Wheels Within Wheels

In the Fibonacci sequence, each number is the sum of the two preceding ones:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, …

This produces two notable secondary patterns: Summing the squares of each pair of adjacent entries yields an even-numbered term in the sequence:

12 + 12 = 2
12 + 22 = 5
22 + 32 = 13
32 + 52 = 34
52 + 82 = 89
82 + 132 = 233
132 + 212 = 610

And the odd-numbered terms between these are the differences of squares of terms taken two by two, two places apart:

22 – 12 = 3
32 – 12 = 8
52 – 22 = 21
82 – 32 = 55
132 – 52 = 144
212 – 82 = 377
342 – 132 = 987

… and so on.

| Science & Math

A Garden Sermon

http://www.geograph.org.uk/photo/4633187
Image: Philip Halling

The Oxford Companion to the Garden notes a curiosity at Packwood House, a Tudor manor house near Lapworth, Warwickshire:

At some time, possibly in the early 18th century, a mount was made beyond the garden walls to the south on the axis of a gateway in the garden walls and the garden door of the house. Long known as the Sermon on the Mount it is crowned with a single yew with, clustering about it on the slopes, further yews representing the twelve apostles and the four evangelists.

The yews are more than 350 years old, but it’s not clear who devised this setting. A drawing of the garden from the 1700s has survived, but there’s no trace of the mount. The earliest known written description of it appears in Reginald Blomfield and F. Inigo Thomas’ The Formal Garden in England (1892). “Blomfield was told that it represented the Sermon on the Mount by the gardener who was clipping the yews when he visited.”

| Oddities

Prime Magic

berloquin prime puzzle

In his 1976 book 100 Numerical Games, French puzzle maven Pierre Berloquin asks whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):

1 2 3 5 7 11 13 17 19

Is it?

Click for Answer
| Puzzles

Many in One

At the site where apartheid police officers arrested Nelson Mandela in 1962, sculptor Marco Cianfanelli has erected 50 laser-cut steel columns. They range in height from 21 to 31 feet and appear randomly placed, but the approach to the site leads visitors down a path at the correct angle, and at a distance of 115 feet their meaning becomes clear.

“The fifty columns represent the fifty years since his capture, but they also suggest the idea of many making the whole, of solidarity,” Cianfanelli said in a statement at the sculpture’s dedication in 2012. “It points to an irony as the political act of Mandela’s incarceration cemented his status as an icon of struggle, which helped ferment the groundswell of resistance, solidarity, and uprising, bringing about political change and democracy.”

06/14/2017 UPDATE: I’m told there’s also a scale model of the sculpture at Constitution Hill in Johannesburg, which may be more accessible. (Thanks, Martin.)

06/14/2017 UPDATE: There’s a similar installation on the wall of 105 Rue du Faubourg-Saint-Denis in Paris (below), by artist Jean-Pierre Yvaral, depicting Vincent de Paul, who established a mission here to care for the needy. (Thanks, Nick.)

http://parisisinvisible.blogspot.co.uk/2009/02/saints-and-sinners-part-1.html
Image: David Partridge

06/19/2017 UPDATE: And Daniël Hoek noted that a portrait of Steve Jobs is hidden in fence pickets in Lower Manhattan, near Silicon Alley:

manhattan jobs portrait

| Art · History

A Stormy Mistress

https://commons.wikimedia.org/wiki/File:Guardi,Francesco_-_The_Departure_of_Bucentaur_for_the_Lido_on_Ascension_Day.jpg

Each Ascension Day between 1311 and 1798, the doge of Venice was rowed into the Adriatic aboard a palatial barge to perform the “Marriage of the Sea,” a ceremony that symbolically wedded Venice to the sea. The ship, known as the Bucentaur, led a solemn procession of boats out of the city, where the doge dropped a consecrated ring into the water with the words Desponsamus te, mare (“We wed thee, sea”) to indicate that the city and the sea were indissolubly one.

