In the 1940s, journalist Stefan Lorant was researching a book on Abraham Lincoln when he came upon a photograph of the president’s funeral procession as it moved down Broadway in New York City. The image was dated April 25, 1865.

As Lorant tried to identify the location, he found that the shuttered house on the left belonged to Cornelius van Schaack Roosevelt, the grandfather of future president Teddy Roosevelt and his brother Elliott. Teddy would have been 6 years old at the time of the procession. And visible in a second-story window are the heads of two boys.

As it happened, Lorant had an opportunity to ask Roosevelt’s widow Edith about the image. “Yes, I think that is my husband, and next to him his brother,” she said. “That horrible man! I was a little girl then and my governess took me to Grandfather Roosevelt’s house on Broadway so I could watch the funeral procession. But as I looked down from the window and saw all the black drapings I became frightened and started to cry. Theodore and Elliott were both there. They didn’t like my crying. They took me and locked me in a back room. I never did see Lincoln’s funeral.”

Image: Wikimedia Commons

A problem from Peter Winkler’s excellent collection Mathematical Puzzles, 2021:

Four bugs live on the four vertices of a regular tetrahedron. One day each bug decides to go for a little walk on the tetrahedron’s surface. After the walk, two of the bugs have returned to their homes, but the other two find that they have switched vertices. Prove that there was some moment when all four bugs lay on the same plane.

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Two for One,_Sotra_Patera,_Mohini_Fluctus_(cropped).png

Mountains on Saturn’s moon Titan are named after mountains in Middle-earth, the fictional setting of J.R.R. Tolkien’s fantasy novels.

The highest peak on Titan is Mount Doom (“Doom Mons”), which rises more than a mile above the surrounding plain. Tolkien’s Mount Doom made its first appearance in The Lord of the Rings in 1954.

By coincidence, science fiction writer Stanley G. Weinbaum had already placed a fictional Mount Doom on Titan in his 1935 story Flight on Titan.

So, in honoring Tolkien, the International Astronomical Union also fulfilled Weinbaum’s vision.

Lincoln at Rest

On the day after Abraham Lincoln’s assassination, Army surgeons Edward Curtis and Joseph Janvier Woodward performed an autopsy at the White House. Curtis mentioned one sobering moment in a letter to his mother:

I proceeded to open the head and remove the brain down to the track of the ball. The latter had entered a little to the left of the median line at the back of the head, had passed almost directly forwards through the center of the brain and lodged. Not finding it readily, we proceeded to remove the entire brain, when, as I was lifting the latter from the cavity of the skull, suddenly the bullet dropped out through my fingers and fell, breaking the solemn silence of the room with its clatter, into an empty basin that was standing beneath. There it lay upon the white china, a little black mass no bigger than the end of my finger — dull, motionless and harmless, yet the cause of such mighty changes in the world’s history as we may perhaps never realize.

He added, “[S]ilently, in one corner of the room, I prepared the brain for weighing. As I looked at the mass of soft gray and white substance that I was carefully washing, it was impossible to realize that it was that mere clay upon whose workings, but the day before, rested the hopes of the nation. I felt more profoundly impressed than ever with the mystery of that unknown something which may be named ‘vital spark’ as well as anything else, whose absence or presence makes all the immeasurable difference between an inert mass of matter owning obedience to no laws but those covering the physical and chemical forces of the universe, and on the other hand, a living brain by whose silent, subtle machinery a world may be ruled.”

Podcast Episode 362: The Leatherman

In 1856, a mysterious man appeared on the roads of Connecticut and New York, dressed in leather, speaking to no one, and always on the move. He became famous for his circuits through the area, which he followed with remarkable regularity. In this week’s episode of the Futility Closet podcast we’ll describe the Leatherman, whose real identity remains unknown.

We’ll also consider the orientation of churches and puzzle over some balky ponies.

