# The Tipping Point

English meteorologist Lewis Fry Richardson (1881-1953) spent the last 25 years of his life trying to establish a mathematical theory of the causes of war. In the first of two books on this subject, Arms and Insecurity, he works out a model of arms races using differential equations and reaches the conclusion that

$\frac{d\left ( U + V \right )}{dt}=\left ( k - \alpha \right )\left \{ U + V - \left [ U_{0} + V_{0} - \frac{g + h}{k - \alpha } \right ] \right \}$

where:

U and V are the annual defense budgets of two parties to a conflict

k is a positive constant representing the response to threat

α is a positive constant representing the fatigue and expense of keeping up defenses

U0 and V0 represent cooperations between the parties, tentatively assumed to remain constant

and g and h represent the “grievances and ambitions, provisionally regarded as constant,” on each side.

The term in brackets is a constant, so Richardson predicted that plotting d(U + V)/dt against (U + V) would produce a straight line. He tried this out using the defense budgets of the Franco-Russian and Austro-German alliances for 1909-14 and got this:

“The four points lie close to a straight line, closer, indeed, than one might expect,” he writes. “Since I first drew this diagram, which was shown at the British Association in Cambridge in 1938, and printed in Nature of 29 October of that year, I have been incredulous about the marvelously good fit. Yet there is no simple mistake. … The mere regularity of these phenomena shows that foreign politics had then a rather machine-like quality, intermediate between the predictability of the moon and the freedom of an unmarried young man.”

The extrapolated straight line hits the x axis at U + V = £194 pounds sterling. “As love covereth a multitude of sins, so the good will between the opposing alliances would just have covered £194 million of defense expenditures on the part of the four nations concerned. Their actual expenditure in 1909 was £199 millions; and so began an arms race which led to World War I.”

(Lewis F. Richardson, Arms and Insecurity, 1949.)

# Presence of Mind

Science teacher Lawrence Beesley was reading a book in his cabin on the Titanic when the engines stopped. Wandering the ship, he heard that an iceberg had passed by but found nothing amiss. But as he was returning to his cabin he noticed something unusual:

As I passed to the door to go down, I looked forward again and saw to my surprise an undoubted tilt downwards from the stern to the bows: only a slight slope, which I don’t think any one had noticed, — at any rate, they had not remarked on it. As I went downstairs a confirmation of this tilting forward came in something unusual about the stairs, a curious sense of something out of balance and of not being able to put one’s feet down in the right place: naturally, being tilted forward, the stairs would slope downwards at an angle and tend to throw one forward. I could not see any visible slope of the stairway: it was perceptible only by the sense of balance at this time.

When the crew began to summon passengers, he returned to A Deck and was accepted on a lifeboat.

(From his 1912 book The Loss of the S.S. Titanic.)

# Ground Rules

Articles of the pirate ship Revenge, captain John Phillips, 1723:

1. Every man shall obey a civil command. The captain shall have one share and a half of all prizes. The master, carpenter, boatswain and gunner shall have one share and [a] quarter.
2. If any man shall offer to run away or keep any secret from the company, he shall be marooned with one bottle of powder, one bottle of water, one small arm and shot.
3. If any man shall steal anything in the company or game to the value of a piece-of-eight, he shall be marooned or shot.
4. If at any time we should meet another marooner [pirate], that man that shall sign his articles without the consent of our company shall suffer such punishment as the captain and company shall think fit.
5. That man that shall strike another whilst these articles are in force shall receive Moses’s Law (that is, forty stripes lacking one) on the bare back.
6. That man that shall snap his arms or smoke tobacco in the hold without a cap on his pipe, or carry a candle lighted without a lantern, shall suffer the same punishment as in the former article.
7. That man that shall not keep his arms clean, fit for an engagement, or neglect his business, shall be cut off from his share and suffer such other punishment as the captain and the company shall think fit.
8. If any man shall lose a joint in time of an engagement, he shall have 400 pieces-of-eight. If a limb, 800.
9. If at any time we meet with a prudent woman, that man that offers to meddle with her without her consent, shall suffer present death.

