From a letter by Phillips Brooks to a friend on the death of his mother, Nov. 19, 1891:
May I try to tell you again where your only comfort lies? It is not in forgetting the happy past. People bring us well-meant but miserable consolations when they tell us what time will do to help our grief. We do not want to lose our grief, because our grief is bound up with our love and we could not cease to mourn without being robbed of our affections.
Temple University anthropologist Wayne Zachary was studying a local karate club in the early 1970s when a disagreement arose between the club’s instructor and an administrator, dividing the club’s 34 members into two factions. Thanks to his study of communication flow among the members, Zachary was able to predict correctly, with one exception, which side each member would take in the dispute.
The episode has become a popular example in discussions of community structure in networks, so much so that scientists now award a trophy to the first person to use it at a conference. The original example is known as Zachary’s Karate Club; the trophy winners are the Zachary’s Karate Club Club.
(Wayne W. Zachary, “An Information Flow Model for Conflict and Fission in Small Groups,” Journal of Anthropological Research 33:4 [1977], 452-473. Thanks to Snehal Shekatkar for the image.)
09/01/2024 Reader Peter Dawyndt points out that the reason for the single exception in Zachary’s prediction is notable. The person whom Zachary assigned to the wrong faction corresponds to node 9 in this graph of the network:
“This person joined the newly founded karate club with supporters of the teacher (node 1) after the split, despite being a weak supporter of the president (node 34). This choice stemmed mainly from opportunism: he was only three weeks away from a test for black belt (master status) when the split in the club occurred. Had he joined the president’s club, he would have had to give up his rank and begin again in a new style of karate with a white (beginner’s) belt, since the president had decided to change the style of karate practiced in his club. Having four years of study invested in the style of the original club’s instructor, the individual could not bring himself to repudiate his rank and start again.”
(Thanks, Peter.)
In the Middle Ages, before the advent of street lighting or organized police forces, fortified cities and towns used to discourage vandals by closing their gates and laying chains across their roads, “as if it were in tyme of warr.” Historian A. Roger Ekirch writes that Nuremberg “maintained more than four hundred sets [of chains]. Unwound each evening from large drums, they were strung at waist height, sometimes in two or three bands, from one side of a street to the other … [and] Paris officials in 1405 set all the city’s farriers to forging chains to cordon off not just streets but also the Seine.”
In some cities, residents who’d returned home for the night were required to give their keys to the authorities. A Paris decree of 1380 reads, “At night all houses … are to be locked and the keyes deposited with a magistrate. Nobody may then enter or leave a house unless he can give the magistrate a good reason for doing so.”
(From Jane Brox, Brilliant: The Evolution of Artificial Light, 2010.)
https://www.youtube.com/watch?v=zW-QGtOAVEg
In 1929, Indiana Bell bought the Central Union Telephone Company of Indianapolis. Central Union’s headquarters building at that time was more than 20 years old and inadequate to the new company’s needs, but rather than demolish it, architect Kurt Vonnegut Sr. (father of the novelist) proposed moving it out of the way.
Over the course of a month, the 10,000-ton building was shifted 52 feet south, rotated 90 degrees, then shifted another 100 feet west. Amazingly, this was all accomplished while the building was open and operating — customer telephone service was never interrupted, and the building’s gas, heat, electricity, and water operated continuously throughout the move.
A new headquarters was built on the old site, and the shifted building stood in its new position until 1963.
What is the minimum number of bishops needed to occupy or attack all squares on an 8 × 8 chessboard?
[A]ccording to the standard traditions, being in hell is the worst thing that could ever happen to anyone. As with less horrendous evils, the first question is how such an evil is, or could be, justified. The theological portrayals of hell make this question the most difficult for the theist to address. Ordinary pain and evil, it may be thought, can be accounted for if events in the future ‘make up for’ what leads to them, but the evil of hell leads nowhere; at no point in the future will something of value make up for the evil of hell or will some reward be granted to those who endure the suffering of hell. Hell is apparently paradigmatic as an example of truly pointless, gratuitous evil. Thus arises the problem of hell.
— Jonathan L. Kvanvig, The Problem of Hell, 1993
In a 2014 blog post for the Wall Street Journal, mathematician Jordan Ellenberg examined the distribution of highlighted passages within Amazon Kindle books as an unscientific measure of how far the average reader progresses through each title before giving up. If the “popular highlights” are clustered densely near the start of a book, that’s (arguably) a sign that many readers abandon the book before reading much farther. Ellenberg gave these examples (each considering the location of the five most highlighted passages in the text):
Hard Choices, by Hillary Clinton, 1.9%
Capital in the Twenty-First Century, by Thomas Piketty, 2.4%
Infinite Jest, by David Foster Wallace, 6.4%
A Brief History of Time, by Stephen Hawking, 6.6%
Thinking, Fast and Slow, by Daniel Kahneman, 6.8%
Lean In, by Sheryl Sandberg, 12.3%
Flash Boys, by Michael Lewis, 21.7%
Fifty Shades of Grey, by E.L. James, 25.9%
The Great Gatsby, by F. Scott Fitzgerald, 28.3%
Catching Fire, by Suzanne Collins, 43.4%
The Goldfinch, by Donna Tartt, 98.5%
Ellenberg called the measure the Hawking Index, after physicist Stephen Hawking’s A Brief History of Time, which is often called “the most unread book of all time” … though it reaches only fourth place even on this short list.
“So take it easy on yourself, readers, if you don’t finish whatever edifying tome you picked out for vacation,” he wrote. “You’re far from alone.”
You need to pack for a midnight flight and the power is out. Your closet contains six pairs of shoes, six black socks, six gray socks, six pairs of brown gloves, and six pairs of tan gloves, but it’s too dark to distinguish colors or to match shoes. How many of each item must you take to be sure of having a matched pair of shoes, two socks of the same color, and a pair of matching gloves?
This problem, by G. Heathcote, won second prize in the Norwich Mercury‘s “King in the Corner” problem tournament, which required that Black’s king begin each problem in one of the board’s four corners. White to mate in two moves.
In 1883, Missouri real estate broker James Reavis announced that he held title to a huge tract of land in the Arizona Territory. If certified, the claim would threaten the livelihoods of thousands of residents. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Baron of Arizona, one of the most audacious frauds in American history.
We’ll also scrutinize British statues and puzzle over some curious floor numbers.
