Search Results for: in a word

A Modest Proposal

https://www.flickr.com/photos/home_of_chaos/7609870922
Image: Flickr

While a visiting fellow at All Souls College, Oxford, in 1978, Claude Shannon pondered a personal challenge he faced there:

An American driving in England is confronted with a wild and dangerous world. The cars have the driver on the right and he is supposed to drive on the left side of the road. It is as though English driving is a left-handed version of the right-handed American system.

I can personally attest to the seriousness of this problem. Recently my wife and I, together with another couple on an extended visit to England, decided to jointly rent a car. … With our long-ingrained driving habits the world seemed totally mad. Cars, bicycles and pedestrians would dart out from nowhere and we would always be looking in the wrong direction. The car was usually filled with curses from the men and with screams and hysterical laughter from the women as we careened from one narrow escape to another.

His solution was “grandiose and utterly impractical — the idle dream of a mathematician”:

How will we do this? In a word, with mirrors. If you hold your right hand in front of a mirror, the image appears as a left hand. If you view it in a second mirror, after two reflections it appears now as a right hand, and after three reflections again as a left hand, and so on.

Our general plan is to encompass our American driver with mirror systems which reflect his view of England an odd number of times. Thus he sees the world about him not as it is but as it would be after a l80° fourth-dimensional rotation.

A corresponding adjustment to the steering system will turn the car left when the driver steers right, and vice versa. And filling the cabin with a high-density liquid will reverse the feeling of centrifugal force as well. “A snorkel provides for his breathing and altogether, with our various devices, he feels very much as though he were at home in America!”

(Claude E. Shannon, “The Fourth-Dimensional Twist, or a Modest Proposal in Aid of the American Driver in England,” typescript, All Souls College, Oxford, Trinity term, 1978; via Jimmy Soni and Rob Goodman, A Mind at Play: How Claude Shannon Invented the Information Age, 2017.)

| Science & Math

Eodermdromes

A spelling net is the pattern made when one writes down one instance of each unique letter that appears in a word and then connects these letters with lines, spelling out the word. For instance, the spelling net for VIVID is made by writing down the letters V, I, and D and drawing a line from V to I, I to V, V to I, and I to D.

Different words produce different spelling nets, of course, but every spelling net is an example of a graph, a collection of points connected by lines. A graph is said to be non-planar if some of the lines must cross; in the case of the spelling net, this means that no matter how we arrange the letters on the page, when we connect them in order we find that at least two of the lines must cross.

A word with a non-planar spelling net is called an eodermdrome, an ungainly name that itself illustrates the idea. The unique letters in EODERMDROME are E, O, D, R, and M. Write these down and run a pen among them, spelling out the word. You’ll find that no matter how the letters are arranged, it’s never possible to complete the task without at least two of the lines crossing:

https://commons.wikimedia.org/wiki/File:Eodermdrome.png
Image: Wikimedia Commons

Ross Eckler sought all the eodermdromes in Webster’s second and third editions; another example he found is SUPERSATURATES:

https://commons.wikimedia.org/wiki/File:Supersaturates2.png
Image: Wikimedia Commons

Since spelling nets are graphs, they can be studied with the tools of graph theory, the mathematical study of such networks. One result from that discipline says that a graph is non-planar if and only if it can be reduced to one of the two patterns marked K5 and K(3, 3) above. Since both EODERMDROME and SUPERSATURATES contain these forbidden graphs, both are non-planar.

