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Last Notes

2026-10-31 10:13:00 GMT

Poles Apart
A problem by Russian mathematician Viktor Prasolov:
A circle is divided by points into 3k arcs such that there are k arcs each of length 1, 2, and 3. Prove that two of the division points are diametrically opposite one another.
SelectClick for Answer
Suppose that this is not the case, that none of the division points are diametrically opposite one another. This means that every arc of length 1 must stand opposite an arc of length 3. Remove one such pair, an arc of length 1 and its opposing arc of length 3. Now we’ve divided the circle into two large arcs.
If one of these large arcs contains m arcs of length 1 and n arcs of length 3, then the other contains n arcs of length 1 and m arcs of length 3. The total number of arcs of length 1 and 3 in the two large arcs is 2(k– 1), so n + m = k – 1.
Apart from arcs of length 1 and 3, each large arc contains only arcs of length 2, which don’t change the parity (odd or even) of its total length. This means that the parity of the length of each large arc will be the same as the parity of k – 1. But the length of each large arc is (6k – 1 – 3)/2 = 3k – 2. That’s a contradiction: k – 1 and 3k – 2 have opposite parities. So our assumption, that none of the division points on the original circle are diametrically opposite one another, cannot be the case.
(From Prasolov’s Problems in Plane and Solid Geometry, 1988.)
https://www.futilitycloset.com/2026/10/31/poles-apart/
#apart #viktorprasolov #answersuppose #russian #solidgeometry
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2026-10-30 21:40:51 GMT

Unquote
“He who lives to see two or three generations is like a man who sits some time in the conjurer’s booth at a fair, and witnesses the performance twice or thrice in succession. The tricks were meant to be seen only once; and when they are no longer a novelty and cease to deceive, their effect is gone.” — Schopenhauer
https://www.futilitycloset.com/2026/10/30/unquote-721/
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#schopenhauer
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2026-10-30 09:47:47 GMT

“Curious Address”
I send you a post-card which I received in the ordinary way by post from my brother, who lives at Sutton Scarsdale, a scattered village near Chesterfield. You will notice that the card was posted at 7.15 p.m. on the 5th October, and it was delivered during the evening of the following day. The address looks a mixture of Greek and German, but on inspection it will be found that each letter is spelled out in full. The pencilled words were inserted by the Post Office officials. The Post Office is often the object of complaints for tardiness in delivery, but I think great credit is due to it for its cleverness and promptness in this case. — Mr. John Alderson, 12, Albert Road, Stroud Green, N.
From the Strand, January 1904. I make out the text as:
Hemr. Jay Hayhelldeehearesohhen
12, Hayhellbehearetea Areohhaydee
Steaareohyoudee Geearehehehen
London N.
https://www.futilitycloset.com/2026/10/30/curious-address/
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#postoffice #address #suttonscarsdale #albertroad #stroudgreen #johnalderson #hayhellbeheareteaareohhaydee #areohhaydeesteaareohyoudee #geearehehehenlondon #chesterfield
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2026-10-29 21:53:51 GMT

Turnabout
An “enigma in praise of women,” from an 1820 miscellany:
Happy that man may pass his life,
Who’s free from matrimonial chains;
Who is directed by a wife,
Is sure to suffer for his pains.
What tongue is able to unfold
The falsehood which in women dwell?
The worth in women you behold
Is almost imperceptible.
Adam could find no solid peace
When Eve was given him for a mate;
Till he beheld a woman’s face,
Adam was in a happy state.
See, in the female race appear
Hypocrisy, deceit, and pride;
Truth, darling of a heart sincere,
In women never can reside.
They’re always studying to employ
Their time in malice and in lies;
Their leisure hours in virtuous joy
To spend, ne’er in their thoughts arise.
Destruction take the men, I say,
Who make the fair their chief delight;
Who no regard to women pay,
Keep reason always in their sight.
“By reading the first and third lines together the Enigma is explained.”
https://www.futilitycloset.com/2026/10/29/turnabout-22/
#adam #happy #enigma #truth #till #hypocrisy #keep
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2026-10-29 13:06:29 GMT

