English by Degrees

In his landmark paper “A Mathematical Theory of Communication,” Claude Shannon experimented with a series of stochastic approximations to English. He started with a sample message in which each of the 26 letters and the space appear with equal probability:

XFOML RXKHRJFFJUJ ZLPWCFWKCYJ FFJEYVKCQSGHYD QPAAMKBZAACIBZLHJQD.

In the next message, the symbols’ frequencies are weighted according to how commonly they appear in English text (for example, E is more likely than W):

OCRO HLI RGWR NMIELWIS EU LL NBNESEBYA TH EEI ALHENHTTPA OOBTTVA NAH BRL.

In the third he linked each letter to its predecessor: After one letter is recorded, the next is chosen in a manner weighted according to how frequently such a pair appears in natural English (a “digram”):

ON IE ANTSOUTINYS ARE T INCTORE ST BE S DEAMY ACHIN D ILONASIVE TUCOOWE AT TEASONARE FUSO TIZIN ANDY TOBE SEACE CTISBE.

In the fourth he applied the same idea to sets of three letters (“trigrams”):

IN NO IST LAT WHEY CRATICT FROURE BIRS GROCID PONDENOME OF DEMONSTURES OF THE REPTAGIN IS REGOACTIONA OF CRE.

In the fifth he shifts from letters to words. Words appear in a manner weighted by their frequency in English (without regard to the prior word):

REPRESENTING AND SPEEDILY IS AN GOOD APT OR COME CAN DIFFERENT NATURAL HERE HE THE A IN CAME THE TO OF TO EXPERT GRAY COME TO FURNISHES THE LINE MESSAGE HAD BE THESE.

Finally, he applies the digram technique to words — each word is chosen based on the frequency with which pairs of words appear in English:

THE HEAD AND IN FRONTAL ATTACK ON AN ENGLISH WRITER THAT THE CHARACTER OF THIS POINT IS THEREFORE ANOTHER METHOD FOR THE LETTERS THAT THE TIME OF WHO EVER TOLD THE PROBLEM FOR AN UNEXPECTED.

Already this is starting to look like English — Shannon notes that the 10-word phrase ATTACK ON AN ENGLISH WRITER THAT THE CHARACTER OF THIS could find a home in a natural sentence without much strain.

He had to stop there, as this was 1948 and he was using paper books. “But the modern availability of computing power has made carrying out such calculations automatically a near-trivial task for reasonably-sized bodies of sample text,” writes UC-Santa Cruz computer scientist Noah Wardrip-Fruin. “As Shannon also pointed out, the stochastic processes he described are comonly considered in terms of Markov models. And, interestingly, the first application of Markov models was also linguistic and literary — modeling letter sequences in Pushkin’s poem ‘Eugene Onegin.’ But Shannon was the first to bring this mathematics to bear meaningfully on communication, and also the first to use it to perform text-generation play.”

(Noah Wardrip-Fruin, “Playable Media and Textual Instruments,” in Peter Gendolla and Jörgen Schäfer, eds., The Aesthetics of Net Literature, 2007.)

Just a Reminder

FC book covers

Both Futility Closet books — Futility Closet: An Idler’s Miscellany of Compendious Amusements and Futility Closet 2: A Second Trove of Intriguing Tidbits — are available now on Amazon. Perfect for chasing away winter doldrums or giving as solstice gifts. Thanks for your support!

Room Service

fischer patent

Parking was already a problem in 1906, so Swiss inventor Martin Fischer offered a car that you can drive right up to your apartment:

The width of the frame is smaller than the distance of the wheels. That distance amounts to at most seventy-five centimeters. Consequently the motor-car can pass through doors of ordinary width and up staircases with such ease that even persons residing on the upper floors of ordinary dwelling-houses will be able to keep such motor-cars without the necessity of providing special storage space on the ground floor.

It’s built low to reduce the risk of tipping over when traveling around sharp curves. But what happens if you meet someone else on the stairs?

Unquote

“One of my chief objections to the management of the universe is that we suffer so much more from our gentler and more amiable vices than from our darkest crimes.” — A.E. Housman, letter to Grant Richards, 1913

Express

On Feb. 19, 1916, as workers were digging a new subway line under the East River toward Brooklyn Heights, a burst of compressed air blew 28-year-old Marshall Mabey up through 12 feet of river bed, through the river, and 25 feet into the air atop a geyser of water. Impossibly, he was not seriously injured. From the New York Times:

‘The first thing that told me something was wrong,’ he related yesterday, ‘was when I saw an opening in the earth ahead of the shield which was used to protect the tunnel as we went along. The hole was then about eighteen inches in size. Frank Driver, my partner, and I grabbed hold of a big plank and threw it at the hole to stop it up. I found that the air pressure was pushing me toward the hole, and I tried to save myself by grabbing the air pipes. I missed them, and then I felt myself being pushed into the hole.

‘As I struck the mud it felt as if something was squeezing me tighter than I had ever been squeezed. I was smothered and I guess I lost consciousness. They tell me I was thrown about twenty-five feet above the water when I came out, but I don’t remember that.

‘I am a good swimmer and I kept my mouth shut and came up to the surface. I had on my big rubber boots and they bothered me but I managed somehow to keep my head above the surface. My left leg was numb but I could move it. Finally men on a pier threw me a rope and I held on until I was taken out of the water.’

