Futility Closet: Recent Episodes

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Your refuge from productivity

Recess, County Galway, Ireland:

Image: Wikimedia CommonsAspelt, Luxembourg:

Image: Wikimedia CommonsBechyne, Czech Republic:

Image: Wikimedia Commons(“In this house, no important person was born, lived, and most importantly did not die, and that is why we live well here.”)

Záblatí-Hlásná Lhota, Czech Republic:

Image: Wikimedia Commons(“Hlásná Lhota – a stone in whose surroundings nothing significant has demonstrably happened for several hundred years”)

Míšov, Czech Republic:

Image: Wikimedia Commons(“On 8 May 1915 in Míšov, the great Czech genius Jára Cimrman just barely missed being involved in something historically important.”)

O’Hungry’s Café, Old Town San Diego State Historic Park:

Image: Wikimedia CommonsYork, Western Australia:

Image: Wikimedia CommonsVilla de Leyva, Boyacá Department, Colombia:

(“On October 13, 1825, nothing happened in this house, nor was anyone important born.”)

The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Add those up and divide the sum by 30 itself and you get 12/5.

The divisors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Add those up and divide the sum by 140 and you also get 12/5.

This makes 30 and 140 a friendly pair. Other members of their little club are 2480, 6200, and 40640.

Interestingly, no one knows whether 10 has such a partner. If it does, its smallest friend is at least 1030.

intendiment
n. intention or purpose

auspicate
v. to begin an undertaking

mercation
n. the act of purchasing something

Alnaschar
n. a person given to unrealistic dreams, expectations, or plans

In the summer of 1967, the Beatles briefly considered buying a set of Greek islands where they could live and work together.

“We were all going to live together now, in a huge estate,” Derek Taylor says in Anthology. “The four Beatles and Brian [Epstein] would have their network at the centre of the compound: a dome of glass and iron tracery (not unlike the old Crystal Palace) above the mutual creative/play area, from which arbours and avenues would lead off like spokes from a wheel to the four vast and incredibly beautiful separate living units. In the outer grounds, the houses of the inner clique: Neil [Aspinall], Mal [Evans], Terry [Doran] and Derek, complete with partners, families and friends.”

John, Paul, and George got as far as touring the islands south of Athens and visiting one they considered buying. But indulging the idea for an afternoon seemed to be enough for them. George said, “We got back on the boat and sailed away, and never thought about the island again.”

“It’s a good job we didn’t do it,” Paul said later, “because anyone who tried those ideas realised eventually there would always be arguments, there would always be who has to do the washing-up and whose turn it is to clean out the latrines. I don’t think any of us were thinking of that.”

In 1915, British evangelist Elizabeth Reid Cotton claimed that she had visited Charles Darwin shortly before his death in 1882, and that he’d told her he regretted advancing the theory of natural selection.

“I was a young man with unformed ideas,” he’d said. “I threw out queries, suggestions, wondering all the time over everything, and to my astonishment, the ideas took like wildfire. People made a religion of them.” He begged her to preach to a gathering at his summer house the following day. “If you take the meeting at three o’clock this window will be open, and you will know that I am joining in with the singing.”

It’s not impossible that Cotton did meet Darwin, but his family denied that he had ever recanted the theory. “Dear Sir,” he had written in an 1880 letter, “I am sorry to inform you that I do not believe in the Bible as a divine revelation, & therefore not in Jesus Christ as the son of God.”

Image: Wikimedia CommonsIn 2002, visitor Nicholas Whitehead erected a road sign to an international airport outside Llandegley, Wales.

There is no such airport.

Image: Wikimedia CommonsIn September 1835, Stendhal wrote on the shore of Lake Albano the initials of the women he had loved: Virginie Kubly, Angela Pietragrua, Adèle Rebuffel, Mina de Griesheim, Mélanie Guilbert, Angelina Bereyter, Alexandrine Daru, Angela Pietragrua, Matilde Dembowski, Clémentine Curial, Giulia Rinieri, and Madame Azur-Alberthe de Rubempré.

“I dreamed deeply of these names, and of the astonishing follies and stupidities they made me commit,” he wrote. “The habitual condition of my life is that of an unhappy lover.”

(From his unfinished autobiography The Life of Henry Brulard, 1890.)

A problem from Joseph Madachy’s Mathematics on Vacation (1966): If these statements are all true, what can we deduce about Major Perkins?

Only bleary-eyed military men ever try to shave with a toothbrush.
No bleary-eyed military men are at all musical.
Men who never try to shave with a toothbrush never play golf.
Major Perkins plays the tuba on Wednesdays.
Only musical people who are golfers forget to change their socks.

| SelectClick for Answer | | --- | | The only thing we know for certain is that Major Perkins plays the tuba on Wednesdays. All the other seeming deductions (that Major Perkins is musical, not bleary-eyed, and not a golfer; that he does not try to shave with a toothbrush, and that he remembers to change his socks) require the assumption that Perkins is a man. |

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A puzzle by Russian mathematician Boris Kordemsky:

A house has 6 stories, each the same height. How many times as long is the ascent to the sixth floor as the ascent to the third?

| SelectClick for Answer | | --- | | 2 1/2 times (5 ÷ 2, not 6 ÷ 3).From The Moscow Puzzles, 1972. |

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“A man doesn’t learn to understand anything unless he loves it.” — Goethe

“A man ought to read just as inclination leads him; for what he reads as a task will do him little good.” — Samuel Johnson

“We soon forget what we have not deeply thought about.” — Proust

Iranian hermit Amou Haji ate carrion, drank from puddles, lived in a hole, smoked dung, and died at 94, a few months after bathing for the first time in 60 years. He said he became a hermit due to “emotional setbacks” after a heartbreak.

English merchant Nathaniel Bentley became known as Dirty Dick when he stopped washing in his late 30s. His filthy shop became a tourist attraction. Interestingly, he too was said to have changed after a ruined love affair, allegedly after his fiancée died on the eve of their wedding. Charles Dickens knew of the story, which may have inspired that of Miss Havisham in Great Expectations.

In the best collective use,
Geese afoot are gaggles
(Even when one goose gets loose,
Falls behind and straggles);

Skein‘s the word for geese in flight.
Turtledoves form dools.
Barren‘s right (though impolite)
For a pack of mules.

Starlings join in murmuration,
Pheasants in a rye,
Larks in lovely exaltation,
Leopards, leap (they’re spry).

Ducks in flight are known as teams;
Paddings when they swim.
Herrings in poetic gleams
Please the wordsmith’s whim.

Cats collect into a clowder,
Kittens make a kindle.
Sloths of bears growl all the louder
As their forces dwindle.

Lapwings gather in deceit,
Apes convene in shrewdness,
Mares in stud (an odd conceit
Bordering on lewdness).

Foxes muster in a skulk,
Squirrels run in drays
While collectives in the bulk
Make up word bouquets.

— Felicia Lamport

A problem by National Security Agency mathematician Wendell W., from the agency’s March 2018 Puzzle Periodical:

Consider the following equations:

a2 × b × c2 × g = 5,100

a × b2 × e × f2 = 33,462

a × c2 × d3 = 17,150

a3 × b3 × c × d × e2 = 914,760

Find positive integers a, b, c, d, e, f, and g, all greater than 1, that satisfy all the equations.

| SelectClick for Answer | | --- | | If all four equations are satisfied, then multiplying all four equations together will produce another valid equation. We obtain:a7 × b6 × c5 × d4 × e3 × f2 × g = 2,677,277,333,530,800,000.The number on the right factors into prime powers as 2,677,277,333,530,800,000 = 27 × 36 × 55 × 74 × 113 × 132 × 17, as can be determined by trial division by the small primes 2, 3, 5, 7, 11, 13, and 17, for instance. So we have the new equation:a7 × b6 × c5 × d4 × e3 × f2 × g = 27 × 36 × 55 × 74 × 113 × 132 × 17.If p is any prime dividing a, then p7 divides the right hand side. Since only 2 appears to the seventh power, the only value p can take is 2. Since a must be greater than 1, we see that 2 must divide a. Because 2 appears to exactly the seventh power on the right, we see that a = 2. Canceling a7 on the left with 27 on the right leaves:b6 × c5 × d4 × e3 × f2 × g = 36 × 55 × 74 × 113 × 132 × 17.Repeating the same argument shows that b = 3, c = 5, d = 7, e = 11, f = 13, g = 17 is the unique solution to the new equation. However, it is still necessary that these values actually satisfy the original four equations, which in fact they do as can be checked easily. (To see why this last step is necessary, try using the same reasoning on the equations: x = 10, y2 = 9, z3 = 25, which clearly has no solutions in integers.) |

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When H.P. Re of Coldwater, Mich., died in 1931, his claim to have the world’s shortest name was up for grabs, and the Associated Press held a sort of contest to find his successor. J. Ur of Torrington, Conn., expressed early confidence because he had no middle initial, but, AP reported:

C. Ek and J. Ek, brothers from Duluth, promptly entered the lists as cochampions. Mrs. V. Ek, not to be outdone, claimed not only the woman’s title, but the mixed doubles championship. A former Duluth policeman said his name was C. Sy.

Then Fairmount, Minnesota, entered E. Py, farmer; Clinton, Iowa, put forward C. Au, J. Au, and W. Au, triple threats; Indiana offered Ed Py, inmate of Newcastle Jail; and Indianapolis made a poor try with Fix Ax.

In the end the palm went to Aaron A of Chicago, who went by A.A., a name that AP noted “leads all others in the Chicago telephone directory, alphabetically as well as longitudinally.” A’s ancestors had been jewelers in Saxony, and a philologist speculated that the surname derived from an old German word for river.

The esoteric programming language Velato uses music as its source code. The first note of a composition establishes a “command root” note, and the intervals that follow specify instructions. The command root can be changed between statements, and the notes that make up a chord can be interpreted in a specified order, so there’s some latitude to help a composition sound “musical.” This program produces the output “Hello, World”:

Here’s what that sounds like:

A few other musical languages: Fugue, VenetianScript, Yet Another Musical Esolang.

Image: Wikimedia CommonsThe world’s smallest island with a building on it is the Bishop Rock, a skerry off the coast of Cornwall. The islet is 46 by 16 meters, and the tower’s base is 10 meters across. Before the installation of a helipad in 1976, visitors would rappel from the tower’s base to waiting boats.

Image: Wikimedia CommonsAmong the Thousand Islands at the head of the Saint Lawrence River is the smallest inhabited island in the world, known as “Just Room Enough.” It accommodates a single house.

Image: Wikimedia CommonsThe “Smallest House in Great Britain” stands on the quay in Conwy, Wales. Built in the 16th century, it has a floor area of 3.05 by 1.8 meters.

Image: Wikimedia CommonsBuilt in 1958, the Little Church in Drumheller, Alberta, is available for ceremonies. It seats six.

Twice a year, objects Hawaii lose their shadows as the sun passes directly overhead.

A “zero shadow day” occurs biannually between the Tropics of Cancer and Capricorn, arriving at each location when the sun’s declination equals its latitude.

A gentleman had a bottle containing 12 pints of wine, 6 of which he was desirous of giving to a friend; but he had nothing to measure it, except two other bottles, one of 7 pints, and the other of 5. How did he contrive to put 6 pints into the 7-pint bottle?

| SelectClick for Answer | | --- | | From George Arnold et al., The Magician’s Own Book, 1857.10/10/2025 UPDATE: The published solution works, but there’s an alternative that gets the job done in 10 steps: Start 12 0 0Fill 7 from 12 5 7 0Fill 5 from 7 5 2 5Empty 5 into 12 10 2 0Empty 7 into 5 10 0 2Fill 7 from 12 3 7 2Fill 5 from 7 3 4 5Empty 5 into 12 8 4 0Empty 7 into 5 8 0 4Fill 7 from 12 1 7 4Fill 5 from 7 1 6 5 That’s from reader Catalin Voinescu. Many thanks to him and to everyone else who wrote in.10/12/2025 UPDATE: Reader Chris Hills presents a standard way of solving this type of problem:In this diagram,each point represents a state of how much wine is in each bottle, the vertical distance from the point to the bottom edge of the big equilateral triangle is the number of pints in the 5-pint bottle, the vertical distance to the left edge is the number in the 7-pint bottle, and the vertical distance to the right edge is the number in the 12-pint bottle. These 3 distances always add up to 12 because of Viviani’s theorem, which you mention in “The Glass Rod Problem.”The amount of wine in each bottle is ≥ 0 pints and ≤ its capacity, so only points in the green area are possible. The points outside the green area represent situations where a bottle is holding more than its capacity.A transfer from one bottle to another is represented by a line from one edge of the green parallelogram to another edge. We can’t stop in the middle, we can only stop a transfer when the giving bottle is empty or the receiving bottle is full.The starting position is the bottom left corner, where all the wine is in the 12-pint bottle. The end position is anywhere on the black line, this is where there are 6 pints in the 7-pint bottle. In this sort of problem, there are always either no solutions or exactly 2 solutions. The solution you gave follows the blue arrows, and takes 12 steps. The red arrows give the other solution, which takes 10 steps. [Thanks, Chris.]In a related class of problems, known as water-fetching puzzles, water is drawn from a well and a prescribed amount must be measured using jugs of stated sizes. H.D. Grossman gave a geometric approach in Scripta Mathematica in 1948. |

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From Lee Sallows:

(Thanks, Lee.)

Mr. Chas. Hy. Heskins, of 94, Blenheim Road, Reading, was good enough to send in this extremely curious and interesting photo. The kettle, it seems, was a disused one, and stood for a long time on a shelf with the lid partly off, much as we see in the photo. One night the mouse got in, possibly in the hope of finding some stray crusts. Why the little animal should take it into his head to leave the inhospitable kettle by the spout is not known, but he did, with the result portrayed in the photo. His head got through all right, and two pathetic little paws; but ‘the force of Nature could no farther go,’ and poor mousie stuck fast. Next morning someone took the kettle in hand, and ‘assisted’ the mouse’s hindquarters with a stick of wood, with the result that he emerged slowly and stiffly, and was finally allowed to hobble painfully away. Truly, a narrow escape in more senses than one!

— Strand, July 1897

— Uriah Parke, Lectures on the Philosophy of Arithmetic and the Adaptation of That Science to the Business Purposes of Life, 1849

Socrates wants to cross a river and comes to a bridge guarded by Plato. The two speak as follows:

Plato: ‘Socrates, if in the first proposition which you utter, you speak the truth, I will permit you to cross. But surely, if you speak falsely, I shall throw you into the water.’

Socrates: ‘You will throw me into the water.’

Jean Buridan posed this conundrum in his Sophismata in the 14th century. Like a similar paradox in Don Quixote, it seems to leave the guardian in an impossible position — whether Socrates speaks truly or falsely, it would seem, the promise cannot be fulfilled.

Some readers offered a wry solution: Wait until he’s crossed the bridge, and then throw him in.

Another blue plaque, this one in Long Itchington, October 2014:

Image: Wikimedia CommonsRelated: Riverside, Iowa, is already congratulating itself as the future birthplace of James T. Kirk.

Billy Wilder’s grave, Westwood Village Memorial Park Cemetery, Los Angeles:

Image: Wikimedia Commons

Image: Wikimedia CommonsAbove: A valid maze can be generated recursively by dividing an open chamber with walls and creating an opening at random within each wall, ensuring that a route can be found through the chamber. The secondary chambers themselves can then be divided with further walls, following the same principle, to any level of complexity.

Below: Valid mazes can even be generated fractally — here a solution becomes available in the third panel, but an unlucky solver might wander forever in the depths of self-similarity at the center of the image.

Image: Wikimedia Commons

Image: Wikimedia CommonsFound this on the Wikimedia Commons — a self-obligating graffito.

This is Euclid’s proof of the Pythagorean theorem — Schopenhauer called it a “brilliant piece of perversity” for its needless complexity:

Erect a square on each leg of a right triangle. From the triangle’s right angle, A, draw a line parallel to BD and CE. This will intersect BC and DE perpendicularly at K and L.
Draw segments CF and AD, forming triangles BCF and BDA.
Because angles CAB and BAG are both right angles, C, A, and G are collinear.
Because angles CBD and FBA are both right angles, angle ABD equals angle FBC, since each is the sum of a right angle and angle ABC.
Since AB is equal to FB, BD is equal to BC, and angle ABD equals angle FBC, triangle ABD is congruent to triangle FBC.
Since A-K-L is a straight line that’s parallel to BD, rectangle BDLK has twice the area of triangle ABD, because they share base BD and have the same altitude, BK, a line perpendicular to their common base and connecting parallel lines BD and AL.
By similar reasoning, since C is collinear with A and G, and this line is parallel to FB, square BAGF must be twice the area of triangle FBC.
Therefore, rectangle BDLK has the same area as square BAGF, AB2.
By applying the same reasoning to the other side of the figure, it can be shown that rectangle CKLE has the same area as square ACIH, AC2.
Adding these two results, we get AB2 + AC2 = BD × BK + KL × KC.
Since BD = KL, BD × BK + KL × KC = BD(BK + KC) = BD × BC.
Therefore, since CBDE is a square, AB2 + AC2 = BC2.

The diagram became known as the bride’s chair due to a confusion in translation between Greek and Arabic.

Image: Bob EmbletonPlaque at St. Ann’s Well, Malvern, Worcestershire, August 2009.

In 1880, an 800-year-old yew tree was threatening the west wall of the church of St Andrew at Buckland in Dover. The community called in landscape gardener William Barron, who solved the problem by boring tunnels under the trunk and then raising the tree’s entire 55-ton mass onto rollers by means of powerful screw jacks. Giant windlasses could then haul the tree 203 feet across the churchard to a safer location.

“The scale of this operation was probably never matched,” writes G.M.F. Drower in Garden of Invention, his 2003 history of gardening innovations. “[A]nd Barron, who had been rather more apprehensive than he let on, later admitted that all the other trees he had moved had been ‘chickens compared to the Buckland Yew.'”

By Wikimedia user Cmglee, a visual proof that a3 – b3 = (a – b)(a2 + ab + b2):

Where did the familiar syllables of solfège (do, re, mi) come from? Eleventh-century music theorist Guido of Arezzo collected the first syllable of each line in the Latin hymn “Ut queant laxis,” the “Hymn to St. John the Baptist.” Because the hymn’s lines begin on successive scale degrees, each of these initial syllables is sung with its namesake note:

Ut queant laxīs
resonāre fibrīs
Mīra gestōrum
famulī tuōrum,
Solve pollūti
labiī reātum,
Sancte Iohannēs.

Ut was changed to do in the 17th century, and the seventh note, ti, was added later to complete the scale.

Vladimir Nabokov composed this puzzle for his wife Véra in 1926. The title, “Crestos lovitxa Sirin,” roughly means “Nabokov’s crossword”: krestlovitska approximates the Russian kreslovitsa, “cross” plus “words”, and Sirin is a pseudonym Nabokov often used, a reference to the creatures of Russian mythology. The upper half of each wing contains the grid, the lower the clues.

Nabokov, a trained entomologist, had published the first crossword in Russian two years earlier. Forty years later, in the Paris Review, he likened writing a novel to creating a crossword: “The pattern of the thing precedes the thing. I fill in the gaps of the crossword at any spot I happen to choose.”

(Adrienne Raphel, The Crossword Mentality in Modern Literature and Culture, dissertation, Harvard University, 2018.)

Image: Wikimedia CommonsConventional stairs are somewhat extravagant: Because users alternate their steps (1), half of each tread goes unused. In close quarters, floor space can be conserved by omitting these unused portions (3), permitting a slope as high as 65 degrees without sacrificing the depth of the treads (2).

Because each tread “overlaps” those that precede and follow it, an alternating staircase might require only half the horizontal space of conventional stairs, and users can face forward when descending, where a ladder would require them to turn. The disadvantage is that they’re steep, and users must take care to begin each traverse with the correct foot. For that reason these stairs may not be safe for children or the elderly.

Below: In the Orange Tower, built in Carpentras at the start of the 14th century, builders set alternate risers at a diagonal to achieve an ascending slope of 45 degrees. “We will recognize that it is never subtlety that our medieval architects lack. But these latter examples only provide service stairs.”

(Eugène Viollet-le-Duc, Dictionary of French Architecture from 11th to 16th Century, 1856.)

If nature be regarded as the teacher and we poor human beings as her pupils, the human race presents a very curious picture. We all sit together at a lecture and possess the necessary principles for understanding it, yet we always pay more attention to the chatter of our fellow students than to the lecturer’s discourse. Or, if our neighbor copies something down, we sneak it from him, stealing what he himself may have heard imperfectly, and add to it our own errors of spelling and opinion.

— G.C. Lichtenberg, quoted in W.H. Auden’s A Certain World, 1970

Raymond Smullyan presented this oddity in his Chess Mysteries of Sherlock Holmes in 1980. Suppose we come upon this abandoned chess game. Can White mate in two moves? The answer seems to be yes. If Black can’t castle, then White can play 1. Ke6 and then promote his g-pawn, giving mate. If Black can castle, that means that neither his king nor his rook has yet moved, and hence he must just have moved his pawn to e5. That permits White to capture the pawn en passant. Now if Black castles then 2. b7 is mate, and if he plays any other move then the g-pawn promotes. Either way, White mates Black on his second move.

But that’s odd. We’ve decided that a mate in two exists, but we can’t show it — and we don’t even know how White commences!

(F. Alexander Norman, “Classicists and Constructivists: A Dilemma,” Mathematics Magazine 62:5 [December 1989], 340-342. See Donkey Sentences.)

Hungarian mathematician Paul Erdős’ epitaph reads “Végre nem butulok tovább” — “I’ve finally stopped getting dumber.”

Image: Wikimedia CommonsThis is beautifully well done — a humiliating list of all the ways your brain can deceive you (click to enlarge).

Designed by John Manoogian III.

Another geometric magic square from Lee Sallows:

(Thanks, Lee!)

Image: Wikimedia CommonsThis is a picture of a cow. If you can’t see it (I couldn’t), there’s an explanatory image on page 66 of John McCrone’s 1991 book The Ape That Spoke.

The experience illustrates how the brain is able to construct a picture from limited data by relying on patterns and experience.

Thomas Jefferson to the Rev. Isaac Story, Dec. 5, 1801, on the afterlife:

When I was young I was fond of the speculations which seemed to promise some insight into that hidden country, but observing at length that they left me in the same ignorance in which they had found me, I have for very many years ceased to read or to think concerning them, and have reposed my head on that pillow of ignorance which a benevolent Creator has made so soft for us, knowing how much we should be forced to use it.

“I have thought it better, by nourishing the good passions & controlling the bad, to merit an inheritance in a state of being of which I can know so little, and to trust for the future to him who has been so good for the past.”

Image: Wikimedia CommonsThese are the punts of Trinity College, Cambridge, moored on the River Cam. What is the significance of their names?

| SelectClick for Answer | | --- | | Inspired by the college’s name, each punt evokes the number three:In the game NOUGHTS & CROSSES, players compete to place three marks in a row.A CODON is a sequence of three nucleotides in a DNA or RNA molecule.In Greek mythology, beauty was deified in the three GRACEs Euphrosyne, Aglaia, and Thalia.A HAIKU has three lines.Three WISE MONKEYs illustrate the maxim “See no evil, hear no evil, speak no evil.”NENYA is one of the three Rings of Power in J.R.R. Tolkien’s fantasy legendarium.FLUFFY is a three-headed dog in J.K. Rowling’s Harry Potter universe.Traditionally after two failures one hopes for a third LUCKY TIME.CHARLES III is king of the United Kingdom.Not shown:LITHIUM has atomic number 3.A BARYON is a subatomic particle made up of three quarks.02/11/2025 UPDATE: Wow, yet more!The additional names include LITTLE KITTEN, CHEER, BRONZE, WISE MAN, PEACE SWEET, GRUFF, MAD GEORGE, DIABOLUS IN MUSICA, HARRY LIME, and POINT TURN.(Thanks, Dmitry.) |

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Steaming from New York to the Azores in 1867, Mark Twain noted a curious companion overhead:

We had the phenomenon of a full moon located just in the same spot in the heavens at the same hour every night. The reason of this singular conduct on the part of the moon did not occur to us at first, but it did afterward when we reflected that we were gaining about twenty minutes every day because we were going east so fast — we gained just about enough every day to keep along with the moon. It was becoming an old moon to the friends we had left behind us, but to us Joshuas it stood still in the same place and remained always the same.

(From The Innocents Abroad.)

02/11/2025 Reader Catalin Voinescu writes:

Mark Twain is talking absolute nonsense here.

The moon is in (almost) the same phase as seen from all over the world. It rises and sets at roughly the same local time, regardless of longitude, and the relation between phase and time of day when the moon is visible is the same everywhere (the full moon peaks at midnight; a week later, the last-quarter moon rises around midnight, peaks in the morning and sets around noon; and so on).

Even ignoring moon phase and local time, the moon rises, peaks and sets almost 50 minutes later every day, so gaining 20 minutes every day would not be enough.

(Thanks, Catalin.)

Reader J. William Hook submitted this curiosity to the Strand in August 1899. Holding the page level with the eyes foreshortens the characters and reveals a love poem:

Art thou not dear unto my heart?
Oh, I search that heart and see
And from my bosom tear the part
That beats not true to thee.

But to my bosom thou art dear,
More dear than words can tell,
And if a fault be cherished there,
‘Tis loving thee too well.

There seems to have been a little vogue for this kind of thing — C. Field submitted a similar image three months later.

(Until William Herschel’s advances in telescopes, stars seemed to have “rays” or “tails.”)

At a dinner given by Mr Aubert in the year 1786, William Herschel was seated next to Mr Cavendish, who was reputed to be the most taciturn of men. Some time passed without his uttering a word, then he suddenly turned to his neighbour and said: ‘I am told that you see the stars round, Dr Herschel’. ‘Round as a button’, was the reply. A long silence ensued till, towards the end of the dinner, Cavendish again opened his lips to say in a doubtful voice: ‘Round as a button?’ ‘Exactly, round as a button’, repeated Herschel, and so the conversation ended.

— Constange A. Lubbock, The Herschel Chronicle, 1933

Image: Wikimedia CommonsAn art gallery with n walls will always be safe with n/3 guards — the guards will always be able arrange themselves to observe the whole gallery.

That’s Chvátal’s art gallery theorem, discovered in 1973 by mathematician Václav Chvátal. Interestingly, it’s true only of two-dimensional floor plans — a three-dimensional gallery may not be safe even if you post a guard at every corner.

Take a 20 × 20 × 20 cube and remove a 12 × 6 channel from the front and back faces; a 6 × 3 channel from the left and right faces; and a 6 × 6 channel from the top and bottom faces, as shown. The result is the Octoplex, eight 4 × 7 × 7 theaters connected to each other and to a central lobby by passages 1 unit wide.

Remarkably, even if we mount a camera at every one of this figure’s 56 corners, there will remain a small region in the central lobby that no camera can see.

(T.S. Michael, “Guards, Galleries, Fortresses, and the Octoplex,” College Mathematics Journal 42:3 [May 2011], 191-200.)

For the past eighty years I have started each day in the same manner. It is not a mechanical routine but something essential to my daily life. I go to the piano, and I play two preludes and fugues of Bach. I cannot think of doing otherwise. It is a sort of benediction on the house. But that is not its only meaning for me. It is a rediscovery of the world of which I have the joy of being a part. It fills me with awareness of the wonder of life, with a feeling of the incredible marvel of being a human being.

— Pablo Casals, Joys and Sorrows, 1970

renitence
n. unwillingness, resistance to persuasion

subdolous
adj. cunning, crafty, sly

autoschediasm
n. something done on the spur of the moment or without preparation

legerity
n. physical or mental quickness

FDR’s secretary of state, Cordell Hull, was famously unforthcoming, concealing his plans and emotions with the skill of a poker player.

When Hull was a legislator in Tennessee, one of his friends bet that he could get a direct answer out of him. He stopped him in the capitol and asked him the time.

Hull took out his timepiece, looked at it, and said, “What does your watch say?”

Julius Caesar thought that elk have no knees.
Duke Ellington’s first piano teacher was named Marietta Clinkscales.
Orizabus subaziro, a rhinoceros beetle, has a palindromic species name.
POSSESSIONLESSNESSES has 9 S’s.
“Books are companions even if you don’t open them.” — Disraeli

In their 1943 handbook The Reader Over Your Shoulder, Robert Graves and Alan Hodge note that writers are prone to exaggerate descriptions of quantity and duration. “There should never be any doubt left as to how much, or how long.” They offer this quantified example:

(100%) Mr. Jordan’s fortune consisted wholly of bar-gold.
(99%) Practically all his fortune consisted of bar-gold.
(95%) His fortune consisted almost entirely of bar-gold.
(90%) Nearly all his fortune consisted of bar-gold.
(80%) By far the greater part of his fortune consisted of bar-gold.
(70%) The greater part of his fortune consisted of bar-gold.
(60%) More than half his fortune consisted of bar-gold.
(55%) Rather more than half his fortune consisted of bar-gold.
(50%) Half his fortune consisted of bar-gold.
(45%) Nearly half his fortune consisted of bar-gold.
(40%) A large part of his fortune consisted of bar-gold.
(35%) Quite a large part of his fortune consisted of bar-gold.
(30%) A considerable part of his fortune consisted of bar-gold.
(25%) Part of his fortune consisted of bar-gold.
(15%) A small part of his fortune consisted of bar-gold.
(10%) Not much of his fortune consisted of bar-gold.
(5%) A very small part of his fortune consisted of bar-gold.
(1%) An inconsiderable part of his fortune consisted of bar-gold.
(0%) None of his fortune consisted of bar-gold.

“This simple, generally accepted, scale is confused by writers who, for dramatic effect, try to make 5% seem more than it is.”

When old Green, the frame-maker, had finished the frame for Holman Hunt’s The Finding of the Saviour in the Temple, Hunt went to see it and told him it was quite satisfactory. ‘Ah,’ said Green, ‘but you’ll see the picture will set it off amazingly.’

— Henry Holiday, Reminiscences of My Life, 1914

When an editor complained that Gerald Kersh used too many long words, Kersh bet him £50 that he could write a story entirely in monosyllables. Kersh won:

We met on the stairs of Time: I was on my way up; he was on his way down. I was young; he was old, and poor — so poor that he did not know when luck would send him a meal and a bed.

Frederic Birmingham published the whole three-page story in his 1958 book The Writer’s Craft.

On May 19, 1914, G. Howell Parr of Baltimore lay down and rolled three continuous miles to win a bet of $1,000. Details, from the New York Times:

Wagered $1,000 he could roll three miles.
Made the time limit June 1.
Started at 8 o’clock last night from the Elk Ridge Kennels.
Finished at 11:10 A M. to-day at Charles Street and University Parkway.
Rolled fifteen hours and ten minutes, with intermissions for rest.
Covered approximately 15,840 feet, or about three miles.
Took about four feet to a roll.
Made about 3,960 rolls.
Won the $1,000.
Every time he rolled he won about 25 cents.

He wore football gear and turned with every fourth revolution into a pillowed chair positioned by his friends, where he’d rest for 30 seconds. “At times the wife approached him solicitously and asked how he felt. He always looked up at her, and smiled and said: ‘Feel fine.'”

Indeed, he felt well enough afterward to go to the racetrack, “where several of his horses were on the day’s programme.” “When asked where he felt the strain of the rolling most, he said, ‘At my wrists; I put so much weight on them.'”

TO WIDOWERS AND SINGLE GENTLEMEN. — WANTED by a lady, a SITUATION to superintend the household and preside at table. She is Agreeable, Becoming, Careful, Desirable, English, Facetious, Generous, Honest, Industrious, Judicious, Keen, Lively, Merry, Natty, Obedient, Philosophic, Quiet, Regular, Sociable, Tasteful, Useful, Vivacious, Womanish, Xantippish, Youthful, Zealous, &c. Address X. Y. Z., Simmond’s Library, Edgeware-road.

— Times, 1842

Image: Wikimedia CommonsAn optical illusion. These circles are concentric.

(Baingio Pinna and Richard L. Gregory, “Shifts of Edges and Deformations of Patterns,” Perception 31:12 [December 2002], 1503-1508.)

Franz Liszt’s 1851 étude “La Campanella” is one of the most technically demanding pieces ever written for piano.

In bar 102, below, the left hand has to jump 35 half-steps, nearly three octaves, in the space of a sixteenth note.

That’s about 46 centimeters.

Image: Wikimedia CommonsSay what you will about hell, it’s very well organized. According to the 17th-century grimoire Ars Goetia, the underworld is ruled by 72 demons, each with its own sigil (above) and served by a sort of infernal bureaucracy:

Aim (also Aym or Haborym) is a Great Duke of Hell, very strong, and rules over twenty-six legions of demons. He sets cities, castles and great places on fire, makes men witty in all ways, and gives true answers concerning private matters. He is depicted as a man (handsome to some sources), but with three heads, one of a serpent, the second of a man, and the third of a cat to most authors, although some say of a calf, riding a viper, and carrying in his hand a lit firebrand with which he sets the requested things on fire.

Wikipedia has a page explaining who does what.

Related: Belphegor’s prime, 1000000000000066600000000000001, is a palindromic prime number with 666 at its heart and 13 zeros on either side. It was discovered by Harvey Dubner; Clifford Pickover named it after a prince of hell responsible for helping people make ingenious inventions and discoveries.

When Qantas’ last Boeing 747 departed Australia to retire in the United States, it drew a kangaroo with its flight path.

“We discover in ourselves what others hide from us, and we recognize in others what we hide from ourselves.” — Vauvenargues

A problem from the January-February 1991 issue of Quantum:

Prove that the area of the yellow rectangle is half that of the full octagon.

| SelectClick for Answer | | --- | | A simple method is to cut the regions into corresponding pieces: |

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Apocryphal but entertaining: Allegedly the Duke of Wellington sent this letter to the British War Office during the Peninsular War of 1808-1814:

Gentlemen:

Whilst marching to Portugal to a position which commands the approach to Madrid and the French forces, my officers have been diligently complying with your request which has been sent by H. M. ship from London to Lisbon and then by dispatch rider to our headquarters.

We have enumerated our saddles, bridles, tents, and tent poles, and all manner of sundry items for which His Majesty’s Government holds me accountable. I have dispatched reports on the character, wit, and spleen of every officer. Each item and every farthing has been accounted for, with two regrettable exceptions for which I beg your indulgence.

Unfortunately, the sum of one shilling and ninepence remains unaccounted for in one infantry battalion’s petty cash and there has been a hideous confusion as to the number of jars of raspberry jam issued to one cavalry regiment during a sandstorm in western Spain. This reprehensive carelessness may be related to the pressure of circumstances since we are at war with France, a fact which may have come as a bit of a surprise to you gentlemen at Whitehall.

This brings me to my present purpose, which is to request elucidation of my instructions from His Majesty’s Government, so that I may better understand why I am dragging an army over these barren plains. I construe that perforce it must be one of two alternative duties, as given below. I shall pursue either one with the best of my ability but I cannot do both:

To train an army of uniformed British clerks in Spain for the benefit of the accountants and copy-boys in London, or perchance

To see to it that the forces of Napoleon are driven out of Spain.

Your most obedient servant,

Wellington

Thomas Taverner published this remarkable problem in the Dubuque Chess Journal in 1889. White is to mate in two moves.

| SelectClick for Answer | | --- | | The impossibly quiet 1. Rh1! leaves Black in zugzwang — he has 19 legal moves, and each one leads immediately to mate:1. … Bxh7 2. Nd5#1. … Bf7 2. Qf5#1. … Be6 2. e3#1. … Bd5 2. Nxd5#1. … Bxc7 2. Rh4#1. … Be7 2. e3#1. … Bf6 2. Qf5#1. … Bg5 2. Qh2#1. … Bh4 2. Rxh4#1. … Rf7 2. Nd5#1. … Rf6 2. Rh4#1. … Rf5 2. Qxf5#1. … Re7 2. Rh4#1. … Re6 2. Nd5#1. … Re5 2. Qg4#1. … Re4 2. fxe4#1. … Re3 2. Bh2#1. … Rxe2+ 2. Nxe2#1. … c3 2. Nd3# |

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Image: Wikimedia Commonsheuretic
adj. of or relating to discovery or invention

Sea travel is not kind to teapots, which tend to drip when pouring, tip over on tables, and chip in storage. Entrepreneur Robert Crawford Johnson solved all these problems by designing a pot in the shape of a cube, with the spout tucked into a corner. His invention, patented in 1917, was quickly adopted by Cunard, and it was still in use on the Queen Elizabeth 2 as late as 1968.

Francis Galton was interested in communicating with Mars as early as 1892, when he wrote a letter to the Times suggesting that we try flashing sun signals at the red planet. At a lecture the following year he described more specifically a method by which pictures might be encoded using 26 alphabetical characters, which could then be transmitted over a distance in 5-character “words,” in effect creating a low-resolution visual telegraph. As a study he reduced this profile of a Greek girl to 271 coded dots, which he found yielded “a very creditable production.”

This had huge implications, he felt. In 1896 he imagined a whole correspondence with a civilization of intelligent ants on Mars; in three and a half hours they catch our attention; teach us their base-8 mathematical notation; demonstrate their shared understanding of certain celestial bodies and mathematical constants; and finally propose a specified 24-gon in which points can be situated by code, like stitches in a piece of embroidery.

That opens a limitless avenue for colloquy — the Martians send images of Saturn, Earth, the solar system, and domestic and sociological drawings, a new one every evening. Galton concludes that two astronomical bodies that are close enough to signal one another with flashes of light already have everything they need to establish “an efficient inter-stellar language.”

Stage actor Leo Reuss was just gaining fame in Berlin when the rising Nazi regime began to restrict the work of Jewish actors. So Reuss invented a new character. Retreating to a cabin in his native Austria, he grew out his beard, bathed in hydrogen peroxide to bleach his hair, studied the speech and mannerisms of farmers, and obtained new papers from a local peasant.

After a year’s effort he had recreated himself as Kaspar Brandhofer, a self-educated Tyrolian actor. When he returned to the stage, his former director Max Reinhardt failed to recognize him and in fact recommended him to Ernst Lothar in Vienna, where in 1936 Reuss played a featured role in the stage adaptation of Fräulein Else. The actors he worked among never suspected the ruse, despite their earlier work together.

Critics hailed the performance, calling Reuss “the humble peasant of the Austrian Alps, the finest natural actor of his generation,” and Lothar offered him a three-year contract. But his eventual confession brought on an uproar, and he decided that the Nazi regime had grown too strong. He emigrated to the United States, where he went on to an active movie career as Lionel Royce, appearing in almost 40 films before his death in 1946.

When E flat made its entrée into the drawing-room, C and G considered it a third person.

‘It’s a dominant,’ thought A flat, while E natural cried out, ‘I recognize it: it’s my leading tone.’

… But the same holds here as in music where the chord of G sharp has not the same meaning, depending on whether you reach it by way of the sharps or of the flats, and does not sound the same as that of A flat to the sensitive ear, though composed of the same notes.

