# 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.)

# Podcast Episode 338: A Point of Law

One dark night in 1804, a London excise officer mistook a bricklayer for a ghost and shot him. This raised a difficult question: Was he guilty of murder? In this week’s episode of the Futility Closet podcast we’ll consider the case of the Hammersmith ghost, which has been called “one of the greatest curiosities in English criminal law.”

We’ll also worry about British spiders and puzzle over some duplicative dog names.

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# Two Birds

Ben Franklin used chess to learn Italian. From his autobiography:

I had begun in 1733 to study languages; I soon made myself so much a master of the French as to be able to read the books with ease. I then undertook the Italian. An acquaintance, who was also learning it, us’d often to tempt me to play chess with him. Finding this took up too much of the time I had to spare for study, I at length refus’d to play any more, unless on this condition, that the victor in every game should have a right to impose a task, either in parts of the grammar to be got by heart, or in translations, etc., which tasks the vanquish’d was to perform upon honour, before our next meeting.

“As we play’d pretty equally,” he wrote, “we thus beat one another into that language.”

# Podcast Episode 337: Lost in a Daydream

In 1901, two English academics met a succession of strange characters during a visit to Versailles. They came to believe that they had strayed somehow into the mind of Marie Antoinette in the year before her execution. In this week’s episode of the Futility Closet podcast we’ll describe the Moberly-Jourdain affair, a historical puzzle wrapped in a dream.

We’ll also revisit Christmas birthdays and puzzle over a presidential term.

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# High and Dry

When the steamship Princess May was grounded in 1910 near Sentinel Island in Alaska’s Lynn Canal, the tide was high and the ship’s momentum forced it well up onto the rocks. There it perched at an angle of 23 degrees for photographer William Case at the height of its extremity.

Happily there was no loss of life, and the vessel was eventually refloated and returned to service.

# The Haidbauer Incident

In 1926, while working as a schoolteacher in Otterthal, Austria, Ludwig Wittgenstein is alleged to have struck an 11-year-old schoolboy, Josef Haidbauer, so that he collapsed unconscious. The incident was reported to the police, and a judge ordered a psychiatric report, but nothing more is known about the case. Ten years later Wittgenstein appeared in the village to ask the forgiveness of children he had hurt. He wrote in a notebook, “Last year with God’s help I pulled myself together and made a confession. This brought me into more settled waters, into a better relation with people, and to a greater seriousness.”

# Podcast Episode 336: A Gruesome Cure for Consumption

In the 19th century, some New England communities grew so desperate to help victims of tuberculosis that they resorted to a macabre practice: digging up dead relatives and ritually burning their organs. In this week’s episode of the Futility Closet podcast we’ll examine the causes of this bizarre belief and review some unsettling examples.

We’ll also consider some fighting cyclists and puzzle over Freddie Mercury’s stamp.

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# Direction

Ancient Egypt was an essentially one-dimensional country strung out along the Nile, which flows from south to north. The winds were conveniently arranged to be predominantly northerly. To go north, a traveler could let his boat drift, while with a sail he could move south against the slow current. For this reason, in the writing of the ancient Egyptians, ‘go downstream (north)’ was represented by a boat without sails, and ‘go upstream (south)’ by a boat with sails. The words (and concepts) or north-south and up-downstream became merged. Since the Nile and its tributaries were the only rivers known to the ancient Egyptians, this caused no difficulties until they reached the Euphrates, which happened to flow from north to south. The resulting confusion in the ancient Egyptian mind is recorded for us to read today in their reference to ‘that inverted water which goes downstream (north) in going upstream (south).’

— P.L. Csonka, “Advanced Effects in Particle Physics,” Physical Review, April 1969, 1266-1281

# Podcast Episode 335: Transporting Obelisks

In the 19th century, France, England, and the United States each set out to bring home an Egyptian obelisk. But each obelisk weighed hundreds of tons, and the techniques of moving them had long been forgotten. In this week’s episode of the Futility Closet podcast we’ll follow the struggles of each nation to transport these massive monoliths using the technology of the 1800s.

We’ll also go on an Australian quest and puzzle over a cooling fire.

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# Podcast Episode 334: Eugene Bullard

Eugene Bullard ran away from home in 1907 to seek his fortune in a more racially accepting Europe. There he led a life of staggering accomplishment, becoming by turns a prizefighter, a combat pilot, a nightclub impresario, and a spy. In this week’s episode of the Futility Closet podcast we’ll tell Bullard’s impressive story, which won him resounding praise in his adopted France.

We’ll also accidentally go to Canada and puzzle over a deadly omission.

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