E Pluribus Unum

Replace each * with a different digit 1-9 to make this equation true:

\displaystyle \frac{*}{**} + \frac{*}{**} + \frac{*}{**} = 1

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Levon’s Divine Underground

In 1985, Levon Arakelyan’s wife asked him to dig a potato cellar in their basement in Arinj, Armenia. He did this, and then continued digging for 23 years. At his death in 2008 he’d produced a network of rooms, steps, and corridors that extended 21 meters beneath the couple’s two-story house. A builder by trade, he did all of this with hand tools. Today his widow runs a small museum and gives tours of her late husband’s strange obsession. More photos here.

Something Borrowed

Image: National Museum of American History

Under enemy fire on March 25, 1945, radio operator Temple Leslie Bourland bailed out of a C-47 over the Rhine. He injured his hip but avoided capture, hiding in a foxhole for two days while using his parachute as a blanket. When Allied troops discovered him he returned to his unit.

That summer he met San Antonio secretary Rosalie Hierholzer, and during their brief courtship he showed her the bullet-riddled parachute, which he kept in his trunk. Rosalie’s aunt Lora offered to make it into a bridal gown, and Rosalie wore it at their wedding. The train still retained some of the military seams.

Philosophical Limericks


Cried the maid: “You must marry me, Hume!”
A statement that made David fume.
He said: “In cause and effect,
There is a defect;
That it’s mine you can only assume.”

— P.W.R. Foot

Thomas Hobbes of Malmesbury thought
Life was nasty and brutish and short;
But contracts, once made,
Would come to our aid,
And ensure modest comfort — at court.

— Peter Alexander

There was a young man who said: “Ayer
Has answered the atheist’s prayer,
For a Hell one can’t verify
Surely can’t terrify —
At least till you know you are there.”

— Anonymous


The roots of the word helicopter are not heli and copter but helico and pter, from the Greek “helix” (spiral) and “pteron” (wing).

G.L.M. de Ponton’s 1861 British patent says, “The required ascensional motion is given to my aerostatical apparatus (which I intend denominating aeronef or helicoptere,) by means of two or more superposed horizontal helixes combined together.”

Podcast Episode 238: The Plight of Mary Ellen Wilson


In 1873 a Methodist missionary in New York City heard rumors of a little girl who was kept locked in a tenement and regularly whipped. She uncovered a shocking case of neglect and abuse that made headlines around the world. In this week’s episode of the Futility Closet podcast we’ll tell how one girl’s ordeal led to a new era in child welfare.

We’ll also outsource Harry Potter and puzzle over Wayne Gretzky’s accomplishments.

See full show notes …

The THOG Problem

Image: Wikimedia Commons

I have picked one color (black or white) and one shape (square or circle). A symbol that possesses exactly one of the properties I have picked is called a THOG. The black circle is a THOG. For each of the other symbols, is it (a) definitely a THOG, (b) undecidable, or (c) definitely not a THOG?

Cognitive psychologist Peter Wason invented this puzzle in 1979 to demonstrate some weaknesses in human thinking. In pilot studies, 0 of 10 student barristers were able to solve it correctly, with one arguing for more than an hour against the correctness of Wason’s solution. Seven of 14 medical students solved it, taking an average of 6.3 minutes. (“This is quite an impressive result.”) One young doctor solved it in his head in about a minute and said, “I would not let any doctor near me who couldn’t solve that problem.” What’s the answer?

Click for Answer

The Blur Building

The media pavilion for the 2002 Swiss National Expo was a cloud. Organizers built a curved building fitted with more than 30,000 nozzles that pumped water from Lake Neuchâtel into a fine mist, creating a floating 90-meter fog bank whose contours were controlled by a computerized weather system.

Artist Antony Gormley took this idea a step further in 2007 with Blind Light, a 10-meter-square glass vitrine filled with mist and lit by 7,000 lux of intense fluorescent light that reduced visibility to less than an arm’s length.

“One could, and did, get temporarily lost in its 90 percent humidity,” writes Richard Hamblyn in Clouds: Nature and Culture (2017). “The intended effect of Gormley’s ‘bright, cuboid cloud’ was to overwhelm the senses, as though one had walked into a cloud, literally and figuratively, entering a cold, damp, unsettling world of enveloping isolation.”

Stirred, Not Shaken

The 1967 version of Casino Royale, starring David Niven, set an unlikely milestone: Its soundtrack album became famous among audio purists for the quality of its sound.

“The legend is that the original master tape had ‘mad’ levels on it,” audiophile Harry Pearson told the New York Times in 1991. “Once the meters pass zero, it means that you’re saturating the tape and running the risk of distortion. On ‘Casino,’ they used a supposedly very fancy grade of tape, and the engineers really pushed it, so the meters were typically running deep into the red — plus one, plus two, plus three, plus four.” The result is an extremely wide dynamic range.

A particular high point is Dusty Springfield’s “The Look of Love” (Track 2). Springfield recorded her vocal in a “tiny isolation booth, so on a really good system, you can hear her voice emerging from what sounds like a little hole in space. She’s not part of the general orchestral acoustic, and once your system gets to a certain point, you can hear that.”

Pearson said the soundtrack came to serve as a benchmark at Absolute Sound, the audiophile bible he founded in 1973. “Whenever we get a piece of equipment that we think is setting new records, out comes ‘Casino,'” he said. “The better your system gets, the more you get out of that album.”

(Thanks, Allen.)