He said he hoped to return to work within a day or two. “Of course I know that Marshall is in danger every time he goes to work,” said his wife, “but all work is dangerous and my husband is as careful as he can be. His job is a good one and I am glad he has it.”

In a Word

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

ploration
n. weeping

begrutten
adj. having a face swollen from weeping

Niobe
n. an inconsolably bereaved woman, a weeping woman

The Butterfly Theorem

Draw a circle, choose any chord PQ, and draw two further chords AB and CD through its midpoint M. Now, if AD and BC intersect PQ at X and Y, M will always be the midpoint of XY.

In Icons of Mathematics (2011), Claudi Alsina and Roger Nelsen write, “The surprise is the unexpected symmetry arising from an almost random construction.” The theorem first appeared in 1815.

Averageness

galton criminal composites

In 1883 Francis Galton tried an experiment: He combined multiple photographs of criminals into composite images, hoping to discover an underlying “type.” He didn’t get a strong result, but he did notice something odd about the composite faces: They tended to be more attractive than the individual images that made them up. He found similar effects with other groups — a composite “sick person” seemed healthier than its constituent images, and a group of good-looking people became even more beautiful in composite. In one case he made a “singularly beautiful combination of the faces of six different Roman ladies, forming a charming ideal profile.”

The lesson seems to be that we find an “average” face most attractive — a face is appealing not because it has unusual features but because it lacks them. For example (below), a University of Toronto study found that the shape of Jessica Alba’s face approaches the average for all female profiles: The distance between her pupils is 46 percent of the width of her face, and the distance between her eyes and her mouth is 36 percent of the length of her face. The fact that we find this attractive makes some evolutionary sense: Natural selection tends to drive out disadvantageous features, so a partner with an “average” face is more likely to be healthy and fertile.

Podcast Episode 37: Edgar Allan Poe’s Graveyard Visitor

https://commons.wikimedia.org/wiki/File:Edgar_Allan_Poe_2_-_edit2.jpg

For most of the 20th century, a man in black appeared each year at the grave of Edgar Allan Poe. In the predawn hours of January 19, he would drink a toast with French cognac and leave behind three roses in a distinctive arrangement. No one knows who he was or why he did this. In this episode of the Futility Closet podcast we review the history of the “Poe Toaster” and his long association with the great poet’s memorial.

We’ll also consider whether Winnie-the-Pooh should be placed on Ritalin and puzzle over why a man would shoot an unoffending monk.

Sources for our segment on the Poe Toaster:

“Mystery Man’s Annual Visit to Poe Grave,” China Daily, Jan. 20, 2008.

“Poe Toaster Remains a Mystery,” WBAL Radio, Jan. 19, 2013.

“‘Toaster’ Rejects French Cognac at Poe’s grave,” Washington Times, Jan. 19, 2004.

Sarah Brumfield, “Poe Fans Call an End to ‘Toaster’ Tradition,” AP News, Jan. 19, 2012.

Liz F. Kay, “Poe Toaster Tribute Is ‘Nevermore’,” Baltimore Sun, Jan. 19, 2010.

Michael Madden, “Yes, Virginia, There Is a Poe Toaster,” Baltimore Sun, Jan. 26, 2011.

Mary Carole McCauley, “Poe Museum Could Reopen in Fall,” Baltimore Sun, Jan. 20, 2013.

Ben Nuckols and Joseph White, “Edgar Allan Poe’s Mysterious Birthday Visitor Doesn’t Show This Year,” Huffington Post, March 21, 2010 (accessed Dec. 1, 2014).

Here’s the only known photo of the toaster, taken at his 1990 apparition and published in the July 1990 issue of Life magazine:

poe toaster

The psychiatric diagnoses of Winnie-the-Pooh and his friends appear in Sarah E. Shea, Kevin Gordon, Ann Hawkins, Janet Kawchuk, and Donna Smith, “Pathology in the Hundred Acre Wood: A Neurodevelopmental Perspective on A.A. Milne,” Canadian Medical Association Journal, Dec. 12, 2000.

Many thanks to Harry’s for supporting this week’s episode. Enter coupon code CLOSETHOLIDAY and get $5 off a Winter Winston set at Harrys.com.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Invertible Minuets

schobert puzzle minuets

In A Thing or Two About Music (1972), Nicolas Slonimsky describes a series of “puzzle minuets” composed by 18th-century harpsichordist Johann Schobert:

Schobert is not a misprint for Schubert. He was an estimable Silesian-born musician who settled in Paris in 1760 and wrote many compositions in the elegant style of the time. Mozart knew his music well and was even influenced by his easy grace in writing piano pieces. Schobert was something of a musical scientist. Among his compositions is a page entitled, ‘A Curious Musical Piece Which Can Be Played on the Piano, on the Violin, and on the Bass, and at that in Different Ways.’ This page contained five minuets, one of which could be played upside down without any change, one which would result in a new piece when turned upside down, and one which would furnish a continuation upside down. Two could be played on the violin and on the bass by assigning the treble clef right side up and the bass clef upside down.

The full page is here. I haven’t tried playing it.

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