The Republic of Codes

Cryptographic Theory and Scientific Networks in the Seventeenth Century

Robert Batchelor, Department of History, Stanford University

November 1, 1999 [Work in Progress, Not for Citation]

 

Every symbolism is built on the ruins of earlier symbolic edifices and uses their materials—even if it is only to fill the foundations of new temples, as the Athenians did after the Persian wars. By its virtually unlimited natural and historical connections, the signifier always goes beyond a strict attachment to a precise signified and can lead to completely unexpected realms. The constitution of symbolism in real social and historical life has no relation to the ‘closed’ and ‘transparent’ definitions of symbols found in a work of mathematics (which, moreover, can never be closed up within itself).

—Cornelius Castoriadis, L’institution imaginaire de la société, (1975)

La plus part de nos raisonnemens, sur tout ceux qui s’entremelent dans les principales veues, se font par un jeu de caracteres, comme on joue du clavesin par coustume en partie, sans que l’ame en cela s’en apperçoive assez, et forge les raisons avec reflexion. Autrement on parleroit trop lentment. Cela sert a mieux entendre comment le corps exprime par ses propres loix tout ce qui passe dans l’ame. Car ce jeu de caracters peut aller loin et va loin en effect, jusqu’à un point qu’on ne pourroit penser des choses abstraites sans aide de caracters arbitraires.

—Gottfried Wilhelm Leibniz

I. Cryptography in the Republic of Letters

Studies on cryptography tend to focus on war and the need for codes to keep secrets closed away from the prying eyes of foreigners. This paper will follow a different path, namely that cryptography as it developed in the seventeenth century worked primarily as a tool for the creation of social networks within a society, and cryptography as a science (a development rooted in the sixteenth and seventeenth centuries) worked as a tool for imagining and instituting social structure. Cryptographic method, perhaps even more that mathematics, lies at the heart of the development of the notion and practice of "science" (scientia: knowledge) in the seventeenth century. The Republic of Letters develops as a Republic of Codes. Unlike courtly notions of manners, the practitioners of these codes deliberately tried to develop them into languages abstracted from social practice (calculus, logic, even law). It was the job of the polymath, the polyglot and the polyhistor to translate between such codes. This paper will look at two Baroque polymaths—Athanasius Kircher and Leibniz—and their attempts to develop a methodical knowledge of cryptography and artificial languages as a solution to the problem of social fragmentation in the Holy Roman Empire in the aftermath of the Thirty Years War.

Both Kircher and Leibniz saw quite clearly the problem of social fragmentation raised by war, religious disputes, the declining use of Latin (which Kircher published in, although he frequently corresponded in the vernacular), and the increasing inability of the Hapsburg emperors to exercise power over the German princes. The emerging global powers of the seventeenth century, England, Holland and France, were gaining strength by carving up direct and indirect spheres of influence in northern Italy and Germany, and dividing up the imperial possessions of Spain and Portugal—all regions formerly under the sway of the emperor and the Hapsburg dynasty. It was once customary to imagine the scientific revolution from the perspective of these emerging powers (usually in terms of national traditions). What this misses, however, is the very fragmented nature of the production of ‘science’ or knowledge during this period, and the way in which cryptography became a method for working through this problem of fragmentation at both a theoretical and practical level. The much-vaunted "Republic of Letters" in Holland and France or the supposed "public sphere" of England were in many ways as provincial as a German or Italian court, albeit on a larger scale. The cryptologists confronted the problem of how to enable communication between various systems of knowledge, each with their own languages, and how to make such communications endure over time.

The cryptologist monitored the line between inclusivity and exclusivity. Careers like Kircher’s or Leibniz’s were based upon not only the fine art of moving and translating between various zones of knowledge production but also their ability to monopolize such transfers. It was less important for them to actually encrypt information than to understand the process through which such encryption might occur. Similarly, although certain princely courts might be entertained by fantasies of alchemical power or global dominance (the eighteenth-century porcelain collection of Augustus the Strong of Saxony, amassed by trading away his regiments, comes to mind), it was more important to develop a way of imagining their relationship to a rapidly changing European social landscape. Theories of recombination, inclusion and exclusion far from being simple ideology enabled planning and development of connections across fragmented social space.

For the purposes of clarity, this paper will make an analytic distinction between codes and ciphers. As a caveat, it should be emphasized that this distinction operates not as an ideal categorical distinction but precisely because of the particular institution of mathematics that developed around 1600 in relation to languages written in alphabetic (esp. Latinate) languages. Ciphers work according to a set rule or rules (the key), which are applied to the individual characters of the message according to either transposition or substitution principles. The most common is a simple alphabetic cipher where twenty-six letters or numbers are rearranged in order to correspond with the traditional order of the alphabet. The cipher became widely used in the Renaissance, the fruits of a methodology that developed out of Arabic texts of algebraic theory and practice arriving from the twelfth century onward. A cipher has no direct relationship with the actual message contained within the code—i.e. it is a substitution or transposition system applied to the superficial form of writing. Ciphers are relatively easy to crack based on principles derived from a general knowledge of the underlying language because all that is necessary is to use letter frequencies to discover the mathematical basis of the cipher and crack it in one fell swoop. Even the most complex mathematical algorithmic keys remain vulnerable to this process of decoding—an argument first made by François Viète (1540-1603) in the late sixteenth century.

