All Together Now

Tomorrow’s date will be written as an eight-digit palindrome around the world, the first time this has happened in 900 years.

The coincidence is rare because countries use differing conventions. February 2, 2020, is a palindrome whether expressed as day/month/year (02/02/2020), month/day/year (02/02/2020), or year/month/day (2020/02/02).

This happened last on November 11, 1111, and it won’t happen again until March 3, 3030.

02/01/2020 UPDATE: A number of readers have pointed out that 12/12/2121 works fine too, and it’s barely more than a century away.

| Oddities

Unquote

“Music is the pleasure the human soul experiences from counting without being aware that it is counting.” — Leibniz

“The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.” — Cocteau

“All musicians are subconsciously mathematicians.” — Thelonious Monk

| Quotations

Policy

https://pixabay.com/en/mark-twain-vintage-author-humorist-391120/

Mark Twain received so many letters from would-be authors that he prepared a standard reply:

Dear Sir or Madam,–Experience has not taught me very much, still it has taught me that it is not wise to criticise a piece of literature, except to an enemy of the person who wrote it; then if you praise it that enemy admires you for your honest manliness, and if you dispraise it he admires you for your sound judgment.

Yours truly,

S.L.C.

| Literature

Black and White

ceriani puzzle

Luigi Ceriani published this curiously ambivalent retrograde puzzle in Europe Echecs in 1960. White is to mate in two moves.

The answer turns on whether White can castle kingside and whether Black can castle queenside. Castling is always deemed to be legal unless it can be proven otherwise. The question of White’s castling comes down to the origin of the rook on a6. If that started on h1, then White may not castle because the rook that’s currently on h1 obviously must have moved in order to get there. If the rook on a6 started on a1, then again White may not castle, because in that case the rook must have got to its present position via e1, since the pawn originally on a2 can have reached its present position on b3 only after the knight on a1 had itself moved there from b3.

That means that if the rook on a6 is not a promoted piece, White cannot castle. If it is a promoted piece, then Black cannot castle, because the white pawn that was promoted must have passed over either d7 or f7 first, which would have forced the black king to move if it had been on its original square. Hence either castling by White or castling by Black is impossible.

Well, if castling by Black is impossible, then White can win by castling himself, since then Black has no escape from 2. Rf8#. And if castling by White is impossible, then White can capture the b5 pawn en passant (followed by mate with the queen), because if Black’s king and rook have not moved then Black’s last move must have been b7-b5. (His last move cannot have been b6-b5 because that would leave White no possible previous move. As it is, with Black’s last move being b7-b5, White’s preceding move must have been R[c6]xa6+.)

(Via John M. Rice, An ABC of Chess Problems, 1970.) (Maybe I’m being obtuse, but isn’t it possible that neither side can castle? In that case both proposed mates fall apart and I don’t see how White can succeed.)

02/03/2020 UPDATE: Ach, I’d just given the answer to my own question: Castling is deemed to be legal unless it can be proven otherwise, and it can’t be proven that neither side can castle. (Thanks, David and Daniel.)

| Puzzles

Genealogy

Reader Jack McLachlan found this curious entry among the marriage notices in the Scots Magazine of January 1790:

At Newburn, near Newcastle, Mr William Dormand, to Miss Hannah Hoy, of that place. The ceremony was attended by the father, mother, brother, sister, aunt, nephew, two husbands, and two wives, and yet there were only four persons present at the marriage.

No explanation is given. How is such an arrangement possible?

Click for Answer
| Puzzles

Moving Art

The 2018 Halloween parade in Kawasaki, Japan, included a procession of famous paintings. The group took home the year’s grand prize, around $4,400. (The last entry is a reference to Cecilia Giménez’s 2012 failed restoration attempt of Elías García Martínez’s Ecce Homo.)

Also:

| Art

“Lion-Eating Poet in the Stone Den”

Chinese-American linguist Yuen Ren Chao composed this passage in classical Chinese; when read in modern Mandarin, every syllable has the sound “shi,” with only the tones differing.

In a stone den was a poet called Shi Shi, who was a lion addict, and had resolved to eat ten lions.
He often went to the market to look for lions.
At ten o’clock, ten lions had just arrived at the market.
At that time, Shi had just arrived at the market.
He saw those ten lions, and using his trusty arrows, caused the ten lions to die.
He brought the corpses of the ten lions to the stone den.
The stone den was damp. He asked his servants to wipe it.
After the stone den was wiped, he tried to eat those ten lions.
When he ate, he realized that these ten lions were in fact ten stone lion corpses.
Try to explain this matter.

Aaron Posehn gives an explanation, including the full text in Chinese, here.

(Thanks, Brad.)

| Language

Marden’s Theorem

https://commons.wikimedia.org/wiki/File:Marden_theorem.svg
Image: Wikimedia Commons

If f(z) is a cubic polynomial with complex coefficients, and if the roots of f are three distinct non-collinear points A, B, and C in the complex plane, then the roots of the derivative f′ are the foci of the unique ellipse inscribed in triangle ABC and tangent to the sides at their midpoints.

The theorem is named for Morris Marden, but it had been proven about a century earlier by Jörg Siebeck.

(Dan Kalman, “The Most Marvelous Theorem in Mathematics,” Math Horizons 15:4 [April 2008], 16-17.)

| Science & Math

An Early Voice

https://www.youtube.com/watch?v=OythrZ5_sdQ

On October 21, 1889, Prussian field marshal Helmuth von Moltke the Elder made two audio recordings on Thomas Edison’s new cylinder phonograph. The first contains a congratulatory message to Edison and an excerpt from Faust, the second a line from Hamlet.

This is the only voice recording we have of a person born in the 18th century — Moltke had been born in 1800, technically the last year of that century. Ironically, he had been known as der große Schweiger, “the great silent one,” for his taciturnity.

| History · Technology