forflitten
adj. severely scolded
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
THEY LIVE RESPECT THAT TELEPHONE
HOLD-HANDSET
THIN-AERIAL-ON-HANDSET AERIAL-MOVES-UP GOD
TELEPHONE-AERIAL
“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.”
Unquote
“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
Given these premises, what can you infer?
- 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.
- 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 their patience in explaining this to me.
Black and White
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).
Sky-High
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.
Here and There
In 1976, Australian monkey trainer Alex Brackstone declared his four-hectare property northeast of Adelaide to be the independent Province of Bumbunga and named himself its governor-general. He was concerned that Australia was drifting toward republicanism and wanted to be sure that at least a part of the continent would always be loyal to the British Crown.
To underscore his devotion to the queen he drew a huge scale model of Great Britain using strawberry plants. He planned to sprinkle each county with authentic soil imported from Britain, but customs authorities put a stop to that, and the strawberries eventually died in a drought. Full points for effort, though.
Related: In her 1981 book The Emperor of the United States of America, Catherine Caufield says that British eccentric John Alington laid out a giant street map of London on the grounds of his estate at Letchworth, to rehearse his laborers who were traveling there to see the Great Exhibition. This article repeats the story, noting that Alington was greatly taken with giant maps: “In 1855, he had a reproduction of the fortifications of Sebastopol built so his workers could better understand the progress of the Crimean War. He also had a pond remodelled into a map of the world, which the men toured in rowboats as he lectured them in geography.” I haven’t been able to confirm this elsewhere, though.
Crossing Guard
Suppose some 2n points in the plane are chosen so that no three are collinear, and then half are colored red and half blue. Will it always be possible to connect each red point with a blue one, in pairs, so that none of the connecting lines intersect?
