Last Thoughts

Belgian painter Antoine Wiertz unveiled a gruesome triptych in 1853: Thoughts and Visions of a Severed Head depicts a guillotined head’s impressions of its final three minutes of awareness.

Wietz added a verbal description of each of the panels. Here’s an excerpt from the second minute, “Under the Scaffold”:

For the first time the executed prisoner is conscious of his position.

He measures with his fiery eyes the distance that separates his head from his body and tells himself, ‘My head really is cut off.’

Now the frenzy redoubles in force and energy.

The executed prisoner imagines that his head is burning and turning on itself, that the universe is collapsing and turning with it, that a phosphorescent fluid is whirling around his skull as it melts down.

In this midst of this horrible fever, a mad, incredible, unheard of idea takes possession of the dying brain.

Would you believe it? This man whose head has been chopped off still conceives of a hope. All the blood that remains bubbles, gushes, and courses with fury through all the canals of life to grasp at this hope.

At this moment the executed prisoner is convinced that he is stretching out his convulsive and rage-filled hands toward his expiring head.

I don’t know what this imaginary movement means. Wait … I understand … It’s horrible!

Oh! My God, what is life that it continues the struggle to the very last drop of blood?

In the same year, American author Theodore Witmer had recorded his own impressions of seeing an execution in the 1840s. “Why don’t somebody give us ‘The Reflections of a Decapitated Man?'” he asked. “If it turned out stupid, he might excuse himself for want of a head.”

So to Speak

What do these words have in common?


Click for solution …

Podcast Episode 77: The Sourdough Expedition

In 1910, four Alaskan gold miners set out to climb Mount McKinley, the highest peak in North America, to win a two-cent bar bet. In this week’s episode of the Futility Closet podcast we’ll tell the surprising story of the Sourdough Expedition, a mountaineering effort that one modern climber calls “superhuman by today’s standards.”

We’ll also hear about a ghoulish tourist destination and puzzle over why a painter would blame himself for World War II.

Sources for our feature on the Sourdough expedition:

Bill Sherwonit, “The Sourdough Expedition,” Alaska 68:4 (May/June 2002), 28.

Jason Strykowski, “Impossible Heights: The Alaskan Miners Who Conquered Mount McKinley,” Wild West 24:4 (December 2011), 20.

Terrence Cole, ed., The Sourdough Expedition, 1985.

W.F. Thompson, “First Account of Conquering Mt. McKinley,” New York Times, June 5, 1910.

Listener mail:

The Telegraph has a photo of the mummies in the Capuchin catacombs in Palermo, Sicily.

Wikipedia has a photo of Rosalia Lombardo, the immaculately preserved 2-year-old embalmed in 1920, and another appears here:

Karen Lange, “Lost ‘Sleeping Beauty’ Mummy Formula Found,” National Geographic News, Jan. 26, 2009 (accessed 10/10/2015).

This week’s lateral thinking puzzle is from Paul Sloane and Des MacHale’s 2005 book Outstanding Lateral Thinking Puzzles.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at Thanks for listening!

Black and White

von meyenfeldt chess puzzle

A poser by F.H. von Meyenfeldt, 1967. What move must Black play to enable a forced mate in two by White?

Click for solution …


Some geometric legerdemain by Argentine magician Norberto Jansenson. (Thanks, Ron.)

The Hydra Game

hydra game

Hercules is battling a hydra. He manages to sever a head, but finds that a new head is generated according to the following rule: We move down one segment from the point where the head was severed and make a copy of the entire subtree above that point. Worse, the rate is increasing — the nth stroke of Hercules’ sword produces n new subtrees.

What will happen? The situation certainly looks dire, but, amazingly, Hercules cannot lose. No matter how large the hydra is, and no matter the order in which he severs the heads, he will always kill the hydra in finitely many turns.

Why? With each step, the complexity in the network is migrating toward the root — and that can’t continue forever. “We basically say that whenever something goes on K steps away from the root, it’s infinitely times worse than anything that is going on K-1 steps away from the root,” Comenius University computer scientist Michal Forišek explains in Slate.

