In 1844 New Orleans was riveted by a dramatic trial: A slave claimed that she was really a free immigrant who had been pressed into bondage as a young girl. In this week’s episode of the Futility Closet podcast we’ll describe Sally Miller’s fight for freedom, which challenged notions of race and social hierarchy in antebellum Louisiana.
We’ll also try to pronounce some drug names and puzzle over some cheated tram drivers.
“To convince any man against his will is hard, but to please him against his will is justly pronounced by Dryden to be above the reach of human abilities.” — Samuel Johnson
“Thou canst not joke an Enemy into a Friend; but thou may’st a Friend into an Enemy.” — Ben Franklin
There is an eternal antagonism of interest between the individual and the world at large. The individual will not so much care how much he may suffer in this world provided he can live in men’s good thoughts long after he has left it. The world at large does not so much care how much suffering the individual may either endure or cause in this life, provided he will take himself clean away out of men’s thoughts, whether for good or ill, when he has left it.
— Samuel Butler, Notebooks
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.)
Either know, or listen to someone who does. You can’t live without understanding, whether your own or someone else’s. There are many, however, who don’t know that they don’t know, and others who think they know, but don’t. Stupidity’s faults are incurable, for since the ignorant don’t know what they are, they don’t search for what they lack. Some individuals would be wise if they didn’t believe that they already were. Given all this, although oracles of good sense are rare, they sit idle, because nobody consults them. Seeking advice will neither diminish your greatness nor refute your ability. In fact, it will enhance your reputation. Engage with reason so misfortune doesn’t contend with you.
— Baltasar Gracián, The Pocket Oracle and Art of Prudence, 1647
Before the 19th century, containers did not come in standard sizes, and students in the 1400s were taught to “gauge” their capacity as part of their standard mathematical education:
There is a barrel, each of its ends being 2 bracci in diameter; the diameter at its bung is 2 1/4 bracci and halfway between bung and end it is 2 2/9 bracci. The barrel is 2 bracci long. What is its cubic measure?
This is like a pair of truncated cones. Square the diameter at the ends: 2 × 2 = 4. Then square the median diameter 2 2/9 × 2 2/9 = 4 76/81. Add them together: 8 76/81. Multiply 2 × 2 2/9 = 4 4/9. Add this to 8 76/81 = 13 31/81. Divide by 3 = 4 112/243 … Now square 2 1/4 = 2 1/4 × 2 1/4 = 5 1/16. Add it to the square of the median diameter: 5 5/16 + 4 76/81 = 10 1/129. Multiply 2 2/9 × 2 1/4 = 5. Add this to the previous sum: 15 1/129. Divide by 3: 5 1/3888. Add it to the first result: 4 112/243 + 5 1/3888 = 9 1792/3888. Multiply this by 11 and then divide by 14 [i.e. multiply by π/4]: the final result is 7 23600/54432. This is the cubic measure of the barrel.
Interestingly, this practice informed the art of the time — this exercise is from a mathematical handbook for merchants by Piero della Francesca, the Renaissance painter. Because many artists had attended the same lay schools as business people, they could invoke the same mathematical training in their work, and visual references that recalled these skills became a way to appeal to an educated audience. “The literate public had these same geometrical skills to look at pictures with,” writes art historian Michael Baxandall. “It was a medium in which they were equipped to make discriminations, and the painters knew this.”
(Michael Baxandall, Painting and Experience in Fifteenth Century Italy, 1988.)
04/10/2021 UPDATE: A reader suggests that there’s a typo in the original reference here. If 9 1792/3888 is changed to 9 1793/3888, the final result is 7 23611/54432, which is exactly the result obtained by integration using the approximation π = 22/7. (Thanks, Mariano.)