— André Gide, journal, January 14, 1912

Mr. Smith goes to Atlantic City to gamble for a weekend. To guard against bad luck, he sets a policy at the start: In every game he plays, he’ll bet exactly half the money he has at the time, and he’ll make all his bets at even odds, so he’ll have an equal chance of winning and of losing this amount. In the end he wins the same number of games that he loses. Does he break even?

| SelectClick for Answer | | --- | | No. Every win multiplies Smith’s holdings by 1.5, and every loss multiplies them by 0.5. One win and one loss (the order is immaterial) leaves him with 0.75 times his initial holdings, and n wins and n losses leaves him with 0.75n his initial assets. Ten such blows will leave him with only about 5 percent of his initial stake.From David L. Book, Problems for Puzzlebusters, 1992. |

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Under Roman law, subjects found guilty of patricide were subjected to poena cullei, the “penalty of the sack” — they were sewn into a leather sack with a snake, a cock, a monkey, and a dog and thrown into water.

In his Life of Artaxerxes, Plutarch describes an ancient Persian method of execution known as scaphism in which vermin devour a victim trapped between mated boats:

Taking two boats framed exactly to fit and answer each other, they lie down in one of them the malefactor that suffers, upon his back; then, covering it with the other, and so setting them together that the head, hands, and feet of him are left outside, and the rest of his body lies shut up within, then forcing him to ingest a mixture of milk and honey before pouring all over his face and body. They then keep his face continually turned towards the sun; and it becomes completely covered up and hidden by the multitude of flies that settle on it. And as within the boats he does what those that eat and drink must needs do, creeping things and vermin spring out of the corruption and rottenness of the excrement, and these entering into the bowels of him, his body is consumed.

Happily Plutarch seems to have based his account on a report by the Greek historian Ctesias, whose reliability has been questioned, so perhaps this never happened.

In the 1970’s, a student of Maoist inclination asked [Columbia philosopher Sidney Morgenbesser] if he disagreed with Chairman Mao’s saying that a proposition can be true or false at the same time. Dr. Morgenbesser replied, ‘I do and I don’t.’

From Morgenbesser’s 2004 New York Times obituary.

“I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops.” — Stephen Jay Gould, The Panda’s Thumb, 1980

Martin Gardner published this puzzle in his “Mathematical Games” column in Scientific American in February 1979. You’re blindfolded and sitting before a lazy susan. On each corner is a glass. Some are right side up and some upside down. On each turn you can inspect any two glasses and, if you choose, reverse the orientation of either or both of them. After each turn the lazy susan will be rotated through a random angle. When all four glasses have the same orientation, a bell will sound. How can you reach this goal in a finite number of turns?

| SelectClick for Answer | | --- | | This algorithm will do it in five turns:1. Choose a pair of glasses that are diagonally opposite and set both right side up. 2. Choose two adjacent glasses. At least one must now be right side up. If the other is upside down, turn it right side up as well. If the bell rings, you’re done; if not, then only one glass is still upside down. 3. Choose a diagonally opposite pair. If one is upside down, turn it up and you’re done. If both are right side up, turn one upside down. Now two glasses are upside down, and these two must be adjacent. 4. Choose two adjacent glasses and reverse the orientation of both. If the bell doesn’t sound then there are now two glasses upside down, and they’re diagonally opposite one another. 5. Choose a diagonally opposite pair and reverse both. The bell will sound. |

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Grip, the talking raven in Dickens’ Barnaby Rudge, was based on a real bird, a pet who lived in the family’s Marylebone home, where she buried items in the garden, terrorized the dog, bit the children, and tore at the family carriage. She died in 1841 after ingesting some lead-based paint, and Dickens wrote her into the novel, which appeared later that year.

Interestingly, when Edgar Allan Poe reviewed the story for Graham’s Magazine, he remarked that “The raven … might have been made more than we see it … Its croaking might have been prophetically heard in the course of the drama.” In 1842, when the two authors met in Philadelphia, Poe was said to be “delighted” that Grip had been based on a real bird.

Poe’s famous poem appeared three years later, and scholars generally agree that Grip had inspired the “ebony bird” — in Dickens’ novel the raven had repeated the phrases “Never say die” and “Nobody” and is described as “tapping at the door” and “knocking softly at the shutter.”

Today Grip’s remains are on display in Philadelphia’s Parkway Central Library, where they may inspire yet more writings.

Image: Wikimedia Commons

Drill a hole straight through the center of a sphere, leaving a band in the shape of a napkin ring. Suppose the height of this band is h. Now take a sphere of a different size and drill a hole through that, contriving the hole’s width so that its depth is again h. Remarkably, the two napkin rings will have the same volume.

As the sphere expands, the band must grow both wider and thinner, and it turns out that these two effects exactly cancel one another. It’s called the napkin ring problem.

Just a striking image: German astronomer Johann Friedrich Julius Schmidt prepared a plaster moon for the Field Columbian Museum in 1898. From the Field Museum Library.

William Linkhaw sang so badly that a grand jury indicted him for disrupting his church’s services. At trial in August 1872, a witness imitated Linkhaw’s singing style and provoked “a burst of prolonged and irresistible laughter, convulsing alike the spectators, the Bar, the jury and the Court.”

It was in evidence that the disturbance occasioned by defendant’s singing was decided and serious; the effect of it was to make one part of the congregation laugh and the other mad; that the irreligious and frivolous enjoyed it as fun, while the serious and devout were indignant.

Linkhaw protested that he felt a duty to worship God. The jury fined him a penny, but the North Carolina Supreme Court set aside the verdict, observing that Linkhaw had had no malicious intent. Justice Thomas Settle wrote, “It would seem that the defendant is a proper subject for the discipline of his church, but not for the discipline of the Courts.”

In 1906 a wit wrote, “although the proof did show / That Linkhaw’s voice was awful / The judges found no valid ground / For holding it unlawful.”

Students beginning with the compass learn to draw this rosette, sometimes called the Flower of Life. If the arcs and the circle have the same radius, a, then the area of one petal is

and the unshaded area of the circle is

Remarkably, though the area we sought is bounded entirely by the arcs of circles, the final expression is independent of π.

Related: When two cylinders of radius r meet at right angles, the volume of their intersection is 16r3/3 — again, no sign of π.

(J.V. Narlikar, “A Pi-Less Area,” Mathematical Gazette 65:431 [March 1981], 32-33.)

C.S. Kipping published this unusual problem in Chess Amateur in 1923. In each position, White is to mate in two moves.

| SelectClick for Answer | | --- | | (a) White castles, threatening 2. Nc7#. Black can capture the knight, but then 2. Rb8 is mate.(b) After 1. Rxe3, Black can’t escape 2. Re8#.The point is that in (a) both sides can castle legally, and in (b) they can’t. (In chess problems castling is deemed legal if king and rook stand on their original squares and it can’t be proven that either must have moved in a hypothetical game.) In (a) White needs to castle because the mere 1. Rf1 allows 1. … d2+, and 1. Rxd3 also won’t work because then it’s Black who can castle to safety. In the reflected position both sides lose the castling expedient, so a new solution becomes possible. |

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Then there is the other secret. There isn’t any symbolysm. The sea is the sea. The old man is an old man. The boy is a boy and the fish is a fish. The shark are all sharks no better and no worse. All the symbolism that people say is shit. What goes beyond is what you see beyond when you know. A writer should know too much.

— Ernest Hemingway, letter to Bernard Berenson, 1952

A reversible print by John Kay, 1789.

Suppose you have a collection of gears pinned to a wall (disks in the plane). When is it possible to wrap a conveyor belt around them so that the belt touches every gear, is taut, and does not touch itself? This problem was first posed by Manuel Abellanas in 2001. When all the gears are the same size, it appears that it’s always possible to find a suitable path for the belt, but the question remains open.

Erik Demaine, Martin Demaine, and Belén Palop have designed a font to illustrate the problem — each letter is a collection of equal-sized gears around which exactly one conveyor-belt wrapping outlines an English letter:

Apart from its mathematical interest, the font makes for intriguing puzzles — when the belts are removed, the letters are surprisingly hard to discern. What does this say?

| SelectClick for Answer | | --- | | SOLID GOLD.You can play with the font here.(Erik D. Demaine et al., “Three Puzzle Fonts,” in Thane Plambeck and Tomas Rokicki, Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers, 2020.) |

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MIT computer scientist Gerald Sussman offered this example to show the importance of sophisticated planning algorithms in artificial intelligence. Suppose an agent is told to stack these three blocks into a tower, with A at the top and C at the bottom, moving one block at a time:

Image: Wikimedia CommonsIt might proceed by separating the goal into two subgoals:

Get A onto B.
Get B onto C.

But this leads immediately to trouble. If the agent starts with subgoal 1, it will move C off of A and then put A onto B:

Image: Wikimedia CommonsBut that’s a dead end. Because it can move only one block at a time, the agent can’t now undertake subgoal 2 without first undoing subgoal 1.

If the agent starts with subgoal 2, it will move B onto C, which is another dead end:

Image: Wikimedia CommonsNow we have a tower, but the blocks are in the wrong order. Again, we’ll have to undo one subgoal before we can undertake the other.

Modern algorithms can handle this challenge, but still it illustrates why planning is not a trivial undertaking. Sussman discussed it as part of his 1973 doctoral dissertation, A Computational Model of Skill Acquisition.

In 1896 the letter above arrived at the New York post office. As there was no Goat Street in New York, the office marked it misdirected and sent it on to Washington, where clerks eventually opened it, looking for further clues. They found this:

Dear Santa, — When I said my prayers last night I told God to tell you to bring me a hobby horse. I don’t want a hobby horse, really. A honestly live horse is what I want. Mamma told me not to ask for him, because I probably would make you mad, so you wouldn’t give me anything at all, and if I got him I wouldn’t have any place to keep him. A man I know will keep him, he says, if you get him for me. I thought you might like to know. Please don’t be mad. — Affectionately, John.

P.S. — A shetland would be enough.

P.S. — I’d rather have a hobby horse than nothing at all.

“I am very sorry to say that John did not get the horse,” wrote Mary K. Davis in the Strand. “Little boys who don’t do as their mothers tell them find little favour with Santa Claus.”

As a footnote to the above, I would like to say that I am getting very tired of literary authorities, on both the stage and the screen, who advise young writers to deal only with those subjects that happen to be familiar to them personally. It is quite true that this theory probably produced A Tree Grows in Brooklyn, but the chances are it would have ruled out Hamlet.

— Wolcott Gibbs, New Yorker, January 6, 1945

nimiety
n. superfluity

brachylogy
n. a condensed expression

scrimption
n. a very small amount or degree

perficient
adj. that accomplishes something; effectual

Leonard Bernstein conducts the Vienna Philharmonic without using his hands, 1984:

This is a variation on a perpetual motion machine proposed by the Indian mathematician Bhāskara II around 1150. Each of the wheel’s tilted spokes is filled with a quantity of sand. As the tubes descend on the right, the sand within them shifts outward, exerting greater torque in the clockwise direction and thus keeping the wheel turning forever.

Unfortunately the same design ensures that there’s always a greater quantity of sand on the left, so nothing happens.

In 1956, ornithologist Chandler Robbins tagged a wild female Laysan albatross at the Midway Atoll National Wildlife Refuge in the North Pacific. The bird, dubbed Wisdom, went on to a stunning career, flying more than 3 million miles, equivalent to 120 trips around the Earth. She has been seen at the atoll as recently as last December, making her, at 72, the the oldest known wild bird in the world.

In that time she’s hatched as many as 36 chicks, a significant contribution to the struggling wild albatross population. The U.S. Fish and Wildlife Service wrote, “Her health and dedication have led to the birth of other healthy offspring which will help recover albatross populations on Laysan and other islands.” Bruce Peterjohn, chief of the North American Bird Banding Program, added, “To know that she can still successfully raise young at age 60-plus, that is beyond words.”

If we have two numbers a and b such that ab + 1 is square, then it’s always possible to find a number c for which ac + 1 and bc + 1 are both square. For example, 8 × 3 + 1 = 25 = 52, and 8 × 21 + 1 = 169 = 132 and 3 × 21 + 1 = 64 = 82.

Proof:

If ab + 1 = m2, then set c = a + b + 2m. Now

ac + 1 = a2 + ab + 2am + 1 = a2 + 2am + m2 = (a + m)2

bc + 1 = ab + b2 + 2bm + 1 = b2 + 2bm + m2 = (b + m)2

Via Edward Barbeau, Power Play, 1997.

Image: Wikimedia CommonsEvery March since 2010, a white stork named Yaren has departed Africa, flown to the village of Eskikaraağaç in Turkey, and landed on the boat of fisherman Adem Yılmaz on the shore of Uluabat Lake. It spends six months in the village, fishing with Yılmaz every morning, then returns to Africa.

A statue of the two now stands in the village’s central square. A live broadcast of stork’s nest is here.

calophantic
adj. pretending or making a show of excellence

velleity
n. a mere wish, unaccompanied by an effort to obtain it

fode
v. to lead on with delusive expectations

magnoperate
v. to magnify the greatness of

Roman diplomat Sidonius Apollinaris describes the hunting skill of Visigoth king Theodoric II:

If the chase is the order of the day, he joins it, but never carries his bow at his side, considering this derogatory to royal state. … He will ask you beforehand what you would like him to transfix; you choose, and he hits. If there is a miss … your vision will mostly be at fault, and not the archer’s skill.

(Quoted in Norman Davies, Vanished Kingdoms, 2012.)

The British post office had to make sense of this address in 1893. It reads “The Right Hon. Sir James Fergusson, P.C., 25, Tedworth Square, S.W.”

Ironically Fergusson had been postmaster-general of Australia.

The writer was Thomas Denman, the future governor-general. The first page of the letter is below: “Dear Sir James, — I hardly think of coming before 11th to London. I am afraid I might …”

Princeton mathematician John Horton Conway memorized π to more than a thousand decimal places by marrying it to the periodic table of the elements:

3 Neutronium 1415926535 Hydrogen 8979323846 Helium 2643383279 Lithium 5028841971 Beryllium …

Between each pair of elements are sandwiched ten digits of π. (Neutronium is Andreas von Antropoff’s notional “element of atomic number zero,” an element with zero protons in its nucleus.) This approach to memorizing digits has a number of virtues:

It’s modular. If you forget one segment you can just look it up and plug it back in to the whole. And you can name the segment you’ve forgotten.
The element names lend some memorable color to each segment.
The 10-digit “mouthfuls” are relatively easy to remember, and since they’re tied to numbered elements you can jump fairly readily to, say, the 216th digit.
They give you an excuse for stopping — you’ve run out of elements!

To remember the elements themselves Conway devised a long mnemonic. It begins

Newt? Hy! He Likes Beryl’s Boring Car for Nites Out in Florid Neon

for

Nn H He Li Be B C N O F Ne.

See the paper below for the whole package — by including unconfirmed hypothetical elements, it encodes 120 mouthfuls, or 1,200 digits.

(John Conway, “Chemical π,” Mathematical Intelligencer 38:4 [December 2016], 7-10.)

Image: Wikimedia CommonsLisbon’s Pavilhão do Conhecimento science museum has four more onlookers than are commonly recognized.

We’ve got a new maid called Chrysanthemum
Who said, “I have just come from Grantham, m’m.
I lost my last place
In the sorest disgrace,
‘Cos I snored through the National Anthem, m’m.

— Anonymous

Further unrhymable words: month, silver, orange, bilge, oblige, poem, Rachel, Carthaginian, W, wasp.

In 2015 Nature published an alarming article suggesting that dragons are real and had only gone to sleep during the Little Ice Age. A medieval document discovered “under a pile of rusty candlesticks” in the Bodleian Library showed that the creatures were once common but had entered a state of brumation when temperatures dropped and their traditional diet of knights began to thin. Rising temperatures in the modern age have correlated with increasing mentions in fictional literature, which “suggests that these fire-breathing lizards are being sighted more frequently.”

It gets worse: “Sluggish action on global warming is set to compound the problem, and policies such as the restoration of knighthoods in Australia are likely to exacerbate the predicament yet further by providing a sustained and delicious food supply.” The date of the article was April 2.

(Andrew J. Hamilton, Robert M. May, and Edward K. Waters, “Here Be Dragons,” Nature 520:7545 [April 2, 2015], 42-43.)

Image: Wikimedia CommonsIn 1991, artist Michael Dennis installed his sculpture Reclining Figure in Vancouver’s Guelph Park.

In 2012, prankster Viktor Briestensky erected the sign below at the park’s southwest corner.

Park staff initially removed the sign, but when a petition gathered 1,800 signatures they replaced it in 2014. The city now recognizes it as an official public art installation.

Image: Wikimedia Commons

“If it were not for the intellectual snobs who pay — in solid cash — the tribute which philistinism owes to culture, the arts would perish with their starving practitioners. Let us thank heaven for hypocrisy.” — Aldous Huxley

Two sets of reversible faces by Rex Whistler, from 1930 — above, Mayor & Judge; below, Scotsman & Englishman.

English poet Winthrop Mackworth Praed was renowned for his charades — this one, published in the 1830s, has never been solved:

Sir Hilary charged at Agincourt,–
Sooth, ’twas an awful day!
And though in that old age of sport
The rufflers of the camp and court
Had little time to pray,
’Tis said Sir Hilary mutter’d there
Two syllables by way of prayer.

My first to all the brave and proud
Who see to-morrow’s sun:
My next, with her cold and quiet cloud,
To those who find their dewy shroud
Before to-day’s be done:
And both together to all blue eyes,
That weep when a warrior nobly dies.

“The best answer I have been able to find is GOOD NIGHT,” wrote Henry Dudeney in 1919. “The two syllables are by way of wish or prayer. We wish nothing but good to the victorious, we leave those have fallen to their ‘dewy shroud’ at night, while to the sorrowful bereaved we cannot do less than wish them a good night.”

But Praed himself left no solution.

In 1979 Auberon Waugh was working as a columnist at Private Eye when his editor offered him a trip to Senegal to help celebrate the anniversary of the magazine’s sister publication. “All I would have to give in exchange was a short discourse in the French language on the subject of breast feeding.”

The assignment struck Waugh as strange but not unaccountable — he’d been writing a regular column in a medical magazine that had touched on that topic.

“So I composed a speech on this subject in French, with considerable labour, only to find when I landed in Dakar that the subject chosen was not breast-feeding but press freedom.” He’d misheard the editor.

“There was no way even to describe the misunderstanding, since la liberté de la Presse bears no resemblance to le nourrisson naturel des bébés.”

(From Waugh’s 1991 autobiography Will This Do?)

Much blood has … been spilled on the carpet in attempts to distinguish between science fiction and fantasy. I have suggested an operational definition: science fiction is something that could happen — but usually you wouldn’t want it to. Fantasy is something that couldn’t happen — though often you only wish that it could.

— Arthur C. Clarke, foreword, The Collected Stories of Arthur C. Clarke, 2000

pluvial
adj. relating to rainfall

A little tap at the window, as though some missile had struck it, followed by a plentiful, falling sound, as light, though, as if a shower of sand were being sprinkled from a window overhead; then the fall spread, took on an order, a rhythm, became liquid, loud, drumming, musical, innumerable, universal. It was the rain.

— Proust, Swann’s Way

A problem by Soviet physicist Viktor Lange:

It’s not uncommon to see two ships traveling down a river at different velocities — this is due to differences in design and engine power.

“But why can rafts which have no engines float down the river with different velocities, too? It has been even noticed that the heavier the raft the higher its velocity. Why is this?”

| SelectClick for Answer | | --- | | The water in a river doesn’t move with a single velocity — friction with the air and the channel slows some of the stream. Water moves fastest just below the surface in midstream:As a raft is laden its draft increases, submerging it into the faster layers, which carry it along more quickly.From Physical Paradoxes and Sophisms, 1987. |

| | | |

Mark Twain approaches the international date line, 1895:

Sept. 8. To-morrow we shall be close to the center of the globe … And then we must drop out a day — lose a day out of our lives, a day never to be found again. We shall all die one day earlier than from the beginning of time we were foreordained to die. We shall be a day behindhand all through eternity. We shall always be saying to the other angels, ‘Fine day today,’ and they will be always retorting, ‘But it isn’t to-day, it’s tomorrow.’ We shall be in a state of confusion all the time and shall never know what true happiness is.

Next Day. Sure enough, it has happened. … While we were crossing the 180th meridian it was Sunday in the stern of the ship where my family were, and Tuesday in the bow where I was. They were there eating the half of a fresh apple on the 8th, and I was at the same time eating the other half of it on the 10th — and I could notice how stale it was, already.

That’s from Following the Equator. “[F]ortunately the ships do not all sail west, half of them sail east. So there is no real loss. These latter pick up all the discarded days and add them to the world’s stock again; and about as good as new, too; for of course the salt water preserves them.”

It must, I think, be allowed, that if a very limited intelligence, whom we shall suppose utterly unacquainted with the universe, were assured, that it were the production of a very good, wise, and powerful Being, however finite, he would, from his conjectures, form beforehand a different notion of it from what we find it to be by experience; nor would he ever imagine, merely from these attributes of the cause, of which he is informed, that the effect could be so full of vice and misery and disorder, as it appears in this life. Supposing now, that this person were brought into the world, still assured that it was the workmanship of such a sublime and benevolent Being; he might, perhaps, be surprised at the disappointment; but would never retract his former belief, if founded on any very solid argument; since such a limited intelligence must be sensible of his own blindness and ignorance, and must allow, that there may be many solutions of those phenomena, which will for ever escape his comprehension. But supposing, which is the real case with regard to man, that this creature is not antecedently convinced of a supreme intelligence, benevolent, and powerful, but is left to gather such a belief from the appearances of things; this entirely alters the case, nor will he ever find any reason for such a conclusion. He may be fully convinced of the narrow limits of his understanding; but this will not help him in forming an inference concerning the goodness of superior powers, since he must form that inference from what he knows, not from what he is ignorant of. The more you exaggerate his weakness and ignorance, the more diffident you render him, and give him the greater suspicion that such subjects are beyond the reach of his faculties. You are obliged, therefore, to reason with him merely from the known phenomena, and to drop every arbitrary supposition or conjecture.

— David Hume, Dialogues Concerning Natural Religion, 1779

In 2013, Japanese refrigeration company Fukushima Industries introduced a new mascot, a happy winged egg:

“I fly around on my awesome wings, patrolling supermarket showcases and kitchen refrigerators. I can talk to vegetables, fruit, meat, and fish and can check on their health! I was born in a Fukushima refrigerator! I love eating and I’m full of curiosity. I think of myself as kind, with a strong sense of justice, but my friends say I’m a bit of a klutz. But I’m always working hard to make myself shine!”

Unfortunately the company named the character “Fukuppy,” a combination of Fukushima and the English word happy.

After the name began to make news in English-speaking countries, Fukushima issued an apology and withdrew it.

In Seven Types of Ambiguity (1949), William Empson describes a particularly inscrutable English newspaper headline:

ITALIAN ASSASSIN BOMB PLOT DISASTER

Bomb and plot, you notice, can be either nouns or verbs, and would take kindly to being adjectives, not that they are anything so definite here. One thinks at first that there are two words or sentences, and a semicolon has been left out as in telegrams: ‘I will tell you for your penny about the Italian Assassin and the well-known Bomb Plot Disaster’; but the assassin, as far as I remember, was actually not an Italian; Italian refers to the whole aggregate, and its noun, if any, is disaster. Perhaps, by being so far separated from its noun, it gives the impression that the other words, too, are somehow connected with Italy; that bombs, plots, and disasters belong both to government and rebel in those parts; perhaps Italian Assassin is not wholly separate in one’s mind from the injured Mussolini.

In fact it’s not clear what the intended meaning had been. Empson says that the main rhythm conveys the sense “This is a particularly exciting sort of disaster, the assassin-bomb-plot type they have in Italy.” In The Wordsworth Book of Usage & Abusage (1995), Eric Partridge suggests that the writer may have meant ITALIAN DISASTER ASSASSIN’S BOMB-PLOT, “There has been in Italy a disaster caused by a bomb in an assassin’s plot.” But he agrees that “even after an exasperating amount of cogitation by the reader,” the meaning is unclear.

Someone said to Socrates that a certain man had grown no better by his travels.

‘I should think not,’ he said; ‘he took himself along with him.’

— Montaigne, Essays

A problem from the 17th Irish Mathematical Olympiad, in 2004:

In a tennis tournament, each player played one match against each of the others. If each player won at least one match, show that there’s a group of three players A, B, C in which A beat B, B beat C, and C beat A.

| SelectClick for Answer | | --- | | This solution, by Titu Zvonaru, is given in the February 2008 issue of Crux Mathematicorum:Suppose that the most unfortunate player beat 3 others. Label the players so that this player is P1 and that the players he beat follow him immediately in the lineup, here as P2, P3, and P4. Since the minimum number of wins is 3, there must be some player Pk such that player P2 beat player Pk and k is greater than 4 (otherwise player P2 could have beaten only players P3 and P4, which would give him the minimum number of wins, contrary to our supposition). This means that player Pk must have beaten player P1, and we can declare that A = P1, B = P2, and C = Pk.The same argument holds for any minimum number of wins. (It wouldn’t work if the minimum were zero, but we’ve been told that’s not the case.) |

| | | |

Sydney is 14 hours ahead of New York, so when it’s noon in Sydney it’s 10 p.m. the previous day in New York.

Suppose you were broadcasting to the U.S. on a news-service hook-up from Sydney, and wanted to tell the American public about an explosion that occurred at 2:30 A.M. in a factory in Sydney.

Would you say ‘There will be an explosion in the Sydney Boiler Works at 2:30 A.M. tomorrow morning?’

Or would you say ‘There was an explosion in the Sydney Boiler Works at 2:30 A.M. tomorrow morning?’

That’s from Gerald Lynton Kaufman’s It’s About Time, from 1935. For the record, the Associated Press would dateline the story SYDNEY and refer to clock times in that location.

The most successful critics are always scribbling things in their programs, largely because it gives them an important and industrious air. Also, it is interesting to try to figure out what you’ve written afterward. Last week, for instance, I made a very helpful note during the second act of a drama called ‘They Walk Alone.’ ‘Lanchstr get face stuck 1 these nights awful if,’ it seemed to say.

— Wolcott Gibbs, “The Theatre,” New Yorker, Jan. 4, 1941

In What a Word!, his 1936 lamentation of English usage, A.P. Herbert takes up a letter written in “officese”:

Madam,
We are in receipt of your favour of the 9th inst. with regard to the estimate required for the removal of your furniture and effects from the above address to Burbleton, and will arrange for a Representative to call to make an inspection on Tuesday next, the 14th inst., before 12 noon, which we trust will be convenient, after which our quotation will at once issue.

He reduces this to:

Madam,
We have your letter of May 9th requesting an estimate for the removal of your furniture and effects to Burbleton, and a man will call to see them next Tuesday forenoon if convenient, after which we will send the estimate without delay.

This shortens the letter from 66 words to 42. Then he cuts it again, to 35 words, or 157 letters against the original 294, a savings of nearly 50 percent:

Madam,
Thank you for your letter of May 9th. A man will call next Tuesday, forenoon, to see your furniture and effects, after which, without delay, we will send our estimate for their removal to Burbleton.

In a large firm, he estimates, cutting “verbose and indolent, obscure, inelegant, and time-devouring monkey-talk” could save a week’s work for two typists.

Elsewhere he considers a memo that reads “Hot-Water Bottles: With reference to the above matter I should like an opportunity of discussing same with you.” The improvement he suggests is “Could we, please, have a talk about Hot-Water Bottles?”

Mark Antony’s funeral oration rendered in Scrabble tiles, by Pete Stickland:

COUNTRYMEN, I AM TO BURY, NOT EULOGIZE, CAESAR; IF EVIL LIVES ON, BEQUEATHING INJURY, GOOD OFT EXPIRES: A PALSIED, AWKWARD DEATH!

The tiles can also spell:

QUEASY RADIOMAN WEPT: GOT TO EYE FEROCIOUS BLAZE OF VIVID AERIAL EXPLOSION, CREMATING WILTED HINDENBURG AT LAKEHURST, N.J.

Unusual personal names collected in Oklahoma by onomastician Thomas Pyles in the 1940s:

A. Noble Ladd
Beverage Porter
Bunker Hill
Charming Fox
Erie Lake
France Paris
Gunga Dean
Harness Upp
Harry Baer
Ima Goose
Jack Frost
Johnny Steele Casebeer
Liberty Bond
Pansy Leafe
Pearl Button
Rose Bush
Safety Reuel First
Winter Frost

Ima Foster and Ura Foster, possibly twin sisters, both received master’s degrees in education at the University of Oklahoma in 1943. “It has been suggested to me that most of the bearers of jocular names come of families in which infant baptism is not practiced, inasmuch as (it is to be hoped) few clergymen would consent to make a travesty of the sacrament of baptism by bestowing such names in christening.”

(Thomas Pyles, “Onomastic Individualism in Oklahoma,” American Speech 22:4 [December 1947], 257-264.)

The so-called four-field approach in anthropology divides the discipline into four subfields: archaeology, linguistics, physical anthropology, and cultural anthropology.

Students call these “stones, tones, bones, and thrones.”

Talking of shaving the other night at Dr. Taylor’s, Dr. Johnson said, ‘Sir, of a thousand shavers, two do not shave so much alike as not to be distinguished.’ I thought this not possible, till he specified so many of the varieties in shaving; — holding the razor more or less perpendicular; — drawing long or short strokes; — beginning at the upper part of the face, or the under; — at the right side or the left side. Indeed, when one considers what variety of sounds can be uttered by the windpipe, in the compass of a very small aperture, we may be convinced how many degrees of difference there may be in the application of a razor.

— James Boswell, Life of Samuel Johnson, 1791

Image: Wikimedia CommonsVenice’s Museo Correr exhibits a pair of wooden implements whose use isn’t immediately clear — they’re chopines, a type of platform shoe popular in the 15th, 16th, and 17th centuries. Worn under a woman’s skirt they could add up to 20 inches to her height, giving her an impressive eminence but an uncertain gait. Shakespeare mocked the trend in Hamlet’s greeting to a visiting player:

“By’r lady, your ladyship is nearer to heaven than when I saw you last, by the altitude of a chopine.”

A centered hexagonal number is a number that can be represented by a hexagonal lattice with a dot in the center, like so:

Image: Wikimedia CommonsStarting at the center, successive hexagons contain 1, 7, 19, and 37 dots. The sequence goes on forever.

The sum of the first n centered hexagonal numbers is n3, and there’s a pretty “proof without words” to show that this is so:

Image: Wikimedia CommonsInstead of regarding each figure as a hexagon, think of it as a perspective view of a cube, looking down along a space diagonal. The first cube here contains a single dot. How many dots must we add to produce the next larger cube? Seven, and from our bird’s-eye perspective this pattern of 7 added dots matches the 7-dot hexagon shown above. The same thing happens when we advance to a 3×3×3 cube: This requires surrounding the 2×2×2 cube with 19 additional dots, and from our imagined vantage point these again take the form of a hexagonal lattice. In the last image our 33 cube must accrete another 37 dots to become a 43 cube … and the pattern continues.

Epigrams of poet Ralph Hodgson:

Oaths in anguish rank with prayers.
The wink was not our best invention.
When crises pall, humdrum is sensational.
But Woman — in whose image made?
A sparrow in a snowstorm with a feather in his bill: that is Faith.
Forget the slush, but keep the snow / Of Christmasses of long ago.
Anniversary: Familiarity breeds content.
Some things have to be believed to be seen.
Who shall paraphrase a tear!
There’s one thing to be said for sin — it does give conscience exercise.
Why not Foremothers?
The Golden Rule was called new-fangled, once upon a time.
Blessed are the children of a nobody.
The handwriting on the wall may be a forgery.

And “The ‘last word’ is only the latest.”

Reader Derek Christie sent in this surprising curiosity after Wednesday’s post about Borromean rings:

Both the ring and the karabiner clip are attached to the cord and can’t be removed.

Now complicate matters by clipping the karabiner onto the ring:

Quite unexpectedly, the cord can now be just pulled away:

(Thanks, Derek.) (A related perplexity: The Prisoners’ Release Puzzle.)

“Rules for the direction of the mind,” from an unfinished treatise by René Descartes:

The aim of our studies must be the direction of our mind so that it may form solid and true judgments on whatever matters arise.
We must occupy ourselves only with those objects that our intellectual powers appear competent to know certainly and indubitably.
As regards any subject we propose to investigate, we must inquire not what other people have thought, or what we ourselves conjecture, but what we can clearly and manifestly perceive by intuition or deduce with certainty. For there is no other way of acquiring knowledge.
There is need of a method for finding out the truth.
Method consists entirely in the order and disposition of the objects towards which our mental vision must be directed if we would find out any truth. We shall comply with it exactly if we reduce involved and obscure propositions step by step to those that are simpler, and then starting with the intuitive apprehension of all those that are absolutely simple, attempt to ascend to the knowledge of all others by precisely similar steps.
In order to separate out what is quite simple from what is complex, and to arrange these matters methodically, we ought, in the case of every series in which we have deduced certain facts the one from the other, to notice which fact is simple, and to mark the interval, greater, less, or equal, which separates all the others from this.
If we wish our science to be complete, those matters which promote the end we have in view must one and all be scrutinized by a movement of thought which is continuous and nowhere interrupted; they must also be included in an enumeration which is both adequate and methodical.
If in the matters to be examined we come to a step in the series of which our understanding is not sufficiently well able to have an intuitive cognition, we must stop short there. We must make no attempt to examine what follows; thus we shall spare ourselves superfluous labour.
We ought to give the whole of our attention to the most insignificant and most easily mastered facts, and remain a long time in contemplation of them until we are accustomed to behold the truth clearly and distinctly.
In order that it may acquire sagacity the mind should be exercised in pursuing just those inquiries of which the solution has already been found by others; and it ought to traverse in a systematic way even the most trifling of men’s inventions though those ought to be preferred in which order is explained or implied.
If, after we have recognized intuitively a number of simple truths, we wish to draw any inference from them, it is useful to run them over in a continuous and uninterrupted act of thought, to reflect upon their relations to one another, and to grasp together distinctly a number of these propositions so far as is possible at the same time. For this is a way of making our knowledge much more certain, and of greatly increasing the power of the mind.
Finally we ought to employ all the help of understanding, imagination, sense and memory, first for the purpose of having a distinct intuition of simple propositions; partly also in order to compare the propositions.
If we perfectly understand a problem we must abstract it from every superfluous conception, reduce it to its simplest terms and, by means of an enumeration, divide it up into the smallest possible parts.
The problem should be re-expressed in terms of the real extension of bodies and should be pictured in our imagination entirely by means of bare figures. Thus it will be perceived much more distinctly by our intellect.
It is generally helpful if we draw these figures and display them before our external senses. In this way it will be easier for us to keep our mind alert.
As for things which do not require the immediate attention of the mind, however necessary they may be for the conclusion, it is better to represent them by very concise symbols rather than by complete figures. It will thus be impossible for our memory to go wrong, and our mind will not be distracted by having to retain these while it is taken up with deducing other matters.

He’d planned a further 15 but did not finish the work. These 21 were published posthumously in 1701.

It is time to bury the nonsense of the ‘incomplete animal.’ As Julian Huxley, the eminent British biologist, once observed concerning human toughness, man is the only creature that can walk twenty miles, run two miles, swim a river, and then climb a tree. Physiologically, he has one of the toughest bodies known; no other species could survive weeks of exposure on the open sea, or in deserts, or the Arctic. Man’s superior exploits are not evidence of cultural inventions: clothing on a giraffe will not allow it to survive in Antarctica, and neither shade nor shoes will help a salamander in the Sahara. I am not speaking of living in those places permanently, but simply as a measure of the durability of men under stress.

— Paul Shepard, The Tender Carnivore and the Sacred Game, 1973

Vatican City has 2.27 popes per square kilometer.
Skylab was fined for littering.
Five-syllable rhyming words in English: vocabulary, constabulary
8767122 + 3287682 = 876712328768
“We die only once, and for such a long time!” — Molière

Above is the only known film footage of Mark Twain, shot at Twain’s Connecticut home in 1909. The women are thought to be his daughters Clara and Jean.

German scientist Gaspar Schott’s 1657 Magia universalis naturæ et artis includes a description of “the music of donkeys”: “the trick, according to Schott, lay in using male donkeys of particular natural pitches and stimulating them to bray with the urine of a female donkey, which will induce the males to make ‘most contented’ noises that the generous might construe as a kind of music.” Schott had argued that “the excessively discordant singing” of men and animals becomes sweeter when encountered rarely.

From Mark A. Waddell, Jesuit Science and the End of Nature’s Secrets, 2015.

Related: the cat organ and the piganino.

rarissima
n. extremely rare books, manuscripts, or prints

In The Book Hunter (1863), John Hill Burton identifies five types of “persons who meddle with books”:

“A bibliognoste, from the Greek, is one knowing in title-pages and colophons, and in editions; the place and year when printed; the presses whence issued; and all the minutiae of a book.”
“A bibliographe is a describer of books and other literary arrangements.”
“A bibliomane is an indiscriminate accumulator, who blunders faster than he buys, cock-brained and purse-heavy.”
“A bibliophile, the lover of books, is the only one in the class who appears to read them for his own pleasure.”
“A bibliotaphe buries his books, by keeping them under lock, or framing them in glass cases.”

These groups seem to have been proposed by French librarian Jean Joseph Rive. Bibliographer Gabriel Peignot added four more:

bibliolyte, a destroyer of books
bibliologue, one who discourses about books
bibliotacte, a classifier of books
bibliopée, “‘l’art d’écrire ou de composer des livres,’ or, as the unlearned would say, the function of an author.”

Proposed cabinet of Dizzy Gillespie, who ran for president in 1964:

Secretary of State: Duke Ellington
Director of the CIA: Miles Davis
Secretary of Defense: Max Roach
Secretary of Peace: Charles Mingus
Librarian of Congress: Ray Charles
Secretary of Agriculture: Louis Armstrong
Ambassador to the Vatican: Mary Lou Williams
Travelling Ambassador: Thelonious Monk
Attorney General: Malcolm X

He said his running mate would be Phyllis Diller. When asked why he was running for president, he said, “Because we need one.”

These circles display an odd property — the three are linked, but no two are linked.

A.G. Smith exhibited this curious variant in Eureka in 1967:

“I leave it to the reader the problem of finding whether Knotung is knotted, and if so, whether it is equivalent to the Borromean Rings, with which it shares the property that cutting any one loop releases the other two completely.”

Image: Wikimedia CommonsScotland’s Paisley Abbey updated its gargoyles in 1991.

In 1975 British biologist Peter Scott proposed dubbing the Loch Ness Monster Nessiteras rhombopteryx after a blurry underwater photograph seemed to show one of the creature’s fins.

He’d intended the name to mean “monster of Ness with diamond-shaped fin,” but the Daily Telegraph pointed out that its letters could be rearranged to spell “Monster hoax by Sir Peter S.”

American lawyer Robert Rines, who led several expeditions to the loch, pointed out that they can also spell “Yes, both pix are monsters, R.”

Dion is a person, a whole man. Theon is that part of Dion that does not include the left foot. Theon is a “proper part” of Dion — he’s part of Dion but not identical with him.

Now suppose we remove Dion’s left foot. What has happened? Do we now have two numerically different objects composed of the same matter and occupying the same place? If not, then either Theon or Dion has ceased to exist. Which? How?

(From Chrysippus.)

Samuel Johnson’s 1755 Dictionary of the English Language defines lizard as “an animal resembling a serpent, with legs added to it.”