A good article describing recreational eodermdrome hunting, by computer scientists Gary S. Bloom, John W. Kennedy, and Peter J. Wexler, is here. One warning: They note that, with some linguistic flexibility, the word eodermdrome can be interpreted to mean “a course on which to go to be made miserable.”

| Language · Science & Math

Oops

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

In 1726, the Swiss naturalist Johann Jakob Scheuchzer mistook the skull and vertebral column of a large salamander from the Miocene epoch for the “betrübten Beingerüst eines alten Sünders” (sad bony remains of an old human sinner) and dubbed it Homo diluvii testis, “the man who witnessed the Deluge.” The fossil lacked a tail or hind legs, so he thought it was the remains of a trampled human child:

It is certain that this [rock] contains the half, or nearly so, of the skeleton of a man; that the substance even of the bones, and, what is more, of the flesh and of parts still softer than the flesh, are there incorporated in the stone; in a word it is one of the rarest relics which we have of that accursed race which was buried under the waters. The figure shows us the contour of the frontal bone, the orbits with the openings which give passage to the great nerves of the fifth pair. We see there the remains of the brain, of the sphenoidal bone, of the roots of the nose, a notable fragment of the maxillary bone, and some vestiges of the liver.

The fossil made its way to Teylers Museum in the Netherlands, where in 1811 Georges Cuvier recognized it as a giant salamander. Ironically, Scheuchzer’s original belief is reflected in the fossil’s modern name, Andrias scheuchzeri — Andrias means “image of man.”

| Science & Math

Footloose

A visitor’s description of William Kingston, a Somerset farmer born without arms, recounted in John Platts, Encyclopedia of Natural and Artificial Wonders and Curiosities, 1876:

He highly entertained us at breakfast, by putting his half-naked feet upon the table as he sat, and carrying his tea and toast between his great and second toe to his mouth, with as much facility as if his foot had been a hand, and his toes fingers. … He then shewed me how he shaves himself with the razor in his toes; and he can comb his own hair. He can dress and undress himself, except buttoning his clothes. He feeds himself, and can bring both his meat or his broth to his mouth, by holding the fork or spoon in his toes. He cleans his own shoes, lights the fire, and does almost any domestic business as well as any other man. … He can milk his cows with his toes, and cuts his own hay, binds it up in bundles, and carries it about the field for his cattle. Last winter he had eight heifers constantly to fodder. The last summer he made all his hay-ricks. He can do all the business of the hay-field (except mowing) as fast and as well with his feet as others can with rakes and forks. … In a word, he can nearly do as much without as others can with their arms.

| Oddities

“WIPEOUT!”

Cynthia Knight composed this in 1983 — a poem typed entirely on the upper row of a typewriter:

O WOE
(we quote you, poor poet)
We tiptoe up, quiet. You peer out. You opt to write
quite proper poetry
to pour out your pretty repertoire.
We try to woo you to write. You pop out; retire to pout.
Torpor? Terror? Ire? Or worry? We pity you, poor poet.
Put out, you rip your poetry up. Too trite?
We try to pique you.
Were your pep to tire, or your power to rot
We prop you up to retype it.
Or were our top priority to trip you
or were etiquette, piety, or propriety to require you to wire up your typewriter to rewrite it …
O! You write witty quip, pert retort. You titter. You write pure, utter tripe too, I purr.
You err
retype your error
weep
wipe your wet typewriter (your property)
We TOWER o’er you, wee tot — were you TWO?
YOU WORE YOUR TOY TYPEWRITER OUT!
We quit.

(“The Poet’s Corner,” Word Ways 16:2 [May 1983], 87-88.)

| Language

Mixed Doubles

In a letter to Maud Standen dated Dec. 18, 1877, Lewis Carroll included a puzzle:

[M]y ‘Anagrammatic Sonnet’ will be new to you. Each line has 4 feet, and each foot is an anagram, i. e., the letters of it can be re-arranged so as to make one word. Thus there are 24 anagrams, which will occupy your leisure moments for some time, I hope. Remember, I don’t limit myself to substantives, as some do. I should consider ‘we dishwished’ a fair anagram.

As to the war, try elm. I tried.
The wig cast in, I went to ride.
‘Ring? Yes.’ We rang. ‘Let’s rap.’ We don’t.
‘O shew her wit!’ As yet she won’t.
Saw eel in Rome. Dry one: he’s wet.
I am dry. O forge! Th’rogue! Why a net?

