For What It’s Worth

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Based on an ancient Hindu game, Snakes and Ladders (Chutes and Ladders in ophidiophobic America) is at heart a morality lesson: As you progress by die roll from square 1 to square 100 and spiritual enlightenment, your way is complicated by virtues and vices. Landing on a snake (or chute) will send you back to an earlier square, and landing on a ladder will send you ahead to a later one. Each of these shortcuts is associated with a precept — “Carelessness” leads to “Injury,” “Study” leads to “Knowledge,” and so on.

In 1993 University of Michigan mathematician S.C. Althoen and his colleagues considered the game as a 101-state absorbing Markov chain. The shortest possible game lasts seven moves, the longest is infinite, and according to their calculations the expected number of moves in the Milton Bradley version of Chutes and Ladders is

\displaystyle  \frac{225837582538403273407117496273279920181931269186581786048583}{5757472998140039232950575874628786131130999406013041613400},

which is about 39.2.

Troublingly, the average length of a game without snakes or ladders (just the 100-square board) is almost exactly 33 moves: “Apparently the snakes lengthen the game more than the ladders shorten it.” And, while adding a ladder will generally shorten the game and adding a snake will lengthen it, this isn’t always the case: In the original game, adding a ladder from square 79 to square 81 lengthens the expected playing time by more than two moves (to about 41.9), since it increases the chance of missing the important ladder leading from square 80 to square 100. And adding a snake from square 29 to square 27 shortens the game by more than a move (to about 38.0), since it offers a second chance at the long ladder from 28 to 84.

So, arguably, we might advance more quickly through life with more vice and less virtue.

(S.C. Althoen, L. King, and K. Schilling, “How Long Is a Game of Snakes and Ladders?”, Mathematical Gazette 77:478 [March 1993], 71-76.)

La

https://en.wikipedia.org/wiki/File:THXDeepNoteScore35thAnniversary.jpg

On its 35th anniversary, THX, the sound quality assurance company founded by George Lucas, released the original score of “Deep Note,” its audio trademark, which debuted at the premiere of Return of the Jedi in 1983 and is now familiar from countless films. Essentially it’s a stupendous D chord; the U.S. trademark registration reads:

The THX logo theme consists of 30 voices over seven measures, starting in a narrow range, 200 to 400 Hz, and slowly diverting to preselected pitches encompassing three octaves. The 30 voices begin at pitches between 200 Hz and 400 Hz and arrive at pre-selected pitches spanning three octaves by the fourth measure. The highest pitch is slightly detuned while there are double the number of voices of the lowest two pitches.

“I like to say that the THX sound is the most widely-recognized piece of computer-generated music in the world,” says James A. Moorer, who wrote it. “This may or may not be true, but it sounds cool.” And now that we have the score you can do this:

Self-Taught

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Image: Flickr

Jazz guitarist Pat Martino had a burgeoning record career by age 20, but in 1976 he began to suffer headaches, followed by mania, depression, and seizures. He attempted suicide several times, but hospitalization and electroshock therapy brought no relief. In 1980 a CT scan discovered an arteriovenous malformation that had begun to hemorrhage, and a surgeon removed 70 percent of Martino’s left temporal lobe.

After the surgery he didn’t know his name, recognize his parents, or know he was a musician. When his father played his old records for him, “I would lie in my bed upstairs and hear them seep through the walls and the floor, a reminder of something that I had no idea that I was supposed to be anymore, or that I ever was.” But when a visiting friend played a major seventh chord, Martino found that he wanted a minor ninth and took up the instrument again.

“As I continued to work out things on the instrument, flashes of memory and muscle memory would gradually come flooding back to me — shapes on the fingerboard, different stairways to different rooms in the house,” he wrote.

Aided by his father, friends, photographs, and mainly by his own recordings, he learned the instrument afresh, “to escape the situation, and to please my father.” Neurosurgeon Marcelo Galarza writes, “The process of memory retrieval took him about two years. Although he never lost his manual dexterity, the necessary skill to play guitar again to his previous musical level took years to bring back.”

In 1987 he recorded his comeback album, The Return, and he’s made more than 20 albums since then. Galarza writes, “To our knowledge, this case study represents the first clinical observation of a patient who exhibited complete recovery from a profound amnesia and regained his previous virtuoso status.”

(Marcelo Galarza et al., “Jazz, Guitar, and Neurosurgery: The Pat Martino Case Report,” World Neurosurgery 81:3 [2014], 651-e1.)

Horse Play

Nick Stafford’s stage adaptation of War Horse, Michael Morpurgo’s 1982 young-adult novel, features a life-size horse puppet devised by the Handspring Puppet Company of South Africa. Three actors cooperate to bring the character to life; philosophically, puppeteer Basil Jones says that Handspring aimed to offer “a real horse on stage, … a horse that is disinterested in what the humans are saying around him” and that remains “slightly unpredictable.” That’s informed by an enormous amount of study and practice — new puppeteers visit stables, watch DVDs, and study horse gaits and psychology in what Jones calls “a total immersion”:

Together with the rehearsals the puppeteers have two months of training before they see their first audience. Over scores of performances, the puppeteers become shamans of the horse. Their intuition as to what their fellow puppeteers are about to do becomes finely tuned. This triple performance is a pretty special event to watch on stage.