Zoology
Description of the Lyon in Edward Topsell’s 1607 bestiary The History of Four-Footed Beasts:
Lyons bones have no marrow in them and are so hard that they will strike fire. Their neck is made of one stiffe bone, without any vertebras. They have five claws on the hinder feet and the balls of their eyes are black. Lyons eat but once in two days, and drink in like manner. Formerly in England a Lyon could tell noble blood from base. There is a variety of Lyon with human faces. As for the rest, the taile of a Lyon is very long, which they shake oftentimes, and by beating their sides therewith they provoke themselves to fight. The nether part of this taile is full of hairs and gristles, and some are of opinion that there is therein a little sting wherewithall the Lyon pricketh itselfe.
He adds, “I would not have the Reader … imagine I have … related all that is ever said of these Beasts, but only [what] is said by many.”
https://www.futilitycloset.com/2026/10/29/zoology-3/
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2026-10-28 21:24:32 GMT

Degree
Political controversies, as Mr. Graham Wallas has pointed out, ought to be conducted in quantitative terms. … The dispute between anarchism and bureaucracy at present tends to take the form of one side maintaining that we want no organization, while the other maintains that we want as much as possible. … Some people think that we keep our rooms too hot for health, others that we keep them too cold. If this were a political question, one party would maintain that the best temperature is the absolute zero, the other that it is the melting point of iron. Those who maintained any intermediate position would be abused as timorous time-servers, concealed agents of the other side, men who ruined the enthusiasm of a sacred cause by tepid appeals to mere reason. Any man who had the courage to say that our rooms ought to be neither very hot nor very cold would be abused by both parties, and probably shot in No Man’s Land. Possibly some day politics may become more rational, but so far there is not the faintest indication of a change in this direction.
— Bertrand Russell, Icarus, 1924
https://www.futilitycloset.com/2026/10/28/degree/
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#grahamwallas #bertrandrussell #man #icarus
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2026-10-28 12:23:27 GMT

Parable
Image: Wikimedia Commons
Anne K. Mellor described Frankenstein as “a book about what happens when a man tries to have a baby without a woman.”
https://www.futilitycloset.com/2026/10/28/parable/
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#wikimediacommons #commonsanne #frankenstein #mellor
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2026-10-27 20:50:22 GMT

Tic-Tac-Don’t
With best play on both sides, conventional tic-tac-toe (noughts and crosses) is always a draw. Played in three dimensions, though, in a 3×3×3 cube, it’s always a win for whichever player manages to take the central cell. In fact, a draw is impossible — there’s no way to fill the “board” with 14 crosses and 13 noughts without completing one or more winning paths.
What if we reverse the object so that the first player to complete such a path loses? Interestingly, in that case seizing the center cell is still the best strategy. Thereafter, whichever cell the second player chooses, the first player should take the cell diametrically opposite. Obviously this can’t create a winning triple that passes through the center, but neither can it create a triple that doesn’t pass through the center, because the second player would necessarily just have completed such a triple himself on the opposite side of the cube.
“So the first player cannot lose,” writes mathematician Solomon Golomb. “Thus, because no draws are possible on the 3×3×3 ‘board,’ he must win!”
(This is similar to the first player’s strategy in Henry Dudeney’s cigar puzzle.)
(Solomon W. Golomb, “Martin Gardner and Ticktacktoe,” in Erik D. Demaine, Martin L. Demaine, and Tom Rodgers, eds., A Lifetime of Puzzles, 2008.)
https://www.futilitycloset.com/2026/10/27/tic-tac-dont/
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#solomongolomb #demaine #martin #tomrodgers #henrydudeney
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2026-10-27 08:57:06 GMT

