Andrzej Bartz offered these “doubly true” alphametics in the May 2017 issue of Word Ways. If the letters in each equation encode digits, what mathematical facts do these expressions represent?
CCCLVI + CCCI + CCLI = CMVIII
ONE + THIRTYNINE + NINETYONE = THREE + NINE + THIRTY + EIGHTYNINE
TWO × TWO + TEN × FIVE = SIX × NINE
On April 8, 1959, when keepers arrived at the Spectacle Reef lighthouse in Lake Huron to prepare it for a new season, they discovered a note:
To Whom It May Concern:
At 1705 hours my plane went down 400 kilometers out at 035 to 050 degrees. I was one mile northeast of here at 5000 feet when my engine went quite dead. I tried to make it in but landed in the water. At that time there were large open areas of water. I did not try to land on the ice as it did not look thick enough. Also I wanted to get as close to this light as possible.
The plane went down in about two minutes after it landed. Before it did it floated close enough to a floe for me to jump. The ice was not over two inches thick. Another large body of water separated me from the light so I waited.
Suddenly the wind shifted to the northeast. The ice I was on started to move. At the very last moment one quarter of the ice ground against the ice packed around the light. My ice floe broke up fast so I ran for the light. I got ashore but was wet from falling in. My clothes froze before I could get the door open.
Once inside I used your towels and overshoes to keep from freezing.
About 2100 I got your stove lit. I hooked up the batteries and lit your warning lamp. The radio receiver worked but the transmitter was dead. I didn’t know enough about it to make it work. I have used the batteries until they are going dead. I sat up last night sending out SOS calls by blinking the main light.
Right now I am deliberating whether to stay here or cross the ice. From the chart I will have eleven miles to travel. There are large water holes, thin ice which had been broken into pieces by the wind yesterday. There is hardly any wind today. We have had two freezing nights, so I ought to make it in about four hours. I want to go now because it is nice weather.
Also I did not file a flight plan so no one will look for me another two or three days. The weather may be bad again.
I have made a mess of your building. I hope you will forgive me. I am going to take some equipment with me, binoculars, coat, hat, blankets, etc. I will turn them into the United States Coast Guard as soon as I get ashore.
Signed,
M.Sgt. William J. Wyman
USAF
The note bore no date. Wyman had departed Saginaw in a Piper Super Cruiser on Feb. 22, headed for the former Kinross Air Force Base near Sault Ste. Marie. He had never arrived. No trace of him was ever found.
(Thanks, Charles.)
In any right triangle, the angle bisector of the right angle divides the square on the hypotenuse into two congruent trapezoids.
fIVe + sIX + seVen
5 + 6 + 7 = 18
IV + IX + V = 18
These are the only three consecutive numbers whose sum equals that of the Roman numerals embedded in their names.
In The King’s English (1997), Kingsley Amis cites an old joke that illustrates the confusing distinction between shall and will:
A swimmer in difficulties was heard to shout, ‘I will drown and nobody shall save me.’ At an inquest on the unfortunate fellow, English jurors wanted a verdict of suicide, Scottish jurors a verdict of death by misadventure, and MacTavish pressed for a rider or footnote rebuking witnesses for making no effort to rescue the victim.
Under the old rule, I shall indicated a prediction and I will denoted a promise or threat. Confusingly, in the second and third persons these meanings were reversed, so that you/she will indicated simple futurity and you/she shall denoted an intention or command. Still more confusingly, old-fashioned speakers of Scottish English reversed this whole understanding of the matter. So while the English jurors thought the swimmer was saying, “It is my intention to drown, and it is my express desire that nobody try to save me,” the Scots took him to say, “I am going to drown and it seems that nobody is going to save me.”
All this has only grown more confused with the popularity of contractions such as I’ll and you’ll, and Americans have generally dispensed with shall and use will for everything. Of the joke, Amis writes, “Nobody tells that one today.”
Some words become famous for their implausibly specific definitions:
ucalegon: a neighbor whose house is on fire
nosarian: one who argues that there is no limit to the possible largeness of a nose
undoctor: to make unlike a doctor
Mrs. Byrne’s Dictionary of Unusual, Obscure, and Preposterous Words, by Josefa Heifetz Byrne, collects examples ranging from atpatruus (“a great-grandfather’s grandfather’s brother”) to zumbooruk (“a small cannon fired from the back of a camel”). My own favorite is groak, “to watch people silently while they’re eating, hoping they will ask you to join them.”
Alas, most of these don’t appear in the magisterial Oxford English Dictionary. Accordingly, in 1981 Jeff Grant burrowed his way into the OED in a deliberate search for obscure words. When he reached the end of A he sent his 10 favorite finds to the British magazine Logophile:
acersecomic: one whose hair was never cut
acroteriasm: the act of cutting off the extreme parts of the body, when putrefied, with a saw
alerion: an eagle without beak or feet
all-flower-water: cow’s urine, as a remedy
ambilevous: left-handed on both sides
amphisbaenous: walking equally in opposite directions
andabatarian: struggling while blindfolded
anemocracy: government by wind
artolatry: the worship of bread
autocoprophagous: eating one’s own dung
“I have been working slowly through ‘B’ and so far my favourite is definitely ‘bangstry’, defined as ‘masterful violence’, an obsolete term that is surely overdue for a comeback.”
