The Backward Club

https://pixabay.com/vectors/cards-game-aces-four-diamonds-161404/

A self-working card curiosity by Shippensburg University mathematician Douglas E. Ensley:

I give you the four aces from a deck of cards and turn my back. Then I ask you to stack the four cards face up with the heart at the bottom, then the club, the diamond, and the spade. Now turn the uppermost card, the spade, face down.

Now you’re invited to perform any of these operations as many times and in any order that you wish:

  • Cut any number of cards from the top of the stack to the bottom.
  • Turn the top two cards over as one.
  • Turn the entire stack over.

When you’ve finished, I ask you to turn the topmost card over, then turn the top two cards over as one, then turn the top three cards over as one. I predict that the club is the only card facing the opposite way from the others, and as long as you’ve followed the directions above, it always will be.

The answer is explained by group theory — see the article below for the details.

(Douglas E. Ensley, “Invariants Under Group Actions to Amaze Your Friends,” Mathematics Magazine 72:5 [December 1999], 383-387.)

| Science & Math

Self-Sacrifice

https://en.wikipedia.org/wiki/File:Mattio_Lovato_hanging_during_self-crucifixion_attempt.jpg

In 1805 a disturbed Venice shoemaker named Matthew Lovat nearly managed to crucify himself. From William Wood Seymour’s The Cross in Tradition, History, and Art, 1898:

Having prepared a cross, he stripped himself naked except for a girdle about his loins. Fearing that he would not be able to attach himself securely to the cross, he covered the lower part with a net, extending from the suppedaneum to the transverse. Having introduced himself into this, he next drove a nail through the palm of his right hand by striking it on the floor until the point appeared on the outside. He then drove a nail through both feet, fastening them to the wood. Tying himself around the waist to the cross, he next wounded himself in the side with a knife. He was yet in the room: to show himself to the people required the exercise of much fortitude and resolution. The foot of the cross having been placed upon the window-sill, he drew himself forward by means of his fingers pressing on the floor, until the lower end, overbalancing the rest, the cross fell outside of the house and hung by ropes previously fixed to sustain it. He then fastened the right hand, already pierced by the nail, to its proper place, but after driving the nail through the left hand he was unable to affix it. This took place at eight o’clock in the morning. As soon as he was seen he was taken down and carried to the hospital where his wounds were completely cured.

I haven’t been able to learn why he thought this was necessary. After an earlier attempt was prevented, “Being interrogated repeatedly as to the motive for his self-crucifixion, he maintained an obstinate silence, except, that he once said to his brother, that that day was the festival of St. Matthew, and that he could give no farther explanation.” After the 1805 attempt, he would say only, “The pride of man must be mortified, it must expire on the cross.” He starved himself to death in an asylum shortly afterward.

| Death · Religion

The Robben Island Notebooks

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

Sentenced in 1964 to life in prison, anti-apartheid activist Ahmed Kathrada got permission during his confinement to pursue a history degree through the University of South Africa. He used his access to books and writing materials to compile a series of secret notebooks in which he recorded quotations that inspired him. Together they form what used to be called a commonplace book — a series of personal memoranda that, taken together, illuminate the spirit of the compiler:

Ofttimes the test of courage becomes rather to live than to die. — Vittorio Alfieri

It is almost a definition of a gentleman to say he is one who never inflicts pain. — Cardinal Newman, The Idea of a University Defined (1873)

One owes respect to the living; but to the dead one owes nothing but the truth. — Voltaire

The triumph of wicked men is always short-lived. — Honore de Balzac, The Black Sheep

(Form of oath-taking among Shoshone Indians is:) The earth hears me. The sun hears me. Shall I lie?

Conrad wrote that life sometimes made him feel like a cornered rat waiting to be clubbed.

Nobody knows what kind of government it is who has never been in prison. — Leo Tolstoy

Leve fit, quod bene fertur onus. (A burden becomes lightest when it is well borne.)

To secure ourselves against defeat lies in our own hands, but the opportunity of defeating the enemy is provided by the enemy himself. — Sun Tzu

Verba volant, scripta manent. (The spoken word flees; the written word remains.) — Ancient Roman adage

(Peter Ustinov explains why he reads so much:) “If you’re going to be the prisoner of your own mind, the least you can do is to make sure it’s well furnished.”

To be without some of the things you want is an indispensable part of happiness. — Bertrand Russell

Altogether “Kathy” compiled seven notebooks over 26 years, drawing not just on his study materials and smuggled newspapers but on 5,000 books donated to the prison library by a Cape Town bookstore. Finally released in 1989, he went on to become a member of Parliament after South Africa’s first democratic elections in 1994 and served as President Nelson Mandela’s parliamentary counsellor until 1999.

