Presence of Mind

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Science teacher Lawrence Beesley was reading a book in his cabin on the Titanic when the engines stopped. Wandering the ship, he heard that an iceberg had passed by but found nothing amiss. But as he was returning to his cabin he noticed something unusual:

As I passed to the door to go down, I looked forward again and saw to my surprise an undoubted tilt downwards from the stern to the bows: only a slight slope, which I don’t think any one had noticed, — at any rate, they had not remarked on it. As I went downstairs a confirmation of this tilting forward came in something unusual about the stairs, a curious sense of something out of balance and of not being able to put one’s feet down in the right place: naturally, being tilted forward, the stairs would slope downwards at an angle and tend to throw one forward. I could not see any visible slope of the stairway: it was perceptible only by the sense of balance at this time.

When the crew began to summon passengers, he returned to A Deck and was accepted on a lifeboat.

(From his 1912 book The Loss of the S.S. Titanic.)

| History

Ground Rules

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Articles of the pirate ship Revenge, captain John Phillips, 1723:

  1. Every man shall obey a civil command. The captain shall have one share and a half of all prizes. The master, carpenter, boatswain and gunner shall have one share and [a] quarter.
  2. If any man shall offer to run away or keep any secret from the company, he shall be marooned with one bottle of powder, one bottle of water, one small arm and shot.
  3. If any man shall steal anything in the company or game to the value of a piece-of-eight, he shall be marooned or shot.
  4. If at any time we should meet another marooner [pirate], that man that shall sign his articles without the consent of our company shall suffer such punishment as the captain and company shall think fit.
  5. That man that shall strike another whilst these articles are in force shall receive Moses’s Law (that is, forty stripes lacking one) on the bare back.
  6. That man that shall snap his arms or smoke tobacco in the hold without a cap on his pipe, or carry a candle lighted without a lantern, shall suffer the same punishment as in the former article.
  7. That man that shall not keep his arms clean, fit for an engagement, or neglect his business, shall be cut off from his share and suffer such other punishment as the captain and the company shall think fit.
  8. If any man shall lose a joint in time of an engagement, he shall have 400 pieces-of-eight. If a limb, 800.
  9. If at any time we meet with a prudent woman, that man that offers to meddle with her without her consent, shall suffer present death.

That’s from Charles Johnson’s General History of the Pyrates, 1724. It’s one of only four surviving sets of articles from the golden age of piracy.

Phillips lasted less than eight months as a pirate captain but captured 34 ships in the West Indies.

| Crime · History · Society

“The Cage Without Birds”

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Felix does not understand how people can keep birds in cages.

‘It’s a crime,’ he says, ‘like picking flowers. Personally, I’d rather sniff them on their stems — and birds are meant to fly, the same way.’

Nonethless he buys a cage, hangs it in his window. He puts a cotton-wool nest inside, a saucer of seeds, and a cup of clean, renewable water. He also hangs a swing in the cage, and a little mirror.

And when he is questioned with some surprise:

‘I pride myself on my generosity,’ he says, ‘each time I look at that cage. I could put a bird in there, but I leave it empty. If I wanted to, some brown thrush, some fat bullfinch hopping around outside, or some other bird of all the kinds we have here would be a captive. But thanks to me, at least one of them remains free. There’s always that …’

— Jules Renard, Les Histoires Naturelles, 1896

| Literature

Person to Person

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The president of a 100-member society receives word that the meeting place must be changed, and he needs to inform the rest of the members. He starts a telephone tree: He informs three members, each of whom informs another three members, and so on until all 100 members have received the news. Using this method, what is the greatest number of members who don’t have to make a call?

Click for Answer
| Puzzles

Blackwell’s Bet

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Two envelopes contain unequal sums of money (for simplicity, assume the two amounts are positive integers). The probability distributions are unknown. You choose an envelope at random, open it, and see that it contains x dollars. Now you must predict whether the total in the other envelope is more or less than x.

Since we know nothing about the other envelope, it would seem we have a 50 percent chance of guessing correctly. But, El Camino College mathematician Leonard Wapner writes, “Unexpectedly, there is something you can do, short of opening the other envelope, to give yourself a better than even chance of getting it right.”

Choose a random positive integer, d, by any means at all. (If d = x then choose again until this isn’t the case.) Now if d > x, guess more, and if d < x, guess less. You’ll guess correctly more than 50 percent of the time.

How is this possible? The random number is chosen independently of the envelopes. How can it point in the direction of the unknown y most of the time? “Think of it this way,” writes Wapner. “If d falls between x and y then your prediction (as indicated by d) is guaranteed to be correct. Assume this occurs with probability p. If d falls less than both x and y, then your prediction will be correct only in the event your chosen number x is the larger of the two. There is a 50 percent chance of this. Similarly, if d is greater than both numbers, your prediction will be correct only if your chosen number is the smaller of the two. This occurs with a 50 percent probability as well.”

So, on balance, your overall probability of being correct is

\displaystyle p + \left ( 1 - p \right )\left ( \frac{1}{2} \right ) = \frac{1}{2} + \frac{p}{2}

That’s greater than 0.5, so the odds are in favor of your making a correct prediction.

This example is based on a principle identified by Stanford statistician David Blackwell. “It’s unexpected and ironic that an unrelated random variable can be used to predict that which appears to be completely unpredictable.”

(Leonard M. Wapner, Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball, 2012, following David Blackwell, “On the Translation Parameter Problem for Discrete Variables,” Annals of Mathematical Statistics 22:3 [1951], 393–399.)

| Science & Math

Podcast Episode 111: Japanese Fire Balloons

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Toward the end of World War II, Japan launched a strange new attack on the United States: thousands of paper balloons that would sail 5,000 miles to drop bombs on the American mainland. In this week’s episode of the Futility Closet podcast, we’ll tell the curious story of the Japanese fire balloons, the world’s first intercontinental weapon.

We’ll also discuss how to tell time by cannon and puzzle over how to find a lost tortoise.

See full show notes …

| History · Podcast

Talking

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Excerpt of a letter from British general Philip Howele to his wife, Sept. 15, 1915:

It is VILE that all my time should be devoted to killing Germans whom I don’t in the least want to kill. If all Germany could be united in one man and he and I could be shut up together just to talk things out, we could settle the war, I feel, in less than one hour. The ideal war would include long and frequent armistices during which both sides could walk across the trenches and discuss their respective points of view. We are really only fighting just because we are all so ignorant and stupid. And if diplomats were really clever such a thing as war could never be. Shall I desert and see if any of them will listen on the other side? My little German officer was rather flabbergasted when the first question I asked him the other morning, when the escort had gone out and shut the door, and after I’d put him in a comfortable chair and given him a cigarette, was, ‘Now first of all do you really hate me, and if so why?’ He said he didn’t. But then later, when I asked him what we could possibly do to stop all this nonsense, he had no suggestions to make. ‘I have my ideas’ he said but somehow couldn’t express them.

Goodnight … and bless you.

P.

| History · Society

Application

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Victor Hugo wrote The Hunchback of Notre-Dame under enormous financial pressure, leaving his table only to eat or sleep.

Finally, his daughter Adèle wrote, “On 14 January, [Notre-Dame] was finished. The bottle of ink that M. Victor Hugo had bought the first day was finished also; he had arrived in the same moment at the last line and at the last drop.

“This gave him, in that moment, the idea of changing his title and calling his novel: What There Is in a Bottle of Ink.”

| Literature