Catalog
Works by German surrealist painter and sculptor Max Ernst:
That Makes Me Piss (1919)
The Little Tear Gland That Says Tick-Tock (1920)
The Dog Who Shits (1920)
Winter Landscape: Gassing of the Vulcanized Iron Maiden to Produce the Necessary Warmth for the Bed (1921)
Two Children Are Threatened by a Nightingale (1924)
The Dove Was Right (1926)
Vision Induced by a String Found on My Table (1927)
Vision Induced by the Words ‘The Immovable Father’ (1927)
Scene of Severe Eroticism (1927)
Garden Airplane-Trap (1935)
The Harmonious Breakfast (1941)
Young Man Intrigued by the Flight of a Non-Euclidean Fly (1942-7)
Sign for a Herring School (1958)
Salvador Dalí invented similarly unusual titles. American avant-garde composer La Monte Young once titled a work The Obsidian Ocelot, The Sawmill, and The Blue Sawtooth High-Tension Line Stepdown Transformer Refracting The Legend of The Dream of The Tortoise Traversing The 189/98 Lost Ancestral Lake Region Illuminating Quotients from The Black Tiger Tapestries of The Drone of The Holy Numbers from The Tortoise, His Dreams And Journeys.
https://www.futilitycloset.com/2026/10/27/catalog-2/
#visioninduced #youngman #winterlandscape #harmoniousbreakfast #herringschool #maxernst #salvadordali #severeeroticism #twochildren #ironmaiden
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2026-10-26 20:51:16 GMT

Black and White
By Mrs. W.J. Baird. White to mate in two moves.
SelectClick for Answer
White wins with the quiet. 1. Qe2! Then:
1. … Kd5 2. Nb4#
1. … b4 2. Nf4#
1. … d5 2. Qc2#
1. … N any 2. Qe4#
From the Illustrated Sporting & Dramatic News, 1902.
https://www.futilitycloset.com/2026/10/26/black-and-white-306/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-26-black-and-white.png
#white #answerwhite #illustratedsporting
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2026-10-26 15:06:16 GMT

Indisposed
FDR’s sense of humor was a winner with the press. One day, when he was laid up in bed with a cold, the Post pulled a classic typographical error. The page one headline read: FDR IN BED WITH COED. Hardly had that early edition reached the White House than a Post reporter picked up the phone to hear: ‘This is Frank Roosevelt. I’d like 100 copies of that first edition of the Post. I want to send it to all my friends.’ Alas, the circulation department had scurried out to recover all the papers from the corner stands and destroy them. FDR never got his 100 copies.
— Kenneth W. Thompson, The Roosevelt Presidency, 1982
https://www.futilitycloset.com/2026/10/26/indisposed/
#fdr #post #whitehouse #bed #frankroosevelt #rooseveltpresidency #coed #kenneth #thompson
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2026-10-25 08:54:33 GMT

The Miracle Stair
Image: Wikimedia Commons
This spiral staircase, in the Loretto Chapel in Santa Fe, has no newel, or central pole — its treads are upheld by stringers, notched structural supports as in a conventional stair, but here the stringers make two complete turns as the helical stair rises 20 feet to the choir loft. All of this is held together by wooden pegs rather than glue or nails.
It was built sometime between 1877 and 1881, but the creator’s identity is not recorded. “It’s a magnificent work of art that humbles me as a master carpenter,” wrote Tim Carter in the Washington Post in 2010. “To create a staircase like this using modern tools would be a feat. It’s mind-boggling to think about constructing such a marvel with crude hand tools, no electricity and minimal resources.”
https://www.futilitycloset.com/2026/10/25/the-miracle-stair/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-25-the-miracle-stair.jpg
#stair #wikimediacommons #lorettochapel #timcarter #washingtonpost #santa
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2026-10-24 08:20:14 GMT

To Be Precise
On what date did Vincent van Gogh paint his 1889 masterpiece The Starry Night? Earlier studies had placed the creation in mid-June of that year, based on a letter the artist had written to his brother Theo around June 18. But Kyung Hee University doctoral candidate Elijah Jeong-hyun Kim noted that an observer in that period should have seen a waning gibbous moon, not the crescent seen in the painting.
Intrigued, he began to compare astronomical simulations, weather records, and van Gogh’s other writings. A better estimate of the scene’s creation, he says, is dawn on July 22, 1889. On that date the crescent moon, Venus, and the Hyades star cluster in the constellation Taurus would have been visible from van Gogh’s window in southern France, and the recorded hot weather would have inspired the cicadas the artist mentions in a letter.
Kim’s article appears in the journal Scientific Reports. “Our conversation with Van Gogh’s other skies is still ongoing,” he told Popular Science. “We plan to tell those stories one by one.”
(Texas State University “forensic astronomer” Donald W. Olson has done similar work, estimating for example that the scene below depicts Le Havre harbor as seen from Claude Monet’s hotel room at 7:35 a.m. on Nov. 13, 1872.) (Thanks, Sharon.)
https://www.futilitycloset.com/2026/10/24/to-be-precise/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-24-to-be-precise-1.jpg
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#vangogh #starrynight #kyunghee #heeuniversity #scientificreports #popularscience #kim #texasstate #claudemonet
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2026-10-23 23:13:20 GMT