“Three blokes walk into a pub. One of them is a little bit stupid, and the whole scene unfolds with a tedious inevitability.” — Bill Bailey

The Scientific Monthly reported a startling discovery in October 1952: the Schuss-yucca, a rare desert plant whose stalk could grow 10 feet in 2 minutes.

Readers’ letters generally joined in the spirit of the hoax — including one that mentioned a boxer who “stopped hiking long enough to inspect a yucca at just the wrong time.”

The plant shot up 16 feet at that moment, dealing him an uppercut that ended his career. “All he would say of the unfortunate incident was ‘Any time a goddam bush can lay me out cold, I know prizefighting ain’t for me.'”

In It’s About Time (1935), Gerald Lynton Kaufman tells the fanciful story of sailor Timothy J. McCloskey, who was born on Leap Day 1876 and thus had celebrated only five birthdays when he went to sea in 1896. No leap year was observed in 1900, and he awoke after the night of February 28, 1904, to find that his ship had crossed the international date line in the night, bypassing Leap Day.

Thus he had to wait from February 29, 1896, to February 29, 1908, to advance from his fifth birthday (celebrated at 20 years of age) to his sixth birthday (celebrated at 32).

In Gilbert and Sullivan’s 1879 operetta The Pirates of Penzance, hero Frederic thinks he has completed his pirate apprenticeship at the end of his 21st year — but learns that he was born on February 29 and so must serve another 63 years to reach his “twenty-first birthday.”

How quaint the ways of Paradox!
At common sense she gaily mocks!
Though counting in the usual way,
Years twenty-one I’ve been alive,
Yet reckoning by my natal day,
I am a little boy of five!

Sign on an English industrial computer, October 1968:

ACHTUNG ALLES LOOKENPEEPERS

Das computermachine ist nicht fur gefingerpoken und mittengrabben. Ist easy schnappen der springenwerk, blowenfusen und poppencorken mit spitssparken. Ist nicht fur gewerken bei das dummkopfen. Das rubbernecken sightseeren keepen hands in das pockets — relaxen und watch das blinkenlights.

(Via Eureka.)

Little-used words:

anopisthograph
adj. having writing on one side only

antapology
n. a reply to an apology

antephialtic
n. something that prevents nightmares

centesimate
v. to select one person in every hundred for a punishment

citramontane
adj. relating to this side of the mountains

demonachize
v. to remove monks from

frounce
n. a canker in the mouth of a hawk

hendecad
n. a period of eleven years

laquearian
adj. armed with a noose

pastinaceous
adj. of the nature of a parsnip

philosophunculist
n. an insignificant philosopher

spartostatics
n. the study of the strength of ropes

swinehood
n. pigs collectively

togated
adj. clad in a toga

trouserdom
n. the domain of those who wear trousers

yealing
n. a person of one’s own age

See Specialists.

I recollect a nurse call’d Ann
Who carried me about the grass,
And one fine day a fine young man
Came up, and kiss’d the pretty lass:
She did not make the least objection!
Thinks I, “Aha!
When I can talk I’ll tell Mamma.”
— And that’s my earliest recollection.

— Frederick Locker-Lampson

Two thousand years ago, a Roman man pressed his hand into a brick that had been set out to dry before firing.

The brick is now held at the Archaeological Museum of Cherchell in Algeria.

From Reddit’s ArtefactPorn.

Aphorisms of Sir Arthur Helps (1813-1875):

The business of the head is to form a good heart, and not merely to rule an evil one, as is generally imagined.
There is hardly a more common error than that of taking the man who has one talent, for a genius.
The world will find out that part of your character which concerns it; that which especially concerns yourself, it will leave for you to discover.
(“An eastern proverb which rightly belongs to the western world”:) People resemble still more the time in which they live, than they resemble their fathers.
The worst use that can be made of success is to boast of it.
Few have wished for memory so much as they have longed for forgetfulness.
The Simoon of the desert is not the only evil that may be avoided by stooping.
War may be the game of kings, but, like the games at ancient Rome, it is generally exhibited to please and pacify the people.
The sun is shining all around, but there are some who will only contemplate their own shadows.
Misery appears to improve the intellect, but this is only because it dismisses fear.
Eccentric people are never loved for their eccentricities.
When we see the rapid motions of insects at evening, we exclaim, how happy they must be! — so inseparably are activity and happiness connected in our minds.
Tact is the result of refined sympathy.
Soothe the present as much as we may; look forward as hopefully as we can to the future, still the dreadful past must overshadow us.
Simple Ignorance has in its time been complimented by the names of most of the vices, and of all the virtues.
Tolerance is the only real test of civilization.
The reasons which any man offers to you for his own conduct, betray his opinion of your character.
An author’s works are his esoteric biography.
The trifling of a great man is never trivial.
If you would understand your own age, read the works of fiction produced in it. People in disguise speak freely.
We must often consider, not what the wise will think, but what the foolish will be sure to say.

“A very useful book might be written with the sole object of advising what parts of what books should be read. It should not be a book of elegant extracts, but should merely refer to the passages which are advised to be read. It might also indicate what are the chief works upon any given subject. For example, take rent; the important passages in Adam Smith, Ricardo, Jones, Mill, and other writers, should be referred to.”

From Thoughts in the Cloister and the Crowd, 1835.

William Browne’s 17th-century poem “Behold, O God!” forms a sort of symbolic acrostic. The text can be read conventionally, scanning each line from left to right, but the letters shown here in bold also spell out three verses from the New Testament:

Luke 23:42: “Lord, remember me when thou comest into thy kingdom.”
Matthew 27:46: “O God, my God, why hast thou forsaken me?”
Luke 23:39: “If thou art the Christ, save thyself and us.”

The three embedded quotes represent the three figures crucified on Golgotha, and the “INRI” at the top of the middle cross stands for IESVS NAZARENVS REX IVDÆORVM — Latin for “Jesus the Nazarene, King of the Jews” (John 19:19).

A puzzle by National Security Agency mathematician Katrina J., from the agency’s September 2017 Puzzle Periodical:

Problem:

Arabella the Spider is saving food for the long winter. Arabella wants to store the bugs she caught on 26 fallen leaves, so she can find them later. But, Arabella doesn’t want to waste time by going through any leaves more than once.

In Arabella’s original web, Arabella can’t get to all of the leaves without crossing some of them more than once. But, if Arabella adds just one web between two of the leaves, she can get to every leaf without repeating. There are four different pairs of leaves that Arabella could connect to solve her problem. Can you find all four possible solutions?

Note: Arabella may take any path she chooses as long as she begins on leaf 1 and ends on leaf 26.

Bonus Puzzle:

Can you show why Arabella cannot get to every leaf without repeats on her web as it is now?

| SelectClick for Answer | | --- | | Solution:This problem has 4 solutions and answers: 5-13, 5-22, 18-13, 18-22. Only the first solution is fully drawn on the solution illustration, but all four are explained below.Explanation:First, let’s re-draw the situation to be less messy! Once we’ve organized the leaves a bit, we see that there are 4 distinct groups of leaves which can only be accessed via one leaf: Group 1 is only accessible via leaf 23, Group 2 via leaf 3, Group 3 via leaf 10, and Group 4 via leaf 11.Here we see the problem — once Arabella has entered a group of leaves, she cannot get out again without crossing the ‘access leaf’ again. For Group 1 this is okay, since Arabella can start on leaf 1, move to leaf 6, then leaf 14, then exit at leaf 23, and doesn’t need to go back in. Similarly, Group 4 contains the last leaf, so Arabella can enter the group from leaf 11, then go to leaf 2, leaf 8, leaf 21, leaf 15, and exit at leaf 26.But for Group 2 and Group 3, Arabella must enter and exit the group. This is where the extra web comes in handy! If we connect a leaf in Group 2 and a leaf in Group 3, then Arabella can go from Group 1 to Group 2 using leaf 23, then Group 2 to Group 3 using the new web, and finally from Group 3 to Group 4 using leaf 7.However, not just any leaves from Group 2 and Group 3 will work. Arabella must cover all of Group 2 before moving to Group 3, and cover all of Group 3 before going to Group 4. This still allows for a few different combinations: from Group 2 we can use leaf 5 or leaf 18; from Group 3 we can use leaf 13 or leaf 22.Here are the different paths Arabella could take for each combination (there are minor variations in all of the paths, such as switching the order of leaves 6 and 14, which are unaffected by the solution choice, but we will not list those):* Leaves 5 & 13 — 1, 6, 14, 23, 3, 18, 25, 12, 20, 17, 9, 5, 13, 16, 19, 24, 4, 22, 10, 7, 11, 2, 8, 21, 15, 26 * Leaves 5 & 22 — 1, 6, 14, 23, 3, 18, 25, 12, 20, 17, 9, 5, 22, 4, 24, 19, 16, 13, 10, 7, 11, 2, 8, 21, 15, 26 |

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On the evening of June 18, 1875, a fire broke out near a bonded storehouse on Ardee Street in Dublin, and by 9:30 some 5,000 hogsheads of whiskey had begun to explode in the heat. “Within an hour,” reported the Irish Examiner, “the surrounding streets resembled canals of flame.”

The “blazing stream … turned into Ardee-street, passed Watkins’ Brewery without damage, but catching the premises at the corner of Chamber-street, set fire to these, and continuing its course down into Mill-street, speedily demolished the entire of the row of small houses forming the south side of that thoroughfare.”

The evacuation was relatively rapid, and no one perished directly due to the fire. But “many of the crowd indulged to excess, drinking in some instances out of their shoes and hats, in which they had collected the whiskey.” As the undiluted spirits were much more potent than bottled retail whiskey, some 24 citizens were hospitalized due to alcohol poisoning, and 13 eventually died.

After his Connecticut home was burgled in September 1908, Mark Twain posted a sign on the front door:

NOTICE

To the Next Burglar

There is nothing but plated ware in this house now and henceforth.

You will find it in that brass thing in the dining-room over in the corner by the basket of kittens.

If you want the basket put the kittens in the brass thing.

Do not make a noise — it disturbs the family.

You will find rubbers in the front hall by that thing which has the umbrellas in it, chiffonier, I think they call it, or pergola, or something like that.

Please close the door when you go away!

Very truly yours,

S.L. Clemens

A maze by Wikimedia user Marianov. Make your way from one black circle to the other.

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From an 1897 Strand feature on odd Bibles:

Perhaps the rarest of all the curious Bibles is the famous ‘Bugge’ Bible, an edition of Matthew’s Bible, published in 1551. In this we read, at Psalms xci., 5, ‘So that thou shalt not nede to be afrayed for anye bugges by nyghte.’

Possibly “bugge” was understood as equivalent to the modern word bogie, or ghost. See Oops.

In 1876 the Belgian Society for the Elevation of the Domestic Cat transported 37 cats from Liège to the surrounding countryside. Released at 2 p.m., the first had found its way home by 6:48, and the rest followed within a day.

“This result has greatly encouraged the society, and it is proposed to establish at an early day a regular system of cat communication between Liège and the neighboring villages,” reported the New York Times.

“Messages are to be fastened in water-proof bags around the necks of the animals, and it is believed that … the messages will be delivered with rapidity and safety.” Somehow the plan wasn’t carried through; it’s hard to imagine why.

Image: Wikimedia CommonsSrinivasa Ramanujan devised this magic square to mark his own birthday. He began with a Latin square (upper right) in which the numbers 1, 2, 3, and 4 appear in each row, column, and long diagonal as well as in the four corners, the four central squares, the middle squares in the top and bottom rows, and the middle squares in the outermost columns. Note the adjustments that would be necessary to reduce the four top cells to zero, and arrange these adjustments in the diagonally reflected pattern shown in the upper left. Now adding these two squares together produces the square in the lower left, which gives us a formula for creating a magic square based on any date (in the format 1 January 2001). The example at lower right is based on Ramanujan’s own birthday, 22 December 1887 (so D = day = 22, M = month = 12, C = century = 18, and Y = year = 87). In this example all 16 numbers are distinct, but that won’t be the case with every date.

After performing in a revival of George Bernard Shaw’s play Candida, Cornelia Otis Skinner received a telegram from the author: EXCELLENT. GREATEST.

She wired back: UNDESERVING SUCH PRAISE.

He responded: I MEANT THE PLAY.

She replied: SO DID I.

A good example of the effect of misplacing a comma is to be found in the ancient oracle — ‘Thou shalt go thou shalt return never by war shalt thou perish.’ By one way of placing the commas, the consulter of the oracle was forbidden to go upon the purposed expedition; by reading it his own way, he went and perished.

— W.T. Dobson, “Literaria,” Dublin University Magazine, August 1873

You and a friend agree to meet on New Year’s Day at the Mozart Café in Vienna. You fly separately to the city but are dismayed to learn that it contains multiple cafés by that name.

What now? On the first day each of you picks a café at random, but unfortunately you choose different locations. On the second day you could both go out searching cafés, but you might succeed only in “chasing each other’s tails.” On the other hand, if you both stay where you are, you’ll certainly never meet. What is your best course, assuming that you can’t communicate and that you must adopt the same strategy (with independent randomization)?

This distressingly familiar problem remains largely unsolved. If there are 2 cafés then the best course is to choose randomly between them each day. If there are 3 cafés, then it’s best to alternate between searching and staying put (guided by certain specified probabilities). But in cases of 4 or more cafés, the best strategy is unknown.

In 2007 a reader wrote to the Guardian, “I lost my wife in the crowd at Glastonbury. What is the best strategy for finding her?” Another replied, “Start talking to an attractive woman. Your wife will reappear almost immediately.”

diallelous
adj. involving circular reasoning

On my challenging an ingenious friend to define time and space, he answered, ‘Time is the condition of two things existing in the same space. Space is the condition of two things existing in the same time.’ This is clever, pointed, and true, but, as may easily be seen, diallelous.

— Francis Garden, A Dictionary of English Philosophical Terms, 1878

Captured by the North Vietnamese in 1965, Navy pilot Jeremiah Denton was forced to participate in a propaganda interview to be broadcast in the United States. Pretending to be oppressed by the television lights, he blinked the word “T-O-R-T-U-R-E” in Morse code — alerting U.S. Naval Intelligence for the first time that American prisoners were being tortured.

In his Investigator’s Guide to Steganography (2003), Gregory Kipper notes that captured soldiers would sometimes use hand signals to transmit messages during photo ops; “often, these gestures were airbrushed out by the media.”

The members of the Flemish Academy, of Anvers, recently determined to frame a word which would be readily intelligible to all who understand the language of Flanders and who had ever seen a horseless carriage, and the result was that after much deep thought they framed the following word: Snelpaardelooszonderspoorwegpetrolrijtuig. This euphonious word signifies ‘a carriage which is worked by means of petroleum, which travels fast, which has no horses and which is not run on rails.’ This is, from one point of view, a fine example of multum in parvo, but it may be questioned whether one extraordinarily long word is preferable to half a dozen short words.

— Georgetown [Colo.] Herald, May 19, 1899

Ferdinand Georg Waldmüller’s painting The Expected is sometimes claimed as evidence of time travel — how else could a woman get an iPhone in 1860?

It’s a prayer book.

Staggering fact: Science historian Clifford Truesdell estimates that “[a]pproximately one-third of the entire corpus of research on mathematics and mathematical physics and engineering mechanics published in the last three-quarters of the eighteenth century” was written by a single person, Leonhard Euler.

The work of compiling Euler’s scientific writings has been going on since 1908 and will fill 81 volumes when complete. Mathematician William Dunham writes, “A typical volume of the Opera Omnia is large, running from 400 to 500 pages — although some contain over 700. In size and weight, such a volume resembles its counterpart from (say) the Encyclopedia Britannica. No one short of an athlete could carry more than five or six at once, and to cart off the entire collection — over 25,000 pages in all – would require a forklift.”

Laplace wrote, “Read Euler, read Euler, he is the master of us all.”

Image: Wikimedia CommonsIn the 17th century, Prince Rupert of the Rhine wondered whether one cube might pass through another of the same size. John Wallis showed that the answer is yes, and, perversely, Pieter Nieuwland showed a century later that one cube can even accept another larger than itself — fully 6 percent larger in the optimal case. The diagram above shows the dimensions (blue) of a square tunnel through a unit cube that will accommodate a second unit cube (green) with room to spare.

Remarkably, all five Platonic solids have the “Rupert property” — a regular tetrahedron, for example, will fit through an identical tetrahedron if the hole is contrived cleverly enough. Whether every convex polyhedron can perform this unlikely feat is an open question.

“Many highly intelligent people are poor thinkers. Many people of average intelligence are skilled thinkers. The power of a car is separate from the way the car is driven.” — Edward de Bono

For a man who left no official writings, French philosopher Jean-Baptiste Botul cut an impressive swath through the early 20th century. Born in 1896, he befriended Marcel Proust, betrothed Marthe Richard, and associated with Simone de Beauvoir, Marie Bonaparte, Jean Cocteau, Jean Giraudoux, Stefan Zweig, and Andre Malraux. At age 50 he resettled in Paraguay, where he founded a town that observed the principles of Kantian philosophy.

Actually, none of that is true. Botul was invented out of whole cloth in 1995 by journalist Frédéric Pagès and promoted by an “Association of the Friends of Jean-Baptiste Botul,” which published works that supposedly advanced his ideas, including The Sexual Life of Immanuel Kant, Nietzsche and the Noonday Demon, and Soft Metaphysics.

The joke has been so successful that an annual prize has been awarded for a work that mentions Botul. The most famous recipient is Bernard-Henri Lévy, who quoted the imaginary philosopher extensively in his 2010 book On War in Philosophy. He acknowledged afterward that he’d fallen for a “well-rigged” hoax.

From Lee Sallows:

(Thanks, Lee!)

The Pythagorean theorem has a reciprocal variant:

Image: Wikimedia CommonsIn combination with the inverse-square law, this means that identical lamps placed at A and B will produce the same light intensity at C as a single lamp at D.

Cannibalism shocks us terribly. Yet I remember talking to an old cannibal who from missionary and administrator had heard news of the Great War raging then in Europe. What he was most curious to know was how we Europeans managed to eat such enormous quantities of human flesh, as the casualties of a battle seemed to imply. When I told him indignantly that Europeans do not eat their slain foes, he looked at me with real horror and asked me what sort of barbarians we were to kill without any real object.

— Bronisław Malinowski, “Anthropology Is the Science of the Sense of Humour,” 1937

Norwegian broadcaster NRK presented this problem during its coverage of the 2021 FIDE World Chess Championship in Dubai. White is to give mate on the move. (Warning — there’s a trick.)

| SelectClick for Answer | | --- | | It’s natural to suppose that we’re looking at this from Black’s side of the board, but that can’t be the case — if it were, Black could not have swapped king and queen without moving a pawn. So we’re looking at the position from White’s point of view, and that means that Black’s pawns are moving down, not up, the board. So 1. Nd3# immediately ends the game: |

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What’s the greatest number of Fridays that can fall in February? We might say five, imagining a leap year in which February 1 falls on a Friday.

“However, it is possible to reckon double the number of Fridays in the month of February alone,” contends Soviet science writer Yakov Perelman. “Imagine a ship plying between Siberia and Alaska and leaving the Asiatic shore regularly every Friday. How many Fridays will its skipper count in a leap-year February of which the 1st is a Friday? Since he crosses the date line from west to east and does so on a Friday, he will reckon two Fridays every week, thus adding up to 10 Fridays in all.”

“On the contrary, the skipper of a ship leaving Alaska every Thursday and heading for Siberia will ‘lose’ Friday in his day reckoning, with the result that he won’t have a single Friday in the whole month.”

(From Astronomy for Entertainment, 1958.)

A pleasing puzzle by Eric LeVasseur:

PI × R2 = AREA

If each letter in this expression (but not the exponent 2) is replaced with a corresponding digit, the resulting equation will be valid. What are the digits?

| SelectClick for Answer | | --- | | 96 × 72 = 4704(Leonard J. Gordon, “Literary Cryptarithmetic by Computer,” Word Ways 23:2 [May 1990], 67-70.)07/17/2024 UPDATE: Reader Dave Lawrence points out that other solutions are possible:76 × 82 = 486477 × 72 = 377386 × 92 = 6966(Thanks, Dave.) |

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It’s illegal to enter the Houses of Parliament wearing a suit of armor, according to a 1313 statute.
“All things in moderation” is an immoderate policy.
If a prime number is made up entirely of 1s (e.g., 11), then the number of its digits is prime.
The word CARBON is itself made up of element symbols (Ca, Rb, O, N). (Dmitri Borgmann)
Interior decorator Nicholas Haslam: “All it comes down to is making a setting in which people look prettier.”

Now, are not those still full of their old carnal nature who ask us: ‘What was God doing before he made heaven and earth? For if he was idle,’ they say, ‘and doing nothing, then why did he not continue in that state forever — doing nothing, as he had always done? If any new motion has arisen in God, and a new will to form a creature, which he had never before formed, how can that be a true eternity in which an act of will occurs that was not there before? For the will of God is not a created thing, but comes before the creation — and this is true because nothing could be created unless the will of the Creator came before it. The will of God, therefore, pertains to his very Essence. Yet if anything has arisen in the Essence of God that was not there before, then that Essence cannot truly be called eternal. But if it was the eternal will of God that the creation should come to be, why, then, is not the creation itself also from eternity?’

— Augustine, Confessions

Image: Wikimedia Commons Herpetologist Mark Scherz named three tiny species of Malagasy frog Mini ature, Mini scule, and Mini mum. * Malacologist Alan Solem named a Fijian land snail Ba humbugi. * The name of each species in the African spider genus Palindroma is a palindrome: P. aleykyela, P. avonova, P. morogorom, P. obmoimiombo, P. sinis. * The binomial name of the crowned slaty flycatcher has 15 syllables: Griseotyrannus aurantioatrocristatus. * Malacologist John Stanisic named an Australian land snail Crikey steveirwini. * The Australian leafhopper genus Dziwneono*, named by entomologist Irena Dworakowska, is Polish for “It is strange.”

In 1977, on receiving a package of insect specimens from a colleague, entomologist Arnold Menke exclaimed, “Aha, a new genus!” His colleague Eric Grissell responded “Ha” doubtfully. Menke was proven right and named the species, an Australian wasp, Aha ha. He ordered a custom registration plate for his car bearing the same phrase. Further odd names.

In Scranton, Pennsylvania, Washington crosses Delaware.

Suppose that each country on Earth has a colony on the moon and that we want to draw maps on which each nation’s territory receives a consistent color. How many colors would we need?

In 1980 Thom Sulanke showed that we might need as many as nine (above), but it’s possible that a particularly challenging map would require more than that. The problem remains unsolved.

In his Reflections, Georg Christoph Lichtenberg mentions a friend who had divided human endeavor into four categories:

During the severe frost of February 1895, a stream of water overflowing Scotland’s Almond Aqueduct began to freeze to the River Almond 120 feet below. Over the course of three nights the mass grew upward until river and bridge were connected by a continuous pillar of ice, the largest such formation on record at the time.

“When the sun shone upon the giant mass,” observed the Strand, “the iridescence was beautiful, and people came from miles around to look at it.”

(Jeremy Broome, “Freaks of Frost,” Strand 12:12 [December 1896], 738-746.)

quisquous
adj. difficult to deal with or settle

quillet
n. a verbal nicety, a subtle distinction

aggiornamento
n. the act of bringing something up to date to meet current needs

irenic
adj. fitted or designed to promote peace

The survivors of the Titanic were picked up by the English passenger steamship Carpathia, which conveyed them to New York. This presented a delicate problem to the Social Register. “In those days the ship that people travelled on was an important yardstick in measuring their standing, and the Register dutifully kept track,” notes Walter Lord in A Night to Remember (1955). “To say that listed families crossed on the Titanic gave them their social due, but it wasn’t true. To say they arrived on the plodding Carpathia was true, but socially misleading. How to handle this dilemma? In the case of those lost, the Register dodged the problem — after their names it simply noted the words, ‘died at sea, 15 April 1912’. In the case of those living, the Register carefully ran the phrase, ‘Arrived Titan-Carpath, 18 April 1912’. The hyphen represented history’s greatest sea disaster.”

Image: Wikimedia CommonsOn Easter Saturday 1921, pharmacologist Otto Loewi dreamed of an experiment that would prove that the transmission of nerve impulses was chemical rather than electrical. He scribbled down the idea and went back to sleep, then discovered the next morning that he couldn’t read the note.

That day, he said, was the longest of his life. Fortunately, the dream returned to him that night, and this time he went immediately to the laboratory. Thirteen years later he received the Nobel Prize for discovering the role of acetylcholine as an endogenous neurotransmitter.

I had not then acquired the technique that I flatter myself now enables me to deal competently with the works of modern artists. If this were the place I could write a very neat little guide to enable the amateur of pictures to deal to the satisfaction of their painters with the most diverse manifestations of the creative instinct. There is the intense ‘By God!’ that acknowledges the power of the ruthless realist, the ‘It’s so awfully sincere’ that covers your embarrassment when you are shown the coloured photograph of an alderman’s widow, the low whistle that exhibits your admiration for the post-impressionist, the ‘Terribly amusing’ that expresses what you feel about the cubist, the ‘Oh!’ of one who is overcome, the ‘Ah!’ of him whose breath is taken away.

— Somerset Maugham, Cakes and Ale, 1930

Alice and Bob are two infinitely intelligent logicians. Each has a number drawn on their forehead. Each can see the other’s number but not their own. Each knows that both numbers are positive integers. An observer tells them that the number 50 is either the sum or the product of the two numbers. Alice says to Bob, “I do not know my number,” and Bob replies, “I do not know my number either.” What is Alice’s number?

| SelectClick for Answer | | --- | | If Bob’s number isn’t a divisor of 50, then 50 must be the sum and Alice will know her number. If Bob’s number is 50, then 50 must be the product and again Alice should know her number. She doesn’t, so Bob’s number must be a proper divisor of 50, that is, 1, 2, 5, 10, or 25.By the same reasoning, if Alice’s number isn’t a proper divisor of 50 then Bob should know his number. Also, after Alice’s utterance Bob can infer that his own number is a proper divisor of 50, following her thinking above. So each number is a proper divisor of 50.Now, if 50 is the sum of the two numbers, then both numbers are 25 (as 25 + 25 is the only way to combine two of the candidate divisors to get 50). This means that if Alice’s number isn’t 25, then Bob can conclude that 50 is a product and can infer his own number. The fact that he can’t do this shows that Alice’s number must be 25 (and Bob’s number is either 2 or 25).(Via Matvey Borodin et al., “It’s Common Knowledge,” Recreational Mathematics Magazine 6:12 [December 2019], 9-32.) |

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Image: Wikimedia Commons

It is related of the Socratic philosopher Aristippus that, being shipwrecked and cast ashore on the coast of the Rhodians, he observed geometrical figures drawn thereon, and cried out to his companions: ‘Let us be of good cheer, for I see the traces of man.’

— Vitruvius, De architectura

Teaching at Cornell in the 1950s, Vladimir Nabokov offered a European fiction course whose exam questions could be distressingly broad or pitilessly specific — some examples are given in an appendix to Lectures on Literature:

Bleak House

Why did Dickens need to give Esther three suitors (Guppy, Jarndyce, and Woodcourt)?
If you compare Lady Dedlock and Skimpole, which of them is the author’s greater success?
Discuss the structure and style of Bleak House.
Discuss John Jarndyce’s house. (Mangles? Surprised birds?)
Discuss the visit to Bell Yard (Neckett’s children; and Mr. Gridley).
Give at least four examples of the “child theme” in Bleak House.
What kind of place was Bleak House — give at least four descriptive details.
Where was Bleak House situated?
How is the “bird theme” linked up with Krook?
How is the “fog theme” linked up with Krook?
Whose style are we reminded of when Dickens raises his voice?
The social side (“upper class” versus “lower class” etc.) is the weakest one in Bleak House. Who was Mr. George’s brother? What part did he play? Should a major reader skip those pages, even if they are weak?
Follow Mr. Guppy through Bleak House.

Madame Bovary

Describe briefly Flaubert’s use of the counterpoint technique in the County Fair scene.
There are numerous thematic lines in Madame Bovary, such as “Horse,” “Plaster Priest,” “Voice,” “The Three Doctors.” Describe these four themes briefly.
Discuss Flaubert’s use of the word “and.”
What character in Madame Bovary behaves in very much the same way as a character in Bleak House does under somewhat similar circumstances? The thematic clue is: “devotion.”
Is there a Dickensian atmosphere about Flaubert’s description of Berthe’s infancy and childhood? (Be specific.)
The features of Fanny Price and Esther are pleasantly blurred. Not so with Emma. Describe her eyes, hair, hands, skin.
Would you say that Emma’s nature was hard and shallow?
Would she prefer a landscape peopled with ruins and cows to one that contained no allusions to people?
Did she like her mountain lakes with or without a lone skiff?
What had Emma read? Name at least four works and their authors.

In his annotated copy of The Metamorphosis, Nabokov, a trained entomologist, observed that “A regular beetle has no eyelids and cannot close its eyes” — and thus Gregor Samsa is “a beetle with human eyes.”

From reader Ian Duff: An alphamagic square is a magic square that remains magic when the number in each of its cells is replaced by the letter count of that number’s written name. For example, each row, column, and long diagonal in this square yields the same sum:

5 22 1828 15 212 8 25 … and that remains true if we replace 5 with 4 (because FIVE has 4 letters), 22 (TWENTY-TWO) with 9, and so on:

4 9 811 7 36 5 10 That example is the only 3×3 English alphamagic square in which each cell contains a distinct positive integer less than 100. There are no such truly sub-100 alphamagic squares in French, but there are two if we permit the derived squares to contain repeated numbers:

39 57 18 10 13 717 38 59 -> 7 10 1358 19 37 13 7 1075 87 57 14 15 1355 73 91 -> 13 14 1589 59 71 15 13 14 39 is TRENTE-NEUF, which has 10 letters, and so on.

(Thanks, Ian.)

A Brooklyn bookseller distributed this card during the 1880 U.S. presidential race between James Garfield and Winfield Scott Hancock. What does it say?

| SelectClick for Answer | | --- | | “You can bet your last dollar that you will see Garfield defeated by Hancock.” |

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“What is research but a blind date with knowledge?” — Will Henry

Alexander Shapovalov suggested an unusual coin-weighing problem for the sixth international Kolmogorov math tournament in 2007:

A judge is presented with 80 coins that all look the same, knowing that there are either two or three fake coins among them. All the real coins weigh the same and all the fake coins weigh the same, but the fake coins are lighter than the real ones.

A lawyer knows that there are exactly three fake coins and which ones they are. The lawyer must use a balance scale to convince the judge that there are exactly three fake coins and that it is impossible for there to be only two fake coins. She is bound by her contract not to reveal any information about any particular coin. How should she proceed?

The lawyer might try dividing the 80 coins into three groups of 26, each group containing one fake coin, with two coins left over. With two weighings she could then show that the three groups have the same weight. From this the judge could conclude that either (a) there are 3 fake coins, one in each group, or (b) there are 2 fake coins, both in the leftover group. The lawyer could then weigh one of the leftover coins against a real coin taken from one of the three groups, to show that these balance. This would prove to the judge that there are 3 fake coins (because if there were only 2 then possibility (b) above would be ruled out). However, this strategy is “indiscreet” — it would reveal to the judge the true character of each of the leftover coins, which the lawyer has pledged not to do. How should she proceed instead?

| SelectClick for Answer | | --- | | Divide the coins into nine piles — call them A1, B1, C1, A2, B2, C2, A3, B3, and C3, with sizes 24, 1, 2, 24, 1, 2, 23, 2, 1, respectively. Now use the scale to show that A1 + B1, A2 + B2, and A3 + B3 balance one another, as do B1 + C1, B2 + C2, and B3 + C3. This shows the judge that there are three different ways in which the fake coins might be distributed: one fake coin in each of A1, A2, A3 (sizes 24, 24, 23) * one fake coin in each of B1, B2, B3 (sizes 1, 1, 2) * one fake coin in each of C1, C2, C*3 (sizes 2, 2, 1)

Each possibility involves 3 fake coins, not 2, and we’ve managed to convey that fact without revealing the character of any particular coin.(Nicholas Diaco and Tanya Khovanova, “Privacy and Counterfeit Coins,” Mathematical Intelligencer 38:3 [September 2016], 6-10.) |

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Image: Wikimedia CommonsThis rock formation, formed possibly thousands of years ago, spans a chasm on Mount Tai, one of the Five Great Mountains of China.

It’s said that anyone who crosses the bridge will live forever.

Image: Wikimedia CommonsUntil 2022, every tiling of the plane eventually repeated itself. Then amateur mathematician David Smith discovered a remarkable tile that will cover an infinite plane but only in a nonperiodic way.

This solves an open problem in mathematics — for years researchers had been seeking an aperiodic monotile, or “einstein,” from the German for “one stone.”

Technically Smith’s tile, known as the “hat,” must be used in combination with its mirror image. But last year his team found another nonperiodic tile, known as the spectre, which is strictly chiral — that is, not only will it tile the plane without its mirror image, but it must be used in this way.

“Did anyone ever have a boring dream?” — Ralph Hodgson

Ulrich von Cranach of Hamburg devised this perpetual motion machine in 1664, offering it to drive pumps in mines. An Archimedean screw raises a succession of iron balls that then descend by a wheel that turns the screw.

Robert Fludd had proposed a water mill in 1618 that used essentially the same design. The anonymous variant below dates from the Middle Ages.

Proverbs from around the world:

See that you are wise, but also learn to appear ignorant. (Armenian)
If men could foresee the future, they would still behave as they do now. (Russian)
Many have suffered for talking; none ever suffered for keeping silent. (Italian)
To listen to a lie is harder than to tell it. (Turkish)
Not your friend but your enemy will tell you who you are. (Greek)
It is not the fault of the post that a blind man cannot see it. (Sanskrit)
A good laugh and a long sleep are the best cures in the doctor’s book. (Irish)
Patience is the door of joy. (German)
If you are standing upright, do not fear a crooked shadow. (Chinese)
The thief is sorry that he is to be hanged, not that he is a thief. (English)
It is the poor who gives alms to the poor. (Japanese)
Before you marry, think what you are doing. (Spanish)
Better wisdom than riches. (Swedish)
Bairns are certain care but no sure joy. (Scottish)
There are forty kinds of lunacy, but only one kind of common sense. (West African)

And “It is easy to throw a stone into the Danube, but rather difficult to get it out.” (Yugoslavia)

I just stumbled into this — in October 1967, IBM published this problem in Eureka, the journal of the Cambridge University Mathematical Society (page 2):

The triplets (whose abilities at walking, cycling, and donkey riding are identical) always leave home together at the last possible minute and arrive at school together on the last stroke of the bell.

They used to walk the 4 1/2 miles, and so had to set out at 8.00; then they acquired a bicycle and found that they did not have to leave home until 8.15 (Charles rode it for the first 1 1/2 miles, left it, and walked on; Donald walked 1 1/2 miles, cycled 1 1/2 miles, and walked again; Edward walked 3 miles and cycled the rest). More recently they have been given a donkey. After experiments to determine the donkey’s speed and to verify that it stood stock still when left, they found that — using the bicycle and the donkey — they did not need to leave home until 8.25. There were several schemes of changing over which they could use to do this, of course; but naturally they chose a scheme which involved the minimum number of changes. Going to school tomorrow Charles will start on foot and Edward will arrive on foot. How far will Donald walk?

In place of an answer they listed the address of their London office, as an invitation to prospective systems analysts. I can’t see that they ever published a solution to the puzzle; I’m posting it here for what it’s worth.

Imprisoned at Theresienstadt during World War II, Czech composer Rudolf Karel wrote a five-act opera, Three Hairs of the Wise Old Man, on toilet paper using the medicinal charcoal he’d been prescribed for his dysentery.

The illness eventually claimed his life, but a sketch of the opera was preserved by a friendly warden, and the orchestrations were finished by Karel’s pupil Zbynek Vostrák.

These two handcarts have the same mass. Newton tells us that equal forces applied to equal masses impart equal accelerations. So why does the second handcart pick up speed more quickly than the first? (This is a Soviet problem; Н is the Russian abbreviation for newtons.)

| SelectClick for Answer | | --- | | In each case a force of 2 newtons is acting to set the body in motion. But in the first case the force of gravity acts on the handcart and the weight itself, while in the second the force imparts an acceleration only to the handcart.From V.N. Lange, Physical Paradoxes and Sophisms, 1987. |

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manqueller
n. a man killer; an executioner

In 1014, after a decisive victory over the Bulgarian Empire at the Battle of Kleidion, Byzantine emperor Basil II followed up with a singularly cruel stroke. He ordered that his 14,000 prisoners be divided into groups of 100; that 99 of each group be blinded; and that the hundredth retain one eye so that he could lead the others home. The columns were then released into the mountains, each man holding on to the belt of the man in front. It’s not known how many were lost on the journey, but when the survivors reached the Bulgar capital, their tsar collapsed at the sight and died of a stroke two days later. Basil is remembered as “the Bulgar slayer.”

From 1995 to 1998, the journal Philosophy and Literature ran a bad writing contest to mark “the most stylistically lamentable passages found in scholarly books and articles.” The final year’s winners:

First prize:

The move from a structuralist account in which capital is understood to structure social relations in relatively homologous ways to a view of hegemony in which power relations are subject to repetition, convergence, and rearticulation brought the question of temporality into the thinking of structure, and marked a shift from a form of Althusserian theory that takes structural totalities as theoretical objects to one in which the insights into the contingent possibility of structure inaugurate a renewed conception of hegemony as bound up with the contingent sites and strategies of the rearticulation of power.

— Judith Butler, “Further Reflections on the Conversations of Our Time,” in the journal Diacritics

Second prize:

If, for a while, the ruse of desire is calculable for the uses of discipline soon the repetition of guilt, justification, pseudo-scientific theories, superstition, spurious authorities, and classifications can be seen as the desperate effort to ‘normalise’ formally the disturbance of a discourse of splitting that violates the rational, enlightened claims of its enunciatory modality.

— Homi K. Bhabha in his book The Location of Culture

Third prize:

As my story is an august tale of fathers and sons, real and imagined, the biography here will fitfully attend to the putative traces in Manet’s work of ‘les noms du père’, a Lacanian romance of the errant paternal phallus (‘Les Non-dupes errent’), a revised Freudian novella of the inferential dynamic of paternity which annihilates (and hence enculturates) through the deferred introduction of the third term of insemination the phenomenologically irreducible dyad of the mother and child.

— Steven Z. Levine in Bradford Collins, ed., Twelve Views of Manet’s Bar

The contest’s only condition was that entries not be ironic: “Deliberate parody cannot be allowed in a field where unintended self-parody is so widespread.” The full list of winners is here.

From an April Fools’ feature in LIFE, April 4, 1938:

The photo appeared in a German paper, which claimed the story was American. “To Germans, actual American goings-on are fantastic enough to be April Fools’ tricks.”

When a goose without feet was hatched in Harvard, Nebraska, in 1987, local inventor Gene Fleming adopted the bird, fitted him with baby-sized shoes, and taught him to walk. In time “Andy” learned to swim and fly as well; he gave inspiration to disabled children and received a lifetime supply of shoes from Nike, but it wasn’t to last — in 1991 he was killed by an unnamed perpetrator.

