Taylor–Couette Flow

This is surprising: A laminar flow induced in a viscous fluid confined in the gap between two rotating cylinders can be (to a large extent) reversible. The dyes here appear to mix, but in fact they’re being stretched into distinct spirals that can then be “unmade” by reversing the direction of the rotation.


“A Polish girl, desperate and vengeful after failing her examination, took a gun, concealed herself in [Alfred] Werner’s garden, and awaited his return. He arrived home. She fired and missed. Werner calmly turned to her and remarked, ‘Your aim is no better than your knowledge of chemistry.'”

— George B. Kauffman, Alfred Werner: Founder of Coordination Chemistry, 2013

(“The Polizeiinspektorat der Stadt Zürich reports that neither the Stadtpolizei nor the Kantonspolizei have any record of the incident. Se non è vero, è ben trovato!”)

Podcast Episode 324: The Bizarre Death of Alfred Loewenstein


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.

See full show notes …

Franklin’s Magickest Square


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.)

An Elevated View


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).



Image: Wikimedia Commons

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.

You can try it here.

“Sleeping Man a Suicide”

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