A code on the other hand works out of the words and phrases of the language and requires a dictionary to crack. The classic example is the use of encrypted Navajo during World War II as a code. The unavailability of dictionaries made cracking the code a kind of translation project equivalent to reading ancient Egyptian without the Rosetta Stone. More commonly, a numerical code substitutes a string of four or five numbers for each word, which requires two dictionaries (word to number and number to word) and is thus referred to as a "two-part code." Decoding such a system works at the level of word frequencies and grammar. The problem with a code is that it is harder to change over time because to enable a code system to function, both parties need the encoding and decoding dictionaries. As a result, codes are easier to crack over time because they require a kind of culture to develop around them, while the cipher key or formula can be changed rapidly to frustrate efforts at decipherment.

The sixteenth century was a golden age for the development of methodologies for producing ciphers. The French diplomat Blaise de Vigenère (1523-1596) in his Traicté des chiffres (1586) compiled and developed many of the most common methods of cipher, while Giambattista della Porta (1535-1615) founded the Accademia dei Secreti in Naples that connected the Renaissance study of the "secrets" of nature to cryptographic method. Much of this flourishing was the result of the work of the abbot Johannes Trithemius (1462-1516). While attending the University at Heidelberg, Trithemius resolved to become a Benedictine monk in 1482 and within a little more than a year he became abbot of Sponheim (subsequently becoming the abbot at Würzburg in 1506). Sponheim was not exactly a center of activity when Trithemius arrived, having reached a low point of four members in the 1450’s, and Trithemius began a campaign in the 1480’s to build it up as a center for learning, constructing a guest wing to house visiting northern humanists and collecting a large library (from 48 to 2000 volumes). In keeping with this concern to put Sponheim on the map of humanist letter and travel networks, his writings articulate a number of systems for secret writing based on ciphers, communication over distance (smoke signals, etc.), language learning (memory arts for Latin), and finally occult and semi-occult methods of psychic communication. Ironically, Trithemius becomes famous because a letter he sends describing this project was never delivered and leaked out into the broader Republic of Letters. His treatise circulated in manuscript form for much of the sixteenth century until it was finally printed by Protestants in Frankfurt in 1606 (the great book center of the Holy Roman Empire until the devastations of the Thirty Years War) and promptly indexed by Rome and the Spanish Inquisition.

The range of interests of Trithemius in terms of language and the notion of secrets is typical for many sixteenth-century writers on the subject. In particular, most exhibit a simultaneous interest in encrypting language while at the same time using it to build social networks (especially teaching Latin) and open up the "secrets" of nature. Part of this stems from the kinds of problems resulting from attempts at forming a "Republic of Letters" in the sixteenth century. This was especially true in the Holy Roman Empire, where the fragmentation of religious institutions was greatest. The humanist solution to such problems was to build a series of letter and social networks by teaching at several different institutions both inside and outside of the empire and maintaining an extensive correspondence in Latin. While methods like those pioneered by Trithemius lay behind the theories of this first manifestation of the Republic of Letters, a consolidated imperial postal system managed by the Taxis (developed from 1490-1516 for emperor Maximilian I) and the polyglot versions of the neo-Latin dictionary of Calepin were the key technologies that allowed it to function. The content of such correspondence largely dealt with questions of patronage networks such as political reports, aristocratic genealogies or introductions for travelers as well as learned discourses based upon maintaining a coherent field of knowledge, referring back to a classical corpus while at the same time keeping the network current on the latest products of the ever-churning presses and arranging access to copies. The good scholar had a large Stammbüch filled with names and details about friends and contacts made during his travels, whom he could correspond with and reach other scholars through. In terms of broader intellectual currents, the construction of coherent cosmologies and systems out of Aristotelian and Platonic methods took pride of place as did the reform of logic, all in the service of constructing a coherent social imaginary for empire and republic. Princes and aristocrats amassed large collections of books, curiosities and natural rarities, to demonstrate the importance of their court as a nodal point of knowledge and society. This is the social and intellectual world that provoked such skepticism in Montaigne, having experienced it in his father’s house during the mid-sixteenth century.

Trithemius was more interested in steganography than cryptography. The methods of steganography ("hidden writing") conceal the existence of a message, so that a secret communication may appear as a picture or a piece of writing on an innocuous subject (ex. every fourth letter of a poem when combined in order gives a message). Cryptography ("secret writing") does not necessarily conceal the existence of a message but instead makes it unintelligible through the use of a cipher or code, and it is the practice of cryptography that was of prime interest to princes and popes who required messages enciphered and deciphered. Conversely, steganography had more to say to the general interests of the sixteenth-century Republic of Letters. The neo-Platonist scholars of the Renaissance thought of the production of knowledge in terms of reading the book of the world. In a realist sense, God’s signs were literally everywhere in nature, so that someone like the famous physician Paracelsus (1493-1541) could argue that "the stars in heaven must be taken together in order that we may read the sentence in the firmament. It is like a letter that has been sent to us from a hundred miles off, and in which the writer’s mind speaks to us." Paracelsus advocated something called the doctrine of signatures, which claimed that the sentences of the stars and other earthly things do not reveal themselves in their entirety but as divine signatures. Conversely, so the theory went, it should be possible to convert the book of the world into an actual book by using the "signature." In other words, the signature acted as a key to God’s great post-Babel cipher. Increasingly, many began to think that the "key" to the cipher was mathematics.