From reader Éric Angelini: During a standard chess game, after Black’s fifth move we notice that three rooks have been captured on the same dark square. Which square is it?

| SelectClick for Answer | | --- | | a3. The game runs:1. b4 a52. h4 axb43. Rh3 Rxa24. Ra3 Rxa35. Rxa3 bxa3The moves are illustrated here (line b). (Thanks, Éric.) |

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If mercy modifies the demands of justice, then to be merciful is perhaps to be unjust. But manifesting injustice is a vice, not a virtue. This seems to mean that mercy is a vice. A sentencing judge has been hired to enforce the rule of law that society has agreed upon. If he tempers this, even through love or compassion, then arguably he’s departing from his sworn obligation. Angelo says in Measure for Measure:

I show [pity] most of all when I show justice,
For then I pity those I do not know,
Which a dismissed offense would after gall,
And do him right that, answering one foul wrong,
Lives not to act another.

(If we try to claim that mercy is a form of justice, so that every act of mercy is just, then we’re saying that one has a right to mercy, that it’s not a gift. That seems wrong too.)

(Jeffrie G. Murphy and Jean Hampton, Forgiveness and Mercy, 1988, via George W. Rainbolt, “Mercy: An Independent, Imperfect Virtue,” American Philosophical Quarterly 27:2 [April 1990], 169-173.)

A conference is attended by 1,000 delegates from various countries. It’s known that any three delegates can speak together without help, though one of the three may have to serve as interpreter for the other two. Prove that all the attendees can be accommodated in double rooms so that the two occupants of each room can speak to each other.

| SelectClick for Answer | | --- | | Choose three delegates at random. Two of them must share a language. Put those two together into a room. Now 998 delegates remain. Again choose three and put the two who can communicate together into a room. Continue until four delegates remain. Call these A, B, C, and D. If all four speak the same language then assign them arbitrarily to the last two rooms. And if (say) A and B can’t communicate directly then both C and D can serve as their interpreters, so we can lodge A with C and B with D.From D.O. Shklyarsky, N.N. Chentsov, and I.M. Yaglom, Selected Problems and Theorems in Elementary Mathematics, 1979. |

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The beginnings of Algebra I found far more difficult [than Euclid], perhaps as a result of bad teaching. I was made to learn by heart: ‘The square of the sum of two numbers is equal to the sum of their squares increased by twice their product.’ I had not the vaguest idea what this meant, and when I could not remember the words, my tutor threw the book at my head, which did not stimulate my intellect in any way.

— The Autobiography of Bertrand Russell, 1967

In the beginning there was Aristotle,
And objects at rest tended to remain at rest,
And objects in motion tended to come to rest,
And soon everything was at rest,
And God saw that it was boring.

Then God created Newton,
And objects at rest tended to remain at rest,
But objects in motion tended to remain in motion,
And energy was conserved and momentum was conserved and matter was conserved,
And God saw that it was conservative.

Then God created Einstein,
And everything was relative,
And fast things became short,
And straight things became curved,
And the universe was filled with inertial frames,
And God saw that it was relatively general, but some of it was especially relative.

Then God created Bohr,
And there was the principle,
And the principle was quantum,
And all things were quantified,
But some things were still relative,
And God saw that it was confusing.

Then God was going to create Furgeson,
And Furgeson would have unified,
And he would have fielded a theory,
And all would have been one,
But it was the seventh day,
And God rested,
And objects at rest tend to remain at rest.

— Tim Joseph

“Everyone believes in the normal law, the experimenters because they imagine that it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.” — Gabriel Lippmann, in a letter to Henri Poincaré

(Thanks, Tom.)

Subtitled “A Novel in Woodcuts,” Lynd Ward’s 1929 parable Gods’ Man unfolds in images, making it an important forebear of the modern graphic novel. A young artist makes his way to the big city, where a masked stranger gives him a magic paintbrush. The adventures that follow remark on the roles of love and commerce in an artist’s life; in the end the stranger returns to claim a reward.

Despite its unusual format, Ward’s book sold more than 20,000 copies during the Depression, and he followed it up with five more wordless novels. When he died in 1985, he was at work on an ambitious seventh, which Rutgers published in 2001.

We instinktivly shrink from eny chaenj in whot iz familyar; and whot kan be mor familyar dhan dhe form ov wurdz dhat we hav seen and riten mor tiemz dhan we kan posibly estimaet? We taek up a book printed in Amerika, and honor and center jar upon us every tiem we kum akros dhem; nae, eeven to see forever in plaes ov for ever atrakts our atenshon in an unplezant wae. But dheez ar iesolaeted kaesez; think ov dhe meny wurdz dhat wood hav to be chaenjd if eny real impruuvment wer to rezult. At dhe furst glaans a pasej in eny reformd speling looks ‘kweer’ or ‘ugly’. Dhis objekshon iz aulwaez dhe furst to be maed; it iz purfektly natueral; it iz dhe hardest to remuuv. Indeed, its efekt iz not weekend until dhe nue speling iz noe longger nue, until it haz been seen ofen enuf to be familyar.

— Walter Ripman and William Archer, New Spelling, 1948

Image: Wikimedia CommonsThe product of the distances from N equally spaced points on a unit circle to a point M that lies on the x axis at distance x from circle origin O and on a line passing through the first point, A0, on the circle equals 1 – xN.

Discovered by Roger Cotes (1682-1716). Here’s a proof.

From reader Dave King:

A certain young lady of Prinknash
Was looking decidedly thinknash.
Her diet restriction
Had proved an addiction
And caused her to swiftly diminknash.

A hungry young student of Norwich
Went into his larder to forwich.
For breakfast he usually
Had bacon or muesli
But today he would have to have porwich.

An ethical diner at Alnwick
Was suddenly put in a palnwick
“This coffee you’ve made
Are you sure it’s Fair Trade?
And I must insist that it’s orgalnwick!”

A Science don, Gonville and Caius,
Kept body parts in his deep fraius.
He didn’t remember
And one dark November
He ate them with cabbage and paius.

A Frenchman now living at Barnoldswick
Was terribly partial to garnoldswick.
The smell of his breath
Drove one lady to death;
She fell from the ramparts at Harnoldswech.

A forceful young prisoner from Brougham
Was confined to a windowless rougham,
So, venting his feelings,
He bashed through the ceiling,
Dispelling the gathering glougham.

(Thanks, Dave.)

The 1937 edition of Webster’s Universal Dictionary of the English Language contains this peculiar entry:

jungftak (jŭngf´ täk) n. a fabled Persian bird, the male of which had only one wing, on the right side, and the female only one wing, on the left side; instead of the missing wings, the male had a hook of bone, and the female an eyelet of bone, and it was by uniting hook and eye that they were enabled to fly, — each, when alone, had to remain on the ground.

This appears to be neither an error nor a trap to catch copyright thieves. When scholar Richard Rex asked about it, an associate editor at the dictionary replied, “[W]e have gone through a good many sources and jungftak simply does not show up. It is quite a curiosity, for the various accounts of Persian mythology do not describe such a bird even under another name.” The entry disappears from editions after 1943. Probably it was a joke, but the story behind it is lost.

(Richard Rex, “The Incredible Jungftak,” American Speech 57:4 [Winter 1982], 307-308.)

Wha lies here? I Johnny Dow.Hoo! Johnny, is that you? Ay, man, but a'm dead now. — Edinburgh epitaph, quoted in Horatio Edward Norfolk, Gleanings in Graveyards, 1861

D.C.B. Marsh proposed this problem in the American Mathematical Monthly in 1957:

“Solve a3 – b3 – c3 = 3abc, a2 = 2(b + c) simultaneously in positive integers.”

There are a number of ways to go about this, but Raymond Huck of Marietta College found a strikingly simple one. 3abc is positive, so the first equation tells us immediately that b < a and c < a. Add these two facts together and we get b + c < 2a, and hence 2(b + c) < 4a. Substituting this conveniently into the second equation, we learn that a2 < 4a and a < 4. The second equation also shows that a is an even number, so a must be 2, and b and c, which are smaller, must both be 1.

(“Solutions,” American Mathematical Monthly 65:1 [January 1958], 43-46, Problem E1266, via Ross Honsberger, Mathematical Morsels, 1979.)

In 2006, German entomologist Jochen-P. Saltin discovered a new species of rhinoceros beetle in Peru, which he dubbed Megaceras briansaltini.

Remarkably, the insect’s horn closely resembles that of Dim, the blue rhinoceros beetle in the Disney film A Bug’s Life, which was released eight years earlier.

“I know of no dynastine head horn that has ever had the shape of the one seen in M. briansaltini, and so its resemblance to a movie character seems like a case of nature mimicking art … or what could be referred to as ‘the Dim Effect,'” wrote entomologist Brett C. Ratcliffe.

“There are numerous examples of art mimicking nature (paintings, sculpture, etc.), but that cannot be the case here, because there had never been a known rhinoceros beetle in nature upon which the creators of Dim could have used as a model for the head horn. In my experience, then, Dim was the first ‘rhinoceros beetle’ to display such a horn, and the discovery of M. briansaltini, a real rhinoceros beetle, came later.”

(Brett C. Ratcliffe, “A Remarkable New Species of Megaceras From Peru [Scarabaeidae: Dynastinae: Oryctini]. The ‘Dim Effect’: Nature Mimicking Art,” The Coleopterists Bulletin 61:3 [2007], 463-467.)

In the 1970s, San Francisco painting contractor Bill Holland discovered he could save money on business cards by listing himself as Zachary Zzzra in the local telephone directory and telling potential customers to find his number at the end of the book.

This worked well until the position was claimed by a Zelda Zzzwramp. He changed his name to Zachary Zzzzra but was overtaken by Vladimir Zzzzzzabakov. So in 1979 he pulled out all stops and became Zachary Zzzzzzzzzra.

Victory brought its trials. “People making illegal calls from phone booths look up the last name in the book and charge them to me,” he admitted to Time. “I don’t pay a damn one of them.”

Absolutely hands down one of the most beautiful places to see from space is the Caribbean. You see an entire rainbow of blue. From the light emerald green to the green-blue to the blue-green to the aquamarine to the slowly increasingly darker shades of blue down to the really deep colors that come with the depths of a really deep ocean. You can see all that at one time from space. It’s very curvy, it’s not harsh geometric lines. It’s swirls and whirls and all kinds of wavy lines. It looks like a piece of modern art.

— Astronaut Sandra Magnus, quoted in Ariel Waldman, What’s It Like in Space?, 2016

Swedish botanist Elias Tillander (1640–1693) was so “harassed by Neptune” during a trip across the Gulf of Bothnia from Stockholm to Turku that he made the return journey overland and changed his name to Tillandz (“by land”).

Linnaeus named the evergreen plant Tillandsia after him — it cannot tolerate a damp climate.

(From Wilfrid Blunt, Linnaeus: The Compleat Naturalist, 2001.)

From Lee Sallows:

(Thanks, Lee!)

In his Schilderboeck of 1604, Flemish artist Karel van Mander writes that his contemporary Marcus Gheeraerts the Elder is a good landscape painter who “often had the habit of including a squatting, urinating woman on a bridge or elsewhere.”

None of Gheeraerts’ landscapes are known to survive, but we have a perspective map of his native Bruges that he completed in 1562 and … there she is.

In 1952, British computer scientist Christopher Strachey taught the Manchester Mark 1 computer to write love letters:

Darling Sweetheart,

You are my avid fellow feeling. My affection curiously clings to your passionate wish. My liking yearns for your heart. You are my wistful sympathy: my tender liking.

Yours beautifully

M. U. C.

Strachey’s original program has been lost, but it was reimplemented by MIT digital media professor Nick Montfort in 2014, and now you can watch it pour out its heart online. (Here’s a PHP implementation.)

On April 11, 1916, inventor Louis Enricht invited a group of reporters to his Long Island home. He showed them a car with an empty gas tank, filled a porcelain pitcher from a garden hose, stirred in a greenish fluid, poured the mixture into the car’s tank, and signaled his son to crank the engine. The car started up. Enricht announced that he’d discovered a gasoline substitute that could be made for a penny a gallon.

Chemists denounced the claim as impossible, but Henry Ford began talks with the inventor. These broke down over a dispute with the Maxim Munitions Corporation, with which Enricht was apparently also talking.

The affair went quiet for a year, but in November 1917 railroad financier Benjamin Yoakum accused Enricht of treason: Yoakum had been financing the project but now Enricht refused to turn over the formula, and Yoakum feared that he may have sold the secret to the German government. Enricht admitted to meeting with the Germans but insisted that he hadn’t given them the formula — in fact, he’d burned the only copy.

In the early 1920s he promoted a similar scheme, claiming he could produce fuel from peat, but this too remained unsubstantiated, and he ended up in Sing Sing. When he died in 1924, he took the secret to endless gasoline with him. Possibly the whole thing was hot air (he had a long history of swindles). Possibly the secret ingredient was really acetone, which would have fired the car’s engine long enough to persuade onlookers but would produce corrosion and in any event was more costly than gas. And just conceivably his claim was true — but no one’s ever been able to rediscover the formula.

In 2015 British computer scientist Chris Patuzzo produced a self-enumerating pangram — a sentence that itemizes its own contents — that records its totals as percentages:

This sentence is dedicated to Lee Sallows and to within one decimal place four point five percent of the letters in this sentence are a’s, zero point one percent are b’s, four point three percent are c’s, zero point nine percent are d’s, twenty point one percent are e’s, one point five percent are f’s, zero point four percent are g’s, one point five percent are h’s, six point eight percent are i’s, zero point one percent are j’s, zero point one percent are k’s, one point one percent are l’s, zero point three percent are m’s, twelve point one percent are n’s, eight point one percent are o’s, seven point three percent are p’s, zero point one percent are q’s, nine point nine percent are r’s, five point six percent are s’s, nine point nine percent are t’s, zero point seven percent are u’s, one point four percent are v’s, zero point seven percent are w’s, zero point five percent are x’s, zero point three percent are y’s and one point six percent are z’s.

The next challenge was to extend the precision beyond one decimal place. Impressively, Matthias Belz produced this specimen in 2017:

Rounded to five decimal places, two point six five two five two percent of the letters of this sentence are a’s, zero point zero eight eight four two percent are b’s, two point six five two five two percent are c’s, zero point four four two zero nine percent are d’s, nineteen point eight zero five four eight percent are e’s, three point four four eight two eight percent are f’s, one point seven six eight three five percent are g’s, two point nine one seven seven seven percent are h’s, seven point eight six nine one four percent are i’s, zero point zero eight eight four two percent are j’s, zero point zero eight eight four two percent are k’s, zero point three five three six seven percent are l’s, zero point one seven six eight three percent are m’s, ten point two five six four one percent are n’s, eight point nine three zero one five percent are o’s, four point seven seven four five four percent are p’s, zero point zero eight eight four two percent are q’s, nine point five four nine zero seven percent are r’s, four point nine five one three seven percent are s’s, nine point six three seven four nine percent are t’s, two point zero three three six zero percent are u’s, two point seven four zero nine four percent are v’s, one point six seven nine nine three percent are w’s, zero point nine seven two five nine percent are x’s, zero point zero eight eight four two percent are y’s and one point nine four five one eight percent are z’s.

These numbers are still rounded, so later that year he surpassed that with an instance giving precisely accurate values:

Exactly three point eight seven five percent of the letters of this autogram are a’s, zero point one two five percent are b’s, three point five percent are c’s, zero point two five percent are d’s, twenty-one point two five percent are e’s, three point seven five percent are f’s, zero point three seven five percent are g’s, one point five percent are h’s, seven point two five percent are i’s, zero point one two five percent are j’s, zero point one two five percent are k’s, zero point three seven five percent are l’s, zero point two five percent are m’s, nine point seven five percent are n’s, seven point five percent are o’s, six point five percent are p’s, zero point one two five percent are q’s, nine point three seven five percent are r’s, five point one two five percent are s’s, ten percent are t’s, zero point three seven five percent are u’s, four point six two five percent are v’s, one point five percent are w’s, zero point five percent are x’s, zero point three seven five percent are y’s and one point five percent are z’s.

Details are here.

There is pictorial license in the same way that there is poetic license. … It is frequently to this that every master owes his most sublime effects: The unfinished condition in Rembrandt’s work, the exaggeration in Rubens. Mediocre men cannot have such daring; they never get outside themselves. Method cannot govern everything; it leads everybody up to a certain point. How is it that not one of the great artists has tried to destroy that mass of prejudices? They were probably frightened at the task, and so abandoned the crowd to its silly ideas.

— Eugène Delacroix (from his journal)

In the 1967 Star Trek episode “The Trouble With Tribbles,” a small furry alien species is introduced on board the Enterprise and after three days grows to 1,771,561 individuals. In 2019 University of Leicester physics undergraduate Rosie Hodnett and her colleagues wondered how long it would take for the creatures to fill the whole starship. Using Mr. Spock’s estimate that each tribble produces 10 offspring every 12 hours and assuming that each tribble occupies 3.23 × 10-3 m3 and that the volume of the Enterprise is 5.94 × 106 m3, they found that the ship would reach its limit of 18.4 × 109 tribbles in 4.5 days.

A separate inquiry found that after 5.16 days the accumulated tribbles would be generating enough thermal energy to power the warp drive for 1 second.

(Rosie Hodnett et al., “Tribbling Times,” Journal of Physics Special Topics, Nov. 18, 2019.)

“When you praise someone you call yourself his equal.” — Goethe

A problem proposed by Mel Stover for the April 1953 issue of Pi Mu Epsilon Journal:

After a meeting of six professors, each man left with another’s hat. The hat that Aitkins took belonged to the man who took Baily’s hat. The man whose hat was taken by Caldwell took the hat of the man who took Dunlop’s hat. And the man who took Easton’s hat wasn’t the one whose hat was taken by Fort. Who took Aitkins’ hat?

| SelectClick for Answer | | --- | | This solution is by Leon Bankoff. Denote each man by his initial and write x → y to indicate that x’s hat was taken by y. We know that B → x → A, where x is the man who took Baily’s hat, and that D → z → y → C, where z is the man who took Dunlop’s hat and y’s hat was taken by Caldwell. These two sequences comprise seven symbols altogether, so x, y, or z must be duplicating A, B, C, or D in one of them. There are two ways to combine the sequences:1. B → D → A → y → C (where x = D and z = A) 2. D → z → B → C → A (where x = C and y = B)

Each of these new sequences has five symbols, so each lacks one. Add s to the first sequence and t to the second to provide this missing link and to make each sequence into an unbroken cycle:1. s → B → D → A → y → C → s 2. t → D → z → B → C → A → t

The first cycle fits the problem statement if we let y = F and s = E, and the second matches if we let t = F and z = E. In either case, Fort took Aitkins’ hat.(“Problem Department,” Pi Mu Epsilon Journal 1:8 [April 1953], 329-330.) |

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Images: Wikimedia
CommonsThis just caught my eye — a feat attributed to the Spanish explorer Alonso de Ojeda, who would later accompany Columbus and name Venezuela:

Queen Isabella being in the tower of the cathedral at Seville, better known as the Giralda, Ojeda, to entertain her majesty, and to give proofs of his courage and agility, mounted on a great beam which projected in the air, twenty feet from the tower, at such an immense height from the ground, that the people below looked like dwarfs, and it was enough to make Ojeda himself shudder to look down. Along this beam he walked briskly, and with as much confidence as though he had been pacing his chamber. When he arrived at the end, he stood on one leg, lifting the other in the air; then turning nimbly round, he returned in the same way to the tower, unaffected by the giddy height, whence the least false step would have precipitated him and dashed him to pieces.

Allegedly he afterward threw an orange to the top of the tower, which would have been at least 88 meters tall at the time. This account is from Washington Irving’s biography of Columbus, and even Irving calls it “unworthy of record, but that it exhibits the singular character of the man.”

Emerson mentions Ojeda’s balancing act in his 1870 essay on success, claiming also that “Olaf, king of Norway, could run round his galley on the blades of the oars of the rowers when the ship was in motion.” I’m not even pursuing that one.

Image: Wikimedia CommonsI just came across this arresting sentence in The Satanic Verses, of all places:

“Turn your watch upside down in Bombay and you see the time in London.”

It appears this is roughly true: Because Indian Standard Time has an offset of UTC+05:30, an analog watch set to Indian time and read upside down will give the time in London — 10:10 becomes 4:40, noon becomes 6:30, and so on. The reverse is also true — a London watch read upside down will give the time in India.

Unfortunately the hand positions are only approximate, and the U.K. observes daylight saving time and India doesn’t, so just now it doesn’t work. Interesting idea, though.

He that is nourished by the acorns he picked up under an oak, or the apples he gathered from the trees in the wood, has certainly appropriated them to himself. Nobody can deny but the nourishment is his. I ask, then, when did they begin to be his? when he digested? or when he eat? or when he boiled? or when he brought them home? or when he picked them up?

— John Locke, An Essay Concerning the True Original, Extent and End of Civil Government, 1689

Early European colonists were staggered at the abundance of fish in the Chesapeake Bay. William Byrd II wrote in his natural history of Virginia:

Herring are not as large as the European ones, but better and more delicious. When they spawn, all streams and waters are completely filled with them, and one might believe, when he sees such terrible amounts of them, that there was as great a supply of herring as there is water. In a word, it is unbelievable, indeed, indescribable, as also incomprehensible, what quantity is found there. One must behold oneself.

More accounts here. “The abundance of oysters is incredible,” marveled Swiss explorer Francis Louis Michel in 1701. “There are whole banks of them so that the ships must avoid them. A sloop, which was to land us at Kingscreek, struck an oyster bed, where we had to wait about two hours for the tide.”

There is nothing contradictory in imagining causal chains that are closed, though the existence of such chains would lead to rather unfamiliar experiences. For instance, it might then happen that a person would meet his own former self and have a conversation with him, thus closing a causal line by the use of sound waves. When this occurs the first time he would be the younger ego, and when the same occurrence takes place a second time he would be the older ego. Perhaps the older ego would find it difficult to convince the younger one of their identity; but the older ego would recall an identical experience long ago. And when the younger ego has become old and experiences such an encounter a second time, he is on the other side and tries to convince some ‘third’ ego of their physical identity. Such a situation appears paradoxical to us; but there is nothing illogical in it.

— Hans Reichenbach, The Direction of Time, 1956

Amsterdam artist Hendrik de Keyser’s 1615 sculpture Screaming Child Stung by a Bee was probably inspired by an idyllium of the Greek poet Theocritus in which Cupid is stung while stealing honey from a hive. When he complains to his mother that so small a creature should cause such great pain, she responds that he himself is small but deals wounds that are grievous.

Painter Joseph Ducreux and sculptor Franz Xaver Messerschmidt also experimented with extreme facial expressions.

From reader Chris Smith:

Pick a three-digit number in which all the digits are different. Example: 314.

Now list every possible combination of two digits from the chosen number. In our example, these are 13, 14, 31, 34, 41, and 43.

Divide the sum of these two-digit numbers by the sum of the three digits in the original number, and you’ll always get 22. In our example, (13 + 14 + 31 + 34 + 41 + 43) / (3 + 1 + 4) = 176/8 = 22.

This works because 10a + b, 10a + c, 10b + a, 10b + c, 10c + a, and 10c + b sum to 22a + 22b + 22c = 22(a + b + c), so dividing by a + b + c will always give 22.

(Thanks, Chris.)

The April 1, 1878, issue of the New York Daily Graphic announced that Thomas Edison had invented a “victuals machine” that would feed the human race:

I made all this food out of the dirt taken from the cellar and water that runs through these pipes. … I believe that in ten years my machines will be used to provide the tables of the civilized world. … I can make cabbages and oranges that have never felt the rain. Nature is full of surprises. Bananas and chocolate can be made out of the very same ingredients, and the methods of combining differ only a trifle.

The last paragraph revealed that the story was a hoax, but many readers didn’t get that far — several newspapers picked up the news, and some readers even tried to order the device. Reporter William Augustus Croffut, who’d concocted the tale, wrote diffidently to Edison on April 4 (above), “Did you see my hoax? And are you in a state of fiery wrath? Or how is it?”

Image: Wikimedia CommonsThe Korean alphabet was designed expressly to increase literacy among the country’s uneducated lower classes, who found traditional Chinese characters hard to recognize and understand. King Sejong the Great promulgated the new letters in 1444 to permit the common people to express themselves conveniently in writing.

It’s said that “a wise man can acquaint himself with them before the morning is over, and even a stupid man can learn them in the space of 10 days.”

Image: Wikimedia CommonsThe upside-down catfish, Synodontis nigriventris, is right side up. Or, rather, it’s adapted to spend most of its time upside down — its belly is darker than its back, and it swims fastest in this inverted position. The behavior may have evolved to help it reach food on the undersides of submerged branches or to breathe dissolved oxygen near the surface.

Here’s a surprise: The Book of Knowledge of Ingenious Mechanical Devices, a 1206 manuscript by the Turkish author Ismail al-Jazari, depicts a chain pump in the form of a Möbius strip. A rope bearing a chain of cups dips them successively into a water source at the bottom and then pours them into a course at the top. The single, continuous rope makes two passes through this route, describing the edges of a strip with a half twist so that the cups suspended between the loops are turned 180 degrees with each pass. This would permit the cups to last longer, since they’re worn more evenly, and even a broken cup might still convey some water with every second pass.

(Julyan H.E. Cartwright and Diego L. González, “Mobius Strips Before Mobius: Topological Hints in Ancient Representations,” Mathematical Intelligencer 38:2 [June 2016], 69-76.)

Albert Einstein used to say that he went to his office at the Institute for Advanced Study “just to have the privilege of walking home with Kurt Gödel.” The two would meet at Einstein’s home each day between 10 and 11 and undertake the half-hour walk to the institute. At 1 or 2 in the afternoon they’d walk back, discussing politics, philosophy, and physics. Biographer Palle Yourgrau estimates that these walks consumed 30 percent of Einstein’s workday.

Einstein’s secretary, Helen Dukas, wrote in 1946, “I know of one occasion when a car hit a tree after its driver suddenly recognized the face of the beautiful old man walking along the street.”

Gödel caused no such problems. “I have so far not found my ‘fame’ burdensome in any way,” he wrote to his mother. “That begins only when one becomes so famous that one is known to every child in the street, as is the case of Einstein.”

(From A World Without Time: The Forgotten Legacy of Godel and Einstein, 2009.)

Utopian socialist Robert Owen opposed corporal punishment, so when he took over the textile mill at New Lanark, Scotland, in 1800, he kept order with a “silent monitor”: Over each worker’s machine was hung a block whose successive sides were painted white, yellow, blue, and black:

The 2,500 toys had their positions arranged every day, according to the conduct of each worker during the preceding day: white indicating superexcellence; yellow, moderate goodness; blue, a neutral condition of morals; and black, exceeding naughtiness.

These ratings were assigned by the departmental overseer, whose own rating was assigned by an under-manager. The final say lay with Owen, to whom workers could appeal, and the daily ratings were recorded in a “book of character” maintained by each department.

This sounds draconian, but combined with Owen’s generous nature it seemed to work. “As time went on,” wrote one biographer, “the yellows and whites gained on the darker hues; and in the later stages of Owen’s management the signs were almost entirely white, with a sprinkling of yellows.”

Above: Antonio Cicognara, Saint George and the Princess, tempera on panel, 1475.

Below: Lewis Carroll, Saint George and the Dragon, photograph, 1874.

Of photography Carroll wrote, “It is my one recreation and I think it should be done well.”

A limerick’s cleverly versed —
The second line rhymes with the first;
The third one is short,
The fourth’s the same sort,
And the last line is often the worst.

— John Irwin

The first automated grocery store in the United States appeared in 1937. At Keedoozle, each customer received a key bearing a roll of paper tape. At a series of display cases, she’d insert her key at each item she wanted and press a button, which would punch a pattern of holes in the tape. At the cashier, an electronic “translator” would total the price and release the requested items through chutes onto a conveyor belt. The customer would wait in a lounge until her packed items were delivered to her.

Founder Clarence Saunders claimed that the automated store required only seven employees, half as many as a traditional supermarket. This permitted a 7.5 percent profit on prices 10 percent lower than competing stores, he said.

The system wasn’t entirely automated — humans kept the stocks filled and bagged the orders — and it could handle only cans and cartons, not fresh meat or vegetables. And it tended to founder when the store got busy. But historians also say that the concept was too far ahead of its time — the American public just wasn’t ready for automated shopping. Only three stores were ever built, and the last closed in 1949.

(Thanks, Abi.)

Image: Wikimedia Commons

Recently I was on the northern Queensland coast of Australia, in an Aboriginal reserve. In the most unlikely spot I encountered a beachcomber, who had been living there for several years. He was looking for floats and bottles, building a raft that would take him around the top of Cape York in one of the most dangerous channels in the world for current and wind — the Torres Straits. I asked him if he knew the risks.

‘I’m not bothered,’ he said. ‘You can go anywhere, you can do just about anything, if you’re not in a hurry.’

That is one of the sanest statements I have ever heard in my life.

— Paul Theroux, Fresh Air Fiend: Travel Writings, 2001

On each of these two black lines is a trio of red points marked by the same distances.

The midpoints of segments drawn between corresponding points are collinear.

(Discovered by Danish mathematician Johannes Hjelmslev.)

There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that ‘remembered’ a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.

— Bertrand Russell, The Analysis of Mind, 1921

Liza Minnelli, daughter of Judy Garland, married Jack Haley Jr., son of the Tin Man.
The Netherlands still sends 20,000 tulip bulbs to Canada each year.
Every positive integer is a sum of distinct terms in the Fibonacci sequence.
HIDEOUS and HIDEOUT have no vowel sounds in common.
“Death is only a larger kind of going abroad.” — Samuel Butler

(Thanks, Colin and Joseph.)

In Leonard Bernstein’s Mass, in which the phrase “me and my soul” is sung repeatedly, the words me and soul are sung to the notes mi and sol.

In the song “Sodomy” in the 1967 rock musical Hair, the word sodomy is sung to the notes so, do, and mi.

(From Dave Morice, The Dictionary of Wordplay, 2001.)

A letter from Lewis Carroll to Nature, March 31, 1887:

Having hit upon the following method of mentally computing the day of the week for any given date, I send it you in the hope that it may interest some of your readers. I am not a rapid computer myself, and as I find my average time for doing any such question is about 20 seconds, I have little doubt that a rapid computer would not need 15.

Take the given date in 4 portions, viz. the number of centuries, the number of years over, the month, the day of the month.

Compute the following 4 items, adding each, when found, to the total of the previous items. When an item or total exceeds 7, divide by 7, and keep the remainder only.

The Century-Item. — For Old Style (which ended September 2, 1752) subtract from 18. For New Style (which began September 14) divide by 4, take overplus from 3, multiply remainder by 2. [The Century-Item is the first two digits of the year, so for 1811 take 18.]

The Year-Item. — Add together the number of dozens, the overplus, and the number of 4’s in the overplus.

The Month-Item. — If it begins or ends with a vowel, subtract the number, denoting its place in the year, from 10. This, plus its number of days, gives the item for the following month. The item for January is ‘0’; for February or March (the 3rd month), ‘3’; for December (the 12th month), ’12.’ [So, for clarity, the required final numbers after division by 7 are January, 0; February, 3; March, 3; April, 6; May, 1; June, 4; July, 6; August 2; September, 5; October, 0; November, 3; and December, 5.]

The Day-Item is the day of the month.

The total, thus reached, must be corrected, by deducting ‘1’ (first adding 7, if the total be ‘0’), if the date be January or February in a Leap Year: remembering that every year, divisible by 4, is a Leap Year, excepting only the century-years, in New Style, when the number of centuries is not so divisible (e.g. 1800).

The final result gives the day of the week, ‘0’ meaning Sunday, ‘1’ Monday, and so on.

Examples

1783, September 18

17, divided by 4, leaves ‘1’ over; 1 from 3 gives ‘2’; twice 2 is ‘4.’

83 is 6 dozen and 11, giving 17; plus 2 gives 19, i.e. (dividing by 7) ‘5.’ Total 9, i.e. ‘2.’

The item for August is ‘8 from 10,’ i.e. ‘2’; so, for September, it is ‘2 plus 3,’ i.e. ‘5.’ Total 7, i.e. ‘0,’ which goes out.

18 gives ‘4.’ Answer, ‘Thursday.’

1676, February 23

16 from 18 gives ‘2.’

76 is 6 dozen and 4, giving 10; plus 1 gives 11, i.e. ‘4.’ Total ‘6.’

The item for February is ‘3.’ Total 9, i.e. ‘2.’

23 gives ‘2.’ Total ‘4.’

Correction for Leap Year gives ‘3.’ Answer, ‘Wednesday.’

(Via Edward Wakeling, Rediscovered Lewis Carroll Puzzles, 1995.)

“One thing you must always remember about Roosevelt is that he is about seven years old.” — Cecil Spring-Rice

“It often happens that the easiest dissection puzzles are the prettiest,” wrote Henry Dudeney in 1914. “Here is a new one that ought to give the reader very little trouble. Cut the figure into five pieces that will fit together and form a square.”

| SelectClick for Answer | | --- | | “Make the cut as shown in the illustration and fit the four triangular pieces into the places enclosed by the dotted lines.” |

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Two hundred kilometers west of Pretoria is a farm called Tweebuffelsmeteenskootmorsdoodgeskietfontein. The name, the longest place name in South Africa, means “the spring where two buffaloes were shot stone dead with one shot.”

As a daughter language of Dutch, Afrikaans is capable of almost endless compounding, at least in principle. In his 1982 Total Book of South African Records, Eric Rosenthal claims that the longest word in the language is Tweedehandsemotorverkoopsmannevakbondstakingsvergaderingsameroeperstoespraakskrywerspersverklaringuitreikingsmediakonferensieaankondiging, “issuable media conference’s announcement at a press release regarding the convener’s speech at a secondhand car dealership union’s strike meeting.” But, as with many such records, the word was contrived expressly and is not in common use.

At Mr Currie’s table I met several ingenious persons, who entertained me with curious and interesting reminiscences. Dr Adam Smith, author of ‘The Wealth of Nations,’ was a native of Kirkcaldy, and in the place composed his great work. While engaged in composition he frequently fell into a condition of reverie, so as to be entirely unconscious of his relations with the external world. Early on a Sunday morning he walked into his garden, his mind occupied with a train of ideas; he unconsciously travelled into the turnpike road, along which he proceeded in a state of abstraction, till he reached Dunfermline, at a distance of fifteen miles. The people were going to church, and the sound of the bells awakened the philosopher from his dream. Arrayed in an old dressing-gown, he was regarded as an oddity.

— Charles Rogers, Leaves From My Autobiography, 1876

When alchemist Georg Honauer (1572-1597) claimed he could convert iron into gold, Duke Friedrich I of Württemberg ordered all the iron in his Mömpelgard armory conveyed to Stuttgart for a demonstration. Honauer panicked and fled but was extradited back to town, where, according to this contemporary woodcut, he was dressed in a gilded garment and hanged on a gilded gallows.

The anonymous printer concludes, er soll besser lernen Gold machen — “he should learn how to make gold better.”

(Thanks, Charlie.)

aegritude
n. an instance of sickness

Utah senator Jake Garn got so comprehensively ill on the space shuttle Discovery in 1985 that he’s remembered in the Garn scale, an informal measure of space sickness. Astronaut Robert Stevenson recalled:

Jake Garn was sick, was pretty sick. I don’t know whether we should tell stories like that. But anyway, Jake Garn, he has made a mark in the Astronaut Corps because he represents the maximum level of space sickness that anyone can ever attain, and so the mark of being totally sick and totally incompetent is one Garn. Most guys will get maybe to a tenth Garn if that high. And within the Astronaut Corps, he forever will be remembered by that.

Garn said, “I’ve been very proud of the fact that they named something after me after all these years, even if it was unofficial.”

Dubious but entertaining: After the Battle of Wauhatchie on the night of October 29, 1863, rumors circulated that Confederate troops had retreated in the darkness because they’d mistaken a stampede of mules for a cavalry charge. Someone wrote a “Charge of the Mule Brigade,” and the Union quartermaster reportedly asked that the gallant mules “have conferred upon them the brevet rank of horses.”

But there are no Southern reports of a mule attack at Wauhatchie, and one Confederate combatant categorically denied the story when it appeared in Grant’s memoir. At best, it appears, some mules broke loose and caused enough confusion to permit the 137th New York Infantry to arrive and oppose the rebels.

“The exact details of whatever the mules did at Wauhatchie will never be precisely known,” writes historian Gene C. Armistead in Horses and Mules in the Civil War (2013), “but the story is too humorous and too good to abandon.”

A puzzle by Polish mathematician Paul Vaderlind:

Is it possible to arrange 25 whole numbers (not necessarily all different) so that the sum of any three successive terms is even but the sum of all 25 is odd?

| SelectClick for Answer | | --- | | Yes. Let E stand for an even number and O for an odd and consider the sequence OEO OEO OEO OEO OEO OEO OEO OEO O. Any group of three consecutive terms contains one even number and two odd, giving an even sum. But 17 of the numbers are odd, so the sum of the whole group is odd.From Vaderlind’s excellent 2002 book The Inquisitive Problem Solver. |

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Vladimir Nabokov’s 1962 novel Pale Fire includes a character named John Shade, a poet who writes the lines

Space is a swarming in the eyes; and time,
A singing in the ears.

In the first edition of his 1964 book The Ambidextrous Universe, Martin Gardner quoted these lines and, as a joke, credited them to Shade rather than Nabokov, listing Shade in the index.

Nabokov, in turn, in his 1969 novel Ada or Ardor: A Family Chronicle had a character quote Gardner’s book and the same two lines of verse:

‘Space is a swarming in the eyes, and Time a singing in the ears,” says John Shade, a modern poet, as quoted by an invented philosopher (‘Martin Gardiner’) in The Ambidextrous Universe, page 165.

Gardner’s book concerns symmetry, and Ada is a palindrome; further, the action in that novel takes place on Anti-Terra, a sort of mirror image of Earth. Nabokov’s 1974 novel Look at the Harlequins!, also influenced by Gardner’s book, concerns a man who can’t distinguish left from right.

(Thanks, Jeff.)

A great portrait is always more a portrait of the painter than of the painted. When we look at a portrait by Holbein or Rembrandt it is of Holbein or Rembrandt that we think more than of the subject of their picture. Even a portrait of Shakespeare by Holbein or Rembrandt could tell us very little about Shakespeare. It would, however, tell us a great deal about Holbein or Rembrandt.

— Samuel Butler, Notebooks, 1912

From Lee Sallows:

(Thanks, Lee!)

A little kingdom contains 66 people, a king and 65 citizens. Each of them, including the king, has a salary of one gold piece. When democracy comes, the king is denied a vote, but he has the power to suggest changes, in particular regarding the redistribution of salaries. The salaries must total 66, and each salary must be a whole number of gold pieces. The citizens will vote on each suggestion, which will pass if more citizens vote for it than against it. Each voter will reliably support a measure if it will increase his salary, oppose it if it will decrease his salary, and otherwise abstain from voting.

