In a Word

n. the act of making or becoming progressively more miserable

adj. bringing sorrow, mournful, gloomy

The Road Coloring Problem

Every road in this little town is a one-way street, and each street is colored either red or blue. This has a helpful effect: If you start at any house in town and follow the sequence blue-red-red three times in a row, you’ll always arrive at the yellow house.

If you follow blue-blue-red three times, you’ll always arrive at the green one.

In 1970 Roy Adler and Benjamin Weiss asked whether it’s always possible to create such a coloring in a given network; in 2009 Avraham Trahtman proved that, within certain constraints, it is.

Carry On

Letter to the Times, Feb. 6, 1946:


I have just written you a long letter.

On reading it over, I have thrown it into the waste paper basket.

Hoping this will meet with your approval,

I am, Sir,

Your obedient Servant,

A.D. Wintle

Passing Through

November 1896 saw the start of a strange wave of airship sightings across the United States — the San Francisco Call published the image above on Nov. 19, claiming that the craft had passed over eastern Sacramento the previous night, where hundreds had seen “its brilliant searchlight traveling over the city, and who will also swear that they heard the voices of its occupants and distinguished their merry song and laughter.”

In the frenzy that followed, the San Francisco Chronicle published an interview with attorney George D. Collins, who claimed that he represented the airship’s inventor, a wealthy Maine man who had spent 17 years and $100,000 perfecting the craft. “The reports from Sacramento the other night were quite true. It was my client’s ship that inhabitants saw. It started from Oroville, in Butte County, and flew in a straight line for sixty miles directly over Sacramento. After running up and down once or twice over the capital, my friend came on a distance of another seventy miles and landed on a spot on the Oakland side of the bay, where the ship now lies guarded by six men. In another six days several defects will be done away with and it is then his intention to fly right over San Francisco.”

That never happened, and Collins was quickly forgotten, but it’s interesting to note that 10 years earlier, in 1886, inventor Moses Cole had patented a strikingly similar “new and improved aerial vessel” (below). “It consists of two semi-spheroidal balloons,” Scientific American had reported, “between which are situated the cabins for the passengers and crew, these being fitted with windows and surrounded by a circular balcony.” Possibly the Call’s artist had used Cole’s patent for inspiration. Or possibly Collins was telling the truth. Or possibly Martians had adopted Cole’s design as a disguise. We’ll never know.

See Just Visiting.

The Suicidal King

Imagine a 1000 x 1000 chessboard on which a white king and 499 black rooks are placed at random such that no rook threatens the king. And suppose the king goes bonkers and wants to kill himself. Can he reach a threatened square in a finite number of moves if Black is trying actively to avoid this?

Click for Answer


The last canto of Dante’s Purgatorio contains this perplexing sentence:

And if perchance
My saying, dark as Themis or as Sphinx,
Fail to persuade thee, (since like them it foils
The intellect with blindness) yet ere long
Events shall be the Naiads, that will solve
This knotty riddle, and no damage light
On flock or field.

When did water nymphs solve the riddle of the Sphinx? It turns out that Dante was relying on a flawed medieval edition of Ovid’s Metamorphoses that rendered Laïades (meaning Oedipus, the son of Laius) as Naïades, or naiads. He believed that water nymphs had ridden their sea monsters across the desert to solve the Sphinx’s riddle.

The version of the story that we know, in which Oedipus solves the riddle, comes from Sophocles’ Oedipus, which, being written in Greek, was unavailable to Dante. And he cast his own version in such exquisite language that it’s now immortal — one classic work misquoting another.

(Thanks, Jim.)

Pi Without Circles

The sum of the squares of the reciprocals of the positive integers is π2/6.

The sum of their fourth powers is π4/90.

The sum of their sixth powers is π6/945.

The area of the region under the Gaussian curve y = ex2 is the square root of π.

The probability that two integers chosen at random will have no prime factor in common is 6/π2.

The integer 8 can be written as the sum of two squares of integers, m2 + n2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2). The integer 7 can’t be written at all as the sum of such squares. Over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why?


“Mr. Hoover, if you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you and you have to battle with only one of them.” — Calvin Coolidge, to Herbert Hoover

Podcast Episode 2: Mass Hysteria, Airborne Sheepdogs and Mark Twain’s Brother

As skywatchers prepared for the return of Halley’s comet in 1910, they heard some alarming scientific predictions: Poisonous gases in the comet’s tail might “snuff out all life on the planet,” “leaving the burnt and drenched Earth no other atmosphere than the nitrogen now present in the air.” How should a responsible citizen evaluate a dire prediction by a minority of experts? In this week’s episode of the Futility Closet podcast, we explore the Halley’s hysteria, remember the alarming predictions made for Y2K, and recall a forgotten novella in which Arthur Conan Doyle imagined a dead Earth fumigated by cosmic ether.

