The Kiss at City Hall

https://www.flickr.com/photos/136879256@N02/22733279398

Robert Doisneau’s iconic photograph of young love in Paris sold thousands of posters, but the identity of the couple remained a mystery for decades. In 1988 Jean-Louis and Denise Lavergne saw it on a magazine cover and thought they recognized themselves: They’d been on the rue de Rivoli on April 1, 1950, and had a diary to prove it, and Lavergne still had the skirt and jacket she’d worn that day. They contacted Doisneau, who greeted them warmly but did not offer to share any of the five-figure income he’d been making each year from the poster.

When they sued him, he revealed that he’d posed the shot using Françoise Delbart and Jacques Carteaud, a couple he’d seen kissing in the street but had not dared at first to photograph. Finally he’d approached them and asked them to repeat the kiss. Delbart said, “He told us we were charming, and asked if we could kiss again for the camera. We didn’t mind. We were used to kissing.”

A thousand bubbles burst, the Lavergnes lost their suit, and Delbart eventually sold the print Doisneau had given her to feign a spontaneous kiss. She didn’t share the proceeds with Carteaud — they’d broken up nine months after the photo was taken.

Fortuitous Numbers

In American usage, 84,672 is said EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO. Count the letters in each of those words, multiply the counts, and you get 6 × 4 × 8 × 3 × 7 × 7 × 3 = 84,672.

Brandeis University mathematician Michael Kleber calls such a number fortuitous. The next few are 1,852,200, 829,785,600, 20,910,597,120, and 92,215,733,299,200.

If you normally say “and” after “hundred” when speaking number names, then the first few fortuitous numbers are 333,396,000 (THREE HUNDRED AND THIRTY THREE MILLION, THREE HUNDRED AND NINETY SIX THOUSAND), 23,337,720,000, 19,516,557,312,000, 56,458,612,224,000, and 98,802,571,392,000.

And 54 works in both French and Russian.

(Michael Kleber, “Four, Twenty-Four, … ?,” Mathematical Intelligencer 24:2 [March 2002], 13-14.)

Subscriber Trouble

A letter to the New York Times Book Review, March 22, 1998:

To the Editor:

I read the review of Nathan Miller’s ‘Star-Spangled Men’ (Feb. 22) by Douglas McGrath, who challenged the reader to produce a sentence with three prepositions in a row, after I had picked my copy of The New York Times up from under the front porch, thankful that I didn’t have to get it down from above the porch roof, and at the same time, knowing that the delivery boy usually threw it to within a foot of the door, leaving me a quick way back in out of the cold each morning, I decided not to yell at him, especially since an argument was not something I wanted to get into outside of the house at this time of the morning, but still thinking that this was a matter that should be taken up from inside of the house by writing a letter to the editor, being careful not to use up to over three or four prepositions in a row in any sentence.

George F. Werner
Edgewood, N.M.

A Keypad Oddity

A.F. Bainbridge of British Aerospace noticed this curiosity in 1991. On a calculator keypad like this:

1 2 3
4 5 6
7 8 9

… choose two three-digit numbers (say, 435 and 667) and multiply them (290145). Now use symmetrical paths on the keyboard to find two “complementary” numbers (that is, symmetrical across the center, here 675 and 443) and multiply those (299025).

The difference between these two products (299025 – 290145 = 8880) will always be evenly divisible by 37.

(A.F. Bainbridge and P.A. Binding, “Symmetrical Paths on a Calculator,” Mathematical Gazette 75:474 [December 1991], 399-401.)

Music and Identity

https://commons.wikimedia.org/wiki/File:Chopin_concert.jpg

What is Chopin’s B Minor Sonata? What constitutes its identity? Not the fact that it’s part of Chopin’s conscious experience, because it continues to exist after his death. And not the fact that it’s part of any listener’s experience, because it continues to exist when those experiences have ended. It can’t be identified with any particular performance, and it’s different from its score, since the sonata is a sounding work and the score is an arrangement of graphic signs.

If the sonata is not material, and if it’s different from the experience of both the composer and the listener (in fact, it continues to exist if no one takes any conscious interest in it at all), how can it exist? How do we discern the same “original” work in a hundred different performances?

Is the sonata an ideal object, immutable and atemporal, like a mathematical concept? Well, no, because Chopin created it at a particular time. Perhaps there is no sonata, only individual performances? But then there’d be no sense in distinguishing a performance from the work itself, or in talking about the identity of a work (“Chopin’s B Minor Sonata”), or in arguing over whether a given performance was faithful to the original.

“For what is the point of saying that one performance rather than another gives a more nearly accurate account of the B Minor Sonata when the sonata does not in fact exist and when there is nothing real with which these performances may be compared?” asks philosopher Roman Ingarden. “Are we really going to agree that such judgments concerning the sonata itself and its performances are all false and stupid?”

(Roman Ingarden, The Work of Music and the Problem of Its Identity, 1986.)

The Paul Rubin Cipher

On the morning of Jan. 20, 1953, the body of 18-year-old Paul Emanuel Rubin was found at the bottom of a ditch near the Philadelphia International Airport. The coroner found there was enough cyanide in his body to “kill 10 men,” and taped to his abdomen was a 7″ x 3″ piece of paper with an enciphered message:

rubin cipher

Rubin’s mother hadn’t seen him since the previous morning, when he’d cut some strips of adhesive tape before leaving the house. He was studying chemistry at New York University and would have had access to cyanide, but his mother said he was in good mental and physical health and hadn’t appeared worried about anything. (About 20 minutes before the body was found, the Rev. Robert M. Anderson had wished Rubin good morning; he found him “wild-eyed” and said “he was staring straight ahead and … the pupils of his eyes were dilated.”)

A friend mentioned that Rubin had been working with codes: “They’re very complicated. Anyone who reads science fiction will know what I mean.” Rubin was carrying a copy of Galaxy Science Fiction, as well as a plastic cylinder containing a signal fuse, the casing of a spent .38 caliber bullet, a “fountain pen gun” of uncertain purpose, four keys, and 47 cents. He’d had $15 when he’d left home the previous morning.

An inquest turned up nothing, and the case was closed in March. The cipher has never been solved. The Cipher Foundation has more details about the case, as well as a link to Rubin’s FBI file (8 MB PDF). The fullest account of the case that I know is in Craig Bauer’s excellent Unsolved!: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies (2017).

A Time Machine

https://commons.wikimedia.org/wiki/File:Thomas_Cole_-_Architect%E2%80%99s_Dream_-_Google_Art_Project.jpg

The life of a good book is far longer than the life of a man. Its author dies, and his generation dies, and his successors are born and die; the world he knew disappears, and new orders which he could not foresee are established on its ruins; law, religion, science, commerce, society, all are transformed into shapes which would astound him; but his book continues to live. Long after he and his epoch are dead, the book speaks with his voice.

— Gilbert Highet, on Juvenal