Up to this point, the interest in cryptography in Europe was somewhat divided between the academic steganography of the Republic of Letters and the practical use of ciphers for preserving secrecy within the networks of letter exchange that spanned Europe. Steganography could be held up as a method for making the work of various scholars on the secrets of the book of nature cosmologically coherent (a linguistic code known among scholars and used as a source of cultural capital), along the lines of Giambattista della Porta’s Accademia dei Secreti. Meanwhile, princes and popes needed actual cryptographers (preferably mathematicians) to create and crack ciphers, in order to keep their court politically central within the correspondence networks of Europe. In other words, the social system addressed by both practices was in many ways the same (although as early as the 1520’s Erasmus was complaining of businessmen using the letter system for vulgar purposes—i.e. not recollection, neither politics or scientia), but the points of entry were radically different. Nevertheless both court and republic depended on each other, a relationship nicely emblematized in the parallel markings of the cipher and the double process of enciphering and deciphering. The tension, pointed to by the skeptics, between the function and the meaning of cipher became increasingly bipolar and subjected to strains, not only the dreaded ‘vulgar’ commerce but also religious and social fragmentation, which it proved unequipped to handle.

II. From Cipher to Code

Galileo’s often-repeated phrase that the Book of Nature was written in the "language of mathematics" proved of course hugely influential in the seventeenth century as a justification for what Husserl called the "institution of geometry." At the core of the Galilean equation was the idea of deciphering the Book of Nature, which meant that the methods of cryptography developed in the sixteenth century became extremely important to the development of scientific practice in the seventeenth century. This was not simply steganography, however, for the "signatures" were themselves only accessible through geometry (and algebra) rather than being directly revealed in language (as for example in Kabbalah). A gap existed in the relation between the language of the letter and the methods of the mathematician. Solving this gap required a kind of code that could translate between the two systems.

In his Of the proficience and advancement of Learning, divine and human (London: 1605), Francis Bacon (1561-1626) warned against the false appearances of things imposed by words. Bacon expressed his suspicion of both language (verba) and the imagination as separate from nature and things (res) and therefore sources of chaotic Babel-like invention. "For words are but the images of matter," argued Bacon, "and except they have life of reason and invention, to fall in love with them is all one as to fall in love with a picture." In order to try and circumvent this problem, Bacon suggested that the corruptions of spoken language might be repaired through a careful attention to language and in particular the science of grammar, for "in regards of the rawness and unskillfulness of the handes, through which they passe, the greatest Matters, are many times carryed in the weakest Cyphars." Bacon criticized Aristotle’s contention (De interpretatione, I, i, 16a3-8 and Plato in the Phaedrus, 274B-278B) that "Words are the images of cogitations, and letters are the images of words," or that writing is but an image of spoken language (Bacon’s "words"). Bacon contended that writing does not require words and that both primitive sign language and the highly advanced Chinese system of characters challenge this notion, "we understand further that it is the use of China and the kingdoms of the high Levant [the Far East] to write in Characters Real, which express neither letters nor words in gross, but Things or Notions; insomuch as countries and provinces, which understand not one another’s language, can nevertheless read one another’s writings, because the characters are accepted more generally than the languages do extend; and therefore they have a vast multitude of characters; as many, I suppose as radical words." The language of science should approach, as much as possible, such "characters real," because writing is the "mint of knowledge" and words are its currency. A real character would work as a gold standard for language, a remedy for the debased moneys in current circulation. According to Bacon, the "broken" relationship between words and things must be repaired and "reintegrated" as much as possible through a science of grammar. Because of this Bacon expresses interest elsewhere in trying to develop an alphabet of nature ("abecedarium naturae"), which would help to organize knowledge but without any particular reference to the truth of the organizational system. The abecedarium has similarities to Bacon’s method for encipherment—in this case using a three or four letter string for identification. Yet, Bacon’s abecedarium remains fundamentally different from the real character, however. While the former is merely a language game intended to help organize thought within instituted social networks, the character would be a real philosophical language that would provide keys to the secrets of nature and a basis for a universal natural philosophy. The latter he sees in terms of a broadly humanist legacy of the sixteenth century, a project in which both Protestants (specifically Lutherans) and Jesuits have pursued as a way of reforming the church and a defense against "both extremes of religion, superstition and infidelity."

On the other side of the channel, René Descartes (1596-1650) suspected that proposals for real characters based upon the relation between images and things were deeply flawed, appropriate only in paradisical utopias like Bacon’s New Atlantis. In a 1629 letter to Mersenne, Descartes explained that the understanding of the "true philosophy" could lead to both the development of an artificial or "universal" language and "true scientific knowledge."

Et si quelqu’un avait bien expliqué quelles sont les idées simples qui sont en l’imagination des hommes, desquelles se compose tout ce qu’ils pensent, et que cela fût reçu par tout le monde, j’oserais espérer ensuite une langue universelle, fort aisée à apprendre, à prononcer et à écrire

The notion of a universal language was based upon the idea of precisely cataloging the elements of the human imagination. The great advantage of such a language would be that it would represent everything "distinctement." Yet, the great problem faced by someone who wanted to create such a language was the nature of the human imagination itself. Although separate from the mind and reason, which were the foundations of Cartesian thought, the imagination nevertheless played an important role for Descartes. As he wrote elsewhere in the Meditations, the imagination not only conceptualized external things but also considers them, "as being present by the power and internal application of my mind." Imagination, in other words, produced the illusion of presence, figures appearing so that can the person can "look upon them as present with the eyes of my mind." As a result, Descartes remains highly suspicious of the imagination because it can produce appearances that have no corresponding reality. Descartes concluded his letter to Mersenne by dismissing hopes for a universal language or a real character as only being possible in a "terrestrial paradise" or "fairyland" because of the confused nature of signification and the variation of human understanding.