It seems to work. In the Daily Telegraph, Charles Spencer wrote that “puppets are often an embarrassment, involving a lot of effort and fuss for negligible returns,” but in this case the puppets are “truly magnificent creations.” The Guardian‘s Michael Billington agreed: “The joy of the evening … lies in the skilled recreation of equine life and in its unshaken belief that mankind is ennobled by its love of the horse.”

Finis

Stanley Kubrick was an avid chess player, and the game in 2001: A Space Odyssey, though it’s incidental, makes sense and seems to have been planned with care. In fact it seems to have been based on an actual game, played between A. Roesch and Willi Schlage in Hamburg in 1910. That game started with the moves 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. Qe2 b5 6. Bb3 Be7 7. c3 0-0 8. 0-0 d5 9. exd5 Nxd5 10. Nxe5 Nf4 11. Qe4 Nxe5 12. Qxa8? Qd3! 13. Bd1 Bh3!:

2001 chess game

Here Roesch (and astronaut Frank Poole) played 14. Qxa6?, picking up a pawn but recklessly abandoning the long diagonal. Schlage (and supercomputer HAL 9000) pounced with 14. … Bxg2. When Poole withdraws the threatened rook, HAL says, “I’m sorry, Frank, I think you missed it: queen to bishop three [threatening 16. … Nh3#], bishop takes queen, knight takes bishop, mate.”

Technically White can hold out a bit longer with 16. Qc8 Rxc8 17. h3 Nxh3+ 18. Kh2, but then the ax falls with 18. … Ng4#. Poole, and Roesch, resigned.

Vicissitude

harry bradshaw bottle

In the 1949 Open Championship, Irish golfer Harry Bradshaw led the first round with a 68, but in the second round his drive at the fifth hole came to rest in the bottom of a broken beer bottle on the fairway.

He probably would have been entitled to take a drop, but he elected to play the ball as it lay, shutting his eyes against the broken glass and swinging as hard as he could. The stroke destroyed the bottle but moved the ball only 25 yards. The setback would leave Bradshaw tied with Bobby Locke, and he lost the ensuing playoff. Arguably the experience with the bottle, and its effect on his equanimity in the rest of that round, had cost him the tournament.

Years later writer Peter Dobereiner asked Bradshaw how many hours of sleep he’d lost reproaching himself for playing the ball as it lay. “Never one single second, sir,” he said. “Of course, if I had sent for a ruling I might have won the championship, but it would not have been right. Locke was the better player. He deserved to win.”

One-Man Band

In the early days of silent movies, large theaters would engage orchestras to play the accompanying music. But starting around 1910, small venues that lacked the money or the space could use a machine instead. In Film Music, music editor Roy M. Pendergast writes, “In addition to music, these machines were capable of providing a battery of sound effects, and they ranged in size from what was essentially a player piano with small percussion setup to elaborate instruments nearly equaling a twenty-piece pit orchestra.” He quotes Samuel A. Peeples in Films in Review:

The crowning achievement of the American Photo Player Company was their Fotoplayer Style 50, only one of which is presently known to survive in operating condition. Among the most splendid automatic musical instruments ever built, it was 21 feet long, 5 feet wide, and 5 feet 2 inches tall. It was capable of recreating the volume of a 20-piece pit orchestra, plus a full-scale theatre pipe-organ, with an incredible range of effects, such as the lowing of cattle, the drumming of hoofs in assorted gaits, several varieties of klaxons, street traffic noises, crackling flames, breaking wood and brush, rifle, pistol and machine gun shots, even the sound of a French 75MM cannon!

Pendergast adds, “One wonders about the quality of genius it must have taken to operate one of these devices.”

Express

high noon train approach

To film the dramatic approach of the train in High Noon, director Fred Zinnemann and cinematographer Floyd Crosby put their camera flat on the ground between the rails a few hundred yards ahead of the station. Zinneman wanted the train to appear as a dot that grew larger as it approached.

When the signal was given to start, “It looked beautiful, moving rapidly with white smoke, which looked even better,” Zinneman wrote later. “Then it let out black smoke, which looked even better. What we didn’t know was that this was the signal that the engine’s brakes were failing.”

When Zinnemann and Crosby realized that the train wasn’t going to stop, Crosby grabbed the camera, but one of its tripod hooks caught on a rail and he lost his grip. The camera fell in front of the engine as it roared past the men. It was badly damaged, but the magazine was intact, and the footage of the train’s approach is in the final film.

(From Michael Francis Blake, Code of Honor, 2003.)