The Centipede Game

Before you are two piles of coins. One contains 4 coins and the other contains 1. If you like, you can keep the larger pile, give me the smaller, and end the game. Or you can pass both piles to me. In that case the size of each pile doubles and I’m given the same option — I can keep the larger pile and give you the smaller one, or I can pass both piles back to you, in which case they’ll double again.

We both know that the game will end after six rounds. At that point I’ll have the coins and will win 128 coins to your 32. You’d be better off stopping the game in round 5, when you’ll have 64 coins and I have 16. But, by similar reasoning, I’d prefer round 4 to round 5, and you’d prefer round 3 to round 4 … if we rely on each other to be purely rational, it seems your best opening move is to end the game at once and keep 4 coins. This is less than you’d make in round 6, but it appears that purely rational play will never reach that round.

In practice, interestingly, human beings don’t do this — almost no one stops at the first opportunity, even after several repetitions of the game. Why they do so is not clear — possibly they’re hoping that their opponent has not reasoned through the whole game, or perhaps they’re agreeing tacitly to cultivate the pot in hopes of being the first one to cash out abruptly; perhaps the satisfaction of anticipating such a victory makes the risk worthwhile.

In lab tests in 2009, economists Ignacio Palacios-Huerta and Oscar Volij found that only 3 percent of games between students ended in the first round, but 69 percent of games between chess players did so. This rose to 100 percent when the first player was a grandmaster. They conclude that the most important factor is common knowledge of the players’ rationality, rather than altruism or social preferences.

(Ignacio Palacios-Huerta and Oscar Volij, “Field Centipedes,” American Economic Review 99 (4): 1619–1635.)

The Little Man

In 1525, more than 100,000 German peasants demanded an end to serfdom and were massacred by the well-organized armies of the ruling class. After observing the ornate memorials with which the aristocrats congratulated themselves, Albrecht Dürer proposed a similarly baroque monument to the slain peasants:

Place a quadrangular stone block measuring ten feet in width and four feet in height on a quadrangular stone slab which measures twenty feet in length and one foot in height. On the four corners of the ledge place tied-up cows, sheep, pigs, etc. But on the four corners of the stone block place four baskets, filled with butter, eggs, onions, and herbs, or whatever you like. In the centre of this stone block place a second one, measuring seven feet in length and one foot in height. On top of this second block place a strong chest four feet high, measuring six and a half feet wide at the bottom and four feet wide at the top. Then place a kettle upside down on top of the chest. The kettle’s diameter should be four and a half feet at the rim and three feet at its bottom. Surmount the kettle with a cheese bowl which is half a foot high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and has a diameter of a foot and a half at the bottom, and of only a foot at the top. Its spout should protrude beyond this. On the top of the butter keg, place a well-formed milk jug, two and a half feet high, and with a diameter which is one foot at its bulge, half a foot at its top, and is wider at its bottom. Into this jug put four rods branching into forks on top and extending five and a half feet in height, so that the rods will protrude by half a foot, and then hang peasants’ tool on it – like hoes, pitchforks, flails, etc. The rods are to be surmounted by a chicken basket, topped by a lard tub upon which sits an afflicted peasant with a sword stuck into his back.

What would that look like?

durer peasants memorial

Beyond the Pale

Expressions banned from use in New Zealand parliamentary debate:

1933
Blowfly-minded

1943
Retardate worm

1946
Clown of the House
Idle vapourings of a mind diseased
I would cut the honourable gentleman’s throat if I had the chance

1949
His brains could revolve inside a peanut shell for a thousand years without touching the sides

1957
Kind of animal that gnaws holes

1959
Member not fit to lick the shoes of the Prime Minister

1963
Energy of a tired snail returning home from a funeral

1966
Shut up yourself, you great ape
Snotty-nosed little boy
You are a cheap little twerp
Ridiculous mouse

1974
Could go down the Mount Eden sewer and come up cleaner than he went in
Dreamed the bill up in the bath
Frustrated warlord

The full list is here. In brighter news, saying that a fellow member “scuttles for his political funk hole” was deemed allowable in 1974.

Round and Round

Since demolishing 78 traffic signals and installing 80 roundabouts, the northern Indiana city of Carmel has reduced the number of accidents by 40 percent and the number of accidents with injuries by 78 percent.

“It’s nearly impossible to have a head-on or T-bone collision when using the roadways, and collisions that do happen tend to occur at much lower speeds,” noted Governing magazine. “Other benefits of roundabouts include reduced fuel consumption, due to a lack of idling, and a construction cost that is at least $150,000 less than installing traffic lights.”

“We have more than any other city in the U.S.,” says mayor James Brainard. “It’s a trend now in the United States. There are more and more roundabouts being built every day because of the expense saved and, more importantly, the safety.”

Green Peace

http://commons.wikimedia.org/wiki/File:CAB_1918_Carnegie_Andrew.jpg

In December 1868, having just turned 33, Andrew Carnegie sat down in New York’s St. Nicholas Hotel and wrote a memo to himself. His net worth was $400,000, and with prudent management he could expect $50,000 in dividends each year for the rest of his life. “Beyond this never earn,” he resolved. “Make no effort to increase fortune, but spend the surplus each year for benevolent purposes. Cast aside business forever except for others.”

