Can two dice be weighted so that the probability of each of the numbers 2, 3, …, 12 is the same?
Mob Rule
Eugene Graves and William Brown patented this grim game in 1902. A row of effigies stand on blocks under a gibbet. Each effigy is fitted with a noose, and the players take turns shooting balls at the blocks, “representing summary punishment meted out to the victim.”
In the patent abstract, the effigies are described only as “notorious criminals and persons opposed to law and order”; Graves and Brown note that these can be varied to suit the “location, place or country for which the game is especially designed.”
“A flag may be provided for each figure to designate the character or nationality of the effigy.” We’re lucky this didn’t catch on.
Church Work
By 1905 parts of Winchester Cathedral were in danger of collapse — the 13th-century builders had rested their structure on a bed of peat, which had been sinking under continuous pressure of 40 tons per square foot. In order to shore up the building, diver William Walker was enlisted to work in the church’s flooded foundations, replacing the peat with sacks and bricks of concrete.
Walker worked in total darkness for more than five years, from 1906 to 1911, handling an estimated 25,800 bags of concrete and 114,900 concrete blocks while wearing a suit that weighed nearly 200 pounds. “In addition,” notes the cathedral’s booklet, “as he was working in a graveyard, there was some risk of infection. However, Walker seems to have regarded his pipe as his sovereign remedy against all possible ills and immediately on his return to the surface, he always lit his pipe.”
As he worked, the business of the cathedral went on as usual. A journalist for the Standard described the scene in 1906: “The last Amen is sung, and the choir and clergy pass slowly and silently into the vestry. Outside the foreman blows his whistle. The great helmet of the diver with its staring goggle eyes, appears above the brink of the shaft, and the diver is helped out of his slimy, dripping shell. And soon choristers and workmen mingle beneath the shadow of the Cathedral.”
When the work was completed in 1912 Walker received the thanks of the king and was appointed a member of the Royal Victorian Order. During World War I a memorial tablet was laid in his honor on the cathedral’s west wall, and a statue of the diver was unveiled in 1964. On a BBC memorial program in 1956, Walker’s assistant William West was asked to remember him. “I think his habits was like mine,” he said. “He was fond of a smoke and when he come up, spell sometime, somebody told him about germs, which didn’t worry him. And he say: ‘Where’s my pipe? Don’t lay it down there.'”
From Life
Sculptor Marc Quinn chose a unique medium for his 1991 self-portrait Self: The life-sized bust is fashioned from nine pints of the artist’s own blood, collected over a period of weeks, poured into a mold, and frozen. It sits in a transparent cube with its own refrigeration unit.
“I have come across viewers who, on seeing Self for the first time, describe a sensation akin to tingling, a kind of spinal over-excitation, or a curious shudder — that involuntary somatic spasm referred to in common speech by the phrase ‘someone walking on one’s grave,’ writes Cambridge philosopher Peter de Bolla in Art Matters (2001). “And for some these immediate somatic responses may quickly give way to a variety of thoughts associated with formally similar presentations of the human head or face: the death mask, waxwork, funerary sculpture, embalmed body, or anatomical model. When this happens, the frisson of the physical encounter rapidly mutates into a jumble of thoughts as if an impulse — call it a spark of affect — sets in motion a series of reactions that leave their trace in whatever permeable surface they encounter.”
Podcast Episode 23: A Victorian Poisoning Mystery
On New Year’s Day 1886, London grocer Edwin Bartlett was discovered dead in his bed with a lethal quantity of liquid chloroform in his stomach. Strangely, his throat showed none of the burns that chloroform should have caused. His wife, who admitted to having the poison, was tried for murder, but the jury acquitted her because “we do not think there is sufficient evidence to show how or by whom the chloroform was administered.”
In this episode of the Futility Closet podcast we’ll learn about Edwin and Adelaide Bartlett’s strange marriage and consider the various theories that have been advanced to explain Edwin’s death. We’ll also sample a 50,000-word novel written without the letter E and puzzle over a sure-footed American’s visit to a Japanese office building.
Two Blows
Theodore Roosevelt’s wife and mother died in the same house on the same day, Valentine’s Day 1884. His wife had just given birth to their daughter Alice, and the pregnancy had hidden her kidney disease. He held her for two hours, had to be torn away to see his mother die of typhoid fever, then returned to his wife, who died in his arms.
In his diary he drew a large X and wrote, “The light has gone out of my life.” Then he fled west to grieve in private.
Cause for Alarm
Sherlock Holmes is walking through the valley of Reichenbach Fall. On a clifftop overhead, Moriarty has perched a boulder. When he pushes it, it will have a 90 percent chance of killing Holmes. Just as he is about to send it over the edge, Watson arrives at the clifftop. Watson can’t see Holmes, so he’s not able to push the boulder safely clear, but he reasons that it’s better to push the boulder in a random direction than to let Moriarty aim it carefully. So he pushes the boulder off the cliff in such a way that Holmes’ chance of dying is reduced to 10 percent.
Unfortunately the boulder crushes Holmes anyway. Watson’s push decreased the chance of Holmes’ death, but it also caused it.
What are we to make of this? Generally speaking, it seems true to say that Pre-emptive pushing prevents death by crushing. That is, Watson’s push was of the sort that made it less likely that Holmes would die — if the scenario were re-enacted many times, with the boulder pushed sometimes by Watson, sometimes by Moriarty, Watson-type pushes would result in fewer deaths. But it also seems true to say that Watson’s pushing the rock caused Holmes to die. But cause and prevent are antonyms. How can both of these statements be true?
(Christopher Read Hitchcock, “The Mishap at Reichenbach Fall: Singular vs. General Causation,” Philosophical Studies, June 1995.)
Black and White
Half and Half
A bisecting arc is one that bisects the area of a given region. “What is the shortest bisecting arc of a circle?” Murray Klamkin asked D.J. Newman. Newman supposed that it was a diameter. “What is the shortest bisecting arc of a square?” Newman answered that it was an altitude through the center. Finally Klamkin asked, “And what is the shortest bisecting arc of an equilateral triangle?”
“By this time, Newman had suspected that I was setting him up (and I was) and almost was going to say the angle bisector,” Klamkin writes. “But he hesitated and said let me consider a chord parallel to the base and since this turns out to be shorter than an angle bisector, he gave this as his answer.”
Was he right?
In a Word
advesperate
v. to grow dark, to become night