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Issue 6 (2014) - Numbers

‘1144000727777607680000 wayes’: Early Modern Cryptography as Fashionable Reading

Katherine Ellison

[1] Cryptography, considered one of the occult sciences until the early seventeenth century, found new status in Britain during and after the Wars of the Three Kingdoms as a respectable, useful scholarly discipline publicly embraced by early modern mathematicians as well as political and military strategists. In manuals published for both general readership and for specialist, court audiences, cryptographers John Wilkins, Noah Bridges, Samuel Morland, and John Falconer launched a rhetorical campaign to legitimize ciphering and deciphering as practical as well as theoretical benefits to English national and financial security. Yet, England’s political and economic confidence was not the sole or even primary objective of the manuals published in unprecedented volume from the 1640s through the 1680s. Though their uses of numbers vary, implicit in Wilkins’s Mercury; or the Secret and Swift Messenger (1641), Bridges’s Stenographie and Cryptographie (1659) and its anonymously published sequel Rarities: or the Incomparable Curiosities in Secret Writing (1665), Morland’s New Method of Cryptography (1666), and Falconer’s Cryptomenysis Patefacta: Or the Art of Secret Information Disclosed without a Key (1685), is the promotion of ciphering and deciphering as a mathematic mode of reading that should be adopted in one’s everyday, particularly domestic, life.[1]

[2] In their recent studies of early modern reading habits, David Scott Kastan and Heidi Brayman Hackel warn scholars not to make assumptions about genre and literacy and convincingly argue that theories of literacy must be backed by archival evidence (Kastan 1999; Brayman Hackel 2005: 9; see also Jardine and Grafton 1990, Sherman 2002, and Sherman 2008). Certainly, I could not jump to conclusions about genre when I first read pedagogical cryptography texts while searching for the key to some ciphers in Sir Thomas Scot’s letters. Mercury, for example, resembles a writing manual yet is also like an arithmetic textbook; it is a study of natural philosophy and also a book of secrets; it is vaguely similar to stenography manuals and yet also reads like a historical romance. It has poetry and teaches ciphers in music and geometry. Bradin Cormack and Carla Mazzio categorize how-to books of the period generally as those that instruct readers ‘how to express yourself’, ‘how to do things’, ‘how to be somebody’, ‘how to look after yourself’, and ‘how to find your way’, and cryptography manuals teach all of these skills. They are guides to rhetorical gesture, but like surgery manuals they also ‘are concerned with emergent professional fields and identities’ (Cormack and Mazzio 2005: 85). The manuals promote new practitioner disciplines, help define the parameters and protocol of specialization, and also dictate modes of civility and self-fashioning. Promoting the recreational popularity of cryptography, the manuals also emphasize self-control of one’s intelligence as a marker of personhood. And certainly, learning to cipher or decipher also means learning to look after oneself.

[3] Though writings on cryptography during the seventeenth century are different enough from one another that they must be attended to separately, manuals between 1641 and the 1680s all widen the definitions of writing and reading to include the analyses of numbers and other computational symbolic systems used in the sciences. Each of the manuals, explicitly or implicitly, addresses contemporary anxieties about communal reading and an author’s lack of control over who reads, or is read, extending even to private correspondence. All are frustrated with confining textuality to the alphabet. As material objects mobile in the community in both manuscript and print form, letters and other documents exchanged hands known and unknown. At the same time that cryptographers propose methods for keeping messages secret within this world of publicity, then, they also offer — or claim to offer — methods not reliant upon a reader’s individual ability to write in alphabetic characters or in languages like English, Latin, or Greek. These manuals do tell readers what to do, but their instruction is not as directive as one might assume: they also tell readers that writing and reading are not activities defined by or restricted to words, sentences, or generic conventions. A citizen who cannot spell can still cipher his or her communication by experimenting with numbers or various symbolic systems. The archives yield much that can help current scholars understand that literacy, during the seventeenth century, was not a simple binary, as rates based on signatures or spelling imply (Cressy 1980; Bennett 1970).

[4] Wilkins’s foundational manual establishes cryptography as an experimental science and natural magic. ‘Experimental science’ and ‘natural magic’ are terms that William Eamon defines as synonymous for some seventeenth-century thinkers, like Wilkins, following the rhetorical footsteps of Roger Bacon: ‘The manipulation of nature by the application of art, the medieval conception of what today we would call scientific technology’ (Eamon 1994: 51; see also Macrakis 2010). By experimenting with and on nature, as through repeatable procedures or processes, one could not only learn the secrets of the universe but harness its powers in such a way that those unaware of the procedures would think they see unexplained magical phenomena. Ciphers were and are, in this sense, scientific technologies to assist human communication. Eamon notes how Wilkins was a transitional figure in the world of seventeenth-century science, like Sir Thomas Browne, but unlike Browne did not publicly decry books of secrets. Rather, Wilkins was well known for his efforts to popularize science. Eamon cites Wilkins’s Mathematical Magick (1648) as an example of one influential effort to increase public interest in mechanical engineering. Wilkins openly combined his knowledge of experimental science, such as through the Oxford Experimental Philosophy Club, with activities that demonstrated how dazzling and entertaining science could be (Eamon 1994: 309). Where cryptography manuals differ from other books of secrets on, for example, potions, alchemy, medicine, or the supernatural is in their focus on reading practices and the potential uses of mathematic knowledge for more effective communication. Mercury, I find, is Wilkins’s attempt before Mathematical Magick to situate mathematics as the foundation of a flexible language of secrecy. Mercury begins to build a new reputation for cryptography as an experimental discipline and a demonstration of natural magic, in contrast to its previous image as a practice of black magic and incantation, such as in Johannes Trithemius’s influential manuscript ‘Steganographia’ (circulated widely in 1499) and his longer work, Polygraphia libri sex, posthumously printed in 1518.[2] Though Polygraphia was largely practical, pushing cryptographers to use multiple media as well as new mathematical approaches, the final step in encryption required chanting for angels to deliver the messages.

[5] Wilkins, Bridges, the Rarities author who only goes by G.B., Morland, and Falconer revised the public image of cryptography, and through it communication by numbers and various numbering systems, as useful in nonmilitary and nonpolitical life as well as in times of war and scandal by using three main rhetorical strategies. First, they present ciphers as learnable, no matter one’s exposure to alphabetic reading and writing systems. In fact, cipher is offered as a language uniquely accessible to readers of all classes and even ethnicities and cultural backgrounds. Second, they present cryptography as most effective when it is experimental and creative, denying that ciphering and deciphering are strictly finite thought processes that follow set steps without imagination. Manuals teaching ciphering also emphasize that the mathematic and geometric foundations of early modern cryptography allow for interpretive liberty. By creative and interpretive, I mean that readers are invited to learn the foundations of ciphering and deciphering but then required to build upon their own personal experiences and observations to reach solutions from various paths. In other words, there is more than one way to cipher, and media as diverse as music, drawing, geometry, and gesture can be as effective as alphabets. Third, music, drawing, geometry, gesture, and other approaches are innately computational and arithmetic in nature. Early modern cryptography was a multimodal discipline in which numbers could be symbolically expressive.