Wolfram Alpha offers some surprising seasonal equations — a bunny:
max(min(-51/25 abs(-(21 x)/(22 a) – (5 y)/(17 a) + 2/11)^(29/16) – 37/17 abs((5 x)/(17 a) – (21 y)/(22 a) + 15/17)^(35/23) + 1, -75/22 abs(-(12 x)/(17 a) – (12 y)/(17 a) + 19/24)^(34/15) – 105/13 abs(-(12 x)/(17 a) + (12 y)/(17 a) + 1/34)^(123/62) + 1, x/a), min(-51/25 abs((21 x)/(22 a) – (5 y)/(17 a) + 2/11)^(29/16) – 37/17 abs(-(5 x)/(17 a) – (21 y)/(22 a) + 15/17)^(35/23) + 1, -75/22 abs((12 x)/(17 a) – (12 y)/(17 a) + 19/24)^(34/15) – 105/13 abs((12 x)/(17 a) + (12 y)/(17 a) + 1/34)^(123/62) + 1, -x/a), min(max(-(177 x^2)/(13 a^2) – 46/15 (y/a + 1/24)^2 + 1, (690 x^2)/(29 a^2) + 63/4 (y/a + 8/17)^2 – 1), 1/10 – ((79 x^2)/(16 a^2) + 16 (y/a + 1/2)^2 – 1) ((16 x^2)/a^2 + (79 y^2)/(16 a^2) – 1), 6287/17 (x/a – 1/9)^2 + 100 (y/a + 1/16)^2 – 1, 6287/17 (x/a + 1/9)^2 + 100 (y/a + 1/16)^2 – 1), -31550/23 (x/a – 2/19)^2 – 62500/49 (y/a + 1/11)^2 + 1, -31550/23 (x/a + 2/19)^2 – 62500/49 (y/a + 1/11)^2 + 1, -18407811/17 (x/a – 1/25)^4 – 250127/15 (y/a + 13/22)^4 + 1, -18407811/17 (x/a + 1/25)^4 – 250127/15 (y/a + 13/22)^4 + 1, -(x/a – 1/2)^2 – (y/a + 5/4)^2 + 1/30, 11/20 – ((y^4/(63 a^4) – y^3/(11 a^3) – y^2/(7 a^2) + (13 y)/(15 a) + x^2/a^2 + 29/43) ((142 x^2)/(15 a^2) + ((-(304 y)/(23 a) – 878/31) x)/a + (1019 y)/(25 a) + (184 y^2)/(13 a^2) + 349/11) ((142 x^2)/(15 a^2) + (((304 y)/(23 a) + 878/31) x)/a + (1019 y)/(25 a) + (184 y^2)/(13 a^2) + 349/11))/(11/19 – y/(8 a))^2, -x^2/a^2 – x/a – (5 y)/(2 a) – y^2/a^2 – 16/9, -(127 x^2)/(21 a^2) – ((-(118 y)/(23 a) – 47/7) x)/a – (559 y)/(15 a) – (173 y^2)/(22 a^2) – 847/19, -(127 x^2)/(21 a^2) – (((118 y)/(23 a) + 47/7) x)/a – (559 y)/(15 a) – (173 y^2)/(22 a^2) – 847/19)>=0
… and an egg:
min(1/5 – sin(16 p sqrt(x^2/(a^2 (1 – y/(10 a))^2) + (9 y^2)/(16 a^2)) (1 – 1/10 (1 – sqrt(x^2/(a^2 (1 – y/(10 a))^2) + (9 y^2)/(16 a^2))) cos(12 tan^(-1)(x/(a (1 – y/(10 a))), (3 y)/(4 a))))), -x^2/(a^2 (1 – y/(10 a))^2) – (9 y^2)/(16 a^2) + 1)>=0
In Poland, Easter Monday is Śmigus-dyngus, in which boys throw water over girls they like and spank them with pussy willow branches. Traditionally, Wikipedia says, “Boys would sneak into girls’ homes at daybreak on Easter Monday and throw containers of water over them while they were still in bed. After all the water had been thrown, the screaming girls would often be dragged to a nearby river or pond for another drenching. Sometimes a girl would be carried out, still in her bed, before both bed and girl were thrown into the water together. Particularly attractive girls could expect to be soaked repeatedly during the day.”
(Thanks, Danesh and Wade.)
In the 19th century, some New England communities grew so desperate to help victims of tuberculosis that they resorted to a macabre practice: digging up dead relatives and ritually burning their organs. In this week’s episode of the Futility Closet podcast we’ll examine the causes of this bizarre belief and review some unsettling examples.
We’ll also consider some fighting cyclists and puzzle over Freddie Mercury’s stamp.
In 1924 architect Frederick Kiesler proposed a house fashioned as a continuous shell rather than an assembly of columns and beams:
The house is not a dome, but an enclosure which rises along the floor uninterrupted into walls and ceilings. Thus the safety of the house does not depend on underground footings but on a strict coordination of all enclosures of the house into one structural unit. Even the window areas are not standardized in size or shape, but are, rather, large and varied in their transparency and translucency, and form part of the continuous flow of the shell.
Storage space is provided between double shells in the walls, radiant heating is built into the floor, and there are no separate bathrooms, as bathing is done in the individual living quarters.
“While the concept of the house does not advocate a ‘return to nature’, it certainly does encourage a more natural way of living, and a greater independence from our constantly increasing automative way of life.”
(Via Ulrich Conrads, The Architecture of Fantasy: Utopian Building and Planning in Modern Times, 1962.)
