The Two-Envelope Paradox

Here are two envelopes. One contains twice as much money as the other. You must choose one, and then consider whether to keep it or exchange it for mine. Which should you do?

It would seem advantageous to switch: Depending on which envelope you started with, you’ll either lose a little or gain a lot. (If your unopened envelope contains $10, for example, the other must contain $5 or $20.)

So we trade envelopes and I offer you the same deal. But now the same reasoning applies, so it makes sense to trade again. Indeed, it seems reasonable to keep exchanging envelopes forever, without ever opening one. How can this be?

| Science & Math

And Many More

In 1891, Robert Louis Stevenson received a letter from a Vermont girl named Annie Ide. Her birthday fell on Christmas, she said, and she seldom received birthday presents.

He replied with a document decreeing that “I, Robert Louis Stevenson, … in consideration that Miss Annie H. Ide, … was born, out of all reason, upon Christmas Day, and is therefore out of all justice denied the consolation and profit of a proper birthday; and considering that I, the said Robert Louis Stevenson, have attained an age when we never mention it, and that I have now no further use for a birthday of any description; … HAVE TRANSFERRED, and DO HEREBY TRANSFER, to the said Annie H. Ide, ALL AND WHOLE my rights and privileges in the thirteenth day of November, formerly my birthday, now, hereby, and henceforth, the birthday of the said Annie H. Ide, to have, hold, exercise, and enjoy the same in the customary manner, by the sporting of fine raiment, eating of rich meats, and receipt of gifts, compliments, and copies of verse, according to the manner of our ancestors.”

He charged her to add “Louisa” to her name, “at least in private,” and to use the birthday “with moderation and humanity”—and he directed that if she neglected these conditions the birthday would revert to the president of the United States. She didn’t.

| Literature

“An Elephant’s Sagacity”

The stories illustrating the sagacity of the elephant are innumerable; but few are more remarkable than the following one recorded by a writer in a Bombay paper upon the authority of an artillery officer, who was a witness of the incident:– The battering train was going to the siege of Seringapatam, when an artilleryman, who was seated on the tumbril of one of the guns, by some accident fell almost directly under the hind wheel. The elephant stationed behind the gun, perceiving the man’s danger, instantly, without any order from its keeper, lifted up the wheel with its trunk, and kept it suspended till the carriage had passed clear of him.

— Henry Williams, A Book of Curious Facts, 1903

| Oddities

Romance at Short Notice

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Bata Kindai Amgoza ibn LoBagola told an inspiring story: Born in West Africa, he wandered to the sea at age 7 and found himself aboard a steamer bound for Scotland. From there he made his way to the United States, where he took up lecturing. His 1930 autobiography, LoBagola; An African Savage’s Own Story, gives vivid details about life in the bush:

“If you should climb a tree, the lion can easily get help from the elephant, because the elephant and the lion are friendly. … [T]he lion tells the elephant that it wants you down from the tree, and the elephant shakes the tree or pulls it up by the roots, and down you come.”

The truth was more prosaic: His real name was Joseph Lee and he was born in Baltimore. “Small opportunities,” wrote Demosthenes, “are often the beginning of great enterprises.”

| Hoaxes

Mind Games

  • Déjà vu — the feeling of having seen an unfamiliar thing previously
  • Déjà vécu — the feeling of having experienced an unfamiliar situation previously
  • Déjà visité — unaccountable knowledge of an unfamiliar place
  • Déjà senti — a sense of “recollection” of an unfamiliar idea
  • Jamais vu — a sense of unfamiliarity with a familiar situation
  • Presque vu — inability to summon a familiar word

Visiting a ruined English manor in 1856, Nathaniel Hawthorne felt “haunted and perplexed” by the idea that he had seen it before. He later realized that Alexander Pope had written a poem about it nearly 100 years earlier.

| Oddities

Termespheres

Dick Termes paints murals on spheres. And he does it with a unique “six-point” perspective technique that permits a remarkable optical illusion.

As you watch this video, try to convince yourself that the front half of the sphere is transparent and that the mural is painted on the concave interior of the farther side — that is, that you’re standing in the center of the pictured room and turning in place to your left. If you succeed, the spin will seem to reverse direction and you’ll find yourself inside the painting:

| Art

Unquote

“Have a place for everything and keep the thing somewhere else. This is not advice, it is merely custom.” — Mark Twain

| Quotations

“Mirage Seen at Buffalo, N. Y.”

The people of Buffalo, N. Y., were treated to a remarkable mirage, between ten and eleven o’clock, on the morning of August 16, 1894. It was the city of Toronto with its harbor and small island to the south of the city. Toronto is fifty-six miles from Buffalo, but the church spires could be counted with the greatest ease. The mirage took in the whole breadth of lake Ontario, Charlotte, the suburbs of Rochester, being recognized as a projection east of Toronto. A side-wheel steamer could be seen traveling in a line from Charlotte to Toronto Bay. Two dark objects were at last found to be the steamers of the New York Central plying between Lewiston and Toronto. A sail-boat was also visible and disappeared suddenly. Slowly the mirage began to fade away, to the disappointment of thousands who crowded the roofs of houses and office buildings. … A close examination of the map showed the mirage did not cause the slightest distortion, the gradual rise of the city from the water being rendered perfectly. It is estimated that at least 20,000 spectators saw the novel spectacle.

— Scientific American, Aug. 25, 1894, quoted in Miscellaneous Notes & Queries

| Oddities

The Wreck of the Titan

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Art doesn’t just imitate life — sometimes it anticipates it. Fourteen years before the Titanic was built, the American Morgan Robertson wrote a novel called The Wreck of the Titan that prefigured the real ship’s destiny with remarkable precision.

The Titanic and the Titan were both triple-screwed British passenger liners with a capacity of 3,000 and a top speed of 24 knots. Both were deemed unsinkable; both carried too few lifeboats. And both sank in April in the North Atlantic after colliding with an iceberg on the forward starboard side.

In another novel, Beyond the Spectrum (1914), Robertson forecast a war between the United States and Japan, including a Japanese sneak attack (on San Francisco). There’s no way to know what more he had in store — he died the following year.

| Literature · Oddities