Crescent Lake

Six kilometers south of Dunhuang in western China lies Crescent Lake, an oasis that once served as a waypoint to the West along the Silk Road. British missionaries Mildred Cable and Francesca French recorded their first sight of it during their travels through the Gobi Desert in the 1920s:

All around us we saw tier on tier of lofty sand-hills, giving the lie to our quest, yet when, with a final desperate effort, we hoisted ourselves over the last ridge and looked down on what lay beyond, we saw the lake below, and its beauty was entrancing.

The lake survived for 2,000 years thanks to its low altitude and sheltered position, but it began to shrink in the 20th century due to population pressures — its depth dropped from 7.5 to 0.9 meters between 1960 and the early 1990s. In 2006 the government stepped in to reverse the decline, and now it’s growing again.

(Via eMORFES.)

Peace and Quiet

Ohio inventor Philip Clover came up with a dramatic way to discourage body snatchers in 1878: a “coffin torpedo.” Basically a live cartridge is attached to the body by hidden wires so that “any attempt to remove the body after burial will cause the … injury or death of the desecrator of the grave”:

The trigger-wires are secured to the arms, legs, or other portion of the body of the corpse in such manner as to induce to the tripping of the trigger should any attempt be made to withdraw the body from the casket. The torpedo is loaded … just prior to the final closing of the casket.

“The torpedo may be placed in variable positions within the casket, and properly concealed by the trimmings of the casket or the apparel of the corpse.” Clover points out that there’s no need to protect the weapon from the elements — by the time it ceases to work, “the body would be of no use to robbers.”

Podcast Episode 154: Spared by a Volcano

The worst volcanic disaster of the 20th century struck Martinique in 1902, killing 30,000 people in the scenic town of Saint-Pierre. But rescuers found one man alive — a 27-year-old laborer in a dungeon-like jail cell. In this week’s episode of the Futility Closet podcast we’ll meet Ludger Sylbaris, who P.T. Barnum called “The Only Living Object That Survived in the Silent City of Death.”

We’ll also address some Indian uncles and puzzle over a gruesome hike.

See full show notes …

An End in Sight

Write down a 0:


Now mentally “flip” this string in binary, exchanging 0s and 1s, and append this new string to the existing one:

0 1

Keep this up and you’ll get a growing string of 0s and 1s:

0 1 1 0
0 1 1 0 1 0 0 1
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0

This is the Thue–Morse sequence, named after two of its discoverers, Axel Thue and Marston Morse. One interesting property of the sequence is that, no matter how far it’s extended, it contains no “cubes,” no instances in which some nonempty string occurs three times in a row. For example, the last line above contains both 11 and 00 but no instance of 111 or 000. (It also contains 1001 twice in a row, but not three times.)

Max Euwe, the Dutch mathematician who was world chess champion from 1935 to 1937, used this principle to show that chess was not a finite game. Under the rules at the time, a chess game would end in a draw if a sequence of moves (with all pieces in the same positions) were played three times in a row. Euwe used the Thue-Morse sequence to show that this need never happen: If 0 represents one set of moves, and 1 represents another, and each set leaves the board position unchanged, then the Thue-Morse sequence shows that two players might step through these routines forever without ever playing one three times in a row.

Modern chess rules have dropped the threefold sequence provision. Instead a draw results when the same board position occurs three times, or when 50 successive moves occur without a capture or a pawn move. Both of these rules limit a game to a finite length (although one player must actually claim the draw).

(Thanks, Pål.)


la rochefoucauld

More maxims of François VI, Duc de La Rochefoucauld (1613–1680):

  • “Fortune shews our Virtues and Vices, as Light does Objects.”
  • “‘Tis never more difficult to speak well than when we are ashamed of our Silence.”
  • “Since great Men can neither bestow Health of Body, nor Peace of Mind, we certainly pay too dear for all else they can.”
  • “Our Wisdom is no less at Fortune’s Mercy than our Wealth.”
  • “The Desire of appearing Persons of Ability often prevents our being so.”
  • “There are some Faults, which when well-managed make a greater Figure than Virtue itself.”
  • “We like better to see those on whom we confer Benefits, than those from whom we receive them.”
  • “We should not be much concerned about Faults we have the Courage to own.”
  • “In the Adversity of our Friends, we always find something that don’t displease us.”
  • “Misers mistake Gold for their Good; whereas ’tis only a Means for attaining it.”
  • “When our Merit declines our Taste declines.”
  • “There is near as much Ability requisite to know how to make use of good Advice, as to know how to act for one’s self.”
  • “We had rather speak ill of ourselves than not speak at all.”
  • “We give up our Interest sooner than our Taste.”
  • “We forgive as long as we love.”

And “We sometimes lose People whom we regret more than we sorrow for; and others whom we are sorry for, yet don’t regret.”


This is clever — during Prohibition, moonshiners wore shoes that left hoofprints. From the St. Petersburg, Fla., Evening Independent, May 27, 1922:

A new method of evading prohibition agents was revealed here today by A.L. Allen, state prohibition enforcement director, who displayed what he called a ‘cow shoe’ as the latest thing from the haunts of moonshiners.

The cow shoe is a strip of metal to which is tacked a wooden block carved to resemble the hoof of a cow, which may be strapped to the human foot. A man shod with a pair of them would leave a trail resembling that of a cow.

“The shoe found was picked up near Port Tampa where a still was located some time ago. It will be sent to the prohibition department at Washington. Officers believe the inventor got his idea from a Sherlock Holmes story in which the villain shod his horse with shoes the imprint of which resembled those of a cow’s hoof.”

(Via Rare Historical Photos.)


In a London paper, of the last week, is the following curious apology for a hasty accusation — ‘A paragraph in our last paper, rather precipitously accuses, with ingratitude, a gentleman who gave two-pence as a reward to a waterman for risking his life in saving a lady who had fallen in the River; but had the writer of that paragraph been acquainted with all the particulars, he probably would have suppressed his censure. — The lady to whom the accident happened was the gentleman’s wife.

Public Advertiser, Aug. 20, 1790


Mozart’s expense book for May 27, 1784, contains a curious entry:

Starling bird. 34 kreutzer.

Das war schön!

He had bought a starling on that date, apparently after asking it to repeat the opening theme of the third movement of his Piano Concerto No. 17 in G, K. 453, which he’d completed a few weeks earlier. The bird had held the first G rather long, and then sharped two Gs in the following measure, but Mozart’s exclamation (“That was beautiful!”) shows that he approved.

He kept the bird for three years, until its death on June 4, 1787, when he buried it in his backyard. Then he arranged a funeral for it in which his friends marched in a procession, sang hymns, and listened to the composer recite a poem. No other written records of the bird appear in his surviving writings, but maybe the two had become collaborators.


Michael Grab balances rocks. He regards it as a combination of art, engineering, and contemplative spiritual practice combining patience, critical thinking, and problem solving. But the only “ingredients” in his sculptures are rocks and gravity — there’s no mortar, cement, or artificial support holding them together; any one of them can be toppled with a finger.

“The most fundamental element of balancing in a physical sense is finding some kind of ‘tripod’ for the rock to stand on. Every rock is covered in a variety of tiny to large indentations that can act as a tripod for the rock to stand upright, or in most orientations you can think of with other rocks. By paying close attention to the feeling of the rocks, you will start to feel even the smallest clicks as the notches of the rocks in contact are moving over one another.”

“There is nothing easy about it. It can frustrate me to my limits, and then I learn. Or it can reveal magic beyond words, and I learn. Sometimes the rock wins, but most of the time I win.”