In 1981, when science journalist Marcus Chown was an undergraduate physics student, his mother watched a profile of Richard Feynman on the BBC series Horizon. She had never shown an interest in science before, and he wanted to encourage her, so when he advanced to Caltech to study astrophysics, he told Feynman of his mother’s interest and asked him to send her a birthday note. She received this:

Happy Birthday Mrs. Chown!

Tell your son to stop trying to fill your head with science — for to fill your heart with love is enough!

Richard P. Feynman (the man you watched on BBC “Horizons”)

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.)

Party Planning

An Englishman buys a horse and hires porters to take the horse up to his apartment on the fourth floor. The porters exert themselves and sweat. Finally they succeed in getting the horse to his apartment.

He asks them to put the horse in the bathtub.

After they finish the job, one of the porters asks him, “Why do you need a horse in the bathtub?”

The Englishman says, “Well, tomorrow evening I’m having a party at home. One of the guests will go into the bathroom, see the horse, come to me and say, ‘You know you have a horse in your bathtub.’ And I’ll tell him, ‘So what?'”

— Sion Rubi, Intelligent Jokes, 2004

The Defenestrations of Prague

On July 30, 1419, Czech priest Jan Želivský was leading his congregation through the streets of Prague to protest corruption in the Catholic church when someone threw a stone at him from the window of the town hall. His followers stormed the hall and threw 13 members of the town council from a high window, killing them.

Remarkably, the same thing happened again in 1618, when King Ferdinand dissolved the Protestant estates in Bohemia. Aggrieved Protestants confronted Catholic officials in the chancellory and threw several of them from a third-floor window. All three survived — Catholics contended that they had been saved by angels, Protestants that they had landed on a dunghill. (Or, a reader suggests, “the Czechs bounced.”)

Black and White

meredith chess problem

By William Meredith. White to mate in two moves.

Click for Answer

Flip Sum

A problem from the 1999 St. Petersburg City Mathematical Olympiad:

Fifty cards are arranged on a table so that only the uppermost side of each card is visible. Each card bears two numbers, one on each side. The numbers range from 1 to 100, and each number appears exactly once. Vasya must choose any number of cards and flip them over, and then add up the 50 numbers now on top. What’s the highest sum he can be sure to reach?

Click for Answer

Out of This World

Tunisia has an unique tourist draw — its southern desert contains the abandoned sets of five Star Wars movies, in which the Sahara stood in for the planet Tatooine.

A list, complete with photos and geographical coordinates, is here.

They’re popular with European tourists, but they won’t last — the 20-building set of Mos Espa, Anakin Skywalker’s hometown, is being engulfed by sand dunes.

In a Word

v. the act or art of driving a chariot or coach

“When I Loved You”

When I loved you
And you loved me,
You were the sea,
The sky, the tree.

Now skies are skies,
And seas are seas,
And trees are brown
And they are trees.

— Charles A. Wagner


Male bees come from unfertilized eggs, so they have mothers but no fathers. Females come from fertilized eggs, so they have parents of both sexes. This produces an interesting pattern: The number of males in a given generation equals the number of females in the succeeding generation. And the number of females in a given generation equals the number of females in the succeeding two generations:

bee population

So the total number of bees, male and female, in generation n is the Fibonacci number Fn.

W. Hope-Jones discovered the relationship in 1921; this example is from Thomas Koshy’s Fibonacci and Lucas Numbers With Applications, 2001.