Pentominoes

https://commons.wikimedia.org/wiki/File:Pentomino_Naming_Conventions.svg
Image: Wikimedia Commons

In 1965, as they were writing the first draft of 2001: A Space Odyssey, Stanley Kubrick showed Arthur C. Clarke a set of 12 plastic tiles. Each tile consisted of five squares joined along their edges. These are known as pentominoes, and a set of 12 includes every possible such configuration, if rotations and reflections aren’t considered distinct. The challenge, Kubrick explained, is to fit the 12 tiles together into a tidy rectangle. Because 12 five-square tiles cover 60 squares altogether, there are four possible rectangular solutions: 6 × 10, 5 × 12, 4 × 15, and 3 × 20. (A 2 × 30 rectangle would be too narrow to accommodate all the shapes.)

Clarke, who rarely played intellectual games, found that this challenge “can rather rapidly escalate — if you have that sort of mind — into a way of life.” He stole a set of tiles from his niece, spent hundreds of hours playing with it, and even worked the shapes into the design of a rug for his office. “That a jigsaw puzzle consisting of only 12 pieces cannot be quickly solved seems incredible, and no one will believe it until he has tried,” he wrote in the Sunday Telegraph Magazine. It took him a full month to arrange the 12 shapes into a 6 × 10 rectangle — a task that he was later abashed to learn can be done in 2339 different ways. There are 1010 solutions to the 5 × 12 rectangle and 368 solutions to the 4 × 15.

https://commons.wikimedia.org/wiki/File:Pentomino_Puzzle_Solutions.svg
Image: Wikimedia Commons

But “The most interesting case, however, is that of the long, thin rectangle only 3 units wide and 20 long.” Clarke became fascinated with this challenge when Martin Gardner revealed that only two solutions exist. He offered 10 rupees to anyone who could find the solutions, and was delighted when a friend produced them, as he’d calculated that solving the problem by blind permutation would take more than 20 billion years.

Clarke even worked the 3 × 20 problem into his 1975 novel Imperial Earth. Challenged by his grandmother, the character Duncan struggles with the task and declares it impossible. “I’m glad you made the effort,” she says. “Generalizing — exploring every possibility — is what mathematics is all about. But you’re wrong. It can be done. There are just two solutions; and if you find one, you’ll also have the other.”

Can you find them?

Click for Answer

“An Interesting War Relic”

https://commons.wikimedia.org/wiki/File:Malaclemys_terrapinHolbrookV1P12A.jpg

A small highland terrapin was captured in 1884 by a Chattanooga gentleman that carries on the smooth surface of its belly the inscription, carved in distinct characters: ‘Union: Co. K, 26th Regt., Ohio Vols.; November 18, 1864.’ It is supposed that some straggling Union soldier, belonging to the command designated, captured the North Georgia quadruped and proceeded to make a living historical tablet of the hard-shell little creeper.

That was twenty years ago. In 1886 when a party of ex-Union captives from Ohio, who were making a tour of the South, passed through Chattanooga, the terrapin was shown them and they could not have shown more delight over the meeting of an old friend. ‘He was the pet of some of our boys,’ said one of the old soldiers, as he fondly patted the terrapin’s back, while the tears filled his eyes and rolled down his cheeks in great drops.

Rome [Ga.] Sentinel, reprinted in W.C. King and W.P. Derby, Camp-Fire Sketches and Battle-Field Echoes, 1886

A Friendly Greeting

https://pixabay.com/en/mark-twain-vintage-author-humorist-391120/

On Nov. 21, 1897, Mark Twain addressed the Vienna Press Club on “The Horrors of the German Language.” He spoke in German; here’s his literal translation:

It has me deeply touched, my gentlemen, here so hospitably received to be. From colleagues out of my own profession, in this from my own home so far distant land. My heart is full of gratitude, but my poverty of German words forces me to great economy of expression. Excuse you, my gentlemen, that I read off, what I you say will.

The German language speak I not good, but have numerous connoisseurs me assured that I her write like an angel. Maybe — I know not. Have till now no acquaintance with the angels had. That comes later — when it the dear God please — it has no hurry.

Since long, my gentlemen, have I the passionate longing nursed a speech on German to hold, but one has me not permitted. Men, who no feeling for the art had, laid me ever hindrance in the way and made naught my desire — sometimes by excuses, often by force. Always said these men to me: ‘Keep you still, your Highness! Silence! For God’s sake seek another way and means yourself obnoxious to make.’

In the present case, as usual it is me difficult become, for me the permission to obtain. The committee sorrowed deeply, but could me the permission not grant on account of a law which from the Concordia demands she shall the German language protect. Du liebe Zeit! How so had one to me this say could — might — dared — should? I am indeed the truest friend of the German language — and not only now, but from long since — yes, before twenty years already. And never have I the desire had the noble language to hurt; to the contrary, only wished she to improve — I would her only reform. It is the dream of my life been. I have already visits by the various German governments paid and for contracts prayed. I am now to Austria in the same task come. I would only some changes effect. I would only the language method — the luxurious, elaborate construction — compress, the eternal parenthesis suppress, do away with, annihilate; the introduction of more than thirteen subjects in one sentence forbid; the verb so far to the front pull that one it without a telescope discover can. With one word, my gentlemen, I would your beloved language simplify so that, my gentlemen, when you her for prayer need, One her yonder-up understands.