Mais n’espérez pas de la voir jamais en usage; cela présuppose de grands changements en l’ordre des choses, et il faudrait que tout le Monde ne fût qu’un paradis terrestre, ce qui n’est bon à proposer que dans le pays des romans.

A universal language that would work at the level of the imagination, describing the actual "things" of the external world, could only produce uniform results in the perfection of Eden or the ideal of fiction. One should, instead, stick with the institution of geometry as a method of rationalizing nature, a divine language grounded upon the cogito’s transmission of being. Descartes ultimately remains skeptical about any possibility of using alternative language games aside from mathematics in the project of rationalizing the world.

The rather brilliant articulations of the connections between these two world ciphers of neo-Platonic secrets and mathematics made in various ways by Galileo, Bacon and Descartes, were in large part enabled by a growing sense of social, religious and political disintegration in the late sixteenth and early seventeenth century that put a strain on humanist networks of scholars working to connect various courtly foci of neo-Platonic recollection. By the mid-seventeenth century social and political collapse in the Holy Roman Empire and England had made coherent European networks of humanist scholars writing in Latin a relic of bygone days. Messages had to be processed across fragmented social, political, religious and linguistic institutions in order to establish and maintain networks, forcing a direct consideration of how to translate language codes as the basis for any sense of a coherent Republic of Letters. By comparison, questions of inclusion or exclusion from those networks according to the possession of secret knowledge seemed provincial and backward-looking. It was in the regions suffering the greatest from these processes of fragmentation in which new theories of artificial languages and codes developed to manage a process of decentralization of knowledge production and networking between various linguistic and epistemological systems.

Due to limitations of space, this paper will only briefly consider the first of these two centers, England between the 1640’s and the 1660’s. Bishop John Wilkins, Sir Thomas Urquhart, Francis Lodwick, George Dalgarno, and Cave Beck all developed projects for either universal or cryptographic languages during the period of the English Civil War and the Interregnum (1642-1660), when the absence of a king and courtly center made the authority of signification a central problem. Wilkins in particular looked back to Bacon’s notion of a ‘real character’ and the Chinese language as a model, "[As the Jesuit] Trigaultius affirms, (Histor Sinens. book I, ch. 5) that though those of China and Japan doe as much differ in their language, as the Hebrew and the Dutch, yet either of them can, by this help of a common character, as well understand the books and letters of the others, as if they were only their own," developing his own series of characters with which to do this. These projects seem to have provided an alternative direction from the more mystical and Renaissance-like interests of exiles from the Holy Roman Empire like the famous "Invisible College" founded in England around 1642 by the German-speaking Pole Samuel Hartlib and the visiting Moravian Protestant mystic and educational reformer Jan Amos Comenius (1592-1670). Moreover, Wilkins kept interest in artificial languages alive in the newly formed Royal Society after 1660, even though Robert Hooke and others mainly used his proposed universal language as a kind of cryptographic game to encode the public announcements of their scientific discoveries.

In terms of the development of the English tradition in relation to Leibniz, however, something should be said about one of Wilkins’s close associates in the formation of the Royal Society, John Wallis. Wallis served as the chief cryptographer for both parliament and the court between 1643 and 1689. In his Treatise on Algebra (1685), he notes that the famous cryptographer and mathematician Viète’s algebraic letter notation for variables (called "species") is really just a characteristic, a system of characters not unlike the artificial language projects of Wilkins and others. This insight allowed him to think of potestates algebricae (algebraic powers) as symbols in their own right, an autonomous system without any reference to a definite number. Yet, oddly enough, Wallis never published any of his work on the connections between cryptography and mathematical notation, just as Newton did not publish his work on the calculus (the source of great controversy in the 1710’s between the followers of Newton and Leibniz). Similarly, when Leibniz (aware of Wallis’s cryptographic work as early as 1668) finally does write to Wallis at the request of the elector of Hanover in 1697, asking if he will educate young Hanoverian men in the secrets of cryptography (which he compares to "calculus" in terms of method), Wallis refuses and gets a royal grant to educate his grandson in the art (William Blencowe, the first official "Decypherer" in England). While at times Wallis declares that mathematical ciphers are virtually impossible to crack because the keys can be changed at will, he also seems aware that with enough mathematical knowledge any cipher can be cracked—thus, the fears of making such knowledge public. For him, the solution is secrecy of method, constructed along the lines of national security and isolation. It is Wallis not Wilkins who leaves the greater legacy in England, and the project of a universal language is abandoned. Philosophically, a similar move can be seen in Lockean empiricism, a "don’t ask, don’t tell policy" about the secrets of nature beyond human sensory power.

The work that developed out of the English Civil War was not directly relevant for the second region in which researches on cryptography and artificial languages developed in the mid-seventeenth century, the territories of the German princes of the Holy Roman Empire in the aftermath of the Thirty Years War (Peace of Westphalia, 1648). Although chronologically later than many of the English publications, scholars in the Holy Roman Empire were not aware of the work done previously in England during the Civil War until the 1670’s. Almost all of these German scholars working on artificial languages and cryptography in the 1660’s either came from or gravitated to the region along the Main river, between the powerful Catholic bishoprics of Würtzburg and Mainz where printing had first developed in Europe during the fifteenth century. Of the four major writers, Johann Joachim Becher, Gaspar Schott, Athanasius Kircher, and Leibniz, only the latter two will be considered here. Both came out of the shattered remnants of humanist culture in the German territories, seemingly looking for ways of translating the large libraries of their fathers into something other than the private memorabilia of a lost age.

