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.
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
“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.
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.”
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.”
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
Parable
Anne K. Mellor described Frankenstein as “a book about what happens when a man tries to have a baby without a woman.”
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.)
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.
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