Above: Spinning DNA into GOD with seven moves.
Doublets, or Word Ladders, is a game invented by Alice in Wonderland author Lewis Carroll for “two little girls who found nothing to do” on Christmas Day 1877, though there is some evidence that writers played with the form during Luther’s Protestant Reformation or perhaps even earlier in the Odyssey. Carroll originally called the the game “word-links,” but by 1879 he had published enough of the puzzles in Vanity Fair magazine to merit a collection by Macmillan titled “Doublets: a word puzzle,” a reference to the witches’ incatation in Macbeth, “Double, double, toil, and trouble.” The name stuck, and the game was an immediate and runaway hit.
The rules are simple: change one word into another by altering a single letter, which counts for a step. Each step needs to read as a word, and the start and end words are often related in some poetic way. Carroll’s explanatory example involved changing HEAD to TAIL in five moves: HEAD / HEAL / TEAL / TELL / TALL / TAIL. Other popular doublets include making a DOOR LOCK, obtaining a LOAN from a BANK, and turning WHEAT into BREAD (more here and here). Later, other gamers followed in Carroll’s footsteps, adding rules for Studdlets, Splices, Splits, and Splinters (see David Miller’s excellent “Word Games for Formal Logic,” here).
In this 1996 article from The Mathematical Gazette, magician, math writer, and Carroll scholar Martin Gardner writes of Stanford computer scientist (and TeX inventor) Donald Knuth’s experiments with using computers to solve doublet puzzles:
[Knuth] constructed a graph on which 5,757 of the most common five-letter English words (proper nouns excluded) are represented by points, each joined by a line to every word to which it can be changed by altering just one letter. The graph has 14,135 lines. […] Most pairs of five-letter words on Knuth’s list can be joined by ladders. Some—Knuth calls them ALOOF words because one of them is “aloof”—have no neighbors. The graph has 671 ALOOF words, such as EARTH, OCEAN, BELOW, SUGAR, LAUGH, FIRST, THIRD, NINTH. Two words, BARES and CORES, are connected to 25 other words; none to a higher number. There are 103 word pairs with no neighbors except each other, such as ODIUM-OPIUM and MONAD-GONAD. Knuth’s 1992 Christmas card featured the smallest ladder (11 steps) that changes SWORD to PEACE by using only words found in the Bible’s Revised Standard Version.
My interest in doublets, of course, extends from my interest in Williams Poems, and I nearly jumped out of my chair when I saw this pamphlet on doublets (scroll down) on the virtual shelf of one of my favorite Amsterdam bookstores a few weeks back. I wish there was some way to turn WILLIAMS into CARROLL, but alas I’m one letter short. What I can do is offer the work of one industrious Lined & Unlined reader, Jason DeFontes, who ran a Williams Word Generator against all the words in a standard English dictionary in order to find those with the most possible Williams Words tucked inside. Those seven with more than fifty Williams Words tucked inside are:
contradistinctions (59 words)
redisplaying (57)
superintendents (56)
antidisestablishmentarianism (55)
autoincremented (55)
disappointments (51)
representationally (50)
DeFontes’s wordchecker ranks “sweethearts” at only 35 words, but that does not include plural forms, which push it up to nearly fifty or so. However, on the list above, “superintendents,” even in its plural form as a root word, carries 56 unique words within it. Pretty impressive.
Later in his article, Martin Gardner notes that “doublets resemble the way in which evolution creates new species by making small random changes in the genes that are along the helical DNA molecule. Carroll himself, although a skeptic of Darwin’s theory, evolved APE to MAN in six steps: APE / ARE / ERE / ERR / EAR / MAR / MAN.” (Gardner points out there is a shorter solution, APE / APT / OPT / OAT / MAT / MAN.) The piece I’ve written above is a first try, inspired at least in part by Gardner’s offhand observation. I like the doublet form, find it a great complement to the Williams Poem, and hope to write more doublets as time goes on.
