“There may now exist great men for things that do not exist.” — Samuel Burckhardt
Podcast Episode 116: Notes and Queries
In this week’s episode of the Futility Closet podcast we’ll explore some curiosities and unanswered questions from Greg’s research, including the love affair that inspired the Rolls Royce hood ornament, a long-distance dancer, Otto von Bismarck’s dogs, and a craftily plotted Spanish prison break.
We’ll also run after James Earl Ray and puzzle over an unsociable jockey.
More Morals
Maxims of François VI, Duc de La Rochefoucauld (1613–1680):
- “We commonly slander more thro’ Vanity than Malice.”
- “We have more Laziness in our Minds than in our Bodies.”
- “There are few People but what are ashamed of their Amours when the Fit is over.”
- “We should not judge of a Man’s Merit by his great Qualities, but by the Use he makes of them.”
- “He who is pleased with Nobody, is much more unhappy than he with whom Nobody is pleased.”
- “There are some disguised Falsehoods so like Truths, that ‘twould be to judge ill not to be deceived by them.”
- “Men sometimes think they hate Flattery, but they hate only the Manner of Flattering.”
- “Acquired Honor is Surety for more.”
- “Innocence don’t find near so much Protection as Guilt.”
- “‘Tis our own Vanity that makes the Vanity of others intolerable.”
- “‘Tis a common Fault to be never satisfied with ones Fortune, nor dissatisfied with ones Understanding.”
- “Envy is more irreconcilable than Hatred.”
- “‘Tis better to employ our Understanding, in bearing the Misfortunes that do befall us, than in foreseeing those that may.”
- “A good Head finds less Trouble in submitting to a wrong Head than in conducting it.”
- “Folly attends us close thro’ our whole Lives; and if anyone seems wise, ’tis merely because his Follies are proportionate to his Age, and Fortune.”
And “As ’tis the Characteristic of a great Genius to say much in a few Words, small Geniuses have on the contrary the Gift of speaking much and saying nothing.”
Moessner’s Theorem
Write out the positive integers in a row and underline every fifth number. Now ignore the underlined numbers and record the partial sums of the other numbers in a second row, placing each sum directly beneath the last entry that it contains.
Now, in this second row, underline and ignore every fourth number, and record the partial sums in a third row. Keep this up and the entries in the fifth row will turn out to be the perfect fifth powers 15, 25, 35, 45, 55 …
If we’d started by ignoring every fourth number in the original row, we’d have ended up with perfect fourth powers. In fact,
For every positive integer k > 1, if every kth number is ignored in row 1, every (k – 1)th number in row 2, and, in general, every (k + 1 – i)th number in row i, then the kth row of partial sums will turn out to be just the perfect kth powers 1k, 2k, 3k …
This was discovered in 1951 by Alfred Moessner, a giant of recreational mathematics who published many such curiosa in Scripta Mathematica between 1932 and 1957.
(Ross Honsberger, More Mathematical Morsels, 1991.)
Decoy
In March 1945 the Japanese painted the giant image of an American B-29 on the Tien Ho airfield in China. They gave it a burning engine and a 300-foot wingspan, so that when viewed from a great altitude it would look like a stricken bomber flying at several thousand feet. Their hope was that this would induce high-flying Allied planes to drop down to investigate, bringing them within range of their anti-aircraft guns. I don’t know whether it worked.
The Atlantic has a collection of similar deceptive exploits from World War II.
Black and White
A “maximummer-selfmate” by T.R. Dawson, from 1934. White wants to force Black to checkmate him, and Black always makes the geometrically longest move available to him. How can White accomplish his goal in three moves?
All Roads
Another puzzle from Kendall and Thomas’ Mathematical Puzzles for the Connoisseur (1971):
Take three consecutive positive integers and cube them. Add up the digits in each of the three results, and add again until you’ve reached a single digit for each of the three numbers. For example:
463 = 97336; 9 + 7 + 3 + 3 + 6 = 28; 2 + 8 = 10; 1 + 0 = 1
473 = 103823; 1 + 0 + 3 + 8 + 2 + 3 = 17; 1 + 7 = 8
483 = 110592; 1 + 1 + 0 + 5 + 9 + 2 = 18; 1 + 8 = 9
Putting the three digits in ascending order will always give the result 189. Why?
In a Word
altivolant
adj. high-flying
aspectable
adj. capable of being seen, visible
terriculament
n. a source of fear
John Lithgow’s eyes pop out of his head momentarily at the climax of “Nightmare at 20,000 Feet,” the final segment in Twilight Zone: The Movie (1983). In the segment, a remake of the famous television episode from 1963, Lithgow plays a nervous air passenger who discovers a gremlin on the wing of his plane. At the moment when he lifts the shade, the edit shows the monster for 17 frames, then Lithgow’s face for 10 frames, then the monster for 42 frames, and then a 5-frame shot of Lithgow’s head incorporating the eye-popping effect.
Of these 5 frames, the first three show a wild-eyed Lithgow, the fourth shows bulging eyes, and the fifth is shown below. “This 5-frame sequence is on the screen for 1/5 second, but the most distorted image is only visible for 1/24 second,” writes William Poundstone in Bigger Secrets. “Blink at the wrong time, and you miss it. But if you watch the shot carefully at normal speed, the sequence is detectable. Lithgow’s eyes seem to inflate with an accelerated, cartoon-like quality.”
Here’s the frame:
The Test
“If you think that you can think about a thing, inextricably attached to something else, without thinking of the thing it is attached to, then you have a legal mind.” — Thomas Reed Powell
A lawyer advertised for a clerk. The next morning his office was crowded with applicants — all bright, many suitable. He bade them wait until all should arrive, and then ranged them in a row and said he would tell them a story, note their comments, and judge from that whom he would choose.
‘A certain farmer,’ began the lawyer, ‘was troubled with a red squirrel that got in through a hole in his barn and stole his seed corn. He resolved to kill the squirrel at the first opportunity. Seeing him go in at the hole one noon, he took his shot gun and fired away; the first shot set the barn on fire.’
‘Did the barn burn?’ said one of the boys.
The lawyer without answer continued: ‘And seeing the barn on fire, the farmer seized a pail of water and ran to put it out.’
‘Did he put it out?’ said another.
‘As he passed inside, the door shut to and the barn was soon in flames. When the hired girl rushed out with more water’ —
‘Did they all burn up?’ said another boy.
The lawyer went on without answer:–
‘Then the old lady came out, and all was noise and confusion, and everybody was trying to put out the fire.’
‘Did any one burn up?’ said another.
The lawyer said: ‘There that will do; you have all shown great interest in the story.’ But observing one little bright-eyed fellow in deep silence, he said: ‘Now, my little man, what have you to say?’
The little fellow blushed, grew uneasy, and stammered out:–
‘I want to know what became of that squirrel; that’s what I want to know.’
‘You’ll do,’ said the lawyer; ‘you are my man; you have not been switched off by a confusion and a barn burning, and the hired girls and water pails. You have kept your eye on the squirrel.’
— Ballou’s Monthly Magazine, February 1892
Impromptu
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Poet Brendan Behan began his career as a housepainter. While in Paris, he was asked to paint a sign on the window of a café to attract English-speaking tourists. He painted:
Come in, you Anglo-Saxon swine
And drink of my Algerian wine.
‘Twill turn your eyeballs black and blue
And damn well good enough for you.
“At least I got paid for it,” he said later. “But I ran out of the place before the patron could get my handiwork translated.”
(From his wife Beatrice’s My Life With Brendan, 1973.)