“If God wants us to do a thing, He should make his wishes sufficiently clear. Sensible people will wait till He has done this before paying much attention to Him.” — Samuel Butler (from his notebook)
An Odd Fact
Mentioned in James Tanton’s Mathematics Galore!:
In 1740 the French mathematician Philippe Naudé sent a letter to Leonhard Euler asking how many ways a positive integer could be written as a sum of distinct positive integers (regardless of their order). In considering the problem Euler found something remarkable.
Let D(n) be the number of ways to write n as a sum of distinct positive integers. So, for example, D(6) is 4 because there are four ways to do this for 6: 6, 5 + 1, 4 + 2, and 3 + 2 + 1.
And let O(n) be the number of ways to write n as a sum of odd integers. So O(6) is 4 because 6 can be written as 5 + 1, 3 + 3, 3 + 1 + 1 + 1, or 1 + 1 + 1 + 1 + 1 + 1.
Euler showed that O(N) always equals D(N).
The Mechanics of History
Like his Celui qui tombe of 2014, acrobat Yoann Bourgeois’s La mécanique de l’Histoire is entirely abstract and yet freighted with meaning.
He presented it at the Panthéon in Paris last year — the site of Léon Foucault’s original rotation-demonstrating pendulum.
Light Reading
Joseph-Henri Flacon found the 1804 French Civil Code too dry, so he rewrote it in rhyming verse.
Support
In early 1919, under the headline “The Great Indian Rope Trick Photographed for the First Time,” the Strand published this image by Lieutenant F.W. Holmes, VC, MM. He said he’d taken it at Kirkee, near Poona, in 1917. An old man had begun “by unwinding from about his waist a long rope, which he threw upwards in the air, where it remained erect. The boy climbed to the top, where he balanced himself, as seen in the photograph, which I took at that moment. He then descended … I offer no explanation.”
London’s Magic Circle invited Holmes to present his photo at a special meeting open to the public, who were asked to wear evening dress “to give a good impression.” Holmes repeated his story, which seemed to challenge the position that the trick had never been performed or was the effect of hallucination or hypnosis.
The editor of the Magic Circular, S.W. Clarke, charged that the photo showed a boy “balanced on top of a rigid rope or pole.” Holmes had already stated that the juggler “had no pole — a thing that would have been impossible of concealment.” But under questioning he admitted that there had been no rope — he’d merely seen a boy balancing atop a bamboo pole and had taken a photo of it.
That should have disposed of the story. But, as often happens, news of the debunking was much less interesting than news of the “proof,” and few newspapers published it. “If the question of the rope trick’s existence arose, and it arose many times,” writes Peter Lamont in The Rise of the Indian Rope Trick, “somebody regularly pointed out that the camera never lied, but nobody ever suspected the photographer. As a result, the Holmes photograph remained for many definitive proof that the rope trick was real.”
Hope and Change
Just stumbled across this in an 1889 newspaper:
To those who love mathematics, here is a simple problem for you to figure out: A man purchased groceries to the amount of 34 cents. When he came to pay for the goods he found that he had only a $1 bill, a 3-cent piece and a 2-cent piece. The grocer, on his side, had only a 50-cent piece and a quarter. They appealed to a bystander for change, but he, although willing to oblige them, had only two dimes, a 5-cent piece, a 2-cent piece and a 1-cent piece. After some perplexity, however, change was made to the satisfaction of everyone concerned. What was the simplest way of accomplishing this?
($1 is worth 100 cents, a quarter 25 cents, and a dime 10 cents.)
Misc
- Ulysses Grant had a horse named Jeff Davis.
- PORTUGUESE MARINE CORPS is an anagram of SINGAPORE SUPREME COURT.
- 15613 = 1 + 56 – 13
- FOUR + SIX = TEN is the highest sum in English with no repeated letters.
- “It is easier to forgive an enemy than to forgive a friend.” — William Blake
Figures
I think Jacques Jouet was the first to notice this. In the first few pages of the Tintin adventure The Secret of the Unicorn, as Tintin visits the Vossenplein antique market in Brussels, Snowy the dog keeps scratching himself. Why?
Apt
The letters in OVERSUFFICIENTLY can be rearranged to spell the English number names for 1, 4, 5, 7, 10, 14, 15, 40, 45, 47, 50, 51, 57, 70, and 74.
The letters in A PLACE FOR EVERYTHING AND EVERYTHING IN ITS PLACE can spell 1, 3, 5, 7, 8, 9, 10, 11, 13, 17, 18, 19, 30, 31, 33, 35, 37, 38, 39, 40, 43, 47, 48, 49, 70, 71, 73, 75, 78, 79, 80, 81, 83, 85, 87, 88, 89, 90, 91, 93, 95, 97, 98, and 99.
And the latter can also spell 26 numbers in the form “one-and-twenty,” from ONE-AND-THIRTY to EIGHT-AND-NINETY.
(Rex Gooch, “Number Names in Words and Phrases,” Word Ways 34:4 [November 2001], 254-258.)
Fair Play
“I understand that a computer has been invented that is so remarkably intelligent that if you put it into communication with either a computer or a human, it can’t tell the difference!” — Raymond Smullyan