Weekend Economists Go Through the Looking Glass May 17-19, 2013

[Demeter]

57. Dodgson's Inventions & Mathematical work

To promote letter writing, Dodgson invented The Wonderland Postage-Stamp Case in 1889. This was a cloth-backed folder with twelve slots, two marked for inserting the then most commonly used penny stamp, and one each for the other current denominations to one shilling. The folder was then put into a slip case decorated with a picture of Alice on the front and the Cheshire Cat on the back. All could be conveniently carried in a pocket or purse. When issued it also included a copy of Carroll's pamphletted lecture, Eight or Nine Wise Words About Letter-Writing.


Another invention is a writing tablet called the nyctograph for use at night that allowed for note-taking in the dark; thus eliminating the trouble of getting out of bed and striking a light when one wakes with an idea. The device consisted of a gridded card with sixteen squares and system of symbols representing an alphabet of Dodgson's design, using letter shapes similar to the Graffiti writing system on a Palm device.

Among the games he devised outside of logic there are a number of word games, including an early version of what today is known as Scrabble. He also appears to have invented, or at least certainly popularised, the Word Ladder (or "doublet" as it was known at first); a form of brain-teaser that is still popular today: the game of changing one word into another by altering one letter at a time, each successive change always resulting in a genuine word. For instance, CAT is transformed into DOG by the following steps: CAT, COT, DOT, DOG.

Other items include a rule for finding the day of the week for any date; a means for justifying right margins on a typewriter; a steering device for a velociam (a type of tricycle); new systems of parliamentary representation; more nearly fair elimination rules for tennis tournaments; a new sort of postal money order; rules for reckoning postage; rules for a win in betting; rules for dividing a number by various divisors; a cardboard scale for the college common room he worked in later in life, which, held next to a glass, ensured the right amount of liqueur for the price paid; a double-sided adhesive strip for things like the fastening of envelopes or mounting things in books; a device for helping a bedridden invalid to read from a book placed sideways; and at least two ciphers for cryptography.
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Within the academic discipline of mathematics, Dodgson worked primarily in the fields of geometry, matrix algebra, mathematical logic and recreational mathematics, producing nearly a dozen books under his real name. Dodgson also developed new ideas in the study of elections (e.g., Dodgson's method) and committees; some of this work was not published until well after his death. He worked as a mathematics tutor at Oxford, an occupation that gave him some financial security.

His mathematical work attracted renewed interest in the late 20th century. Robbins' and Rumsey's investigation of Dodgson Condensation, a method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem.