“Caput Ei Abscidite!”


Clive Harcourt Carruthers’ 1964 book Alicia in Terra Mirabili begins at once, without a preface:

Aliciam iam incipiebat plurimum taedere iuxta sororem suam in ripa sedere nec quidquam habere quod faceret.

Semel et saepius in librum oculos coniecerat quem soror legebat: sed ei inerant nec tabulae nec sermones. ‘Quid adiuvat liber,’ secum reputabat Alicia, ‘in quo sunt nullae tabulae aut sermones?’

Itaque cogitabat (nempe ut lucidissime poterat, nam tempestate calida torpebat semisomna) num operae pretium esset surgere et flosculos carpere, modo ut sertum nectendo se delectaret, cum subito Cuniculus Albus oculis rubeis prope eam praeteriit.

Only a brief “Glossarium” at the end might give a clue to its origin:

aureorum decoctio malorum: orange marmalade
Baro Cordium: Knave of Hearts
Feles Cestriana: Cheshire Cat
lusio pilae et mallei: croquet
thea: tea

Hoist, Petard


The U.S. Navy submarine USS Tang was sunk by her own torpedo. Patrolling off China in October 1944, she fired at a Japanese transport and the electric torpedo, its rudder jammed, curved to the left in a great circle. The submarine put on emergency power to escape the circle, but it had only seconds to do so. Captain Richard O’Kane later said, “The problem was akin to moving a ship longer than a football field and proceeding at harbor speed clear of a suddenly careening speedboat.”

It struck her abreast the aft torpedo room and she went down in 180 feet of water. Seventy-eight men were lost, and the nine who survived were picked up by a Japanese frigate and taken prisoner. Until the accident the Tang had had the most successful submarine patrol in the war.

War and Peace


On the morning of the World War I armistice, Nov. 11, 1918, American fighter ace Eddie Rickenbacker took off against orders and made his way to the front. He arrived at Verdun at 10:45 and flew out over the no-man’s-land between the armies. Less than 500 feet off the ground, “I could see both Germans and Americans crouching in their trenches, peering over with every intention of killing any man who revealed himself on the other side.”

I glanced at my watch. One minute to 11:00, thirty seconds, fifteen. And then it was 11:00 a.m. the eleventh hour of the eleventh day of the eleventh month. I was the only audience for the greatest show ever presented. On both sides of no-man’s land, the trenches erupted. Brown-uniformed men poured out of the American trenches, gray-green uniforms out of the German. From my observer’s seat overhead, I watched them throw their helmets in the air, discard their guns, wave their hands. Then all up and down the front, the two groups of men began edging toward each other across no-man’s-land. Seconds before they had been willing to shoot each other; now they came forward. Hesitantly at first, then more quickly, each group approached the other.

Suddenly gray uniforms mixed with brown. I could see them hugging each other, dancing, jumping. Americans were passing out cigarettes and chocolate. I flew up to the French sector. There it was even more incredible. After four years of slaughter and hatred, they were not only hugging each other but kissing each other on both cheeks as well.

Star shells, rockets and flares began to go up, and I turned my ship toward the field. The war was over.

(From his autobiography.)

Sign Play

Like any language, sign language partakes in jokes, puns, and wordplay. Dorothy Miles’ poem “Unsound Views” observes that hearing people seem to be slaves to their telephones. In English, there’s no obvious pun in the next-to-last line, “They live to serve their telephone God.” But in British Sign Language it runs


“Here, the aerial on the telephone handset is signed with the ‘G’ handshape that refers to long, thin objects,” explains Rachel Sutton-Spence in Analysing Sign Language Poetry. “The BSL sign GOD is also made using a ‘G’ handshape, albeit in a different location, but when the aerial is moved up to the location where GOD is normally articulated, the pun elevates the telephone to the status of a god.”

One more: In Miles’ poem “Exaltation,” a stand of trees seems to part the sky “And let the peace of heaven shine softly through.” In the American Sign Language version, this can be glossed as ALLOW PEACE OF HEAVEN LIGHT-SHINES LIGHT/HAND-TOUCHES-HEAD. The form of the sign LIGHT is made with a fully open ‘5’ handshape, but in this context the handshape can be seen simply as a hand. “If LIGHT-TOUCHES-HEAD is interpreted as HAND-TOUCHES-HEAD, the obvious question is ‘Whose hand?’ and the obvious answer is ‘God’s.’ In many cultures, placing hands gently upon a person’s head is taken as a blessing.”



“As centuries pass by, the mass of works grows endlessly, and one can foresee a time when it will be almost as difficult to educate oneself in a library, as in the universe, and almost as fast to seek a truth subsisting in nature, as lost among an immense number of books.” — Diderot

A Cognitive Illusion

Image: Flickr

Given these premises, what can you infer?

  1. If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
  2. There is a king in the hand.

Practically everyone draws the conclusion “There is an ace in the hand.” But this is wrong: We’ve been told that one of the conditional assertions in the first premise is false, so it may be false that “If there is a king in the hand, then there is an ace.”

But almost no one sees this. Princeton psychologist Philip Johnson-Laird writes, “[Fabien] Savary and I, together with various colleagues, have observed it experimentally; we have observed it anecdotally — only one person among the many distinguished cognitive scientists to whom we have given the problem got the right answer; and we have observed it in public lectures — several hundred individuals from Stockholm to Seattle have drawn it, and no one has ever offered any other conclusion.” Johnson-Laird himself thought he’d made a programming error when he first discovered the illusion in 1995.

Why it happens is unclear; in puzzling out problems like this, we seem to focus on what’s true and neglect what might be false. Computers are much better at this than we are, which ironically might lead a competent computer to fail the Turing test. In order to pass as human, writes researcher Selmer Bringsjord, “the machine must be smart enough to appear dull.”

(Philip N. Johnson-Laird, “An End to the Controversy? A Reply to Rips,” Minds and Machines 7 [1997], 425-432.)

10/18/2016 UPDATE: Readers Andrew Patrick Turner and Jacob Bandes-Storch point out that if we take the first premise to mean material implication (and also allow double negation elimination), then not only can we not infer that there must be an ace, but we can in fact infer that there cannot be an ace in the hand — exactly the opposite of the conclusion that most people draw! Jacob offers this explanation (XOR means “or, but not both”, and ¬ means “not”):

I’ll use the shorthand “HasKing” to be a logical variable indicating whether there is a king in the hand.
Similarly, “HasAce” is a variable which indicates whether there is an ace in the hand.

We’re given two statements:

#1: (HasKing → HasAce) XOR ((¬HasKing) → HasAce).

#2: HasKing.

#2 has just told us that our “HasKing” variable has the value “true”.

So, we can fill this in to #1, which becomes “(true → HasAce) XOR (false → HasAce)”.

I’ll call the sub-clauses of #1 “1a” & “1b”, so #1 is “1a XOR 1b”.

1a: “(true → HasAce)” is a logical expression that’s equivalent to just “HasAce”.

1b: “(false → HasAce)” is always true — because the antecedent, “false”, can never be satisfied, the consequent is effectively disregarded.

Recall what statement #1 told us: (1a XOR 1b). We now know 1b is true, so 1a must be false. Thus “HasAce” is false: there is not an ace in the hand.

Jacob also offered this demonstration in Prolog. Many thanks for Andrew and Jacob for the patience in explaining this to me.

Black and White

dawson half-move chess puzzle

One more chess curiosity by T.R. Dawson: How can White mate in two half moves?

The answer is to play the first half of Bg1-f2, and the second half of Bf1-g2, thus getting the white bishop from g1 to g2 and giving mate.

A fair-minded reader might ask why Black can’t pull the same trick, transferring his bishop from b8 to b7 to block the check. The answer, Dawson argues, is that some of the constituent moves are illegal: Black can’t combine Bb8-c7 and Bc8-b7 because a bishop on c8 would put the white king in an unreal check on h3; and he can’t combine Bb8-a7 and Ba8-b7 because a8 is occupied.

From Caissa’s Fairy Tales (1947).



A memory of Lewis Carroll by Lionel A. Tollemache:

He was, indeed, addicted to mathematical and sometimes to ethical paradoxes. The following specimen was propounded by him in my presence. Suppose that I toss up a coin on the condition that, if I throw heads once, I am to receive 1d.; if twice in succession, 2d.; if thrice, 4d.; and so on, doubling for each successful toss: what is the value of my prospects? The amazing reply is that it amounts to infinity; for, as the profit attached to each successful toss increases in exact proportion as the chance of success diminishes, the value (so to say) of each toss will be identical, being in fact, 1/2d.; so that the value of an infinite number of tosses is an infinite number of half-pence. Yet, in fact, would any one give me sixpence for my prospect? This, concluded Dodgson, shows how far our conduct is from being determined by logic.

Actually this curiosity was first noted by Nicholas Bernoulli; Carroll would have met it in his studies of probability. Tollemache wrote, “The only comment that I will offer on his astounding paradox is that, in order to bring out his result, we must suppose a somewhat monotonous eternity to be consumed in the tossing process.”

(Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898.)

Podcast Episode 120: The Barnes Mystery


In 1879 a ghastly crime gripped England: A London maid had dismembered her employer and then assumed her identity for two weeks, wearing her clothes and jewelry and selling her belongings. In this week’s episode of the Futility Closet podcast we’ll describe the murder of Julia Thomas and its surprising modern postscript.

We’ll also discover the unlikely origins of a Mary Poppins character and puzzle over a penguin in a canoe.


Early airplanes were sometimes attacked by confused eagles.

Alberta, Canada, has been rat-free for 50 years.

Sources for our feature on the murder of Julia Thomas:

Elliott O’Donnell, ed., Trial of Kate Webster, 1925.

Transcript of Kate Webster’s trial at the Old Bailey.

“The Richmond Murder,” Glasgow Herald, May 29, 1879.

“Kate Webster Hanged,” Reading [Pa.] Eagle, July 31, 1879.

Matt Blake, “Attenborough Skull Mystery Finally Solved,” Independent, July 5, 2011.

Cigdem Iltan, “The Skull in the Backyard,” Maclean’s 124:28 (July 25, 2011), 37.

Image: Wikimedia Commons

Park Road, Richmond, today. At left is the site of the former Mayfield Cottages, where the murder took place. At center is the home of naturalist Sir David Attenborough. At right is the site of the former Hole in the Wall pub. Thomas’ skull was discovered in 2010 at the site of the pub’s stables.

Listener mail:

GitHub, “System Bus Radio” (retrieved Sept. 2, 2016).

Catalin Cimpanu, “Emitting Radio Waves from a Computer with No Radio-Transmitting Hardware,” Softpedia, March 2, 2016.

A 40-second rendition of the discarded Mary Poppins song “Admiral Boom.”

Wikipedia, Mary Poppins (film)” (retrieved Sept. 2, 2016).

This week’s lateral thinking puzzles were contributed by listeners Matt Sargent and Jacob Bandes-Storch.

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!