Art and Commerce

Before the 19th century, containers did not come in standard sizes, and students in the 1400s were taught to “gauge” their capacity as part of their standard mathematical education:

There is a barrel, each of its ends being 2 bracci in diameter; the diameter at its bung is 2 1/4 bracci and halfway between bung and end it is 2 2/9 bracci. The barrel is 2 bracci long. What is its cubic measure?

This is like a pair of truncated cones. Square the diameter at the ends: 2 × 2 = 4. Then square the median diameter 2 2/9 × 2 2/9 = 4 76/81. Add them together: 8 76/81. Multiply 2 × 2 2/9 = 4 4/9. Add this to 8 76/81 = 13 31/81. Divide by 3 = 4 112/243 … Now square 2 1/4 = 2 1/4 × 2 1/4 = 5 1/16. Add it to the square of the median diameter: 5 5/16 + 4 76/81 = 10 1/129. Multiply 2 2/9 × 2 1/4 = 5. Add this to the previous sum: 15 1/129. Divide by 3: 5 1/3888. Add it to the first result: 4 112/243 + 5 1/3888 = 9 1792/3888. Multiply this by 11 and then divide by 14 [i.e. multiply by π/4]: the final result is 7 23600/54432. This is the cubic measure of the barrel.

Interestingly, this practice informed the art of the time — this exercise is from a mathematical handbook for merchants by Piero della Francesca, the Renaissance painter. Because many artists had attended the same lay schools as business people, they could invoke the same mathematical training in their work, and visual references that recalled these skills became a way to appeal to an educated audience. “The literate public had these same geometrical skills to look at pictures with,” writes art historian Michael Baxandall. “It was a medium in which they were equipped to make discriminations, and the painters knew this.”

(Michael Baxandall, Painting and Experience in Fifteenth Century Italy, 1988.)

04/10/2021 UPDATE: A reader suggests that there’s a typo in the original reference here. If 9 1792/3888 is changed to 9 1793/3888, the final result is 7 23611/54432, which is exactly the result obtained by integration using the approximation π = 22/7. (Thanks, Mariano.)

Out of the Way

Thomas Heatherwick designed this “rolling bridge” in 2002 as part of a redevelopment of London’s Paddington Basin. When not in use it curls into an octagon half the width of the waterway, and when extended the eight sections form a 12-meter footbridge.

It won the 2005 British Structural Steel Design Award in 2005.

“American Ships Head to Gulf”

In a forum on Testy Copy Editors in 2009, editor Mike O’Connell posted a headline from the newspaper Japan Today: “Violinist Linked to JAL Crash Blossoms.” He asked, “what do you call these kinds of strangely phrased hedlines? is there a word for them?”

The answer suggested itself — a crash blossom is headline that’s painfully ambiguous, usually due to unwise ellipsis, double meaning, or tortured syntax. Linguist Ben Zimmer gave some examples in the New York Times the following year:

Giant Waves Down Queen Mary’s Funnel
MacArthur Flies Back to Front
Eighth Army Push Bottles Up Germans
McDonald’s Fries the Holy Grail for Potato Farmers
British Left Waffles on Falklands
Gator Attacks Puzzle Experts

And the Language Log blog lists examples from time to time:

Infant Pulled From Wrecked Car Involved in Short Police Pursuit
Letter Bombs Accused in Court
Mexico Mine Missing Declared Dead
Queen Mary Having Bottom Scraped
Two Soviet Ships Collide — One Dies
Soviet Virgin Lands Short of Goal
Smoking Riskier Than Thought
Headless Corpse Accused in Court

Here’s an archive.

Double Duty

On Nov. 5, 1996, Election Day in the United States, the New York Times crossword puzzle carried a surprising clue:

39. Lead story in tomorrow’s newspaper (!), with 43A

43 across turned out to be ELECTED, but 39 across might be either CLINTON or BOBDOLE — both possibilities had seven letters. Was the Times venturing to guess the outcome of the day’s election?

No. Composer Jeremiah Farrell had contrived each of the seven down clues to admit of two possible answers, so that no matter which candidate won, the newspaper might claim a “correct” result.

Crossword editor Will Shortz called Farrell’s ambiguous effort his favorite puzzle of all time.

(Thanks, Andrew.)

A Reindeer Cyclone

Russian photographer Lev Fedoseyev captured this drone footage on March 24 on the Kola Peninsula in the Arctic Circle.

When threatened, a herd of reindeer runs in a circle, making it hard for a predator to target any individual. The fawns are at the center.

First Contact

Moving beyond attempts at merely contacting the dead, artist Attila von Szalay claimed to be the first researcher to actually record the discarnate voices of the spirit world. Von Szalay’s quest began in 1936, while he worked in his darkroom. He claimed to hear in this darkened chamber the voice of his deceased brother calling his name. A subsequent interest in Yoga, meditation, and Eastern philosophy made him better able to hear such voices, and in 1941 he attempted for the first time to record the spirits on a 78 rpm record (with disappointing results). It wasn’t until 1956 that von Szalay ‘successfully’ recorded such phenomena, this time using a reel-to-reel tape recorder. Perhaps unaware of their importance in the history of telecommunications, the first recorded spirit voices offered such banal messages as ‘This is G!,’ ‘Hot dog, Art!,’ and ‘Merry Christmas and Happy New Year to you all.’ These pioneering sessions were reported by noted psychic researcher Raymond Baylass in a letter to the Journal of the American Society for Psychical Research in 1959.

— Jeffrey Sconce, Haunted Media: Electronic Presence From Telegraphy to Television, 2000

False Memory
Image: Wikimedia Commons

On Aug. 2, 1980, a bomb exploded in the main railway station in Bologna, killing 85 people and wounding 200. The blast broke a large clock on the outside wall of the building. It was repaired and continued to run for 16 years, but the image of the clock with its hands fixed at 10:25 became a symbol of the event, and when it stopped working in 1996 its hands were set permanently to that time to commemorate the tragedy.

In 2009 psychologist Stefania de Vito and her colleagues surveyed 180 people who worked at the station or used the trains regularly. Of 173 who knew that the clock is now stopped, 92 percent said that it had always been broken. 79 percent, including all 21 railway employees surveyed, claimed to have seen it set always to 10:25. Of 56 citizens who regularly took part in the official annual commemoration, only 6 remembered correctly that the clock had been working in the past.

“These data indicate that individual memory distortions shared by a large group of people develop into collective false memories,” de Vito writes. In this case, the clock’s symbolic importance “acted as suggestive information and obscured the real experience of seeing the clock working, either as a misleading cue at retrieval or as catalysis for a semantic representation drawn from weak encoding.”

(Stefania de Vito, Roberto Cubelli, and Sergio Della Sala, “Collective Representations Elicit Widespread Individual False Memories,” Cortex 45:5 [2009], 686-687.)