The king is greedy. What’s the highest salary he can arrange for himself?

| SelectClick for Answer | | --- | | Impressively, he can get 63 gold pieces. He starts by proposing that just over half of the 65 citizens (33 voters) have their salaries doubled to 2 gold pieces, at the expense of the other 33 voters, including himself. Then he does the same thing again, proposing that just over half (17) of the 33 salaried voters receive an increase to 3 or 4 gold pieces, while the remaining 16 in that group are reduced to zero. By continuing in this manner he can reduce the number of salaried voters to 9, 5, 3, and finally 2, with each receiving 33 gold pieces. Then the king can propose that three of the unsalaried citizens receive a salary of 1 gold piece if these two large salaries are now reassigned to himself.From Peter Winkler’s excellent Mathematical Puzzles, 2021. |

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Now this last example is very interesting. What happened when Christ broke the bread at the Last Supper? He broke a thing into fragments. But each piece contained the whole: that is, his entire body. And, again, what happens if the Host, after it has been consecrated by a priest, falls to the floor of the church and crumbles, and if a mouse then eats the crumbs? Does the mouse eat Christ’s body? I do not wish to develop this argument, merely to remind you that this was one of the arguments used by Protestant reformers to ridicule Catholic practice.

— Jacqueline Lichtenstein, “The Fragment: Elements of a Definition,” in William Tronzo, ed., The Fragment: An Incomplete History, 2009

One night in 1939, Wolcott Gibbs’ 4-year-old son Tony began chanting a song in the bathtub. It was sung “entirely on one note except that the voice drops on the last word in every line”:

He will just do nothing at all.
He will just sit there in the noonday sun.
And when they speak to him, he will not answer them,
Because he does not care to.
He will stick them with spears and throw them in the garbage.
When they tell him to eat his dinner, he will just laugh at them.
And he will not take his nap, because he does not care to.
He will not talk to them, he will not say nothing.
He will just sit there in the noonday sun.
He will go away and play with the Panda.
He will not speak to nobody because he doesn’t have to.
And when they come to look for him they will not find him.
Because he will not be there.
He will put spikes in their eyes and put them in the garbage.
And put the cover on.
He will not go out in the fresh air or eat his vegetables.
Or make wee-wee for them, and he will get thin as a marble.
He will do nothing at all.
He will just sit there in the noonday sun.

Pete Seeger liked this so much that he made a song of it — he called it “Declaration of Independence”:

Here’s a unit square. Prove that, if nine points are identified in the square’s interior, we can always find three of them that form a triangle of area 1/8 or less.

| SelectClick for Answer | | --- | | Cut the square into four smaller squares, each of which has a side length of 1/2. Now one of these smaller squares must contain at least three of the points. And the largest triangle that these points can form has an area half that of the small square — or 1/8. |

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Image: Wikimedia CommonsHong Kong contains a street named Rednaxela Terrace. It’s hard not to notice that this is Alexander spelled backward, but the origin of the name is uncertain.

In Signs of a Colonial Era (2009), Andrew Yanne and Gillis Heller claim that the street had been named Alexander Terrace after its original owner but that a clerk recorded the name backward, as the Chinese language was written right to left at the time.

Another possibility is that the name is linked to New York abolitionist Robert Alexander Young’s 1829 pamphlet Ethiopian Manifesto, which contains the name Rednaxela.

In writing novels as well as plays the cardinal rule is to treat the various characters as if they were chessmen, and not try to win the game by altering the rules; for instance, not move the knight as if it were a pawn, and so on. Again the characters ought to be strictly defined, and not put out of action in order to help the author to accomplish his purpose; for, on the contrary, it is through their activity alone he should try to win. Not to do this is to appeal to the miraculous, which is always unnatural.

— The Reflections of [Georg Christoph] Lichtenberg, 1908

A puzzle by A. Vasin from the July-August 1993 issue of Quantum:

Two numbers are mirror numbers if each presents the digits of the other in reverse order, such as 123 and 321. Find two mirror numbers whose product is 92,565.

| SelectClick for Answer | | --- | | This solution is by V. Dubrovsky. The size of the product shows that the factors must have three digits each. So let one of them be abc (or 100a + 10b + c) and the other be cba. The product ends in 5, so either a or c must be 5. Say that’s a. The other factor starts with 5, and 92,565 / 500 < 200, so c must be 1. As to b, we can see that the 6 in 92,565 is the last digit of 5b + b, or 6b, so b must be either 1 or 6, and we can test these candidates to learn that it’s 6. The numbers we seek are 561 and 165. |

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“Should a garden look as if the gardener worked on his knees? I ask you.” — Lincoln Steffens

Image: Wikimedia CommonsIn 2005 Yale psychologists Deena Skolnick and Paul Bloom asked children and adults about the beliefs of fictional characters regarding other characters — both those that exist in the same world, such as Batman and Robin, and those that inhabit different worlds, such as Batman and SpongeBob SquarePants.

They found that while both adults and young children distinguish these two types of relationships, young children “often claim that Batman thinks that Robin is make-believe.”

“This is a surprising result; it seems unlikely that children really believe that Batman thinks Robin is not real,” they wrote. “If they did, they should find stories with these characters incomprehensible.”

One possible explanation is that young children can find it hard to take a character’s perspective, and so might have been answering from their own point of view rather than Batman’s. In a second study, kids acknowledged that characters from the same world can act on each other.

But this is a complex topic even for grownups. “James Bond inhabits a world quite similar to our own, and so his beliefs should resemble those of a real person. Like us, he should think Cinderella is make-believe. On the other hand, Cinderella inhabits a world that is sufficiently dissimilar to our own that its inhabitants should not share many of our beliefs. Our intuition, then, is that Cinderella should not believe that James Bond is make-believe; she should have no views about him at all.”

(Deena Skolnick and Paul Bloom, “What Does Batman Think About Spongebob? Children’s Understanding of the Fantasy/Fantasy Distinction,” Cognition 101:1 [2006], B9-B18. See Author!, Truth and Fiction, and Split Decision.)

Chinese proverbs:

Enough feathers can sink a boat.
Laziness in youth spells regret in old age.
The dog that bites won’t bare his teeth.
Full of courtesy, full of craft.
Suspicions create imaginary fears.
No clouds, no rain; no rules, no gain.
One fight sullies two persons; one compromise benefits two persons.
Walk a road and it becomes familiar; do a job and it becomes easy.
Worry doesn’t seek out people — people find worry on their own.
Three people of a common mind can conquer the world.
The going is toughest toward the end of a journey.
The guilty party is the first to sue.
If you fall down by yourself, get up by yourself.
Thieves in the dark hate the moonlight.
Every drama requires a fool.
Perseverance is worth more than a vast estate.
Prolonged illness makes a doctor of a patient.
Smart people also do stupid things.
The masses decide what is right and wrong.
Gossip won’t harm a good person as stirring won’t spoil good wine.

And “Learning is like paddling a canoe against the current — you will regress if you don’t advance.”

Image: Wikimedia CommonsDoes the green dot above flash before, as, or after the red dot reaches it? Most people say after, but in fact the flash occurs before the red dot arrives (below). This anomaly is known as the flash-lag effect, and its cause is unclear. Possibly it’s a sign that the visual system extrapolates the position of a moving object more readily than that of an unpredictably flashing one.

Image: Wikimedia Commons

Paper airplanes existed long before real airplanes.

Every Little Boy’s Book, from 1864, includes instructions for a “paper dart”:

“The paper dart, when thrown from the hand, rarely hits the object aimed at, as it generally makes a graceful curve in passing through the air.”

Via Vox.

Henry James’ 1903 novella The Beast in the Jungle features his famously tortured syntax:

It led, briefly, in the course of the October afternoon, to his closer meeting with May Bartram, whose face, a reminder, yet not quite a remembrance, as they sat much separated at a very long table, had begun merely by troubling him rather pleasantly.

James Thurber parodied this with “The Beast in the Dingle”:

He had brought himself so fully in the end, poor Grantham, to accept his old friend’s invitation to accompany her to an ‘afternoon’ at ‘Cornerbright’ that now, on the very porch of the so evident house, he could have, for his companion, in all surrender, a high, fine — there was no other word for it — twinkle.

His original title was “The Return of the Screw.” See Homage and A Prose Maze.

James McNeill Whistler hated the work of J.M.W. Turner.

A lady once asked him, “Oh, Mr. Whistler, my husband has discovered in a secondhand shop what he thinks are two real Turners. Will you come and tell us whether they are real Turners or imitation Turners?”

“Well, ma’am,” Whistler said, “now that’s really a fine distinction.”

When a thread is pulled horizontally from the underside of a wound spool, the spool rolls in the direction of the pulling force, counter to intuition. When the thread is pulled upward vertically, the spool rolls in the opposite direction.

Why the difference? The spool must rotate about its point of contact with the table, but the direction of torque, clockwise or counterclockwise, varies with the angle of the thread. Interestingly there’s a critical angle at which the spool does not roll but slides.

[Parrhasius], it is recorded, entered into a competition with Zeuxis, who produced a picture of grapes so successfully represented that birds flew up to the stage-buildings; whereupon Parrhasius himself produced such a realistic picture of a curtain that Zeuxis, proud of the verdict of the birds, requested that the curtain should now be drawn and the picture displayed; and when he realized his mistake, with a modesty that did him honour he yielded up the prize, saying that whereas he had deceived birds Parrhasius had deceived him, an artist.

From Pliny the Elder, Naturalis Historia. See Demo.

Image: Thomas Wilkenventifact
n. a stone shaped by windblown sand

In 1696 lightning struck an oak in Normandy, and the resulting fire hollowed out the tree. Villagers filled the space with two chapels, reached by a spiral staircase that circles the trunk. Now perhaps a thousand years old, the Chêne chapelle is still in use today.

See Al Fresco.

Tennyson was plagued by autograph hunters.

As a pretext, one wrote to him asking which was the better dictionary, Webster’s or Ogilvie’s.

He replied by cutting the word Ogilvie’s from the letter, pasting it to a blank sheet of paper, and mailing it back.

See Pen Fatigue.

By substituting images for claims, the pictorial commercial made emotional appeal, not tests of truth, the basis of consumer decisions. The distance between rationality and advertising is now so wide that it is difficult to remember that there once existed a connection between them. Today, on television commercials, propositions are as scarce as unattractive people. The truth or falsity of an advertiser’s claim is simply not an issue. A McDonald’s commercial, for example, is not a series of testable, logically ordered assertions. It is a drama — a mythology, if you will — of handsome people selling, buying and eating hamburgers, and being driven to near ecstasy by their good fortune. No claims are made, except those the viewer projects onto or infers from the drama. One can like or dislike a television commercial, of course. But one cannot refute it.

— Neil Postman, Amusing Ourselves to Death, 1985

In 1885, seeking a way to depict vocal sounds visually, Welsh singer Megan Watts Hughes invented the eidophone, a chamber capped with an elastic membrane that would resonate when the singer sang into a tube. When she spread the disk with a thin layer of sand or glycerine, standing waves would register as visible patterns resembling forget-me-nots, daisies, marigolds, chrysanthemums, and sunflowers.

“Stepping out of doors,” she wrote, “[I] have seen their parallels living in the flowers, ferns, and trees around me; and … the hope has come to me that these humble experiments may afford some suggestions in regard to nature’s production of her own beautiful forms.”

The field of study she helped to pioneer is now known as cymatics — see Chladni Figures.

You know the watch argument was [William] Paley’s greatest effort. A man finds a watch and it is so wonderful that he concludes that it must have had a maker. He finds the maker and he is so much more wonderful than the watch that he says he must have had a maker. Then he finds God, the maker of the man, and he is so much more wonderful than the man that he could not have had a maker. This is what the lawyers call a departure in pleading.

— Robert G. Ingersoll, “Why I Am an Agnostic,” 1896

Seinfeld began and ended with the same line.

The Massachusetts School Law of 1642 declared ignorance to be a satanic ill:

It being one chief project of that old deluder, Satan, to keep men from the knowledge of the Scriptures, as in former times by keeping them in an unknown tongue, so in these latter times by persuading from the use of tongues, that so that at least the true sense and meaning of the original might be clouded and corrupted with love and false glosses of saint-seeming deceivers; [we resolve] that learning may not be buried in the grave of our forefathers, in church and commonwealth, the Lord assisting our endeavors.

It ordered every town of more than 50 families to hire a teacher and every town of more than 100 families to establish a grammar school, an early step toward public education in the United States.

Image: Wikimedia CommonsArtist Gert Neuhaus painted this mural on a Berlin wall in 1989.

He called it The Phoenix.

Dorothy Parker said that James Thurber’s cartoon figures had the “semblance of unbaked cookies.”
In typing AUTHENTICITY, the left and right hands alternate.
P.G. Wodehouse wrote the last 26 pages of Thank You, Jeeves in one day.
INTERROGATIVES is an anagram of both REINVESTIGATOR and TERGIVERSATION.
1232882 + 3287682 = 123288328768

(Thanks, Steve.)

A puzzle by Y. Ionin, from the September/October 1990 issue of Quantum:

Three frogs occupy three vertices of a square. When one frog jumps over another, it lands beyond it at the same distance that had originally separated them. Can any frog reach the fourth vertex?

| SelectClick for Answer | | --- | | No. Impose coordinates so that the frogs sit at (0,0), (1,0), and (0,1). Now when a frog at (x, y) jumps over a frog at (a, b), it lands at (2a – x, 2b – y). Thus the parities of each frog’s coordinates never change. At the start each frog had at least one even coordinate, so none of them can ever reach a point with two odd coordinates, such as (1,1).See the issue, Solution M14 on page 59, for a visual proof. |

In a French journal Oscar Wilde once saw the drawing of a bonnet.

Under it were the words “With this style the mouth is worn slightly open.”

A puzzle by Steven T., a systems engineer at the National Security Agency, from the NSA’s September 2016 Puzzle Periodical:

Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.

The athletes are named Adam, Bob, and Charlie.

Adam finished first overall with 22 points.
Bob won the Javelin event and finished with 9 points overall.
Charlie also finished with 9 points overall.

Question: Who finished second in the 100-meter dash (and why)?

| SelectClick for Answer | | --- | | First, realize that the total points awarded is 40. Given that we are dealing with integers that means the total number of Events (TE) times the total number of points awarded in an event (TP) must equal 40. We can quickly eliminate some possibilities.

| Events (TE) | Points (TP) | | 1 | 40 | Not possible since we know there are at least two events. | | 2 | 20 | Not possible since Adam and Bob both won 1 event. There would be no way for Bob and Charlie to finish with the same points. | | 4 | 10 | A possibility. | | 5 | 8 | A possibility. | | 8 | 5 | Not possible, since 1st > 2nd > 3rd > 0 means the minimum number of points awarded HAS to be 6 (3, 2, 1). | | 10 | 4 | Same reason. | | 20 | 2 | Same reason. | | 40 | 1 | Same reason. |

So we now know it was either 4 events with 10 points awarded in an event or 5 events with 8 points awarded. Let’s look at the 4/10 situation first. The possible points for each place with 10 overall points available is (all other combinations are impossible because of the 1st > 2nd > 3rd > 0 constraint):* 5, 3, 2 Not possible as there is no way to get to 22 points in 4 events (greatest possible points would be 20). * 5, 4, 1 Same reason. * 6, 3, 1 Not possible, since no combination of 4 numbers can get to 22 points (3 × 6 + 3 = 21, 4 × 6 = 24). * 7, 2, 1 A possibility — let’s look further.

Can we get Adam to 22? Yes. Adam can finish 1st 3 times and 3rd once (in the Javelin). 3 × 7 + 1 = 22.Can we get Bob to 9? Nope. Bob won the Javelin (7 points). There’s no way to get to 9 with the remaining event/point combinations. Sooooo …There must be 5 events with a total of eight points (we’re getting close). Let’s look at the possible points (again, the other combinations are not possible because of the 1st > 2nd > 3rd > 0 constraint):* 4, 3, 1 Not possible as there is no way to get to 22 points (4 × 5 = 20 is maximum) * 5, 2, 1 Looks like this is the winner. Let’s check.

Can we get Adam to 22? Yes. Adam can finish 1st 4 times and 2nd once (4 × 5 + 2). Since we know Bob finished 1st in the Javelin, Adam must have finished 2nd.Can we get Bob to 9? Yes. Bob finished 1st in the Javelin (5 points) and finished 3rd 4 times (4 ×1) for a total of 9 points.Can we get Charlie to 9? Yes. Charlie finished 3rd in the Javelin (1 point) and must have finished 2nd in the 4 other events (4 × 2) for a total of 9 points.Since Charlie finished 2nd in EVERY EVENT OTHER THAN THE JAVELIN, he MUST have finished 2nd in the 100-meter dash. Here is a little table:

| Javelin | Event 2 | Event 3 | Event 4 | 100m Dash | Total | | Adam | 2nd (2 pts) | 1st (5 pts) | 1st (5 pts) | 1st (5 pts) | 1st (5 pts) | 22 pts | | Bob | 1st (5 pts) | 3rd (1 pt) | 3rd (1 pt) | 3rd (1 pt) | 3rd (1 pt) | 9 pts | | Charlie | 3rd (1 pt) | 2nd (2 pts) | 2nd (2 pts) | 2nd (2 pts) | 2nd (2 pts) | 9 pts |

|

In a 1963 issue of Bokmakierie, a magazine for birdwatchers, Frank A. Goodliffe described a curiously familiar species he called Clericus polydenominata, the “dog-collared sombre blackbird”:

Identification: Similar to common laity but plumage and behaviour should serve to differentiate. Plumage black with narrow white collar — unbroken at throat. Feet black, of leathery appearance. Beak pink — often with blueish tint during winter months. When in groups are often seen with wings folded behind rump. … Habits: Usually found congregating with flocks of common laity, the females of which are frequently seen with plumage of vivid colours. Nesting: This usually occurs close to old buildings with spires. They are usually very friendly and may be seen around nesting sites of common laity at tea-time. … Call: The voice is distinctive, commencing ‘Brrrrr–rethren’ and continuing low and pleasant — often prolonged. Usually sings in congregations.

In a private booklet published four years later, M.A. Traylor suggested that the species belonged in the family of bishop birds.

(From Curiosities of Biological Nomenclature.)

“How happy many people would be if they cared about other people’s affairs as little as about their own.” — G.C. Lichtenberg

“Most people enjoy the inferiority of their best friends.” — Lord Chesterfield

“We all have strength enough to endure the misfortunes of others.” — La Rochefoucauld

“I set it down as a fact that if all men knew what each said of the other, there would not be four friends in the world.” — Pascal

In an April 3, 1971, letter to the editor of the Saturday Review, reader K. Jason Sitewell reported some alarming news: A congressman named A.F. Day had introduced a bill that would abolish all private parks of more than 50 acres and all public recreation areas that were used by fewer than 150 people a day. The practical effect would be to abolish the nation’s golf courses.

Sitewell said he understood Day’s motive because he’d grown up with him. The congressman’s grandfather had “perished in a sand trap,” and his father had died of a coronary after hitting 19 balls into a pond.

An uproar followed. Country clubs vowed to fight the bill, constituents besieged their representatives, and editorials decried the measure, which Golf World called “as ominous a threat to golf as anything that has come along.”

But eventually it became clear that there was no such bill and readers saw the link between the purported congressman’s name and the date of Sitewell’s letter. It turned out that the whole thing had been a jape cooked up by Review editor and inveterate prankster Norman Cousins.

“I wrote apologies to each subscriber who had been offended or angered,” Cousins wrote. “I begged my golfing friends, who threatened to have me barred from every course in the nation, to forgive me for my joke. I suffered enough every time I played, I told them, and penance was awaiting me on each tee.”

From Lee Sallows:

(Thanks, Lee!)

That is a simple rule, and easy to remember. When I, a thoughtful and unblessed Presbyterian, examine the Koran, I know that beyond any question every Mohammedan is insane; not in all things, but in religious matters. When a thoughtful and unblessed Mohammedan examines the Westminster Catechism, he knows that beyond any question I am spiritually insane. I cannot prove to him that he is insane, because you never can prove anything to a lunatic — for that is a part of his insanity and the evidence of it. He cannot prove to me that I am insane, for my mind has the same defect that afflicts his. All Democrats are insane, but not one of them knows it; none but the Republicans and Mugwumps know it. All the Republicans are insane, but only the Democrats and Mugwumps can perceive it. The rule is perfect: in all matters of opinion our adversaries are insane.

— Mark Twain, Christian Science, 1907

Putting mercury in contact with an aluminum plate has some surprising consequences (2:05).

Joe invents a time machine. He travels back in time and meets Emily, and they have a child, Bill. Bill grows up, meets Carol, and has a child, Joe. Joe grows up and invents a time machine, and so on.

Joe and Bill are each the other’s father and son, and each man is his own grandfather.

From Dave Morice’s Alphabet Avenue, 1997. See “Proof That a Man Can Be His Own Grandfather” and Oedipus Wrecked. Robert Heinlein’s 1959 story “‘–All You Zombies–‘” is even more confusing.

When Charles Dickens was editing Household Words, a young writer named Laman Blanchard submitted an interminable poem titled “Orient Pearls at Random Strung.”

Dickens mailed it back with a note: “Dear Blanchard, too much string — Yours, C.D.”

Antique dealer Leopoldo Franciolini (1844–1920) was so prolific in creating fraudulent musical instruments that scholars are still trying to sort out the confusion he left behind. The modern stewards of Frederick Stearns’ collection write:

In this case, we have an Alto Clarinet in F. … It is a composite instrument with four sections: two are leather-covered maple, … the barrel appears to have been purloined from a bass clarinet … the bell from an oboe. The mouthpiece appears to be re-purposed from a bass clarinet. … The simultaneous crudeness and creativity demonstrated in [Franciolini’s] catalogue is greatly entertaining. More troubling, however, is the shadow cast upon the flawed judgment of Frederick Stearns in his last years of collecting.

The catalog description of a harpsichord in the Stearns collection reads, “One could say that it is the only surviving instrument ever crafted by the maker Rigunini, however, given that not a single person by the name of Rigunini ever seems to have drawn breath, we might assume that Franciolini invented the name and forged the date.”

When the FDA ordered Ilario Fabbrini to recall 29,188 frozen cheese and mushroom pizzas in 1973, fearing a botulism outbreak, the Michigan pizza magnate went them one better: He buried the pies ceremonially in an 18-foot hole before a crowd of hundreds, including Michigan governor William Milliken.

“I admire your spunk and your spirit,” Milliken told him. “You are an example for businessmen all over the country who are facing tough problems. You are fighting back and I’m sure you will succeed.”

Fabbrini had hoped to make a virtue of necessity, giving up the pizzas but gaining at least some publicity and goodwill in the process. The recall was the largest of its kind to date in American history.

Unfortunately the FDA later ruled out botulism, which meant that the whole escapade had been needless.

Fabbrini sued his suppliers and eventually won the case, but Papa Fabbrini Pizzas went out of business in the early 1980s.

The Rev. John Dobson’s 1815 Elements of Geometry contains no stops except for a period at the end of each paragraph.

In writing a sketch of Dobson’s life, Augustus De Morgan omitted the punctuation.

“He would not stop for any one,” he wrote. “Why should I stop for him?”

armisonous
adj. resounding with arms

The Battle of the Somme began with a weeklong artillery bombardment in which more than a million shells were fired at the German lines. A soldier describes the first day:

The sound was different, not only in magnitude but in quality, from anything known to me. It was not a succession of explosions or a continuous roar; I at least, never heard either a gun or a bursting shell. It was not a noise; it was a symphony. And it did not move. It hung over us. It seemed as though the air were full of vast and agonized passion, bursting now with groans and sighs, now into shrill screaming and pitiful whimpering … And the supernatural tumult did not pass in this direction or in that. It did not begin, intensify, decline and end. It was poised in the air, a stationary panorama of sound, a condition of the atmosphere, not the creation of man.

At the Battle of Messines in June 1917, 19 mines comprising 600 tonnes of explosives were detonated, producing the largest man-made explosions in history to that date. One witness recalled that the “earth rocked as though a giant hand had roughly shaken it.”

(John Ellis, Eye-Deep in Hell, 1989, via Joy Damousi et al., eds., Museums, History and the Intimate Experience of the Great War, 2020.)

On June 17, 1794, Charles-Henri Sanson, high executioner of the First French Republic, guillotined more than 50 “conspirators” in 28 minutes, including an 18-year-old girl who seemed so fragile that “a tiger would have pitied her.” That night he wrote in his diary: Terrible day. The guillotine devoured 54. My strength went, my heart failed me. That evening, sitting down to dinner, I told my wife that I could see spots of blood on my napkin. … I don’t lay claim to any sensibility I don’t possess: I have seen too often and too close up the sufferings and death...

A problem from the National Bank of New Zealand Competition 2000, via Crux Mathematicorum, November 2006: Humanity is visited by three alien races, the Kweens, the Ozdaks, and the Merkuns. Kweens always speak the truth, and Ozdaks always lie. In any group of aliens, a Merkun never speaks first; when it does speak, it tells the truth if the previous statement was a lie and lies if the previous statement was truthful. The three alien races can tell one another apart, but to humans they all look the same. A delegation of three aliens visits Earth. At least one of...

Linguist John Quijada designed the experimental language Ithkuil to permit “maximal communication in the most efficient manner”: Cognition processes far more information than natural languages typically express, and natural languages are full of vagueness and ambiguity; Ithkuil tries to express deep levels of cognition precisely while making the speaker’s intent clear. The results can be striking. The 19-word English phrase “On the contrary, I think it may turn out that this rugged mountain range trails off at some point” can be expressed in two words in Ithkuil. And the passage above reads “As our vehicle leaves the ground and plunges...

[My brother Michael] remembered that I (then between four and five years old) was greatly concerned with petty consistency as the story unfolded, and that on one occasion I interrupted: ‘Last time, you said Bilbo’s front door was blue, and you said Thorin had a golden tassel on his hood, but you’ve just said that Bilbo’s front door was green and that Thorin’s hood was silver’, at which my father muttered ‘Damn the boy’, and then strode across the room to his desk to make a note.

— Christopher Tolkien, recalling a series of Christmas readings in the late 1920s in which The Hobbit took shape, quoted in Christina Scull and Wayne G. Hammond, The J.R.R. Tolkien Companion and Guide: Reader’s Guide, 2006

Entries in the keyword index of C. Bernard Ruffin’s Last Words (1995), a collection of the final utterances of famous people:

bored: I’m b. 98; I am b. of it all 393
comfortable: I am c. 154; perfectly c. 307; very c. 549; quite c. 752; most c. and pleasant life 873; c. enough to die 1223
cry/crying: don’t c. 498, 712, 1397; you mustn’t c. 654; nothing to c. about 654; do not c. 957; why are you c. 1152; you’re not c. 1648; you cannot c. 1651; departed with a sad c. 1700
damn/damned: d. it! 463, 883; can’t see a d. thing 580; God d. it! 645, 814; God d. the whole friggin’ world 645; God d. you! 719, 733; lot of d. foolery! 907; so d. much left 1137; a god-d. hotel room 1398; your d. lies 1443; all the d.-fool things you do 1469; I’m so d. tired 1623; God d. 1836; d. tired 1858; take the d. thing away 1960
dark: why is it so d. 352; too d. 493, 1425; leap in the d. 898; the d. way of the Church 936; life is d. to me 1192; laboring from daylight to d. 1251; long, d. road 1428; d. o’er the way 1499; go home in the d. 1509
grieve: do not g. for me 46; it is wrong to g. about it 10; don’t g. 146; do not g. 207, 1453; g. not for my death 592; why should you g., daughter 899
sad: s. that I have to leave 118; you mustn’t be s. 654; it’s s. to live on a Monday 1535; parted with a s. cry 1700
worry: don’t w. about me 194; don’t w. 455, 777, 1515; I am not w. 782; do not w. 795; does not w. me at all 1152; nothing to w. about 1167 that does not w. me 1418; don’t you w. about anything 1727

Minutes before his death, retired Supreme Court justice Felix Frankfurter told an aide visiting him in the hospital, “I hope I don’t spoil your Washington’s birthday.”

When the 15th-century Benedictine abbot Johannes Trithemius died in 1516, he left behind a three-volume work that was ostensibly about magic — specifically, how to use spirits to send secret messages over distances. Only when the Steganographia and its key were published in 1606 did it become clear that it was really a book of ciphers — the “incantations” were encrypted instructions for concealing secret messages in letters sent between correspondents. Books I and II were now plain enough, but Book III remained mysterious — it was shorter than the first two books, and its workings were not mentioned in...

While we’re at it … in 1973 attorney Mark M. Orkin compiled Canajan, Eh?, a lexicon of Canadian English, which he says is distinguished by “a nimiety of neologisms, an impudicity of pronunciation, a crapulence of grammar, a prurience of syntax, and a necrosis of Mare Canisms”:

ardic: the far north, home of the Esk Moze
beinck: a building where Canajans keep their money
dodder: a female child
fishle: duly authorized
gradge: a building for storing or repairing automobiles
hiss tree: study of past events
Knighted States: the Mare Can nation
Pam Sundy: the Sunday before Easter
quorpus: fifteen minutes past the hour
sign tist: person well-versed in a branch of signs
slong: the principal Canajan salutation on parting
Tronna: the cabbidal of Untario
worsh: to cleanse oneself or one’s clothing
zmarra fack: introductory verbal aid

In his introduction, Orkin writes that “forners need exercise no caution in using this text since all terms discussed will be understandable by somebody somewhere in Canada.” He published a companion volume, French Canajan, hé?, in 1975.

Also: Australian, Baltimorese, Texan.

In 1913, as festivities were planned for the wedding of Kaiser Wilhelm II’s daughter, Berlin’s Hotel Adlon had to move the Kaiser’s brother-in-law from the fourth floor to the second because the tsar could not ride the elevator:

Russian court protocol governed every step the tsar took and nowhere did it mention an elevator. Thus there were no instructions for how the tsar and his retinue were to behave in such a situation. Should he enter the cab first? Was he permitted to keep his hat on? Who should operate the elevator’s crank? and God knows what else.

The protocol had survived unchanged from the days of Catherine the Great. Catherine, of course, had never ridden an elevator for the simple reason that there weren’t any back then, and that’s why the protocol contained not one word about this means of vertical transportation. … At any rate, an apartment on the second floor was prepared for Duke Ernst Gunther zu Schleswig-Holstein.

From Andreas Bernard, Lifted: A Cultural History of the Elevator, 2014.

This just caught my eye — in Beyond Dance, her 2001 account of Hungarian choreographer Rudolf Laban’s late career in industrial consulting, Eden Davies quotes a “traditional Spanish proverb”:

High intelligence + high action = leaders of the world
High intelligence + low action = the academics
Low intelligence + low action = those needed to do humble jobs
Low intelligence + high action = these people menace world stability

“He who knows only his own side of the case knows little of that.” — John Stuart Mill

Is this art? It’s a drawing made by Austrian scholar and mystic Rudolf Steiner, who traveled Europe between 1919 and 1924 giving more than 5,000 lectures on “spiritual science,” art, medicine, agriculture, and economics. During the lectures Steiner would draw on the blackboard, and in 1919 his colleague Emma Stolle, apparently realizing the drawings’ value, began placing sheets of black paper over the blackboards in order to capture them. Steiner himself doesn’t seem to have intended the drawings as beautiful, only as vehicles to express his ideas. Here’s the point he was illustrating with the image above, from a lecture...

Three photographers and three cannibals come to a river. The boat can carry only two people at a time. The cannibals will eat any group of photographers that they outnumber (on either side of the river). How can all six people safely cross the river?

| SelectClick for Answer | | --- | | A cannibal and a photographer cross the river together. Then the photographer rows back alone.Now two cannibals cross and one of them returns.Next two photographers cross and one of them returns along with a cannibal.Now two photographers cross and one cannibal returns.Finally two cannibals cross, and one of them returns to pick up the last cannibal.I think this was originally a Mensa puzzle. I found it in James F. Fixx’s Solve It!, from 1978. |

| | | |

For his 2017 book Nabokov’s Favorite Word Is Mauve, statistician and journalist Ben Blatt ran thousands of books through a computer to analyze the particulars of the authors’ use of language. Among many other things, he found that each of these authors uses the indicated phrase in more than half their works:

Jane Austen: “with all my heart”
Ray Bradbury: “at long last”
Tom Clancy: “by a whisker”
William Faulkner: “sooner or later”
George R.R. Martin: “black as pitch”
Herman Melville: “through and through”
Salman Rushdie: “the last straw”
Tom Wolfe: “sinking feeling”

A few other interesting points:

Ernest Hemingway used -ly adverbs only 80 times in 10 novels. By contrast, E.L. James (Fifty Shades of Grey) used 155 instances in three books.
Elmore Leonard used 49 exclamation points per 100,000 words. James Joyce used 1,105.
Chuck Palahniuk uses the word suddenly twice per 100,000 words. J.R.R. Tolkien used it 78 times.
45 percent of American Harry Potter fan fiction used the word brilliant more often than J.K Rowling.
46 percent of Danielle Steele’s opening sentences mention weather. Joseph Conrad, Hemingway, Sinclair Lewis, Toni Morrison, Kurt Vonnegut, and Palahniuk never do this.

In 1970 Dirk Robson offered Krek Waiter’s Peak Bristle, a pronouncing dictionary for visitors to England’s West Country: Armchair: Question meaning “What do they cost?” As in: “Armchair yer eat napples, mister?” Claps: Fall to pieces. Door: Female child. Hard tack: Cardiac failure. Justice Swell: Expression of right and proper behaviour; as in: “No, we dingo way, we stay dome. Justice swell — trained all week.” Rifle: Deserving. Sill Sernt: Government employee. Sunny’s Cool: Bible class for the young. Yerp: The Continent. Examples from the field: News vendor: “Snow end twit! Miniature rout of yes-dees news, yore rupture rise into...

In 1970 Dirk Robson offered Krek Waiter’s Peak Bristle, a pronouncing dictionary for visitors to England’s West Country:

Armchair: Question meaning “What do they cost?” As in: “Armchair yer eat napples, mister?”

Claps: Fall to pieces.

Door: Female child.

Hard tack: Cardiac failure.

Justice Swell: Expression of right and proper behaviour; as in: “No, we dingo way, we stay dome. Justice swell — trained all week.”

Rifle: Deserving.

Sill Sernt: Government employee.

Sunny’s Cool: Bible class for the young.

Yerp: The Continent.

Examples from the field:

News vendor: “Snow end twit! Miniature rout of yes-dees news, yore rupture rise into daze!”

Patron: “Sway lie fizz, knit?”

And:

Woman at bus stop: “Fortify mince we bin stand near! Chews 2B bad, butts pasta joke now.”

Her companion: “Feud Dunce eye sedden walk tome, weed bin thereby now.”

Robson put out a companion volume, Son of Bristle, the following year, “with a special section on the famous Bristle ‘L.'” I’ll see if I can find that.

Suppose a 5 × 9 rectangle is partitioned into a set of 10 rectangles with integer dimensions. How can we prove that some two of these smaller rectangles are congruent?

| SelectClick for Answer | | --- | | List all the possible rectangles in the set in order of increasing area:{1 × 1, 1 × 2, 1 × 3, 1 × 4, 2 × 2, 1 × 5, 1 × 6, 2 × 3, 1 × 7, 1 × 8, 2 × 4, …}These have areas, respectively, of {1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, …}. If all the 10 small rectangles had different areas, then their minimum total area would be 1 + 2 + 3 + 4 + 4 + 5 + 6 + 6 + 7 + 8 = 46, which is greater than that of the larger rectangle in which they must fit (5 × 9 = 45). So some duplication is unavoidable.From Quantum, via Ross Honsberger’s Mathematical Delights, 2019. |

| | | |

Pyrrho the philosopher being one day in a boat in a very great tempest, shewed to those he saw the most affrighted about him, and encouraged them, by the example of a hog that was there, nothing at all concerned at the storm. Shall we then dare to say that this advantage of reason, of which we so much boast, and upon the account of which we think ourselves masters and emperors over the rest of all creation, was given us for a torment? To what end serves the knowledge of things if it renders us more unmanly? if we thereby lose the tranquillity and repose we should enjoy without it? and if it put us into a worse condition than Pyrrho’s hog? Shall we employ the understanding that was conferred upon us for our greatest good to our own ruin; setting ourselves against the design of nature and the universal order of things, which intend that every one should make use of the faculties, members, and means he has to his own best advantage?

— Montaigne, “That the Relish for Good and Evil Depends in Great Measure Upon the Opinion We Have of Them,” 1580

arrident
adj. pleasant

agrised
adj. terrified

presentific
adj. causing something to be present in the mind

cacology
n. a bad choice of words

Shortly after physicist Anthony French joined the MIT faculty in 1962, he was asked to teach an introductory mechanics course to hundreds of freshmen.

“I wanted to be cautious about giving it a name,” he said. “So I called it, blandly, ‘Physics: A New Introductory Course.’

“I couldn’t imagine how I could have been so stupid. The students read that as ‘PANIC’ … it was known forever afterwards as the PANIC course.”

Imagine a set of people all living in the same building. Half of them think it is a hotel, the other half think it is a prison. Those who think it a hotel might regard it as quite intolerable, and those who thought it was a prison might decide that it was really surprisingly comfortable. So that what seems the ugly doctrine is one that comforts and strengthens you in the end. The people who try to hold an optimistic view of this world would become pessimists: the people who hold a pretty stern view of it become optimistic. —...

Items that fell forward during the last moments of the Titanic, listed in Walter Lord’s A Night to Remember, 1955: 29 boilers 800 cases of shelled walnuts 15,000 bottles of ale and stout 30 cases of golf clubs and tennis rackets 30,000 fresh eggs 5 grand pianos a 50-phone switchboard 8 dozen tennis balls a jeweled copy of the Rubáiyát of Omar Khayyám 2 reciprocating engines a 1912 Renault Type CB Coupe de Ville Also tons of coal, a cask of china intended for Tiffany’s, dozens of potted palms, innumerable shuffleboard sticks, “tumbling trellises, ivy pots and wicker chairs in...

Okay, that’s enough of that.

A late, beautiful contribution by Lee Sallows: See “Extra Magic” Realized. (Thanks, Lee!)

After 17 years, I think I’m going to take a bit of a break for a little while. I may post irregularly while I decide whether to continue. In the meantime the blog archive and the podcast are still available. Thanks, as always, for reading! Greg P.S. Wow, thanks for all your kind messages! There are too many to respond to, but I’m reading every one. Thanks again!

A puzzle by Mel Stover: Move the minus sign to make an expression equivalent to nine fifty. (If you sense a trick, you’re right.)

Literary scholar Robert Hauptman calls this “marginal emendation run amok” — it’s a page from Henry James’ 1877 novel The American as James revised it anxiously for a new edition in 1907. He had decided the plot was unconvincing and asked for so many changes that two copies of the book had to be inlaid page by page on larger sheets to give him room to mark all the revisions. On the last page, above, “James has partially or fully crossed out 16 of the 19 lines and rewritten the text for the definitive New York edition in the margins...

By Éric Angelini. A regular chess game reached this position after Black’s fifth move. Four pieces have moved. Which ones?

This is interesting — in order for a simple arch to stand, its shape when inverted must fit into the limits described by a hanging chain (a catenary). Spanish Catalan architect Antoni Gaudí followed this principle in designing some of his buildings — he created inverted models and let the shapes of hanging chains or weighted strings determine the shapes of the arches.

In the early 1940s a curious question began to circulate among the members of the Princeton physics department. An ordinary lawn sprinkler like the one shown here would turn clockwise (in the direction of the long arrow) as its jets ejected water (short arrows). If you reversed this — that is, if you submerged the sprinkler in a tank of water and induced the jets to suck in the fluid — would the sprinkler turn in the opposite direction? The problem is associated with Richard Feynman, who was a grad student at the time (and who destroyed a glass container...

