Charles Trigg proposed this festive cryptarithm in the American Mathematical Monthly in 1956:
MERRY XMAS TO ALL
If each letter is a unique representation of a digit, and each word is a square integer, what are these four numbers?
Long Haul
Recognize this locomotive? You’ve almost certainly seen it before: Built in 1891, “Sierra No. 3” was adopted by Hollywood in 1948 and became “the most photographed locomotive in the world,” appearing in The Red Glove, The Terror, The Virginian, The Texan, Young Tom Edison, Sierra Passage, Wyoming Mail, High Noon, The Cimarron Kid, Kansas Pacific, The Moonlighter, Apache, Rage at Dawn, The Return of Jack Slade, Texas Lady, The Big Land, Terror in a Texas Town, Man of the West, Face of a Fugitive, The Outrage, The Rare Breed, The Great Race, The Perils of Pauline, Finian’s Rainbow, A Man Called Gannon, The Great Bank Robbery, Joe Hill, The Great Northfield Minnesota Raid, Oklahoma Crude, Nickleodeon, Bound for Glory, The Apple Dumpling Gang Rides Again, The Long Riders, Pale Rider, Blood Red, Back to the Future Part III, Unforgiven, and Bad Girls.
Gary Cooper alone starred in four movies with it, including High Noon; Clint Eastwood, who appeared with it in Rawhide, Pale Rider, and Unforgiven, said it was “like a treasured old friend.” TV shows:
The Lone Ranger, Tales of Wells Fargo, Casey Jones, Rawhide, Overland Trail, Lassie, Death Valley Days, The Raiders, Petticoat Junction, The Wild Wild West, The Big Valley, The Legend of Jesse James, Scalplock, Iron Horse, Cimarron Strip, Dundee and the Culhane, The Man From U.N.C.L.E., Ballad of the Iron Horse, Gunsmoke, Bonanza, The Great Man’s Whiskers, Inventing of America, Little House on the Prairie, Law of the Land, A Woman Called Moses, Lacy and the Mississippi Queen, Kate Bliss and the Ticker Tape Kid, The Night Rider, The Last Ride of the Dalton Gang, Belle Starr, East of Eden, Father Murphy, The A-Team, Bonanza: The Next Generation, The Adventures of Brisco County, Jr., and Doctor Quinn, Medicine Woman.
William L. Withhuhn, former transportation history curator at the Smithsonian Institution, wrote, “Sierra Railway No. 3 has appeared in more motion pictures, documentaries, and television productions than any other locomotive. It is undisputedly the image of the archetypal steam locomotive that propelled the USA from the 19th century into the 20th.”
Recoupling
From reader Dave Lawrence: What is notable about these 14 sets of words?
accost commit launch deeded adhere heckle silent versed ampere arrive angers theses chance ascent tester stored chaste ascend tinder seeded cohere heckle silent versed debase mucked refile stress demure riffle silent versed endure shelve riling nested forego recess gossip needed herein advice resins stones rebate locket career tested recast costar pirate esters remade astute surest rested
The Feynman Ciphers
In 1987, Chris Cole posted a message to the sci.crypt Usenet group:
When I was a graduate student at Caltech, Professor Feynman showed me three samples of code that he had been challenged with by a fellow scientist at Los Alamos and which he had not been able to crack. I also was unable to crack them. I now post them for the net to give it a try.