[6] As Karen Britland and Sarah Poynting have recently shown, political use of cipher was relatively uninspired during the wars. Queen Henrietta Maria, Charles I, their treasurer Sir Richard Forster, Charles II, and other important players relied mostly on substitution ciphers, which by contemporary cryptographers’ standards were notoriously flimsy methods. Nadine Akkerman finds this to be the case in the correspondence of Elizabeth Stuart as well. Elizabeth used seven substitution systems across her letters to various correspondents, and though the systems would be altered when there was suspicion of a breach, ‘keys were used for decades’ and, Akkerman suggests, Elizabeth ‘placed rather too much trust in them’ (Akkerman 2011: 1055). The instruction occurring in contemporary manuals is more sophisticated. The manuals promote ciphering logic as a kind of reading that requires more than mere substitution. And finally, they make this argument while highlighting the status of cryptography as a former occult practice. In other words, they do not deny the occult history of the discipline but rather capitalize upon the popularity of occult publications and books of secrets.

[7] Though non-specialists use the terms ‘code’ and ‘cipher’ interchangeably, as did some seventeenth-century cryptographers, my use distinguishes codes as meaningful substitutions (for example, the number 28 is code for King and so has meaning) and ciphers as the process or steps involved in arriving at meaning. Codes require a codebook; ciphers require following algorithmic instructions determined in a key. In other words, ciphers are mathematic, in the general sense that mathematics is the study of patterns and structures, while codes can be whatever an encoder says they are. Seventeenth-century cryptographers were more interested in ciphering than coding because the existence of a codebook meant that all of a party’s messages could be decoded easily if the book was discovered or captured during battle. Keeping keys near ciphers (or even writing the keys down), of course, was also irresponsible and dangerous: this was a lesson learned the hard way four years after the publication of Mercury, when Charles I’s private papers, including his cipher keys, were taken during the Battle of Naseby on June 14, 1645 and published as The Kings Cabinet Opened. The most secure ciphers, the manuals explain, require ingenuity, cannot be recorded simply as a sequence of clear steps, and yet can be swiftly solved. Geometric shapes one might recognize at a glance but that are not codes, hand gestures in particular sequences, calculable musical notes, and even patterned flashes of light can communicate secretly and swiftly, as Wilkins’s title boasts, and demand a kind of reading that recognizes arithmetic functions as literacy.

[8] National or political security and maneuvering were not the only objectives of early modern cryptography manuals. David Underdown and, more recently, Geoffrey Smith, have discussed the necessity and popularity of ciphering during the Wars of the Three Kingdoms, but the manuals have not been discussed as influential in military or court practice as, for example, the Scottish Army made plans to invade England or Charles I maneuvered locations during hiding (Smith 2010: 101-03). Only Lois Potter grants the publication of Mercury a prominent position in contemporary politics, noting that its appearance in 1641 not coincidentally paralleled the dissolution of the Star Chamber and George Thomason’s decision to start collecting every publication he could starting that same year (1989:1-2; see also Woolf 1990). She sees Mercury more as a theoretical statement than a political one, however, as a sign of the public’s desire for openness. She does suggest that since Wilkins had sympathies with Parliament, Mercury could be an exposure of Charles I’s opacity. Yet Wilkins’s political alliance is not clear. Like most cryptographers, including Morland and John Wallis, Wilkins served under multiple regimes. He was a Royalist who served Cromwell and Charles II (Shapiro: 1969: 3). Morland served Cromwell but worked as double agent to organize Charles II’s return (Dickinson 1970). John Wallis, arguably the most skilled cryptographer of the era but unpublished in that discipline until the eighteenth century, was employed by Cromwell, Charles II, and William and Mary with apparently seamless transition. Much less is known about Bridges, a clerk for Parliament, beyond clues in Stenographie and Cryptographie that he may have been promised a post in Charles II’s office. Little has been written about Falconer. David Kahn notes that Falconer was entrusted with James II’s private cipher before he ascended to the throne, according to a genealogical book marked ‘Falconer’s Writings’ on the spine in the New York Public Library (1996: 1016). Regarding politics perhaps all we can conclude, as Wilkins’s biographer Barbara Shapiro does, is that Wilkins (and I would add all the major cryptographers of the period) ‘were [always] in the right place at the right time’ (1969: 3).

[9] Wilkins, Bridges, G.B., Morland, and Falconer were most interested in the instructional process of creating and reading secret messages with mathematic precision and everyday use. The strengths of each manual differ, however. Mercury demonstrates the use of what Wilkins calls ‘philosophical numbers’, a precursor to his universal language in An Essay Towards a Real Character, and a Philosophical Language (1668) twenty-seven years later. A philosophical number is universal; it represents ‘any such measure, whereby we judge the differences betwixt severall substances’ (Wilkins 1641: 107; see also Heeffer and Van Dyck 2010). All cultures use philosophical numbers, he notes, and with little effort any two correspondents of different cultures, even if they speak wildly different native tongues, can understand the meaning of their philosophical numbering systems. Similarly, cultures with linguistic difference may use musical notation, chemical symbols, or astronomical signs similar enough to be understood by non-natives. Philosophical numbers are the inspiration for Wilkins’s growing obsession with a universal language scheme built upon ‘things’ that would finally unite the ‘seventy-two Languages of the first confusion’ (1641: 110).[3] The ciphers Wilkins is most known for, then, are geometric and spatially dynamic. Shapes that appear random in nature may be ciphers to be solved using a series of steps familiar only to the insider correspondents. The shape of a hand gesture, the pattern of movement in a person’s gait, or even the shape traced by the eye can all be ciphers and thus require algorithmic solution.

[10] Though with a different rhetorical agenda than Mercury and through a string of bizarre examples, Bridges’s Stenographie and Cryptographie also offers an approach to the discipline that foregrounds numbers as expressive media for secret communication. Bridges’s Stenographie and Cryptographie opens as a primer in shorthand and ends as a critique of the false claims of accessibility in cryptography manuals. The first section, which includes chapters of linguistic sophistication on how to write single and double consonants, dipthongs, prepositions, clauses, and other syntactic elements stenographically, is quite unlike Mercury in that it requires a high level of alphabetic literacy. The dedication to the reader stresses not only that readers must be able to write well but that they must excel at ‘faire writing’, or elegant penmanship, and the lessons in stenography exclude any reader who is not familiar with the intricacies of English grammar in writing (Bridges 1659: ‘In Commendation of Faire Writing’). The second section on cryptography begins with praise of Wilkins and the lessons of Mercury and then quickly unfolds as a critique of Wilkins’s rhetoric of accessibility. Bridges acknowledges Wilkins’s contributions to the discipline and the sophistication of his ciphers, but his main impetus is to distinguish between ciphering and deciphering as distinct skills and counter Wilkins’s open invitation to the everyday person, even without mathematic or linguistic education, to aspire to decipher. Bridges excerpts examples from Mercury and walks readers through the mathematic variations possible; the number of combinations one might have to sort through to arrive at one of Wilkins’s solutions, Bridges shows, proves that only those with mathematic ability and training in cryptography can truly decipher. Ciphering can indeed be done without advanced literacy in numbers or alphabets, but most alleged decipherers, Bridges argues, have been frauds ‘in quest of a picklock’ (1659: 31). ‘Yet with submission to the Authors [Wilkins’s] great judgment and learning’, Bridges writes, ‘I take leave to say there are those who pretend an ability of unfolding any Character’ (1659: 30). Pretenders attempt to impress political authorities, and as the authorities are also not experts, often succeed in securing courtly confidence and undeserved positions. Though even a non-expert can create a cipher, only the truly mathematically skilled can solve it. Bridges’s argument is based on the astounding number of transmutations possible when ciphers have upward of nine to twenty four letters. He uses the example of the following verse:

            Quod sat sit (sors) da, fed ne post tu                                                                                                                           rape de me.