During a visit to a club in 1775, Samuel Johnson was observed to put several Seville oranges into his pocket after squeezing their juice into a drink he’d made for himself. The friends who saw this “seemed to think that he had a strange unwillingness to be discovered.” Visiting Johnson the next morning and seeing the orange peels scraped and cut into pieces on a table, James Boswell asked about them: JOHNSON. ‘I have a great love for them.’ BOSWELL. ‘And pray, Sir, what do you do with them? You scrape them it seems, very neatly, and what next?’ JOHNSON....

A thought-provoking piece of nonsense by Russian absurdist poet Daniil Kharms: Philosopher! I am writing to you in answer to your letter which you are about to write to me in answer to my letter which I wrote to you. A violinist bought a magnet and was carrying it home. Along the way, hoods jumped him and knocked his cap off his head. The wind picked up the cap and carried it down the street. The violinist put the magnet down and ran after the cap. The cap fell into a puddle of nitric acid and dissolved. In the meantime,...

Part of New York is standing still. In 1978, artist Alan Sonfist reclaimed a rubble-strewn lot on the corner of West Houston Street and La Guardia Place in Greenwich Village and re-established the vegetation, soil and rock formations that had existed there before the Western settlers arrived. “As in war monuments that record the life and death of soldiers, the life and death of natural phenomena such as rivers, springs and natural outcroppings need to be remembered,” he wrote in a 1968 manifesto proposing the project. Interestingly, he’d hoped to do even more than this: “On Canal Street I propose...

I don’t know whether this is contrived or whether a student offered it on an actual exam — Ed Barbeau presented “this little beauty of a howler” in the January 2002 College Mathematics Journal, citing Ross Honsberger of the University of Waterloo in Ontario.

In his Harmonices Mundi of 1619, Johannes Kepler wrote, “The heavenly motions are nothing but a continuous song for several voices, to be perceived by the intellect, not by the ear; a music which, through discordant tensions, through syncopations and cadenzas as it were, progresses toward certain pre-designed six-voiced cadences, and thereby sets landmarks in the immeasurable flow of time.” In 1979 Yale geologist John Rodgers and musician Willie Ruff scaled up the frequencies of the planetary orbits into the range of human hearing so that Kepler’s “harmony of the world” could become audible: Mercury, as the innermost planet, is...

In The Interpretation of Dreams, Freud recalls “the defensive argument of a man who was accused by his neighbour of having returned a kettle to him in a damaged condition”: In the first place, he said, he had returned the kettle undamaged; in the second, it already had holes in it when he borrowed it; and thirdly, he had never borrowed the kettle from his neighbour at all. “But so much the better,” Freud notes. “If even one of these three methods of defence is recognised as valid, the man must be acquitted.”

Lewis Carroll and Alfred, Lord Tennyson, became improbable acquaintances in the 1850s, a few years before Carroll published Alice’s Adventures in Wonderland. The young author sent a letter to his cousin, May 11, 1859, after one memorable visit to the laureate: Tennyson told us that often on going to bed after being engaged on composition he had dreamed long passages of poetry (‘You, I suppose,’ turning to me, ‘dream photographs?’) which he liked very much at the time, but forgot entirely when he woke. One was an enormously long one on fairies, where the lines from being very long at...

The land speed record for a petrol-powered rail vehicle was set way back in 1931, when aircraft engineer Franz Kruckenberg experimented with a “rail zeppelin” on German railway lines. An aircraft engine drove a rearward-facing propeller to accelerate a lightweight aluminum body to the startling speed of 230.2 km/h (143.0 mph), a railway record that held until 1954. The vehicle evolved over a few years but was eventually dropped in favor of other high-speed designs.

In Jane Austen’s Pride and Prejudice, the residents of Longbourn consider Mr. Darcy arrogant, proud, and conceited because of his reactions to village people. Of Elizabeth Bennet he says, “She is tolerable; but not handsome enough to tempt me; and I am in no humour at present to give consequence to young ladies who are slighted by other men.” Later, when she spurns his proposal, he tells her directly, “Nor am I ashamed of the feelings I related. They were natural and just. Could you expect me to rejoice in the inferiority of your connections? To congratulate myself on the...

In medieval chess, each of the eight pawns was associated with a commoner’s occupation. From king rook pawn to queen rook pawn: Laborer (farmer) Smith Notary Merchant Physician Innkeeper City watchman or guard Ribald or town courier The merchant stood before the king, the doctor before the queen. Jacopo de Cessolis used the game as the basis for a series of sermons on morality — he says that a philosopher invented the game to show his cruel king “the maners and conditicions of a kynge of the nobles and of the comun people and of theyr offices and how they...

A curious puzzle by Dartmouth mathematician Peter Winkler: You’ve just joined the Coin Flippers of America, and fittingly the amount of your dues will be decided by chance. You’ll name a head-tail sequence of length 5, and then a coin will be flipped until that sequence appears in five consecutive flips. Your dues will be the total number of flips in U.S. dollars; for instance, if you choose HHHHH and it takes 36 flips to produce a run of five heads, then your annual dues will be $36. What sequence should you pick? At first it seems that it shouldn’t...

An observation by Oxford University mathematician Nick Trefethen: A student leaves university in America with a transcript full of information. Even with grade inflation, there are thirty marks of A or A- or B+ or B to look at, each one attached to a different course like Advanced Calculus or 20th Century Philosophy or Introduction to Economics. Grade-point averages are constructed from these transcripts and reported to three digits of accuracy. An Oxford graduate finishes with no transcript, just a degree result which may be a First, a II.1, a II.2, a Third, a Pass, or a Fail. Failures are...

There are 12 people in a room. Some always tell the truth, and the rest always lie. #1 says, “None of us is honest.” #2 says, “There is not more than 1 honest person here.” #3 says, “There are not more than 2 honest people here.” #4 says, “There are not more than 3 honest people here.” #5 says, “There are not more than 4 honest people here.” #6 says, “There are not more than 5 honest people here.” #7 says, “There are not more than 6 honest people here.” #8 says, “There are not more than 7 honest people...

Prague artist Robert Barta’s installation Crossing Half a Million Stars consists of 500,000 ball bearings covering the floor of a room. The visitors themselves create a spontaneous performance as they try to make their way across it.

A puzzle by Henry Dudeney: ‘There’s a mouse in one of these barrels,’ said the dog. ‘Which barrel?’ asked the cat. ‘Why, the five-hundredth barrel.’ ‘What do you mean by the five-hundredth? There are only five barrels in all.’ ‘It’s the five-hundredth if you count backwards and forwards in this way.’ And the dog explained that you count like this: 1 2 3 4 5 9 8 7 6 10 11 12 13 So that the seventh barrel would be the one marked 3 and the twelfth barrel the one numbered 4. ‘That will take some time,’ said the cat,...

In 1913 Canadian politician Sam Hughes proposed the MacAdam Shield Shovel, a spade that could double as a protective shield in the trenches — it was provided with a hole through which a soldier could survey the enemy. Some 20,000 had been manufactured before it was discovered that the blade was not remotely bulletproof, and it wasn’t much use as a shovel … because there was a hole in it.

Early experimenters in electricity sometimes dealt in frogs’ thighs. Dissecting a frog creates an “injury potential” in its muscles, which can then be arranged in series to produce a kind of biological battery. Carlo Matteucci strung together 12 to 14 half-thighs to make a “frog battery” strong enough to decompose potassium iodide; he was able to induce some effect even with living frogs. Matteucci did similar work with eel, pigeon, and rabbit batteries. In 1803 Giovanni Aldini used a galvanoscope made of frogs to detect current in a circuit that ran from an ox’s tongue to its ear through Aldini’s...

This map shows mountain symbols above a river symbol. Suppose that, in the part of the world that the map represents, there really are mountains in the location that the map indicates. But suppose that there are also mountains on the other side of the river — where no mountains are indicated on the map. Would we say that the map is inaccurate? People tend to say yes — in general, if a marker appears on a map, then we tend to think that the absence of the marker reflects an absence of that feature from the corresponding location. But...

The town of Bozouls in the south of France sits at the edge of a horseshoe-shaped canyon 300 feet deep, the product of 2 million years of erosion of the region’s limestone plateau by rivers and glaciers. Because the outcrop at the center of the horseshoe is accessible only from the south, it makes an ideally defensible position, and a castle was built there in the 9th century, of which only ruins remain. In medieval times guards in towers monitored the approach 24 hours a day. One historic building still survives: The 12th-century St. Faustus church sits right on the...

Typographer John Langdon created this pleasingly ornate ambigram in 2005. It reads the same upside down. More at his site.

On a dry summer day in California, physicist Julius Sumner Miller was driving slowly near the desert when a friend overtook him on the left. The friend’s wife, in the passenger seat, reached out to hand him a package of gum. Their hands were no less than 3 inches apart when “a terrific discharge took place which possessed the classical physiological effects. The shock was momentarily disabling, as a three-inch spark in air can well be.” Miller published an inquiry about this in the American Journal of Physics and received a reply from R.F. Miller of B.F. Goodrich in Ohio....

The Treaty of Versailles contains a macabre clause: ARTICLE 246. Within six months from the coming into force of the present Treaty, … Germany will hand over to His Britannic Majesty’s Government the skull of the Sultan Mkwawa which was removed from the Protectorate of German East Africa and taken to Germany. Mkwawa was a tribal leader in German East Africa who opposed colonization. After his defeat in battle, the Germans had sent his skull to Berlin. When the United Kingdom inherited the colony after World War I, the British sought to return the skull to the Wahehe people, but...

A poignant little detail I found in Jay Scarfone and William Stillman’s The Wizardry of Oz: For the 1939 film version of The Wizard of Oz, MGM designated a flying monkey named Nikko to serve as the Wicked Witch’s familiar. Unlike the other monkeys, Nikko has very small wings. An early script, dated July 5, 1938, explains that the Witch had clipped his wings to ensure his servitude. In that script, it’s Nikko who presses the water bucket into Dorothy’s hands at the critical moment.

A problem by Russian mathematician Vyacheslav Proizvolov: At a party each girl danced with three boys, and each boy danced with three girls. Prove that the number of girls at the party was equal to the number of boys.

The ACLU found John Scopes by running a newspaper ad seeking a teacher willing to test the law about teaching human evolution in the classrooms of Tennessee. From the May 4, 1925, edition of the Chattanooga Times: We are looking for a Tennessee teacher who is willing to accept our services in testing this law in the courts. Our lawyers think a friendly test case can be arranged without costing a teacher his or her job. Distinguished counsel have volunteered their services. All we need now is a willing client. Scopes wasn’t a biology teacher but had filled in for...

As the 19th century advanced, the White House began to seem increasingly cramped. In 1889, the centennial of the U.S. presidency, First Lady Caroline Harrison suggested adding an art wing to the east and an administrative wing to the west, with glass-enclosed palm gardens, plant conservatories, and a lily pond completing the quadrangle, creating a private inner courtyard (top). Congress shot it down. In 1900 Army engineer Colonel Theodore Bingham offered his own plan, which would add a massive two-story cylindrical wing at each flank, with domes and lanterns patterned after those at the Library of Congress (middle and bottom)....

Carved into the brickwork of a cylindrical tower at Cambridge University’s New Museums Site is a great crocodile. It was commissioned by Pyotr Kapitza, who had moved to Cambridge from Russia expressly to work with Ernest Rutherford, the father of nuclear physics. Kapitza called his mentor “crocodile,” a title that Russians traditionally confer on great men (and also, Kapitza said, because Rutherford’s thunderous voice announced his approach, just as the crocodile in Peter Pan was announced by the ticking watch in its belly). Eric Gill carved the animal into the side of the Mond Laboratory, which was erected in 1933...

Amazingly, the notion of a black hole was first posited in 1783, by the English natural philosopher John Michell. In a paper read before the Royal Society that November, he wrote: Let us now suppose the particles of light to be attracted in the same manner as all other bodies with which we are acquainted; that is, by forces bearing the same proportion to their vis inertiae (or mass), of which there can be no reasonable doubt, gravitation being, as far as we know, or having any reason to believe, an universal law of nature. … [I]f the semi-diameter of...

Biologist and mathematician D’Arcy Thompson advanced a strange new idea in his 1917 book On Growth and Form: He found that if you draw the outline of an animal or plant on an ordinary Cartesian grid, and then you put the grid through some mathematical transformation (stretching it, for example, so that its squares become rhombuses), very often the resulting shape is that of a related real creature. What can that mean? Thompson doesn’t really say. He thought that the biologists of his day overemphasized evolution in explaining the form and structure of living things; he preferred to look for...

A problem by Raymond Smullyan. The diagram above shows the final position in a chess game in which nothing has moved from a white square to a black one or vice versa. One piece has been omitted from the diagram. What color is the square that it stands on?

Card expert John Scarne tells the story of an elderly, distinguished gentleman, apparently slightly inebriated, who one night began observing the play at a Houston roulette table. Presently he began to complain about how unlucky he was. “What do you mean, unlucky?” the croupier asked. “Number 32 just won, didn’t it?” the man said. “Yes, but you didn’t have a bet down,” said the croupier. “What’s unlucky about that?” “Oh, yes, I did,” the man said. “I made a $10 mind bet on 26 and lost!” He gave the croupier a $10 bill. “I always pay my losses,” he said,...

I just liked this: When Augustus Saint-Gaudens broke an engagement with Mark Twain, he sent him this wordless apology. (From Albert Bigelow Paine’s 1912 biography of Twain.)

In a 1978 article in the New England Journal of Medicine, Massachusetts General Hospital psychiatrist James E. Groves categorized the patients “whom most physicians dread”: “Dependent clingers” escalate from normal requests for reassurance to “repeated, perfervid, incarcerating cries for explanation, affection, analgesics, sedatives and all forms of attention imaginable.” They may have severe, even life-threatening disorders, or they may have no discernible illness at all. “Entitled demanders” use “intimidation, devaluation and guilt-induction to place the doctor in the role of the inexhaustible supply depot.” They may even try to control the doctor by withholding payment or threatening to sue. “Manipulative...

A Slander traveling rapidly through the land upon his joyous mission was accosted by a Retraction and commanded to halt and be killed. ‘Your career of mischief is at an end,’ said the Retraction, drawing his club, rolling up his sleeves and spitting on his hands. ‘Why should you slay me?’ protested the Slander. ‘Whatever my intentions were, I have been innocuous, for you have dogged my strides and counteracted my influence.’ ‘Dogged your grandmother!’ said the Retraction, with contemptuous vulgarity of speech. ‘In the order of nature it is appointed that we two shall never travel the same road.’...

In 1880 Charles Hinton (inventor of the baseball gun) turned his attention to the fourth dimension, that unseen world whose behavior seems so baffling to ordinary thinkers. In his 1888 book A New Era of Thought, he announced a unique way to think about it, a set of 81 colored cubes that correspond to the 81 parts of a 3 × 3 × 3 × 3 hypercube. By creating a set of wooden cubes, painting them according to Hinton’s instructions, and working through the prescribed exercises, the reader could learn to visualize the fourth dimension as intuitively as the third:...

A puzzle by Henry Dudeney: When visiting with a friend one of our hospitals for wounded soldiers, I was informed that exactly two-thirds of the men had lost an eye, three-fourths had lost an arm, and four-fifths had lost a leg. ‘Then,’ I remarked to my friend, ‘it follows that at least twenty-six of the men must have lost all three — an eye, an arm, and a leg.’ That being so, can you say exactly how many men were in the hospital? It is a very simple calculation, but I have no doubt it will perplex a good many...

Here’s a striking sign of the pervasive influence of the Industrial Revolution: It darkened England’s moths. Before 1811, the peppered moth, Biston betularia, had a white body. But as soot darkened trees, lighter-bodied insects became more visible to birds and other predators. By 1848 the frequency of dark-bodied moths in industrial regions had increased dramatically, one of the first documented instances of Darwin’s principle of natural selection. American geneticist Sewall Wright called it “the clearest case in which a conspicuous evolutionary process has actually been observed.” Somewhat related: A curious wartime observation by Gertrude Stein, in Alsace, from The Autobiography...

“Perchance the best chance of reproducing the ancient Greek temperament would be to cross the Scots with the Chinese.” — Hugh McDiarmid

In 1837 English journalist Albany Fonblanque wrote, “Sir Robert Peel was a smooth round peg, in a sharp-cornered square hole, and Lord Lyndenurst is a rectangular square-cut peg, in a smooth round hole.” Which of these is the better fit? In other words, which is larger, the ratio of the area of a circle to a circumscribed square, or the area of a square to a circumscribed circle? In two dimensions, these ratios work out to π/4 and 2/π, respectively, so a round peg fits better into a square hole than a square peg into a round hole. But, strangely,...

The wordplay journal Word Ways has made a tradition of revising the familiar rhyme “Mary Had a Little Lamb” under various constraints. Some examples: Alliteration: James Puder, WW February 1998 Astral Aries’ avatar, alabaster “Aly,” Ann adopted; allies are Ann and Ann’s argali. Ann, an able autodidact, academic angst avoids; And arch Aly’s Argus-eyed act awes astonished anthropoids. Pangram (uses all 26 letters): A. Ross Eckler, WW February 1989 Mary had a little lamb with fleece extremely white; Instead of grazing, all alone, the lamb kept her in sight. It followed her to school one day, which was against the...

Nominative determinism is the theory that people gravitate toward occupations that reflect their names. In 1994 New Scientist noted that a new book, Pole Positions: The Polar Regions and the Future of the Planet, had been written by one Daniel Snowman, and that another, London Under London: A Subterranean Guide, received just two weeks later, had been written by Richard Trench. Psychologist Jen Hunt of the University of Manchester pointed out an article on incontinence in the British Journal of Urology whose authors were A.J. Splatt and D. Weedon. If the theory is valid, then the naming of children is...

A man goes into a 7-11 store, buys four items, and notices that the bill totals $7.11. Even more interestingly, the product of the four prices is 7.11. What are the prices? The answer is $1.20, $1.25, $1.50, and $3.16. There’s no thunderbolt insight to find; the problem yields to patient consideration. Who came up with it? The most common credit I’ve seen is Doug Brumbaugh of the University of Central Florida. I found it in Crux Mathematicorum; see problem M203 in the September 2006 issue for Richard K. Guy’s solution.

When a high voltage difference is applied, a liquid bridge of deionized water can sustain itself between two beakers even when they’re separated by 25 millimeters. British engineer William Armstrong first reported this in an 1893 lecture. The phenomenon is known to be founded in surface polarization, but it’s still not completely understood.

“The usual Attic dinner consisted of two courses, the first a kind of porridge, and the second a kind of porridge.” — Alfred Zimmern

On Feb. 23, 1950, a railroad signal worker discovered the badly mangled body of a man in a tunnel south of Salzburg, Austria. Among its torn clothes police found the diplomatic passport and service identification of U.S. Navy captain Eugene S. Karpe, who’d been returning to the United States after serving for three years as naval attaché in Rumania. It appeared that Karpe had fallen from the door of the Arlberg-Orient Express as the train sped around a curve in the dark of night. The train car had very small windows, and the doors had been locked automatically before the...

Postscript of a letter from Benjamin Franklin to the Abbé André Morellet, July 1779: P.S. To confirm still more your piety and gratitude to Divine Providence, reflect upon the situation which it has given to the elbow. You see in animals, who are intended to drink the waters that flow upon the earth, that if they have long legs, they have also a long neck, so that they can get at their drink without kneeling down. But man, who was destined to drink wine, is framed in a manner that he may raise the glass to his mouth. If the...

This just caught my eye in an old issue of the Mathematical Gazette, a note from P.G. Wood. Suppose we’re designing a cylinder that’s closed at both ends and must encompass a given volume. What relative dimensions should we give it in order to minimize its surface area? A young student thought, well, if we slice the cylinder with a plane that passes through its axis, the plane’s intersection with the cylinder will form a rectangle. And if we spin that rectangle, it’ll sweep out the surface area of the cylinder. So really we’re just asking: Among all rectangles of...

Advice in problem solving: “You must always invert.” — Carl Gustav Jacob Jacobi “Whenever you can, count.” — Francis Galton “Each problem that I solved became a rule, which served afterwards to solve other problems.” — Descartes “By studying the masters, not their pupils.” — Niels Henrik Abel “Truth is the offspring of silence and meditation. I keep the subject constantly before me and wait ’til the first dawnings open slowly, by little and little, into a full and clear light.” — Isaac Newton

Twice widowed, English artist Mary Delany (1700-1788) took up a remarkable new career in her 70s: She created a series of detailed and botanically accurate portraits of plants, devising them from tissue paper and coloring them by hand: With the plant specimen set before her she cut minute particles of coloured paper to represent the petals, stamens, calyx, leaves, veins, stalk and other parts of the plant, and, using lighter and darker paper to form the shading, she stuck them on a black background. By placing one piece of paper upon another she sometimes built up several layers and in...

Here’s one way to end a composition: Johann Jakob Froberger’s Suite II in C major, Lamento sopra la dolorosa perdita della Real Msta di Ferdinando IV, Re de Romani, ends with a picture of the clouds of heaven welcoming the soul of Ferdinand IV as it climbs up a scale of three octaves. It was written to lament the death of the King of the Romans in 1654. Elsewhere Froberger had marked the fatal fall of lutenist Charles Fleury down a flight of stairs with a descending scale of two octaves. Perhaps he was just very literal-minded. (From Wilfrid Hodges,...

This sounds apocryphal, but it’s interesting. According to Texas lore, John Higginson, owner of the Memphis, El Paso & Pacific Railroad, faced a problem in the 1860s. He had committed to serve the route between Marshall, Texas, and Shreveport, La., but the Civil War had reduced his stock to three boxcars. How could he maintain regular service between two cities 40 miles apart with no engine? He did it (the story goes) by loading a team of oxen into the first boxcar; freight and passengers into the second car; and the train’s crew and management into the third car. At...

A puzzle by V. Dubrovsky, from Quantum, January-February 1992: In a certain planetary system, no two planets are separated by the same distance. On each planet sits an astronomer who observes the planet closest to hers. Prove that if the total number of planets is odd, there must be a planet that no one is observing.

Here’s one solution to the population problem: In 1967 Buckminster Fuller patented a giant floating geodesic sphere enclosing a city, hoping to reduce the economic and environmental costs of using land for housing. Each sphere would be a mile in diameter, enclosing an enormous volume of air that would be warmed by the sun, enabling it to carry buildings bearing thousands of people. The structural weight of even a half-mile sphere would be a thousandth the weight of the air inside, and heating the air even 1 degree would raise the whole structure like a hot-air balloon. By opening and...

I don’t know why I find this so striking: It’s a diagram that accompanies the article on deer hunting in Denis Diderot’s Encyclopédie. Rather than presenting a single image with a caption, it combines a vignette of a deer hunt with an illustration of the antlers and piles of dung that are dropped by stags of different ages, together with a musical score showing the notes sounded by the hunting party at different stages of the pursuit. “Taken as a whole the hunting plates offer few clues for reading their complex hybrid of imagery and notations as an ensemble,” write...

In his 1946 essay “Politics and the English Language,” George Orwell “translates” Ecclesiastes 9:11 into “modern English of the worst sort”: I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. Objective consideration of contemporary phenomena compels the conclusion that success or failure in competitive activities exhibits no tendency to be commensurate with innate capacity, but that a considerable element of...

Strategies to memorize π sometimes rely on devising a sentence with words of representative lengths. Isaac Asimov offered this one: How I want a drink, alcoholic, of course, after the heavy lectures involving quantum mechanics! Count the letters in each word and you get 3.14159265358979. That’s not the best strategy, though: What shall we do about zero? And it’s hard to reel off the digits impressively for friends when you have to stop and count the letters in each word. Arthur Benjamin, a mathematician at Harvey Mudd College, suggests using a phonetic code instead: 1 = t or th or...

Samuel Pepys wrote his famous diary in shorthand, but he took a further precaution when writing about his amorous adventures — he adopted words based on Spanish, French, and Italian: “I did come to sit avec [with] Betty Michell, and there had her main [hand], which elle [she] did give me very frankly now, and did hazer [make] whatever I voudrais avec l’ [would have with her], which did plaisir [pleasure] me grandement [greatly].” “The garbled foreign phrases he often used for sexual incidents had something to do with concealment perhaps, much more with his pleasure in marking off sexual...

Usain Bolt is such a great sprinter that his distinctions may extend to other worlds. In 2013, University of Leicester physics undergraduate Hannah Lerman and her colleagues determined that the Jamaican athlete was one of the few humans who could get aloft on Saturn’s moon Titan with wings strapped to his arms. Factoring in Titan’s gravity and atmospheric density, Lerman found that a person could take flight in a normal-sized wingsuit only if they could run at 11 meters per second. “This speed has been reached but only by the fastest human runners, for example, Usain Bolt, who ran almost...

In 1993, Greenland issued a 7.25-krone stamp depicting a locally fished crab that it labeled Chionoecetes oiliqo. The stamps were issued first in sheet form, but when they were reissued five months later in an eight-stamp booklet pane, collectors noticed something odd: The crabs’ Latin name had changed to Chionoecetes opilio. What had happened? It turns out that the second name is correct; apparently during production the species name opilio had been mirror-reversed by accident. By a very unlikely coincidence, in the sans-serif typeface used all of its letters reversed into valid counterparts, producing a meaningless word that looked plausibly...

Arthur and Robert are identical twins. One always lies, and the other always tells the truth, but you don’t know which is the liar. One day you meet one of them and want to find out whether it’s Arthur or Robert. But you can ask only one yes/no question, and the question can’t contain more than three words. What question will do? Alternatively, suppose you want to find out whether it’s Arthur or Robert who’s truthful. What three-word yes/no question will reveal the answer?

Argentina had a surprise on July 10, 1945: The German submarine U-530 turned up at Mar del Plata and surrendered. Commander Otto Wermuth said that he’d received orders on May 8 to cease hostilities and proceed to the nearest United Nations port for surrender. He’d thought this was an enemy trick and decided to intern his submarine and crew in a neutral country. He chose Argentina thinking that it had not declared war and turned up there two months after the German surrender. That created a fertile field for speculation that the sub had been transporting Nazi gold or leaders...

A paradox by the German mathematician Martin Löb: Let A be any sentence. Let B be the sentence: ‘If this sentence is true, then A.’ Then a contradiction arises. Here’s the contradiction. B makes the assertion “If B is true, then A.” Now consider this argument. Assume B is true. Then, by B, since B is true, A is true. This argument shows that, if B is true, then A. But that’s exactly what B had asserted! So B is true. And therefore, by B, since B is true, A is true. And thus every sentence is true, which is...

By W. Timbrell Pierce. White to mate in two moves.

“My own opinion is that belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence. The more certitude one assumes, the less there is left to think about, and a person sure of everything would never have any need to think about anything and might be considered clinically dead under current medical standards, where the absence of brain activity is taken to mean that life has ended.” — Robert Anton Wilson

The Statue of Liberty’s disembodied arm stood in Madison Square from 1876 to 1882. It had been agreed that Frédéric Bartholdi would create the statue while the United States paid for the pedestal. Americans were a bit behindhand in offering donations, so Bartholdi sent along the arm and torch to help inspire contributions. It took six years of benefit concerts, auctions, souvenir photos, and other mementos, but the full statue was finally dedicated on Liberty Island on October 28, 1886.

In the January 2001 issue of the College Mathematics Journal, University of Calgary mathematician Jonathan Schaer offers this simple proof that arctan 1 + arctan 2 + arctan 3 = π. The sum of the angles of this large triangle is 180°. And the diagram shows that its lower left angle is arctan 3, its lower right angle is arctan 2, and its top angle is part of an isosceles right triangle. So arctan 1 + arctan 2 + arctan 3 = 180°, or π radians. “No words, even no symbols!” (“Miscellanea,” College Mathematics Journal 32:1, 68-71.)

Actress Ilka Chase married Louis Calhern in 1926, but he divorced her the following year to marry Julia Hoyt. Sorting through her possessions afterward, she discovered a set of engraved calling cards that she’d had printed with the name Mrs. Louis Calhern. “They were the best cards — thin, flexible parchment, highly embossed — and it seemed a pity to waste them, and so I mailed the box to my successor,” she wrote later. “But aware of Lou’s mercurial marital habits, I wrote on the top one, ‘Dear Julia, I hope these reach you in time.’ “I received no acknowledgment.”...

volant adj. engaged in flight espieglerie n. impish or playful behaviour; mischief apopemptic adj. pertaining to leave-taking or departing réclame n. publicity or notoriety In 1953, 61-year-old British ace Christopher Draper flew an Auster monoplane under 15 of the 18 bridges on the Thames, negotiating 50-foot arches at 90 mph. “I did it for the publicity,” he told the press. “For 14 months I have been out of a job, and I’m broke. I wanted to prove that I am still fit, useful and worth employing. … It was my last-ever flight — I meant it as a spectacular swan...

Suppose that your dream-life underwent a remarkable change. Suppose that on going to bed at home and falling asleep, you found yourself to all appearances waking up in a hut raised on poles at the edge of a lake. A dusky woman, whom you realize to be your wife, tells you to go out and catch some fish. The dream continues with the apparent length of an ordinary human day, replete with an appropriate and causally coherent variety of tropical incident. At last you climb up the rope ladder to your hut and fall asleep. At once you find yourself...

On Sept. 8, 1880, an explosion tore through the Seaham Colliery, a coal mine in County Durham in the North of England, filling both shafts with debris and trapping scores of men in the burning seams. Most of the 164 dead were found where they had been working, suggesting that death had come quickly, but some of those farther from the shafts appear to have survived for hours or even longer in pockets of air — the oil in some of their lamps was exhausted. Some of these men had had time to leave messages to those who might find...

Set into the corner of Seventh Avenue and Christopher Street in Manhattan’s West Village is a triangular plaque reading PROPERTY OF THE HESS ESTATE WHICH HAS NEVER BEEN DEDICATED FOR PUBLIC PURPOSES. The “Hess triangle” is a remnant from a property dispute that unfolded here 100 years ago: The city was claiming eminent domain in order to demolish hundreds of buildings and expand the subway, but surveyors overlooked this 65-centimeter triangle, owned by Philadelphia landlord David Hess. Hess, outraged at the loss of his five-story apartment building, refused to donate the triangle to the public and added the plaque as...

John Bevis’ 2010 book Aaaaw to Zzzzzd: The Words of Birds collects the nonsense words that birders have invented to try to convey bird calls and songs: ag ag ag ag arr: fulmar beesh: scaled quail bek bek bek: red-throated loon chack-weet weet-chack: northern wheater djadjadja: twite ee woomp: bittern hup-hup-a-hwooo: red-billed pigeon kakakowlp-kowlp: yellow-billed cuckoo kuk-kuk-cow-cow-cow-cowp-cowp: pied-billed grebe quickquickquickquick: cuckoo seedle seedle seedle chup chup: hermit warbler tiutiu-tiutiutiuk-swee: yellowhammer trrrrk: wrentit tzew-zuppity-zuppity-zup: rufous hummingbird weeta weeta weeta che che che: Lucy’s warbler wheet-tsack-tsack-tsack: stonechat zeeda-zeeda-zeeda-sissi-peeso: goldcrest zoo zee zoo zoo zee: black-throated green warbler Other interpreters have used actual...

In 1764 Oxfordshire squire Edward Horne decided that the parish church of St Leonard on Watlington Hill would look more impressive with a spire. So he gave it one: By cutting a narrow mark 270 feet long into the chalk soil beyond the building, he was able to perch a foreshortened triangle atop the church when it was viewed in perspective from his house. Local residents maintain the mark to this day.

“Always let your conscience be your guide,” Jiminy Cricket tells Pinocchio. And so we are constantly telling one another: We seem to believe that following our convictions, whatever they are, is better than “giving in to temptation,” regardless of the outcome. Similarly, resisting temptation and doing what I feel is morally right is somehow praiseworthy, even if it can be shown that my convictions were mistaken. We are saying: If you believe it is wrong for you to do X then it is wrong for you to do X. And if you do have such a conviction: You believe it...

A clever conundrum from the U.K. Government Communications Headquarters Christmas Puzzle Quiz — it doesn’t even appear to be a question: 42°15′N 72°15′W, 53°52′N 44°50′E, 37°49′N 85°29′W, 39°37′N 75°56′W, 40°57′N 40°17′E, 51°54′N 02°04′W? The answer is 52°12′N 1°41′W. The listed coordinates identify Ware, Issa, Bardstown, North-East, Of, and Cheltenham. Where is a Bard’s town northeast of Cheltenham? Stratford-upon-Avon! Its own coordinates make up the answer. GCHQ is a great fount of excellent original puzzles — some are given on their website, they’ve published two collections, and they regularly post brainteasers on Twitter.

Preparing to visit the Dardanelles in July 1915, Winston Churchill sealed a message in an envelope marked “To be sent to Mrs. Churchill in the event of my death”: Do not grieve for me too much. I am a spirit confident of my rights. Death is only an incident, & not the most important wh happens to us in this state of being. On the whole, especially since I met you my darling one I have been happy, & you have taught me how noble a woman’s heart can be. If there is anywhere else I shall be on the...

In 1848 the French commune of Le Plessis-Piquet distinguished itself with a restaurant built in the boughs of a chestnut tree. Owner Joseph Gueusquin named it Le Grand Robinson, after the treehouse in Swiss Family Robinson. “Word spread and people started to make the eight-mile pilgrimage from Paris,” writes Pete Nelson in Treehouses of the World. “Soon, other entrepreneurs began opening their own treehouse restaurants. At the height of its popularity, there were ten such restaurants and countless other treehouse attractions.” The trend persisted even into the 1960s, drawing a steady stream of curious diners to Le Plessis-Piquet — in...

From Lee Sallows: Earlier this year, Futility Closet featured a puzzle based upon the well-known 7-segment display. Less well known is the 15-cell display shown in Figure 1, in which each decimal digit appears as a pattern of highlighted cells within a 3×5 rectangle. Call these the small rectangles. Observe also that the digit 1 is represented as the vertical column of 5 cells in the centre of its small rectangle rather than as either of the two alternative columns immediately to left and right, a detail that is important in view of what follows. Figure 1. Figure 2 shows...

Gottfried Leibniz held that no two distinct objects can have exactly the same properties. But, Max Black asked, “Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron, had a diameter of one mile, that they had the same temperature, colour, and so on, and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other.” (We might object that the two spheres are discernible because they occupy different positions in space, but...

A brainteaser by Y. Bogaturov, via Quantum, November-December 1991: In square ABCD, point L divides diagonal AC in the ratio 3:1 and K is the midpoint of side AB. Prove that angle KLD is a right angle.

CUNY philosopher Noël Carroll notes, “It is a remarkable fact about the creatures of horror that very often they do not seem to be of sufficient strength to make a grown man cower. A tottering zombie or a severed hand would appear incapable of mustering enough force to overpower a co-ordinated six-year-old. Nevertheless, they are presented as unstoppable, and this seems psychologically acceptable to audiences.” Why is this? (From his Philosophy of Horror, 1990.)

As children Maurice Baring and his brother Hugo invented a gibberish language in which the word for yes was Sheepartee and the word for no was Quiliquinino. This grew so tiresome to the adults around them that they were eventually threatened with a whipping: The language stopped, but a game grew out of it, which was most complicated, and lasted for years even after we went to school. The game was called ‘Spankaboo.’ It consisted of telling and acting the story of an imaginary continent in which we knew the countries, the towns, the government, and the leading people. These...

Welsh mathematician Robert Recorde’s 1543 textbook Arithmetic: or, The Ground of Arts contains a nifty algorithm for multiplying two digits, a and b, each of which is in the range 5 to 9. First find (10 – a) × (10 – b), and then add to it 10 times the last digit of a + b. For example, 6 × 8 is (4 × 2) + (10 × 4) = 48. This works because (10 – a)(10 – b) + 10(a + b) = 100 + ab, and it saves the student from having to learn the scary outer reaches...

Edith Wharton was “reading” before she knew the alphabet. As a young girl she found Washington Irving’s 1832 book Tales of the Alhambra in her parents’ library and discovered “richness and mystery in the thick black type”: At any moment the impulse might seize me; and then, if the book was in reach, I had only to walk the floor, turning the pages as I walked, to be swept off full sail on the sea of dreams. The fact that I could not read added to the completeness of the illusion, for from those mysterious blank pages I could evoke...

Convalescing from pneumonia one winter, Mary L. Daniels occupied herself by collecting all the digressions to the reader in the 47 novels of Anthony Trollope. Victorian fiction permitted a writer to stop in mid-story and expound his own views, and Trollope indulged this privilege with staggering frequency — together his digressions fill nearly 400 pages of close-set type, practically a novel’s worth in themselves. Some examples: “Throughout the world, the more wrong a man does, the more indignant is he at wrong done to him.” “A man cannot rid himself of a prejudice because he knows or believes it to...

By George E. Carpenter. White to mate in two moves.

When Raymond Smullyan was teaching probability at Princeton, he told one class about the birthday paradox — the fact that if there are 23 people in a room, the chances are greater than 50 percent that at least two of them share a birthday. There were only 19 students in the classroom, so he said that the chance that two of them shared a birthday was quite small. One boy said, “I’ll bet you a quarter that two of us here have the same birthday.” Smullyan thought about that for a moment and said, “Oh, of course! You know the...

Shozo Hayama spent 50 years collecting jinmenseki, rocks that resemble human faces, before founding the Chinsekikan (“hall of curious rocks”) in Chichibu, Japan, two hours northwest of Tokyo. Inside are 900 such rocks, from Elvis and Jesus to E.T. and Nemo from Finding Nemo. The only requirement is that the effects occur naturally, without human artifice. Hayama passed away in 2010, but his daughter keeps the museum running today. (Thanks, Randy.)

In 840 the Frankish Benedictine monk Rabanus Maurus composed 28 poems in which each line comprises the same number of letters. That’s impressive enough, but he also added painted images behind each poem that identify subsets of its letters that can be read on their own. The final poem of the volume shows Rabanus Maurus himself kneeling in prayer at the foot of a cross whose text forms a palindrome: OROTE RAMUS ARAM ARA SUMAR ET ORO (I, Ramus, pray to you at the altar so that at the altar I may be taken up, I also pray). This text...

Iowa State University mathematician Alexander Abian was a quiet man with a bold idea: He believed that blowing up the moon would solve most of humanity’s problems. In thousands of posts on Usenet, he maintained that destroying the moon would eliminate Earth’s wobble, canceling the seasons and associated calamities such as hurricanes and snowstorms. “You make a big hole by deep drilling, and you put there atomic explosive,” he explained in 1991. “And you detonate it — by remote control from Earth.” “I was questioned about it,” wrote English astronomer Patrick Moore in Fireside Astronomy (1993). “I pointed out, gently,...

“I have always been of the opinion that unpopularity earned by doing what is right is not unpopularity at all but glory.” — Cicero

In 2011, Monash University mathematician Burkard Polster set out to answer a practical question: How precariously can you place a laptop computer on a crowded bedside table so that it will take up minimal space without falling off? Assuming that both the table and the laptop are rectangular, and that the laptop’s center of gravity is its midpoint, it turns out that the optimal placement occurs when the laptop’s midpoint coincides with one of the table’s corners and the footprint is an isosceles right triangle, as above. This also assumes that the table is reasonably sized. But then, if it’s...