See full show notes …

The Wilcoxon Speech

The war drama Mrs. Miniver dominated the box office in 1942 and won six Oscars, but it’s remembered today chiefly for its final scene, in which a town vicar gives an inspiring speech in a bombed church, exhorting his flock to “free ourselves and those who come after us from the tyranny and terror that threaten to strike us down.”

The film was made before America had formally entered the war, and director William Wyler had rewritten this speech repeatedly on the night before shooting, in hopes that it would sway public opinion. “I’m a warmonger,” he said simply. “I was deeply concerned about Americans being isolationists. Mrs. Miniver obviously was a propaganda film.”

It succeeded beyond his hopes. Churchill claimed that the speech was “propaganda worth a hundred battleships,” and after a private screening at the White House, Franklin Roosevelt asked that it be translated into French, German, and Italian, broadcast throughout Europe on the Voice of America, and air-dropped in millions of leaflets into German-occupied territories.

Henry Wilcoxon, the actor who delivered the speech, must have had his own feelings about this — his only brother had been fatally injured at Dunkirk in 1940.


Ogden Nash’s 1975 poetry collection I Wouldn’t Have Missed It contains an intriguing index of last lines:

A weirdo of fifty, 347
Alone, in the dusk, with the cleaning fluid, 239
And bring me half a dozen smelts, 193
And jam the bloody airwaves on the Seventeenth of March, 199
And join that lama, 217
And leave casements to Keats and me, 332
And the hell with the first fourteen, 346
And Zeus said, Yes, I’m an atheist, 351
But Custard keeps crying for a nice safe cage, 100
But the sensible fish swims down, 28
But you need an orgy, once in a while, 56
Fell through the parlor floor today, 214
He counted them while being digested, 379
How old is Spring, Miranda?, 103
I wish the kipper had a zipper, 321
Is hoping to outwit a duck, 221
It’s kind of fun to be extinct, 265
Kek kek kek, whoosh, kek kek kek, whoosh!, 327
Of deathless celluloid vowels, 192
The proper size for a child, 95
Thus saving the price of a bugle, 63
To tell a lizard from a skunk, 190
We can cling to our fleece, Hot Cha!, 52
Why, they’re crazy, 144

The longest is “That Man has to go continually to the dentist to keep his teeth in good condition when the chief reason he wants his teeth in good condition is so that he won’t have to go to the dentist, 154.”


Drape a chain of evenly spaced weights over a pair of (frictionless) inclined planes like this. What will happen? There’s more mass on the left side, but the slope on the right side is steeper. Simon Stevin (1548-1620) realized that in fact the chain won’t move at all — if it did, we could link the ends as shown and produce a perpetual motion machine.

This is remembered as the “Epitaph of Stevinus.” Richard Feynman wrote, “If you get an epitaph like that on your gravestone, you are doing fine.”

Hope and Change

u.s. coins

The denominations of U.S. coins make intuitive sense, but they can be unwieldy: It can take up to eight coins to assemble an amount up through 99¢. Indeed, producing 99¢ takes (1 × 50¢) + (1 × 25¢) + (2 × 10¢) + (4 × 1¢). What five denominations would minimize the number of coins ever needed to make change?

In The Math Chat Book, Frank Morgan reports that with coins of 1¢, 3¢, 11¢, 27¢, and 34¢, you never need more than 5 coins to make change. For example, now 99¢ = (2 × 34¢) + (1 × 27¢) + (1 × 3¢) + (1 × 1¢). Of the 1,129 possible solutions, this one requires the fewest coins on average (3.343).

Unfortunately, this system is a bit tricky too — to assemble some totals, it’s more efficient to use a few middle-size coins rather than starting with the largest value possible. For example, if you assemble 54¢ by starting with a 34¢ coin, it takes four additional coins to gather the remaining 20¢: (1 × 11¢) + (3 × 3¢). It would have been simpler to choose 2 × 27¢, but that’s not immediately evident.