Nostr notes by Futility Closet (Unofficial)

Poles Apart A problem by Russian mathematician Viktor Prasolov: A ...

2026-10-31T10:13:00Z

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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Unquote “He who lives to see two or three generations is like a ...

2026-10-30T21:40:51Z

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/

#schopenhauer

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“Curious Address” I send you a post-card which I received in ...

2026-10-30T09:47:47Z

“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/

#postoffice #address #suttonscarsdale #albertroad #stroudgreen #johnalderson #hayhellbeheareteaareohhaydee #areohhaydeesteaareohyoudee #geearehehehenlondon #chesterfield

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Turnabout An “enigma in praise of women,” from an 1820 ...

2026-10-29T21:53:51Z

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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Zoology Description of the Lyon in Edward Topsell’s 1607 ...

2026-10-29T13:06:29Z

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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Degree Political controversies, as Mr. Graham Wallas has pointed ...

2026-10-28T21:24:32Z

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/

#grahamwallas #bertrandrussell #man #icarus

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A Late Addition Holst’s The Planets premiered in 1918, 12 years ...

2026-10-22T01:48:45Z

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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Criticism The library of St John’s College, Oxford, used to ...

2026-10-21T19:53:16Z

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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Relativity Fixed to the front of the clock case in the north ...

2026-10-20T22:37:18Z

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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Two for One The plot of Lady Chatterley’s Lover in the meter of ...

2026-10-20T10:26:43Z

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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Query Winner of a clerihew contest sponsored by Games magazine in ...

2026-10-19T21:56:20Z

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/

#descartesdepart #therefore #games

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Strike Up the Bland In 1986, Michael Kinsley, editor of The New ...

2026-10-19T09:47:37Z

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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Alphabetical Disorder In the 19th century, the index to the ...

2026-10-18T11:57:11Z

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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Throughput Take a piece of string about six feet in length, and ...

2026-10-17T09:28:04Z

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/

#conjuringbook #ownconjuring #boy

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Lineage If the last 50,000 years of man’s existence were ...

2026-10-16T21:38:15Z

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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The Ringelmann Effect In studying the relationship between ...

2026-10-16T10:35:29Z

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/

An Orderly Vacation A puzzle from Peter Winkler’s excellent ...

2026-10-16T08:03:18Z

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/

“We and They” Father, Mother, and Me, Sister and Auntie say ...

2026-10-16T07:20:30Z

“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/

The Karidis Keyboard When IBM released the ThinkPad 701 ...

2026-10-16T04:21:39Z

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/