Canadian prime minister Mackenzie King took peculiar note of the relative position of clock hands. This began as early as 1918, when his diary shows that he began to notice moments when the hands overlapped (as at 12:00) or formed a straight line (as at 6:00). By the 1940s the diary sometimes refers to clock hands several times a day. On Aug. 25, 1943, when Franklin Roosevelt was visiting Ottawa, King wrote a whole “Memo re hands of clock”:

  • “Exactly 10 past 8 when I looked at clock on waking — straight line.”
  • “12 noon when noon day gun fired & I read my welcome to President — together.”
  • “25 to 8 when I was handed in my room a letter from Churchill re supply of whiskey to troops … — both together.”

A year later, Nov. 2, 1944: “As I look at the clock from where I am standing as I dictate this sentence, the hands are both together at 5 to 11.”

Biographer Robert Macgregor Dawson writes, “What significance he attached to the occurrences is difficult to determine; there is no key to his interpretation.” But one clue comes later in 1944, when King records a conversation with Violet Markham: “As I … went to take the watch out of my pocket, to show her how the face had been broken, I looked at it and the two hands were exactly at 10 to 10. I mentioned it to her as an illustration of my belief that some presence was making itself known to me. That I was on the right line, and that the thought was a true one which I was expressing.” But the two had been discussing the death of King’s dog, so the meaning is still very obscure.

(From C.P. Stacey, A Very Double Life, 1976.)

Organic Chemistry

findig benzene

In a joke issue of the Berichte der Deutschen Chemischen Gesellschaft in 1886, F.W. Findig offered an article on the constitution of benzene in which he finds that “zoology is capable of rendering the greatest service in clearing up the behavior of the carbon atom”:

Just as the carbon atom has 4 affinities, so the members of the family of four-handed animals possess four hands, with which they seize other objects and cling to them. If we now think of a group of six members of this family, e.g. Macacus cynocephalus, forming a ring by offering each other alternately one and two hands, we reach a complete analogy with Kekulé’s benzene-hexagon (Fig. 1).

Now, however, the aforesaid Macacus cynocephalus, besides its own four hands, possesses also a fifth gripping organ in the shape of a caudal appendix. By taking this into account, it becomes possible to link the 6 individuals of the ring together in another manner. In this way, one arrives at the following representation: (Fig. 2).

“It appears to me highly probable that a complete analogy exists between Macacus cynocephalus and the carbon atom,” Findig wrote. “In this case, each C-atom also possesses a caudal appendix, which, however, cannot be included among the normal affinities, although it takes part in the linking. Immediately this appendix, which I call the ‘caudal residual affinity’, comes into play, a second form of Kekulé’s hexagon is produced; this, being obviously different from the first, must behave differently.”

(From John Read, Humour and Humanism in Chemistry, 1947.)

Cyclic Billiards


A puzzle from Colin White’s Projectile Dynamics in Sport (2010): Suppose a billiard table has a length twice its width and that a rolling ball loses no energy to bounces or friction but simply caroms around the table forever. Call the angle between the launch direction and the long side of the table α. At what angle(s) should the ball be hit so that it will arrive back at the same point on the table and traveling in the same direction, so that its motion is cyclic, following the same path repeatedly?

Click for Answer



In the U.S. presidential election of 1884, Republican James G. Blaine was accused of having sold his influence in Congress and of manipulating stocks. Democrat Grover Cleveland had fathered a child out of wedlock and had paid a substitute $150 to take his place in the Civil War. One journalist wrote:

Mr. Blaine has been delinquent in office but blameless in private life, while Mr. Cleveland has been a model of official integrity but culpable in his personal relations. We should therefore elect Mr. Cleveland to the public office which he is so qualified to fill and remand Mr. Blaine to the private station which he is so admirably fitted to adorn.

The people agreed, narrowly electing Cleveland and breaking a six-election losing streak for the Democrats.