I beseech you, from me yourself counsel to let, execute these mentioned reforms. Then will you an elegant language possess, and afterward, when you some thing say will, will you at least yourself understand what you said had. But often nowadays, when you a mile-long sentence from you given and you yourself somewhat have rested, then must you a touching inquisitiveness have yourself to determine what you actually spoken have. Before several days has the correspondent of a local paper a sentence constructed which hundred and twelve words contained, and therein were seven parentheses smuggled in, and the subject seven times changed. Think you only, my gentlemen, in the course of the voyage of a single sentence must the poor, persecuted, fatigued subject seven times change position!

Now, when we the mentioned reforms execute, will it no longer so bad be. Doch noch eins. I might gladly the separable verb also a little bit reform. I might none do let what Schiller did: he has the whole history of the Thirty Years’ War between the two members of a separable verb in-pushed. That has even Germany itself aroused, and one has Schiller the permission refused the History of the Hundred Years’ War to compose — God be it thanked! After all these reforms established be will, will the German language the noblest and the prettiest on the world be.

Since to you now, my gentlemen, the character of my mission known is, beseech I you so friendly to be and to me your valuable help grant. Mr. Potzl has the public believed make would that I to Vienna come am in order the bridges to clog up and the traffic to hinder, while I observations gather and note. Allow you yourselves but not from him deceived. My frequent presence on the bridges has an entirely innocent ground. Yonder gives it the necessary space, yonder can one a noble long German sentence elaborate, the bridge-railing along, and his whole contents with one glance overlook. On the one end of the railing pasted I the first member of a separable verb and the final member cleave I to the other end — then spread the body of the sentence between it out! Usually are for my purposes the bridges of the city long enough; when I but Potzl’s writings study will I ride out and use the glorious endless imperial bridge. But this is a calumny; Potzl writes the prettiest German. Perhaps not so pliable as the mine, but in many details much better. Excuse you these flatteries. These are well deserved.

Now I my speech execute — no, I would say I bring her to the close. I am a foreigner — but here, under you, have I it entirely forgotten. And so again and yet again proffer I you my heartiest thanks.

Reportedly his spoken German was actually excellent (PDF), and he delivered the address without reading the text.

He’d been sparring with German for some time — his essay “The Awful German Language” had appeared as an appendix to A Tramp Abroad in 1880.

An Empire’s Lamentation

wellington cortege

When the Duke of Wellington died in 1852, his funeral procession was watched by a crowd of 1.5 million people. To commemorate it, Henry Alken and George Augustus Sala painted a panorama fully 20 meters long, which was released the following year:

Wellington had certainly earned some distinction — his style was proclaimed in the London Gazette:

Arthur,
Duke and Marquess of Wellington,
Marquess Douro, Earl of Wellington,
Viscount Wellington and Baron Douro,
Knight of the Most Noble Order of the Garter,
Knight Grand Cross of The Most Honourable Order of the Bath,
One of Her Majesty’s Most Honourable Privy Council, and
Field Marshal and Commander-in-Chief of Her Majesty’s Forces.
Field Marshal of the Austrian Army,
Field Marshal of the Hanoverian Army,
Field Marshal of the Army of the Netherlands,
Marshal-General of the Portuguese Army,
Field Marshal of the Prussian Army,
Field Marshal of the Russian Army,
and
Captain-General of the Spanish Army.
Prince of Waterloo, of the Kingdom of the Netherlands, Duke of Ciudad Rodrigo
and Grandee of Spain of the First Class.
Duke of Victoria, Marquess of Torres Vedras, and Count of Vimiera in Portugal.
Knight of the Most Illustrious Order of the Golden Fleece, and of the Military Orders
of St. Ferdinand and of St. Hermenigilde of Spain.
Knight Grand Cross of the Orders of the Black Eagle and of the Red Eagle of Prussia.
Knight Grand Cross of the Imperial Military Order of Maria Teresa of Austria.
Knight of the Imperial Orders of St. Andrew, St. Alexander Newski, and St. George of Russia.
Knight Grand Cross of the Royal Portuguese Military Order of the Tower and Sword.
Knight Grand Cross of the Royal and Military Order of the Sword of Sweden.
Knight of the Order of St. Esprit of France.
Knight of the Order of the Elephant of Denmark.
Knight Grand Cross of the Royal Hanoverian Guelphic Order.
Knight of the Order of St. Januarius and of the Military Order of St. Ferdinand and
of Merit of the Two Sicilies.
Knight or Collar of the Supreme Order of the Annunciation of Savoy.
Knight Grand Cross of the Royal Military Order of Maximilian Joseph of Bavaria.
Knight of the Royal Order of the Rue Crown of Saxony,
Knight Grand Cross of the Order of Military Merit of Wurtemberg.
Knight Grand Cross of the Military Order of William of the Netherlands.
Knight of the Order of the Golden Lion of Hesse Cassel,
and
Knight Grand Cross of the Orders of Fidelity and of the Lion of Baden.

