Quarters

From Lancelot Hogben’s Mathematics in the Making, an appealingly memorizable table of basic trigonometric values:

hogben table

See Alison’s Triangle.

(Thanks, Tom.)

You’ve Got Mail

A great deal of the work of the post office would then be to regulate the use of these personal television channels. Much of the information now sent by mail could be sent through the air on the personal channel, to be viewed in the home or to be printed out for a more or less permanent record. …

Very likely there will be a signal light to indicate that a message is waiting to be viewed. When the personal channel is then activated, each item stored will be displayed in turn. Each can be scanned and erased, scanned and temporarily returned to storage, or scanned and printed out, after which the next item would appear. It will be very much like going through one’s mail today, with its mixture of personal items and advertising, in which some are discarded, some put aside, and some filed.

– Isaac Asimov, “The Individualism to Come,” New York Times, Jan. 7, 1973

Sociable Numbers

The sum of the proper divisors of 14316 is 19116.
The sum of the proper divisors of 19116 is 31704.
The sum of the proper divisors of 31704 is 47616.
The sum of the proper divisors of 47616 is 83328.
The sum of the proper divisors of 83328 is 177792.
The sum of the proper divisors of 177792 is 295488.
The sum of the proper divisors of 295488 is 629072.
The sum of the proper divisors of 629072 is 589786.
The sum of the proper divisors of 589786 is 294896.
The sum of the proper divisors of 294896 is 358336.
The sum of the proper divisors of 358336 is 418904.
The sum of the proper divisors of 418904 is 366556.
The sum of the proper divisors of 366556 is 274924.
The sum of the proper divisors of 274924 is 275444.
The sum of the proper divisors of 275444 is 243760.
The sum of the proper divisors of 243760 is 376736.
The sum of the proper divisors of 376736 is 381028.
The sum of the proper divisors of 381028 is 285778.
The sum of the proper divisors of 285778 is 152990.
The sum of the proper divisors of 152990 is 122410.
The sum of the proper divisors of 122410 is 97946.
The sum of the proper divisors of 97946 is 48976.
The sum of the proper divisors of 48976 is 45946.
The sum of the proper divisors of 45946 is 22976.
The sum of the proper divisors of 22976 is 22744.
The sum of the proper divisors of 22744 is 19916.
The sum of the proper divisors of 19916 is 17716.
The sum of the proper divisors of 17716 is 14316 again.

Insult to Injury

http://www.freeimages.com/photo/1192859

Shortly after his travel book Alexandria appeared in December 1922, E.M. Forster received a regretful letter from the publisher, Whitehead Morris & Co. There had been a fire in the warehouse and the entire edition had been burned. Fortunately, it had been insured, and they enclosed a substantial check in compensation.

“A few weeks later Forster received a yet more regretful letter from the publishers,” notes editor Lawrence Durrell in the book’s 1961 edition. “The books had been found intact, in a cellar which had escaped the flames. This, in view of the insurance money, his publishers wrote, had created a most awkward situation, and they had taken the only way out: they burnt the books deliberately.”

All Right, Then

Index entries in Hilaire Belloc’s The Aftermath: Or, Gleanings From a Busy Life, 1903:

Abingdon, History of, by Lord Charles Gamber, see Pulping, p. 187.
Advertisement, Folly and Waste of, see Pulping, p. 187.
All Souls, College of, see Pulping, p. 187.
Cabs, Necessity of, to Modern Publisher, see Pulping, p. 187.
Cabs to Authors, Unwarrantable Luxury, see Pulping, p. 187.
Call, Divine, to a Literary Career, see Pulping, p. 187.
Dogs, Reputation Going to the, see Pulping, p. 187.
England, Source and Wealth of, see Pulping, p. 187.
Fame, see Pulping, p. 187.
Genius, Indestructibility of, see Pulping, p. 187.
India, Lord Curzon’s Views on, see Pulping, p. 187.
Jesuits, Their Reply to “Huguenot,” see Pulping, p. 187.
“Mamma,” “Darling Old,” Story for Children, by the Countess of K——, see Pulping, p. 187.
Name, Real, of “Diplomaticus,” see Pulping, p. 187.
Rhodes, Cecil, Numerous Lives of, see Pulping, p. 187.
Suzanna and the Elders, Sacred Poem, see Pulping, p. 187.
Uganda Railway, Balance-sheet of, see Pulping, p. 187.

So runs the whole thing, right up to the summary “W.X.Y.Z., see Pulping, p. 187″ at the end.

There’s also an entry for “Pulping, p. 187.”

