Big Finish

Here’s one way to end a composition: Johann Jakob Froberger’s Suite II in C major, Lamento sopra la dolorosa perdita della Real Msta di Ferdinando IV, Re de Romani, ends with a picture of the clouds of heaven welcoming the soul of Ferdinand IV as it climbs up a scale of three octaves.

It was written to lament the death of the King of the Romans in 1654. Elsewhere Froberger had marked the fatal fall of lutenist Charles Fleury down a flight of stairs with a descending scale of two octaves. Perhaps he was just very literal-minded.

(From Wilfrid Hodges, “The Geometry of Music,” in John Fauvel et al., Music and Mathematics, 2006.)

July 24, 2022July 23, 2022 | Art

The Oxen Railroad

This sounds apocryphal, but it’s interesting. According to Texas lore, John Higginson, owner of the Memphis, El Paso & Pacific Railroad, faced a problem in the 1860s. He had committed to serve the route between Marshall, Texas, and Shreveport, La., but the Civil War had reduced his stock to three boxcars. How could he maintain regular service between two cities 40 miles apart with no engine?

He did it (the story goes) by loading a team of oxen into the first boxcar; freight and passengers into the second car; and the train’s crew and management into the third car. At Marshall, Higginson would start the train coasting down a long descending grade, and at the bottom they’d unload the oxen, hitch them to the front of the train, and drive them until they reached the top of the next hill. Then they’d load the oxen into the first car again and ride down the hill. At Shreveport they’d turn around and use the same method to get home.

In The Humor and Drama of Early Texas (2002), George U. Hubbard writes, “With gravity for the downgrades and oxen for the level areas and the upgrades, the little railroad managed to operate in both directions on a timely and consistent schedule.” With no competition on the Marshall-Shreveport line, Higginson (supposedly) maintained a profitable railroad with no engine at all.

Hubbard cites B.A. Botkin’s A Treasury of Railroad Folklore, from 1953. I find that the Southwestern Historical Quarterly ran an item giving essentially the same details in the early 1950s, citing a Texas newspaper of 1918, and Railway World mentioned it in 1911, quoting the Fort Worth Record (which calls it an “old railroad story”). I can’t find any corroboration beyond that. Good story, though!

July 23, 2022July 22, 2022 | Oddities · Technology

Scrutiny

A puzzle by V. Dubrovsky, from Quantum, January-February 1992:

In a certain planetary system, no two planets are separated by the same distance. On each planet sits an astronomer who observes the planet closest to hers. Prove that if the total number of planets is odd, there must be a planet that no one is observing.

	Select Click for Answer
Of the n planets in the system, consider the two that are closest together. These two astronomers must be looking at each other. If any of the remaining n – 2 astronomers are looking at one of these planets, then there won’t be enough astronomers left to observe all the remaining n – 2 planets. On the other hand, if none of the remaining astronomers are looking at the two closest-set planets, then we can discard those two and ask our original question of the n – 2 planets that remain: Which two are closest together? Again, those two astronomers must be observing each other. And so on. Each time we discard a pair of planets we’ll have some odd number remaining. But that number can’t decrease forever (it can’t be negative). We must eventually arrive at 1, a planet that no astronomer is observing.

Click for Answer

July 22, 2022July 21, 2022 | Puzzles

Cloud Nine

Here’s one solution to the population problem: In 1967 Buckminster Fuller patented a giant floating geodesic sphere enclosing a city, hoping to reduce the economic and environmental costs of using land for housing. Each sphere would be a mile in diameter, enclosing an enormous volume of air that would be warmed by the sun, enabling it to carry buildings bearing thousands of people. The structural weight of even a half-mile sphere would be a thousandth the weight of the air inside, and heating the air even 1 degree would raise the whole structure like a hot-air balloon. By opening and closing polyethylene “curtains,” the occupants could keep the sphere floating at a chosen altitude. The cities could be tethered to mountaintops or float freely, enabling them (for example) to travel to disaster sites in a matter of days, and permitting humans to “converge and deploy around Earth without its depletion.”

“Cloud Nine is probably possible, but even Bucky didn’t expect to see one soon,” writes J. Baldwin in BuckyWorks: Buckminster Fuller’s Ideas for Today (1996). “He offered it as a jarring exercise, intended to stimulate the imaginative thinking we’re going to need if the billions of new Earth citizens predicted to arrive soon are to have decent housing.”

July 22, 2022July 21, 2022 | Technology

Multimedia

I don’t know why I find this so striking: It’s a diagram that accompanies the article on deer hunting in Denis Diderot’s Encyclopédie. Rather than presenting a single image with a caption, it combines a vignette of a deer hunt with an illustration of the antlers and piles of dung that are dropped by stags of different ages, together with a musical score showing the notes sounded by the hunting party at different stages of the pursuit.

“Taken as a whole the hunting plates offer few clues for reading their complex hybrid of imagery and notations as an ensemble,” write John Bender and Michael Marrinan in The Culture of the Diagram (2010). Perhaps as a result, the encyclopedia article requires nearly 10 pages.

