The Philosophical Breakfast Club by Laura J. Snyder Page B

in ciphers during the 1830s. In 1835, Babbage employed his considerable skills in cryptanalysis to aid his friend and fellow founder of the Astronomical Society, Francis Baily, who was writing a book on John Flamsteed (1646–1719), the first Astronomer Royal. Baily was attempting to establish the accuracy of Flamsteed’s observations from the Royal Observatory at Greenwich, and the cause for some known errors in those observations. In his writings, Flamsteed had suggested that the problems were due to an error in his mural arc, the angle-measuring device built right into a wall lying on the prime meridian at Greenwich, marking the point of zero longitude. If the mural arc was responsible for the errors, the fault would lie with its builder, notwith Flamsteed himself. Baily found a letter from Abraham Sharp, Flamsteed’s assistant, written in response to a query from a Mr. Crosthwait about whether such an error existed. Sharp’s letter, however, was written in a cipher, so Baily was unable to learn its contents. He mentioned the problem to Babbage, who, “by a laborious and minute examination and comparison of all the parts,” Baily later explained, was able to decipher the letter. This enabled Baily to discover that the errors arose not from the mural arc, as Flamsteed had rather deceptively implied, but from the refraction table he had used. 21 Thanks to Babbage, Baily was able to solve a problem about Flamsteed’s observations that had haunted astronomers for over a century. It also influenced later astronomers’ opinions of the first Astronomer Royal; Herschel told Beaufort that reading Baily’s book had diminished his opinion of Flamsteed as a person and an astronomer. 22
    At around this time—just when Babbage was most involved with the newly founded Statistical Society of London, and the Statistical Section of the British Association—he began to apply statistics to the problem of deciphering, nearly a century before William F. Friedman, who is generally considered the first to have done so. 23 In a letter to Quetelet, which the Belgian translated and had published in a French journal, Babbage listed tables of the relative frequencies of double letters in English, French, Italian, German, and Latin. In English, it turns out, the most frequently doubled letter is l, which occurs 27.8 times in 10,000 letters (16.1 times in the middle of a word, 11.7 times at the end). The next most frequently doubled letter is
e
, 18.8 times in the middle of a word, and 1.9 times at the end. The rarest doubled letter is
g
, which is found only 1.5 times in 10,000 letters. 24
    Babbage also began to count the relative frequency of the occurrence of single letters, and made lists of the most common two- and three-letter words, organizing them by their consonant/vowel pattern, such as CCV, VCC, CVC, VCV, CVV, VVC, and VVV. Then he began to order words that end in
-ion
according to word length. 25 He started writing dictionaries of words that began with each of the twenty-six letters of the alphabet, ordered by how many letters were in each word. All of this was to be part of a planned book, called
The Philosophy of Decyphering
, but Babbage never actually wrote it.
    Babbage had realized that these kinds of statistical studies would be invaluable in deciphering any monoalphabetic cipher. In a monoalphabetic cipher, letters in the plain text are substituted by letters in an alphabetdefined differently from the standard ordered alphabet. This cipher alphabet can be shifted (e.g., instead of “a,b,c,d” you might have “b,c,d,e” or “c,d,e,f”), inverted (“z,y,x,w”), or ordered by the use of a key word or phrase, in which case the cipher alphabet begins with the key word and then continues with the rest of the alphabet, in order but minus the letters already appearing in the key word (e.g., key word “leopard”: l,e,o,p,a,r,d,b,c,f,g,h,i,j,k,m,n,q,s,t,u,v,w,x,y,z).
    In order to encrypt a message using this cipher alphabet,