One of his former warders, Christo Brand, told him, “I was supposed to be your master, but instead you became my mentor.”

(Sahm Venter, ed., Ahmed Kathrada’s Notebook From Robben Island, 2005.)

| History · Quotations · Society

Misc

  • Thomas Jefferson, John Adams, and James Monroe all died on July 4.
  • Australia is wider than the moon.
  • NoNRePReSeNTaTiONaLiSm can be assembled from chemical symbols.
  • 1 × 56 – 1 – 7 = 15617
  • “‘Needless to say’ is, needless to say, needless to say.” — Enoch Haga
| History · Language · Quotations · Science & Math · Trivia

His Image

https://doi.org/10.1371/journal.pone.0198745
Images: PLOS One

In 2018 a team of researchers at the University of North Carolina presented 511 American Christians with randomly paired pictures of faces and asked them to identify which of the pair more closely resembled the face of God. By combining the selected faces, the psychologists could produce a composite image of the Creator as envisioned by various groups. (Here, the image on the left is God as young participants imagine him; the one on the right is how he’s seen by older participants.)

Liberals tend to imagine that God is younger, more feminine, and more loving than conservatives, and African-Americans picture a God who looks more African-American than Caucasians do, but the traditional image of the powerful older man with the flowing beard is nowhere to be seen.

“People’s tendency to believe in a God that looks like them is consistent with an egocentric bias,” said senior author Kurt Gray. “People often project their beliefs and traits onto others, and our study shows that God’s appearance is no different — people believe in a God who not only thinks like them, but also looks like them.”

One exception, though: Men and women believed in an equally masculine-looking God.

(Joshua Conrad Jackson, Neil Hester, and Kurt Gray, “The Faces of God in America: Revealing Religious Diversity Across People and Politics,” PLOS One, June 11, 2018.)

| Religion · Science & Math

The Mystery Tombstone

In Plymouth, Tobago, lies a tomb with an enigmatic inscription:

Within these walls are deposited the bodies of Mrs. Betty Stiven and her child. She was the beloved wife of Alex B Stiven to the end of his days will deplore her death which happened upon the 25th day of Nov. 1783 in the 23rd year of her age. What was remarkable of her, she was a mother without knowing it, and a wife without letting her husband know it except by her kind indulgences to him.

Theories abound, but there’s no consensus as to its meaning.

| Oddities

Reciprocity

In 2006, Math Horizons challenged its readers to pose a problem in such a way that it contained its own answer. Rheta Rubenstein of the University of Michigan-Dearborn offered a pair of questions that answer one another:

  1. What fraction of the letters in three-eighths are vowels?
  2. What fraction of the letters in one-third are vowels?

(“Self-Answering Problems,” Math Horizons 13:4 [April 2006], 19.)

| Science & Math

“Valentine by a Telegraph Clerk”

Another poem by James Clerk Maxwell:

The tendrils of my soul are twined
With thine, though many a mile apart.
And thine in close coiled circuits wind
Around the needle of my heart.

Constant as Daniel, strong as Grove.
Ebullient throughout its depths like Smee,
My heart puts forth its tide of love,
And all its circuits close in thee.

O tell me, when along the line
From my full heart the message flows,
What currents are induced in thine?
One click from thee will end my woes.

Through many a volt the weber flew,
And clicked this answer back to me;
I am thy farad staunch and true,
Charged to a volt with love for thee.

| Poems · Technology

Ambition

https://commons.wikimedia.org/wiki/File:The_Unfinished_Obelisk,_Aswan,_AG,_EGY_(48027110231).jpg

In a quarry at Aswan lies an unfinished obelisk, the largest the ancient Egyptians ever attempted. It’s 137 feet long and weighs more than 1,000 tons, more than two jumbo jets or 200 African elephants. If it had been completed it would have weighed more than twice as much as any other obelisk that the Egyptians ever erected. Cracks appeared in the granite before workers could carve it from the bedrock, so the project was abandoned.

“The obelisk is so large that it makes a cameo appearance in Cecil B. DeMille’s 1923 silent film The Ten Commandments,” writes Egyptologist Bob Brier in Cleopatra’s Needles (2021). “In one scene we see Israelites toiling under the whip of a cruel taskmaster, pulling a large block of stone up an inclined ramp. That incline is the unfinished obelisk!”

| History · Technology