A Wand’ring Minstrel

Gilbert and Sullivan gained fame around the world for their operettas. But where W.S. Gilbert could be impatient and irascible, Arthur Sullivan was full of lively good humor. Vernon Blackburn remembered a curious incident from his travels:

It so happened that I journeyed to Rome almost immediately after my hearing for the first time The Yeomen of the Guard. I was full of its melodies, full of its charm; and one night walking through the Piazza di Spagna, I was whistling the beautiful concerted piece, ‘Strange Adventure,’ whistling it with absolutely no concern and just for the love of the music. A window was suddenly opened and a little face looked out in the moonlight, while a thin voice exclaimed in apparent seriousness: ‘Who’s that whistling my music?’ I looked up with astonishment and with some awe, and told the gentleman that if he were Sir Arthur Sullivan it was his music that I was whistling; and, said I, I thought that the copyright did not extend to Italy. I remember how he convulsed with laughter somewhat to my discomfiture, and closed the window to shut out the chill of the night. I never dared at that period of life to make any call upon one whom I considered to be so far above the possibilities of intercourse.

In his 1908 memoir, baritone Rutland Barrington remembered: “There was invariably enormous competition for seats at the Savoy premieres, and it was difficult to find room for all friends. On one occasion a great personal friend of Sullivan’s, Mr Reuben Sassoon, had applied too late, and backed his application with a piteous appeal to Sullivan for help. He at once said to Carte, ‘If he’ll change the first letter of his name, I’ll give him a seat in the orchestra.'”

A Miserable Vacation

twine puzzle

Your eccentric uncle has dropped you into the middle of Twine Island, which is festooned with one continuous loop of twine. The twine never crosses itself, but it snakes everywhere, and the island is too hilly for you to see the whole layout at once. As a character-building exercise, your uncle offers you a million dollars if you can determine whether you’re inside the loop or outside. How can you do this?

Click for Answer

Pieces of Pi

bailey-borwein-plouffe formula

Here’s something remarkable: This formula, discovered in 1995 by David Bailey, Peter Borwein, and Simon Plouffe of the University of Quebec at Montreal, permits the calculation of isolated digits of π — it’s possible to calculate, say, the trillionth digit of π without working out all the preceding digits.

The catch is that it works only in base 2 (binary) and base 16 (hexadecimal), but not in base 10. So it’s possible to know, say, that the five trillionth binary digit of π is 0, but there’s no way to convert the result into its decimal equivalent without working out all the intervening binary digits.

“The new formula allows the calculation of the nth base 2 or base 16 digit of π in a time that is essentially linear in n, with memory requirements that grow logarithmically (very slowly) in n,” writes David Darling in The Universal Book of Mathematics. “One possible use of the Bailey-Borwein-Plouffe formula is to help shed light on whether the distribution of π’s digits are truly random, as most mathematicians suppose.”

Everything Must Go

https://commons.wikimedia.org/wiki/File:Microcosm_of_London_Plate_032_-_Drury_Lane_Theatre_(colour).jpg

When the Drury Lane theater was closed in 1709, Joseph Addison published a fanciful list of the properties for sale:

  • Spirits of right Nantz brandy, for lambent flames and apparitions.
  • Three bottles and a half of lightning.
  • One shower of snow in the whitest French paper.
  • Two showers of a browner sort.
  • A sea, consisting of a dozen large waves; the tenth bigger than ordinary, and a little damaged.
  • A dozen and a half of clouds, trimmed with black, and well-conditioned.
  • A rainbow, a little faded.
  • A set of clouds after the French mode, streaked with lightning, and furbelowed.
  • A new moon, something decayed.
  • A pint of the finest Spanish wash, being all that is left out of two hogsheads sent over last winter.
  • A coach very finely gilt, and little used, with a pair of dragons, to be sold cheap.
  • A setting-sun, a pennyworth.
  • An imperial mantle made for Cyrus the Great, and worn by Julius Caesar, Bajazet, King Harry the Eighth, and Signor Valentini.
  • A basket-hilted sword, very convenient to carry milk in.
  • Roxana’s night-gown.
  • Othello’s handkerchief.
  • The imperial robes of Xerxes, never worn but once.
  • A wild boar, killed by Mrs. Tofts and Dioclesian.
  • A serpent to sting Cleopatra.
  • A mustard-bowl to make thunder with.
  • Another of a bigger sort, by Mr. D—-s’s directions, little used.
  • Six elbow-chairs, very expert in country dances, with six flower-pots for their partners.
  • The whiskers of a Turkish Bassa.
  • The complexion of a murderer in a band-box; consisting of a large piece of burnt cork, and a coal-black peruke.
  • A suit of clothes for a ghost, viz. a bloody shirt, a doublet curiously pinked, and a coat with three great eyelet-holes upon the breast.
  • A bale of red Spanish wool.
  • Modern plots, commonly known by the name of trapdoors, ladders of ropes, vizard-masks, and tables with broad carpets over them.
  • Three oak-cudgels, with one of crab-tree; all bought for the use of Mr. Penkethman.
  • Materials for dancing; as masks, castanets, and a ladder of ten rounds.
  • Aurengezebe’s scymitar, made by Will. Brown in Piccadilly.
  • A plume of feathers, never used but by Œdipus and the Earl of Essex.

“Mr. D—-” is John Dennis, a critic. Elsewhere Addison wrote, “If we may believe our logicians, man is distinguished from all other creatures by the faculty of laughter.”

Alphametic

A puzzle from reader Steven Moore:

moore alphametic 1

Find A, B, and C as distinct integers. There is only one solution.

Click for Answer

Extra Magic

sallows geometric magic square

From Lee Sallows:

The traditional magic square is a square array of n×n distinct numbers, their magical property being that the sum of the n numbers occupying each row, column, and diagonal is the same. A variation on this theme that I introduced in 2011 is the geometric magic square in which distinct geometrical figures (usually planar shapes) occupy the cells of the array rather than numbers. The magical property enjoyed by such an array is then that the n shapes making up each row, column, and diagonal can be fitted together as in a jigsaw puzzle so as to yield (i.e. tile) a new compound shape that is the same in each case.

Beyond ‘ordinary’ geometric magic squares, it turns out that the combinative properties of shapes are such as to enable ‘magical’ constructions that are denied to analogous structures using numbers. For example, at left in the figure above is seen a 3×3 square of a kind that cannot be realized using distinct numbers rather than shapes. Note first that the square is to be understood as ‘toroidally-connected’, which is to say, as if inscribed on a torus. Its left-hand edge is then to be interpreted as adjacent to its right-hand edge and its top edge adjacent to its bottom edge. Its magical property is then that the four pieces contained within any 2×2 subsquare can be assembled to produce an identical shape, in this case a rectangle of size 4×5. In all there are nine such subsquares to be found in the square, as seen (again in a square) at right. Note that three of the pieces are disjoint, my attempts to produce a similar solution using nine unbroken pieces having failed. So whereas a 3×3 magic square, numerical or geometric, satisfies at least 8 separate conditions ( 3 rows + 3 columns + 2 diagonals), the square here shown satisfies one more.

(Thanks, Lee!)

Ink

In 2011, after attorney Walter Maksym had filed the same complaint three times, federal judge Diane Sykes threw out the case, noting that “[e]ach iteration of the complaint was generally incomprehensible and riddled with errors, making it impossible for the defendants to know what wrongs they were accused of committing.” As an example she cited this passage — a single sentence of 345 words:

That pursuant to the RICO Act, Defendants extortive activities constituted a Pattern of Racketeering activity and conspiracy involving violations of 1956(a)(1)(B)(ii), and 18 U.S.C. § 1341 (wire fraud—the use of interstate mail or wire facilities, here telephone and facsimile transmissions), or the causing of any of those things promoting unlawful activity), and 18 U.S.C. § 1951 (interference with commerce and extortion by using and threatening to use legitimate governmental powers to obtain an illegitimate objectives under color of official right by wrongful plan, extortion, intimidation and threat of force and/or other unlawful consequence and through fear and misuse of there office to obstruct, hinder, interfere with, and/or affect commerce and the use and enjoyment of Plaintiffs’ property and obtaining, as uniformed public officials payment for unwanted services to which they were not entitled by law, attempting to conceal from the United States of America their true and correct income and the nature thereof so obtained from Plaintiffs in order to attempt to evade paying lawful taxes thereon in violation of 26 U.S. § 7201, et. seq., thereby using the governmental powers with which they have been entrusted to gain personal or illegitimate rewards and payments which they knew or should have known were made and/or obtained in return for the colorable official acts as aforesaid, and knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity, conducts or attempts to conduct such a financial transaction which in fact involves the proceeds of specified unlawful activity with the intent to promote the carrying on of specified unlawful activity all in violation of RICO and the other laws set forth herein, inter alia, as well as acts chargeable under any of the following provisions of the laws of the State of Illinois 720 ILCS 5/33-3(d) (official misconduct); 720 ILCS 5/1211 (criminal home invasion); 720 ILCS 5/19-4 (criminal trespass to a residence) 720 ILCS 5/19-4); (theft 720 ILCS 5/16 (a)(1)&(2) by knowingly obtaining or exerting unauthorized and/or through threat control over Plaintiff’s property as aforesaid.

Sykes found 23 sentences of 100 words or more in Maksym’s complaint, and added that “much of the writing is little more than gibberish.” Maksym blamed the problems on his recent cancer treatment, saying that he had an “impeccable record.”

See Running On.

A New World

https://commons.wikimedia.org/wiki/File:Atomic_Energy_Laboratory.jpg
Image: Wikimedia Commons

Offered in 1950, the alarmingly named Gilbert U-238 Atomic Energy Laboratory was exactly that — a children’s chemistry set that included radioactive material, in this case four glass jars containing uranium-bearing (U-238) ore samples.

“Produces awe-inspiring sights!” read the catalog. “Enables you to actually SEE the paths of electrons and alpha particles traveling at speeds of more than 10,000 miles per SECOND! Electrons racing at fantastic velocities produce delicate, intricate paths of electrical condensation — beautiful to watch. Viewing Cloud Chamber action is closest man has come to watching the Atom!”

It sounds rather worse than it was — in 2020 IEEE Spectrum determined that the likely radiation exposure was “minimal, about the equivalent to a day’s UV exposure from the sun” if the samples were not removed from their containers, in accordance with the safety instructions.

Children were not the best market for a fairly sophisticated kit, and fewer than 5,000 were sold, but creator Alfred Carlton Gilbert didn’t go hungry — he’d also invented the Erector Set.

Autopilot

On Boxing Day 1927, the Thames sailing barge Lady Daphne entered the difficult waters of the Isles of Scilly and passed with seeming assurance among its many rocky hazards. At length she began to veer toward land, though, and the islanders dispatched a lifeboat, which caught up with the ship just as she beached herself safely on the island of Tresco.

The only living thing aboard was a canary in a cage. Daphne‘s skipper had been washed overboard, and the remaining two crew members had abandoned the barge off the Cornish coast. Unmanned, she had somehow sailed herself among the rocks to a patch of safe sand.

Reverse Angle

https://pixabay.com/photos/moon-full-moon-sky-night-sky-lunar-1859616/

Just a little detail that I thought was interesting: Famously the moon appears larger when it’s near the horizon, but you can defeat this illusion by bending over and viewing it between your legs.

Why this works isn’t clear — possibly it’s because the image is inverted on the retina, or it may be an effect of inverting the body’s orientation.

(Stanley Coren, “The Moon Illusion: A Different View Through the Legs,” Perceptual and Motor Skills 75:3 [1992], 827-831; Atsuki Higashiyama and Kohei Adachi, “Perceived Size and Perceived Distance of Targets Viewed From Between the Legs: Evidence for Proprioceptive Theory,” Vision Research 46:23 [2006], 3961-3976.)