“The Encyclopedia’s treatment of stag hunting is extraordinary for mobilizing a full range of written language, abstract and arbitrary notations, indexical icons, and pictorial tableaux in an attempt to diagram the highly ritualized, courtly craft of tracking animals under the Ancien Régime.”

Diderot provided similarly remarkable diagrams for “hunting at force,” the kill, boar hunting, and wolf hunting.

July 21, 2022July 20, 2022 | Art · Literature

Downgrade

In his 1946 essay “Politics and the English Language,” George Orwell “translates” Ecclesiastes 9:11 into “modern English of the worst sort”:

I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.

Objective consideration of contemporary phenomena compels the conclusion that success or failure in competitive activities exhibits no tendency to be commensurate with innate capacity, but that a considerable element of the unpredictable must invariably be taken into account.

Orwell’s English instructor at St. Cyprian’s School, Cicely Vaughan Wilkes, had translated the parable of the Good Samaritan into “oratory and journalese” to illustrate the principles of good writing. Orwell’s companion Walter John Christie wrote that Wilkes had emphasized “simplicity, honesty, and avoidance of verbiage” — and pointed out that these qualities can be seen in Orwell’s writing.

July 20, 2022July 20, 2022 | Literature

Words and Numbers

Strategies to memorize π sometimes rely on devising a sentence with words of representative lengths. Isaac Asimov offered this one:

How I want a drink, alcoholic, of course, after the heavy lectures involving quantum mechanics!

Count the letters in each word and you get 3.14159265358979. That’s not the best strategy, though: What shall we do about zero? And it’s hard to reel off the digits impressively for friends when you have to stop and count the letters in each word.

Arthur Benjamin, a mathematician at Harvey Mudd College, suggests using a phonetic code instead:

1 = t or th or d
2 = n
3 = m
4 = r
5 = l
6 = sh, ch, or j
7 = k or hard g
8 = f or v
9 = p or b
0 = s or z

Once we’ve memorized this list, we can turn a whole string of digits into a single word simply by inserting vowels between the consonants. So, for example, 314 could be represented by meter, motor, meteor, matter, mother, etc. The consonants h, w, and y, which don’t appear in the list, can be used like additional vowels.

Using this method, it takes only three sentences to encode the first 60 digits of π:

3. 1415 926 5 3 58 97 9 3 2 384 6264
My turtle Pancho will, my love, pick up my new mover Ginger.

3 38 327 950 2 8841 971
My movie monkey plays in a favorite bucket.

69 3 99 375 1 05820 97494
Ship my puppy Michael to Sullivan’s backrubber!

Now we just need a way to remember the sentences …

(Arthur T. Benjamin, “A Better Way to Memorize Pi: The Phonetic Code,” Math Horizons 7:3 [February 2000], 17.)

July 20, 2022July 19, 2022 | Science & Math

Romance Language

Samuel Pepys wrote his famous diary in shorthand, but he took a further precaution when writing about his amorous adventures — he adopted words based on Spanish, French, and Italian:

“I did come to sit avec [with] Betty Michell, and there had her main [hand], which elle [she] did give me very frankly now, and did hazer [make] whatever I voudrais avec l’ [would have with her], which did plaisir [pleasure] me grandement [greatly].”

“The garbled foreign phrases he often used for sexual incidents had something to do with concealment perhaps, much more with his pleasure in marking off sexual experiences through special words and so heightening the excitement of reliving them,” writes Claire Tomalin in Samuel Pepys: The Unequalled Self. “It is the clever schoolboy as lover, showing off to himself in two ways at once.”

July 19, 2022July 19, 2022 | Language · Literature

In a Word

ambilogy
n. uncertain or doubtful meaning; ambiguity

raddled
adj. of a person: confused, fuddled

trilapse
n. a third lapse

recreant
adj. defeated

When a twelfth-century youth fell in love he did not take three paces backward, gaze into her eyes, and tell her she was too beautiful to live. He said he would step outside and see about it. And if, when he got out, he met a man and broke his head — the other man’s head, I mean — then that proved that his — the first fellow’s — girl was a pretty girl. But if the other fellow broke his head — not his own, you know, but the other fellow’s — the other fellow to the second fellow, that is, because of course the other fellow would only be the other fellow to him, not the first fellow who — well, if he broke his head, then his girl — not the other fellow’s, but the fellow who was the — Look here, if A broke B’s head, then A’s girl was a pretty girl; but if B broke A’s head, then A’s girl wasn’t a pretty girl, but B’s girl was. That was their method of conducting art criticism.

— Jerome K. Jerome, Idle Thoughts of an Idle Fellow, 1886

July 19, 2022July 18, 2022 | Language

Revelation

The invention of logarithms came on the world as a bolt from the blue. No previous work had led up to it, foreshadowed it, or heralded its arrival. It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought.

— Lord Moulton on the 300th anniversary of John Napier’s 1614 book Description of the Wonderful Canon of Logarithms. E.W. Hobson called the invention “one of the very greatest scientific discoveries that the world has seen.”

July 18, 2022July 17, 2022 | Science & Math