Enlightenment
“I pay the schoolmaster, but ’tis the schoolboys that educate my son.” — Emerson, journal, May 25, 1849
https://www.futilitycloset.com/2026/10/23/enlightenment-5/
https://www.futilitycloset.com/wp-content/uploads/2010/09/2010-09-13-such-such-were-the-joys.jpg
#emerson #may
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2026-10-23 11:07:17 GMT

Smile
When 22-year-old student Christian LeBlanc fed a basket of bananas to a group of elephants on the Thai island of Koh Phangan in 2015, one of them seized his GoPro camera by its mount, and when the self-timer triggered the shutter he got “the worlds first ever Elfie.”
“Elephants are incredibly intelligent and it definitely makes you wonder if it was a conscious action,” he wrote. So who gets the credit? For now, in the judgment of Wikimedia, “This file is in the public domain because, as the work of a non-human animal, it has no human author in whom copyright is vested.”
https://www.futilitycloset.com/2026/10/23/smile-4/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-23-smile.jpg
#kohphangan #christianleblanc #elephants #elfie #thai #wikimedia
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2026-10-23 08:16:52 GMT

Counterparts
A brilliant device from the Japanese television variety show Kasou Taishou. Another:
https://www.futilitycloset.com/2026/10/22/counterparts/
#kasoutaishou #another
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2026-10-22 22:31:13 GMT

False Prospect
Because he had to earn a living painting portraits, Thomas Gainsborough could not spend as much time sketching outdoors as he would have liked. So he arranged pieces of moss, rock, vegetables, and mirror into tabletop “landscapes” that he could paint at night by candlelight.
Joshua Reynolds recalled him collecting “broken stones, dried herbs, and pieces of looking glass, which he magnified and improved into rocks, trees, and water.” Another visitor wrote, “I … have more than once sat by him of an evening and seen him make models … for landscape scenery on a little old-fashioned folding oak table. … He would place cork or coal for his foregrounds; make middle grounds of sand and clay, bushes of moss and lichens, and set up distant woods of broccoli.”
https://www.futilitycloset.com/2026/10/22/false-prospect/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-22-false-prospect.jpg
#thomasgainsborough #joshuareynolds
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2026-10-22 01:48:45 GMT

A Late Addition
Holst’s The Planets premiered in 1918, 12 years before Pluto was discovered.
So in 2000 Colin Matthews wrote an eighth movement, “Pluto, the Renewer,” to complete the cycle.
(I’m not sure of its status since 2006, when the International Astronomical Union reclassified Pluto a dwarf planet.)
https://www.futilitycloset.com/2026/10/21/a-late-addition/
#pluto #colinmatthews #astronomicalunion #internationalastronomical #renewer
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2026-10-21 19:53:16 GMT

Criticism
The library of St John’s College, Oxford, used to hold a copy of Spenser’s The Faerie Queene that bore a student’s penciled comment on the last page:
“First I thought Troilus And Criseyde was the most boring poem in English. Then I thought Beowulf was. Then I thought Paradise Lost was. Now I know that The Faerie Queen is the dullest thing out. Blast it.”
It had been written by Philip Larkin, who had studied English there in the 1940s.
https://www.futilitycloset.com/2026/10/21/criticism/
#faeriequeene #paradiselost #english #philiplarkin #oxford #college #first #john #spenser
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2026-10-20 22:37:18 GMT

Relativity
Fixed to the front of the clock case in the north transept of Chester Cathedral is a poem by Henry Twells (1823–1900):
When as a child I laughed and wept,
Time crept.
When as a youth I waxed more bold,
Time strolled.
When I became a full grown man,
Time RAN.
When older still I daily grew,
Time FLEW.
Soon I shall find, in passing on,
Time gone.
O Christ! wilt Thou have saved me then?
Amen.
He called it “Time’s Paces.”
https://www.futilitycloset.com/2026/10/20/relativity-5/
#henrytwells #chestercathedral #ran #flew #christ #paces #thou
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2026-10-20 10:26:43 GMT

