Balance

A normal die is painted so that it has four green faces and two red. Then it’s shaken in a cup and thrown repeatedly onto a table. You’re invited to guess which of these three sequences results. If you guess wrong you lose $10; and if you guess right you win $30.

  1. RGRRR
  2. GRGRRR
  3. GRRRRR

Most people express the preferences 2, 1, 3, in that order. Red is less likely than green, but it predominates in all three sequences, so many subjects explain that sequence 2 is more “balanced,” and therefore more probable. In fact 65 percent of all subjects (excluding expert statisticians and people whose business is probability) show a strong propensity to vote for sequence 2, even when it’s pointed out explicitly that sequence 1 is just sequence 2 minus the first throw — so sequence 2 cannot be more likely!

“The longer the sequence, the less probable it is, independently of its being ‘balanced’ or ‘unbalanced,'” writes Massimo Piattelli-Palmarini in Inevitable Illusions. “This shows how resistant certain cognitive illusions are. Many other more complex examples have been advanced, and these show that even professional statisticians are sometimes subject to the same illusion.”

| Science & Math

Reunion

I was just researching wartime superstitions and came across this striking anecdote. Major Hubert Knilans was an American bomber pilot who flew with the No. 619 Squadron in the RAF during World War II. As he was climbing to cruising altitude one evening, “The upper sky before me was still somewhat lighted. A figure of a woman several thousand feet high slowly emerged into my startled view.”

He realized she had the face of a young woman he’d loved but who had died suddenly of pneumonia some years earlier. “She had a slight smile on her lips as I flew towards her. The vision slowly melted into the darkening sky around us.”

He says he was “a bit uneasy” over this vision, uncertain “if she had appeared to reassure me that she would keep me from harm or if she was welcoming me into her world of the hereafter.”

Apparently it was the former — he finished the mission successfully and wrote up the encounter in his private memoir A Yank in the RCAF.

| Oddities

Head Over Heels

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Image: John Allan

In his 1703 Description of the Western Islands of Scotland, Martin Martin describes an alarming tradition concerning a beetling rock formation in St. Kilda:

In the face of the rock, south from the town, is the famous stone, known by the name of the mistress-stone; it resembles a door exactly; and is in the very front of this rock, which is twenty or thirty fathom [120-180 feet, 37-55 meters] perpendicular in height, the figure of it being discernible about the distance of a mile; upon the lintel of this door, every bachelor-wooer is by an ancient custom obliged in honour to give a specimen of his affection for the love of his mistress, and it is thus; he is to stand on his left foot, having the one half of his sole over the rock, and then he draws the right foot further out to the left, and in this posture bowing, he puts both his fists further out to the right foot; and then after he has performed this, he has acquired no small reputation, being always after it accounted worthy of the finest mistress in the world: they firmly believe that this achievement is always attended with the desired success.

“This being the custom of the place, one of the inhabitants very gravely desired me to let him know the time limited by me for trying of this piece of gallantry before I design’d to leave the place, that he might attend me,” he added. “I told him this performance would have a quite contrary effect upon me, by robbing me both of my life and mistress at the same moment.”

| Society

Literally

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As Arthur Conan Doyle’s 1893 story “The Adventure of the Reigate Squire” begins, Sherlock Holmes is recuperating after the unspecified-but-apparently-quite-taxing case of the “Netherlands-Sumatra company,” which left him lying exhausted in the Hotel Dulong in Lyons. Watson writes:

The triumphant issue of his labours could not save him from reaction after so terrible an exertion, and at a time when Europe was ringing with his name, and when his room was literally ankle-deep with congratulatory telegrams, I found him prey to the blackest depression.

Leslie S. Klinger’s New Annotated Sherlock Holmes includes this droll footnote:

Carol P. Woods calculates that to fill the average French hotel room to ‘ankle-deep’ would require 10,741 crumpled telegrams; and she muses that Holmes’s illness was caused not entirely by the exertions put forth in the Netherlands-Sumatra case but also by the telegram-crumpling itself, which would have required slightly over 179 hours of opening, reading, crumpling, and tossing.

| Literature

Eventful

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Letizia Ramolino was born in 1750. In her 85 years of life she gave birth to Napoleon Bonaparte, saw the French monarchy collapse, witnessed the French Revolution, and saw her son crowned emperor. Then she saw his death, the collapse of his empire, and the restoration of the monarchy.

She died in 1836, 15 years after her most famous son.

| History

Three Predictions

In Season 8, Episode 7 of Penn & Teller’s magic competition show Fool Us, magician Hans Petter Secker appears to predict the outcome of three successive rounds of rock-paper-scissors, though Secker oversees the game remotely from Norway and the players are invited to exchange items before each round. How is this accomplished?

Click for Answer
| Entertainment · Science & Math

Pointlessness Exalted

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Image: Wikimedia Commons

Dodgers outfielder Gary Thomasson was a big disappointment in Japan — in 1980 he was signed to the Yomiuri Giants for a record-breaking sum, then nearly set a record for strikeouts before injuring his knee and retiring.

Artist Akasegawa Genpei took a strange inspiration from this: He defined a “Thomasson” as “an object, part of a building, that was maintained in good condition, but with no purpose, to the point of becoming a work of art.” For example, in Tokyo he’d noticed a well-maintained stairway with a blank wall at its top, and a ticket window that had been boarded up but whose tray had been assiduously permitted still to function.

Akasegawa’s colleague Chikuma Shobo eventually published a whole taxonomy of Thomassons: useless doorways, useless staircases, useless windows, doors to nowhere, senseless signs. Just like art, these items have no purpose in society, but they’re preserved with care, to the point that they seem to be exhibits in themselves. “However, these objects do not appear to have a creator, making them even more art-like than regular art.”

| Art

Out, Out!

In 1990, University of Houston English professor Earl Dachslager wrote to the New York Times “to settle once and for all the debate over the first references in print to the game of baseball.” He had found 11 in Shakespeare:

  • “And so I shall catch the fly” (Henry V, Act V, Scene ii).
  • “I’ll catch it ere it come to ground” (Macbeth, III, v).
  • “A hit, a very palpable hit” (Hamlet, V, ii).
  • “You may go walk” (The Taming of the Shrew, II, i).
  • “Strike!” (Richard III, I, iv).
  • “For this relief much thanks” (Hamlet, I, i).
  • “You have scarce time to steal” (Henry VIII, III, ii).
  • “O hateful error” (Julius Caesar, V, i).
  • “Run, run, O run!” (King Lear, V, iii).
  • “My arm is sore” (Antony and Cleopatra, II, v).
  • “I have no joy in this contract” (Romeo and Juliet, II, ii).

“I trust that the question of who first wrote about baseball is now finally settled.”

| Entertainment · Literature

Small World

Artist François Abelanet created this perspective-based illusion outside the city hall in Paris in 2011. Ninety gardeners worked for five days to prepare an area of 1500 square meters.

Abelanet called it Qui croire? (Who to Believe?).

| Art