Meditations of Marcus Aurelius: “I am constantly amazed by how easily we love ourselves above all others, yet we put more stock in the opinions of others than in our own estimation of self. … How much credence we give to the opinions our peers have of us and how little to our very own!” “Drama, combat, terror, numbness, and subservience — every day these things wipe out your sacred principles, whenever your mind entertains them uncritically or lets them slip in.” “A cucumber is bitter. Throw it away. There are briars in the road. Turn aside from them. This...

scrutator n. a person who investigates ambagical adj. obscure butyraceous adj. of the nature of, resembling, or containing butter delibation n. a slight knowledge of something In “The Adventure of the Six Napoleons,” Sherlock Holmes makes an enigmatic allusion: “You will remember, Watson, how the dreadful business of the Abernetty family was first brought to my notice by the depth which the parsley had sunk into the butter upon a hot day.” He says nothing more. In The New Annotated Sherlock Holmes, Leslie Klinger writes, “Numerous pastiches and analyses of the ‘Abernetty business’ have been written and are surveyed in...

Cruising the Mediterranean in 1962, the American aircraft carrier USS Independence came upon a full-rigged sailing ship with a striped hull, a teak deck, and an ornamented bow and stern. With a light signal the carrier asked, “Who are you?” The ship answered, “Training ship Amerigo Vespucci, Italian navy.” The Independence replied, “You are the most beautiful ship in the world.”

In 1967, a foot powder was elected mayor of a town in Ecuador. During municipal elections in Picoazá, an urban parish of 4,000 people on the Pacific coast, a foot deodorant company called Pulvapies offered the advertising slogan “Vote for any candidate, but if you want well-being and hygiene, vote for Pulvapies.” That’s innocent enough. But “on the eve of the election, the company distributed a leaflet the same size and color as the official voting papers, saying: ‘For Mayor: Honorable Pulvapies,'” reported the New York Times. The result was that, when the votes were counted, the foot powder had...

On July 19, 1695, this notice appeared on page 3 of a weekly London pamphlet: A Gentleman about 30 Years of Age, that says he had a Very Good Estate, would willingly Match himself to some Good Young Gentlewoman that has a Fortune of 3000l. or thereabouts, and he will make Settlement to Content. It’s believed to be the world’s first lonely hearts ad. The pamphlet’s publisher, John Houghton, wrote, “‘Tis probable such Advertisements may prove useful.” (Francesca Beauman, Shapely Ankle Preferr’d, 2011.)

A book lover is thinking of buying six books from a group of eight. The price of each book is a whole number of dollars, and none is less than $2. The prices are such that each possible selection of six books would cost the buyer a different sum. In the end he can’t make up his mind and buys all eight books. What is the smallest amount he must pay? Each choice of six books from the group of eight leaves two behind. The price of each possible omitted pair must be unique, or else the corresponding sextets would...

A reader let me know about this: In Vancouver, Washington, there’s a library for “unwanted” manuscripts — manuscripts that no publisher wanted to publish. The Brautigan Library was inspired by Richard Brautigan’s 1971 novel The Abortion: An Historical Romance 1966, which describes a library for “the unwanted, the lyrical and haunted volumes of American writing.” Authors could place their manuscripts anywhere they liked on the library’s shelves, happy to have them preserved there though no readers could find them. Inspired by this, in 1990 Todd Lockwood, of Burlington, Vermont, started The Brautigan Library, inviting submissions of unpublished manuscripts and encouraging...

The first motion picture to feature a live cat is believed to be this 1894 short in which French physiologist Étienne-Jules Marey drops an inverted feline to watch it land on its feet. When the experiment was published in Nature in 1894, the editors wrote, “The expression of offended dignity shown by the cat at the end of the first series indicates a want of interest in scientific investigation.”

In a monastery cloisters on the edge of Venice is a sundial inscribed with the motto Horas non numero nisi serenas. Literally that means “I don’t count the hours unless they are serene ones” (or “I count only the sunny hours”). “But it really means, ‘When I come to die, the only moments that matter will have been the moments when I was at ease,'” writes Harry Mount in Amo, Amas, Amat and All That. Of the motto, William Hazlitt wrote, “There is a softness and a harmony in the words and in the thought unparalleled.”

More entries from unusual indexes: From Robert Burton’s Anatomy of Melancholy: Cabbage brings heaviness to the soul, 192 Calis, who would wash in no common water, 397 Fish discommended, 192; defended, 398 Genesis, thought inadvisable reading, 771 Kisses, honest and otherwise, 701 et seq. Pork, naught for quasy stomachs, 190 Roman courtesans, their elegancy of speech, 699 Spider in a nutshell, medicine for ague, 596 Statues, love in, 649 Venison, a melancholy meat, 190 Verjuice and oatmeal is good for a parrot, 80 note And from Gilbert White’s 1789 The Natural History and Antiquities of Selborne: ANNE, Queen, came to...

In the Pisco Valley on Peru’s Nazca Plateau is a band of 5,000 to 6,000 holes, each about 1 meter in diameter and 100 centimeters deep. The band, which averages about 20 meters in width, starts at the edge of a valley and extends about 1.5 kilometers up a hill understandably known as Cerro Viruela, or Smallpox Hill. (You can see its extent in Google Earth.) No one knows who dug the holes or why. They’re circular and lined with stone, resembling pits found elsewhere that serve as resting places for mummies. But these are empty. Possibly they were designed...

Two trains set out at 7 a.m., one headed from A to B and the other from B to A. The first reaches its destination in 8 hours, the second in 12. At what hour will the two trains pass one another?

This is a miniature, a tiny replica of an English dining room of the late 18th century. Between 1932 and 1940, American artist Narcissa Niblack Thorne made 100 such diminutive rooms, often enlisting architects, designers, and craftsmen whose talents became available during the Depression. Ninety-nine of the miniatures are still in existence, most on display at the Art Institute of Chicago, where they serve as documents of the decorating styles of periods past. Generally designed on a scale of one inch per foot, many of them include authentic materials: bowls of real silver, chandeliers of real crystal, even original paintings...

In the game Chomp, two players begin with a rectangular grid. The first player chooses any square and removes it from the grid, together with all the squares above and to the right of it. The second player chooses one of the remaining squares and removes that, together with all the squares above it and to its right. The two take turns in this way until one of them is forced to remove the last square. That player loses. If the starting grid is square, can either player force a win?

A self-working card curiosity by Shippensburg University mathematician Douglas E. Ensley: I give you the four aces from a deck of cards and turn my back. Then I ask you to stack the four cards face up with the heart at the bottom, then the club, the diamond, and the spade. Now turn the uppermost card, the spade, face down. Now you’re invited to perform any of these operations as many times and in any order that you wish: Cut any number of cards from the top of the stack to the bottom. Turn the top two cards over as...

In 1805 a disturbed Venice shoemaker named Matthew Lovat nearly managed to crucify himself. From William Wood Seymour’s The Cross in Tradition, History, and Art, 1898: Having prepared a cross, he stripped himself naked except for a girdle about his loins. Fearing that he would not be able to attach himself securely to the cross, he covered the lower part with a net, extending from the suppedaneum to the transverse. Having introduced himself into this, he next drove a nail through the palm of his right hand by striking it on the floor until the point appeared on the outside....

Sentenced in 1964 to life in prison, anti-apartheid activist Ahmed Kathrada got permission during his confinement to pursue a history degree through the University of South Africa. He used his access to books and writing materials to compile a series of secret notebooks in which he recorded quotations that inspired him. Together they form what used to be called a commonplace book — a series of personal memoranda that, taken together, illuminate the spirit of the compiler: Ofttimes the test of courage becomes rather to live than to die. — Vittorio Alfieri It is almost a definition of a gentleman...

Thomas Jefferson, John Adams, and James Monroe all died on July 4. Australia is wider than the moon. NoNRePReSeNTaTiONaLiSm can be assembled from chemical symbols. 1 × 56 – 1 – 7 = 15617 “‘Needless to say’ is, needless to say, needless to say.” — Enoch Haga

In 2018 a team of researchers at the University of North Carolina presented 511 American Christians with randomly paired pictures of faces and asked them to identify which of the pair more closely resembled the face of God. By combining the selected faces, the psychologists could produce a composite image of the Creator as envisioned by various groups. (Here, the image on the left is God as young participants imagine him; the one on the right is how he’s seen by older participants.) Liberals tend to imagine that God is younger, more feminine, and more loving than conservatives, and African-Americans...

In Plymouth, Tobago, lies a tomb with an enigmatic inscription: Within these walls are deposited the bodies of Mrs. Betty Stiven and her child. She was the beloved wife of Alex B Stiven to the end of his days will deplore her death which happened upon the 25th day of Nov. 1783 in the 23rd year of her age. What was remarkable of her, she was a mother without knowing it, and a wife without letting her husband know it except by her kind indulgences to him. Theories abound, but there’s no consensus as to its meaning.

In 2006, Math Horizons challenged its readers to pose a problem in such a way that it contained its own answer. Rheta Rubenstein of the University of Michigan-Dearborn offered a pair of questions that answer one another: What fraction of the letters in three-eighths are vowels? What fraction of the letters in one-third are vowels? (“Self-Answering Problems,” Math Horizons 13:4 [April 2006], 19.)

Another poem by James Clerk Maxwell: The tendrils of my soul are twined With thine, though many a mile apart. And thine in close coiled circuits wind Around the needle of my heart. Constant as Daniel, strong as Grove. Ebullient throughout its depths like Smee, My heart puts forth its tide of love, And all its circuits close in thee. O tell me, when along the line From my full heart the message flows, What currents are induced in thine? One click from thee will end my woes. Through many a volt the weber flew, And clicked this answer back...

In a quarry at Aswan lies an unfinished obelisk, the largest the ancient Egyptians ever attempted. It’s 137 feet long and weighs more than 1,000 tons, more than two jumbo jets or 200 African elephants. If it had been completed it would have weighed more than twice as much as any other obelisk that the Egyptians ever erected. Cracks appeared in the granite before workers could carve it from the bedrock, so the project was abandoned. “The obelisk is so large that it makes a cameo appearance in Cecil B. DeMille’s 1923 silent film The Ten Commandments,” writes Egyptologist Bob...

By Joseph Kling. White to mate in two moves.

What is sound? We’re told that it’s a wave traveling through a medium, but we don’t hear sounds as existing in the air; we hear them as located at the place where they’re generated. Is sound a quality of an object or of the surrounding medium? “Listening to the birds outside your window, the students outside your door, the cars going down your street, in the vast majority of cases you will perceive those sounds as being located at the place where they originate,” writes St. Joseph’s University philosopher Robert Pasnau. “But if sounds are in the air, as the...

British tongue twisters: United States twin-screw steel cruisers. I shot three shy thrushes. You shoot three shy thrushes. The rain ceaseth and sufficeth us. A wicked cricket critic. Many an anemone sees an enemy anemone. All I want is a proper cup of coffee, Made in a proper copper coffee pot. You can believe it or not — I want a cup of coffee In a proper coffee pot. Tin coffee pots or Iron coffee pots, They’re no use to me, If I can’t have a Proper cup of coffee In a proper copper coffee pot I’ll have a cup...

Deposition of Elizabeth Brett, a Hertfordshire farmer’s servant, regarding an alarming experience on Sept. 15, 1784: This deponent, on her oath, saith, that on Wednesday the 15th day of September instant, between four and five o’clock in the afternoon, she, this deponent, being then at work in her master’s brewhouse, heard an uncommon and loud noise, which, on attending to it, she conceived to be the sound of men singing as they returned from harvest-home. That upon going to the door of the house she perceived a strange large body in the air, and, on approaching it in a meadow-field...

Oxford zoologists Tim Guilford and Dora Biro discovered a surprise in 2004: Homing pigeons sometimes just follow roads like the rest of us. Although the birds have inbuilt magnetic compasses, they fall back on the known landscape when they’re in familiar territory, following the lines of motorways and trunk roads. Guilford and Biro strapped cameras and GPS devices to pigeons’ backs and watched them follow the A34 Oxford Bypass, turning at traffic lights and curving around roundabouts. They write, “One dominant linear feature, the A34 Oxford Bypass, appears to be associated with low entropy for much of its length, even...

A puzzle from R.M. Abraham’s Diversions & Pastimes, 1933: A prisoner escapes from Dartmoor Prison and has half-an-hour’s start of two warders and a bloodhound who race after him. The warders’ speed is 4 miles per hour; the dog’s 12 miles per hour, but the prisoner can only do 3 miles per hour. The dog runs up to the prisoner and then back to the warders, and so on back and forth until the warders catch the prisoner. How far does the dog travel altogether?

“Money is never spent to so much advantage as when you have been cheated out of it; for at one stroke you have purchased prudence.” — Schopenhauer

Hungarian physician Alexander Lenard spent seven years translating Winnie-the-Pooh into Latin: ‘Quid ergo est, Porcelle?’ dixit Christophorus Robinus lectulo exsurgens. ‘Heff,’ dixit Porcellus anhelitum ducens ut vix loqui posset, ‘heff — heff — heffalumpus!’ ‘Ubi?’ ‘Illic,’ exclamavit ungulam agitans Porcellus. ‘Qualum praebet speciem?’ ‘Sicut — sicut — habet maximum caput quod unquam vidisti. Aliquid magnum et immane — sicut — sicut nihil. Permagnum — sane, putares — nescio — permagnum nihil. Sicut caccabus.’ When it reached the New York Times bestseller list in 1960, the Christian Science Monitor wrote, “It is hard to conceive of a Latin work more calculated...

kirkify v. to make like a Presbyterian church in appearance (This is in Nathaniel Hawthorne’s English Note-Books of 1857: “Then we went to St Giles’s Cathedral, which I shall not describe, it having been kirkified into three interior divisions by the Covenanters.”)

An anecdote from Oliviu Felecan and Alina Bughesiu’s Onomastics in Contemporary Public Space, 2013: A Zulu owned a dog that used to roll in dirt and dung when it was young. When it came to the house, everyone shouted, “Phuma phela!”, meaning “Get out now!” or “Get out, then!” As the dog became more disciplined it was allowed into the house and the phrase simply became its name. But if Get Out Now was now the dog’s name (asked the confused interviewer), then surely it was used to call the dog into the house? ‘Yes, that is so,’ was the...

Suppose that Schweitzer and Gandhi are equally saintly and that Green and White are equally unsavory characters with long criminal records. Suppose that on separate occasions Green gratuitously slaps Schweitzer in the face, Schweitzer gratuitously slaps White in the face, and Gandhi gratuitously slaps Schweitzer in the face. If guilt were proportional, not just to the offence, but to the moral uprightness of the offended party, then Green would incur more guilt and liability to punishment than would Schweitzer. For since Schweitzer is worthier than White, Green’s failure to show respect for Schweitzer was more grievous than Schweitzer’s failure to...

The second act of Alban Berg’s 1937 opera Lulu includes a three-minute sequence that’s a musical palindrome — after the first 90 seconds, there’s an ascending piano arpeggio, a pause … and then the music unfolds in reverse, a perfect mirror image back to the start. This music accompanies a silent film that is itself a palindrome in some ways — for example, three people arrest Lulu and put her in prison, and then three liberate her. And Lulu’s husbands in Act I are played by the same singers as her clients in Act III.

Lewis Carroll was an early enthusiast of photography, though he seems to have found the social aspects trying — he published this poem in 1857: From his shoulder Hiawatha Took the camera of rosewood, Made of sliding, folding rosewood; Neatly put it all together. In its case it lay compactly, Folded into nearly nothing; But he opened out the hinges, Pushed and pulled the joints and hinges, Till it looked all squares and oblongs, Like a complicated figure In the Second Book of Euclid. This he perched upon a tripod — Crouched beneath its dusky cover — Stretched his hand,...

This style of compound magic square was first devised by Kenneth Kelsey of Great Britain. The numbers 70-94 appear in the blue boxes, making a pandiagonal magic square. The numbers 95-110 appear in the yellow circles, making a pandiagonal magic square of their own. And embedding one in the other produces a compound square — the numbers in the circles can be added to the numbers in the squares in either of the adjoining sections. So, for example, the second row, 87 + 79 + 91 + 83 + 70 = 410, can include the row of circles above it...

In her 1914 book Una Mary: The Inner Life of a Child, Una Hunt, the daughter of geologist Frank Wigglesworth Clarke, set out to describe the subjective world of her young girlhood. Here’s an example — she had created an imaginary land she called My Country in which her alternate self, Una Mary, lived, and then established it in the Persian rug in the parlor, where her chessmen could play out their adventures: A very yellow palm-leaf in one corner of the pattern was the Holy Land. I thought it was holey, full of holes. I had simply heard some...

Stand a bicycle so that one pedal is in its lowest position and one in its highest. Now if we pull backward on the low pedal, will the bicycle move forward or backward? Intuition suggests it will move forward: We’re turning the pedals in the same direction that a rider would, and normally this motion drives the rear wheel to propel the bike forward. Surprisingly, though, in the experiment the bike moves backward. That’s because (in most bikes, in most gears) each pedal is constantly moving forward with respect to the ground. So pulling backward on the pedal doesn’t produce...

I forgot to mention that I donned a kilt for the Highland Ball at Glenferness. It was anxious work at first, as it is a garment with no notion of privacy, and delights in giving all present tantalising glimpses of things unseen. However, with careful manipulation and a pair of drawers, I got through the evening tolerably. It is quite comfortable to dance in, but should be a godsend to mosquitoes. — Sir Alan Lascelles, diary, September 15, 1907

res angusta domi n. straitened financial circumstances appaumé adj. having the hand opened out so as to display the palm mammering n. a state of hesitation or doubt manuduction n. careful guidance dactylonomy n. the art of counting on the fingers belve v. to shout or roar

Soliloquy of a mayfly, imagined by Benjamin Franklin in a 1778 letter to Madame Brillon: It was the opinion of learned philosophers of our race, who lived and flourished long before my time, that this vast world, the Moulin Joly, could not itself subsist more than eighteen hours; and I think there was some foundation for that opinion, since, by the apparent motion of the great luminary that gives life to all nature, and which in my time has evidently declined considerably towards the ocean at the end of our earth, it must then finish its course, be extinguished in...

Can any 10 points on a plane always be covered with some number of nonoverlapping unit discs? It’s not immediately clear that the answer is yes. The most efficient way to pack circles together on the plane is the hexagonal packing shown above; it covers about 90.69 percent of the surface. But if our 10 points are inconveniently arranged, it’s not clear that we’ll always be able to shift the array of circles around in order to get them all covered. In this case there’s a neat proof that takes advantage of a technique called the probabilistic method — if,...

At Princeton in the 1940s, Albert Einstein became a close friend of logician Kurt Gödel, whose incompleteness theorems lie at the heart of modern mathematics. Toward the end of his life Einstein said that his “own work no longer meant much, that he came to the Institute merely … to have the privilege of walking home with Gödel.” In 1947 Einstein and economist Oskar Morgenstern accompanied Gödel to his U.S. citizenship exam because they were concerned about his unpredictable behavior: During his voluminous preparation for the exam, Gödel said, he had uncovered a flaw in the U.S. constitution that could...

I found this surprising. What’s the volume of a ball of radius 1 in various dimensions? In one dimension it’s a line segment of length 2. In two dimensions it’s a unit disc in the plane, with area π. In three dimensions it’s a unit ball with volume 4π/3. Intuitively we might expect the number to keep rising. But it doesn’t! In fact it peaks at five dimensions, and it drops quite sharply after that. In 20 dimensions the volume is only 0.026, and the limiting value is zero. Wikipedia explains the math.

Natural philosopher John Wilkins’ Mathematical Magick of 1648 contains a startling passage in which he foretells the advantages of a long-range submarine, or “ship, wherein men may safely swim underwater”: ‘Tis private; a man may thus go to any coast of the world invisibly, without being discovered or prevented in his journey; ‘Tis safe; from the uncertainty of Tides, and the violence of Tempests, which do never move the sea above five or six paces deep. From Pirates and Robbers which do so infest other voyages; from ice and great frosts, which do so much endanger the passages toward the...

A curious physics puzzle from Mark Levi’s excellent Why Cats Land on Their Feet: Suppose two astronauts, Al and Bob, are strapped to opposite ends of a space capsule’s interior, Al on the left and Bob on the right. Al is holding a large helium balloon, and everything is at rest. If Al pushes the balloon toward Bob, which way will the capsule drift? It would be reasonable to guess that the capsule will drift to the left. Newton’s third law says that action equals reaction, so as Al pushes the balloon to the right, the balloon pushes Al to...

Japanese pilot Kaname Harada recalls air combat in World War II: The initial feeling after shooting down someone was relief, because it was not me who was shot down. My next thought was that I was a better pilot, so I felt superior to the enemy aviator who was shot down. These feelings lasted only for a short time. When we shot at each other, we were at very close range, and during this time I could see my opponent’s face very well. When I saw the enemy’s face, it looked terrible because he was going down. Soon after this...

In May 1936 a publisher invited Albert Einstein to contribute a message to be sealed in a metal box in the cornerstone of a new library wing in his country home, to be opened a thousand years hence. He sent this: Dear Posterity, If you have not become more just, more peaceful, and generally more rational than we are (or were) — why then, the Devil take you. (From Helen Dukas and Banesh Hoffmann, eds., Albert Einstein, the Human Side, 1979.)

In June 1829, English curate Patrick Brontë brought home a box of 12 wooden toy soldiers for his 12-year-old son Branwell. Branwell shared them with his sisters: “This is the Duke of Wellington! It shall be mine!” shouted 13-year-old Charlotte, and 11-year-old Emily and 9-year-old Anne soon took up avatars of their own. This was the start of an enormous imaginative undertaking — soon the four had invented names and personalities for their soldiers and had begun inventing a shared history in which the “Young Men” traveled to the west coast of Africa; settled there after a war with the...

Aristotle referred to humans as the “state-building animal.” Other names our species has proposed for itself, in various writings: Homo absconditus: “man the inscrutable” Homo adorans: “worshipping man” Homo aestheticus: “aesthetic man” Homo amans: “loving man” Homo animalis: “man with a soul” Homo avarus: “man the greedy” Homo creator: “creator man” Homo demens: “mad man” (the only creature with irrational delusions) Homo discens: “learning man” Homo domesticus: “domestic man” (because he builds his environment) Homo duplex: “double man” (because of his animal and social tendencies) Homo economicus: “economic man” Homo educandus: “to be educated” (we require education to reach maturity)...

Obscure words from Paul Hellweg’s Insomniac’s Dictionary, 1989:

tomecide: the destruction of a book

lampadomancy: augury by torch flame

shotclog: a drinking companion tolerated because he pays for the drinks

allonym: the name of a real person borrowed by an author

ephelides: freckles

feuterer: someone who keeps a dog

hypnopedia: the process of learning while asleep (e.g. by listening to a recording)

girouettism: the practice of frequently altering personal opinions to follow popular trends

panchreston: a broadly inclusive thesis that purports to cover all aspects of its subject but usually ends up as an unacceptable oversimplification

grangousier: one who will swallow anything

A few facetious Latinisms collected by Michael Quinion:

ferroequinologist: a railroad enthusiast (“one who studies the iron horse”)

infracaninophile: a lover of the underdog

anti-fogmatic: an alcoholic drink that counteracts the effects of fog

In 2014 a Futility Closet reader led me to elephantocetomachia, “a fight between an elephant and a whale,” a valuable word assembled from spare parts. And my notes say that vacansopapurosophobia means “fear of blank paper” — a useful expression, even if it’s not in the dictionary.

Here are two 16th-century German portraits of seated ladies wearing hats, shown in three-quarter view. The one on the left was painted by Hans Holbein, the one on the right by the lesser-known Hans Krell. A panel of 12 specialists agreed that the Holbein painting had more artistic merit, and subjects who said they were familiar with art agreed with them. But individuals with no art expertise often chose the “wrong” painting, the Krell. This would suggest that people’s judgment in art is shaped by their expertise.

But Holbein is also much more famous than Krell, and this factor is likely to influence judgments too. How important is it? That’s not clear.

“Only if we can show that art experts across cultures agree on the comparative aesthetic merit of works they have never seen before and never heard of can we conclude there is consensus independent of cultural learning,” notes Boston College psychologist Ellen Winner. “This kind of study has not been done.”

(Ellen Winner, How Art Works, 2018.)

A golfer takes a swing at a golf ball. Fortunately it’s a good shot, and the ball heads for the cup. Unfortunately, a squirrel, rather dangerously positioned near the cup, kicks the ball away, thus decreasing the ball’s chance of landing in the cup. Fortunately, the ball then hits the branch of a nearby tree and is deflected into the cup.

“Question: was the squirrel’s kick a cause of the hole-in-one?” asks Australian National University philosopher Helen Beebee. “According to some philosophers’ intuitions, the answer is yes. According to others, the answer is no: the ball went in despite the kick. According to a third view, the kick was a cause of the hole-in-one and the hole-in-one occurred despite the kick.” Who’s right?

(Helen Beebee, “Do Causes Raise the Chances of Effects?”, Analysis 58:3 [July 1998], 182-190. The original example is due to Deborah A. Rosen.)

Articles observed by the crew of Welsh pirate Bartholomew Roberts (1682-1722):

Every man has a vote in affairs of moment; has equal title to the fresh provisions, or strong liquors, at any time seized, and may use them at pleasure, unless a scarcity makes it necessary, for the good of all, to vote a retrenchment.
Every man to be called fairly in turn, by list, on board of prizes because, (over and above their proper share) they were on these occasions allowed a shift of clothes: but if they defrauded the company to the value of a dollar in plate, jewels, or money, marooning was their punishment.
No person to game at cards or dice for money.
The lights and candles to be put out at eight o’clock at night: if any of the crew, after that hour still remained inclined for drinking, they were to do it on the open deck.
To keep their piece, pistols, and cutlass clean and fit for service.
No boy or woman to be allowed amongst them. If any man were to be found seducing any of the latter sex, and carried her to sea, disguised, he was to suffer death.
To desert the ship or their quarters in battle, was punished with death or marooning.
No striking one another on board, but every man’s quarrels to be ended on shore, at sword and pistol.
No man to talk of breaking up their way of living, till each had shared £1,000. If in order to do this, any man should lose a limb, or become a cripple in their service, he was to have 800 dollars, out of the public stock, and for lesser hurts, proportionately.
The captain and quartermaster to receive two shares of a prize: the master, boatswain, and gunner, one share and a half, and other officers one and a quarter.
The musicians to have rest on the Sabbath Day, but the other six days and nights, none without special favour.

That’s from Charles Johnson’s A General History of the Pyrates (1724), via naval historian David Cordingly’s Under the Black Flag (1995). In the early years of the 18th century, Cordingly writes, a pirate captain “had absolute power in battle and when ‘fighting, chasing, or being chased,’ but in all other matters he was governed by the majority wishes of the crew.”

In a 1993 segment on National Public Radio, Will Shortz challenged listeners to construct sentences that use only two consonants, such as “Can Connie, a nice niece in Canaan, can-can on a canoe in uncanny innocence?”

The winner, sent in by Dawne Bear and Rachel Chanin, was “See Tess taste-test Sissy’s sassy tea to attest to its tastiest status.” Other entries:

Beddy-bye, baby boy! Bid Daddy bye-bye! (Jim Hamilton)
Babs’ boss, Bobb, sobs as Bea’s base beau, Bubba, abuses sea bass. (Roxanne Bogucka)
A good guide dog did guide Dad. (Joe Cahill, Susan Morse)
Did dull addled Lady Della deal old ally, idle loaded Daddy Leo, a leaden dolly load o’ dilled eel? (Dorothy Thayer)
Dear Radio Reader: Did Eduardo, a rodeo rider, dare ride a rare red doe, or did Dario, a dour dude, roar “I rode a ruder, redder deer”? Adieu, Dierdre. (Bernell Scott)
At tea, a tattooed idiot did ode to a dead toad (a tad odd!). (Matt Hulen)
Otto, Thea! Out to the auto to toot to the heath! Tote the tot that hath the teeth to eat the hat! (Uh-oh, it hit Thea.) Aha, tie the hat to the tot! Ta-ta! (Bruce and Barbara Lessey)
Sally, a sassy lass, says “Susie is a souse — also loose”. Sly Susie says “I’ll sue!” (Aarne Hartikka)
A little tale to titillate — title: Lolita. (Toby Gottfried)
Name me: I am anyone, I am no one; I’m an anima, a meanie, a ninny, a mommy in a muumuu, a nun in a mini; I am many; I am one – I am Man. (Wayne Eastman)
At a roar in a ruin near our nunnery, I ran in a rare noon rain. (Nancy Gannon)
Sue supposes Pa possesses poise as Pa passes Sue pea soup. Sue, pious as a spouse, passes Pa pie. (Jay Cary)
“Wow,” we roar, “we are aware we wore wire a wry way. We’re a wee raw! We rue!” (Sylvia Coogan)

In presenting these in Word Ways the following May, editor Ross Eckler noted that “No one discovered that palindromes sometimes work: too hot to hoot; Madam, I’m Adam; name no one man.”

This shepherd thought poetic thoughts

As by the flocks he sat;

But while he wrote his verses,

The goat fed on his hat.

Children’s author and illustrator Peter Newell collected a whole series of such reversible images in Topsys and Turvys (1893) and a sequel. He followed these up with The Hole Book (1908), in which young Tom Potts accidentally fires a gun, sending a bullet through a town; The Slant Book (1910), a book shaped like a rhombus in which a runaway baby carriage careens downhill; and The Rocket Book (1912), in which a janitor’s son sends a rocket upward through 21 successive floors of an apartment building.

The Hole Book was manufactured with a hole right through it — on each page the physical hole shows the mayhem caused by the bullet, deflating bagpipes, severing kite strings, sounding a bass drum, and blowing up a car, among many other things. It’s finally stopped by a cake:

And this was lucky for Tom Potts,

The boy who fired the shot —

It might have gone clean round the world

And killed him on the spot.

During World War I, British physicist G.I. Taylor was asked to design a dart to be dropped onto enemy troops from the air. He and a colleague dropped a bundle of darts as a trial and then “went over the field and pushed a square of paper over every dart we could find sticking out of the ground.”

When we had gone over the field in this way and were looking at the distribution, a cavalry officer came up and asked us what we were doing. When we explained that the darts had been dropped from an airplane, he looked at them and, seeing a dart piercing every sheet remarked: ‘If I had not seen it with my own eyes I would never have believed it possible to make such good shooting from the air.’

(The darts were never used — “we were told they were regarded as inhuman weapons and could not be used by gentlemen.”)

(From T.W. Körner, The Pleasures of Counting, 1996.)

Modern lighting is so ubiquitous that we scarcely think about it, but from prehistory to A.D. 1782 there were just a few primitive means to banish the dark, chiefly fires, rushlights, and tallow candles. And even these were rather precious — in the 17th century John Aubrey wrote of William Oughtred that “his wife was a penurious woman and would not allow him to burne candle after supper, by which means many a good notion is lost.” In 1763 James Boswell was midway through a night of writing when disaster struck:

About two o’clock in the morning I inadvertently snuffed out my candle, and as my fire before that was long before black and cold, I was in a great dilemma how to proceed. Downstairs did I softly and silently step to the kitchen. But, alas, there was as little fire there as upon the icy mountains of Greenland. With a tinder box is a light struck every morning to kindle the fire, which is put out at night. But this tinder box I could not see, nor knew where to find. I was now filled with gloomy ideas of the terrors of the night. I was also apprehensive that my landlord who always keeps a pair of loaded pistols by him, might fire at me as a thief.

What did he do? “I went up to my room, sat quietly until I heard the watchman calling ‘past three o’clock’. I then called to him to knock at the door of the house where I lodged. He did so, and I opened to him and got my candle re-lumed without danger. Thus was I relieved and continued busy until eight the next day.”

(William T. O’Dea, The Social History of Lighting, 1958.)

By J. Paul Taylor. White to mate in two moves.

| SelectClick for Answer | | --- | | 1. Be4! and mate must follow. From Elementary Chess Problems, 1880. |

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Artist Patrick Hughes calls this illusion “reverspective” — the “end” of each gallery hallway is actually nearest the viewer.

“Hughes acknowledges that these types of paintings have been his most successful and they continue to intrigue him,” writes Brad Honeycutt in The Art of Deception. “As such, he says that he could very well concentrate on creating paradoxical perspective pictures for the rest of his days.”

More examples.

A puzzle by Sam Loyd:

John the milkman has two 10-gallon cans full of milk. Two customers have a 5- and a 4-quart measure and want 2 quarts put into each measure. How can he accomplish this?

“It is a juggling trick pure and simple, devoid of trick or device, but it calls for much cleverness to get two exact quarts of milk into those measures employing no receptacles of any kind except the two measures and the two full cans.”

| SelectClick for Answer | | --- | | Call one of the 10-gallon cans A and the other B. Fill the 5-quart pail from can A. Pour the 5-quart pail into the 4-quart pail. Empty the 4-quart pail into can A. Pour the 5-quart pail into the 4-quart pail. Fill the 5-quart pail from can A. Fill the 4-quart pail from the 5-quart pail. Empty the 4-quart pail into can A. Fill the 4-quart pail from can B. Pour the 4-quart pail into can A. This fills can A and leaves 2 quarts in the 4-quart pail. “Thus the milkman has supplied each of his customers with exactly two quarts of milk and solved his perplexing problem.” From Loyd’s Cyclopedia of Puzzles, 1914. See also Well Done. |

American painter William Rimmer produced this enigmatic image in 1872. A man runs through a palace. Is he fleeing or pursuing? What is the ghostly figure in the parallel corridor beyond him? And whose shadow is entering from the right?

No one knows. “As the title confirms, the painting turns a general situation into an ambivalent one,” writes Victor I. Stoichita in A Short History of the Shadow (1997). “There have been numerous attempts to specify its contents, but these have only resulted in the principle being misunderstood, for everything leads us to believe that it was Rimmer’s intention to create a story that functioned through its enigmatic form.”

A puzzle from Eureka, March 1957:

These drawings depict an object as seen from above and from the front. What does it look like when viewed from the side? The object has no curved surfaces, and all hidden edges in such drawings are represented by dotted lines.

| SelectClick for Answer | | --- | |

(From the Eureka Digital Archive, published under a Creative Commons license.) |

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In England and France, from the 1500s to the 1700s, the placement of a letter writer’s signature on the page conveyed meaning as to his relationship with the recipient. In his 1568 letter-writing manual Enimie of Idlenesse, William Fulwood writes that the subscription and signature of the letter “must be doone according to the estate of the writer, and the qualitie of the person to whom wee write: For to our superiors wee must write at the right side in the neither end of the paper, saying: By your most humble and obedient sonne, or seruant, &c. Or, yours to commaund, &c. And to our equals we must write towards the middest of the paper, saying: By your faithfull friend for euer, &c. Or, yours assured, &c. To our inferiours wee may write on high at the left hand, saying: By yours, &c.”

In 1601 John Donne married Anne More without the blessing of her father, who was lieutenant of the Tower of London. Donne was incarcerated, and in his letters begging for clemency he crammed his signature into the bottom right-hand corner of the page to signal his self-abasement.

(From Sam Willis and James Daybell, Histories of the Unexpected, 2018.)

There was an artist once, and he painted a picture. Other artists had colours richer and rare, and painted more notable pictures. He painted his with one colour, there was a wonderful red glow on it; and the people went up and down, saying, ‘We like the picture, we like the glow.’

The other artists came and said, ‘Where does he get his colour from?’ They asked him; and he smiled and said, ‘I cannot tell you’; and worked on with his head bent low.

And one went to the far East and bought costly pigments, and made a rare colour and painted, but after a time the picture faded. Another read in the old books, and made a colour rich and rare, but when he had put it on the picture it was dead.

But the artist painted on. Always the work got redder and redder, and the artist grew whiter and whiter. At last one day they found him dead before his picture, and they took him up to bury him. The other men looked about in all the pots and crucibles, but they found nothing they had not.

And when they undressed him to put his grave-clothes on him, they found above his left breast the mark of a wound — it was an old, old wound, that must have been there all his life, for the edges were old and hardened; but Death, who seals all things, had drawn the edges together, and closed it up.

And they buried him. And still the people went about saying, ‘Where did he find his colour from?’ And it came to pass that after a while the artist was forgotten — but his work lived.

— Olive Schreiner, Dreams, 1891

In James Thurber’s 1957 fairytale book The Wonderful O, two pirates, Black and Littlejack, assail the innocent island of Ooroo, seeking hidden treasure. Frustrated with their unsuccessful search, Black issues an edict banning the letter O, which he hates (his mother had once become wedged in an O-shaped porthole; “we couldn’t pull her in and so we had to push her out”). Accordingly the orchestra loses its violins, cellos, and trombones; the villagers must move from cottages to huts; and so on. One laments:

They are swing chas. What is slid? What is left that’s slace? We are begne and webegne. Life is bring and brish. Even schling is flish. Animals in the z are less lacnic than we. Vices are filled with paths and scial intercurse is baths. Let us gird up ur lins like lins and rt the hrrr and ust the afs.

I’ll leave you to read the resolution yourself.

For a more recent fable about an island beset by a letter shortage, see Mark Dunn’s progressively lipogrammatic 2001 novel Ella Minnow Pea. Maybe it’s the same island!

A puzzle from the 1998 Moscow Mathematical Olympiad, via Peter Winkler’s excellent Mathematical Puzzles, 2021:

An anthropologist is surrounded by a circle of natives. Each native either always lies or always tells the truth. The anthropologist asks each native whether the native to his right is a liar or a truth teller. From their answers, she’s able to deduce the fraction of the circle who are liars. What is the fraction?

| SelectClick for Answer | | --- | | The key is to notice that if all the liars were changed to truth-tellers and vice versa, none of the answers would change. So if the fraction x can be determined, it must have the property that x = 1 – x, and x must be 1/2. |

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Death is always on the way, but the fact that you don’t know when it will arrive seems to take away from the finiteness of life. It’s that terrible precision that we hate so much. But because we don’t know, we get to think of life as an inexhaustible well. Yet everything happens only a certain number of times, and a very small number, really. How many more times will you remember a certain afternoon of your childhood, some afternoon that’s so deeply a part of your being that you can’t even conceive of your life without it? Perhaps four or five times more. Perhaps not even that. How many more times will you watch the full moon rise? Perhaps twenty. And yet it all seems limitless.

— Paul Bowles, The Sheltering Sky, 1949

In the 1990s, South Baltimore native Gordon Beard compiled a series of phrasebooks to help bewildered travelers understand his city’s residents:

amblanz — ambulance

bobwar — barbed wire

corter — quarter

flare — flower

goff — golf

har — hire

keerful — careful

mare — mayor

neck store — next door

orning — awning

plooshin — pollution

roolty — royalty

twunny — twenty

varse — virus

warsh — wash

yewmid — humid

John Goodspeed, for 17 years a columnist at the Baltimore Evening Sun, had compiled his own list in the 1960s:

ahrsh — Irish

chowld — child

dayon — down

harrid — Howard

koor — car

larnix — larynx

nass — nice

owen — on

shares — showers

urshter — oyster

Apparently the confusion has persisted for decades. “The life of a Baltimore Army lieutenant may have been saved by Baltimore during the Battle of the Bulge in World War II,” Goodspeed once reported. “Military police suspected him of being a German spy in an American uniform, but an M.P. from Baltimore heard the lieutenant pronounce his home town as ‘Balamer’ and passed him as genuine. Only a native can say it that way.”

