The Vowel Triangle

Chris McManus discovered this oddity. If W and Y are accepted as vowels, that gives us AEIOUWY. Starting with O, number these according to their positions on a circular alphabet without starting the count over for A (that is, O is the 15th letter of the alphabet, so it’s assigned number 15; beyond Z we’d reach A as the “27th” letter; and so on). Now write these numbers into a triangle, again starting with O:

   O                15
 U W Y           21 23 25
A  E  I         27  31  35

Each of the five lines in the figure gives a different arithmetic progression:

UWY: difference of 2
AEI: difference of 4
OUA: difference of 6
OWE: difference of 8
OYI: difference of 10

(David Morice, “Kickshaws,” Word Ways 34:4 [November 2001], 292-305.)

| Language

Podcast Episode 232: The Indomitable Spirit of Douglas Bader

https://commons.wikimedia.org/wiki/File:Squadron_Leader_Douglas_Bader,_CO_of_No._242_Squadron,_seated_on_his_Hawker_Hurricane_at_Duxford,_September_1940._CH1406.jpg

Douglas Bader was beginning a promising career as a British fighter pilot when he lost both legs in a crash. But that didn’t stop him — he learned to use artificial legs and went on to become a top flying ace in World War II. In this week’s episode of the Futility Closet podcast we’ll review Bader’s inspiring story and the personal philosophy underlay it.

We’ll also revisit the year 536 and puzzle over the fate of a suitcase.

See full show notes …

| History · Podcast · Society

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.

| Art

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.)

| Language · Science & Math

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.

| Language

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.)

| Science & Math

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.)

| Art