I never got on good
relations with the world
first I had nothing
the world wanted
then the world had
nothing I wanted
— A.R. Ammons
Cultivation
Many people know that you can form a pentagon by tying a strip of paper in a simple overhand knot.
Stephen Bleecker Luce’s seamanship manual of 1863 tells how to fold a blade of grass into an octagon (below):
It is first doubled short over itself, then 1 under 2, — leaving a space, then 2 over 1, and down through the centre of the triangle; next 1 over 2, and down through the centre, coming out on the opposite side, and so on until an octagonal figure is formed.
That’s pretty terse, but I think I’ve almost managed to do it tonight. Keep your eye on the drawing of the finished piece, and don’t form and flatten the finished shape until you’ve done all the weaving.
(Via The Ashley Book of Knots.)
Math Notes
The sum or difference of any pair of the numbers {150568, 420968, 434657} is a square:
420968 + 150568 = 7562
420968 – 150568 = 5202
434657 + 420968 = 9252
434657 – 420968 = 1172
434657 + 150568 = 7652
434657 – 150568 = 5332
Miracles and Agents
Jones tells a mountain to hop into the sea and it does so. Has he performed a miracle?
Well, no, writes University of Birmingham philosopher George Chryssides. If Jones repeats his feat, then he’s revealed an underlying causal principle that’s amenable to study just like the rest of the natural world. If he doesn’t repeat the feat, then there’s no support for the idea of a link between his command and the mountain’s movement — we know only that the two events coincided, not that one caused the other.
“In order … to determine the answer to the question, ‘Did Jones move the mountain?’ … we must ascertain whether similar effects would follow similar putative causes,” Chryssides writes. “Either an allegedly miraculous event is a violation of scientific law, in which case it could not be performed by an agent, or else it is performed by an agent, in which case it could not be a violation of scientific law.”
(George D. Chryssides, “Miracles and Agents,” Religious Studies 11:3 [September 1975], 319-327.)
Levine’s Sequence
In the summer of 1997 mathematician Lionel Levine discovered a sequence of numbers: 1, 2, 2, 3, 4, 7, 14, 42, 213, 2837, … . It’s made up of the final term in each row of this array:
1 1
1 2
1 1 2
1 1 2 3
1 1 1 2 2 3 4
1 1 1 1 2 2 2 3 3 4 4 5 6 7
1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 7 7 7 8 8 9 9 10 10 11 12 13 14
…
The array is built from a simple rule. Start with 1 1 and regard each line as a recipe for building the next one: Read it from right to left and think of it as an inventory of digits. The first line, 1 1, would be read “one 1 and one 2,” so that gives us 1 2 for the second line. The second line (again, reading from right to left) would be read “two 1s and one 2,” giving 1 1 2 for the third line.
And so on. That’s it. It’s excruciatingly simple, “yet it seems likely that the 20th term say is impossible to compute,” wrote N.J.A. Sloane that November. At that time only 15 terms were known, the last being 508009471379488821444261986503540. Two further terms have since been found, bringing us up to 5347426383812697233786139576220450142250373277499130252554080838158299886992660750432. And the 20th is still out of sight.
See the link below (page 15) for more.
(Neil J.A. Sloane, “My Favorite Integer Sequences,” in C. Ding, T. Helleseth, and H. Niederreiter, Sequences and Their Applications: Proceedings of SETA ’98, 2012, 103-130.)
The Gymnasticon
Here’s a surprisingly modern-looking exercise machine from 1796. Essentially it’s a set of flywheels turned by hand cranks and foot treadles; Francis Lowndes said he patented it “to give and apply motion and exercise, voluntary or involuntary, to the limbs, joints, and muscles of the human body.”
He claimed he’d successfully used it to treat gout, palsy, rheumatism, debility, and contraction, but he said it would be equally useful for healthy people in sedentary occupations, according to the Monthly Magazine: “The merchant, without withdrawing his attention from his accounts, and the student, while occupied in writing or reading, may have his lower limbs kept in constant motion by the slightest exertion, or by the assistance of a child.”
Podcast Episode 246: Gene Tierney’s Secret Heartbreak
At the height of her fame in 1943, movie star Gene Tierney contracted German measles during pregnancy and bore a daughter with severe birth defects. The strain ended her marriage to Oleg Cassini and sent her into a breakdown that lasted years. In this week’s episode of the Futility Closet podcast we’ll describe Tierney’s years of heartbreak and the revelation that compounded them.
We’ll also visit some Japanese cats and puzzle over a disarranged corpse.
Free Enterprise
Until the 1990s it was arguably legal to purchase stolen goods in London’s Bermondsey Market without fear of prosecution.
The market operated under the ancient law of marché ouvert, or “open market,” a medieval legal concept that allowed for the open sale of stolen goods between the sunset and sunrise in designated markets in a city.
The idea was that if you were robbed and you didn’t check to see whether your stolen property was being sold in a local market, then you weren’t taking reasonable steps to recover it.
Surprisingly, Bermondsey Market operated under this law until 1995, when a stolen Joshua Reynolds painting was sold there for 100 pounds and the purchaser avoided prosecution for handling stolen goods by arguing that the sale was subject to these rules. The loophole has since been abolished.
(Thanks, Cathy.)
05/01/2019 UPDATE: A better explanation: It was never legal to sell or buy stolen goods knowingly. Ordinarily if a buyer is convicted of handling stolen goods then a court can order the goods returned to the original owner, and even without a criminal prosecution the owner can still seek recovery of their goods by appealing to a principle of the common law known as “nemo dat quod non habet” (“no one may give what he does not have”) — even if a buyer pays a fair price for goods she doesn’t know are stolen, she can’t obtain “good title,” ownership that defeats the claims of others, so the original owner can still recover the goods. “Market overt” is an exception to the nemo dat rule — until 1995, anything bought in good faith at a market overt in England became the legal property of the buyer, including title, even if it turned out to have been stolen — the original owner had no legal redress.
Market overt regulations were regarded as a valuable form of consumer protection when they were instantiated in the 12th century, but by the end of the 20th they had become known as the “thieves’ charter” for the dodgy sales they permitted. “It is a good thing it’s been stopped,” one Bermondsey trader told the Guardian in 1995. “People knew that market overt gave them a licence to bring stolen stock down here once a week.”
(Thanks, David.)
Words and Music
In 2004, Canadian musician Andrew Huang wrote a song that encodes the first 101 digits of π.
Also: A “piku” is a haiku whose word lengths reflect the digits of π:
How I love a verse
Contrived to unhusk dryly
One image nutshell
“An Infernal Palindrome”
William Hone’s Every-Day Book of 1837 repeats a story in which St. Martin meets the devil, who asks why he is walking to Rome rather than riding. The saint commands him to become a beast of burden, the devil assumes the shape of a mule, and Martin jumps onto his back and spurs him on his way by repeatedly making the sign of the cross. At length the devil says:
Signa te, Signa: temere me tangis et angis:
Roma tibi subito motibus ibit amor.
That means “Cross, cross thyself — thou plaguest and vexest me without necessity; for, owing to my exertions, Rome, the object of thy wishes, will soon be near.” And each line is a palindrome, reading the same backward and forward.
Hone adds, “These lines have been quoted imperfectly and separately in ‘Encyclopedies’ and other books, under the words ‘Palindromical verses;’ but the reader will not easily meet with the legendary tale, which gives them historical consistence and meaning.”