Letter counting: A stem cell for cryptology, quantitative linguistics, and statistics

Bernard Ycart
Université Grenoble Alpes
Summary

Counting letters in written texts is a very ancient practice. It has accompanied the development of cryptology, quantitative linguistics, and statistics. In cryptology, counting frequencies of the different characters in an encrypted message is the basis of the so called frequency analysis method. In quantitative linguistics, the proportion of vowels to consonants in different languages was studied long before authorship attribution. In statistics, the alternation vowel-consonants was the only example that Markov ever gave of his theory of chained events. A short history of letter counting is presented. The three domains, cryptology, quantitative linguistics, and statistics, are then examined, focusing on the interactions with the other two fields through letter counting. As a conclusion, the eclecticism of the scholars of past centuries, their background in humanities, and their familiarity with cryptograms, are identified as contributing factors to the mutual enrichment process which is described here.

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References

Alberti, Leon Battista
2010 [1467] “De Componendis Cifris”. Translated by Kim Williams. The Mathematical Work of Leon Battista Alberti ed. by Kim Williams, Lionel March & Stephen R. Wassel, 171–200. Basel: Birkäuser-Springer.Google Scholar
Al-Kadi, Ibrahim A.
1992 “Origins of Cryptology: The Arab contributions”. Cryptologia 16.97–126. DOI logoGoogle Scholar
Andresen, Julie T[etel]
1996 Linguistics in America, 1769–1924: A critical history. London: Routledge.Google Scholar
Babbage, Charles
1832 “On the Advantage of a Collection of Numbers, to be Entitled the Constants of Nature and Art”. Edinburgh Journal of Science, New Series 6.334–340.Google Scholar
1864 Passages from the Life of a Philosopher. London: Green.Google Scholar
Bailey, Richard W[eld]
1969 “Statistics and Style: A historical survey”. Statistics and Style ed. by Lubomir Doložel & Richard W. Bailey, 217–236. New York: American Elsevier.Google Scholar
Bauer, Friedrich L.
2007 [1 1997] Decrypted Secrets: Methods and maxims of cryptology. 4th ed. Berlin: Springer.Google Scholar
Birgegård, Ulla
1985 Johan Gabriel Sparwenfeld and the Lexicon Slavonicum: His contribution to 17th century Slavonic lexicography. Uppsala: Almqvist & Wiksell for the Bibliotheca R[egalis] Universitatis Upsaliensis.Google Scholar
Breithaupt, Christian
1737 Ars Decifratoria sive Sciencia occultas scripturas solvendi et legendi. Helmstedt: Weygand.Google Scholar
Brillouin, Léon
2004 [1 1956] Science and Information Theory. Mineola, N.Y.: Dover.Google Scholar
Burke, Peter
2012 A Social History of Knowledge. Volume II: From the Encyclopédie to Wikipedia. Cambridge: Polity Press.Google Scholar
Carnicer García, Carlos J. & Javier Marcos Rivas
2005 Espías de Felipe II: Los servicios secretos del imperio español. Madrid: la Esfera de los Libros.Google Scholar
Conradi, David Arnold
1739 Cryptographia denudata, sive Ars decifrandi. Leiden: Philippus Bonk.Google Scholar
[Conradi, David Arnold
] 1742 “The Art of Deciphering”. The Gentleman’s Magazine 12.133–135, 185–186, 241–242, 473–475.Google Scholar
Cover, Thomas M. & Joy A. Thomas
2006 Elements of Information Theory. New York: Wiley.Google Scholar
Davies, Damian W.
2002 Presences that Disturb: Models of Romantic Influence in the Literature and Culture of the 1790s. Cardiff: University of Wales Press.Google Scholar
Davys, John
1737 An Essay on the Art of Decyphering. London: Gilliver & Clarke.Google Scholar
De Morgan, Augustus
1882 [1851] “Letter to Rev. W. Heald Aug. 18, 1851”. Memoir of Augustus De Morgan ed. by Sophia Elizabeth De Morgan, 214–216. London: Green.Google Scholar
Falconer, John
1685 Cryptomenysis Patefacta or the Art of Secret Information Disclosed without a Key. London: Brown.Google Scholar
Friedman, William F.
1936 “Edgar Allan Poe, Cryptographer”. American Literature 8.266–280. DOI logoGoogle Scholar
Good, Irving J.
1979 “Studies in the History of Probability and Statistics. XXXVII: A. M. Turing’s statistical work in World War II”. Biometrika 66.393–396. DOI logoGoogle Scholar
Grafton, Anthony
2000 Leon Battista Alberti, Master Builder of the Italian Renaissance. Cambridge, Mass.: Harvard University Press.Google Scholar
Grieve, Jack W.