III. Athanasius Kircher

The last of nine children, Athanasius Kircher was born in Fulda in 1602, where he attended the Jesuit college. His father had an excellent library, strong in both theology and mathematics, which burned during the Thirty Years War. During the 1620’s and 1630’s, Kircher moved from university to university as a member of the Jesuit order, frequently fleeing as Protestant forces come to raze the town in which he is working. In 1631, he left the empire entirely for a three-year stint at Avignon, finally receiving an appointment to the Jesuit Collegio in Rome in 1634 to teach mathematics. Rome was perfect for Kircher, its regular communications with the imperial court in Austria allowed Kircher to exploit his connections in the empire (which in spite of the devastating war still had the best postal system in Europe) while at the same time hooking into the global correspondence network that the Jesuits had developed over the past century. Kircher actually refused an offer from Ferdinand II to take a post at the court in Vienna in the 1635, preferring the safety and stability of Rome. Between 1634 and 1680 when he died, he published 44 books (most of which were underwritten by Ferdinand III and Leopold I) and corresponded with over 760 different people around the globe.

After the Peace of Wesphalia (1648), the Holy Roman Empire essentially split into two units, the Kaiser and the Reich, all still nominally governed by the emperor but giving the German princes much more authority. Both Ferdinand III and Leopold I pursued an aggressive policy of Catholicization in Bohemia and Austria, forcing Protestants like Comenius to flee westward. Yet, these developments infuriated the Pope. Instead of being able to use the imperial framework as a broad European vehicle for propagation of the faith, Catholicism had begun to fragment along national and secular lines. The Jesuits came to play a key role in all of this, especially in the Austrian and Bohemian territories where they took over the universities of Prague and Vienna and developed a powerful network of colleges, confiscating Protestant presses and burning books along the way. This institutional framework coupled with a near-monopoly of subsidized printing presses meant that the Jesuits were a powerful force in the empire. Many humanists saw this as a positive development. In a land shattered by war, Jesuits like Kircher were the only guarantors of cosmopolitan and Latinate values. Kircher himself corresponded closely with various centers in the Holy Roman Empire, not only the Hapsburg court in Vienna but also Protestant German princes like Duke August of Brunswick (the heir of the Duke who had published the work on Trithemius) as well as his various Jesuit pupils like Gaspar Schott (1608-1666).

Moreover, Jesuits were important propagators of the new interest in mathematics as a kind of universal scientific language. Mathematics, and especially geometry, had been at the core of the Jesuit enterprise since the late sixteenth century when Clavius (1538-1612) published the first printed Latin edition of Euclid’s Elements at the Jesuit Collegio Romano. It would also be the Jesuits who would press the cause of mathematical education in the Holy Roman Empire in the mid-seventeenth century. Schott, Kircher and the Jesuits Albrecht Kurz (Albertus Curtius), Théodore Moretus, Adam Kochanski and Grégoire de St. Vincent were at the center of Ferdinand III’s efforts to promote the study of mathematics and astronomy in the empire. Kircher and Schott worked in tandem on a calculating machine using wooden rods for Ferdinand III (as well as for the young Archduke Karl Joseph of Austria) designed to simplify mathematical operations. Much of this work has been interpreted in the context of courtly diversions, and certainly some of it like the famous debate over quadrature (squaring the circle) appears in hindsight to be a rather specifically sited language game. But Ferdinand III’s interest in mathematics concerned above all the problem of rationalizing military space for the purposes of uniting an empire torn apart by war. The Jesuits latched onto this highly political desire to help garner court patronage and propagate the Catholic faith (a strategy they were also attempting to implement in the Chinese empire using a similar rationale). Mathematics, like a code, leaks in through openings in the social imaginary and proceeds to institute anew.

In his most sophisticated moments, Kircher attempted to fuse mathematics and linguistics (grammar, translation), using a methodology derived from cryptography and artificial languages. Before he died in 1657, Ferdinand III (according to Kircher) asked him to pursue the project of developing a universal language as a way of unifying the empire and extending its range of communication across the globe, the upshot of which was the "Mathematical Organ" or calculating machine. His Polygraphia Nova et Universalis (Rome: 1663), dedicated to Leopold I, contained three different systems for cryptographic writing. Two of these were essentially cipher systems cribbed from Trithemius and Vigenère respectively. The other method, however, claimed "linguarum omnium ad unam reductio." While Kircher thought his method had the potential for universal translation, it was actually based on language groupings comprehended through polyglot dictionaries. At the core of the project was a basic assumption that languages on a given continent are related to each other. His model code used a simplified version (Latin, Italian, French, Spanish and German) of the grouping for European languages that clearly relied on a polyglot dictionary for its composition. Like his contemporary Johann Becher, Kircher combined the standard polyglot dictionary with a form of numerical dictionary that had been pioneered in the 1650’s by Cave Beck to organize a series of tables of 1048 groups of words (on 32 pages marked by Roman numerals, each with 32 to 40 lines). So for example, XIII, 34 of "Dictionarium B" reads "magnitudo, grandezza, grandeur, grandeza, grösse" for greatness. The words are organized according to the alphabetical order of the initial Latin column. Kircher also gives some arbitrary signs so that cases, tenses, plurals, etc. can be added to the numbers substituted for words. At this point, Kircher has done little more than created a one-part code for going from Latin into another language. But Kircher also includes a "Dictionarium A," in which each column is ordered alphabetically and each word numbered according to its place in "Dictionarium B." The result is similar to Marconi’s code for transmitting wireless messages. As an artificial language, however, the project disappoints. It uses a limited vocabulary with strict constraints on grammar and makes no claim to helping to promote thought, except by enabling translation across national languages. Kircher has essentially updated the old polyglot dictionary of the sixteenth century for the Holy Roman Empire of the mid-seventeenth century, an empire where mathematics rather than Latin worked as a rationalizing and centralizing force for social order.

