In 1928, Belgian financier Alfred Loewenstein fell to his death from a private plane over the English Channel. How it happened has never been explained. In this week’s episode of the Futility Closet podcast, we’ll describe the bizarre incident, which has been called “one of the strangest fatalities in the history of commercial aviation.”
We’ll also consider whether people can be eaten by pythons and puzzle over an enigmatic horseman.
When a friend showed him a 16 × 16 magic square devised by Michel Stifelius, Ben Franklin went home and composed the square above, “not willing to be outdone.” An admirer describes its properties:
1. The sum of the sixteen numbers in each column or row, vertical or horizontal, is 2,056. — 2. Every half column, vertical or horizontal, makes 1,028, or just one half of the same sum, 2,056. — 3. Any half vertical row added to any half horizontal, makes 2,056. — 4. Half a diagonal ascending added to half a diagonal descending, makes 2,056, taking these half diagonals from the ends of any side of the square to the middle of it, and so reckoning them either upward, or downward, or sideways. — 5. The same with all the parallels to the half diagonals, as many as can be drawn in the great square: for any two of them being directed upward and downward, from the place where they begin to that where they end, make the sum 2,056; thus, for example, from 64 up to 52, then 77 down to 65, or from 194 up to 204, and from 181 down to 191; nine of these bent rows may be made from each side. — 6. The four corner numbers in the great square added to the four central ones, make 1,028, the half of any column. — 7. If the great square be divided into four, the diagonals of the little squares united, make, each, 2,056. — 8. The same number arises from the diagonals of an eight sided square taken from any part of the great square. — 9. If a square hole, equal in breadth to four of the little squares or cells, be cut in a paper, through which any of the sixteen little cells may be seen, and the paper be laid on the great square, the sum of all the sixteen numbers seen through the hole is always equal to 2,056.
Franklin wrote, “This I sent to our friend the next morning, who, after some days, sent it back in a letter with these words: ‘I return to thee thy astonishing or most stupendous piece of the magical square, in which’ — but the compliment is too extravagant, and therefore, for his sake as well as my own, I ought not to repeat it. Nor is it necessary; for I make no question but you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician.”
(“Clavis,” “Magic Squares,” The Mirror of Literature, Amusement, and Instruction 4:109 [Oct. 23, 1824], 293-294.) (Thanks, Walker.)
12/21/2020 UPDATE: The square appeared originally in 1767 in James Ferguson’s Tables and Tracts, Relative to Several Arts and Sciences and was reprinted a year later in the Gentleman’s Magazine. Only the second publication credits Franklin. I don’t have a date for Franklin’s purported composition, so I don’t know what to make of this. (Thanks, Tom.)
This bird’s-eye view of Amsterdam, painted in 1652 by Dutch artist Jan Micker, depicts even the shadows of clouds.
It presents the city as it appeared in 1538 … because it was inspired by an even earlier painting, by Cornelis Anthonisz (below).
Invented independently by Piet Hein and John Nash, the game of Hex is both simple and deep. Each player is assigned two opposite sides of the board and tries to connect them with an unbroken chain of stones. Draws are impossible, and in principle it can be shown that the first player has a winning strategy (if the second player had such a strategy, the first player could “steal” it with a move in hand). But succeeding in practical play requires careful, subtle thought.
BANGOR, England, August 14. — Evidence that he may have cut his throat while asleep was given at an inquest at Bangor on the body of Thornton Jones, a lawyer. ‘Suicide while temporarily insane,’ was the verdict.
He lived 80 minutes after the infliction of the wound, during which time, it was stated, he cried out to his wife and son, ‘Forgive me! Forgive me!’
Then motioning for a paper and pencil, he wrote: ‘I dreamt that I had done it. I awoke to find it true.’
— Washington D.C. Evening Star, August 14, 1924
Around January 31 and November 11 each year, the setting sun illuminates the “Infinite Corridor,” the 251-meter hallway that runs through five main buildings at MIT.
The hallway isn’t optimally aligned, so the phenomenon lasts only about 2 minutes. MIT maintains a page with predictions, etiquette, background, and more photos.