Two for One
The plot of Lady Chatterley’s Lover in the meter of Longfellow’s Song of Hiawatha, by Martin Woodhead:
You shall hear how Lady Constance,
Tiring of her wounded husband
(Poor Sir Clifford, high war-hero,
Inconvenienced by shrapnel),
Found a gamekeeper called Mellors
Who would teach her in his lunch-hour
(And in language frank and fearless
Such as wives and servants blush at)
To admire the lower orders
While that blighted Bart, Sir Clifford
(Let us waste no pity on him,
For the man was paraplegic),
In his new electric wheelchair
Tried to drive it up a tunock —
Tried and tried, and couldn’t make it.
From a Spectator competition. Chatterley in Field & Stream. Hiawatha in condensed matter physics.
https://www.futilitycloset.com/2026/10/20/two-for-one-5/
#sirclifford #poorsir #ladyconstance #martinwoodhead #tried #ladychatterley #hiawatha #bart #found #inconvenienced
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2026-10-19 21:56:20 GMT

Query
Winner of a clerihew contest sponsored by Games magazine in 1983:
Did Descartes
Depart
With the thought
“Therefore I’m not”?
https://www.futilitycloset.com/2026/10/19/query-9/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-19-query-1.jpg
#descartesdepart #therefore #games
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2026-10-19 09:47:37 GMT

Strike Up the Bland
In 1986, Michael Kinsley, editor of The New Republic, spotted the headline “Worthwhile Canadian Initiative” in the New York Times and challenged his readers to come up with a more boring one. This was a tall order: The Times head, someone said, manages to be “not only boring as a whole, but boring word by word.” Submissions included:
“U.S. Leadership Needed” (New York Times)
“Trade, A Two-Way Street” (New York Times)
“Beyond the News, Larger Issues” (New York Times)
“Thoughts at Graduation Time” (New York Times)
“Continue Manned Flight in Space” (New York Times)
“Chill Falls on Warming Relations Between Australia and Indonesia” (New York Times)
“University of Rochester Decides to Keep Name” (New York Times)
“Dramatic Changes Fail to Materialize on Hill” (Washington Post)
“Surprises Unlikely in Indiana” (Chicago Tribune)
“CIA Analysis Sees Soviet Economy in Need of Changes” (San Diego Union)
“Prevent Burglary by Locking House, Detectives Urge” (Boston Globe)
“Methodists Oppose Use of Nuclear Arms” (New York Times)
“Economist Dies” (Wisconsin State Journal)
“Turbulent Days for Donald D. Engen” (New York Times)
The winner was found in the New York Times science section: “Debate Goes on Over the Nature of Reality.”
https://www.futilitycloset.com/2026/10/19/strike-up-the-bland/
#newyork #yorktimes #newrepublic #bland #graduationtime #michaelkinsley #canadianinitiative #worthwhilecanadian #dramaticchanges #bostonglobe
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2026-10-18 11:57:11 GMT

Alphabetical Disorder
In the 19th century, the index to the London Times was compiled by Samuel Palmer. Palmer had an unusual way of working, which apparently wasn’t noticed until 1890, when a mystified reader, Corrie Thompson, wrote to Notes and Queries with some examples:
An article about a boy sentenced for stealing a twopenny pie was indexed under “Atrocious Criminal.”
An article about a floating chapel loosed from its moorings was indexed under “Disgraceful Act.”
An article about a storm at Saône-et-Loire was indexed under “Fatal Storm.”
An article about a spell of dry weather was indexed under “Present Dry Season.”
An article about two women imprisoned for stealing a mare and for shooting at a man were indexed under “Rather uncommon for Females.”
Apparently Palmer had simply been compiling headlines without reading the articles. This accounts for entries such as “Extraordinary Escape of Boy at Erith Station, From a Bull Being on the Line” and “Extraordinary Marriage Adventure.” Thompson wrote, “One would expect to find this system adopted in a ‘table of contents,’ but surely it is out of place in an ‘index.'”
One wonderful exception, which Palmer apparently wrote himself:
“Death of Jane Thomas in her Mother’s Arms in Holborn at Joy in Seeing her parent at the Stage Door to Receive her.”
https://www.futilitycloset.com/2026/10/18/alphabetical-disorder/
#palmer #londontimes #atrociouscriminal #samuelpalmer #disgracefulact #corriethompson #extraordinary #fatalstorm #apparently #dryseason
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2026-10-17 09:28:04 GMT