(Thanks, James.)

Art and Science

http://www.microbialart.com/galleries/fleming/

Alexander Fleming, the discoverer of pencillin, grew “germ paintings” of living bacteria on blotting paper. He made this 4-inch portrait, titled “Guardsman,” in 1933.

“If a paper disc is placed on the surface of an agar plate, the nutrient material diffuses through the paper sufficiently to maintain the growth of many microorganisms implanted on the surface of the paper,” he wrote. “At any stage, growth can be stopped by the introduction of formalin. Finally the paper disc, with the culture on its surface, can be removed, dried, and suitably mounted.”

Here’s a gallery. “Even in Fleming’s time this technique failed to receive much attention or approval. Apparently he prepared a small exhibit of bacterial art for a royal visit to St Mary’s by Queen Mary. The Queen was ‘not amused and hurried past it’ even though it included a patriotic rendition of the Union Jack in bacteria.”

No Connection

https://www.youtube.com/watch?v=ke-H5EEqvRs

In a garden in Ōtsuchi, in the Iwate prefecture on Japan’s east coast, stands an inoperative phone booth that’s nonetheless been used by more than 10,000 people since the 2011 earthquake and tsunami that killed 15,000 people and displaced hundreds of thousands more. The booth, known as the “Kaze no Denwa Box,” or Phone Booth of the Winds, was built by 69-year-old Itaru Sasaki so that local residents could communicate with loved ones who are dead or missing. Sasaki never connected the line, but callers still use the phone to speak to the departed, or write messages on a notepad, trusting that the wind will carry them to their intended recipients.

“In such a stricken environment, it might have been easy to perceive this disconnected phone booth as a whimsical art project incommensurate with the scale of loss experienced by the survivors for whom it was intended,” writes Ariana Kelly in Phone Booth (2015). “But quite the opposite has happened, and for the past several years there has been a steady stream of visitors to the booth, both from Ōtsuchi and other parts of Japan. Perhaps it provides a necessary terminus, a destination in a place marked by eradication. Perhaps one antidote to tragedy is useless beauty, or just uselessness.”

Quiet Time

neuhaus alarm clock

In 1979, artist Max Neuhaus proposed a silent alarm clock. Or, rather, a clock that awakens one with silence:

Instead of a bell which begins with a sudden clang and gradually dies away, this concept is precisely the opposite. The sound is introduced gradually; beginning inaudibly it grows slowly over a period of minutes and, at its height, suddenly disappears. The long subtle emergence of the sound causes it to go unnoticed. It becomes apparent only at the instant of its disappearance, creating a sense of silence.

The change would awaken you. It’s not even really silence that you’d hear — the normal background sounds would still be there. But “in this silent moment, for a few seconds after the sound has gone, a subtle transparent aural afterimage is superimposed on the everyday sounds of the environment, a spontaneous aural memory or reconstruction perhaps, shared by all who notice it, engendered by the sound’s disappearance.”

Unquote

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“We speak of a manly man, but not of a whaley whale. If you wanted to dissuade a man from drinking his tenth whisky, you would slap him on the back and say, ‘Be a man.’ No one who wished to dissuade a crocodile from eating his tenth explorer would slap it on the back and say, ‘Be a crocodile.'”

— G.K. Chesterton, The Religious Doubts of Democracy, 1903

Podcast Episode 138: Life in a Cupboard

patrick fowler

In this week’s episode of the Futility Closet podcast we’ll tell two stories about people who spent years confined in miserably small spaces. North Carolina slave Harriet Jacobs spent seven years hiding in a narrow space under her grandmother’s roof, evading her abusive owner, and Irishman Patrick Fowler spent most of World War I hiding in the cabinet of a sympathetic family in German-occupied France.

We’ll also subdivide Scotland and puzzle over a ballerina’s silent reception.

See full show notes …

Ecommerce

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In 1857 The Leisure Hour tried to imagine life in London a century in the future, that is, in 1957. Many of the predictions seem sadly optimistic (for instance, the eradication of crime), but one in particular stands out:

I observed that from each of these district shops innumerable electric wires branched off in all directions, communicating with several houses in the district to which it belonged. Thus, no sooner did a house-keeper stand in need of any article than she could despatch the order instantaneously along the wire, and receive the goods by the very first railway carriage that happened to pass the store. Thus, she saved her time, and she lost no money, because all chaffering and cheapening, and that fencing between buyer and seller, which was once deemed a pleasure, had been long voted a disgraceful, demoralizing nuisance, and was done away with.

You can read the whole thing at the Public Domain Review.