Equality in Death

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It is like a play. But when the curtain falls, the one who played the king, and the one who played the beggar, and all the others — they are all quite alike, all one and the same; actors. And when in death the curtain falls on the stage of actuality … then they also are all one; they are human beings. All are that which they essentially were, something we did not see because of the difference we see. They are all human beings. The stage of art is like an enchanted world. But just suppose that some evening a common absent-mindedness confused all the actors so they thought they really were what they were representing. Would this not be, in contrast to the enchantment of art, what one might call the enchantment of an evil spirit, a bewitchment? And likewise suppose that in the enchantment of actuality (for we are, indeed, all enchanted, each one bewitched by his own distinctions) our fundamental ideas became confused so that we thought ourselves essentially to be the roles we play. Alas, but is this not the case? It seems to be forgotten that the distinctions of earthly existence are only like an actor’s costume.

— Kierkegaard, Works of Love, 1847

| Society

Curioser and Curioser

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“I’m sure I’m not Ada, for her hair goes in such long ringlets, and mine doesn’t go in ringlets at all; and I’m sure I can’t be Mabel, for I know all sorts of things, and she, oh! she knows such a very little! Besides, she’s she, and I’m I, and — oh dear, how puzzling it all is! I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is — oh dear! I shall never get to twenty at that rate!”

So frets Alice outside the garden in Wonderland. Is the math only nonsense? In his book The White Knight, Alexander L. Taylor finds one way to make sense of it: In base 18, 4 times 5 actually is 12. And in base 21, 4 times 6 is 13. Continuing this pattern:

4 times 7 is 14 in base 24
4 times 8 is 15 in base 27
4 times 9 is 16 in base 30
4 times 10 is 17 in base 33
4 times 11 is 18 in base 36
4 times 12 is 19 in base 39

And here it becomes clear why Alice will never get to 20: 4 times 13 doesn’t equal 20 in base 42, as the pattern at first seems to suggest, but rather 1X, where X is whatever symbol is adopted for 10.

Did Lewis Carroll have this in mind when he contrived the story for Alice? Perhaps? In The Magic of Lewis Carroll, John Fisher writes, “It is hard … not to accept Taylor’s theory that Carroll was anxious to make the most of two worlds; the problem as interpreted by Taylor interested him, and although it wouldn’t interest Alice there was no reason why he shouldn’t use it to entertain her on the level of nonsense. It is even more difficult to suppose that he, a mathematical don, inserted the puzzle in the book without realising it.”

In the Winter 1971 edition of Jabberwocky, the quarterly publication of the Lewis Carroll Society, Taylor wrote, “If you find a watch in the Sahara Desert you don’t think it grew there. In this case we know who put it there, so if he didn’t record it that tells us something about his recording habits. It doesn’t tell us that the mathematical puzzle isn’t a mathematical puzzle.”

| Literature · Science & Math

Folds of Stone

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Image: Wikimedia Commons

Giuseppe Sanmartino’s 1753 sculpture Veiled Christ is so convincing that for 200 years a legend circulated that an alchemist had transformed a real shroud into marble.

In fact a close examination shows that Sanmartino carved the whole work, shroud and all, from a single block of stone. Antonio Canova said he would give up 10 years of his own life to produce such a masterpiece.

| Art

Prior Art

karl krøyer patent

On Sept. 14, 1964, a Kuwaiti freighter capsized, drowning its cargo of sheep and threatening to contaminate the drinking water of Kuwait City. To raise the ship quickly, Danish inventor Karl Krøyer proposed using a tube to fill it with buoyant bodies. Accordingly, 27 million plastic balls were airlifted from Berlin and pumped into the freighter’s hold, and on Dec. 31 the ship rose, saving the insurance company nearly $2 million.

Krøyer patented his technique in the United Kingdom and Germany, but (the story is told) the Dutch application was rejected because a Dutch examiner found the 1949 Donald Duck comic The Sunken Yacht, by Carl Barks, in which Donald and his nephews raise a yacht by filling it with ping-pong balls.

Ping-pong balls are buoyant, and the ducks used a tube to feed them into the yacht, so the Dutch office ruled that this destroys the novelty of Krøyer’s invention — it may be just a comic book, but it had made the essential idea public 15 years before Krøyer tried to claim it.