Throughput
Take a piece of string about six feet in length, and tie the ends together. Pass it through a button-hole of your coat; hitch one thumb at each end, hook the little fingers into the upper strings of the opposite hand. Then draw the hands well outward, and the string will look very complicated, as in the engraving.
To get out the string, loose the hold of the right thumb and left finger, and separate the hands smartly, when the string will appear to have been pulled out through the substance of your coat.
— The Boy’s Own Conjuring Book, 1860
https://www.futilitycloset.com/2026/10/17/throughput-2/
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#conjuringbook #ownconjuring #boy
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2026-10-16 21:38:15 GMT

Lineage
If the last 50,000 years of man’s existence were divided into lifetimes of approximately sixty-two years each, there have been about 800 such lifetimes. Of these 800, at least 650 were spent in caves. Only during the last seventy lifetimes has it been possible to communicate effectively from one lifetime to another — as writing made it possible to do. Only during the last six lifetimes did masses of men ever see a printed word. Only during the last four has it been possible to measure time with any precision. Only in the last two has anyone anywhere used an electric motor. And the overwhelming majority of all the material goods we use in daily life today have been developed within the present, the 800th, lifetime.
— Alvin Toffler, Future Shock, 1970
https://www.futilitycloset.com/2026/10/16/lineage/
#alvintoffler #futureshock
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2026-10-16 12:35:27 GMT

Lingua Franca
Mathematician Giuseppe Peano created an auxiliary language to facilitate communication between people of different nations. Latin already served as an international language, he reasoned; “Latino sine flexione” could retain that language’s vocabulary but simplify its grammar as much as possible. In a 1908 speech announcing the idea, he began speaking in classical Latin and adopted each simplification as he described it until he was speaking in the new language. Here’s the Lord’s Prayer:
Nostro patre, qui es in caelos,
que tuo nomine fi sanctificato;
que tuo regno adveni;
que tuo voluntate es facto
sicut in caelo et in terra.
Da hodie ad nos nostro pane quotidiano,
et remitte ad nos nostro debitos,
sicut et nos remitte ad nostro debitores.
Et non induce nos in tentatione,
sed libera nos ab malo.
Amen.
In the end it was not widely adopted, but most of Peano’s books and papers are written in his proposed language.
https://www.futilitycloset.com/2026/10/09/lingua-franca-3/

2026-10-16 10:35:29 GMT

The Ringelmann Effect
In studying the relationship between productivity and efficiency in 1913, French agricultural engineer Maximilien Ringelmann found that members of a group perform worse on average as the size of the group increases. In a tug of war, as the size of a team grows, each member begins to “loaf,” relying on his teammates to put forth the necessary effort. Worse, the team’s growing size makes it increasingly difficult to coordinate its actions.
Interestingly, though, ants have been shown to increase in efficiency when working in teams. New World army ants can carry larger loads as a team than if the burden were distributed among them individually, and Weaver ants organize pulling chains that can effectively double the strength of each member. So “the Ringelmann effect” isn’t inescapable.
https://www.futilitycloset.com/2026/10/09/the-ringelmann-effect/

2026-10-16 10:00:06 GMT

Road Thoughts
A puzzle by Sam Loyd:
Here is a pretty problem which I figured out during a ride from Bixley to Quixley astride a razor-back mule. I asked Don Pedro, a native guide who walked ahead of me pulling the mule forward by its reins, if my steed had another gait. He said it had but that it was much slower, so I pursued my journey at uniform speed. To encourage Don Pedro, who was my chief propelling power, I said we would pass through Pixley, so as to get some liquid refreshments; and from that moment he could think of nothing but Pixley.
After we had been traveling for forty minutes I asked how far we had gone. Don Pedro replied: ‘Just half as far as it is to Pixley.’
After creeping along for seven miles more I asked: ‘How far is it to Quixley?’ He replied as before: ‘Just half as far as it is to Pixley.’
We arrived at Quixley in another hour, which induces me to ask you to determine the distance from Bixley to Quixley.
SelectClick for Answer
Two time intervals are given, but they’re not needed to solve the problem. The first question is asked between Bixley and Pixley; call that point x. The second question is asked between Pixley and Quixley; call that point y. The distance between x and y is 7 miles. The distance from x to Pixley is two-thirds the distance from Bixley to Pixley, and the distance from y to Pixley is two-thirds the distance between Pixley and Quixley. So the distance from x to y, 7 miles, is two-thirds the total distance, which must be 10.5 miles.
https://www.futilitycloset.com/2026/10/10/road-thoughts/