Yet, Kircher’s efforts were not all geared towards making language work like mathematics. Although he taught mathematics at the Collegio Romano at this time, his interests gravitated towards linguistics. His initial publication in Rome was the Prodromus Coptus sive aegypticaus (1636). Kircher had been interested in Egyptian hieroglyphics since his student days in the Holy Roman Empire, when he had seen an example in Speier. The Prodromus Coptus tried to crack the unsolved ‘code’ of ancient Egyptian writing in two directions. Initially, Kircher wanted to trace ancient Egyptian backward from contemporary Coptic. Kircher partnered with Pietro della Valle who had edited a Coptic-Arabic dictionary and who believed that Coptic would provide enough clues to translate hieroglyphs. The Prodromus Coptus contains a sketch of Coptic grammar, and Kircher’s Lingua Aegyptica restituta (1643), which was created in close partnership with Valle, provides a much fuller picture of Coptic. By the early 1650’s, Egyptology had become a kind of minor industry for Kircher, in theory a method for attracting patronage from pope Innocent X, who generally was ill-disposed towards the Jesuits but like his sixteenth-century predecessors enjoyed mounting obelisks in various piazzas around Rome. The Obeliscus Pamphilius (1650) was based completely on the obelisk Innocent X placed in the Forum Agonale, while the Oedipus Aegypticus (1652-4) attempted to make full translations of several different hieroglyphic texts. In producing these texts in the 1650’s, however, Kircher abandoned the initial idea (which incidentally was insightful and substantially correct) of translating backwards from Coptic in favor of using the methods of cryptanalytic word substitution to translate the hieroglyphics directly. Borrowing from Bacon’s idea of a "real character," Kircher believed that each hieroglyph stood for a philosophical concept. While this produced translations much more quickly, the results were entirely arbitrary and relatively quickly recognized as specious (notably by Leibniz). This foray into translating Egyptian has traditionally made Kircher into the brunt of jokes about the un-Enlightened and allegorical nature of Baroque Jesuit scholarship. But in many ways, Kircher’s studies laid important groundwork in terms of the insight about the relation between Coptic and Egyptian (and the diachronic nature of languages generally) as well as the virtual impossibility of cracking languages as codes—that is systems with their own unique grammar and signifier/signified relations.

Moreover, there was a second direction for translating hieroglyphs that Kircher laid out in the Prodromus Coptus, the idea that ancient Chinese was a form of ancient Egyptian. While this notion was based upon a set of equally arbitrary and false assumptions, it proved more productive. Kircher’s attempts to translate Chinese were based upon the discovery of a "Sino-Syrian Monument," now known as the Nestorian Stele. Sometime between 1623 and 1625 a nine-foot tall limestone tablet was discovered by workmen digging in the suburbs of Sian in the northwestern Chinese province of Shensi, near where the capital Ch’ang-an had been located in the Tang dynasty. The inscription consisted of a central text of around 1800 Chinese characters as well as about fifty words and names in a version of Syriac along the borders. At the top of the tablet, and the source of great excitement for the Jesuits, was an engraved cross, proving that Christianity had at some time in the remote past been introduced into China. The implications of the stone’s inscriptions boded well for the Jesuit project of accommodation, which argued that direct translations from Latin into Chinese were permissible in missionary work. If Christianity had been introduced into China during the Tang dynasty then translation of ideas between China and Europe could be justified, as Kircher and others would argue.

The inscription on the tablet told the story of a missionary who introduced Christianity into Asia in 631 and its growth under imperial patronage until the year 781 (the date of the tablet’s erection). Father Alvaro Semedo, who was probably the first Jesuit to see the actual stone in the 1620’s, described it in his Relatione delle Grande Monarchia della Cina (Rome: 1641). Yet, long before his account appeared, a Portuguese translation of the text was sent from Macao in November of 1627, this was then translated into Italian in 1631 and published as an anonymous pamphlet. Kircher had it retranslated into Latin and published in his Prodromus Coptus in 1636. He installed a rubbing of the tablet in his museum in Rome. It was thus Kircher rather than Semedo who capitalized on the inscription and created a stir about it in Europe during the late 1630’s.

Obviously, the translation that Kircher published initially was far from definitive, and he was besieged with anti-Jesuit critiques of the authenticity of the inscription and monument. About a year after the Polish Jesuit and missionary Michael Boym arrived in Rome, Kircher enlisted him and some Chinese converts to translate the rubbing he had of the tablet in November of 1654. Boym had been waiting for some time to gain an audience with Innocent X (who would eventually die in January of 1655), but the Pope’s anti-Jesuit sentiments had kept him from achieving his goals. Kircher had at this time been engaged in his project to unite papal and imperial patronage through Egyptology, so recruiting Boym for work on Chinese must have seemed a logical move for both parties. It is not altogether clear what happened in the process of creating a new translation of the stele, as Boym’s Chinese was not very good and the converts seem to have been in a somewhat limited position (both politically and perhaps in terms of their knowledge of Chinese characters), but in the final result, published in Kircher’s China Illustrata, it is Kircher’s methodology that hovers over the translation process.

