The Veiled Virgin
Image: Wikimedia Commons

Sculptor Giovanni Strazza probably completed this bust of a veiled Virgin Mary in the early 1850s. It was transported to Newfoundland and placed in the Episcopal Palace next to St. John’s Basilica.

“To say that this representation surpasses in perfection of art, any piece of sculpture we have ever seen, conveys but weakly our impression of its exquisite beauty,” wrote a local newspaper. “The possibility of such a triumph of the chisel had not before entered into our conception. Ordinary language must ever fail to do justice to a subject like this — to the rare artistic skill, and to the emotions it produces in the beholder.”

The Sea Island Problem

The Chinese mathematician Liu Hui offered this technique in a text composed about 500 years after Euclid. We’re on the mainland, and we want to find the height of a mountain on a distant island without crossing the sea.

Liu Hui showed that this can be accomplished by setting up two poles of a known height in a line with the mountain …
Image: Wikimedia Commons

… and by appealing to a principle of complementary rectangles — here the red and the blue rectangles have the same area:
Image: Wikimedia Commons

By using that principle it’s possible to recast the problem in terms of values that we can measure: the height of the poles (CD), the “offset” from which the top of the mountain can just be sighted from ground level over the top of each pole (DG and FH), and the distance between the poles (DF). Putting all that together we can find both the height of the mountain:

 \displaystyle \frac{CD \times DF}{FH - DG} + CD

and the distance between the first pole and the mountain:

 \displaystyle \frac{DG \times DF}{FH - DG}

without ever leaving the mainland. Penn State University mathematician Frank Swetz concluded that “in the endeavours of mathematical surveying, China’s accomplishments exceeded those realized in the West by about one thousand years.”


Rejection letter sent by the University of Portland’s Portland Magazine, devised by editor Brian Doyle:

Thank you for your lovely and thoughtful submission to the magazine, which we are afraid we are going to have to decline, for all sorts of reasons. The weather is dreary, our backs hurt, we have seen too many cats today and as you know cats are why God invented handguns, there is a sweet incoherence and self-absorption in your piece that we find alluring but we have published far too many of same in recent years mostly authored by the undersigned, did we mention the moist melancholy of the weather, our marriages are unkempt and disgruntled, our children surly and crammed to the gills with a sense of entitlement that you wonder how they will ever make their way in the world, we spent far too much money recently on silly graphic design and now must slash the storytelling budget, our insurance bills have gone up precipitously, the women’s basketball team has no rebounders, an aunt of ours needs a seventh new hip, the shimmer of hope that was the national zeitgeist looks to be nursing a whopper of a black eye, and someone left the toilet roll thing empty again, without the slightest consideration for who pays for things like that. And there were wet towels on the floor. And the parakeet has a goiter. And the dog barfed up crayons. Please feel free to send us anything you think would fit these pages, and thank you for considering our magazine for your work. It’s an honor.

From Letters of Note.

Podcast Episode 234: The Dig Tree,_Wills_and_King,_1861.jpg

In 1860 a party of explorers set out to traverse the Australian continent, but bad management and a series of misfortunes sent it spiraling toward tragedy. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Victorian Exploring Expedition and its dramatic climax at Cooper’s Creek.

We’ll also try to validate Archimedes and puzzle over an unlucky thief.

See full show notes …

Good and Ugly

Technical but interesting: Designer Iginio Lardani’s title sequence for The Good, the Bad and the Ugly contains only one error, and it’s in Lardani’s own credit (2:33 above).

“[A]n ‘error’ specific to optical printing caused by improper loading of the footage and mask being composited — Newton’s rings — appears in his title card alongside the text stating ‘TITLES | LARDANI,” notes film historian Michael Betancourt in Semiotics and Title Sequences (2017).

