Beginners’ Welsh

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From a letter from Adam Sedgwick to his niece Fanny Hicks, July 23, 1846:

The miserable damp weather made me rheumatic and low-spirited, so I nursed one day in Carnarvon and then drove to Pwllheli. What a charming name! In order to pronounce the first part (Pwll), you must blow out your cheeks just as you do when puffing at a very obstinate candle; then you must rapidly and cunningly put your tongue to the roof of your mouth behind the fore teeth, and blow hard between your cheeks and your tongue, holding your tongue quite steady all the while, as a man does a spade just before he is going to give it a good thrust with his right foot. With such a beautiful direction you cannot fail to pronounce Pwll quite like a genuine Celt. Should the word be Bwlch, take care to observe the previous directions, only, in addition, while the wind is whistling between your rigid tongue (sticking forwards spade-fashion), and your distended cheeks, contrive by way of a finale to give a noise with your throat such as you make when an intrusive fishbone is sticking in it.

He added, “If you put off writing for a day or two, why then address me at Post Office, Machynlleth, North Wales. … yn is sounded as the grunt given by a broken-winded pavier.”

The Masked Marauders

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In 1969, as a joke, Rolling Stone published a review of a nonexistent album by a nonexistent band, a supposed “supergroup” made up of John Lennon, Paul McCartney, Mick Jagger, and Bob Dylan. Editor Greil Marcus had intended this as a self-evident parody of groups like Blind Faith and Crosby, Stills, Nash & Young, but readers began clamoring for the album. So Marcus and editor Langdon Winner recruited a Berkeley skiffle band and retroactively recorded a few of the songs that had been mentioned in the review.

When California radio stations began to play these songs, the hoax took on a life of its own. Marcus began to shop the band to major labels, and Warner Bros. won the contract with a $15,000 advance. The Masked Marauders came out that November with liner notes making it clear that the whole thing was a joke. Nonetheless, on the strength of its own bootstrapped glamor the record sold 100,000 copies and spent 12 weeks on the Billboard charts.

Related: In 2004 Dave Stewart and Kara DioGuardi invented a band called Platinum Weird that they insisted had existed in 1974. Supposedly it had been a partnership between Stewart and a mysterious singer/songwriter named Erin Grace who, among other accomplishments, had introduced Stevie Nicks to Lindsey Buckingham. In July 2006 VH1 even aired a documentary in which Ringo Starr, Bob Geldof, Elton John, and Mick Jagger pretended to reminisce about the band. On the same day, though, Stewart admitted to the Los Angeles Times that the whole thing had been a hoax.

“Lots of artists from the ’60s created mythology about themselves,” he said. “We’re in our own perception of our own world. So what’s reality and what’s not?”

(Thanks, Jeremy.)

“By Deputy”

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As Shakespeare couldn’t write his plays
(If Mrs. Gallup’s not mistaken),
I think how wise in many ways
He was to have them done by Bacon;
They might have moldered on the shelf,
Mere minor dramas (and he knew it!),
If he had written them himself
Instead of letting Bacon do it.

And if it’s true, as Brown and Smith
In many learned tomes have stated,
That Homer was an idle myth,
He ought to be congratulated,
Since thus, evading birth, he rose
For men to worship at a distance;
He might have penned inferior prose
Had he achieved a real existence.

To him and Shakespeare men agree
In making very nice allusions;
But no one thinks of praising me,
For I compose my own effusions;
As others wrote their works divine
And they immortal thus today are,
Perhaps had someone written mine
I might have been as great as they are.

— Arthur St. John Adcock

The Asymmetric Propeller

asymmetric propeller theorem

Arrange three congruent equilateral triangles so that their corners meet at a point, like the red triangles above. The arrangement doesn’t have to be symmetric; the triangles can even overlap. Now draw lines BC, DE, and FA to complete a hexagon inscribed in a circle. The midpoints of these three lines will form the vertices of an equilateral triangle.