The first, marked “Easier,” was this:
MEOTAIHSIBRTEWDGLGKNLANEA INOEEPEYSTNPEUOOEHRONLTIR OSDHEOTNPHGAAETOHSZOTTENT KEPADLYPHEODOWCFORRRNLCUE EEEOPGMRLHNNDFTOENEALKEHH EATTHNMESCNSHIRAETDAHLHEM TETRFSWEDOEOENEGFHETAEDGH RLNNGOAAEOCMTURRSLTDIDORE HNHEHNAYVTIERHEENECTRNVIO UOEHOTRNWSAYIFSNSHOEMRTRR EUAUUHOHOOHCDCHTEEISEVRLS KLIHIIAPCHRHSIHPSNWTOIISI SHHNWEMTIEYAFELNRENLEERYI PHBEROTEVPHNTYATIERTIHEEA WTWVHTASETHHSDNGEIEAYNHHH NNHTW
Jack Morrison of NASA’s Jet Propulsion Laboratory had it solved the next day: “It’s a pretty standard transposition: split the text into 5-column pieces, then read from lower right upward.” This yields the opening of Chaucer’s Canterbury Tales:
WHANTHATAPRILLEWITHHISSHOURESSOOTET HEDROGHTEOFMARCHHATHPERCEDTOTHEROOT EANDBATHEDEVERYVEYNEINSWICHLICOUROF WHICHVERTUENGENDREDISTHEFLOURWHANZE PHIRUSEEKWITHHISSWEETEBREFTHINSPIRE DHATHINEVERYHOLTANDHEETHTHETENDRECR OPPESANDTHEYONGESONNEHATHINTHERAMHI SHALVECOURSYRONNEANDSMALEFOWELESMAK ENMELODYETHATSLEPENALTHENYGHTWITHOP ENYESOPRIKETHHEMNATUREINHIRCORAGEST HANNELONGENFOLKTOGOONONPILGRIM
But the other two ciphers have never been solved, despite 30 years of trying. Here they are:
#2 (“Harder”)
XUKEXWSLZJUAXUNKIGWFSOZRAWURORKXAOS LHROBXBTKCMUWDVPTFBLMKEFVWMUXTVTWUI DDJVZKBRMCWOIWYDXMLUFPVSHAGSVWUFWOR CWUIDUJCNVTTBERTUNOJUZHVTWKORSVRZSV VFSQXOCMUWPYTRLGBMCYPOJCLRIYTVFCCMU WUFPOXCNMCIWMSKPXEDLYIQKDJWIWCJUMVR CJUMVRKXWURKPSEEIWZVXULEIOETOOFWKBI UXPXUGOWLFPWUSCH
#3 (“New Message”)
WURVFXGJYTHEIZXSQXOBGSVRUDOOJXATBKT ARVIXPYTMYABMVUFXPXKUJVPLSDVTGNGOSI GLWURPKFCVGELLRNNGLPYTFVTPXAJOSCWRO DORWNWSICLFKEMOTGJYCRRAOJVNTODVMNSQ IVICRBICRUDCSKXYPDMDROJUZICRVFWXIFP XIVVIEPYTDOIAVRBOOXWRAKPSZXTZKVROSW CRCFVEESOLWKTOBXAUXVB
Feynman, apparently, couldn’t break them either.
Eh
Tenth-century merchant captain Bjarni Herjólfsson spent his summers trading in Scandinavia but returned to his native Iceland each winter to visit his parents. In 986 he was told that his father had sailed to Greenland with Erik the Red, so he followed them west. Lacking a map or a compass, he was blown off course by a storm, and when the weather cleared he sighted a wooded country with low hills. This couldn’t be Greenland, so he sailed north, and after two days he came upon a second land, level and wooded. Despite his crew’s protestations, Bjarni didn’t stop here either, but sailed north three days more, when he sighted a land of mountains and glaciers. This couldn’t be Greenland either, so he sailed away from it, and after four days by a lucky chance he landed at his father’s estate.
Today, writes University of Manitoba historian T.J. Oleson, “There are strong arguments for the view that the three lands seen by Bjarni were Newfoundland, Labrador, and Baffin Island” — he was probably the first European to sight the east coast of North America, but he’d been too incurious to investigate.
Podcast Episode 180: An Academic Impostor
Marvin Hewitt never finished high school, but he taught advanced physics, engineering, and mathematics under assumed names at seven different schools and universities between 1945 and 1953. In this week’s episode of the Futility Closet podcast we’ll trace the curious career of an academic impostor, whose story has been called “one of the strangest academic hoaxes in history.”