After the Treaty of Versailles, Polish general Jozef Haller marked his country’s renewed access to the Baltic Sea by throwing a ring into the water with the words “In the name of the Holy Republic of Poland, I, General Jozef Haller, am taking control of this ancient Slavic Baltic Sea shore”:

https://commons.wikimedia.org/wiki/File:Zaslubiny_Polski_z_morzem.jpg

His act was repeated in 1945 in several ceremonies by members of the First Polish Army, who threw rings, dipped flags, and swore an oath pledging their nation’s devotion to the Baltic. The text of the oath was later printed in the Polish Army newspaper Zwyciezymy: “I swear to you, Polish Sea, that I, a soldier of the Homeland, faithful son of the Polish nation, will not abandon you. I swear to you that I will always follow this road, the road which has been paved by the State National Council, the road which has led me to the sea. I will guard you, I will not hesitate to shed my blood for the Fatherland, neither will I hesitate to give my life so that you do not return to Germany. You will remain Polish forever.”

| History

Podcast Episode 157: The Brutal History of Batavia’s Graveyard

https://commons.wikimedia.org/wiki/File:Ongeluckige_voyagie_vant_schip_Batavia_(Plate_3).jpg

In 1629, a Dutch trading vessel struck a reef off the coast of Australia, marooning 180 people on a tiny island. As they struggled to stay alive, their leader descended into barbarity, gathering a band of cutthroats and killing scores of terrified castaways. In this week’s episode of the Futility Closet podcast we’ll document the brutal history of Batavia’s graveyard, the site of Australia’s most infamous shipwreck.

We’ll also lose money in India and puzzle over some invisible Frenchmen.

See full show notes …

| History · Podcast

Breathless

https://commons.wikimedia.org/wiki/File:Arturo_Ricci_Nachmittagstee.jpg

This looks exhausting — flirting signals, from Daniel R. Shafer’s Secrets of Life Unveiled, 1877:

“Handkerchief flirtations”:

Drawing it across the lips: Desiring an acquaintance
Drawing it across the cheek: I love you
Drawing it across the forehead: Look, we are watched
Drawing it through the hands: I hate you
Dropping it: We will be friends
Folding it: I wish to speak with you
Letting it rest on the right cheek: Yes
Letting it rest on the left cheek: No
Letting it remain on the eyes: You are so cruel
Opposite corners in both hands: Do wait for me
Over the shoulder: Follow me
Placing it over the right ear: How you have changed
Putting it in the pocket: No more love at present
Taking it by the centre: You are most too willing
Twisting it in the left hand: I wish to be rid of you
Twisting it in the right hand: I love another
Winding it around the forefinger: I am engaged
Winding it around the third finger: I am married

“Glove flirtations”:

Biting the tips: I wish to be rid of you very soon
Clenching them, rolled up in right hand: No
Drawing half way on left hand: Indifference
Dropping both of them: I love you
Dropping one of them: Yes
Folding up carefully: Get rid of your company
Holding the tips downward: I wish to be acquainted
Holding them loose in the right hand: Be contented
Holding them loose in the left hand: I am satisfied
Left hand with the naked thumb exposed: Do you love me?
Putting them away: I am vexed
Right hand with the naked thumb exposed: Kiss me
Smoothing them out gently: I am displeased
Striking them over the shoulder: Follow me
Tapping the chin: I love another
Tossing them up gently: I am engaged
Turning them inside out: I hate you
Twisting them around the fingers: Be careful, we are watched
Using them as a fan: Introduce me to your company

“Fan flirtations”:

Carrying in right hand: You are too willing
Carrying in right hand in front of face: Follow me
Carrying in left hand: Desirous of an acquaintance
Closing it: I wish to speak with you
Drawing across the forehead: We are watched
Drawing across the cheek: I love you
Drawing across the eyes: I am sorry
Drawing through the hand: I hate you
Dropping: We will be friends
Fanning fast: I am engaged
Fanning slow: I am married
Letting it rest on right cheek: Yes
Letting it rest on left cheek: No
Open and shut: You are cruel
Open wide: Wait for me
Shut: I have changed
Placing it on the right ear: You have changed
Twirling in left hand: I love another
With handle to lips: Kiss me