Kircher used the interpretation of the "Sino-Syrian Monument" as the launching point for his major book on China, China monumentis qua sacris profanis, nec non variis naturae et artis spectaculis, aliarumque rerum memorabilium argumentis illustrata (Amsterdam: 1667) or China Illustrata as it is commonly called. As the title suggests, Kircher promised to reveal the secrets of the vast empire of China emblematically (Illustrata) through the light of its monuments. Yet, a broader conception brought the whole work together. Kircher read (and illustrated) China as an earthly embodiment of Plato’s republic, a vast, modern and populous empire ruled by philosopher-kings. He justified this move by literally bounding the book with the process of translating written Chinese—the code that gave access (neo-Platonically) to the reality of China.

None of this would be all that interesting if Kircher simply repeated the neo-Platonic Renaissance logic of translating signs to get at the book of the world. Yet, Chinese as a language made this picture more complicated than it might first appear. In China Illustrata, Kircher uses what he calls the "Triple Method of Interpretation" to translate the stele. This involves three moves. First the Chinese characters are Latinized into spoken Mandarin. Second, the literal meaning of the words is given in Latin. To do this, Kircher breaks down the tablet as if it were a code, dividing it according to a numerical grid in which each character would in theory stand for an individual word. The Latinized versions of the characters from method I are each given reference numbers so they can be utilized in combination with method two. This is, of course, based on a fundamental misunderstanding of the Chinese language as a Baconian "real character," the same mistake Kircher had made about ancient Egyptian. Finally, because methods I and II make for odd reading (since they completely ignore grammar and meanings derived from more than one character), method III is "to paraphrase the meaning of the Chinese inscription," which "avoids the word order of the Chinese whenever possible, since its syntax is strange to Europeans."

The need for the special method comes from the nature of written Chinese as, according to Kircher, "significative characters which show an entire concept in a single character." Kircher makes a complicated historical argument that places the invention of Chinese characters by Fohi as a direct descendent of the writing of Noah and the ancient Egyptians through the colonization of China by Zoroaster (the first Cham) and Hermes Trismegistos. Both Egyptian writing and by implication Chinese writing are based upon pictures of actual things and are thus natural writing in the neo-Platonist sense, emblems of the book of the world. Kircher argues, however, that the two systems are different in that while Egyptian writing expresses mysteries, Chinese writing only borrowed those characters "necessary for expressing the thoughts of the mind," that is to say Chinese is a philosophical rather than a mystic language. Kircher goes on to contend that the very structure of the characters in Chinese is logical, each one mathematically building on previous characters to express more complicated concepts.

At the end of China Illustrata, Kircher raises the problem of the double code of the Chinese language.

The Chinese language is very ambiguous and one word will often express ten or twenty different meanings depending upon the different tone with which it is pronounced. Therefore, as I have said it is very difficult and one has to spend a great deal of labor and intense study and a thousand new starts to be able to speak it. The Mandarin language is common to the entire empire and it is principally used in the court and in the judgment halls of the King. These are at Pequin and at Nanchin. This languages is used in the entire kingdom, just as Castelian is used in Spain and Tuscan in Italy. The characters are used through the entire empire as also in Japan, Korea, Cochin China and Tonchin, but the languages are very different. Hence the books and letters of Cochin China, Korea, and Tonchin are all written with the same characters, but the people cannot speak to each other. Just so the Arabic numerals are understood and used all over Europe, but with quite different pronunciations, so these characters are pronounced differently, but have the same meaning. It is one thing to know the characters and another to be able to speak Chinese. A foreigner who has a good memory and studious habits can learn to read the Chinese books, but still not be able to speak, nor to understand speech. It is necessary for the apostolic men doing God’s business to know the idiomatic language.

Kircher goes on to explain the invention of tonal notation by the Jesuit Jacob Pantoya to help in learning spoken Mandarin as well as the use of Latinized written Chinese to the same ends. Latin as well as the (mathematical) musical scale become the tools with which the Jesuits can move from the general (written Chinese characters) to the particular (local dialects). It is necessary to know both the characters in order to read and understand the Chinese past (the Nestorian Stele being the great example) as well as the tonal language so one can communicate and actually enter into the society. Characters give history, tones give access to various social institutions, only when these are used in tandem as a double code does the social-historical emerge.

The workings of the Chinese language parallel the double code of Kircher’s cryptography. Mathematics is no longer enough to rationalize the empire, for mathematics is merely a system of signs (mathema—what is learned) like any other and must be imposed upon alternate symbolic orders. It is no accident that Kircher compares Chinese characters to Arabic numerals. Like all forms of imperial knowledge mathematics literally requires encoding. As in China, a supposedly meritocratic elite must agree upon a common philosophical language ("Mandarin"), which can then be decoded in any particular situation to fit the special circumstances of local, ethnic, religious and national language games. Again the analogy is that of an aspiring empire consolidating ethnicities—Castile in Spain, Florence in Italy. It is not enough for any one person (i.e. Descartes) to make a philosophical link with the divine to institute mathematics, but science requires a network of elites trained in language like the Chinese literatti. The process must be both social and exclusive, and the literatti must be adept at coding and decoding between various language systems. Kircher, who tried to turn himself into a universal translator and central letter exchange for both the Holy Roman Empire and the far-flung Jesuit network, embodies this process of encoding as poly-mathes.

