Heads and Tails

Let’s play a coin-flipping game. At stake is half the money in my pocket. If the coin comes up heads, you pay me that amount; if it comes up tails, I pay you.

Initially this looks like a bad deal for me. If the coin is fair, then on average we should expect equal numbers of heads and tails, and I’ll lose money steadily. Suppose I start with $100. If we flip heads and then tails, my bankroll will rise to $150 but then drop to $75. If we flip tails and then heads, then it will drop to $50 and then rise to $75. Either way, I’ve lost a quarter of my money after the first two flips.

Strangely, though, the game is fair: In the long run my winnings will exactly offset my losses. How can this be?

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It’s true that if the number of wins equals the number of losses, as expected, I’ll lose money. But the sequence of flips won’t always match our expectations so precisely — it may favor heads or tails. And when it favors heads, I’ll make a lot of money. Suppose we play four games in a row, with two flips per game, starting with $100: Here I lose fully 75 percent of the games we play — but my winnings are so great in the fourth case that they offset the whole foregoing series of (relatively small) losses. Such cases are rare, but they’re so lucrative that in the long run my bankroll is unchanged.

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August 28, 2012February 6, 2013 | Puzzles · Science & Math

Rules of Thumb

“If an elderly but distinguished scientist says that something is possible he is almost certainly right, but if he says that it is impossible he is very probably wrong.” — Arthur C. Clarke

“When, however, the lay public rallies around an idea that is denounced by distinguished but elderly scientists and supports that idea with great fervor and emotion — the distinguished but elderly scientists are then, after all, probably right.” — Isaac Asimov

August 28, 2012August 27, 2012 | Science & Math · Society

“Curious Accident”

On Monday last an accident of a singular but distressing nature happened to one of our townsmen. A pair of fanners were being conveyed in a cart along the road to the Whins, when, from some cause or other, the horse ran off. Mr. Drummond, millwright, the person who has met with the accident, at first stepped forward to stop the horse, but, fearing danger, started hastily back. Behind Mr. Drummond was a lad bearing an axe upon his shoulder. Upon the sharp edge of the instrument Mr. Drummond unfortunately ran, and the consequence was that his nose was very nearly cut off. So complete was the cut the nose fell over upon the mouth, and was suspended by the slightest portion of the integument. Mr Drummond instantly applied his handkerchief to his face, and proceeded to Dr. Brotherston, who was fortunately in his own house at the moment. As may be supposed, the sight was a hideous one, the accident presenting an insight into the interior of the face. We are happy to say that, under Dr. Brotherston’s judicious treatment, the nose has been replaced, and there is every hope of the cure being so effectual that scarcely any trace of the accident will by and by be visible.

— Alloa Advertiser, reprinted in the Times, Dec. 18, 1855

August 27, 2012August 26, 2012 | Oddities

The Leaning Virgin

On Jan. 15, 1915, a shell hit the Basilica of Notre-Dame de Brebières in Albert, France. Its crowning statue of Mary and the infant Jesus was flung forward and teetered over the building’s facade, but it did not fall.

“We went through the place today where the Virgin Statue at the top of the Church was hit by a shell in January,” wrote chaplain Rupert Edward Inglis to his wife in October. “The statue was knocked over, but has never fallen, I sent you a picture of it. It really is a wonderful sight. It is incomprehensible how it can have stayed there, but I think it is now lower than when the photograph was taken, and no doubt will come down with the next gale.”

But it didn’t. The virgin remained suspended over Albert for three years, during which British, French, and German forces all invented legends for it, commonly saying that the war would end when it finally fell. They were nearly right: The statue finally came down in April 1918, seven months before the armistice.

The basilica has since been rebuilt, and it bears a replica of the original statue.

August 27, 2012August 26, 2012 | History · Oddities

Connection

At 3:35 a.m. on Aug. 14, 1888, off the coast of Nova Scotia, Second Officer Jørgensen of the Danish steamer Geiser was asleep in his bunk when he was awakened by a “frightful crash.” As he rolled out of his bunk, the bow of another ship “crashed its way through the walls of my stateroom, making an enormous hole and blocking the door so I couldn’t get out.” Desperately he grabbed the anchor chain of the strange ship “and climbed up to her deck just as the Geiser gave one last lurch and went down out of sight, with her decks covered with shrieking, despairing people.”

He found himself aboard Geiser‘s sister ship Thingvalla, which had been plying the same line between New York and Copenhagen. In the stormy night, Thingvalla’s prow had struck Geiser amidships, and she sank in seven minutes. Thingvalla’s boats rescued 14 passenger and 17 crew, leaving 126 unaccounted for — most of the passengers died in their bunks.

See The “Miracle Girl.”