Bridges notes that this verse ‘is variable 39916800 wayes’ (1659: 33). He does not offer any definition of transmutation, but his examples demonstrate that the concept is similar to Wilkins’s philosophical numbers in that both involve the use of one symbolic system to articulate the inexpressible. Though Blaise Pascal and Gottfried Leibniz are credited with the first theory of transmutation as a foundational principle of trigonometry, Bridges and other mathematicians were also experimenting with the concept during the same decades. The applicability of transmutation in encryption and decryption is particularly evident in manuals like Stenographie and the work later published by cryptographer and mathematician John Wallis. Transmutation is, generally, the expression of intangible or intractable quantities in rational numbers; in other words, the translation of very large, voluminous, and even potentially infinite possibilities in terms that can be more easily grasped using analogies familiar to a culture. ‘If the said verse were written in all its varieties’, for example, ‘it would make at the least 3323 such volums [sic] as is Ovids Metamorphosis’ (Bridges 1659: 33). Further, given that Metamorphoses contains 12,012 verses, ‘if they were all written one under another, in one roll of paper in the form of a long square, allowing but an inch of the roll in length to every 6 verses, that roll would extend in length 105 English miles’ (Bridges 1659: 33). Only after his mathematic exercise in transmutation does he note that his point is simple: ‘methinks if these great pretenders [to deciphering] did but consider what a prodigious number the transmutation of the 24 letters will produce, and how skill in number doth furnish us with mysterious and hidden things, which present a world of confusion, they should be strangely abasht’ (Bridges 1659: 32-3).

[11] Though the 1665 Rarities, authored by G.B., is considered a sequel to Stenographie and includes some of the same examples, it frames itself as a commentary on the inaccessibility of Stenographie’s lessons and, like Mercury, revises examples for the non-expert reader. Similarly to Mercury, which focuses on multimodal and even bodily geometric cipher — the creation of signs using hand shapes, for example — Rarities opens the potential graphic field of cryptography to include everyday objects and movements familiar to all of his readers. Rarities also incorporates demonstrations of transmutation, but those demonstrations are so hyperbolic as to become satirical. G.B. begins by explaining ‘easie Examples’ of transposition using the phrase ‘God with us’ in order to build reader confidence (1665: 7). The first two are indeed easy: they are basic substitution ciphers in which, for instance, the key ‘2345’ is lined up with the phrase, each number indicating the alphabetic character shift (G.B. 1665: 4):

G o d w i t h u s.
2 3 4 5 2 3 4 5 2

If the agreed upon alphabet omits j and v (and therefore is a b c d e f g h i k l m n o p q r s t u w x y z), the cipher will appear as:

i r h b l x m a u

The correspondent would know the key and therefore to shift the letters backward to reach the original message. G. B. understands that such ciphers are not secure, so having helped the reader see that ciphering is not necessarily difficult he shares more complicated cases that ‘I must confess my self much delighted in’ (1665: 5). He goes on to describe an example that appears in an unnamed previous manual, which is most likely Stenographie, but without, he finds, adequate instruction: ‘Under this Cypher I found the Example set down, but no Directions thereon, nor could I possibly find out the contrivement till I met with the Authors Directions in the Second Edition of the following Tracts, as I formerly hinted’ (G.B. 1665: 12). I will consider the implication of G.B.’s work across cryptography publications in the next sections, as well as the fact that the manual he consults is missing instructions, but here it suffices to emphasize that G.B.’s mathematical purpose is to appear to clarify those other editions and demonstrate his ability, even as a self-proclaimed novice, to illuminate what was most complex in past examples. Also valuable to G.B. is using computation to prove that complex ciphers require independent thinking beyond rote instruction: the untrained mind can learn how to fill in the blanks in the exercises and how to use numbers even without formal education. Ciphering and deciphering, in other words, do not follow set instructions that one need merely memorize. The interpretive process can vary by individual and even by cipher, and multiple paths may lead to the same solutions.

[12] Morland’s New Method (1666) represents the most computationally challenging of the mid-century manuals, though it shares with Rarities and Mercury an emphasis on creative problem-solving. New Method least resembles contemporary conduct manuals, and Morland’s purposes are clearly political and military, not domestic literacy, reform. I include this manual because it is in conversation with the others, however; Morland was aware of and explicitly resistant to the popularization of the discipline for everyday use. He criticizes previous manuals without naming them, remarking that ‘the ordinary Methods of Cryptography, (vulgarly termed Writing in Cypher) where they are weakly contrived, or carelessly written’ may ‘with much pains and industry’ be solved by unintended recipients (Morland 1666: 7). Published expressly for Charles II and his court, this short pamphlet works immediately through what Morland sees to be the most secure ciphers, all of which require complex steps using various mathematic principles. Morland’s ciphers are based entirely upon the concept of a ‘numerical alphabet’ that requires lengthy instructions and knowledge of geometry (1666: 8). Instructions may determine whether a message should be deciphered using a parallelogram, triangle, trapezoid, rhombus, or a polygon simple or central in transcription in ascending columns, diagonally, or even in a serpentine pattern. For one example, Morland notes that there are ‘295288899039603018847 618609643519999999 false ways’ to cipher the message but only one that is true (1666: 8). Morland muses that no kind of genius could decipher a message with this complexity of instructional steps: ‘Now how any Mortal should hope in all his life time, (were he sure to live Quadrillions of Trillions, of Billions of Methusalem’s years!) to hit upon so many Heterogeneous Quasita mentioned in the premises, for which he has in a manner no Data, it cannot enter into my Understanding’.  He sarcastically notes that only the ‘Black Art’ could possibly illuminate such a full-proof method (Morland 1666: 8). New Method is also an advertisement for Morland’s Machina Cyclologica Cryptographica, a series of connected cipher disks for computing that was not innovative in basic design but built from impressive metals and marketable to a fashionable public. Though he scolds other cryptographers for carelessly written manuals that damage the credibility of the discipline, he also engages in profitable outreach to non-specialists. His cipher disk even features a red rose at its center. Morland invented several pocket-sized machines in gold, silver, and bronze that helped mathematics appeal to eager consumers, his Cyclologica Cryptographica among the more useful (Ellison 2013).