2026-10-16 09:21:18 GMT

Shelf Concepts
Henry Wheatley’s 1878 monograph “What Is an Index?” gives a list of “titles of books that have given trouble to bibiographers” or been assigned to the wrong subjects:
Maria Edgeworth’s “Essay on Irish Bulls” and a treatise on the Great Seal of the United States have both been listed under Zoology.
A description of Napier’s bones, John Napier’s manual calculating device, has been listed under Anatomy.
“Under the Microscope,” poet Algernon Charles Swinburne’s 1872 invective against critic Robert Buchanan, has been listed under Optical Instruments.
A volume of poetry titled The Viol and the Lute has been listed under Musical Instruments.
John Ruskin’s Notes on the Construction of Sheepfolds, an 1851 pamphlet on divinity, has been listed under Agriculture.
Scottish minister William McEwen’s writings on biblical types have been listed under Printing.
Best: German naturalist Johann Heinrich Linck’s De stellis marinis liber singularis, a treatise on sea stars, has been listed under Astronomy.
https://www.futilitycloset.com/2026/10/11/shelf-concepts/

2026-10-16 08:41:50 GMT

Singing Lessons
Image: Wikimedia Commons
When the local population of rufous-collared sparrows dwindled in Buenos Aires, scientists found an innovative way to teach mating calls to younger birds: They consulted hand-drawn annotations of sparrow songs that had been made in the 1960s and used a computer to broadcast simulated versions in local habitats. Within three months a local bird was heard copying parts of the song. Similar efforts have succeeded in England and Australia, and scientists are beginning to stockpile databases of birdsong to aid future generations. “One day we’ll be grateful to have all those records,” physicist Gabriel Mindlin told the Guardian.
Birds mimicking human technology: Technical Fowl, Pitching In, Ghosts of Scotland. (Thanks, Sharon.)
https://www.futilitycloset.com/2026/10/16/singing-lessons/
https://www.futilitycloset.com/wp-content/uploads/2026/10/2026-10-16-singing-lessons.jpg

2026-10-16 08:03:18 GMT

An Orderly Vacation
A puzzle from Peter Winkler’s excellent Mathematical Puzzles (2021):
A certain island contains a network of roads. Each road segment (between one intersection and the next) has its own name. If d is the average number of road segments that meet at an intersection, show that it’s possible to take a drive on the island that traverses at least d road segments and hits them in alphabetical order.
SelectClick for Answer
Each road has two ends, so the total number of road ends observed at the island’s intersections is twice the number of roads on the island. The number we’re calling d, the average number of road segments that meet at an intersection, is thus 2m/n, where m is the number of roads on the island and n is the number of intersections.
Station a pedestrian at each intersection. At time 1, let the pedestrians at either end of the alphabetically first road traverse it, changing places. At time 2, let the pedestrians who find themselves at either end of the alphabetically second road do the same. Continue this procedure until it’s been applied to all the roads. At the end of this exercise each pedestrian will have followed an alphabetical path (because we addressed the roads in alphabetical order). Each road is traversed twice, and the number of pedestrians equals the number of intersections on the island. So the average number of roads that each pedestrian traverses is 2m/n = d.
https://www.futilitycloset.com/2026/10/13/an-orderly-vacation/