We’ll also try on a flashproof scarf and puzzle over why a healthy man would check into a hospital.
Works in Progress
Because weather and daylight change continually, Claude Monet believed that any visual effect lasts for only seven minutes, much too brief to paint — he said he wanted to “render my impressions before the most fugitive effects.”
His solution was to work on multiple canvases at once, putting a new one on the easel every seven minutes or so to capture the effect he was after. Georges Clemenceau once found him in a poppy field juggling four different canvases: “He was going from one to the other, according to the position of the sun.” In 1885 Guy de Maupassant watched him stalking about Etretat; no longer a painter, “he was a hunter. He walked along, trailed by children carrying canvases, five or six canvases representing the same subject at various hours of the day and with varying effects. He would pick them up or drop them one by one according to how the sky changed.”
When Monet visited London in 1901 to capture the “unique atmosphere” of the city’s fog, John Singer Sargent found him surrounded by 90 canvases, “each one the record of a momentary effect of light over the Thames. When the effect was repeated and an opportunity occurred for finishing the picture, the effect had generally passed away before the particular canvas could be found.”
“I am chasing a dream,” Monet once said. “I want the impossible.”
(Ross King, Mad Enchantment, 2016.)
The Interlace
Designed by German architect Ole Scheeren, Singapore’s Interlace apartment complex was named 2015 World Building of the Year for its innovative form, which resembles 31 conventional buildings stacked atop one another, like Jenga blocks. Each block comprises six stories, but they’re stacked four high, so there’s a maximum of 24 floors, and nearly every unit has an excellent view. Viewed from above they form eight hexagons, each with a swimming pool, and the stacking ensures that light and air can flow among the blocks.
In Architecture Review, Laura Raskin wrote, “Architect Ole Scheeren hypothesized that dense urban residential living didn’t have to occur in an isolating skyscraper — and he was right.”
Sound and Sense
In this passage from Tennyson’s Morte d’Arthur, the mail-clad Sir Bedivere carries his wounded king down to a lake by a narrow path along a cliff:
Dry clash’d his harness in the icy caves
And barren chasms, and all to left and right
The bare black cliff clang’d round him, as he based
His feet on juts of slippery crag that rang
Sharp-smitten with the dint of armed heels —
And on a sudden, lo! the level lake,
And the long glories of the winter moon.
“This passage is particularly interesting in the sudden change from the harsh imitative sounds describing the trip itself to the peaceful passage, dominated by liquids and nasals, representing the arrival at the shore,” writes Calvin Brown in Music and Literature.
He gives two examples of poets attempting to imitate musical timbres. Detlev von Liliencron’s Die Musik kommt describes the progress of a military band through a little German village:
Klingling, tschingtsching und Paukenkrach,
Noch aus der Ferne tönt es schwach,
Ganz leise bumbumbumbum tsching,
Zog da ein bunter Schmetterling,
Tschingtsching, bum, um die Ecke?
And the first stanza of Paul Verlaine’s Chanson d’automne famously imitates a violin:
Les sanglots longs
Des violons
De l’automne
Blessent mon cœur
D’une langueur
Monotone.
In The Craft of Translation, John Biguenet writes, “English simply has no matching nasal sounds in words that would convey the meaning, unless we turn to trombones, and then we have changed instruments.”
Truth and Purity
In 2014 England’s University of Sheffield unveiled “the world’s first air-cleansing poem,” four stanzas by literature professor Simon Armitage that are printed on a 10-by-20-meter panel coated with particles of titanium dioxide that use sunlight and oxygen to clear the air of nitrogen oxide pollutants.
“This is a fun collaboration between science and the arts to highlight a very serious issue of poor air quality in our towns and cities,” said science professor Tony Ryan, who collaborated on the project. “This poem alone will eradicate the nitrogen oxide pollution created by about 20 cars every day.”
Armitage said, “Poetry often comes out with the intimate and the personal, so it’s strange to think of a piece in such an exposed place, written so large and so bold. I hope the spelling is right!”