“The Strangest Soccer Match Ever”

The football teams of Barbados and Grenada found themselves in a bizarre situation in a qualification round for the 1994 Carribean Cup. In order to advance to the finals, Barbados had to win this game by a margin of two goals; in any other outcome Grenada would qualify. Also, the tournament organizers had stated that if the teams reached a draw, extra time would be added to the match in which every goal would count double, the so-called “golden goal.”

Barbados was leading 2-0 when Grenada scored a goal in the final four minutes. With so little time remaining, the Barbados players conferred and, to everyone’s surprise, turned on their own goal, evening the score at 2-2. Their strategy was clear: If they could maintain this tie for the remaining few minutes, they’d be rewarded with an extra 30 minutes of playing time in which a single goal would give them the two-point margin they needed.

The Grenadians, realizing this, spent the last two minutes trying to get control of the ball and send it into their own goal — this would end the game at 3-2 and deny Barbados its two-goal margin.

The Barbadians, realizing this, began defending the Grenadian goal, effectively reversing the whole game. To add to the confusion, some Grenadians tried to make regular goals as well, which left Grenada attacking both goals, Barbados defending both, and most players and supporters utterly bewildered. The Barbadians eventually succeeded in holding the score at 2-2 — and made a winning goal in the extra time.

“I feel cheated,” complained Grenadian manager James Clarkson. “The person who came up with these rules must be a candidate for a madhouse. The game should never be played with so many players running around the field confused. Our players did not even know which direction to attack: our goal or their goal. I have never seen this happen before. In football, you are supposed to score against the opponents to win, not for them.” The Caribbean Cup retired the golden goal rule shortly thereafter.

(Thanks, Karl.)

Podcast: Episode 19

https://commons.wikimedia.org/wiki/File:Duncan_Grant_artwork_for_a_British_Post_Office_poster.jpg

In 1898, 19-year-old W. Reginald Bray made a thorough study of British postal regulations, which laid out rules for mailing everything from bees to elephants and promised that “all letters must be delivered as addressed.” He resolved to give the service “a severe test without infringing its regulations.”

In this episode of the Futility Closet podcast we’ll review the antics that followed, in which Bray sent turnips, bicycle pumps, shoes, and even himself through the British post. We’ll also sympathize with Lucius Chittenden, a U.S. Treasury official who had to sign 12,500 bonds in one harried weekend in 1862, and puzzle over the worrying train journey of a Wall Street banker.

You can listen using the player above, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset. The show notes are on the blog. Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Leonardo’s Robot

https://commons.wikimedia.org/wiki/File:Leonardo-Robot3.jpg

In 1495 Leonardo da Vinci devised a mechanical knight that could sit up, open and close its arms, move its head on flexible neck, and open its visor. The plans have been lost, but we know it was made of wood, brass, and leather and operated by cables, possibly driven by a water wheel. The Duke of Milan displayed it at a pageant near the end of the 15th century, perhaps at the wedding of his niece.

Roboticist Mark Elling Rosheim built a working replica of the knight in 2002 using the sketches that remain, detailed in his book Leonardo’s Lost Robots. He thinks it may have been designed to accost an unwary visitor by remote control. “It is almost like something one would find in an old time amusement park, a piece for the scary haunted mansion or tunnel of love — or a labyrinth, which was the 16th century equivalent. The Knight would be excellent at grabbing someone with its arms in a bear hug. … Perhaps the visor would rise, revealing a hideously contorted, sculpted face.”

“Perhaps the great mystery surrounding this lost robot of Leonardo can be summed up by the master himself in the giant scrapbook known as the Codex Atlanticus. In the sheets for this project, we read an incomplete sentence with which Leonardo tried out his pen: ‘Tell me if ever, tell me if ever anything was built in Rome …’ Leonardo may be expressing his frustration and anxiety about a project near and dear to his heart that because of external pressures could not be born.”

Rich Earth

Why do the elements ytterbium, yttrium, terbium, and erbium have similar names?

Because all four of them were first discovered in ore from the same mine near the Swedish village of Ytterby.

Holmium, thulium, and gadolinium were discovered at the same source — leading some to call Ytterby the Galápagos of the periodic table.

In a Word

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macrobian
adj. long-lived

annosity
n. fullness of years, length of life, agedness

Index entries from A. Lapthorn Smith’s How to Be Useful and Happy From Sixty to Ninety, 1922:

Absurdity of voluntary retirement at sixty
Adding ten years to life
Alcohol as cure for insomnia, very bad
All day in garden
Beard, long white, don’t wear
Carriage and pair shortens life
Cause of insomnia must be found
Cook, good, source of danger to elderly men
Crime to die rich
Engine drivers over sixty, what to do with them
Garrett, Mrs., of Penge, active voter at 102
If no relatives, spend on poor
Young people, company of, at sixty, how to keep

See Jonathan Swift’s “Resolutions — When I Come to Be Old.”

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