Podcast Episode 76: Get Out of Jail Free

https://commons.wikimedia.org/wiki/File:German_Monopoly_board_in_the_middle_of_a_game.jpg
Image: Wikimedia Commons

During World War II, the British Secret Service found a surprising way to help Allies in Nazi prisoner-of-war camps: They used doctored Monopoly sets to smuggle in maps, files, compasses, and real money. In this week’s episode of the Futility Closet podcast we’ll tell the story behind this clever ploy, which may have helped thousands of prisoners escape from Nazi camps.

We’ll also hear listeners’ thoughts on Jeremy Bentham’s head, Victorian tattoos, and phone-book-destroying German pirates and puzzle over murderous cabbies and moviegoers.

See full show notes …

| Podcast

Easy Pi

Here’s a simple algorithm that Yoshiaki Tamura and Yasumasa Kanada used to calculate π to 16 million places. It’s based on Gauss’ study of the arithmetic-geometric mean of two numbers. “Instead of using an infinite sum or product, the calculation goes round and round in a loop,” writes David Wells in The Penguin Dictionary of Curious and Interesting Numbers. “It has the amazing property that the number of correct digits approximately doubles with each circuit of the loop.” Start with these values:

\mathrm{A}=1
\mathrm{X}=1
\mathrm{B}=1/\sqrt{2}
\mathrm{C}=1/4

Then follow these instructions:

\textrm{Let}\: \mathrm{Y}=\mathrm{A}

\textrm{Let}\: \mathrm{A}=\displaystyle\frac{\mathrm{A}+\mathrm{B}}{2}

\textrm{Let}\: \mathrm{B}=\sqrt{\mathrm{BY}}

\textrm{Let}\: \mathrm{C}=\mathrm{C}-\mathrm{X}(\mathrm{A}-\mathrm{Y})^{2}

\textrm{Let}\: \mathrm{X}=2\mathrm{X}

\textrm{PRINT}\: \displaystyle\frac{\left ( {\mathrm{A}+\mathrm{B}} \right )^{2}}{{4\mathrm{C}}}

The last instruction prints the first approximation to π; then you loop up to the top and run through the instructions again.

Running through the loop just three times gives an approximation to π that’s already correct to 5 decimal places:

Loop 1: 2.9142135
Loop 2: 3.1405797
Loop 3: 3.1415928

And running the loop a mere 19 times gives π correct to more than 1 million decimal places.

| Science & Math

Worldly Wise

Proverbs from around the world:

  • A pretty basket does not prevent worries. (Congo)
  • Good painters need not give a name to their pictures; bad ones must. (Poland)
  • Sickness comes riding on horseback and goes away on foot. (Belgium)
  • The spectator is a great hero. (Afghanistan)
  • Those who have to go ten miles must regard nine as only halfway. (Germany)
  • The world is dark an inch ahead. (Japan)
  • Those who place their ladder too steeply will easily fall backward. (Czech Republic)
  • All the wealth of the world is in the weather. (Scotland)
  • Those whose mother is naked are not likely to clothe their aunt. (Sudan)
  • To be in the habit of no habit is the worst habit in the world. (Wales)
  • What is bad luck for one is good luck for another. (Ghana)
  • Good luck is the guardian of the stupid. (Sweden)
  • A change is as good as a rest. (England)
  • Good scribes are not those who write well, but who erase well. (Russia)
  • There is no such thing as a pretty good omelette. (France)
  • Of all the thirty-six alternatives, running away is the best. (China)
| Quotations

Paperwork

https://en.wikipedia.org/wiki/File:Delian_origami.svg
Image: Wikimedia Commons

Three ancient problems are famously impossible to solve using a compass and straightedge alone: doubling the cube, trisecting an angle, and squaring the circle. Surprisingly, the first two of these can be solved using origami.

In the first, doubling the cube, we’re given the edge of one cube and asked to find the edge of a second cube whose volume is twice that of the first; if the first cube’s edge length is 1, then we’re trying to find \sqrt[3]{2}. Begin by folding a square of paper into three equal panels (here’s how). Then draw up bottom corner P as shown above, so that it’s touching the top edge while the bottom of the first crease, Q, touches the second crease as shown. Now point P divides the top edge into two segments whose proportions are 1 and \sqrt[3]{2}.

https://en.wikipedia.org/wiki/File:Origami_Trisection_of_an_angle.svg
Image: Wikimedia Commons

To trisect an angle, begin by marking the angle in one corner of a square (here’s it’s CAB). Make a horizontal fold, PP’, anywhere across the square. Then divide the space below this crease in half with another crease, QQ’. Fold the bottom left corner up so that corner A touches QQ’ (at A’) and P touches AC. Now A’AB is one-third of the original angle, CAB.