[13] Cryptography historians are perhaps most interested in Falconer’s Cryptomenysis, credited with the first use of columnar transposition (Kahn 1996: 155). Columnar transposition entails writing a message in columns of pre-determined length according to a keyword. In fact, this was not Falconer’s innovation but already noted in Rarities and Morland’s manual, with Morland creating newer approaches to that method than Falconer demonstrates. However, Falconer does include other ciphers that are not found in earlier manuals, among them a witty letter that reads one message when whole and a second, contradictory message, when folded in half. Falconer is, perhaps not surprisingly, most influenced by Wilkins and even includes a number of Wilkins’s examples, but Falconer is more invested in contemporary shortcomings in deciphering than innovations in ciphering. He does not share Wilkins’s fascination with the potential of a universal language built upon the concept of philosophical numbers, but his project to popularize mathematics as a mode of everyday reading, and through it to legitimize cryptoanalysis as a respectable discipline necessary for the success of a nation, is evident from the opening pages of Cryptomenysis. Falconer acknowledges that ‘secret intelligence’ has certainly worked in the background of most human conflict and that even during England’s recent military conflicts, ‘People of both Kingdoms, studyed a part of this BLACK A*t’ (Falconer 1685: ‘To the Reader’).[4] Yet, he quickly notes, there is no denying that secure methods of private communication are absolutely necessary during times of war and peace. Nodding toward the popularity of the cryptography manual as a genre, he observes that ciphering has received much attention, and many manuals have boasted the innovation of ciphers that cannot be solved without keys. Deciphering has received less attention, but he is confident that with experience, those who solve ciphers can be as innovative as those who write them. He is careful to point out that he disagrees with those who make fabulous claims about their abilities to solve any cipher no matter its difficulty, as I will show Morland taunting in his New Method. Falconer is not unrealistic: he believes not that any reader can solve any cipher with experience but, rather, that once one understands the rules of deciphering, s/he can apply those rules across languages and, with creativity and much practice, solve riddles without access to keys. ‘It is true, the unridling of such Mysteries, is more immediately the Province of those who sit at the Helm of Affairs, Military and Civil’, he writes, ‘Yet if a private Sentinel, by deciphering an intercepted Epistle, should save an Army, &c. ‘tis no Crime, I hope, that he be more clear sighted than his Superiours’. Emphasizing the need for such skills to be taught to a general public, he notes that ‘Knowledge of Uncyphering should not be confined to a Corner’ (Falconer 1685: B4).

[14] Looking across this sample of manuals published during and after the Wars of the Three Kingdoms, one can see that even if their political goals are vague or secondary, the immediate historical contexts may in part explain each manual’s interest in promoting cryptography as a mathematic discipline well-suited for domestic literacy. Wilkins, writing as conflict is clearly underway, carefully addresses two audiences. He is sensitive to specialists desiring better methods for the immediate communication needs of the wars, and he is also mindful of nonmilitary readers frightened by the turmoil and seeking more control over their private correspondence. Stenographie and Cryptographie is published in 1659, and in it Bridges hints that undeserving frauds have impressed political decision-makers and secured eminent positions while those with true expertise, rigorous training, and value to the new regime, perhaps like himself, are overlooked. Rarities and New Method are of a different political decade and published when one could look back in hindsight at past successful and failed alliances and communication methods. While both G.B. and Morland continue promotion of cryptography, and while both seek to profit from teaching the discipline, G.B. mediates between specialist and non-specialist audiences and Morland writes strictly for the court. Falconer’s manual balances complex ciphers for expert users with methods that even the least expert could use for recreational correspondence, such as hiding a message within the text of an unfolded letter.

Ciphering as Accessible Pedagogy

[15] By the early seventeenth century, literate audiences were made up of diverse populations of readers. Readers were of different skill levels, demonstrated mastery of more or fewer languages, and sought out texts based on different tastes and expectations. Jennifer Andersen and Elizabeth Sauer, like Roger Chartier, focus on the ways in which ‘modes of reading become more various and distinct’ during the early modern period (Andersen and Sauer 2002: 4; Chartier 1989: 174; See also Sharpe 2000: 55 and Ingram 2002: 169). Examination of epigrams and other paratextual elements of printed books that address and even attempt to typify readers, in particular, characterizes one of the approaches to the history and theory of reading that Jennifer Richards and Fred Schurink survey in the 2010 special issue of Huntington Library Quarterly. While the trend in book history has been toward materiality and emphasis on ‘use’ as articulated by, for example, William Sherman in Used Books (2007), genres that invite interactivity are also attracting scholars of reading history. Cryptographers found a subject that appealed to remote, anonymous, numerous readers from diverse religious backgrounds, a spectrum of social situations, and from both sides of the political divide, and their manuals provide a ‘model for utilitarian reading’, to use Richards and Schurink’s phrase (2010: 351).

[16] On the title page of Rarities, G.B. reaches across this broad audience to promote his book: his readers include ‘Ministers of State’, ‘Ladies’, and ‘every ordinary person’. He notes there that his manual is ‘publish’d to promote the Publick, to delight the Ingenious, and encourage the Industrious’. Cecile Jagodzinski agrees that the ‘target audience for these letter-books and cipher keys was wide, ranging from the upwardly mobile soldier to the pining lover’. ‘Ciphers and letters’, she writes, ‘became the conveyors of everyday life and familiar relationships for commoners as well as kings’ (1999: 86). I find that male and female readers of all social ranks and professions were invited by the authors to find their own uses for the manuals, and I would add that more than being merely students, the readers of these manuals were required to navigate the genre, to make connections, and to even enter debate about what had been and would continue to be the uses of the craft in the past and future.

[17] What does it mean, though, for ciphers to be ‘the conveyors of everyday life’ (Jagodzinski 1999: 86)? Answering this question reveals the differences between cryptography manuals and the related but not synonymous genre of the arithmetic textbook. While both arithmetic and cryptography manuals share the rhetoric of universal reader usefulness, arithmetic textbooks often, but not always, welcome only the experienced student of arithmetic, and demand (but not necessarily demonstrate) absolute linear reading. It is important that problems are solved in a standardized way; accounting methods for merchants, for example, should be consistent across the profession. Cryptography manuals are not linear reading experiences and emphasize multiplicity in problem solving. Even their instructions omit steps or move quickly between lessons, whereas early modern math textbooks proceed step-by-step, scaffolding knowledge. Travis D. Williams outlines the basic structure of the arithmetic textbook beginning with even the earliest primers of the sixteenth century. The genre is largely ‘scholastic’ in content and organization, he finds, moving logically through basic operations to fractions and other more complex functions (2012: 171). Cryptography manuals emphasize that readers need no prior knowledge of the discipline to succeed, whereas many arithmetic textbooks caution that readers need a solid foundation in, at the very least, addition and subtraction. Karen Britland convincingly summarizes that ‘cipher invites a kind of non-linear and comparative reading that encourages one to look beneath the veil of cipher in the hope of uncovering a truth’ (2014: 23; see also Edwards 2003). My only addition to Britland’s point here would be that the manuals provide alternative reading models and, by publicly embracing the formerly ‘occult Art’ of cryptography, as Falconer refers to it, the manuals popularize a multimodal kind of computational thinking that allows for interpretive flexibility (Falconer 1685: ‘Introduction’ B). Cryptography manuals are also not training readers to be professional cryptographers. Citizens can adopt various methods, tweak them, and use them for serious purposes or personal entertainment.