That’s called the asymmetric propeller theorem, and it’s been known since the 1930s. But in 1979 Beverly Hills dentist and geometry enthusiast Leon Bankoff told Martin Gardner of some further discoveries. Bankoff never found time to write them up, so after the dentist’s death in 1997 Gardner published them in the College Mathematics Journal:

  • The three equilateral triangles need not be congruent. Each can be of any size and the theorem still holds.
  • The triangles need not meet at a point. They can meet at the corners of any equilateral triangle.
  • They need not even be equilateral! If three similar triangles of any sizes meet at a point, the midpoints of the three added lines will form a triangle similar to each of the “propellers.”
  • The similar triangles need not meet at a point! If they meet at the corners of a fourth triangle (of any size) that’s similar to each propeller, then the midpoints of the added lines will form a triangle similar to each propeller, provided that the vertices of the central triangle touch the corresponding corners of the propellers.

Given all this flexibility, Gardner asked, do the propellers even have to be triangles? It turns out that the answer is yes. Still, the discoveries above form a fitting tribute to Bankoff, whom Gardner called “one of the most remarkable mathematicians I have been privileged to know.”

(Martin Gardner, “The Asymmetric Propeller,” College Mathematics Journal 30:1 [January 1999], 18-22.)

The Uncounted

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It was a good answer that was made by one who when they showed him hanging in a temple a picture of those who had paid their vows as having escaped shipwreck, and would have him say whether he did not now acknowledge the power of the gods, — ‘Aye,’ asked he again, ‘but where are they painted that were drowned after their vows?’ And such is the way of all superstition, whether in astrology, dreams, omens, divine judgments, or the like; wherein men, having a delight in such vanities, mark the events where they are fulfilled, but where they fail, though this happens much oftener, neglect and pass them by.

— Francis Bacon, Novum Organum, 1620

Howdunit

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Raymond Chandler’s 10 rules for writing a detective novel:

  1. It must be credibly motivated, both as to the original situation and the dénouement.
  2. It must be technically sound as to the methods of murder and detection.
  3. It must be realistic in character, setting and atmosphere. It must be about real people in a real world.
  4. It must have a sound story value apart from the mystery element: i.e., the investigation itself must be an adventure worth reading.
  5. It must have enough essential simplicity to be explained easily when the time comes.
  6. It must baffle a reasonably intelligent reader.
  7. The solution must seem inevitable once revealed.
  8. It must not try to do everything at once. If it is a puzzle story operating in a rather cool, reasonable atmosphere, it cannot also be a violent adventure or a passionate romance.
  9. It must punish the criminal in one way or another, not necessarily by operation of the law. … If the detective fails to resolve the consequences of the crime, the story is an unresolved chord and leaves irritation behind it.
  10. It must be honest with the reader.

That’s from Chandler’s notebooks. As it happens, Dashiell Hammett, Ronald Knox, and S.S. Van Dine all came up with similar lists. Mystery writers must be very methodical people.

Parrondo’s Paradox

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Imagine a staircase with 1001 stairs, numbered -500 to 500. You’re standing in the middle, on stair 0, and you want to reach the top. On each step you can play either of two coin-flipping games — if the result is heads then you move up a step; if it’s tails then you move down a step:

  • In game 1 you flip coin A, which is slightly biased: It comes up heads 49.5 percent of the time and tails 50.5 percent.
  • In game 2 you use two coins, B and C. Coin B produces heads 9.5 percent of the time and tails 90.5 percent. Coin C produces heads 74.5 percent of the time and tails 25.5 percent. In game 2 if the number of the stair you’re on is a multiple of 3 then you flip coin B; otherwise you flip coin C.

Both of these are losing games — if you played either game 1 or game 2 exclusively, you’d eventually find yourself at the bottom of the staircase. But in 1996 Spanish physicist Juan Parrondo found that if you play the two games in succession in random order, keeping your place on the staircase as you switch between them, you’ll rise to the top of the staircase. It’s not, properly speaking, a paradox, but it’s certainly counterintuitive.

This example is from David Darling’s Universal Book of Mathematics. (Thanks, Nick.)