2005 Quantitative Authorship Attribution: A history and an evaluation of techniques. M.A. thesis, Simon Fraser University, Burnaby, B.C.Google Scholar
Hacking, Ian
1990 The Taming of Chance. Cambridge: Cambridge University Press. DOI logoGoogle Scholar
Hastings, James
1902 Dictionary of the Bible Dealing with its Language, Literature, and Contents. Vol. IV (pleroma – zuzim). New York: Charles Scribner’s Sons.Google Scholar
Hitt, Parker
1916 Manual for the Solution of Military Ciphers. Fort Leavenworth, Kansas: Press of the Army Service Schools.Google Scholar
Hufbauer, Karl
1982 The Formation of the German Chemical Community (1720–1795). Berkeley: University of California Press.Google Scholar
Kahn, David
1996 [1 1967] The Codebreakers: The story of secret writing. Rev. ed. New York: Scribner.Google Scholar
Kelley, Page H., Daniel S. Mynatt & Timothy G. Crawford
1998 The Masorah of Biblia Hebraica Stuttgartensia. Grand Rapids, Mich.: Eerdmans.Google Scholar
Klüber, Johannes Ludwig
1809 Kryptographik: Lehrbuch der Geheimschreibekunst (Chiffrirund Dechiffrirkunst). Tübingen: J. G. Cotta.Google Scholar
Kraus, Kari
2009 “Conjectural Criticism: Computing past and future texts”. Digital Humanities Quarterly 3:4. No page given.Google Scholar
Kullback, Solomon
1976 Statistical Methods in Cryptanalysis. Laguna Hills, Calif.: Aegean Park Press.Google Scholar
Lieber, Francis
1835 “Consonants”. Encyclopedia Americana ed. by Francis Lieber, Edward Wigglesworth, Thomas G. Bradford & Henry Vethake, vol. III, 449–453 Philadelphia: Desilvern.Google Scholar
Link, David
2006a “Traces of the Mouth: Andrei Adreyevich Markov’s mathematization of writing”. History of Science 44.321–348. DOI logoGoogle Scholar
2006b “Chains to the West. Markov’s theory of connected events and its transmission to Western Europe”. Science in Context 19.561–589. DOI logoGoogle Scholar
Markov, Andrey A.
2006 [1913] “An Example of Statistical Investigation of the Text Eugene Onegin Concerning the Connection of Samples in Chains”. Translated by Gloria Custance and David Link. Science in Context 19.591–600. DOI logoGoogle Scholar
Meister, Aloys
1906 Die Geheimschrift im Dienste der Päpstlichen Kurie von ihren Anfängen bis zum Ende des XVI. Jahrhunderts. Paderborn: Ferdinand Schöningh.Google Scholar
Mercanti, Fabio & Paola Landra
2007 “I ‘Ludi Matematici’ di Leon Batista Alberti”. EIRIS 2.15–47.Google Scholar
Meirion [i.e., William Owen Pughe
] 1799 “Proportion of Vowels and Consonants in Different Languages”. The Monthly Magazine 7.5–6.Google Scholar
Mollin, Richard A.
2005 Codes: The guide to secrecy from ancient to modern times. Boca Raton, Fla.: Chapman & Hall. DOI logoGoogle Scholar
Morse, Edward L.
ed. 1914 Samuel F. B. Morse: His letters and journals. Vol. II. Boston: Houghton Mifflin.Google Scholar
Mrayati, Mohammed, Yahia Meer Alam & Hassan at-Tayyan
2002 Al Kindī’s Treatise on Cryptanalysis. (= Series on Arabic Origins of Cryptology, 1.) Damascus: KFCRIS & KACST.Google Scholar
2003a Ibn ‘Adlān’s Treatise al-mu’allaf lil-malik al-’Ašraf. (= Series on Arabic Origins of Cryptology, 2.) Ibid.Google Scholar
2003b Ibn ad-Durayhim’s Treatise on Cryptanalysis. (= Series on Arabic Origins of Cryptology, 3.) Ibid.Google Scholar
Mrayati, Mohammed, Yahia Meer Alam, & Hassan at-Tayyan
2005 Ibn Dunaynīr’s book: Expositive Chapters on Cryptanalysis. (= Series on Arabic Origins of Cryptology, 4.) Ibid.Google Scholar
Mrayati, Mohammed, Yahia Meer Alam & Hassan at-Tayyan
2007 Two Treatises on Cryptanalysis. (= Series on Arabic Origins of Cryptology, 6.) Ibid.Google Scholar
Peng, Roger D. & Nicolas W. Hengartner
2002 “Quantitative Analysis of Literary Styles”. The American Statistician 56.175–185. DOI logoGoogle Scholar
Perec, Georges
1973 “Histoire du lipogramme”. Oulipo: La littérature potentielle, 73–89. Paris: Gallimard.Google Scholar
Perret, Paul-Michel
1890 “Les règles de Cicco Simonetta pour le déchiffrement des écritures secretes (4 juillet 1474)”. Bibliothèque de l’École des Chartes 51.516–525. Paris.Google Scholar
Pesic, Peter
1997 “François Viète – father of Modern cryptanalysis”. Cryptologia 21.1–29. DOI logoGoogle Scholar
Petruszewycz, Micheline
1979a “A. A. Markov, ses probabilités en chaîne et les statistiques linguistiques”. Mathématiques et Sciences Humaines 66.5–42.Google Scholar
1979b “Contribution pour servir à l’étude du choix que fit A. A. Markov d’un domaine d’application de sa théorie des chaînes”. Mathématiques et Sciences Humaines 66.43–49.Google Scholar
1983 “Chaînes de Markov et statistiques linguistiques”. Mots 7.85–95. DOI logoGoogle Scholar
Pierce, John R.