[18] Addressed to a wide audience of novice and specialist puzzlers, cryptography manuals proclaim the accessibility of their craft. Even as Morland boasts that only dark magic could help eavesdroppers solve messages written in his ciphers, he still assures readers that his instructions are accessible and the ‘learned Reader will easily perceive that it may yet be read and transcribed in a very great number of other different ways and Methods’ (1666: 4). Certainly, claims of easy learning and multiple pathways to the same solution are common in instructional manuals on various subjects during the seventeenth century. Yet, there are distinct differences between these claims when one compares arithmetic textbooks and cryptography manuals. In a 1629 copy of Arithmaticke: Or, an Itroduction [sic] to learne to reckon with the Pen, or with Counters, in whole Numbers or broken, republished numerous times throughout the sixteenth and seventeenth centuries, the (unknown) author stresses the necessity of mathematics for ‘all manner of persons’ (1629: ‘To the Reader’ A2). The author acknowledges that most arithmetic manuals are not accessible to a general readership’s understanding, so the goal of Arithmaticke is to be clearer in instruction. The reader address does not, however, claim the education will be easy and cautions that readers must proceed in the precise order of the lessons: ‘For if you leape to the second part before you have perfected the first, or to the thirde, before you have seene the second: you shall never prosper nor profit in this Arte’ (1629: ‘To the Reader’ A2). Likewise, William Barton’s Arithmeticke abreviated Teaching the art of tennes or decimals to worke all questions in fractions as whole numbers (1634) addresses the reader to establish the discipline’s usefulness and accessibility. Though Barton notes he will try to be clear in his instruction, however, the textbook requires sophisticated past knowledge and is designed for serious mathematic scholasticism. Henry Phillippes’s edited version of Baker’s Arithmetick: Teaching The Perfect Work and Practice of Arithemetick both in Whole Numbers and Fractions (1670), also published often during the period, assumes the need for all citizens to understand mathematics but warns readers in the epistle dedicatory that it is not accessible to everyone: ‘Let none enter here that is ignorant in Arithmetick’. Unlike cryptography manuals that require no previous mathematical or linguistic knowledge, Baker’s textbook is only for those with prior ‘school-day’ or merchant experience (1670: ‘The Epistle Dedicatory’).

[19] Dedicatory poems that precede Mercury resemble the praise readers would have been accustomed to in conduct manuals. In couplets that open one dedicatory poem in Mercury’s front matter, Tobias Worlrich is so confident that the material is easily learnable that he remarks, ‘I’m loth to tell thee what rare things they be,/ Read thou the book, and then thou’lt tell them me’ (Wilkins 1641: ‘To the Reader’). Cryptography is the ‘Mint of Knowledge’ and any ‘man that deals in Traffick’ and ‘who profess the Knowledge of Nature or Reason’ can learn to write and read code. Though poetry ‘is not in every man’s power’ and ‘requires such a natural Faculty as cannot be taught’, ciphering has universal potential and can be learned quickly (Wilkins 1641: 11, 20). With the system he begins to envision during Mercury and that he will continue in his Essay Towards a Real Character, Wilkins promises that citizens from around the world will be able to learn a common, universal language in a very short time. Cryptography manuals emphasize the accessibility of the craft to non-specialist readers, and as the essential skill of the modern citizen. To discount cryptographers’ claims as mere convention would be to underestimate the literacy reform project that they explicitly champion.

[20] Throughout Mercury, Wilkins emphasizes how easy it is to learn ciphering and how, as the teacher, he has streamlined his instructions for more efficient learning. ‘It were an easie matter for a man that had leasure and patience for such enquiries’, he writes, ‘to find out sundry Arguments of this kind for any purpose’ (1641: 65). As he works through one complex cipher, he assures the reader that ‘for the easier apprehending of this, I shall explain it in an example’ (Wilkins 1641: 57). Occasionally Wilkins even stops his instructions to assure readers that they now know so much they do not need him: ‘There may be divers other ways to this purpose, but by these you may sufficiently discern the nature of the rest’ (1641: 60). Wilkins and Morland emphasize that there is more than one way to follow a particular cipher, and anyone ‘from the Arctick to the Antartick Star’ will be able to learn the art of cryptography and ‘freely traffick through the Universe’ (Wilkins 1641: ‘To Mercury the Elder’).

[21] To further prove how learnable cryptography is, Wilkins frames his manual as the product of his own learning experience, stating at the very beginning that Mercury was inspired by Francis Godwin’s Nuntius Inanimatus (1629), which described a hypothetical telegraph system.[5] Wilkins notes that he at first questioned the validity of Godwin’s outrageous claims to teach readers how to ‘discourse with a Friend, though he were in a close Dungeon, in a besieged City, or a hundred miles off’ (1641: ‘To The Reader’). Yet the credibility of Godwin persuades him to read further and to study the history of cryptography and secret writing; with studious diligence, he ‘attained mine own ends’ and masters the language (Wilkins 1641: ‘To the Reader’). Exhilarated by his own ability to learn an ancient practice that he at first thinks is a type of magic, he writes Mercury to distill the information from his extensive studies and efficiently pass his learning onto the everyday citizen without the time or leisure to read Aristotle, Polybius, Julius Africanus, Frontinus, Isaac Casaubon, Johannes Walchius, Gerardus Vossius (the Latin name for Dutch scholar Gerrit Janszoon), and the many others who make up his bibliography. Wilkins presents himself as a student who has easily mastered the craft and is now passing it onto his readers.

[22] From 1641 until at least the Revolutionary War and the beginnings of American intelligence, authors of cryptography manuals presented themselves as imperfect readers, not as masters passing on their craft to students. In 1685, Falconer’s epistle to his reader explains that ‘a few years ago, having had some discourse with a Gentleman, concerning the Possibility of Resolving any Writing in Secret Character, and the means to perform it; I was taken with the Novelty of the Thing’. Cryptomenysis is thus presented as a kind of journal, as ‘the account of my Discoveries in this progress’ (Falconer 1685: ‘To the Reader’). G.B. also creates ethos through his identification with the reader in Rarities. He tries to serve as a mediator between the curious audience and cryptographers of the past, who were more skilled than they revealed. He begins his epistle to the reader recounting that he is about to publish ciphers that were ‘plunder’d from the Author of the following Tracts’ and ‘came shortly after to my hands, and have lain by me to little purpose’. He explains that he kept the papers so long without publishing them because ‘my great pains to make some progress therein came to nothing untill he in his second Edition gave the Learner Directions how to proceed’ (G.B. 1665: 1).[6] He then describes his efforts to understand the ciphers and stresses that ‘I have no ends beyond the kindness I owe to the common capacities, and the publick’ in sharing ‘that rare Art’ (G.B. 1665: 2). His loyalty to his reader is so strong, in fact, that he suggests that he has risked his life in letting them see the ciphers: ‘I mean well to all, and so consequently have the less to account for: but however I am concluded, I shall shortly (if I live) be Thy more useful Friend G.B.’ (1665: 2). Repeatedly throughout the manual he reiterates his innocence and stresses that he is merely trying to help the reader with those ‘easie Examples (of which I lately thought my self as ignorant as any that are to learn)’ (G.B. 1665: 3). This intimate relationship with the reader draws audiences to the manuals and helps make the genre so popular that some historians and literary scholars have observed that ‘it became quite the fashion to learn to write in cipher’ (Jagodzinski 1999: 85).

