Good Boy

Rita A. Della Vecchia’s 1988 invention pets your dog while you’re at the office:

One of the primary elements of this relationship of man with domestic pets seems to be the scratching, stroking and petting of a pet that can be accomplished by its human symbiont by reason of his greater dexterity. … The instant invention provides a mechanical device to simulate this activity for pets without requiring human attention, with the thought that, by reason of the learned behavior of such animals, the animal will associate this activity, as to its source of origin, with its human symbiont.

Thanks to other inventors, you can offer the same treatment to your baby and even to yourself.

Three Puzzles

1. You are midway through dealing a bridge hand when a nuclear apocalypse destroys civilization. The bridge table is still upright, and your friends are willing to keep playing, but you can’t remember where you left off dealing. How can you finish dealing this hand without having to start over?

2. Can I stand behind you while you stand behind me?

3. My bed is 10 feet from the light switch. But last week I turned off the light, dashed across the room, and was in bed before the room got dark. How did I manage this?

Click for Answer

Crackpot Apocalypse

Various writers throughout the 19th century confidently reported that they’d found the true and exact value of π. Unfortunately, they all gave different answers. In 1977 DePauw University mathematician Underwood Dudley tried to make sense of this by compiling 50 of their pronouncements:

pi estimates - underwood dudley

He concluded that π is decreasing. The best fit is πt = 4.59183 – 0.000773t, where t is the year A.D. — it turns out we passed 3.1415926535 back in 1876 and have been heading downward ever since.

And that means trouble: “When πt is 1, the circumference of a circle will coincide with its diameter,” Dudley writes, “and thus all circles will collapse, as will all spheres (since they have circular cross-sections), in particular the earth and the sun. It will be, in fact, the end of the world, and … it will occur in 4646 A.D., on August 9, at 4 minutes and 27 seconds before 9 p.m.”

There is some good news, though: “Circumferences of circles will be particularly easy to calculate in 2059, when πt = 3.”

(Underwood Dudley, “πt,” Journal of Recreational Mathematics 9:3, March 1977, p. 178)

Name Deals

In the 19th century an eccentric Frenchman willed his estate to his 12 nephews and nieces on the condition that “every one of my nephews marries a woman named Antonie and that every one of my nieces marries a man named Anton.” They had also to name each firstborn child Antonie or Anton, and each nephew must celebrate his marriage on one of St. Anthony’s days. “If, in any instance, this last provision was not complied with before July 1896, one-half of the legacy was in that case to be forfeited.” (The Irish Law Times and Solicitors’ Journal, July 8, 1905)

William Stanislaus Murphy left his entire estate to Harvard University to fund a scholarship for students named Murphy. By a will dated April 28, 1717, John Nicholson of London left the residue of his estate to poor English Protestants named Nicholson.

When Elias Warner Leavenworth died in 1887 he funded a scholarship of $900 a year for a student named Leavenworth to attend Yale. Hamilton College of Clinton, N.Y., has its own Leavenworth scholarship; it hasn’t been awarded since 1994, but, a spokeswoman told told the New York Times, “there will always be Leavenworths out there.”


“If all our misfortunes were laid in one common heap, whence everyone must take an equal portion, most people would be contented to take their own and depart.” — Socrates

The Phantom Save

Andy fires a shot at the goal, but it’s deflected by his opponent Bill. If Bill had not reached the ball, it would have struck Charlie, Andy’s teammate. Roberto Casati asks, “Should Bill get credit for the save?”

He: Not quite. After all, the ball was not going to score anyway; it would have hit Charlie’s body.

She: But neither would it be right to say that anything happened thanks to Charlie. After all, Charlie did nothing.

He: But then who is responsible for spoiling Andy’s shot?

“Cases like this one are indicative of a deep conceptual tension,” Casati writes. “I am walking in the rain. My umbrella is open and I am wearing a hat, so my head is not getting wet. But why is that so? It’s not because of the umbrella, because I’m wearing my hat. And it’s not because of my hat, for I have an umbrella.”

From Casati’s excellent book Insurmountable Simplicities. See also In the Dark.

Mr. Big

One Filmer, defending witches in England, is said to have made this ingenious defense. His clients were charged, as was usual, with being accessory to the devil. Under the common law there could be no accessory unless there was also a principal; and no accessory could be convicted until the principal was convicted; for if the principal be acquitted there is no guilty principal and hence can be no accessory. Consequently until the principal be convicted the accessory cannot be tried.

Taking advantage of this state of the law, Filmer argued that his clients could not be tried until their alleged principal had been tried and convicted, and how could this be done? Only according to the law of the land. In the first place how could the devil be summoned? The officer serving the precept would either be obliged to go to the devil and summons him personally, or, failing that, would be obliged to leave a copy of the precept at his usual place of abode. Although admiring friends of the officer may from time to time have advised him to do both, yet the practical application of such advice is an impossibility. Then assuming the respondent to be duly summoned, he would be entitled to a trial by a jury of his peers. But His Satanic Majesty has no peers, and even if he had, they would be certain to be in collusion with the respondent and would certainly acquit him. Under any circumstances therefore how could his accessories be tried?

— H.C. Shurtleff, “The Grotesque in Law,” American Law Review, January-February 1920

Math Notes

614,656 = 284
6 + 1 + 4 + 6 + 5 + 6 = 28

1,679,616 = 364
1 + 6 + 7 + 9 + 6 + 1 + 6 = 36

8,303,765,625 = 456
8 + 3 + 0 + 3 + 7 + 6 + 5 + 6 + 2 + 5 = 45

52,523,350,144 = 347
5 + 2 + 5 + 2 + 3 + 3 + 5 + 0 + 1 + 4 + 4 = 34

20,047,612,231,936 = 468
2 + 0 + 0 + 4 + 7 + 6 + 1 + 2 + 2 + 3 + 1 + 9 + 3 + 6 = 46


Queen Elizabeth acceded up a tree. When her father, George VI, died in 1952, the princess was staying at the Treetops Hotel in Kenya, essentially an enormous treehouse built into a fig in the Aberdare National Park. While she returned quickly to Britain, hunter Jim Corbett wrote in the visitors’ logbook:

“For the first time in the history of the world, a young girl climbed into a tree one day a Princess and after having what she described as her most thrilling experience she climbed down from the tree next day a Queen — God bless her.”

Point of Information

Sexauer is an ordinary German name referring to one who came from Sexau, in Germany. Looking for a Mr. Sexauer, a man in Washington called at the Senate Interstate and Foreign Commerce Committee. Helping him, a girl employee called the Banking and Currency Committee by telephone to check, and inquired politely, ‘Do you have a Sexauer over there?’

‘Listen,’ the girl switchboard operator snapped, ‘We don’t even have a ten-minute coffee break anymore.’

— Elsdon C. Smith, Treasury of Name Lore, 1967