guttatim
adv. drop by drop
supernaculum
adv. to the last drop
stillatitious
adj. falling in drops
quantulum
n. a small amount or portion
Sea Music
The lovely Irish folk tune Port na bPúcaí (“The Music of the Fairies”) had mystical beginnings — it’s said that the people of the Blasket Islands heard ethereal music and wrote an air to match it, hoping to placate unhappy spirits. Seamus Heaney’s poem “The Given Note” tells of a fiddler who took the song “out of wind off mid-Atlantic”:
Strange noises were heard
By others who followed, bits of a tune
Coming in on loud weather
Though nothing like melody.
Recent research suggests that, rather than fairies, the islanders may have been hearing the songs of whales transmitted through the canvas hulls of their fishing boats. Humpback whales pass through Irish waters each winter as they migrate south from the North Atlantic, and their songs seem to resemble the folk tune.
Ronan Browne, who plays the air above on Irish pipes, writes, “In the mid 1990s I went rooting through some cassettes of whale song and there in the middle of the Orca (Killer Whale) section I heard the opening notes of Port na bPúcaí!”
No one can say for certain whether the one inspired the other, of course, but if it didn’t it’s certainly a pleasing coincidence.
(Thanks, James.)
A Late Contribution
A ghost co-authored a mathematics paper in 1990. When Pierre Cartier edited a Festschrift in honor of Alexander Grothendieck’s 60th birthday, Robert Thomas contributed an article that was co-signed by his recently deceased friend Thomas Trobaugh. He explained:
The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom’s simulacrum remarked, ‘The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf.’ Awaking with a start, I knew this idea had to be wrong, since some perfect complexes have a non-vanishing K0 obstruction to extension. I had worked on this problem for 3 years, and saw this approach to be hopeless. But Tom’s simulacrum had been so insistent, I knew he wouldn’t let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor.
Thomason himself died suddenly five years later of diabetic shock, at age 43. Perhaps the two are working again together somewhere.
(Robert Thomason and Thomas Trobaugh, “Higher Algebraic K-Theory of Schemes and of Derived Categories,” in P. Cartier et al., eds., The Grothendieck Festschrift Volume III, 1990.)
“The Mostly German Philosophers Love Song”
By Colorado classics teacher Jeremy Boor:
MP3, lyrics, and chords are on his website.
Cross Purposes
The daily New York Times crossword puzzle fills a grid measuring 15×15. The smallest number of clues ever published in a Times puzzle is 52 (on Jan. 21, 2005), and the largest is 86 (on Dec. 23, 2008).
This set Bloomsburg University mathematician Kevin Ferland wondering: What are the theoretical limits? What are the shortest and longest clue lists that can inform a standard 15×15 crossword grid, using the standard structure rules (connectivity, symmetry, and 3-letter words minimum)?
The shortest is straightforward: A blank grid with no black squares will be filled with 30 15-letter words, 15 across and 15 down.
The longest is harder to determine, but after working out a nine-page proof Ferland found that the answer is 96: The largest number of clues that a Times-style crossword will admit is 96, using a grid such as the one above.
In honor of this result, he composed a puzzle using this grid — it appears in the June-July 2014 issue of the American Mathematical Monthly.
(Kevin K. Ferland, “Record Crossword Puzzles,” American Mathematical Monthly 121:6 [June-July 2014], 534-536.)
Unquote
“The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” — F. Scott Fitzgerald
“It is the mark of an educated mind to be able to entertain a thought without accepting it.” — Aristotle
“Education enables you to express assent or dissent in graduated terms.” — William Cory
“Education is the ability to listen to almost anything without losing your temper or your self-confidence.” — Robert Frost
“To change an opinion without a mental process is the mark of the uneducated.” — Geoffrey Madan
“To have doubted one’s own first principles is the mark of a civilized man.” — Oliver Wendell Holmes
Podcast Episode 45: Crossing Africa for Love
When Ewart Grogan was denied permission to marry his sweetheart, he set out to walk the length of Africa to prove himself worthy of her. In this week’s episode of the Futility Closet podcast we’ll find out whether Ewart’s romantic quest succeeded.
We’ll also get an update on the criminal history of Donald Duck’s hometown, and try to figure out how a groom ends up drowning on his wedding night.
Black and White
By W.A. Shinkman. This is a self-mate in two moves: White makes a move, Black is allowed to make any legal reply, then White plays a second move that forces Black to checkmate him.
All for One
A flock of starlings masses near sunset over Gretna Green in Scotland, preparatory to roosting after a day’s foraging. The flock’s shape has a mesmerisingly fluid quality, flowing, stretching, rippling, and merging with itself. Similarly massive flocks form over Rome and over the marshlands of western Denmark, where more than a million migrating starlings form an enormous display known as the “black sun.”
What rules produce this behavior? In the 1970s scientists thought that the birds might be following an electrostatic field produced by the leader. Earler, in the 1930s, one paper even suggested that they use thought transference.
But in 1986 computer graphics expert Craig Reynolds found that he could create a lifelike virtual flock (below) using a surprisingly simple set of rules: direct each bird to avoid crowding nearby flockmates, steer toward the average heading of nearby flockmates, and move toward the center of mass of nearby flockmates.
Studies with real birds seem to bear this out: Under rules like these a flock can react sensitively to a change in direction by any of its members, permitting the whole group to respond efficiently as one organism. “News of a predator’s approach can be communicated rapidly through the flock by whichever of the hundreds of birds on the outside notice it first,” writes Gavin Pretor-Pinney in The Wavewatcher’s Companion. “When under attack by a peregrine falcon, for instance, starling flocks will contract into a ball and then peel away in a ribbon to distract and confuse the predator.”
“Illustrated Verse”
slow, But if it breaks it comes down up goes elevator The so.
— Yale Record, 1900-1919