Canada’s “victory nickel,” struck from 1943 to 1945, included a special message to stimulate the war effort: Engraved around the rim were the words WE WIN WHEN WE WORK WILLINGLY in Morse Code.
The coin was reissued in 2005 to commemorate the 60th anniversary of V-E Day.
Princeton mathematician John Horton Conway investigated this curious permutation:
3n ↔ 2n
3n ± 1 ↔ 4n ± 1
It’s a simple set of rules for creating a sequence of numbers. In the words of University of Calgary mathematician Richard Guy, “Forwards: if it divides by 3, take off a third; if it doesn’t, add a third (to the nearest whole number). Backwards: if it’s even, add 50%; if it’s odd, take off a quarter.”
If we start with 1, we get a string of 1s: 1, 1, 1, 1, 1, …
If we start with 2 or 3 we get an alternating sequence: 2, 3, 2, 3, 2, 3, …
If we start with 4 we get a longer cycle that repeats: 4, 5, 7, 9, 6, 4, 5, 7, 9, 6, …
And if we start with 44 we get an even longer repeating cycle: 44, 59, 79, 105, 70, 93, 62, 83, 111, 74, 99, 66, 44, …
But, curiously, these four are the only loops that anyone has found — start with any other number and it appears you can build the sequence indefinitely in either direction without re-encountering the original number. Try starting with 8:
…, 72, 48, 32, 43, 57, 38, 51, 34, 45, 30, 20, 27, 18, 12, 8, 11, 15, 10, 13, 17, 23, 31, 41, 55, 73, 97, …
Paradoxically, the sequence climbs in both directions: Going forward we multiply by 2/3 a third of the time and by roughly 4/3 two-thirds of the time, so on average in three steps we’re multiplying by 32/27. Going backward we multiply by 3/2 half the time and by roughly 3/4 half the time, so on average in two steps we’re multiplying by 9/8. And every even number is preceded by a multiple of three — half the numbers are multiples of three!
What happens to these chains? Will the sequence above ever encounter another 8 and close up to form a loop? What about the sequences based on 14, 40, 64, 80, 82 … ? “Again,” writes Guy, “there are many more questions than answers.”
(Richard K. Guy, “What’s Left?”, Math Horizons 5:4 [April 1998], 5-7; and Richard K. Guy, Unsolved Problems in Number Theory, 2004.)
Telegraph companies generally charged by the length of a message, so enterprising customers started using codes in place of common phrases. Here are some sample codes, from the ABC Universal Commercial Electric Telegraphic Code of 1901:
Nalezing – Do only what is absolutely necessary
Nalime – Will only do what is absolutely necessary
Nallary – It is not absolutely necessary, but it would be an advantage
Naloopen – It is not absolutely necessary, but well worth the outlay
If you and I both have a copy of the code book, then I can send you the word Nallary in place of the phrase “It is not absolutely necessary, but it would be an advantage” — a savings of 10 words or 51 characters without any loss of information.
Most of these code books are pretty hard-headed (here’s another), but there’s a wonderful exception — Sullivan & Considine’s Theatrical Cipher Code of 1905, “Adapted Especially to the Use of Everyone Connected in Any Way With the Theatrical Business”:
Filacer – An opera company
Filament – Are they willing to appear in tights
Filander – Are you willing to appear in tights
Filar – Ballet girls
Filaria – Burlesque opera
Filature – Burlesque opera company
File – Burlesque people
Filefish – Chorus girl
Filial – Chorus girls
Filially – Chorus girls who are
Filiation – Chorus girls who are shapely and good looking
Filibuster – Chorus girls who are shapely, good looking, and can sing
Filicoid – Chorus girls who can sing
Filiform – Chorus man
Filigree – Chorus men
Filing – Chorus men who can sing
Fillet – Chorus people
Fillip – Chorus people who can sing
Filly – Comic opera
Film – Comic opera company
Filler – Comic opera people
Filtering – Desirable chorus girl
It’s in the public domain, but I haven’t been able to find the full text online — I’m getting this from Craig Bauer’s (excellent) Secret History: The Story of Cryptology. I’ll update this post if I manage to find more.
09/28/2017 UPDATE: A reader sent me the whole book.
In 1971 a mysterious man hijacked an airliner in Portland, Oregon, demanding $200,000 and four parachutes. He bailed out somewhere over southwestern Washington and has never been seen again. In today’s show we’ll tell the story of D.B. Cooper, the only unsolved hijacking in American history.
We’ll also hear some musical disk drives and puzzle over a bicyclist’s narrow escape.
