2 P to view:
She was not handsome; shall I tell U Y?
U R 2 know her I was all S Q.

L 8 she was, and prattling like a J;
How little, M L E! did you 4 C,
The grave should soon M U R U, cold as clay,
And you shall cease to be an N T T!

While taking T at Q with L N G,
The M T grate she rose to put a :
Her clothes caught fire — no 1 again shall see
Poor M L E, who now is dead as Solon.

O L N G! in vain you set at 0
G R and reproach for suffering her 2 B
Thus sacrificed; to J L U should be brought,
Or burnt U 0 2 B in F E G.

Sweet M L E K into S X they bore,
Taking good care the monument 2 Y 10,
And as her tomb was much 2 low B 4,
They lately brought fresh bricks the walls to 10.

— Horace Smith, in A Budget of Humorous Poetry, 1866

(This is a bit more recondite than the Ellen Gee poem. “D 0” is decipher, “1 0 to” is one ought to, N is enlarge, 10 is heighten, and “X U V E,” I am pleased to understand, is exuviae, “an animal’s cast or sloughed skin.” Let’s hope it stopped here.)