Futility Closet

Three condemned prisoners share a cell. A guard arrives and tells them that one has been pardoned.

"Which is it?" they ask.

"I can't tell you that," says the guard. "I can't tell a prisoner his own fate."

Prisoner A takes the guard aside. "Look," he says. "Of the three of us, only one has been pardoned. That means that one of my cellmates is still sure to die. Give me his name. That way you're not telling me my own fate, and you're not identifying the pardoned man."

The guard thinks about this and says, "Prisoner B is sure to die."

Prisoner A rejoices that his own chance of survival has improved from 1/3 to 1/2. But how is this possible? The guard has given him no new information. Has he?

Colin Rose makes mathematical works of art:

Many more at his website.

Allen, Brown, and Carr run a shop. At least one of them must always be present to mind the shop, and when Allen leaves he always takes Brown with him.

This means that, if Carr were out, these statements would be true simultaneously:

1. If Allen is out then Brown is in (to mind the shop).
2. If Allen is out then Brown is out (because Allen always takes Brown with him).

This is a contradiction; they cannot be true together. Therefore, logically, Carr must always be in the shop.

(From Lewis Carroll.)

Suspend a metal coat hanger on a length of string, wrap the ends of the string around your index fingers, and insert your fingers in your ears. Now swing the hanger gently against the edge of table. What do you hear?

If the Earth did move at a tremendous speed, how could we keep a grip on it with our feet? We could walk only very, very slowly; and should find it slipping rapidly under our footsteps. Then, which way is it turning? If we walked in the direction of its tremendous speed, it would push us on terribly rapidly. But if we tried to walk against its revolving — ? Either way we should be terribly giddy, and our digestive processes impossible.

– Margaret Missen, The Sun Goes Round the Earth, quoted in Patrick Moore, Can You Speak Venusian?, 1972

In 1957 ornithologists marked a Manx shearwater, a migrating seabird, on Bardsey Island off Wales.

In April 2002 they discovered the same bird was still alive and still gamely flying to South America each winter.

In the intervening 45 years, they calculated, it had covered 5 million miles.

See also Longest Migration.

You'd pay $1,000 to witness my mastery of the black arts, wouldn't you? Of course you would.

1. Buy a brand-new deck of cards.
2. Discard the jokers, cut the deck 13 times, and deal it into 13 piles.
3. Now stand back … Ph'nglui mglw'nafh C'thulhu R'lyeh wgah'nagl fhtagn!
4. Look at the cards. Presto! They have magically grouped themselves by value — all the aces are in one pile, kings in another, etc.

You owe me $1,000.

In July 1838, Charles Darwin was considering whether to propose to his cousin, Emma Wedgwood. Ever the rationalist, drew up a balance sheet:

At the bottom he wrote "Marry – Marry – Marry Q.E.D." They were wed in January.

Donald Knuth is so revered among computer scientists that they won't cash his checks.

Knuth offers a standard reward of $2.56 (one "hexadecimal dollar") to the first finder of each error in his published books. Since 1981 he has written more than $20,000 in checks, but most of the recipients have simply framed them as points of pride.

"There's one man who lives near Frankfurt who would probably have more than $1,000 if he cashed all the checks I've sent him," Knuth said in an October 2001 lecture. "Even if everybody cashed their checks, it would still be more than worth it to me to know that my books are getting better."