Parallelogram Puzzle

parallelogram puzzle

Point E lies on segment AB, and point C lies on segment FG. The area of parallelogram ABCD is 20 square units. What’s the area of parallelogram EFGD?

Click for Answer



“A Kiss and Its Consequences,” English carte de visite, 1910.

In 1965, Caltech computer scientist Donald Knuth privately circulated a theorem that, “under special circumstances, 1 + 1 = 3”:

Proof. Consider the appearance of John Martin Knuth, who exhibits 
the following characteristics:

Weight      8 lb. 10 oz.      (3912.23419125 grams)         (3)
Height      21.5 inches          (0.5461 meters)            (4)
Voice          loud               (60 decibels)             (5)
Hair         dark brown       (Munsell 5.0Y2.0/11.8)        (6)


He conjectured that the stronger result 1 + 1 = 4 might also be true, and that further research on the problem was contemplated. “I wish to thank my wife Jill, who worked continuously on this project for nine months. We also thank Dr. James Caillouette, who helped to deliver the final result.”

(From Donald E. Knuth, Selected Papers on Fun & Games, 2011.)



A Scrabble player needs a way to recognize the potential in any collection of tiles. If your rack contains the seven letters AIMNSTU, for example, what eighth letter should you be watching for to create an acceptable eight-letter word?

If you arrange your seven letters into the word TSUNAMI, and if you’ve memorized the corresponding phrase COASTAL HARM, then you have your answer: Any of the letters in that phrase will produce an acceptable eight-letter word:


TSUNAMI: COASTAL HARM is an example of an anamonic (“anagram mnemonic”), a tool that tournament players use to memorize valuable letter combinations. Devising useful anamonics is itself an art form in the Scrabble community — one has to create a memorable phrase using a constrained set of letters. Some are memorable indeed:


“One of the first anamonics I ever read, back in 1998, was PRIEST: EVERYONE COMPLAINED OF THE SODOMY,” wrote Jeff Myers in Word Ways in May 2007. “I couldn’t believe it. The letters in that phrase — no more and no less — could combine with PRIEST to make 7-letter words.”

When the word list TWL06 appeared, PERITUS became a legal word. That’s PRIEST + U, so the mnemonic phrase now needed to include a U. “One simple fix is: EVERYONE COMPLAINED OF YOUTH SODOMY,” wrote Myers. “Now maybe even more startling.”

John Chew maintains canonical lists of anamonics using the official Tournament Word List and the alternate SOWPODS list.

Podcast Episode 116: Notes and Queries


In this week’s episode of the Futility Closet podcast we’ll explore some curiosities and unanswered questions from Greg’s research, including the love affair that inspired the Rolls Royce hood ornament, a long-distance dancer, Otto von Bismarck’s dogs, and a craftily plotted Spanish prison break.

We’ll also run after James Earl Ray and puzzle over an unsociable jockey.


Workers constructing Washington’s Grand Coulee Dam in 1942 fed a cable through a 500-foot drain by tying a string to an alley cat’s tail.

A 2001 earthquake in Olympia, Wash., drew a graceful rose with a sand-tracing pendulum.

Sources for this week’s feature:

The best source I can find regarding the origins of the Rolls Royce hood ornament is this Telegraph article from 2008, in which Montagu’s son says, “My father and Eleanor shared a great passion. It was a grand love affair – perhaps even the love of his life. All this happened before my father met my mother. But I understand my father’s first wife knew about the mistress. She was very tolerant of her and they got on very well.” But this quote is given in the service of promoting a film about the affair, which makes it less objective than I’d like. (Paul Tritton of the Rolls-Royce Owners’ Club of Australia disputes the story here.)

Alexandre Dumas’ habit of eating an apple every morning beneath the Arc de Triomphe is described in this New York Times article, among many other modern sources. The earliest mention I can find is a 1911 article in the Dietetic and Hygienic Gazette, attributing the intervention to Hungarian physician David Gruby. I’ve confirmed that Gruby served as a physician to Dumas (père et fils), but I can’t find anything about an apple.