August 27, 2012August 26, 2012 | Oddities

The Paradox of Taste

It’s commonly said that beauty is in the eye of the beholder: In contemplating a work of art, the impressions we form are subjective, so all judgments should be equally valid.

“Beauty is no quality in things themselves,” writes David Hume. “It exists merely in the mind which contemplates them, and each mind perceives a different beauty. One person may even perceive deformity where another is sensible of beauty, and every individual ought to acquiesce in his own sentiment without pretending to regulate those of others.”

Why then do we account some tastes “good” and some “bad”? If I say I prefer John Ogilby to John Milton, “no one pays attention to such a taste; and we pronounce without scruple the sentiment of these pretended critics to be absurd and ridiculous.” But “the principle of the natural equality of tastes is then totally forgot, and while we admit it on some occasions where the objects seem near an equality, it appears an extravagant paradox, or rather a palpable absurdity, where objects so disproportioned are compared together.” Why?

August 26, 2012August 26, 2012 | Art

Unquote

“The image of myself which I try to create in my own mind in order that I may love myself is very different from the image which I try to create in the minds of others in order that they may love me.” — W.H. Auden

August 26, 2012August 25, 2012 | Quotations

Divine Mystery

A poem on transubstantiation by Luis de León, quoted by Robert Southey in Letters Written During a Short Residence in Spain and Portugal:

If this we see be bread, how can it last,
So constantly consum’d, yet always here?
If this be God, then how can it appear
Bread to the eye, and seem bread to the taste?
If bread, why is it worshipp’d by the baker?
If God, can such a space a God comprise?
If bread, how is it, it confounds the wise?
If God, how is it that we eat our Maker?
If bread, what good can such a morsel do?
If God, how is it we divide it so?
If bread, such saving virtue could it give?
If God, how can I see and touch it thus?
If bread, how could it come from heav’n to us?
If God, how can I look at it and live?

August 25, 2012August 24, 2012 | Poems · Religion

Enough

essex whale attack

On Nov. 20, 1820, the Nantucket whaler Essex was attacking a pod of sperm whales in the South Pacific when an immense 85-foot whale surfaced about 100 yards off the bow. It spouted two or three times, dove briefly, then charged and “struck the ship with his head just forward of the fore chains,” reported mate Owen Chase. “He gave us such an appalling and tremendous jar as nearly threw us all on our faces. The ship brought up as suddenly and violently as if she had struck a rock, and trembled for a few moments like a leaf. We looked at each other in perfect amazement, deprived almost of the power of speech.”

The whale passed under the ship and lay on the surface, stunned at first and then convulsing. Chase ordered men to the pumps and called back the boats, but as the Essex began to settle in the water a man called, “Here he is — he is making for us again.”

“I turned around, and saw him about one hundred rods directly ahead of us, coming down with apparently twice his ordinary speed, and to me it appeared with tenfold fury and vengeance in his aspect,” Chase wrote. “The surf flew in all directions, and his course towards us was marked by a white foam of a rod in width, which he made with a continual violent threshing of his tail.” The second blow stove in the Essex’s bows, and the whale “passed under the ship again, went off to leeward, and we saw no more of him.”

If this was vengeance, it was well accomplished. The Essex sank more than 1,000 miles from land; of the 21 crew who piled into three boats, only eight would survive, three on a barely habitable island and five after resorting to cannibalism during three months at sea. The whale acquired a further kind of immortality: Chase’s account of the disaster, written on his return to Massachusetts, helped inspire Herman Melville to write Moby-Dick.

August 25, 2012August 24, 2012 | Oddities

Black and White

“The Forlorn Hope,” by J. Paul Taylor, 1878. White to mate in two moves.

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The White King looked around, and noted how Our ranks were thinned and broken, so that now Our small successes were not worth the cost; And said, “We must resign, the day is lost!” “But not the Knight!” so spake a horseman brave: “My steed says neigh, the day we yet may save.” Then turned the King, and, frowning darkly, said: “Such jesting, good Sir Knight, may cost your head. He who would make a pun at such a time Is capable of any other crime; But one more chance I give you — Forward ride, And lead a hope forlorn. If good betide, Perhaps I may forgive you for the pun, And if you fall but little harm is done!” Forth spurred the Knight, regardless of his life, And rode at once where thickest raged the strife. To such a spot he dashed, that whilst he braved Five sorts of slaughter, still the day he saved; For should the foeman dare to lay him low, He leaves his King a prey to vassal’s blow; And should the King himself the victim slay, A priest steps in with stroke that none can stay; Whilst if they should decide to spare the Knight, And try to shield their Monarch from his might, They yet would fail, for still his falchion bright Descends with fell effect from left or right.