The sum of 2k – 4
From one to thirteen plus a score,
Over eleven,
Plus eighteen times seven,
Equals six cubed and not a bit more.
(Will Nediger, “Can Math Limericks Survive?”, Word Ways 37:3 [August 2004], 238.)
The sum of 2k – 4
From one to thirteen plus a score,
Over eleven,
Plus eighteen times seven,
Equals six cubed and not a bit more.
(Will Nediger, “Can Math Limericks Survive?”, Word Ways 37:3 [August 2004], 238.)
“Let us take a typical case. A gentleman and his wife, calling on friends, find them not at home. The gentleman decides to leave a note of regret couched in a few well-chosen words, and the first thing he knows he is involved in this:
We would have liked to have found you in.
“Reading it over, the gentleman is assailed by the suspicion that he has too many ‘haves,’ and that the whole business has somehow been put too far into the past. … He takes an envelope out of his pocket and grimly makes a list of all the possible combinations, thus getting:”
“If he has married the right kind of woman, she will hastily scratch a brief word on a calling card, shove it under the door, and drag her husband away.”
— James Thurber, “Ladies’ and Gentlemen’s Guide to Modern English Usage,” 1931
In his Canterbury Puzzles of 1907, Henry Dudeney posed a now-famous challenge: How can you cut an equilateral triangle into four pieces that can be reassembled to form a perfect square?
Dudeney’s beautiful solution was accompanied by a rather involved geometric derivation. It seems unlikely that he worked this out laboriously in approaching an answer to the problem, but how then did he reach it?
Here’s one possibility: If a strip of squares is draped adroitly over a strip of triangles, their intersection forms a wordless proof of the task’s feasibility:
Whether that was Dudeney’s path to the solution is not known, but it appears at least plausible.
The joists in the tower in which Montaigne wrote his Essays are inscribed with his favorite quotations from Greek and Latin authors, many of which appear in his writings: “It is not so much things that torment man, as the opinions he has of things.” “Every reasoning has its contrary.” “Wind swells bladders, opinion swells men.”
He wrote, “The room pleases me because it is somewhat difficult of access, and retired, as much on account of the utility of the exercise, as because I there avoid the crowd. Here is my seat, my place, my rest. I try to make it purely my own, and to free this single corner from conjugal, filial, and civil community.”
The numbers in the diagram below correspond to this table in the German Wikipedia. English translations are here.
In large Latin letters on the central rafter are the words “I DO NOT UNDERSTAND. I PAUSE. I EXAMINE.”
“The discovery of a new dish does more for human happiness than the discovery of a new star.” — Jean Anthelme Brillat-Savarin
Make an inverted triangle of hexagonal cells with side length 3n + 1, and color the cells in the top row randomly in three colors. Now color the cells in the second row according to these rules:
When you’ve finished the second row, continue through the succeeding ones, applying the same rules. Pleasingly, no matter how large the triangle, the color of the last cell can be predicted at the start: Just apply our two guiding rules to the endmost cells in the top row. If those two cells are both red, the last cell will be red. If one is red and one is yellow (as in the figure above), the bottom cell will be blue.
The principle was discovered by Newcastle University mathematician Steve Humble in 2012. Gary Antonick gives more background here, and see the paper below for a mathematical discussion by Humble and Ehrhard Behrends.
(Ehrhard Behrends and Steve Humble, “Triangle Mysteries,” Mathematical Intelligencer 35:2 [June 2013], 10-15.)
George Orwell’s six rules of writing, from “Politics and the English Language,” 1946:
But “one could keep all of them and still write bad English.”
English novelist Winifred Ashton had a disastrous gift for inadvertent double entendre. From Cole Lesley’s biography of Noël Coward:
The first I can remember was when poor Gladys was made by Noël to explain to Winifred that she simply could not say in her latest novel, ‘He stretched out and grasped the other’s gnarled, stumpy tool.’ The Bloomers poured innocently from her like an ever-rolling stream: ‘Olwen’s got crabs!’ she cried as you arrived for dinner, or ‘We’re having roast cock tonight!’ At the Old Vic, in the crowded foyer, she argued in ringing tones, ‘But Joyce, it’s well known that Shakespeare sucked Bacon dry.’ It was Joyce too who anxiously inquired after some goldfish last seen in a pool in the blazing sun and was reassured, ‘Oh, they’re all right now! They’ve got a vast erection covered with everlasting pea!’ ‘Oh the pleasure of waking up to see a row of tits outside your window,’ she said to Binkie during a weekend at Knott’s Fosse. Schoolgirl slang sometimes came into it, for she was in fact the original from whom Noël created Madame Arcati: ‘Do you remember the night we all had Dick on toast?’ she inquired in front of the Governor of Jamaica and Lady Foot. Then there was her ghost story : ‘Night after night for weeks she tried to make him come …’
“Why could she not have used the word ‘materialise’?” wrote Lesley, who was Coward’s secretary. “But then if she had we should never have had the fun.” See Shocking!
I think I mentioned this on the podcast at some point: One summer morning in 1815, proprietor William Butterfield opened the White Wells at Ilkley, West Yorkshire, to a sound of whirring:
All over the water and dipping into it was a lot of little creatures, all dressed in green from head to foot, none of them more than eighteen inches high, and making a chatter and jabber thoroughly unintelligible. They seemed to be taking a bath, only they bathed with all their clothes on.
Soon, however, one or two of them began to make off, bounding over the walls like squirrels. Finding they were all making ready for decamping, and wanting to have a word with them, he shouted at the top of his voice — indeed, he declared afterwards, he couldn’t find anything else to say or do — ‘Hallo there!’ Then away the whole tribe went, helter skelter, toppling and tumbling, heads over heels, heels over heads, and all the while making a noise not unlike a disturbed nest of young partridges.
That’s the account recorded by Charles C. Smith in the Folk-Lore Record of 1878. Butterfield had died in 1844, but Smith had the story from his associate John Dobson, who described the bathman as “a good sort of a man, honest, truthful, and steady, and as respectable a fellow as you could find here and there.” The fairies made no comment.
Josiah Winslow’s programming language Bespoke encodes instructions into the lengths of words, producing programs that look like poetry. This one prints the phrase “Hello, World!”:
more peppermint tea? ah yes, it's not bad I appreciate peppermint tea it's a refreshing beverage but you immediately must try the gingerbread I had it sometime, forever ago oh, and it was so good! made the way a gingerbread must clearly be baked in fact, I've got a suggestion I may go outside to Marshal Mellow's Bakery so we both receive one
Related: In the early 1980s, Frank Hayes was so vexed with the S-100 computer bus that he wrote a sea shanty about it:
(Thanks, Jeremiah.)