The first of these constructions is due to Peter Messer, the second to Hisashi Abe. Strictly speaking, each uses creases to produce a marked straightedge, which is not allowed in classical construction, but they’re pleasingly simple solutions to these vexing problems. There’s more at origami wizard Robert Lang’s website.

| Science & Math

Cruel and Unusual

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A king is angry at two mathematicians, so he decrees the following punishment. The mathematicians will be imprisoned in towers at opposite ends of the kingdom. Each morning, a guard at each tower will flip a coin and show the result to his prisoner. Each prisoner must then guess the result of the coin flip at the other tower. If at least one of the two guesses is correct, they will live another day. But as soon as both guesses are incorrect, they will be executed.

On the way out of the throne room, the mathematicians manage to confer briefly, and they come up with a plan that will spare them indefinitely. What is it?

Click for Answer
| Puzzles

Absent Fiends

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The nonexistence of horrific creatures is, so to speak, not only a fact, but it would also appear to be a fact that is readily available to and acknowledged by the consumers of horrific fictions. However, audiences do appear to be frightened by horror fictions; indeed, they would seem to seek out such fictions, at least in part, either in order to be frightened by them or with the knowledge and assent that they are likely to be frightened by them. But how can one be frightened by what one knows does not exist?

— Noël Carroll, The Philosophy of Horror, 1990

| Oddities

In a Word

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manuductory
adj. that leads by or as by the hand

ante-ambulate
v. to walk before, as an usher

oxter
v. to support by the arm, walk arm in arm with; to take or carry under the arm; to embrace, put one’s arm around

| Language

The Agony Column

In the summer of 1977, a disconcerting series of personal advertisements began appearing in the London Times:

DR. MOREAU requires lab. assistant. Experience not necessary. Strong stomach.

DR. MOREAU seeks Harley St. offices. Soundproofing essential.

HEART OF BABOON, eye of newt and other spare parts required by Dr. Moreau.

QUESTION for Dr. Moreau: What do you do with the leftovers?

WERE YOU cut out to be a patient of Dr. Moreau?

DON’T MAKE a pig of yourself without consulting Dr. Moreau.

DR. MOREAU will have you in stitches.

DR. MOREAU goes in one ear and out the other.

I’M JUST WILD about Dr. Moreau. He has so much animal magnetism.

IF YOU WANT TO GET AHEAD see Dr. Moreau.

OVERWEIGHT? Dr. Moreau will cut you down to size.

ARE YOU A MAN – or a mouse? Get an expert opinion from Dr. Moreau.

DR. MOREAU made a monkey out of me. See what he can do for you.

LEND a hand to Dr. Moreau and you’ll never get it back.

DR. MOREAU does brain transplants while you wait.

UNFORTUNATELY Dr. Moreau’s services are not available on the National Health.

DR. MOREAU is coming soon. Can’t you feel it in your bones?

The last one appeared on Sept. 3. American International Pictures’ production of The Island of Dr. Moreau, starring Burt Lancaster and Michael York, opened later that month.

(From Peter Haining, The H.G. Wells Scrapbook, 1978.)

| Entertainment

A New Angle

liu problem

I just ran across this in an old Math Horizons article — Andy Liu, vice president of the International Mathematics Tournament of the Towns, calls it “one all-time favorite geometric gem.” Given the four angles shown, compute angle CAD. “It sounds like a trivial exercise at first, and therein lies its charm.”

Liu doesn’t give the solution, but he does give a hint — I’ll put that in a spoiler box in case you want to work on the problem first.

Click for Answer
| Science & Math

Wanted

Items requested in the 2000 Baylor College Linguistic Scavenger Hunt:

  1. the word for “cheese” in Estonian
  2. the longest word in English that uses no letter more than once
  3. a nine-letter English word that has only one syllable
  4. the sound that a dog makes in Swedish
  5. the regional word for “drinking fountain” that’s used in Wisconsin
  6. the language that Jesus spoke
  7. the American equivalent of the British word “ex-directory”
  8. five words that are legal plays in Scrabble and that have only two letters, one of which is “x”
  9. the motto of the Klingon Language Institute
  10. identity of the person who said, “England and America are two countries divided by a common language.”
Click for Answer
| Language · Puzzles