[23] Admittedly, the pose that Wilkins, Falconer, and G.B. adopt as students of cryptography sharing information with their similarly novice readers is immediately challenged by the knowledge they display. The poems that follow Wilkins’s epistle dedications, for example, praise his learning and reputation. The first poem, by Sir Francis Kinaston, represents him as the offspring, ‘Mercury the yonger’, of Trithemius and Gustavus Selenus, the pseudonym of August, Duke of Braunschweig-Lüneberg. Both were accomplished cryptographers of the early sixteenth and early seventeenth centuries, respectively. Wilkins is a genealogic inevitability, a cryptographer so talented that even ‘the winde,/ Should it contend, would be left farre behind’ (Wilkins 1641: ‘To Mercury the Elder’). In a second poem, Anthony Aucher addresses Wilkins as an ‘unknown God’ and in the third, Richard West emphasizes Wilkins as author and artist with timeless authority, more genius than Plato or any other philosopher or scientist in history: ‘This Dutchman writes a comment, that Translates,/ A Third Transcribes; Your pen alone Creates/ New necessary Sciences’ (Wilkins 1641: ‘To the Unknown Author; Wilkins 1641: ‘To his honour’d Friend I.W. on his learned Tract’). Ironically, these poetic dedications, and even West’s declaration that Wilkins is neither student nor compiler but creator, help establish the persona of cryptographer as curious reader. Because others assert Wilkins’s talent and trustworthiness, Wilkins need not do it himself. Further, the poems emphasize the experimental, magical, and natural. Cryptography is a marvel to admire and enjoy.

[24] Wilkins and the flattering poets that populate the beginning of Mercury assure readers that cryptography is a common sense language; gestures, sounds, movements, glances, and even nods can communicate according to predetermined systems, yet they are mathematically accessible because they are bodily. In fact, repeated emphasis on cryptography as corporeal help the authors build the reputation of cryptography as natural. It is not the subject of this essay to explore how cryptography assumes the living body as mathematic form — with multiple parts for counting, repeatable and calculable movements, and geometric shapes and lines to be computed — but all of the manuals operate according to this implicit theory. Richard West stresses that:

You tell us how we may by Gestures talke:
How Feet are made to speak, as well as walke:
How Eyes discourse, how mystique Nods contrive;
Making our Knowledge, too, Intuitive. (Wilkins 1641: ‘To his honour’d Friend’)

The ability to cipher begins not with scholastic mastery of math but with a kind of common sense understanding of how patterns function in nature. Richard West claims that Wilkins can provide a coping mechanism for individual readers operating within a wide audience, giving them strategies for recognizing and creating patterns to maintain their privacy while remaining part of a diverse crowd. Patricia Meyer Spacks helpfully notes that privacy ‘has little to do with the much-debated split between “public” and “private”; indeed, using codes or ciphers to communicate is not simply the opposite of making that communication public (2003: 3). Language as articulated through arithmetic provides attractive textual solutions to eavesdropping because it can circulate freely in the public yet hide thoughts that at least two people want to keep between themselves. Patterns hide and yet express. Cipher is not simply private language; it moves in wide circles, read by many but only fully understood by a few. It is the language of ‘psychological privacy’ which Spacks distinguishes from physical privacy (2003: 7). West’s italicized emphasis on ‘intuition’ shows that Mercury promotes cryptography as a skill anyone can learn to protect their thoughts because it is a natural ability that can be mastered with tuned senses and heightened awareness of one’s surroundings, a part of being human and interacting with the world. It is not just the special talent of mathematical prodigies working in isolation from others. By publishing their secrets (or pretending to), they also affirm that privacy should not only be a privilege of the powerful but the commoner as well. 

Cryptography as Experimental Science

[25] Ciphering would seem to be the one type of writing, and cryptanalysis the one type of reading, that eliminates interpretive plurality by purposely splitting audiences into those with the key and those without. Yet in early modern cryptography manuals, interpretive unpredictability begins as early as the pedagogical introduction to the craft. Cryptographers open readers up to an infinite textual territory, giving them new tools and then setting them free in a landscape of numbers and letters with potentially meaningful patterns they could never see before. G.B., for example, challenges readers to work independently, to interpret freely a type of language that one would assume is not open to diverse interpretations. When G.B. decides to ‘only hint that method’ and consequently let go of the reader’s hand, he creates a cognitive moment of parataxis, a situation in which readers must take information merely presented or juxtaposed without explanation and make their own meanings through experimentation (1665: 6). On the fifth page of his lessons, G.B. quits two more codes, the first because it is ‘not sufficiently secure against an artificial scrutiny’ and the next because it is a rather delightful code but too ‘obvious to the meanest capacities’ (1665: 5-6). Readers willing to work to understand those abandoned codes must, in the first case, repeat the directions many more times and, in the second case, look back to the second edition G.B. refers to often. The only assumption these authors make about their wide audiences, in fact, is that they are familiar with the genre of the cryptography manual. G.B.’s references to the unnamed second edition assumes prior reader knowledge. Wilkins does not make such ambiguous references, probably because Mercury is the first of many manuals to follow, yet he, too, builds from other works like Godwin’s. As well as linking unidentified texts, Rarities also has sketchy connections between chapters — G.B. moves abruptly from codes to invisible ink, for example. The logical gaps in the sources, chapter topics, and ciphering, however, are less problematic the more one understands the genre’s conventions. It is as though cryptographers draw and depend upon a collective text, and readers who want to understand a cipher more fully know they can look at previous manuals to find similar (or identical, since the manuals commonly replicate the same material) example. Cryptography manuals are intertextual, demonstrating awareness of other works in the genre and referencing them clearly. Little unattributed lifting of material occurs; copied examples are usually cited. Parataxis extends beyond the pages of the manual immediately in front of readers because they are encouraged to look across the genre.

[26] Both G.B. and Morland emphasize the interpretive liberty computational ciphers grant them even as they instruct toward ‘true’ or right answers. Recalling Bridges’s use of transmutation to prove that untrained decipherers could never discover the solution to ciphers written in more than nine characters, G.B. takes on the Latin verse example that Bridges provides, though G.B. uses two lines of the verse instead of just one. Bridges had computed that the one line of verse (‘Quod sat sit (sors) da, fed ne post tu rape de me’) has 39,916,800 transmutations. G.B. recalculates that Latin line and a second to conclude that it is more accurately ‘variable 1144000727777607680000 wayes, the words rape & neque standing alwayes as they are’ (1665: 15). G.B. then goes further:

But if they change places (as they may once) then the former number of varieties will be doubled thus 2288001455555215360000. Those written in all varieties according to 6 Verses or 3 Disticks in the depth of an inch, each Verse 3 inches long, would fill a roll of Paper of 3 inches breadth 62444484876533760000 feet long, whose weight would make 99857918246056 of our ordinary Cart loads. (1665: 15)

G.B. continues this series of computations, all prompted by musing upon how many variations a reader might find in the process of solving one cipher, for another page and a half. ‘If written on a piece of paper’, he notes, the variations ‘would cover the face of the earth 3,055 times’ and the ‘ink that should write the varieties would load 27 billion, 159 million, 778 thousand, 763 Carts and would fill a pool of 1 74/100 foot depth as broad as the whole Mediteranean [sic] Sea’ (1665: 16). G.B.’s intent in providing these familiar analogies to express intractable quantities is not to reveal fraud, as is the case in Bridges’s manual. With a wider audience and a more playful, even comic, tone, G.B.’s transmutations stress the number of possibilities as interpretively liberating.