We also consider the odd legacy of an Australian prime minister who disappeared in 1967, investigate the role of balloon-borne sheepdogs during the Siege of Paris, learn why Mark Twain’s brother telegraphed the entire Nevada constitution to Washington D.C. in 1864, and offer a chance to win a book in the next Futility Closet Challenge.

Our main feature this week concerns the hysteria that greeted the return of Halley’s comet in 1910, based on ill-founded fears that compounds in the comet’s tail would poison the atmosphere.

This seems to have inspired to Arthur Conan Doyle to write The Poison Belt, a 1913 novella in which “our planet has swum into the poison belt of ether, and is now flying deeper into it at the rate of some millions of miles a minute.” (Thanks to Jason Holt for this tip.)

We mentioned also that Australian prime minister Harold Holt disappeared while in office in 1967 — he’d gone swimming near Portsea in an area known for its strong rip tides and was never seen again.

The Harold Holt Memorial Swimming Centre, in Melbourne, was under construction at the time and was named in his memory — a swimming pool named for a man who probably drowned:

On March 17 we’d noted that the Nevada Territory had sent its entire constitution to Washington D.C. by telegraph in 1864, in order to join the Union before Election Day. The last leaf of the 175-page transcription, below, shows the word count and cost; Jim Russell, Michael Kindell, and Bruce Barnfield all wrote in to note that it also bears the signature of Orion Clemens, who was secretary of the territory — and Mark Twain’s brother.

Here are three references that mention that balloon-borne sheepdogs were used to carry dispatches during the Siege of Paris:

  • Robert Lowry Sibbet’s The Siege of Paris (1892) notes that “the Général Faidherbe sailed on the 13th inst. [1870] and landed a few miles from Bordeaux. M. Hurel took out five bulldogs which, he believes, will return to Paris with dispatches in their collars. The owners of the dogs are to receive two hundred francs for every dispatch they bring back.”
  • Alistair Horne’s The Fall of Paris: The Siege and the Commune 1870-71 (2007) notes that altogether some 65 manned balloons left Paris during the siege, carrying “164 passengers, 381 pigeons, 5 dogs, and nearly 11 tons of official dispatches.”
  • Michael Howard’s The Franco-Prussian War, published last year, confirms that five dogs were sent, but gives no further details.

I’ve just acquired John Fisher’s 1965 book Airlift 1870, a thorough account of the balloon and pigeon post during the siege, which seems to confirm the dog story — I’ll discuss that in an upcoming episode.

This week’s Futility Closet Challenge is inspired by Douglas Adams and John Lloyd’s 1983 book The Meaning of Liff, which they describe as a “dictionary of things that there aren’t any words for yet.” Take any place name and invent a useful new definition for it. Examples from their book:

  • clun: “A leg which has gone to sleep and has to be hauled around after you.”
  • hoggeston: “The action of overshaking a pair of dice in a cup in the mistaken belief that this will affect the eventual outcome in your favour and not irritate everyone else.”
  • moffat: “That part of your coat which is designed to be sat on by the person next to you on the bus.”

We propose that sheboygan should mean “to recognize an actor in a movie but not be able to place him.” A secondary definition is “to mistake the downbeat of a song during an instrumental introduction, leaving you helpless to reorient yourself until the melody starts” (I’m always confused by “All Along the Watchtower”).

Post your own entry below or mail it to by Friday, March 28. Our favorite entry will win a copy of our book, Futility Closet: An Idler’s Miscellany of Compendious Amusements.

Thanks again to Doug Ross for the music in this episode.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at The show notes are on the blog, where you can also enter your submissions in this week’s Challenge. Many thanks to Doug Ross for the music in this episode.

Next week we plan to discuss the sad, enigmatic tale of Lillian Alling, an immigrant who grew disenchanted with New York and decided to walk home to Siberia; explore the curious significance of October 4 to Samuel Taylor Coleridge; and offer a new Futility Closet Challenge. If you have any questions or comments you can reach us at Thanks for listening!

In a Word

n. a hoarder of books

In the rare book collection of the archives at Caltech is a copy of Adrien-Marie Legendre’s 1808 text on number theory. It comes from the collection of Eric Temple Bell, who taught mathematics at Caltech from 1926 to 1953. Inside the book is an inscription in Bell’s handwriting:

This book survived the San Francisco Earthquake and Fire of 18 April, 1906. It was buried with about 600 others, in a vacant lot, before the fire reached the spot. The house next door to the lot fell upon the cache; the tar from the roof baked the 4 feet of dirt, covering the books, to brick, and incinerated all but 4 books, of which this is one. Signed: E. T. Bell. Book buried just below Grace Church, at California and Stockton Streets. House number 729 California Street.

During the Great Fire of London in 1666, Samuel Pepys came upon Sir William Batten burying his wine in a pit in his garden. Pepys “took the opportunity of laying all the papers of my office that I could not otherwise dispose of” and later buried “my Parmazan cheese, as well as my wine and some other things.” I don’t know whether he ever recovered them.