2026-10-16 07:20:30 GMT

“We and They”
Father, Mother, and Me,
Sister and Auntie say
All the people like us are We,
And every one else is They.
And They live over the sea,
While We live over the way,
But — would you believe it? — They look upon We
As only a sort of They!
We eat pork and beef
With cow-horn-handled knives.
They who gobble Their rice off a leaf,
Are horrified out of Their lives;
And They who live up a tree,
And feast on grubs and clay,
(Isn’t it scandalous?) look upon We
As a simply disgusting They!
We shoot birds with a gun.
They stick lions with spears.
Their full-dress is un-.
We dress up to Our ears.
They like Their friends for tea.
We like Our friends to stay;
And, after all that, They look upon We
As an utterly ignorant They!
We eat kitcheny food.
We have doors that latch.
They drink milk or blood,
Under an open thatch.
We have Doctors to fee.
They have Wizards to pay.
And (impudent heathen!) They look upon We
As a quite impossible They!
All good people agree,
And all good people say,
All nice people, like Us, are We
And every one else is They:
But if you cross over the sea,
Instead of over the way,
You may end by (think of it!) looking on We
As only a sort of They!
— Kipling
https://www.futilitycloset.com/2026/10/13/we-and-they/

2026-10-16 05:51:01 GMT

What’s New, Pussycat?
Tom Jones’ “Sex Bomb” rendered in the style of a 16th-century chanson, by music theory lecturer Jonas Quin:
Via MetaFilter.
https://www.futilitycloset.com/2026/10/14/whats-new-pussycat/

2026-10-16 05:07:32 GMT

Esprit de Corps
Someone asked Wellington, at a dinner party, what was the most inane remark he had ever heard. His reply — possibly not politically correct — was that before a battle in the Peninsular War he had heard a Portuguese General address his troops saying, ‘Remember, men, you are Portuguese.’
— From Alec Guinness’ commonplace book
https://www.futilitycloset.com/2026/10/14/esprit-de-corps/

2026-10-16 04:21:39 GMT

The Karidis Keyboard
When IBM released the ThinkPad 701 subnotebook in 1995, users got a surprise. The unit was only 24.6 centimeters wide, but opening the lid presented a keyboard more than 4 centimeters wider. The secret was a dissection: The keyboard was stored in two pieces, each roughly a right triangle, and as the lid was opened these slid to either side, with one moving downward until they merged into a full-sized keyboard. (Mathematician Greg Frederickson wrote, “You find yourself opening and closing the lid repeatedly just to watch this movement!”)
The effect was so pleasing that the “butterfly keyboard” entered the permanent collection of Manhattan’s Museum of Modern Art, but IBM discontinued the feature when it retired the 701. Designer John Karidis said, “The butterfly keyboard was no longer necessary, because people moved to larger displays. Where the butterfly approach makes sense is where you want the largest keyboard possible in combination with an 8-inch or 10-inch display.”
https://www.futilitycloset.com/2026/10/15/the-karidis-keyboard/

2026-10-16 03:21:34 GMT

In a Word
janiform
adj. having two faces, sides, or contrasting aspects
esemplastic
adj. having the function of moulding into unity; unifying
theriomorphic
adj. having the form of a wild beast
anabiosis
n. a coming to life again; revival, resuscitation
From the Strand, December 1903:
The only violin in the world made from the claw of a giant lobster has just been completed by John H. Dadmun, of 429, Berkley Street, Camden, N.J. This unique instrument, strange to say, can be made to produce as sweet musical tones as any high-class violin. Its owner gives the following as the story of its life.
The lobster from which the claw was taken was caught off Gloucester, Mass., in March 1862. In time it came to Concord, N.H., where Mr. Dadmun saw it. At that time the lobster weighed seventeen pounds and a half. A single claw weighed five pounds and a quarter. The claw that Mr. Dadmun preserved, after the lobster had gone the way of such things, was thirteen and a quarter inches long, seven inches broad, and three and a quarter inches thick.
Preserved among other curiosities of the Dadmun household the giant claw remained a claw for many years. One day it occurred to its owner that it was shaped something like a violin, and he tried the experiment of fashioning it to look more like that popular musical instrument. After much patient effort Mr. Dadmun managed to transform the claw into a violin that could be played. The tone was very sweet, but not loud enough for an orchestra. Experiment proved that by changing the fittings and settings the tone could be made much louder. As it is now the violin when played properly sounds exactly like any other violin. It is doubtless the most curious musical instrument ever made.
https://www.futilitycloset.com/2026/10/15/in-a-word-715/
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