[27] Morland also humors the reader with semantic multiplicity when he stresses that his example code has ‘Millions of Millions, of Millions, of Millions, of Millions, of Millions, of distinct Orders’ (1666: 7). Similarly, Morland explains the creative decisions a cipherer and decipherer can make:

It is evident, that every such Figure containing but 9 Columnes, admits of no less than Three Hundred Sixty two Thousand, eight Hundred and eighty different Transpositions. And others of them, as Fig.VI. and VII. Containing 18 Columnes, admit of Six Thousand four Hundred and two Millions of Millions, of different Transpositions; More by Three Hundred seventy three Thousand, seven Hundred and five Millions; More by Seven Hundred twenty and eight Thousand; And there being in the Writing 81 Letters, they make an Oblong containing 27 Columnes and three Lines, And consequently such a Figure will admit of 10888869450418352160768000000 distinct Transpositions. (1666: 4)

Morland’s pains to illustrate the creative possibilities open to cryptographers serve as much for self-flattery as they do advocacy for the popular uses of mathematics as multimodal reading. Yet, such illustrations of the interpretive possibilities of cryptographic thinking become conventions in the manuals. Falconer makes a similar, less boastful argument twenty years later that further legitimizes cryptography, but he reveals even more explicitly that alphabetic thinking is and always has been, in a sense, mathematic in nature. He uses the same kind of logic, showing readers how the number of transpositions possible using a 24-letter alphabet would reach ‘to the Man in the Moon’ (Falconer 1685: 5). ‘To be serious’, he continues, ‘you find twenty four Letters have 620448401733239439360000 several Positions’ (1685: 5). To a cryptographer, letters and numbers are interchangeable communicational characters, but numbers, in a sense, are even more expressive than letters because they can illustrate the enormous scale on which the human mind is capable of thinking. Falconer uses this convincing example, of course proven through computation: ‘If one Writer in one day write forty Pages, every one containing forty Combinations, 40 multiplied by 40, gives 1600, the Number he compleats in one day, which multiplied by 366, the Number (and more) of Days in a Year; a Writer in one Year shall compass 585600 distinct Rows’ (1685: 5). ‘Therefore in a thousand million of years’, Falconer concludes, ‘he could write 585600000000000, which being again multiplied by 1000000000, the number of Writers supposed, the Product will be 585600000000000000000000, which wants of the number of Combinations no less than 34848401733239439360000’ (1685: 5-6). This computation, of course, does not take into account that cipherers can work not only with letters and numbers but also with invented characters, ‘arithmetical figures’, and other symbols to express themselves.

Cryptography and Occult Mystery

[28] Many of the lessons in the manuals omit necessary instructions, end without resolution, or pair problems with the wrong solutions. G.B. explicitly admits he will ‘only hint that method’ (1665: 6). Kahn, a historian of cryptography, notes in a short section on this period that seventeenth-century manuals ‘stained cryptology so deeply with the dark hues of esoterism that some of them still persist, noticeably coloring the public image of cryptology’ and regrettably, because of seventeenth-century cryptography manuals, ‘People still think cryptanalysis mysterious’ (Kahn 1996: 93). Certainly, at times, the manuals seem esoteric even though they claim their appeal to a wide, novice readership. G.B. writes in the final lines of his first chapter, ‘The rest of the Discourse is in shorthand and Algebraical Characters, which I cannot make out’ (1665: 17). Such a dismissal prevents readers not educated in algebra to pursue the cipher any further, yet it also supports G.B.’s claim to be an unskilled cryptographer finding his way alongside the readers. From the abandoned ciphers to missing alphabets and typographical oversights, the manuals foreground their topics as mysterious even as they stress their accessibility. I have argued elsewhere that this self-reflexive awareness of and playfulness with reader expectations, and the relationship between the narrating novice voice and the reader as student, represents one nonliterary example of growing skepticism about idealized history and romance that would root the early novel (Ellison 2008). Here, I am more interested in how purposeful or accidental error promotes arithmetic as a domestic mode of reading by utilizing the language of mystery that is part of cryptography’s occult past. Eamon’s work helps to clarify the relationship between experimental science and the occult during the seventeenth century, when Royal Society members including Wilkins worked to establish credibility for experimentation and reposition experimental science as academic. John Henry explains how certain aspects of the occult became absorbed by the soon-to-be mainstream sciences of the seventeenth century. The result, he notes, is that the occult became fragmented. What would have once passed as magic in a previous age was renamed and repositioned: alchemy became chemistry; astrological principles grounded astronomy; incantation was legitimized as cryptography (Henry 2008: 1; see also Moran 2005).  Michael McKeon makes a similar but less specific claim when he recognizes that the increased publication of books promising the disclosure of secrets, some complete with recipes, could ‘be seen as a subtle reconception of the parallel between experimental technique and the natural phenomena it sought to know’ (2006: 65). The experiential techniques of occult sciences like alchemy were useful for Royal Society scientists, as was occult performativity. Anthony Grafton posits a similar argument but in reverse, arguing that the occult enveloped the practices and rhetoric of contemporary mathematics and engineering to bolster its credibility (2005: 17). Texts such as Wilkins’s own Mathematical Magick also demonstrate, for Grafton, a ‘technological brand of magic’ in which the new sciences did not replace the occult sciences but rather could justify their disciplines as legitimately useful as well as divinely inspired (2005: 18).

[29] I believe that cryptography manuals sacrifice accuracy, in part, because ciphers that work are not necessary for the genre to participate in the contemporary agenda to situate numbers and patterns, in all their functions, as useful as well as magical. Cryptography manuals invite a diverse readership to entertain itself with novelty, topicality, variety, secrecy, and the promise of an interactive experience, all conventions Barbara Benedict cites as important to the early anthology (1996: 5). If readers did not learn how to write or read ciphers or codes, they could content themselves with believing that they were part of a secret. That readers could not always make the ciphers work only supported the status of cryptography as a ‘marriage of magic and engineering’, in Grafton’s words (2005: 35).

[30] G.B. critiques the ways in which previous manuals are riddled with error and misleadingly complicated instructions. If readers missed those errors while enjoying earlier manuals like Wilkins’s, G.B.’s assessment no doubt opens their eyes to the inaccuracies of the genre. In the ‘Epistle to the Reader’, G.B. claims that when he was reading an earlier manual ‘my great pains to make some progress therein came to nothing’ (1665: 1). G.B. is correct: previous manuals exhibit so many problems with the codes and ciphers that the marginalia in some copies show reader work that stops abruptly in mid-solution. I argue elsewhere that these mistakes, misleading explanations, missing elements in the codes, and even misnumbered pages in Mercury, Cryptomenysis, and New Method cause readers to lose their way in the complicated pages and, in some cases, give up on learning the craft (Ellison 2011). I also find that the manuals challenge reader comfort with textual conventions; as the position of page numbers, the order of sections, the appearance of particular genres like dedications and paratext, and even margin size became more standardized with print, users of texts developed blind spots and assumptions that disallowed them from processing error as significant. For example, blots of ink were so common that ciphers could easily be hidden in their patterns, and instructions paired with the wrong examples could be written off as mere printing flaws. In his dedication to Charles, Earl of Middleton, Falconer admits that his manual has ‘defects’ but begs that readers not mistake those as a reflection upon his patron. Falconer then as much as admits that he has made significant errors, apologizing for using an entirely wrong alphabet for one cipher, though he does not specify which. G.B. promises that he has therefore corrected mistakes and distilled the confusing directions and will ‘lead thee by the hand from familiar Examples, and the beginnings of that Art (as I find them in his Papers) to the sublime curiosities thereof’ with ‘easie Examples (of which I lately thought my self as ignorant as any that are to learn)’ (1665: 2-3). But then, right away, G.B. breaks his promise. On the very next page, when he notes that the manual he is citing ‘has purposely disordered the Letters in their ranks to perplex the inquisitor’, he says he will ‘only hint that method and proceed’ to the next code that ‘is more ready and pleasant’ (G.B. 1665: 6). He does not disorder the letters – he just stops in the middle of his directions.