Man must have an idol — The amassing of wealth is one of the worst species of idolatry. No idol more debasing than the worship of money. Whatever I engage in I must push inordinately therefor should I be careful to choose that life which will be the most elevating in its character. To continue much longer overwhelmed by business cares and with most of my thoughts wholly upon the way to make more money in the shortest time, must degrade me beyond hope of permanent recovery.

He kept the memo for the rest of his life, and by the time of his death in 1919 he had given away $350,695,650, nearly $5 billion today, endowing universities, museums, libraries, and initiatives to support science, the arts, and world peace. “The man who dies rich, dies disgraced,” he wrote. “Money can only be the useful drudge of things immeasurably higher than itself. … Mine be it to have contributed to the enlightenment and the joys of the mind, to the things of the spirit, to all that tends to bring into the lives of the toilers of Pittsburgh sweetness and light. I hold this the noblest possible use of wealth.”

Far From Home

Two or three of them got round me and begged me for the twentieth time to tell them the name of my country. Then, as they could not pronounce it satisfactorily, they insisted that I was deceiving them, and that it was a name of my own invention. One funny old man, who bore a ludicrous resemblance to a friend of mine at home, was almost indignant. ‘Ung-lung!’ said he, ‘who ever heard of such a name? — ang-lang — anger-lang — that can’t be the name of your country; you are playing with us.’ Then he tried to give a convincing illustration. ‘My country is Wanumbai — anybody can say Wanumbai. I’m an ‘orang-Wanumbai; but, N-glung! who ever heard of such a name? Do tell us the real name of your country, and then when you are gone we shall know how to talk about you.’

— Alfred Russel Wallace, “The Aru Islands,” The Malay Archipelago, 1869

Quick Thinking

commons.wikimedia.org/wiki/File:Straßenkämpfe_in_Rouen_1859.jpg

During one of the many nineteenth-century riots in Paris the commander of an army detachment received orders to clear a city square by firing at the canaille (rabble). He commanded his soldiers to take up firing positions, their rifles leveled at the crowd, and as a ghastly silence descended he drew his sword and shouted at the top of his lungs: ‘Mesdames, m’sieurs, I have orders to fire at the canaille. But as I see a great number of honest, respectable citizens before me, I request that they leave so that I can safely shoot the canaille.’ The square was empty in a few minutes.

— American psychiatrist Paul Watzlawick, Change: Principles of Problem Formation and Problem Resolution, 1974

Land Under England

In 1862, journalist John Hollingshead accompanied a crew of workers into the sewers under London, “feeling a desire to inspect a main sewer almost from its source to its point of discharge into the Thames.” At one point he asked his guides about the unusual things they had found underground.

‘Well,’ he said, ‘the most awful things we ever find in the sewers is dead children. We’ve found at least four of ’em at different times; one somewhere under Notting Hill; another somewhere under Mary’bone; another at Paddington; and another at the Broadway, Westminster.’

‘We once found a dead seal,’ struck in one of the men pushing the boat.

‘Ah,’ continued Agrippa, ‘so we did. That was in one of the Westminster sewers — the Horseferry Road outlet, I think, and they said it had been shot at Barnes or Mortlake, and had drifted down with the tide. … We sometimes find live cats and dogs that have got down untrapped drains after house-rats; but these animals, when we pick ’em up, are more often dead ones.’

‘They once found a live hedgehog in Westminster,’ said another of the men. ‘I’ve heard tell on it, but I didn’t see it.’

At one point, on being told he was beneath Buckingham Palace, “Of course my loyalty was at once excited, and, taking off my fan-tailed cap, I led the way with the National Anthem, insisting that my guides should join in chorus. Who knows but what, through some untrapped drain, that rude but hearty underground melody found its way into some inner wainscoting of the palace, disturbing some dozing maid of honour with its mysterious sounds, and making her dream of Guy Fawkes and many other subterranean villains?”

Open and Shut

In 1917 Ben Hecht and Maxwell Bodenheim agreed to debate one another before a Chicago literary society. They chose the topic “Resolved: That People Who Attend Literary Debates Are Imbeciles.”

Hecht took the podium, surveyed the crowd, and said, “The affirmative rests.”

Bodenheim rose and said, “You win.”

Cheap Grace

From an undated letter from Benjamin Franklin to Anne Louise Brillon:

A Beggar asked a rich Bishop for Charity, demanding a pound. — ‘A Pound to a beggar! That would be extravagant.’ — ‘A Shilling then!’ — ‘Oh, it’s still too much!’ — ‘A twopence then or your Benediction.’ — ‘Of course, I will give you my Benediction.’ — ‘I don’t want it, for if it were worth a twopence, you wouldn’t give it me.’

Elsewhere Franklin wrote, “I would rather have it said, ‘He lived usefully’ than ‘He died rich.'”