No one quite seems to know whether this story is true — Krøyer, his patent attorney, and the examiner have now passed away; the documentation was destroyed years ago; and the grounds for the Dutch rejection aren’t clear. But it still makes a vivid example for intellectual property lawyers.

carl banks donald duck comic

| Society · Technology

Notice

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In Dante’s Inferno, a sign above the gate to hell reads LASCIATE OGNI SPERANZA, VOI CH’ENTRATE.

There are many ways to translate this (Robert Ripley claimed to find 100), but a common one is ABANDON YE ALL HOPE WHO ENTER HERE.

By an unlikely coincidence, this yields ABANDON Y.A.H.W.E.H.

(Discovered by Dave Morice.)

| Language · Literature · Religion

Borrowed Trouble

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“There is nothing so wretched or foolish as to anticipate misfortunes. What madness it is in your expecting evil before it arrives!” — Seneca

“How much pain have cost us the evils which have never happened!” — Thomas Jefferson

“Our worst misfortunes never happen, and most miseries lie in anticipation.” — Balzac

“Ills that never happened, have chiefly made thee wretched.” — Martin Farquhar Tupper

“I remember the old man who said he had had a great many troubles in his life, but the worst of them never happened.” — James Garfield

“Let us be of good cheer, however, remembering that the misfortunes hardest to bear are those which never come.” — James Russell Lowell

“Real difficulties can be overcome; it is only the imaginary ones that are unconquerable.” — Theodore N. Vail

| Quotations

Podcast Episode 186: The Children’s Blizzard

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In January 1888, after a disarming warm spell, a violent storm of blinding snow and bitter cold suddenly struck the American Midwest, trapping farmers in fields, travelers on roads, and hundreds of children in schoolhouses with limited fuel. In this week’s episode of the Futility Closet podcast we’ll describe the Children’s Blizzard, one of the most harrowing winter storms in American history.

We’ll also play 20 Questions with a computer and puzzle over some vanishing vultures.

See full show notes …

| History · Podcast

Paper Chase

Izhar Gafni makes bicycles out of cardboard. The Israeli mechanical engineer can make a 20-pound bicycle that will support a rider of nearly 250 pounds, and its low-cost components make it unattractive to thieves — Gafni fashions the frame, wheels, handlebars, and saddle from sheets of cardboard that are folded and glued together; the tires and drive belt are recycled rubber, and the seat and some of the gears are made of recycled plastic bottles. “It’s one of the most green products you can imagine,” his partner Nimrod Elmish told the Times of Israel in 2012.

The company is pursuing partnerships to distribute cardboard bicycles and wheelchairs in Africa at little to no cost for the end user. “There is much to say about cardboard,” Elmish said. “This bicycle is the beginning of a materials revolution.”

| Technology

Stopwatch Cinema

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High Noon unfolds in real time — the running time of the story closely parallels the running time of the film itself. Producer Stanley Kramer said that the filmmakers hoped this would “create a sense of urgency as the noon hour approached.” Director Fred Zinnemann wrote the word CLOCK next to many scenes in his script, and he prepared a list of inserts in which clocks would be prominently visible:

Scene 36 — Marshal’s Office — Clock 10:40 a.m.
Scene 60 — Marshal’s Office — Clock 10:51 a.m.
Scene 76 — Helen’s Room — Clock 10:55 a.m.
Scene 86 — Marshal’s Office — Clock 11:02 a.m.
Scene 96 — Helen’s Room — Clock 11:05 a.m.
Scene 101 — Marshal’s Office — Clock 11:07 a.m.
Scene 130 — Saloon — Clock 11:19 a.m.
Scene 144 — Mart Howe’s House — Clock 11:26 a.m.
Scene 231 — Saloon — Clock 11:44 a.m.
Scene 256 — Hotel Lobby — Clock 11:50 a.m.
Scene 303 — Saloon — Clock 11:59 a.m.
Scene 312 — Saloon — Clock 12:00 p.m.

An insert for Scene 294 was never shot — it would have started on a pendulum and panned up to show a clock with no hands, superimposed on a closeup of Gary Cooper’s Will Kane. Zinnemann said he’d got the idea from a handless clock he’d seen in front of a funeral home on Sunset Boulevard. He said it “would have intensified the feeling of panic.”

(From Michael Francis Blake, Code of Honor, 2003.)

| Entertainment