[31] Although missing information and error would seem to damage the credibility of the authors, it may instead strengthen the relationship the authors work to build with their readers. On the one hand, readers searching the manual for scandalous secrets and reading for ‘leasure studies’, as Wilkins expects, will not necessarily pause to try each example; the façade of technicality lends the text enough authenticity to make the intrigue interesting (1641: ‘To the Right honorable George, Lord Berkley’). On the other hand, readers who do discover the inaccuracies are further convinced of the difficulties surrounding secret writings. Readers of cryptography manuals expected instability in their texts; that was, indeed, one of the attractions of the subject. Cryptography also makes visible the many ways in which language can be easily manipulated and adapted to different audiences; that, too, is a defining characteristic of the craft. Integral to the effectiveness of error in keeping the attention of readers is the way in which it creates, rather than undermines, the authority of the author and, in the end, gives readers what they expect while still surprising them along the way. As we know from Sharpe’s convincing study of early modern reading, by the end of the seventeenth century authors no longer needed kings or other important political patrons to establish their authority (2000: 31). And as Jagodzinski finds, authority, when it is attainable through authorship alone, becomes a fragile construction, an authorial characteristic that must be earned through an established relationship with the reader rather than asserted as fact (Jagodzinski 1999: 10).


[32] The consensus thus far in historical studies of early modern cryptography and cryptology, specifically from the viewpoint of literary scholars, is that the use of ciphering to create and solidify social ingroups and outgroups, to position oneself in relation to political peers, was as much if not more important than the content of the messages and whether or not they could be solved (See Akkerman 2011 and Britland 2014). To focus too much on the political self-fashioning at stake in showing one could cipher, however, is to overlook the practical distinctions cryptographers like Wilkins, Bridges, G.B., Morland, and Falconer make when they favor one type of symbolic system over another. While Wilkins advocates for philosophical numbers, Bridges demonstrates the potential of transmutation. Morland presents a rigorous numerical alphabet and Falconer presents advancements such as columnar transposition at the same time that he offers more novice-friendly methods that entail object manipulation such as folding. These preferences are part of a larger campaign — not necessarily coordinated amongst them but building rhetorically over time — to rethink the notion of modern reading in multimodal communication systems.

[33] Where early modern cryptography manuals differ from arithmetic textbooks of the same decades is in their invitation to readers to participate in the intimate secrets of political intrigue while, at the same time, they allow or even orchestrate obstacles that prevent readers from fully learning those secrets. The impenetrability of seventeenth-century cryptography that Kahn cites is not an exaggeration, but it is arguably also not an accident. The manuals do not teach exactly what they proclaim to teach, but they have another lesson: arithmetic methodology is and should be experimental, creative, and interpretative, a continuous negotiation with a text whose author works in contract with a wide, diverse audience with varied expectations, skill levels, and commitment to the material. Ciphering, which might seem the most formulaic of all linguistic practices, becomes the stage upon which cryptographers can most effectively prove the complexity of literacy.

[34] Seventeenth-century cryptographers were both mathematicians and rhetoricians, both skilled masters of narrative and technological pioneers. Wilkins even claims matter-of-factly that his subject ‘doth also belong unto one of the liberall Arts’ (1641: 11). The stories they embed in their manuals have been so riveting, in fact, that nearly all twentieth- and twenty-first-century histories of cryptography, and even a large number of technical textbooks and course syllabi, repeat their stories verbatim, often without any idea who the original authors were. Recognizing contemporary repercussions of more diverse literacy and the move toward liberal reader interpretation, Wilkins, Bridges, Falconer, G.B, and their colleagues helped popularize mathematics and mathematic thinking, presenting communication by ‘philosophical numbers’ and ‘numeric alphabets’ as interpretive. They embraced the historical occult mystery and power of numbers yet stressed that even the most daring mathematical adventures could be learned from the safety of anyone’s desk.

Illinois State University


[1] References to all of the cryptography manuals except Rarities are from first editions viewed in person in the following collections. The relationship between Bridges’s Stenographie and Cryptographie and Rarities is worth noting. In 1659, Noah Bridges published Stenographie and Cryptographie, with a second edition in 1663. In 1665, Rarities appeared anonymously. Both are printed by J.G. The scan of the 1659 Stenographie scholars access on Early English Books Online is from the Bodleian Library and is bound with Rarities, so Rarities has been attributed to Bridges; however, Stenographie and Rarities are separately paginated, have their own signatures, and are on different paper stocks. A note on the back of Stenographie’s title page indicates the two works have been grafted together, presumably by a later binder or owner. Thank you to Katherine Hunt and Rebecca Tomlin for verifying the Bodleian copy. Copies of Stenographie in the Philip Mills Arnold Semeiology Collection as well as at the Rare Book and Manuscript Library at the University of Illinois at Urbana-Champaign also provide evidence that the two texts are separate publications.[back to text]

[2] Trithemius was a pseudonym for Johann Heidenberg.[back to text]

[3] Cryptography predates universal language schemes but is a personal inspiration for Wilkins’s later project. See Wollock 2011, Markley 1993, Cohen 1977, Cram and Maat 2001, Knowlson 1975, Lewis 2007, and Glidden 1987: 191.[back to text]

[4] Falconer does not indicate which ‘kingdoms’ he is referring to here when he uses ‘both’, but his examples imply he is referencing England and Scotland, not Ireland.[back to text]

[5] Some sources, like Mercury, spell Godwin’s text Nuntius Inanimatus, while others, such as William Poole in his recent 2006 article in The Seventeenth Century, spell it Nuncius Inanimatus. I use Wilkins’s spelling for this essay. See Poole 2006.[back to text]

[6]This statement would seem to provide evidence that G.B. is referring to Noah Bridges’s two editions of Stenographie and Cryptographie, yet it is still unclear why Bridges’s papers ended up in G.B.’s hands, if they are different people and G.B. is not an abbreviation for Bridges, or why, if they are the same person, Bridges publishes the first two editions under his own name but disguises his identity in the third.[back to text]


Nadine Akkerman. (ed.). 2011. The Correspondence of Elizabeth Stuart, Queen of Bohemia, 3 vols (Oxford: Oxford University Press)

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Arithmaticke: Or, An Itroduction to learne to reckon with the Pen, or with Counters, in whole Numbers or broken. 1629. (London) [STC (2nd ed.)/14122]

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