(From Word Ways, November 1981.)
A week after songwriter Jim Croce died in a plane crash in 1973, his wife, Ingrid Jacobson, received this letter:
Dear Ing,
I know I haven’t been very nice to you for some time, but I thought it might be of some comfort, Sweet Thing, to understand that you haven’t been the only recipient of JC’s manipulations. But since you can’t hear me and can’t see me, I can’t bullshit, using my sneaky logic and facial movements. I have to write it all down instead, which is lots more permanent. So it can be re-read instead of re-membered, so, it’s really right on the line.
I know that you see me for who I am, or should I say, as who I are. ‘Cause I’ve been lots of people. If Medusa had personalities or attitudes instead of snakes for her features, her name would have been Jim Croce. But that’s unfair to you and it’s also unhealthy for me. And I now want to be the oldest man around, a man with a face full of wrinkles and lots of wisdom.
So this is a birth note, Baby. And when I get back everything will be different. We’re gonna have a life together, Ing, I promise. I’m gonna concentrate on my health. I’m gonna become a public hermit. I’m gonna get my Master’s Degree. I’m gonna write short stories and movie scripts. Who knows, I might even get a tan.
Give a kiss to my little man and tell him Daddy loves him.Remember, it’s the first sixty years that count and I’ve got 30 to go.
I Love you,
Jim
(From Ingrid’s 2012 memoir, I Got a Name: The Jim Croce Story.)
Lexicon Recentis Latinitas, published by the Vatican, invents Latin versions of modern words and phrases, so students can refer to items that didn’t exist in the ancient world:
bestseller: liber maxime divenditus
car wash: autocinetorum lavatrix
Christmas tree: arbor natalicia
disc brakes: sufflamen disci forma
dishwasher: escariorum lavator
to flirt: lusorie amare
leased property: locatio in emptionem convertibilis
pinball machine: sphaeriludium electricum nomismate actum
refrigerator: cella frigorifera
to slack off on the job: neglegenter operor
television: instrumentum televisificum
traffic jam: fluxus interclusio
washing machine: machina linteorum lavatoria
These examples are from a selection published in 1991 in Harper’s, which said that 75 percent of the 18,000 entries in that year’s edition were terms that had never had Latin equivalents. I can’t find the whole book, but the Vatican website offers an Italian-Latin glossary with some entries in English (hot pants are brevíssimae bracae femíneae).
In the 19th century, British polymath William Barnes tried to reform English by limiting it to words of Saxon-English origin. Where no “Teutonic” words were available to express his meaning, he made up alternatives, such as sky-sill for horizon, glee-craft for music, wort-lore for botany, hearsomeness for obedience, somely for plural, and folkwain for omnibus.
In 1948, Richard Lister challenged the readers of the New Statesman to write the opening paragraphs of a novel set in present-day London in this style of reformed English. Reader D.M. Low offered this:
As Ernest was wafted up on the dredger from the thorough-hole at Kingsway he was inwardly upborne to see Pearl again; but, alas, evenly castdown for the blue-eyed bebrilled booklearner was floating downwards on the other ladderway. It was now or never. Ernest fought back against the rising stairs and the gainbuildfulness of hirelings bound for work. Pushing aside fingerwriters, shophelpers and even deeded reckoning-keepers, by an overmanly try he reached the bottom eventimeously with Pearl.
‘What luck! Can you eat with me tonight? I know a fair little upstaker near here.’
‘Oh! I can’t. My Between-go is in Fogmonth, and I must get through and …’
The rumble of the ambercrafty wagonsnake drowned her words.
‘Hark! There’s the tug. I must fly.’
It was hard to be wisdomlustful. Forlorn in his trystlessness Ernest sought Kingsway again and dodging hire-shiners and other self-shifters recklessly headed towards the worldheadtownly manystreakiness of the Strand.
He appended this glossary:
dredger: escalator.
ladderway: escalator.
upborne: elated.
evenly: equally.
bebrilled: bespectacled, (German Brille).
booklearner: student.
gainbuildfulness: obstructiveness.
fingerwriters: typists, cf. dattilografa.
deeded reckoning keepers: chartered accountants.
overmanly: superhuman.
eventimeously: simultaneously.
upstaker (less correctly upstoker): restaurant.
Between go: student slang for Between while try out i.e., Intermediate Examination.
Fogmonth: November.
ambercrafty: electric, lit. electric powered.
wagonsnake: train (archaic and poet.).
tug: train cf. German Zug.
wisdomlustful: philosophical.
trystlessness: disappointment.
hire-shiners: taxis.
self-shifters: automobiles.
manystreakiness: variety.
worldheadtownly: cosmopolitan.
Other readers had suggested eyebiting for attractive, lip-hair for moustache, slidehorn for trombone, and smokeweed for cigarette. The winning entries are here.
Wikimedia user Tarquin points out that the natural rhythm of spoken language can be used to teach polyrhythms.
Above: The phrase “cold cup of tea,” spoken naturally, approximates a rhythm of 2 against 3.
Below: The phrase “what atrocious weather” approximates 4 against 3.