This appears to be an inside joke meant for other title designers. According to his son, Lardani had complete freedom in creating the design. Betancourt writes, “Recognizing this specific ‘error’ in the card stating ‘TITLES LARDANI’ depends on technical knowledge of the optical printing process. … given the technical perfection in the rest of the sequence, it is not just a ‘beginner’s mistake,’ but implies a conscious choice to include this compositing error in the design.”

“It is a joke only comprehensible (even recognizable) by an audience that recognizes the Newton’s rings and understands what they are — an error in the optical printing; this knowledgeable audience specifically includes title sequence designers rather than the general public. … Because it is specifically a specialized, technical mistake, its recognition will be severely limited to his peers — suggesting that they are the ones being addressed by it.”

Mood Indigo

In the 1870s Philadelphia’s Augustus Pleasonton convinced himself that blue light had almost miraculously beneficial properties: He and his followers insisted that it cured disease, promoted hair growth, banished deafness, even resolved insanity. In 1871 he patented a greenhouse (or bluehouse, I suppose) that would “accelerate the growth and maturity of plants and animals.”

It fell to Scientific American to point out that cobalt blue glass diminishes all rays across the visible spectrum; it just diminishes blue and violet light somewhat less than other wavelengths. A plant (or anything else) would receive more blue light simply standing in the sun than hidden in Pleasonton’s hut.

The fad faded, and by the inventor’s death in 1894 it had been forgotten. “It is amusing to see people making fools of themselves,” observed the Boston Globe, “but it soon grows wearisome.”

Set Dressing

William Wellman vowed that his 1927 dogfight movie Wings would contain no stock footage or studio fakery. But after assembling his own planes and film crew, he kept them resolutely on the ground for weeks. When Paramount asked what was missing, he gave them a bewildering answer: clouds.

“Motion on the screen is a relative thing,” he said. “A horse runs on the ground or leaps over fences or streams. We know he is going rapidly because of his relation to the immobile ground.” But a plane alone in the sky may produce no sense of motion at all unless there are clouds around it — and the skies above Wellman’s San Antonio shooting location remained stubbornly clear.

Producer Jesse Lasky later wrote, “There were days on end of perfect sunshine, and our $200-a-week director wouldn’t turn a camera, while overhead mounted at thousands of dollars a day. I confess that we were about ready to yank him off the picture and replace him with someone who would be more amenable.”

In the end they were glad they waited — when the clouds arrived, Wellman’s cameramen took off, and Wings won the first Academy Award for Best Picture.

Outside the Box

An old puzzle asks: Without lifting your pencil from the paper, can you draw a series of four straight lines that passes through all nine points in this grid?

outside the box 1

The trick is to realize that the lines can extend beyond the grid’s area:

outside the box 2

In 1970 Solomon Golomb and John Selfridge found a way to draw a closed path of eight segments that passes through all 25 points in this grid:

outside the box 3

Can you?

Click for Answer

Full Circle

Before they departed on Apollo 16 in April 1972, lunar module pilot Charles Duke told commander John Young about an eerie dream he’d had. The two of them were driving the lunar rover toward the North Ray crater when they crossed a ridge and discovered a set of tire tracks. They followed them, and after an hour they came upon another lunar rover that had been standing on the moon’s surface for thousands of years. In it were two dead astronauts who looked like Duke and Young.

In folklore seeing one’s double can be an omen of imminent death, but Duke didn’t take it that way. “I felt kind of comfortable,” he said later. “I took parts from this other vehicle, to show to the people down at Houston.”

But the impression remained with him as the mission departed for the moon. “The dream was so vivid that when we were landing I looked out of the window to the north to see if there were any tracks on the surface of the moon,” he said. “The landscape was very similar to what I [had] seen in my dream.”

On April 23, he found himself driving the rover with Young toward the North Ray crater and couldn’t resist looking for a second set of tracks. There was none, of course, but while he was distracted the rover began to slide backward down the slope and he had to fight to keep it from overturning. When they came to a stop the rover’s tracks extended ahead of them up the slope.

Young said, “Charlie, you said you were going to see some other tracks on the Moon.”