“[Braxton] Bragg was a remarkably intelligent and well-informed man, professionally and otherwise. He was also thoroughly upright. But he was possessed of an irascible temper, and was naturally disputatious. A man of the highest moral character and the most correct habits, yet in the old army he was in frequent trouble. As a subordinate he was always on the lookout to catch his commanding officer infringing his prerogatives; as a post commander he was equally vigilant to detect the slightest neglect, even of the most trivial order.
“I have heard in the old army an anecdote very characteristic of Bragg. On one occasion, when stationed at a post of several companies commanded by a field officer, he was himself commanding one of the companies and at the same time acting as post quartermaster and commissary. He was first lieutenant at the time, but his captain was detached on other duty. As commander of the company he made a requisition upon the quartermaster — himself — for something he wanted. As quartermaster he declined to fill the requisition, and endorsed on the back of it his reasons for so doing. As company commander he responded to this, urging that his requisition called for nothing but what he was entitled to, and that it was the duty of the quartermaster to fill it. As quartermaster he still persisted that he was right. In this condition of affairs Bragg referred the whole matter to the commanding officer of the post. The latter, when he saw the nature of the matter referred, exclaimed: ‘My God, Mr. Bragg, you have quarrelled with every officer in the army, and now you are quarrelling with yourself!'”
— Personal Memoirs of U.S. Grant, 1885
Astronomer Thomas Dick believed that every planet in the solar system was inhabited. In his 1838 book Celestial Scenery he worked out that they contain 21 trillion inhabitants in all — assuming “280 inhabitants to a square mile, which is the rate of population in England.”
In 2000, mathematician Mike Keith rearranged the letters in Shakespeare’s Sonnet 143 to tell a familiar story:
Lo, as a careful huswife runs to catch
One of her feathered creatures broke away,
Sets down her babe and makes all swift dispatch
In pursuit of the thing she would have stay,
Whilst her neglected child holds her in chase,
Cries to catch her whose busy care is bent
To follow that which flies before her face,
Not prizing her poor infant’s discontent:
So run’st thou after that which flies from thee,
Whilst I, thy babe, chase thee afar behind;
But if thou catch thy hope turn back to me,
And play the mother’s part: kiss me, be kind.
So will I pray that thou mayst have thy Will,
If thou turn back and my loud crying still.
The gal named Mary shuffles through the house —
But view her as she strokes her frisky lamb,
Whose brow is whiter than a snowy mouse,
Fleece chalky as French cliffs of epigram
Each place she’d bathe, attain or hie without
(To parish church or at the stuffy crypt),
The lamb’s instinct did follow her about
(So close around that twice she nearly tripped).
Back to her class that zany lamb would fly
And cause a hubbub (then they fetched it in);
It whacked the inkwell, overturn’d the pie,
Though this was chief and total public sin.
“Anoint this lofty one,” the brats then cried,
“For now it’s certain: school is rather fried!”
(Michael Keith, “Another Mary Sonnet,” Word Ways 33:3 [August 2000], 233.)
In November 1970, a man and his daughters came upon the charred remains of a woman in the foothills near Bergen, Norway. Some personal items were nearby, and two suitcases were later found at the railway station, but all identifying marks had been removed from all of these.
An autopsy showed the woman had been incapacitated by phenobarbital and poisoned by carbon monoxide, and she’d consumed 50 to 70 sleeping pills. A notepad found in one of the suitcases suggested that she’d traveled throughout Europe using at least eight false identities. She’d last been seen alive when she’d checked out of her room at the Hotel Hordaheimen two days earlier; she’d paid in cash and requested a taxi. During her stay she’d appeared guarded and kept to her room.
The woman has never been identified. Her death was attributed to the sleeping pills, and she was interred in a Bergen graveyard. A 2017 analysis of her teeth suggested that she’d been born in Germany around 1930 and had perhaps moved to France as a child. In 2005 a resident of Bergen said he’d seen a woman hiking on a hillside outside town five days before the discovery of the body, dressed lightly and followed by two men. She’d seemed about to speak to him but had not. He’d reported the encounter to the police, but no investigation was made.
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