That’s from Charles Johnson’s General History of the Pyrates, 1724. It’s one of only four surviving sets of articles from the golden age of piracy.

Phillips lasted less than eight months as a pirate captain but captured 34 ships in the West Indies.

# Podcast Episode 111: Japanese Fire Balloons

Toward the end of World War II, Japan launched a strange new attack on the United States: thousands of paper balloons that would sail 5,000 miles to drop bombs on the American mainland. In this week’s episode of the Futility Closet podcast, we’ll tell the curious story of the Japanese fire balloons, the world’s first intercontinental weapon.

We’ll also discuss how to tell time by cannon and puzzle over how to find a lost tortoise.

Sources for our feature on Japanese fire balloons:

Ross Coen, Fu-Go, 2014.

James M. Powles, “Silent Destruction: Japanese Balloon Bombs,” World War II 17:6 (February 2003), 64.

Edwin L. Pierce and R C. Mikesh, “Japan’s Balloon Bombers,” Naval History 6:1 (Spring 1992), 53.

Lisa Murphy, “One Small Moment,” American History 30:2 (June 1995), 66.

Larry Tanglen, “Terror Floated Over Montana: Japanese World War II Balloon Bombs, 1944-1945,” Montana: The Magazine of Western History 52:4 (Winter 2002), 76-79.

Henry Stevenson, “Balloon Bombs: Japan to North America,” B.C. Historical News 28:3 (Summer 1995), 22-23.

Associated Press, “Japanese Balloon Bombs Launched in Homeland,” May 30, 1945.

Associated Press, “Japanese Launch Balloon Bombs Against United States From Their Home Islands,” May 30, 1945.

Associated Press, “Balloon Bombs Fall One by One for Miles Over West Coast Area,” May 30, 1945.

Russell Brines, “Japs Gave Up Balloon Bomb System After Launching 9,000 of Them,” Associated Press, Oct. 2, 1945.

“Enemy Balloons Are Still Found,” Spokane Daily Chronicle, Feb. 5, 1946.

Hal Schindler, “Utah Was Spared Damage By Japan’s Floating Weapons,” Salt Lake Tribune, May 5, 1995.

Here’s a U.S. Navy training film describing the balloons — thanks to listener Brett Bonner for sending this in:

Listener mail:

Wikipedia, “Time Ball” (accessed June 16, 2016).

Wikipedia, “Nelson Monument, Edinburgh” (accessed June 16, 2016).

“One O’Clock Gun,” Edinburgh Castle, Historic Environment Scotland.

“Places to Visit in Scotland – One O’Clock Gun, Edinburgh Castle,” Rampant Scotland.

“Tributes to Castle’s Tam the Gun,” BBC News, Nov. 17, 2005.

Sofiane Kennouche, “Edinburgh Castle: A Short History of the One O’Clock Gun,” Scotsman, Jan. 27, 2016.

Here’s a time gun map of Edinburgh from 1861:

“For every additional circle of distance from the Castle, subtract one second from the instant of the report of the ‘Time-Gun’ to give the exact moment of 1 o’clock.” Additional details are here.

“The Smallest Artillerist,” San Francisco Call, June 20, 1895.

This week’s lateral thinking puzzle was devised by Sharon Ross. Here are two 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 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 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 podcast@futilitycloset.com. Thanks for listening!

# Talking

Excerpt of a letter from British general Philip Howele to his wife, Sept. 15, 1915:

It is VILE that all my time should be devoted to killing Germans whom I don’t in the least want to kill. If all Germany could be united in one man and he and I could be shut up together just to talk things out, we could settle the war, I feel, in less than one hour. The ideal war would include long and frequent armistices during which both sides could walk across the trenches and discuss their respective points of view. We are really only fighting just because we are all so ignorant and stupid. And if diplomats were really clever such a thing as war could never be. Shall I desert and see if any of them will listen on the other side? My little German officer was rather flabbergasted when the first question I asked him the other morning, when the escort had gone out and shut the door, and after I’d put him in a comfortable chair and given him a cigarette, was, ‘Now first of all do you really hate me, and if so why?’ He said he didn’t. But then later, when I asked him what we could possibly do to stop all this nonsense, he had no suggestions to make. ‘I have my ideas’ he said but somehow couldn’t express them.

