The Phantom Save

http://commons.wikimedia.org/wiki/File:Soccer_(PSF).png

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.

| Science & Math

Mr. Big

http://commons.wikimedia.org/wiki/File:Pandemonium.jpg

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

| Religion · Society

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

| Science & Math

Elevation

http://en.wikipedia.org/wiki/File:Treetops_Hotel_Eric_Sherbrooke_Walker.jpg

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.”

| History

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

| Language

Classical Works

In 1989, the Finnish news service Nuntii Latini began broadcasting the news in Latin.

Not to be outdone, in 1995 Finnish literature professor Jukka Ammondt recorded an album of Elvis songs sung in Latin. It includes Nunc Hic Aut Numquam (“It’s Now or Never”), Non Adamare Non Possum (“Can’t Help Falling in Love”), Cor Ligneum (“Wooden Heart”), and Tenere Me Ama (“Love Me Tender”).

“Two years later,” writes linguist Mikael Parkvall, “he followed up the success with the album Rocking in Latin, featuring classics such as Quate, Crepa, Rota (better known as ‘Shake, Rattle and Roll’).”

Lewis Carroll’s uncle Hassard Dodgson rendered one of his nephew’s poems into Latin elegiacs. Do you recognize it?

Hora aderat briligi. Nunc et Slythæia Tova
Plurima gyrabant gymbolitare vabo;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuêre Rathi.

“Cave, Gaberbocchum moneo tibi, nate cavendum
(Unguibus ille rapit. Dentibus ille necat.)
Et fuge Jubbubbum, quo non infestior ales,
Et Bandersnatcham, quae fremit usque, cave.”

Ille autem gladium vorpalem cepit, et hostem
Manxonium longâ sedulitate petit;
Tum sub tumtummi requiescens arboris umbrâ
Stabat tranquillus, multa animo meditans.

Dum requiescebat meditans uffishia, monstrum
Praesens ecce! oculis cui fera flamma micat,
Ipse Gaberbocchus dumeta per horrida sifflans
Ibat, et horrendum burbuliabat iens!

Ter, quater, atque iterum cito vorpalissimus ensis
Snicsnaccans penitus viscera dissecuit.
Exanimum corpus linquens caput abstulit heros
Quocum galumphat multa, domumque redit.

“Tune Gaberbocchum potuisti, nate, necare?
Bemiscens, puer! ad brachia nostra veni.
Oh! frabiusce dies! iterumque caloque calâque
Laetus eo!” ut chortlet chortla superba senex.

Hora aderat briligi. Nunc et Slythæia Tova
Plurima gyrabant gymbolitare vabo;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuêre Rathi.

| Language

The Author’s Eye

http://commons.wikimedia.org/wiki/File:Maugham.jpg

Excerpts from Somerset Maugham’s notebook:

  • “No action is in itself good or bad, but only such according to convention.”
  • “People are never so ready to believe you as when you say things in dispraise of yourself; and you are never so much annoyed as when they take you at your word.”
  • “An action is not virtuous merely because it is unpleasant to do.”
  • “The more intelligent a man is the more capable is he of suffering.”
  • “However harmless a thing is, if the law forbids it most people will think it wrong.”
  • “I don’t know why it is that the religious never ascribe common sense to God.”
  • “All this effort of natural selection, wherefore? What is the good of all this social activity beyond helping unessential creatures to feed and propagate?”
  • “I can imagine no more comfortable frame of mind for the conduct of life than a humorous resignation.”
| Literature

The Infected Checkerboard

the infected checkerboard

From the Soviet magazine KVANT, 1986:

On an n × n checkerboard, a square becomes “infected” if at least two of its orthogonal neighbors are infected. For example, if the main diagonal is infected (above), then the infection will spread to the adjoining diagonals and on to the whole board. Prove that the whole board cannot become infected unless there are at least n sick squares at the start.

The key is to notice that when a square is infected, at least two of its edges are absorbed into the infected area, while at most two of its edges are added to the boundary of the infection. Thus the perimeter of the infected area can’t increase; in order for the full board (with perimeter 4n) to become infected, there must be at least n infected squares to begin with.

| Science & Math