Braess’ Paradox

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.

March 8, 2016March 7, 2016 | Science & Math

Even-Handed

GIROLAMO SAVONAROLA alternates vowels and consonants.

(Thanks, Joseph.)

March 7, 2016March 6, 2016 | Language

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.

See full show notes …

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.)

March 6, 2016March 5, 2016 | History

Unsinkable

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.”

March 5, 2016March 4, 2016 | Oddities

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.)

March 4, 2016 | Poems

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.”

March 4, 2016March 3, 2016 | Technology

“Elegy”

“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.)

March 3, 2016March 16, 2016 | Language · Poems

Mass Transit

A city has 10 bus routes. Is it possible to arrange the routes and bus stops so that if one route is closed it’s still possible to get from any one stop to any other (possibly changing buses along the way), but if any two routes are closed, there will be at least two stops that become inaccessible to one another?

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Yes. Think of 10 straight lines in the plane, no two of which are parallel and no three of which meet at the same point. Let the lines be the bus routes and the points of intersection be the stops. At the start we can get from any one stop to any other, either directly (if they’re on the same line) or with just one change. If we remove one line, it’s still possible to get from any stop to any other with at most one change. But if we discard two lines, then one stop — the one at their intersection — will have no bus routes passing through it and thus become inaccessible to all the other stops. (From A.M. Yaglom and I.M. Yaglom, Challenging Mathematical Problems With Elementary Solutions, 1964.) 03/04/2016 UPDATE: If multiple transfers are permitted, a simpler solution is to make a ring of the stops, with each successive pair connected by a route. Remove any one route and the graph remains connected, but remove any two it disconnects: I think this may be a matter of translation. The Yagloms say that one makes a bus journey “possibly changing along the way.” Their own solution requires only one transfer. Thanks to everyone who wrote in about this, and thanks to Herschel for the diagram.

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