Goodnight … and bless you.

P.

# Progress

What Did George the Third Know?

He never saw a match.
He never saw a bicycle.
He never saw an oil stove.
He never saw a steamboat.
He never saw a gas engine.
He never saw a type-writer.
He never saw a phonograph.
He never saw a steel plough.
He never took laughing gas.
He never rode on a tram car.
He never saw a fountain pen.
He never saw a railway train.
He never knew of Evolution.
He never saw a postage stamp.
He never saw a pneumatic tube.
He never saw an electric railway.
He never saw a reaping machine.
He never saw a set of artificial teeth.
He never saw a telegraph instrument.
He never heard the roar of a Krupp gun.
He never saw a threshing machine, but used a flail.
He never saw a pretty girl work on a sewing machine.
He never saw a percussion cap, nor a repeating rifle.
His grandmother did his mending with a darning needle.
He never listened to Edison’s mocking machine or phonograph.
When he went to a hotel he walked upstairs, for they had no lifts.
He never saw a steel pen, but did all his writing with a quill.
He never held his ear to a telephone, or talked to his wife a hundred miles away.
He never saw a fire engine, but when he went to a fire, he stood in line and passed buckets.
He never knew the pleasure and profit to be derived from reading Science Siftings.

Science Siftings, 1894

# Misc

• Consecutive U.S. presidents Grant, Hayes, and Garfield were all born in Ohio and served as Civil War generals.
• Travel due south from Buffalo and you’ll reach the Pacific Ocean.
• Oliver Wendell Holmes Jr. shook hands with both John Quincy Adams and John F. Kennedy.
• This false statement is not self-referential.
• “When you have no basis for an argument, abuse the plaintiff.” — Cicero

In the 2004 film Shark Tale, the shark Lenny coughs up several items onto a table. Among them is a Louisiana license plate, number 007 0 981. The same plate is retrieved from sharks in both Jaws and Deep Blue Sea.

# Unquote

‘As to moral courage, I have very rarely met with the two o’clock in the morning courage. I mean, unprepared courage, that which is necessary on an unexpected occasion, and which, in spite of the most unforeseen events, leaves full freedom of judgment and decision.’

— Napoleon, to Emmanuel, comte de Las Cases, Journal of the Private Life and Conversations of the Emperor Napoleon at Saint Helena, 1824

# Last Words

Note found in the pocketbook of an English corporal killed during the battle of the Somme:

Dear Mother

I am writing these few lines severely wounded. We have done well our Batt. advanced about 3 quarters of a mile. I am laid in a shell hole with 2 wounds in my hip and through my back. I cannot move or crawl. I have been here for 24 hours and never seen a living soul. I hope you will receive these few lines as I don’t expect anyone will come to take me away, but you know I have done my duty out here now for 1 year and 8 months and you will always have the consolation that I died quite happy doing my duty.

Must give my best of love to all the cousins who [have] been so kind to me since I have been out here and the Best of love to Arthur and Harry and all at Swinefleet. xxx

He was identified as John Duesbery of Bradford, and the note and his other belongings were sent home to his family. In The Quick and the Dead, Richard van Emden writes, “His grave would have been marked in a rudimentary way, perhaps with a piece of wood or an upturned rifle, but whatever was placed there it was subsequently destroyed and John’s body lost.”

# No Waiting

In 1892 … a law firm in the American West came up with the idea of a divorce papers vending machine. For a while, at least, legal divorce papers were items that could be bought from a vending machine in Corinne, Utah. A purchaser could insert \$2.50 in coins, pull a lever on the side of the machine, and pick up his papers from a delivery drawer that popped open like a cash register drawer. Those papers were then taken to the local law firm — whose name was printed on the form — where the names of the divorcing couple were written in and witnessed.

— Kerry Segrave, Vending Machines: An American Social History, 2002