In 1812 Percy Shelley and his wife Harriet had committed themselves to a vegetarian diet. During their residence in Ireland that March, Harriet sent a note to a friend in Dublin:
Sunday morng.
17 Grafton StreetMrs. Shelley’s comps. to Mrs. Nugent, and expects the pleasure of her company to dinner, 5 o’clock, as a murdered chicken has been prepared for her repast.
Isaac Bashevis Singer once said, “I am a vegetarian for health reasons — the health of the chicken.”
French mathematician Joseph Bertrand offered this observation in his Calcul des probabilités (1889). Inscribe an equilateral triangle in a circle, and then choose a chord of the circle at random. What is the probability that this chord is longer than a side of the triangle? There seem to be three different answers:
1. Choose two random points on the circle and join them, then rotate the triangle until one of its vertices coincides with one of these points. Now the chord is longer than a side of the triangle when its farther end falls on the arc between the other two vertices of the triangle. That arc is one third of the total circumference of the circle, so by this argument the probability is 1/3.
2. Choose a radius of the circle, choose a point on that radius, and draw a chord through that point that’s perpendicular to the radius. Now imagine rotating the triangle so that one of its sides also intersects the radius perpendicularly. Our chord will be longer than a side of the triangle if the point we chose is closer to the circle’s center than the point where the triangle’s side intersects the radius. The triangle’s side bisects the radius, so by this argument the probability is 1/2.
3. Choose a point anywhere in the circle and draw the chord for which this is the midpoint. This chord will be longer than a side of the triangle if the point we chose falls within a concentric circle whose radius is half the radius of the larger circle. That smaller circle has one-fourth the area of the larger circle, so by this argument the probability is 1/4.
Further methods yield still further solutions. After more than a century, the implications of Bertrand’s conundrum are still being discussed.
Through his innovative stage machines, architect Nicola Sabbatini summoned lightning, fire, hell, storms, gods, and clouds to the sets of 17th-century Venetian operas. The effect could be spectacular — characters braved moving waves, flew through the air, and descended into the underworld.
His illusions, which came to be known as scènes à l’italienne, were best viewed from “the prince’s seat,” the center of the seventh row, where “all the objects in the scene appear better … than from any other place.” The scene above, undertaken with stage designer Giacomo Torelli, depicts Apollo’s palace as a city among the clouds in Francesco Sacrati’s La Venere Gelosa (1643).
But they didn’t always work. Where one libretto read, “Here one sees descend an enormous machine, which arrives at the level of the gloria from the level of the floor of the stage, forming a majestic stairway of clouds, by which Jove descends, accompanied by a multitude of deities and celestial goddesses,” one critic wrote, “A stairway of clouds? For shame! / pardon me, architect: / it was a ladder to climb to the roof.”
“We erect monuments so that we shall always remember, and build memorials so that we shall never forget.” — Arthur Danto
In 1799 two Royal Navy ships met on the Caribbean Sea, and their captains discovered they were parties to a mind-boggling coincidence that would expose a crime and make headlines around the world. In this week’s episode of the Futility Closet podcast we’ll tell the story of the shark papers, one of the strangest coincidences in maritime history.
We’ll also meet some Victorian kangaroos and puzzle over an expedient fire.
There are almost exactly as many inches in a mile (63,360) as there are astronomical units in a light-year (63,241.1).
“He who falls in love meets a worse fate than he who leaps from a rock.” — Plautus
(The painting is by Edmund Leighton, 1852–1922. He called it simply Off.)
What is the shape of the moon’s path around the sun? The moon orbits the earth, and the earth orbits the sun, so many of us imagine it looks something like the image on the left, a looping motion in which the moon periodically slides “backward” during its progress around the larger body.
But it’s not! The shape is closer to a 13-gon with rounded corners; there are no loops. Helmer Aslaksen, a mathematician at the National University of Singapore, writes, “I like to visualize this as follows. Imagine you’re driving on a circular race track. You overtake a car on the right, and immediately slow down and go into the left lane. When the other car passes you, you speed up and overtake on the right again. You will then be making circles around the other car, but when seen from above, both of you are driving forward all the time and your path will be convex.”
(Thanks, Drake.)
Rudyard Kipling described the car as a ‘petrol-piddling monster.’ Queen Victoria called it a ‘very shaky and disagreeable conveyance altogether.’ … As had the cycle before it, the car had a tendency to frighten horses and thus cause great antagonism in other travelers and bystanders. A frequent, joking explanation of the horses’ reactions was, ‘How would you act if you saw a pair of pants coming down the street with no one in them?’
— M.G. Lay, Ways of the World: A History of the World’s Roads and of the Vehicles That Used Them, 1992
The title of this painting is electrifying: Ben Jonson and William Shakespeare Playing at Chess. Unfortunately, its authenticity has been subject to debate for more than a century. It came to light only in 1878, when it was purchased for $18,000 by Colonel Ezra Miller, and the authenticating documents were lost in a fire 17 years later.
Supporters claim that it was painted by Karel van Mander (1548-1606), and in the best possible case it would give us new likenesses of Jonson and Shakespeare painted by a contemporary. But a biography of van Mander, probably written by his brother, makes no mention of this painting, nor of the artist ever visiting London, and while Shakespeare here appears younger than Jonson, in fact he was eight or nine years older.
“It is understandable that there is still curiosity about Shakespeare’s life, physical features, and reputation,” wrote Roehampton Institute scholars Bryan Loughrey and Neil Taylor in 1983. “If the chess portrait were genuinely a portrait of Shakespeare and Jonson, the painting would be of unique interest. Unfortunately, most of the arguments that have been advanced in its favor are untenable.”
Real or fake, Shakespeare has the better of Jonson in this game — he can mate on the move:
(Bryan Loughrey and Neil Taylor, “Jonson and Shakespeare at Chess?” Shakespeare Quarterly 34:4 [Winter 1983], 440-448.)