PICTURES = PIECRUST
INSATIABLE = BANALITIES
SHATTERING = STRAIGHTEN
CORSET = ESCORT
RECLAIM = MIRACLE
TRANSPIRE = TERRAPINS
INTEGRAL = TRIANGLE
Darryl Francis finds that LISMORE, MINNESOTA is an anagram of REMAIN MOTIONLESS.
“There is a well-known story in The Spectator, of a lover of Lady Mary Boon, who, after six months’ hard study, contrived to anagrammatize her as Moll Boon; and upon being told by his mistress, indignant at such a metamorphosis, that her name was Mary Bohun, he went mad.” — William Sandys, ed., Specimens of Macaronic Poetry, 1831
In 1971, Word Ways encouraged its readers to find the anagram that this sad man had worked so hard for. What they found was MOLDY BALLOON.
Unlike the visual or literary arts, music seems to be impossible to describe in words — we’re forced to choose between the senselessly subjective and the incomprehensibly technical. Rutgers philosopher Peter Kivy cataloged four common types of music criticism:
There just doesn’t seem to be an adequate way to convey the experience of hearing a piece of music without actually playing it for someone. “Description of music is in a way unique,” Kivy writes. “When it is understandable to the nonmusician, it is cried down as nonsense by the contemporary musician. And when the musician or musical scholar turn their hands to it these days, likely as not the non-musician finds it as mysterious as the Cabala, and about as interesting as a treatise on sewage disposal.”
(From The Corded Shell, 1980.)
The blinking light atop the Capitol Records tower spells out the word HOLLYWOOD in Morse code.
It’s done so ever since the building opened in 1956.
Suppose that there’s a power outage in your neighborhood. If someone calls the electric company, they’ll send someone to fix the problem. This puts you in a dilemma: If someone else makes the call, then you’ll benefit without having to do anything. But if no one calls, then you’ll all remain in the dark, which is the worst outcome:
This is the “volunteer’s dilemma,” a counterpart to the famous prisoner’s dilemma in game theory. Each participant has a greater incentive for “free riding” than acting, but if no one acts, then everyone loses.
A more disturbing example is the murder of Kitty Genovese, who was stabbed to death outside her New York City apartment in 1964. According to urban lore, many neighbors who were aware of the attack chose not to contact the police, trusting that someone else would make the call but hoping to avoid “getting involved.” Genovese died of her wounds.
In a 1988 paper, game theorist Anatol Rapaport noted, “In the U.S. Infantry Manual published during World War II, the soldier was told what to do if a live grenade fell into the trench where he and others were sitting: to wrap himself around the grenade so as to at least save the others. (If no one ‘volunteered,’ all would be killed, and there were only a few seconds to decide who would be the hero.)”
The Guinness Book of World Records lists the Yaghan word mamihlapinatapai as the “most succinct word.” It’s defined as “a look shared by two people, each wishing that the other would initiate something that they both desire but which neither wants to begin.”
(From William Poundstone, Prisoner’s Dilemma, 1992.)
Hat-wearing rules in the British House of Commons, 1900:
At all times remove your hat on entering the House and put it on upon taking your seat; remove it again on rising for whatever purpose. If the MP asks a Question he will stand with his hat off and he may receive the Minister’s answer seated and with his hat on. If, on a Division, he should have to challenge the ruling of the Chair, he will sit and put his hat on. If he wishes to address the Speaker on a Point of Order not connected with a Division, he will do so standing with his hat off. When he leaves the Chamber to participate in a Division he will take his hat off, but will vote with it on.
As the century wore on hats grew rare, but technically a Member still had to be properly “seated and covered” to raise a Point of Order during a Division. Accordingly the Serjeant at Arms began to keep two collapsible opera hats for the purpose. In Great Political Eccentrics, Neil Hamilton writes, “Often, several Members wished to raise Points of Order in rapid succession, causing the opera hat to race around the Chamber like a relay baton.”
During one hot spell in July 1893, T.P. O’Connor called Joseph Chamberlain a Judas and a brawl broke out. In the words of Chamberlain’s biographer, “one could see the teeth set, the eyes flashing, faces aflame with wrath and a thicket of closed fists beating about in wild confusion.”
In the midst of this the Serjeant at Arms appeared and addressed himself to a Member standing below the gangway. “I beg your pardon,” he said, “but you’re standing up with your hat on, which you know is a breach of order.”
09/15/2016 UPDATE: The tradition lives on in the Australian House of Representatives: Just two weeks ago MP Christopher Pyne, stuck without a tophat, held a sheet of paper over his head while speaking to Labor’s Tony Burke. Members are required to “speak covered” when the Speaker has called a division.
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.”