“Now, whenever you kill a head, you very slightly simplified something that is K steps away. And even though you get a lot of new stuff in return, all that stuff is only K-1 steps away, and hence the entire result is still simpler than it was before.”

(Laurie Kirby and Jeff Paris, “Accessible Independence Results for Peano Arithmetic,” Bulletin of the London Mathematical Society 14 [1982], 285-293.)

In a Word

adj. apt, fit, or suitable

adj. pertaining to dancing

Hermit crabs adopt other creatures’ castoff shells for protection. But as they grow, crabs must move into successively larger shells. This produces a curious phenomenon: When a crab finds a shell that’s too big for it, it waits nearby. Other crabs may accumulate, forming a little conga line of dissatisfied shell seekers. Finally a “Goldilocks” crab arrives — a crab large enough to claim the new shell — and now each waiting crab can move into the shell abandoned by its larger neighbor. By cooperating to share a scarce resource, the whole species benefits.

The same thing happens in human societies — when one person finds a new apartment, car, or job, she leaves behind her old one, and the vacancy passes down through society until the final unit is cast away or destroyed. It’s called a vacancy chain.

(Thanks, Duncan.)

Fundamental Things Apply


In the final scene of Casablanca, the airplane is made of plywood. The film was shot shortly after the Japanese attacked Pearl Harbor, and California was bracing for a new attack, so movie studios were severely restricted from shooting on location and forbidden entirely from filming at airports. So the movie was shot on soundstages at the Warner Bros. studios in Burbank, and Soundstage #1, as it turned out, was too small to accommodate a real airplane.

So prop men built a half-size Lockheed Electra 12A out of plywood and balsa, and little people in jumpsuits were hired to bustle around it. The fog — a rarity in Morocco — helped to sell the effect.

Also: Dooley Wilson was an accomplished singer, but he couldn’t play the piano. “During the filming of Casablanca, a Warners staff musician, Elliott Carpenter, played the piano to the side of the set so that Wilson could get his bearings,” writes Jeff Siegel in The Casablanca Companion. “It’s also Carpenter’s playing that was dubbed into the film. The charade went off so well that when Wilson appeared for a nightclub gig after the movie was released, the club’s manager asked him why he wasn’t going to play the piano in his act.”

Shifting Gears

A puzzle by French puzzle maven Pierre Berloquin:

Timothy rides a bicycle on a road that has four parts of equal length.

The first fourth is level, and he pedals at 10 kph.

The second fourth is uphill, and he pedals at 5 kph.

The third fourth is downhill, and he rides at 30 kph.

The fourth fourth is level again, but he has the wind at his back, so he goes 15 kph.

What is his average speed?

Click for solution …


Image: Flickr

We’ve been making things awfully hard on spirits. The standard Ouija board lays out the alphabet in two simple rows, which means it’s easy for the dead to tell us about FEEDERS but terribly hard to refer to LAYAWAY, even though these words are equally long.

In the interests of better communication, Eric Iverson made a study of this for the August 2005 issue of Word Ways. Using an image of a Ouija board, he counted the number of pixels that a planchette would have to travel in order to spell out various English words. The results are dismaying: The most exhausting four-letter word, MAMA, requires fully 17 times as much travel as the simple FEED. Longer words are more consistent: The hardest 23-letter word, DISESTABLISHMENTARIANISM, requires little more work than the easiest, ELECTROENCEPHALOGRAPHIC. But do dead people have that kind of stamina?

What’s the answer? Iverson experimented with different layouts and found a hexagonal grid that minimizes the average travel distance for a typical word (see the link below). And he found a checkerboard grid that’s 3 percent more efficient than that. Even rearranging the letters on a standard board to ZXVGINAROFUPQ JKWCHTESDLMYB rather than the standard alphabet increases efficiency by about a third. Now maybe we can have some better conversations.

(Eric Iverson, “Traveling Around the Ouija Board,” Word Ways 38:3 [August 2005], 174-177.)

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