University of California psychologist Diana Deutsch discovered this illusion in 1973. Play the file using stereo headphones. If you hear a high tone in one ear and a low tone in the other, decide which ear is hearing the high tone. Then reverse the headphones and play the file again.

“Despite its simplicity, this pattern is almost never heard correctly, and instead produces a number of illusions,” Deutsch writes. Some people hear a single moving tone; some hear silence; some notice no change when the headphones are reversed. Some impressions even seem to vary with the handedness of the subject!

What you’re hearing is simply an octave interval, with the high note played in one ear and the low in the other, the two regularly switching places. Seen on paper it’s remarkably simple, which makes the confusion all the more striking. Deutsch suspects that two different decision mechanisms are being invoked at once — one determines what pitch we hear, and the other determines where it’s coming from. More info here.

Most people would agree that children have special duties to their parents, even once the children have grown up. We might feel an obligation to keep in touch with them, for example, or to care for them in their old age. Where do these duties come from?

Certainly my parents have done a great deal for me, so perhaps I owe them a debt. But it seems there’s no way to repay this debt completely, and I seem to owe it regardless of how great (or small) a burden I was to them as a child. (Also my obligation to them seems to vary with my own circumstances, which is not the case with other debts.)
Perhaps what I really owe them is an appropriate gratitude for what they’ve done for me. But this doesn’t seem right either — if I help my mother through a difficult time, fundamentally it’s because she wants me there, not to show that I recognize and appreciate what she’s done for me. Also, I seem to feel a duty to her even if I required relatively little sacrifice as a child, which is not normally how we think about gratitude.
Maybe my parents and I are friends, and I owe them the duties that come with friendship. But I can’t choose to end our relationship, as I can with friends, and I would never feel an obligation to provide medical care (say) for my friends, as I would for my parents.

Each of these explanations is unsatisfactory, writes Boston University philosopher Simon Keller. “Each tries to assimilate the moral relationship between parent and child to some independently understood conception of duty, but this relationship is different in structure and content from any that we are likely to share with anyone apart from a parent.” So what’s the source of our obligation to our parents?

(Simon Keller, “Four Theories of Filial Duty,” Philosophical Quarterly 56:223 [April 2006], 254-274.)

A puzzle from the excellent Riddler feature at FiveThirtyEight, via Oliver Roeder’s 2018 collection The Riddler:

Your eccentric friend Nigel flies from Heathrow to an airport somewhere in the 48 contiguous states, then hires a car and drives around the country, touching the Atlantic and Pacific Oceans and the Gulf of Mexico, then returns to the airport at which he started and flies home. If he crossed the Ohio River once, the Missouri River twice, the Mississippi River three times, and the Continental Divide four times, then there’s one state that we can say for certain that he visited on his trip. What is it?

| SelectClick for Answer | | --- | | Image: Wikimedia Commons Minnesota. In order to cross a river an odd number of times and still return to the original airport, Nigel must “go around” the river somehow. That’s not hard with the Ohio, but the Mississippi is enormous and practically divides the country. So in order to cross it three times and return to his airport, at some point he’d have had to go around the source at Lake Itasca, Minnesota. |

Image: Wikimedia Commons Korf’s Clock

Korf’s clock is of a novel sort

In which two pairs of hands are used:

One pair points forwards as it ought,

The other backwards a la Proust.

When it says eight it’s also four,

When it says nine it’s also three;

A single glance and you no more

Need fear the ancient Enemy.

For with this wondrous clock you’ll find

As, Janus-like, it turns about

(To such an end it was designed)

Time simply cancels itself out.

Palmström’s Clock

But Palmström’s clock has a “higher” power,

Balanced as lightly as a flower.

Scorning a set pedestrian pace,

It keeps time with a certain grace

And will, in answer to a prayer,

Go en retard, en arriéré.

One hour, two hours, three hours indeed,

Sympathizing with our need!

Though clockwork in its outward part

It hides within — a tender heart.

— Christian Morgenstern

Above: Built in 1586, the town hall in the old Jewish ghetto of Prague bears two clocks: a traditional clock tower with four faces bearing Roman numerals and a second clock bearing Hebrew numerals. The hands on the conventional clocks turn clockwise; those on the Hebrew clock turn counterclockwise. (Thanks, Danesh.)

A puzzle from James F. Fixx’s More Games for the Superintelligent, 1976:

A man who likes trains walks occasionally to a nearby railroad track and waits for one to go by. Afterward he notes whether he saw a passenger train or a freight. After several years his notes show that 90 percent of the trains he’s seen have been passenger trains. One day he meets an official of the railroad and is surprised to learn that the passenger and freight trains on this line are precisely equal in number. If the man timed his trips to the track at random, why did he see such a disproportionate number of passenger trains?

| SelectClick for Answer | | --- | | All the trains run hourly, but the freight trains follow six minutes after the passenger trains. So if the man arrives at the track at random, his odds of arriving after a freight train and before a passenger train are 9 to 1; for 54 out of every 60 minutes, a passenger train will be the next to pass. |

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Image: Wikimedia Commons In 1964, sociolinguist William Labov ran a revealing experiment in three New York department stores, Saks Fifth Avenue, Macy’s, and S. Klein. Of the three, Saks generally commanded the highest prestige and S. Klein the lowest. Labov had found that one marker of social stratification in the city was the pronunciation of the letter R, and he wanted to see whether this was reflected in the speech of the salespeople at the various stores.

He did this by approaching a salesperson in each store and asking directions to a department on the fourth floor. When the salesperson told him “Fourth floor,” he leaned forward and said, “Excuse me?” This forced the person to say the phrase “Fourth floor” again, this time rather self-consciously.

As expected, Labov found that salespeople at the upscale Saks tended to pronounce their Rs, while those at the lower-priced Klein tended to the broader New York pronunciation “fawth flaw.” But when asked to repeat the phrase, those at Macy’s and Klein’s tended to amend their pronunciation to sound more “classy.”

“How can we account for the differences between Saks and Macy’s?” Labov wrote. “I think we can say this: the shift from the influence of the New England prestige pattern [r-less] to the mid-Western prestige pattern [r-full] is felt most completely at Saks. The young people at Saks are under the influence of the r-pronouncing pattern, and the older ones are not. At Macy’s there is less sensitivity to the effect among a large number of younger speakers who are completely immersed in the New York City linguistic tradition. The stockboys, the young salesgirls, are not as yet fully aware of the prestige attached to r-pronunciation. On the other hand, the older people at Macy’s tend to adopt this pronunciation: very few of them rely upon the older pattern of prestige pronunciation which supports the r-less tendency of older Saks sales people.”

In separate interviews Labov found that two thirds of New Yorkers felt that outsiders disliked the city accent. “They think we’re all murderers,” one man told him. A woman said, “To be recognized as a New Yorker — that would be a terrible slap in the face.”

(William Labov, The Social Stratification of English in New York City, 2006.)

A brainteaser from the Soviet science magazine Kvant, via Quantum, January/February 1991:

Bobby found the sum of three consecutive integers, then of the next three consecutive integers, then multiplied these two sums together. Could the product have been 111,111,111?

| SelectClick for Answer | | --- | | No. One of the two groups must contain one even number and two odd ones. The sum of these three numbers must be even, so the product of the two sums must be even as well. |

| | | |

William Wallace Cook (1867-1933) claimed to have worn out 25 typewriters in as many years turning out hundreds of nickel and dime novels, all of them written in the same format, 40,000 words divided into 16 chapters of five single-spaced pages each. At the end of his career he published his system for generating plots, billed as “Plotto, an invention which reduces literature to an exact science.”

The “invention” is really a list of story ideas, all molded to Cook’s basic notion of a plot: “Purpose, opposed by Obstacle, yields Conflict.” The protagonist wants to find happiness in love and courtship, married life, or enterprise; he encounters a conflict and must reach a resolution. What makes the book fun is the absurd specificity of some of the ideas. Here’s an example:

1367

(b) (1083)(1287)

A has invented a life preserver for the use of shipwrecked persons*

A, in order to prove the value of the life preserver he has invented, dons the rubber suit, inflates it and secretly, by night, drops overboard from a steamer on the high seas.** (1414b) (1419b)

The numbers refer to elements that might be varied, to related plots, and to character types that might figure in the story. Varying the combinations might produce several million different stories. This is certainly formulaic, but, Cook said, “There are any number of highbrow authors who will ridicule this invention in public and use it in private.” (In fact both Alfred Hitchcock and Erle Stanley Gardner admitted in interviews that they’d read the book, which went through multiple editions.)

The numbered master list gives 1,462 plots, all linked with character symbols and apparently all thought up by the author. The full text is on the Internet Archive.

By George E. Carpenter. White to mate in two moves.

| SelectClick for Answer | | --- | | 1. Bd7! and the queen will mate. From Chess Problems, 1886. |

| | | |

Albrecht Dürer’s 1514 engraving Melencolia I includes this famous magic square: The magic sum of 34 can be reached by adding the numbers in any row, column, diagonal, or quadrant; the four center squares; the four corner squares; the four numbers clockwise from the corners; or the four counterclockwise.

In Power Play (1997), University of Toronto mathematician Ed Barbeau points out that there’s even more magic when we consider squares and cubes. Take the numbers in the first two and the last two rows:

16 + 3 + 2 + 13 + 5 + 10 + 11 + 8 = 9 + 6 + 7 + 12 + 4 + 15 + 14 + 1

162 + 32 + 22 + 132 + 52 + 102 + 112 + 82 = 92 + 62 + 72 + 122 + 42 + 152 + 142 + 12

Or alternate columns:

16 + 5 + 9 + 4 + 2 + 11 + 7 + 14 = 3 + 10 + 6 + 15 + 13 + 8 + 12 + 1

162 + 52 + 92 + 42 + 22 + 112 + 72 + 142 = 32 + 102 + 62 + 152 + 132 + 82 + 122 + 12

Most amazingly, if you compare the numbers on and off the diagonals, this works with both squares and cubes:

16 + 10 + 7 + 1 + 13 + 11 + 6 + 4 = 2 + 3 + 5 + 8 + 9 + 12 + 14 + 15

162 + 102 + 72 + 12 + 132 + 112 + 62 + 42 = 22 + 32 + 52 + 82 + 92 + 122 + 142 + 152

163 + 103 + 73 + 13 + 133 + 113 + 63 + 43 = 23 + 33 + 53 + 83 + 93 + 123 + 143 + 153

In his 2014 book Describing Gods, Graham Oppy presents the “divine liar” paradox, by SUNY philosopher Patrick Grim:

X believes that (1) is not true.

If we suppose that (1) is true, then this tells us that X believes that (1) is not true. But if an omniscient being believes that (1) is not true, then it follows that (1) is not true. So the assumption that (1) is true leads to a contradiction.

Suppose instead that (1) is not true. That is, suppose that it’s not the case that X believes that (1) is not true. If an omniscient being fails to believe that (1) is not true, then it’s not true that (1) is not true. So this alternative also leads to a contradiction.

But, on the assumption that there is an omniscient being X, either it’s the case that (1) is true or it’s the case that (1) is not true.

“So, on pain of contradiction,” Oppy explains, “we seem driven to the conclusion that there is no omniscient being X.”

(Also: Patrick Grim, “Some Neglected Problems of Omniscience,” American Philosophical Quarterly 20:3 [July 1983], 265-276.)

The lost art of floriography assigned meanings to flowers so that lovers could exchange messages with “talking bouquets.” In his 1839 Language of Flowers, English journalist Frederic Shoberl rendered an entire verse by French poet Évariste de Parny as the combination of 16 flowers:

Aimer est un destin charmant,

C’est un bonheur qui nous enivre,

Et qui produit l’enchantement.

Avoir aimé, c’est ne plus vivre,

Hélas! c’est avoir acheté

Cette accablante vérité,

Que les serments sont un mensonge,

Que l’amour trompe tôt ou tard,

Que l’innocence n’est qu’un art,

Et que le bonheur n’est qu’un songe.

“It may be thus rendered: ‘To love is a pleasure, a happiness, which intoxicates; to love no longer, is to live no longer; it is to have bought this sad truth, that innocence is falsehood, that love is an art, and that happiness is a dream.'”

A tiny detail, but I thought it was interesting: Scottish writer Henry Drummond believed that sub-Saharan Africa was so well networked with footpaths that an explorer could walk from Zanzibar westward “never in fact leaving a beaten track” until “his faithful foot-wide guide lands him on the Atlantic seaboard.” From his Tropical Africa of 1888:

Now it may be a surprise to the unenlightened to learn that probably no explorer in forcing his passage through Africa has ever, for more than a few days at a time, been off some beaten track. Probably no country in the world, civilized or uncivilized, is better supplied with paths than this unmapped continent. Every village is connected to some other village, every tribe with the next tribe, every state with its neighbour, and therefore with all the rest. The explorer’s business is simply to select from the network of tracks, keep a general direction, and hold on his way.

This is repeated in J.W. Gregory’s The Story of the Road (1931) and in M.G. Lay’s Ways of the World (1992). Gregory admits only afterward that this may have been true in Nyasaland, the district that Drummond had visited, but it’s hardly the case elsewhere. “One evening, after the porters had suffered one of many repeated disappointments at not finding a human path, I removed their gloom, as they sat around the camp fires, by translating to them the passage from Henry Drummond. Their laughter showed that they concluded that the reports of European travellers, like those they told themselves on their return to the coast, were not always to be taken literally.”

apolactize

v. “to spurne with the heele” (from Henry Cockeram’s English Dictionarie of 1623)

tripudiary

adj. pertaining to dancing

Any stranger behind the scenes at Her Majesty’s Theatre on the opening night of Adeline Genée and the Imperial Russian Ballet would have been amazed (stated The Melbourne Age on Monday) at a little incident that was enacted just before Mlle. Genée made her entrance from the wings. Mr. Hugh Ward approached the great dancer, and, raising his foot, kicked her on the leg. The astonishment would have increased on it being noticed that Mlle. Genée, far from being incensed at this apparent liberty, was greatly pleased at it, and rippled with laughter. Mlle. Genée explained the incident in this way. ‘You see,’ she said, ‘while I am not exactly over-superstitious, there are still some little things I pay regard to, and one of them is that before I make my first appearance anywhere I must be given a ‘good luck kick’ prior to making my entrance. I mentioned this jokingly to Mr. Ward when I arrived in Sydney, and he said it would give him the greatest pleasure to present me with the lucky kick on the opening night of the season. So he has come all the way from Sydney to do so.’

— Adelaide Register, June 25, 1913

In Book 11 of the Odyssey, Odysseus encounters his mother in Hades and asks her seven questions. She answers all seven, but strangely in reverse order:

A – What killed you?

B – A long sickness?

C – Or Artemis with her arrows?

D – How is my father?

E – How is my son?

F – Are my possessions safe?

G – Has my wife been faithful?

G – Your wife has been faithful.

F – Your possessions are safe.

E – Your son is thriving.

D – Your father is alive but in poor condition.

C – Artemis did not kill me with her arrows.

B – Nor did a sickness kill me.

A – But my longing for you killed me.

This reversal is called chiasmus, and it appears throughout oral literature. Apart from its aesthetic effect, it’s thought that it may have helped ancient poets to remember long passages and to recall the structure of a complex story. Of the Iliad, classicist Cedric Whitman writes, “Not only are certain whole books of the poem arranged in self-reversing, or balancing, designs, but the poem as a whole is, in a way, an enormous hysteron proteron, in which books balance books and scenes balance scenes by similarity or antithesis, with the most amazing virtuosity.”

Some of these patterns are wrought on such a huge scale that it’s hard to believe that a listening audience could even recognize them. Why then offer them? Whitman gives two reasons. One, a poet might perform a feat of virtuosity for its own sake, even if the audience overlooks it. And two, “The human mind is a strange organ, and one which perceives many things without conscious or articulate knowledge of them, and responds to them with emotions necessarily and appropriately vague.”

(Cedric Whitman, Homer and the Heroic Tradition, 1958; and Steve Reece, “The Three Circuits of the Suitors: A Ring Composition in Odyssey 17-22,” Oral Tradition, 10:1 [1995], 207-229.)

In 1884, as engineers sawed brownstone out of a quarry near Manchester, Conn., amateur paleontologist Charles Owen realized that one block contained the hind part of a skeleton. He alerted professor Othniel Charles Marsh, who managed to acquire the block, but the corresponding stone containing the skeleton’s fore part had already been carted off for use in a new highway bridge.

In the ensuing years the identity of that bridge was forgotten, but in 1967, as a new highway was being constructed, Yale paleontologist John Ostrom saw an opportunity. He surveyed 60 bridges in the Manchester area and identified one 40-foot span over Hop Creek as the likeliest candidate. Then, in 1969, as that bridge was replaced, he and his colleagues examined more than 300 likely blocks at the site.

They found two 500-pound blocks that showed distinct fossil markings, and in New Haven Ostrom determined that one of the visible bones matched a thigh bone that Marsh had recovered 85 years earlier. The complete skeleton had belonged to a member of Ammosaurus, a genus that roamed the northeastern United States 200 million years ago.

(Thanks, Glenn.)

Image: Wikimedia Commons Colombian activist César López came up with a striking new peace symbol in 2003 — the escopetarra, a guitar fashioned from a gun.

The word combines the Spanish escopeta (shotgun) and guitarra (guitar). López made the first from a Winchester rifle and a Stratocaster; he’s since built four more and given them to various Latin American artists and cities and to the United Nations, which displayed it at a disarmament conference.

López told the BBC that he got the idea when he saw a soldier carrying his weapon like a guitar. “From there sprang the idea of joining the worst invention of mankind can be joined with the most beautiful,” he said. “Some of the AK-47s have the barrels marked with each of the victims. So we mark the barrels with the songs we play.”

This is pleasing: The first library card catalogs were made using playing cards. During the French Revolution the government created a new system of public libraries, and in order to inventory the books they created the “French Cataloging Code of 1791,” in which bibliographic data was written on playing cards, which were sturdy, uniform, and plentiful. A photo is here.

In The Card Catalog, its affectionate tribute to this now outmoded tool, the Library of Congress notes that 1.2 million cards representing more than 3 million volumes were recorded using this system within 3 years. “Although the ambitious cataloging project did not result in the formation of a national catalog, it did demonstrate the potential of utilizing a uniform format.” (Also: “Deuces and aces were reserved for the longest titles, as those cards had the most space on which to write.”)

“The true delight is in the finding out, rather than in the knowing.” — Isaac Asimov

What does this mean?

``` PMVEB DWXZA XKKHQ RNFMJ VATAD YRJON FGRKD TSVWF TCRWC RLKRW ZCNBC FCONW FNOEZ QLEJB HUVLY OPFIN ZMHWC RZULG BGXLA GLZCZ GWXAH RITNW ZCQYR KFWVL CYGZE NQRNI JFEPS RWCZV TIZAQ LVEYI QVZMO RWQHL CBWZL HBPEF PROVE ZFWGZ RWLJG RANKZ ECVAW TRLBW URVSP KXWFR DOHAR RSRJJ NFJRT AXIJU RCRCP EVPGR ORAXA EFIQV QNIRV CNMTE LKHDC RXISG RGNLE RAFXO VBOBU CUXGT UEVBR ZSZSO RZIHE FVWCN OBPED ZGRAN IFIZD MFZEZ OVCJS DPRJH HVCRG IPCIF WHUKB NHKTV IVONS TNADX UNQDY PERRB PNSOR ZCLRE MLZKR YZNMN PJMQB RMJZL IKEFV CDRRN RHENC TKAXZ ESKDR GZCXD SQFGD CXSTE ZCZNI GFHGN ESUNR LYKDA AVAVX QYVEQ FMWET ZODJY RMLZJ QOBQ-

```

No one knows. Cryptologist Louis Kruh discovered it in the New York Public Library’s rare book room in 1993 among some old material from the U.S. Army Signal School. In 1915 first lieutenant Joseph O. Mauborgne had created what he believed was a more secure cipher than the ones currently in use, and had offered this challenge to see if his colleagues could break it. Kruh found no solution in the archive, and he published it in both The Cryptogram and Cryptologia, inviting their readers to try their hands at it. As far as I know, none succeeded.

Mauborgne described it as a “a simple, single-letter substitution cipher adapted to military use.” He invited the director of the Army Signal School to place it on a bulletin board and allow the officers there to work on it for three months and then to post the solution “to show why the standard method of attacking a substitution cipher fails in this case.” “If any attack upon this cipher is successful, I shall be glad to hear of it,” he wrote.

Kruh, who died in 2010, noted that “it was probably solved or otherwise deemed unsuitable for use because there is no knowledge of a new cipher being adopted by the Army around that time.” If a solution was found, I don’t believe anyone alive today knows what it is.

(Louis Kruh, “A 77-Year-Old Challenge Cipher,” Cryptologia 17:2 [April 1993], 172-174.)

Irritated at the way bestseller lists were compiled in the 1950s, late-night radio host Jean Shepherd asked his listeners to visit bookstores and request a nonexistent book, I, Libertine, by the imaginary author Frederick R. Ewing.

The number of requests drove the title onto the New York Times bestseller list, and, encouraged by its popularity, bookstores began to order the novel. So Shepherd and publisher Ian Ballantine got novelist Theodore Sturgeon to write it, following the plot that Shepherd had described to his listeners. (Sturgeon fell asleep while trying to write the whole book in one marathon session, so Ballantine’s wife Betty had to write the last chapter.)

Ballantine Books published the novel in September 1956, using a photo of Shepherd in place of Ewing, and donated the proceeds to charity.

The Wall Street Journal exposed the hoax a few weeks before publication. “Mr. Ballantine’s idea, though simple enough, was a startling one, for publishers consider it one of the greatest possible tragedies to print a book later discovered to be the work of a literary faker,” wrote reporter Carter Henderson. “At Simon & Schuster, Inc., faces still redden when Joan Lowell’s autobiographical ‘Cradle of the Deep’ is mentioned even though this phony tale of a young girl’s spectacularly adventurous life at sea was published in 1929.”

Tim Minchin explores a key distinction.

In the early days of motoring, bicycle patrolmen with Britain’s Automobile Association would sometimes warn AA members of nearby speed traps. In a 1910 legal case, Chief Justice Lord Alverston found this practice illegal — in effect the patrolman would be “obstructing an officer in the course of his duty.”

So AA adopted a new policy — an AA patrolman would salute any car that bore an AA badge … unless there was a speed trap nearby. The AA Handbook warned members, “It cannot be too strongly emphasised that when a patrol fails to salute, the member should stop and ask the reason why, as it is certain that the patrol has something of importance to communicate.”

The new system was used until the 1960s.

Image: Flickr In 1943, Texas panhandle farmer Ray L. Batman converted his farm into a family partnership by transferring some assets to his teenage son, Gerald. But it turned out that the son had no actual desire to become his father’s partner, and in fact Ray had taken the measures against the advice of his accountant, apparently in order to reduce his income tax liability. The IRS deemed the partnership illegitimate and assessed Ray and his wife a fine of $10,000 each.

This meant that, when the family sued the head of the IRS, the case was recorded as Batman v. Commissioner.

John G. Browning collected some further odd case titles for the Texas Bar Journal in 2011:

Schmuck v. United States

United States v. Dolt

Klump v. Duffus

Plough v. Fields

Silver v. Gold

Brain v. Mann

Juicy Whip v. Orange Bang

United States v. Estate of Grace

State of Indiana v. Virtue

Death v. Graves

Easter Seals Society for Crippled Children v. Playboy Enterprises

Julius Goldman’s Egg City v. United States

United States v. Bad Marriage

United States v. Vampire Nation

“And let’s just say that some plaintiffs have identity issues, as demonstrated by I Am the Beast Six Six Six of the Lord of Hosts in Edmond Frank MacGillivray Jr. Now. I Am the Beast Six Six Six of the Lord of Hosts IEFMJN. I Am the Beast Six Six Six of the Lord of Hosts. I Am the Beast Six Six Six of the Lord of Hosts OTLOHIEFMJN. I Am the Beast SSSOTLOHIEFMJN. I Am the Beast Six Six Six. Beast Six Six Six Lord v. Michigan State Police, et al., File No. 5:89:92, 1990 U.S. Dist. Lexis 8792 (W.D. Mich. July 12, 1990). I hear his friends just call him ‘Six.'”

A romantic puzzle from Albert H. Beiler’s Recreations in the Theory of Numbers:

An ardent swain said to his lady love, some years ago, ‘Once when a week ago last Tuesday was tomorrow, you said, “When a day just two fortnights hence will be yesterday, let us get married as it will be just this day next month.” Now sweetheart, we have waited just a fortnight so as it is now the second of the month let us figure out our wedding day.’

Beiler’s book came out in 1964, so he gives the answer Tuesday, March 17, 1936 — the couple are speaking on March 2, discussing a conversation they had on February 17. Obviously the answer is not unique — “Tuesday, March 17, 1908, is another solution but then the swain would not be very young.” Basically we need a leap year in which March 17 falls on a Tuesday. Beiler finds these occur also in 1964 and 1992 — and one did in 2020 as well.

In 1906, when Teddy Roosevelt endorsed a plan to simplify the spelling of difficult words, Englishman Harry Graham offered a scheme of his own:

When Theo: Roos: unfurled his bann:

As Pres: of an immense Repub:

And sought to manufact: a plan

For saving people troub:

His mode of spelling (termed phonet:)

Affec: my brain like an emet:

And I evolved a scheme (pro tem.)

To simplify my mother-tongue,

That so in fame I might resem:

Upt: Sinc:, who wrote “The Jung:”

And rouse an interest enorm:

In conversational reform.

I grudge the time my fellows waste

Completing words that are so comm:

Wherever peop: of cult: and taste

Habitually predom:

‘Twould surely tend to simpli: life

Could they but be curtailed a trif:

For is not “Brev: the soul of Wit”?

(Inscribe this mott: upon your badge)

The sense will never suff: a bit,

If left to the imag:

Since any pers: can see what’s meant

By words so simp: as “husb:” or “gent:”

When at some meal (at dinn: for inst:)

You hand your unc: an empty plate,

Or ask your aunt (that charming spinst:)

To pass you the potat:,

They have too much sagac:, I trust,

To give you sug: or pepp: or must:

If you require a slice of mutt:

You’ll find the selfsame princ: hold good,

Nor get, instead of bread and butt:,

Some tapioca pudd:,

Nor vainly bid some boon-compan:

Replen: with Burg: his vacant can.

At golf, if your oppon: should ask

Why in a haz: your nib: is sunk,

And you explain your fav’rite Hask:

Lies buried in a bunk:,

He cannot very well misund:

That you (poor fooz:) have made a blund:

If this is prob: — nay, even cert: —

My scheme at once becomes attrac:

And I (pray pard: a litt: impert:)

A public benefac:

Who saves his fellow-man and neighb:

A deal of quite unnecess: lab:

Gent: Reader, if to me you’ll list:

And not be irritab: or peev:,

You’ll find it of tremend: assist:

This habit of abbrev:,

Which grows like some infec: disease,

Like chron: paral: or German meas:

And ev’ry living human bipe:

Will feel his heart grow grate: and warm

As he becomes the loy: discip:

Of my partic: reform,

(Which don’t confuse with that, I beg,

Of Brander Matth: or And: Carneg:)

“”T is not in mort: to comm: success,”

As Shakes: remarked; but if my meth:

Does something to dimin: or less:

The expend: of public breath,

My country, overcome with grat:,

Should in my hon: erect a stat:

My bust by Rod: (what matt: the cost?)

Shall be exhib:, devoid of charge,

With (in the Public Lib: at Bost:)

My full-length port: by Sarge:

That thous: from Pitts: or Wash: may swarm

To worsh: the Found: of this Reform.

Meanwhile I seek with some avid:

The fav: of your polite consid:

On March 28, 1912, bacteriologist Almroth Wright wrote a letter to the London Times arguing that women should be denied the vote and in fact kept away from politics altogether in light of their psychological shortcomings. Two days later the Times printed this response. It was signed “One of the Doomed” but in fact had been penned by 26-year-old Clementine Churchill, wife of Winston:

March 30th, 1912

To the Editor of The Times.

Sir,

After reading Sir Almroth Wright’s able and weighty exposition of women as he knows them the question seems no longer to be ‘Should women have votes?’ but ‘Ought women not to be abolished altogether?’

I have been so much impressed by Sir Almroth Wright’s disquisition, backed as it is by so much scientific and personal experience, that I have come to the conclusion that women should be put a stop to.

We learn from him that in their youth they are unbalanced, that from time to time they suffer from unreasonableness and hypersensitiveness, and that their presence is distracting and irritating to men in their daily lives and pursuits. If they take up a profession, the indelicacy of their minds makes them undesirable partners for their male colleagues. Later on in life they are subject to grave and long-continued mental disorders, and, if not quite insane, many of them have to be shut up.

Now this being so, how much happier and better would the world not be if only it could be purged of women? It is here that we look to the great scientists. Is the case really hopeless? Women no doubt have had their uses in the past, else how could this detestable tribe have been tolerated till now? But is it quite certain that they will be indispensable in the future? Cannot science give us some assurance, or at least some ground of hope, that we are on the eve of the greatest discovery of all — i.e., how to maintain a race of males by purely scientific means?

And may we not look to Sir Almroth Wright to crown his many achievements by delivering mankind from the parasitic, demented, and immoral species which has infested the world for so long?

Yours obediently,

C.S.C.

(‘One of the Doomed’)

By John Brown. White to mate in two moves.

| SelectClick for Answer | | --- | | 1. Qe7! and the queen or bishop will mate. From Chess Strategy, 1865. |

| | | |

Having lost both his legs at the Second Battle of Bull Run, James Tanner had settled into life as a government stenographer in the Ordnance Department in Washington, D.C., when on April 14, 1865, he was suddenly summoned to the building next to his boarding house, where Abraham Lincoln lay dying. Between midnight and 1:30 a.m., using shorthand, he recorded the accounts of those who had witnessed the assassination, and, he said later, “in fifteen minutes I had testimony enough to hang Wilkes Booth, the assassin, higher than ever Haman hung.” Here’s a sample, the statement of actor William Henry Hawk, who had been performing at Ford’s Theatre that night:

I was on the stage at the time of the firing & heard the report of the pistol. My back was towards the Presidents box at the time. I heard something tear & somebody fell & as I looked towards him he came in the direction in which I was standing & I believe to the best of my knowledge that it was John Wilkes Booth. Still I am not positive that it was him. I only had one glance at him as he was rushing towards me with a dagger & I turned and run & after I run up a flight of stairs I turned and exclaimed ‘My God that’s John Booth.’ I am acquainted with Booth. I met him the first time a year ago. I saw him today about one o’clock. Said I ‘how do you do Mr. Booth’ and he says ‘how are you Hawk.’ He was sitting on the steps of Fords Theatre reading a letter. He had the appearance of being sober at the time. I was never intimate with him. He had no hat on when I saw him on the stage. In my own mind I do not have any doubt but that it was Booth. He made some expression when he came on the stage but I did not understand what.

Tanner’s notes are known as the Tanner Manuscript — you can read them at the Internet Archive.

During World War II, British thespian Maurice Evans toured the Central Pacific with a stripped-down version of Hamlet in which all the male actors were G.I.s. He cut down and sped up the text so that the play ran in 2 hours and 45 minutes, so that the men could return to their quarters on time.

“As I remember, on opening night, Hamlet seemed like a flop,” recalled one participant. “There was barely a murmur of response from the house and a fair amount of gloom backstage. We were later told that the audience had been reminded that this was not some cheap skin show but a classic, and that they were to show respect for Shakespeare and for Hamlet, who happened to be, by God, an officer in the United States Army. With this misunderstanding cleared up, future audiences were much more enthusiastic.”

In fact the “G.I. Hamlet” proved so successful that when the war was over Evans moved it to New York and then toured the country. He didn’t mean to be typed as a Shakespearean actor, he said; he just wanted audiences to enjoy the plays as “rattling good shows.”

This is Charles Darwin’s first diagram of an evolutionary tree, from his First Notebook on Transmutation of Species. He drew it around July 1837, barely a month after he’d opened his first full transmutation notebook.

“Case must be that one generation should have as many living as now,” he wrote. “To do this and to have as many species in same genus (as is) requires extinction. Thus between A + B the immense gap of relation. C + B the finest gradation. B + D rather greater distinction. Thus genera would be formed. Bearing relation to ancient types with several extinct forms.”

At the top he’s written “I think.”

In a Midlands pub in October 1888, a Londoner named Alfred Blanchard told the landlord that he was the Whitechapel murderer. He repeated the statement to several people and was taken to the Duke Street police station, where he quickly recanted his confession. He had been in the pub for nine hours and drunk about five and a half pints of beer. From the Birmingham Press Gazette:

About half-past twelve o’clock he asked witness what kind of detectives they had in Birmingham. Witness told him he believed them to be very clever men. Prisoner said that it would be a funny thing if the Whitechapel murderer were to give himself up in Birmingham. Witness acquiesced, and prisoner continued, ‘I am the Whitechapel murderer.’ Turning round to an elderly gentleman sitting in the bar, prisoner said, ‘Look here, old gentleman; perhaps you would not think there was a murderer in the house.’ ‘I don’t know about that,’ replied the customer; ‘you might not look unlike one.’ Prisoner said, ‘I am one, then.’ Later on the old gentleman asked prisoner had he got the knife with him, and he answered that he had left a long knife behind him. Someone asked prisoner how he did the murders without making the victims scream. He explained that this was done ‘simply by placing the thumb and finger on the windpipe and cutting the throat with the right hand.’ He said he had ‘done six of them in London.’ He was sober when he made this statement. Turning round to witness prisoner said, ‘You are a fool if you don’t get the thousand pounds reward offered for me; you may as well have it as anyone else.’

He told the magistrate’s clerk that he had been drinking for two or three days before this and hoped that the press would be kind enough not to mention his case. He was dismissed with the admonition, “What a foolish man you have been.”

Inventor Thaddeus Cahill offered a startling advance in 1895: An electronic keyboard instrument that could distribute music over the nation’s telephone networks. By combining sine waves according to Hermann Helmholtz’s new theories, the device could approximate the tone of any given instrument using electrical dynamos.

After hearing a demonstration at the Hotel Hamilton, Ray Stannard Baker wrote in McClure’s, “The first impression the music makes upon the listener is its singular difference from any music ever heard before: in the fullness, roundness, completeness, of its tones.”

Unfortunately, the device required an enormous amount of electricity, it disrupted the New York telephone network, and it was rapidly overtaken by other inventions in an immensely fruitful period. Cahill had hoped to fund it through subscriptions, and this quickly became impossible. But it had its adherents — Mark Twain’s friend Albert Bigelow Paine recalled a social gathering at the Clemens home at which the author demonstrated the instrument:

“Clemens was filled with enthusiasm over the idea. He made a speech a little before midnight, in which he told how he had generally been enthusiastic about inventions which had turned out more or less well in about equal proportions. He did not dwell on the failures, but he told how he had been the first to use a typewriter for manuscript work; how he had been one of the earliest users of the fountain-pen; how he had installed the first telephone ever used in a private house, and how the audience now would have a demonstration of the first telharmonium music so employed. It was just about the stroke of midnight when he finished, and a moment later the horns began to play chimes and ‘Auld Lang Syne’ and ‘America.'”

Susan Finden named her cat Casper because he kept disappearing, visiting doctor’s offices, office buildings, and pharmacies near her Weymouth home. When she moved to Plymouth in 2006 she was too busy to monitor his daily activities, and so three years later she was surprised to learn that he was riding buses. The drivers, who looked out for him, told her that he would journey 11 miles to the city center and back, sitting on a favored seat. They would let him out opposite his house.

“I couldn’t believe it at first, but it explains a lot,” she said. “He loves people and we have a bus stop right outside our house so that must be how he got started — just following everyone on.”

Ironically, or perhaps inevitably, he was finally killed by a taxi. The news of his death brought condolences from around the world, and Finden wrote a best-selling book. “He will be greatly missed,” she wrote in a note posted on Casper’s usual bus stop. “He was a much-loved pet who had so much character. Thank you to all those who befriended him.”

barkable

adj. able to bark

There’s a word for you! Eileen Power’s The Wool Trade in English Medieval History (1941) quotes a 13th-century treatise on estate management:

It profiteth the lord to have discreet shepherds, watchful and kindly, so that the sheep be not tormented by their wrath, but crop their pasture in peace and joyfulness; for it is a token of the shepherd’s kindness if the sheep be not scattered abroad but browse around him in company. Let him provide himself with a good barkable dog and lie nightly with his sheep.

Bonus: hinnible means able to neigh or whinny.

From reader Derek Christie:

Each player in a game of cribbage has a hand of four cards. A single further card is turned up and serves as the fifth card in every player’s hand. Part of the game involves scoring your hand. You get points for any combination of cards that adds to 15, like 9 4 2; for two or more of any rank, like 3 3; or for any run of three or more, like Ace 2 3. The Jack, Queen, and King each score 10. Show that if a 5 has been turned up, every player must score some points.

| SelectClick for Answer | | --- | | Try and make a hand that doesn’t score. The turnup is a 5. This means you must choose 4 different additional cards from the group 1 2 3 4 6 7 8 9, and to avoid scoring, the resulting hand mustn’t include any pairs or runs or any combination of cards that adds to 10. Since you can’t have two cards adding to 10, you’ll need to choose one card from each of the pairs 9 1, 8 2, 7 3, and 6 4. Try 6 from 6 4. Now you have 5 6. You can’t have 7 (which would produce a run), so you must take the 3, giving 5 6 3. But this is a dead end: Now you must avoid both the 1 and the 9, since each of these produces a 15. So you can’t get anywhere with the 6 from the 6 4 pair. Try the other card from that pair, the 4. Now you have 4 5. You can’t have 3 (producing a run), so you must take the 7, giving 4 5 7. Now you can’t take 8 (since this would produce 15), so you must take the 2, giving 2 4 5 7. And now both the 1 and the 9 again give 15, another dead end. With both the 6 and the 4 excluded, there’s no way to assemble a hand of four cards that can remain scoreless with a turnup card of 5. So every hand must score something. (Thanks, Derek.) |

In the early 1900s, a train company left a coffin in the rain, resulting in “mutilation” of the corpse. The widow sought damages, which raised a poignant question: Who owns a corpse? An earlier case had held that once it’s buried a corpse belongs to the ground; a person who dug it up improperly would be guilty merely of trespass. But another case had deemed a corpse “quasi-property”: It may belong to no one, but certainly the kin have an interest in it. Joseph Henry Lumpkin of the Georgia Supreme Court wrote:

Death is unique. It is unlike aught else in its certainty and its incidents. A corpse in some respects is the strangest thing on earth. A man who but yesterday breathed and thought and walked among us has passed away. Something has gone. The body is left still and cold, and is all that is visible to mortal eye of the man we knew. Around it cling love and memory. Beyond it may reach hope. It must be laid away. And the law — that rule of action which touches all human things — must touch also this thing of death. It is not surprising that the law relating to this mystery of what death leaves behind cannot be precisely brought within the letter of all the rules regarding corn, lumber and pig iron.

The court ruled in favor of the widow, and this view is widely held today: The survivors have the right to take possession of a body and dispose of it.

“No man chooses evil because it is evil; he only mistakes it for happiness, the good he seeks.” — Mary Wollstonecraft