1973 “The Early Days of Information Theory”. IEEE Transactions on Information Theory 19.3–8. DOI logoGoogle Scholar
Poe, Edgar Allan
1986 The Annotated Tales of Edgar Allan Poe. Ed. by Stephen Peithman. New York: Avenel.Google Scholar
Quetelet, Adolphe
1828 Correspondance Mathématique et Physique. Tome IV. Bruxelles: Hayez.Google Scholar
1829 Correspondance Mathématique et Physique. Tome V. Ibid.Google Scholar
1832 Correspondance Mathématique et Physique. Tome VII. Ibid.Google Scholar
1853 Compte rendu des travaux du Congrès général de statistique. Bruxelles: Hayez.Google Scholar
1873 “Notice sur Charles Babbage”. Annuaire de l’Académie Royale des sciences des lettres et des Beaux-arts de Belgique 39.149–165.Google Scholar
Reed, William J.
2001 “The Pareto, Zipf and Other Power Laws”. Economics Letters 74.15–19. DOI logoGoogle Scholar
Richardson, Mary, John Grabosek, Diann Reischman & Phyllis Curtiss
2004 “Morse Code, Scrabble, and the Alphabet”. Journal of Statistics Education 12:3. No page given. DOI logoGoogle Scholar
Sacco, Luigi
1951 [Original Italian ed. 1926] Manuel de Cryptographie. Paris: Payot.Google Scholar
Selenus, Gustavus [i.e., August the Younger of Brunswick-Lüneburg
] 1624 Cryptomenytices et Cryptographiae Libri IX. Lüneburg: Johann & Heinrich Stern.Google Scholar
Shannon, Claude E[lwood]
1948 “A Mathematical Theory of Communication”. Bell System Technical Journal 27.379–423, 623–656. DOI logoGoogle Scholar
Shannon, Claude E.
1949 “Communication Theory of Secrecy Systems”. Bell System Technical Journal 28.656–715. DOI logoGoogle Scholar
1951 “Prediction and Entropy of Printed English”. Ibid. 30.50–64.Google Scholar
Stigler, Stephen M.
1999 Statistics on the Table: The history of statistical concepts and methods. Cambridge, Mass.: Harvard University Press.Google Scholar
Stopes, Charlotte C.
1888 The Bacon–Shakspere Question. London: Johnson.Google Scholar
Strasser, Gerhard F.
1983 “The Noblest Cryptologist: August the Younger of Brunswick-Lüneburg (Gustavus Selenus) and his cryptological activities”. Cryptologia 7:3.193–217. DOI logoGoogle Scholar
Thicknesse, Philip
1772 A Treatise on the Art of Decyphering, and of Writing in Cypher. London: Brown.Google Scholar
Valerio, Paul-Louis Eugène
1893 De la Cryptographie: Essai sur les méthodes de déchiffrement. Paris: Baudoin.Google Scholar
Vesin, Charles François
1838 Traité d’obscurigraphie. Paris: Goullet.Google Scholar
Vitevitch, Michael S. & Paul A. Luce
1999 “Probabilistic Phonotactics and Neighborhood Activation in Spoken Word Recognition”. Journal of Memory and Language 40.374–408. DOI logoGoogle Scholar
Wepman, Dennis
Butts, Alfred Mosher”. American National Biography Online. New York: Oxford University Press.
Wheatley, Henry Benjamin
1862 Of Anagrams. Hertford: Austin.Google Scholar
Williams, Charles B.
1956 “Studies in the History of Probability and Statistics IV: A note on early statistical study of literary style”. Biometrika 43.248–256.Google Scholar
Yasuoka, Koichi & Motoko Yasuoka
2011 “On the Prehistory of QWERTY”, Zimbun 42.161–174.Google Scholar
Ycart, Bernard
2013 “Alberti’s Letter Counts”. Literary and Linguistic Computing. DOI logo (print version in press).Google Scholar
Yule, George U[dny]
1944 The Statistical Study of Literary Vocabulary. Cambridge: Cambridge University Press.Google Scholar
Zipf, George K[ingsley]
1949 Human Behavior and the Principle of Least Effort: An introduction to human ecology. New York: Addison-Wesley.Google Scholar