For example, the first foot in the first line, “As to,” can be rearranged to spell OATS. Carroll left no solution, but he did add a parting riddle to which we have the answer:

“To these you may add ‘abcdefgi,’ which makes a compound word — as good a word as ‘summer-house.'” What is it?

Click for Answer
| Puzzles

Round and Round

https://archive.org/details/MathematicsCanBeFun-Eng-YakovPerelman/page/n11/mode/2up

‘I had quite a bit of fun playing hide-and-seek with a squirrel,’ he said. ‘You know that little round glade with a lone birch in the centre? It was on this tree that a squirrel was hiding from me. As I emerged from a thicket, I saw its snout and two bright little eyes peeping from behind the trunk. I wanted to see the little animal, so I started circling round along the edge of the glade, mindful of keeping the distance in order not to scare it. I did four rounds, but the little cheat kept backing away from me, eyeing me suspiciously from behind the tree. Try as I did, I just could not see its back.’

‘But you have just said yourself that you circled round the tree four times,’ one of the listeners interjected.

‘Round the tree, yes, but not round the squirrel.’

‘But the squirrel was on the tree, wasn’t it?’

‘So it was.’

‘Well, that means you circled round the squirrel too.’

‘Call that circling round the squirrel when I didn’t see its back?’

‘What has its back to do with the whole thing? The squirrel was on the tree in the centre of the glade and you circled round the tree. In other words, you circled round the squirrel.’

‘Oh no, I didn’t. Let us assume that I’m circling round you and you keep turning, showing me just your face. Call that circling round you?’

‘Of course, what else can you call it?’

‘You mean I’m circling round you though I’m never behind you and never see your back?’

‘Forget the back! You’re circling round me and that’s what counts. What has the back to do with it?’

— Yakov Perelman, Mathematics Can Be Fun, 1927

| Oddities

Homage à Fromage

https://commons.wikimedia.org/wiki/File:DoubleGlou.png

For his 1992 palindrome dictionary From A to ZOtamorf, Stephen J. Chism set out to gather all the reversible expressions in English that had been published up to that point. He divides them sensibly into single words; phrases and sentences; poems; and personal and place names — but the last chapter is titled FOR SOME REASON CHEESE:

A duo Gouda
Ate Feta?
Cheese not dairy. Myriad tone? See H.C.
Cheese? See H.C. …
Disk Colby block, Sid.
Edam Hannah made
He ate feta, eh?
He made lives evil. Edam, eh?
Lay block Colby, Al.
No Brie, Irbon?
No Romano on a moron …
Not Lit, Stilton?
Note Swiss: “I.W. Seton”
Why block Colby, H.W.?

“I don’t propose to explain it,” he writes. “Cheese is as unlikely as it is likely; a seemingly ordinary food product. Why, then, do we find it treated more thoroughly in palindromes than any other substance?”

| Language

Plunges in Dumbness

In his adopted home of Majorca, Robert Graves once encountered a memorable tourist leaflet:

They are hollowed out in the see coast at the municipal terminal of Capdepera, at nine kilometer from the town of Arta in the Island of Mallorca, with a suporizing infinity of graceful colums of 21 meter and by downward, wich prives the spectator of all animacion and plunges in dumbness The way going is very picturesque, serpentine between style mountains, til the arrival at the esplanade of the vallee called ‘The Spider’ There are good enlacements of the railroad with autobuses of excursion, many days of the week, today actually Wednesday and Satturday Since many centuries renown foreing visitors have explored them and wrote their eulogy about, included Nort-American geoglogues

He commemorated it with a poem:

Such subtile filigranity and nobless of construccion
Here fraternise in harmony, that respiracion stops
While all admit their impotence (though autors most formidable)
To sing in words the excellence of Nature’s underprops,
Yet stalactite and stalagmite together with dumb language
Make hymnes to God wich celebrate the strength of water drops

The whole thing is here.

| Language · Poems