The incidents of the Savoy Hotel cloakroom and the Travellers Club suicide are both described in N.T.P. Murphy’s A Wodehouse Handbook (2013). The suicide rule is mentioned at the end of this Telegraph article, which gives me hope that it’s true, but I can’t find anything more comprehensive.

The story of the Providence United Methodist Church is told in both Randy Cerveny’s Freaks of the Storm (2005) and Rick Schwartz’s Hurricanes and the Middle Atlantic States (2007). Snopes says it’s “mostly true.”

In Constable’s Clouds, published by the National Galleries of Scotland 2000, Edward Morris writes, “It is this moment of early morning light — and what has been described as ‘the atmosphere of stillness tinged with expectancy’ — that Constable translates into the finished canvas.”

Judith Collins mentions Joseph Beuys’ responsibility for snow in her introduction to Andy Goldsworthy’s Midsummer Snowballs (2001).


Reader Olga Izakson found the description of Tiras, Otto von Bismarck’s “dog of the empire,” in Robert K. Massie’s Dreadnought (1991). A few further links.

The role of Esperanto in the planning of the 1938 San Cristobál prison break is described (I think) here.

In 1600 William Kemp published a pamphlet chronicling his 1599 morris dance to Norwich, Kemps Nine Daies Wonder, to quiet doubters.

The allegation that Margaret Thatcher ordered the identities of British government employees to be encoded in the word spacing of their documents appears in Gregory Kipper’s Investigator’s Guide to Steganography (2003). I’ve found it in other technical documents, but these tend to cite one another rather than an authoritative source.

Listener mail:

Madison Kahn, “60 Hours of Hell: The Story of the Barkley Marathons,” Outside, May 8, 2013.

Wikipedia, “Barkley Marathons” (accessed Aug. 6, 2016).

Wikipedia, “Kaihogyo,” (accessed Aug. 6, 2016).

Adharanand Finn, “What I Learned When I Met the Monk Who Ran 1,000 Marathons,” Guardian, March 31, 2015.

Associated Press, “Japanese Monks Endure With a Vow of Patience,” June 10, 2007.

Here’s a corroborating link for this week’s lateral thinking puzzle (warning: spoiler).

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!

More Morals

la rochefoucauld

Maxims of François VI, Duc de La Rochefoucauld (1613–1680):

  • “We commonly slander more thro’ Vanity than Malice.”
  • “We have more Laziness in our Minds than in our Bodies.”
  • “There are few People but what are ashamed of their Amours when the Fit is over.”
  • “We should not judge of a Man’s Merit by his great Qualities, but by the Use he makes of them.”
  • “He who is pleased with Nobody, is much more unhappy than he with whom Nobody is pleased.”
  • “There are some disguised Falsehoods so like Truths, that ‘twould be to judge ill not to be deceived by them.”
  • “Men sometimes think they hate Flattery, but they hate only the Manner of Flattering.”
  • “Acquired Honor is Surety for more.”
  • “Innocence don’t find near so much Protection as Guilt.”
  • “‘Tis our own Vanity that makes the Vanity of others intolerable.”
  • “‘Tis a common Fault to be never satisfied with ones Fortune, nor dissatisfied with ones Understanding.”
  • “Envy is more irreconcilable than Hatred.”
  • “‘Tis better to employ our Understanding, in bearing the Misfortunes that do befall us, than in foreseeing those that may.”
  • “A good Head finds less Trouble in submitting to a wrong Head than in conducting it.”
  • “Folly attends us close thro’ our whole Lives; and if anyone seems wise, ’tis merely because his Follies are proportionate to his Age, and Fortune.”

And “As ’tis the Characteristic of a great Genius to say much in a few Words, small Geniuses have on the contrary the Gift of speaking much and saying nothing.”