The War of the Ring

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Of The Lord of the Rings, W.H. Auden wrote, “I rarely remember a book about which I have had such violent arguments. Nobody seems to have a moderate opinion: either, like myself, people find it a masterpiece of its genre or they cannot abide it.”

Among the naysayers, Edmund Wilson wrote, “One is puzzled to know why the author should have supposed he was writing for adults. There are, to be sure, some details that are a little unpleasant for a children’s book, but except when he is being pedantic and also boring the adult reader, there is little in The Lord of the Rings over the head of a seven-year-old child.”

Tolkien seemed philosophical about the difference. He wrote in the foreword to the second edition:

The prime motive was the desire of a tale-teller to try his hand at a really long story that would hold the attention of readers, amuse them, delight them, and at times maybe excite them or deeply move them. As a guide I had only my own feelings for what is appealing or moving, and for many the guide was inevitably often at fault. Some who have read the book, or at any rate have reviewed it, have found it boring, absurd, or contemptible; and I have no cause to complain, since I have similar opinions of their works, or of the kinds of writing that they evidently prefer.

He wrote elsewhere:

The Lord of the Rings
is one of those things:
if you like it you do:
if you don’t, then you boo!

| Literature

Podcast Episode 112: The Disappearance of Michael Rockefeller

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In 1961, Michael Rockefeller disappeared after a boating accident off the coast of Dutch New Guinea. Ever since, rumors have circulated that the youngest son of the powerful Rockefeller family had been killed by the headhunting cannibals who lived in the area. In this week’s episode of the Futility Closet podcast, we’ll recount Rockefeller’s story and consider the different fates that might have befallen him.

We’ll also learn more about the ingenuity of early sportscasters and puzzle over a baffled mechanic.

See full show notes …

| Oddities · Podcast

The Tipping Point

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English meteorologist Lewis Fry Richardson (1881-1953) spent the last 25 years of his life trying to establish a mathematical theory of the causes of war. In the first of two books on this subject, Arms and Insecurity, he works out a model of arms races using differential equations and reaches the conclusion that

\frac{d\left ( U + V \right )}{dt}=\left ( k - \alpha \right )\left \{ U + V - \left [ U_{0} + V_{0} - \frac{g + h}{k - \alpha } \right ] \right \}

where:

U and V are the annual defense budgets of two parties to a conflict

k is a positive constant representing the response to threat

α is a positive constant representing the fatigue and expense of keeping up defenses

U0 and V0 represent cooperations between the parties, tentatively assumed to remain constant

and g and h represent the “grievances and ambitions, provisionally regarded as constant,” on each side.

The term in brackets is a constant, so Richardson predicted that plotting d(U + V)/dt against (U + V) would produce a straight line. He tried this out using the defense budgets of the Franco-Russian and Austro-German alliances for 1909-14 and got this:

richardson defense budgets

“The four points lie close to a straight line, closer, indeed, than one might expect,” he writes. “Since I first drew this diagram, which was shown at the British Association in Cambridge in 1938, and printed in Nature of 29 October of that year, I have been incredulous about the marvelously good fit. Yet there is no simple mistake. … The mere regularity of these phenomena shows that foreign politics had then a rather machine-like quality, intermediate between the predictability of the moon and the freedom of an unmarried young man.”

The extrapolated straight line hits the x axis at U + V = £194 pounds sterling. “As love covereth a multitude of sins, so the good will between the opposing alliances would just have covered £194 million of defense expenditures on the part of the four nations concerned. Their actual expenditure in 1909 was £199 millions; and so began an arms race which led to World War I.”

(Lewis F. Richardson, Arms and Insecurity, 1949.)

| History · Science & Math

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