“Parasol flirtations”:

Carrying it elevated in left hand: Desiring acquaintance
Carrying it elevated in right hand: You are too willing
Carrying it closed in left hand: Meet on the first crossing
Carrying it closed in right hand by the side: Follow me
Carrying it over the right shoulder: You can speak to me
Carrying it over the left shoulder: You are too cruel
Closing up: I wish to speak to you
Dropping it: I love you
End of tips to lips: Do you love me?
Folding it up: Get rid of your company
Letting it rest on the right cheek: Yes
Letting it rest on the left cheek: No
Striking it on the hand: I am very displeased
Swinging it to and fro by the handle on left side: I am engaged
Swinging it to and fro by the handle on the right side: I am married
Tapping the chin gently: I am in love with another
Twirling it around: Be careful; we are watched
Using it as a fan: Introduce me to your company
With handle to lips: Kiss me

(From Elizabeth Aldrich, From the Ballroom to Hell: Grace and Folly in Nineteenth-Century Dance, 1991.)

| Language · Society

Copycats

In 1988, workers found a 5-year-old bottlenose dolphin trapped in a canal lock in South Australia. She was taken to a commercial aquarium for medical treatment, where she was named Billie and housed with the trained dolphins who performed for oceanarium visitors there. One of the behaviors that the trained dolphins had learned was tailwalking, emerging vertically from the water and beating their tails to move backward as though walking on the water.

When Billie had recovered she was released back into the wild, but conservationist Mike Bossley continued to monitor her. He was surprised to see her tailwalking — she had never received any training during her recuperation and must have learned this spontaneously from the trained dolphins. “The behavior has no known utility in the wild and, as you can imagine, uses up a fair amount of energy, but Billie kept it up,” write biologists Hal Whitehead and Luke Rendell in The Cultural Lives of Whales and Dolphins (2014).

Not only that, but other wild dolphins began tailwalking themselves. Bossley reported, “Another female dolphin called Wave began performing the same behavior, but does so with much greater regularity than Billie. Four adult female dolphins have also been seen tailwalking,” as have several calves. Just last month conservationist Jenni Wyrsta saw a wild dolphin named Bianca do 33 tailwalks in a row in the Port River, in sets of two and three. “I’ve never seen a dolphin do double, let alone triple tailwalks,” she told the Portside Messenger.

Whitehead and Rendell write, “So, a behavior learned in captivity, with no obvious function beside play, has apparently gone on to become something of a hit in the wild and persists to this day, twenty-five years following Billie’s release and after Billie’s own death in 2009.”

| Science & Math

The Baltic Way

https://commons.wikimedia.org/wiki/File:Baltsk%C3%BD%C5%98et%C4%9Bz.jpg
Image: Wikimedia Commons

On August 23, 1989, two million peaceful demonstrators joined hands across Estonia, Latvia, and Lithuania to protest the occupation of the Baltic states by the Soviet Union. The chain, 675 kilometers long, connected the capitals of Vilnius, Riga, and Tallinn. Coordinated by portable radios, the protesters peacefully joined hands for 15 minutes at 7 p.m. local time, saying they wanted to demonstrate solidarity among the three nations in their desire for independence.

“This is something I feel in my heart,” said Rita Urbanovich, who had brought her 7-year-old twin sons to a spot along the Viljandi Highway outside Tallinn. “We suffered. Our whole country suffered — every person. And I brought my children because this is my way to explain to them why independence is important for their future.”

Moscow responded with heated rhetoric but backed down when the activists appealed to the United Nations. Within seven months, Lithuania had declared its independence, and by the end of 1991 all three Baltic states were free.

| History

Hocus Pocus

Allan William Johnson discovered this “magic square of squares” in 1990:

 302   2462   1722    452

 932   1162    662   2582

1262   1382   2372    442

2602     32    542   1502

Each row, column, and long diagonal totals 93025, or 3052.

| Science & Math