memoria technica cipher, The

Cryptologia, Jul 2003 by Abeles, Francine F

ABSTRACT: A comprehensive analysis of the ciphers invented by Charles L. Dodgson (Lewis Carroll) and how he used them indicate that his Memoria Technica (1875), a variant of a mnemonic scheme first proposed by Richard Grey in 1730, is properly viewed as Dodgson's fifth cipher system. He used his Memoria Technica cipher as a tool in work that was never published, a projected book whose working title was "Logarithms by Lightning: A Mathematical Curiosity." The logarithms project, a joint work with his colleague, Robert Edward Baynes, is examined in detail.

KEYWORDS: Dodgson, Carroll, Grey, Baynes, cryptography, cipher, Memoria Technica, logarithm, algorithm.

INTRODUCTION

Throughout his life, Charles L. Dodgson (Lewis Carroll, 1832-1898) was in the thrall of games, puzzles, codes, and ciphers. He invented these to amuse his friends, and for several other reasons. Codes and games have in common a set of rules which, for codes and ciphers, enables messages to be converted from plaintext to code or ciphertext, and, for games and many puzzles, is the basis for playing the game or solving the puzzle. Dodgson also enjoyed conveying a sense of mystery that his secret codes, riddles, and magical tricks share. He communicated many of these inventions in letters. Dodgson was a prolific letter writer, sending and receiving 98,721 letters according to the correspondence numbering system he kept for his Letter Register. [2, p. xvi] These letters often contained coded text, anagrams, riddles, acrostics, or puzzles based on mathematical or logical principles. Some of his letters required a mirror to read, others had to be read backwards.

Dodgson, as Lewis Carroll, is best known for his literary achievements, of which Alice in Wonderland and Through the Looking Glass are his most famous prose writings, and The Hunting of the Snark, the longest nonsense poem in the English language and his best piece of poetry that he also wrote for children. One characteristic of his work is the integration of his literary and mathematical thinking. Another is the appearance of the same ideas in different guises evolving over a long period of time.

In this paper, I show that his Memoria Technica, a variant of a scheme first proposed by Richard Grey (1694-1771) over a century earlier to assist people in retaining numerical data such as dates and measurements, brought together his interests in letter writing, poetry, puzzles, codes, and mathematics. [6C, Item 3] Dodgson's interest in Grey's system initially was motivated by his own difficulty remembering dates. It evolved into an unusual method for remembering not only important dates, but also logarithms and the digits of the numbers [pi] and e, as well as becoming a subject for his letters, and a tool for teaching memory aids.

DODGSON'S CIPHERS

Dodgson's interest in ciphers and in mnemonics began early in his life. On 15 February 1856, at the age of 24, he confided in his diary that he was thinking of writing an article on cipher for the London comic magazine, The Train, a piece that never materialized. [12, v. 2, p. 42] Less than a year later, in a diary entry on the last day of 1857, he included the statement, "Chronology by Memoria Technica" a reference to Grey's scheme for remembering dates as one of the things he wished to remember and use when traveling by train, presumably to avoid wasting time. [8, p. 136]

We know that in the ten year period, 1858-1868, Dodgson invented four ciphers, the two of the Vigenere type are known as the Alphabet Cipher (1868) and the Key -Vowel Cipher (1858). The Telegraph Cipher (1868) is a Beaufort cipher, and the Matrix Cipher (1858) is a Variant Beaufort cipher.1 [1, 10, 11]

Dodgson communicated his discoveries about the Alphabet and Telegraph ciphers to his child friends, the sisters Agnes and Edith Argles in letters he wrote to them in April 1868. In the last of these, dated 29 April, he enclosed a poem using the Telegraph Cipher, with the keyword fox, to encipher it.2[2, pp. 116-119] And in October 1869, he wrote a rebus letter to another child friend, Georgina (Ina) Watson. [2, pp. 142-44] As late as 1893, he used his ciphers when writing letters. [8, p. xxv] Enid Stevens recalls that when he wrote to her as a child of twelve, "[H]e loved ciphers: he very often wrote letters to me in cipher, and I had to solve them." [4, p. 398]

GREY'S MEMORIA TECHNICA

Richard Grey, author of a book on English ecclesiastical law, published his Memoria Technica, Or Method of Artificial Memory in 1730, and the edition of 1851 is probably the one Dodgson used until 27/28 October 1875 when he created his own version. Grey's system in Figure 1 qualifies as a cipher system, albeit not a secret one, where each of the digits is replaced by a letter or diphthong. [9, p. 1]

Grey wrote, " The representation of numbers by letters of the alphabet hath been a thing in practice, more or less, almost in every language. The only thing wanting was to make that representation further useful, by substituting vowels, as well as consonants, for the numerical figures, in such manner and proportion, that any number might be formed into a word capable of being articulately pronounced, and consequently more perfectly remembered." [9, p. xiii]