For the Record

At one point in Samuel Beckett’s 1951 novel Molloy, the title character finds himself at the seaside and “lays in a store of sucking stones”:

They were pebbles but I call them stones. Yes, on this occasion I laid in a considerable store. I distributed them equally between my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones.

It occurs to him that this method won’t ensure that every stone is eventually sucked, and he works out a plan that will achieve this. This takes eight pages, “one of the longest and most detailed accounts of someone working at a mathematical problem in a work of fiction,” according to Richard Phillips in Numbers: Facts, Figures and Fiction.

Maddeningly, in the end Molloy throws away all the stones but one, “for they all tasted exactly the same.”

Banishing Gloom

quin historical atlas

For his Historical Atlas of 1830, Edward Quin took a different approach than other cartographers: Rather than present history as a series of discrete moments, he illustrates the growth of knowledge by covering the earth in obscuring clouds that are beaten back from panel to panel.

“In Quin’s Historical Atlas, the world is shown first in darkness, with clouds obscuring everything outside the Garden of Eden,” note Anthony Grafton and Daniel Rosenberg in Cartographies of Time. “Gradually, as history reveals more of the world, the clouds roll back. Turning the pages of the atlas is a bit like riffling through a flip book, watching darkness recede and the world known to Europeans grow.”

“A Cheap Correspondence”

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A curious story of two poor lovers, whose system of correspondence was confined to an ingenious cipher of ink-blots on the outside of the letter, is told by the Poet Coleridge. In one of his walks in the Lake district, he saw the postman offer a letter to the servant-girl at a village inn, who, after carefully looking at the address, returned the document to the postman, telling him that she could not take it in, as she was too poor to pay the postage. Thereupon, Coleridge stepped forward, and giving the postman the shilling required for the letter, handed it to the girl. To his surprise, she did not appear as pleased as he had expected; and when the postman was out of hearing, she explained the matter by confessing to the poet that the whole of the letter consisted in its address and certain exterior blots and marks, and that it was the method adopted by her lover and herself to keep up an unpaid-for correspondence in the days of dear postage.

— Thomas Hood, The Book of Modern English Anecdotes, 1872

Little Wars

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H.G. Wells played war games. In 1913 he published a set of rules for playing with miniature infantry, cavalry, and artillery, worked out with his friend Jerome K. Jerome while playing with toy soldiers after lunch one day.

He fired that day a shot that still echoes round the world. An affair — let us parallel the Cannonade of Valmy and call it the Cannonade of Sandgate — occurred, a shooting between opposed ranks of soldiers, a shooting not very different in spirit — but how different in results! — from the prehistoric warfare of catapult and garter. ‘But suppose,’ said his antagonists; ‘suppose somehow one could move the men!’ and therewith opened a new world of belligerence.

With another friend and a lot of playtesting, he worked out a set of rules by which two players contend for control of a battlefield, “little brisk fights in which one may suppose that all the ammunition and food needed are carried by the men themselves.”

In two or three moves the guns are flickering into action, a cavalry melee may be in progress, the plans of the attack are more or less apparent, here are men pouring out from the shelter of a wood to secure some point of vantage, and here are troops massing among farm buildings for a vigorous attack. The combat grows hot round some vital point. Move follows move in swift succession. One realises with a sickening sense of error that one is outnumbered and hard pressed here and uselessly cut off there, that one’s guns are ill-placed, that one’s wings are spread too widely, and that help can come only over some deadly zone of fire.

http://www.gutenberg.org/files/3691/3691-h/3691-h.htm

When Wells published his rules in August 1913, the Spectator raved that “there can be no doubt at all as to the excellence of Little Wars as a game for its own sake” — “Mr. Wells describes his new game and sets out its rules so attractively, and has, moreover, added to his description such alluring photographs, that his readers will find it hard indeed not to hurry out to the toy-shop round the corner, raise the necessary levies, and fall down forthwith upon hands and knees to emulate his achievements in the Battle of Hook’s Farm.”

Happily, since it was published a century ago, the whole thing is in the public domain — it’s available at Project Gutenberg.

Through the Looking-Glass

In 2015, to celebrate the 150th anniversary of the publication of Alice’s Adventures in Wonderland, master sculptor Karen Mortillaro created 12 new sculptures, one for each chapter in Lewis Carroll’s masterpiece. Each takes the form of a table topped with an S-cylindrical mirror, with a bronze sculpture on either side. The sculpture that stands before the mirror is anamorphic, so that the curved mirror’s reflection “undistorts” it, giving it meaning:

http://rmm.ludus-opuscula.org/PDF_Files/Mortillaro_AnamorphicSculpture_49_61(4_2015)_low.pdf

“The S-cylindrical mirror is ideal for this project because it allows for the figures on one side of the mirror to be sculpted realistically, while those on the opposite side of the mirror are distorted and unrecognizable,” Mortillaro writes. “The mirror is symbolic of the parallel worlds that Alice might have experienced in her dream state; the world of reality is on one side of the mirror; and the world of illusion is on the mirror’s opposite side.”

Mortillaro’s article appears in the September 2015 issue of Recreational Mathematics Magazine.

Split Decision

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In December 2013 a U.S. District Court decided that copyright in the fictional characters Sherlock Holmes and Dr. Watson had expired, but only for the characters as they’re depicted in the earlier novels by Arthur Conan Doyle. Aspects of the characters that are mentioned only in the later novels — such as Dr. Watson’s athletic background, first described in a 1924 short story — are considered new “increments of expression” of those characters, and remain protected.

That makes eminent sense for writers and lawyers, but what about poor Dr. Watson, anxiously stirring the fire at 221B Baker Street? Does he have an athletic background or doesn’t he? The copyright law seems to apply to a version of him that does, and not to one that doesn’t. Should we say there are two Dr. Watsons? That doesn’t seem right.

Worse, “If an author now wants to write a new Holmes novel, but is prohibited from mentioning almost everything pertaining to Professor Moriarty (who only rose to prominence in the later work Valley of Fear), how can we say that he is still writing about the ‘the same’ Holmes, given how much his character was formed through the interaction with his nemesis?” ask legal scholars Burkhard Schafer and Jane Cornwell. “Does this not render any new Holmes necessarily ‘incomplete,’ that is lacking character traits and memories Holmes is ‘known to’ possess, according to the canonical work?”

Even the “public domain” Holmes seems to multiply in this light. We learn that Holmes has an older brother, Mycroft, in “The Adventure of the Greek Interpreter,” published in 1893. But if Mycroft is older than Sherlock, then surely he’s been Sherlock’s brother ever since Sherlock’s birth in 1854. Does the early Sherlock (in, say, A Study in Scarlet) have a brother?

(Burkhard Schafer and Jane Cornwell, “Law’s Fictions, Legal Fictions and Copyright Law,” in Maksymilian Del Mar and William Twining, eds., Legal Fictions in Theory and Practice, 2015.)

AWOL

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A harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression (so an example is 1/1, 1/2, 1/3, 1/4 …). When tutoring mathematics at Oxford, Charles Dodgson had a favorite example to illustrate this:

According to him, it is (or was) the rule at Christ Church that, if an undergraduate is absent for a night during term-time without leave, he is for the first offence sent down for a term; if he commits the offence a second time, he is sent down for two terms; if a third time, Christ Church knows him no more. This last calamity Dodgson designated as ‘infinite.’ Here, then, the three degrees of punishment may be reckoned as 1, 2, infinity. These three figures represent three terms in an ascending series of Harmonic Progression, being the counterparts of 1, 1/2, 0, which are three terms in a descending Arithmetical Progression.

— Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898

Pentominoes

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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.

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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

A Friendly Greeting

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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.

The Harcourt Interpolation

Here are two transcriptions of a speech by Home Secretary Sir William Harcourt, reprinted in the London Times on Jan. 23, 1882. At left is the column as it originally appeared; at right is the same speech in a hastily issued replacement edition. What’s the difference between them?

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In the column on the left, about midway down, a disgruntled compositor has inserted the line “The speaker then said he felt inclined for a bit of fucking.”

The paper issued an apology and suppressed the offending edition as well as it could, but that only increased public interest, driving the price of a copy up from threepence to £5 in some areas (it would reach £100 by the 1990s). The Times’ quarterly index recorded the offense:

Harcourt (Sir W.) at Burton on Trent, 23 j 7 c
———Gross Line Maliciously Interpolated in a
Few Copies only of the Issue, 23 j 7 d — 27 j 9 f

The paper tried to rise above all this, but it made a new rule: If you sack a compositor, get him off the premises immediately.

(Thanks, Alejandro.)