IV. Leibniz

Kircher may have been systematic about this process of network formation in practice as a polymath, but as any reader of his corpus will quickly realize, he had no coherent theory to comprehend his actions. The great theorist of the republic of codes would also come out of those regions of the Holy Roman Empire ruled by the German princes. Gottfried Wilhelm Leibniz was born in Leipzig in 1646, two years before the end of the Thirty Years War. Unlike Kircher who was constantly fleeing Swedes and Protestants during his formative years, Leibniz grew up in the aftermath of war. He was the son of a Lutheran university professor belonging to a semi-noble family, his great uncle Paul Leibniz having received a coat of arms around 1600 from Emperor Rudolph II for military service in Hungary. Yet, Leibniz, like Kircher, came out of the world of the burghers, a product of the once vital and vibrant towns of Germany. Leibniz taught himself Latin at the age of seven or eight (his father died when he was six), almost willing himself into the dying world of humanist Latin as a way of comprehending his father’s primary legacy to him, a vast library that had survived the wars of the early part of the century.

After coming of age, Leibniz gravitated southwards in search of opportunity, first to Nürnberg and later to Mainz where he worked as the secretary for the famous court minister Johann Christian von Boineburg. Like Leibniz, Boineburg was originally a Protestant, but he had converted to Catholicism for reasons of political expediency and an interest in religious reconciliation (in spite of a conditional offer to receive membership in the Paris Académie des Sciences, Leibniz never converted). Boineburg’s primary efforts, however, were geared towards the cause of raising the status of Johann Philipp von Schönborn, elector of Mainz from 1647 to 1673, within the empire at the expense of Hapsburg power. To this end, Boineburg developed a series of diplomatic schemes in the late 1660’s and 1670’s to maintain stability in central Europe, ranging from lobbying for the election of the Count Palatine Phillip Wilhelm von Neuburg as King of Poland to encouraging the French at Leibniz’s suggestion to invade Egypt as a military distraction. From 1672 to 1676, Leibniz went on a diplomatic mission to Paris and London for Boineburg, which although doing little to aid Boineburg’s efforts proved to be an extremely productive period for Leibniz. Paris and later London enabled Leibniz to meet a wide range of people engaged in various types of research and scholarly pursuits and to translate the concerns of the courts and universities of the southern German princes into a broader agenda for connecting the fragmentary elements of the Republic of Letters.

From his earliest writings, it is clear that Leibniz struggles with the paradoxical relationship between language and mathematics in the republic of codes of the empire. Philosophically, Leibniz wants both the mathematical simplicity of the cipher and the complexity of a linguistic system. The young Leibniz optimistically sees this as possible in a kind of pre-established (or previously instituted) harmony. One of the most important authors for Leibniz in these early years did not come out of the English Royal Society circles but was a major intellectual figure in the English Civil War—Thomas Hobbes. Hobbes defined human reason as "reckoning" (i.e. calculating), and the young Leibniz approved wholeheartedly of this definition in his "De Arte Combinatoria" (1666) as an easy solution to his problems.

But when the tables or categories of our art of complication have been formed, something greater will emerge. For let the first terms, of the combination of which all others consist, be designated by signs; these signs will be a kind of alphabet. It will be convenient for the signs to be as natural as possible—e.g. for one, a point; for numbers, points; for the relations of one entity to another, lines; for the varioum of angles or of extremities in lines, kinds of relations. If these are correctly and ingeniously established, this universal writing will be as easy as it is common, and will be capable of being read without any dictionary; at the same time, a fundamental knowledge of all things will be obtained. The whole of such a writing will be made of geometrical figures, as it were, and of a kind of pictures—just as the ancient Egyptians did, and the Chinese do today. Their pictures, however, are not reduced to a fixed alphabet, i.e. to letters, with the result that a tremendous strain on the memory is necessary, which is the contrary of what we propose.

Even at this point, Leibniz as an attentive reader of Schott and Kircher knew the issues current in the debates over artificial languages—an emphasis on pictorial characters or ‘geometrical figures’ modeled on Chinese and Egyptian writing, the strains produced by the code model that requires a dictionary, the desire for something that mediates between these two elements. What he imagined here, if it was anything beyond idle speculation, seems perhaps close to Morse Code (dots and dashes, a code for communication not unlike his binary) or a text that would later fascinate him, the Chinese Yijing.

Yet, things begin to get more complicated for Leibniz as he tried to actually conceptualize the process of mathematics as a combinatory language. Hobbes critiqued modern "Analysis Symbolica" or algebra as being merely an abbreviatory device, useless for the progress of mathematical thought.

But the so-called ‘symbolica,’ which is used by many scholars, who believe that it is truly analytic, is neither analytic nor synthetic. It is merely an adequate abbreviation of arithmetical calculations, and not even of geometrical ones, for it does not contribute either to the teaching or to the learning of geometry but only to the quick and succinct compilation of what was already discovered by geometricians. Even though the use of symbols may facilitate the discourse about propositions which are wide apart from each other, I am not sure whether such a symbolic discourse, when employed without the corresponding ideas of things, is indeed to be considered useful.

Leibniz’s initial response to such ideas can be found in his, "On the Demonstration of Primary Propositions" (ca. 1671-1672). The central question in this essay is whether chains of reasoning (demonstration) yield new propositions, and not merely repetition of ideas in new form. Leibniz does not frame his argument as a radical break from tradition, remaining strictly rooted in Platonic categories of recollection. He takes up Hobbes’s argument with a simple thought experiment. In the case of the equation 2x2=4 is "4" anything more than a "numerical name, whose use—afterwards—in speaking and calculating, is more economical?" No one could actually calculate without such "names or numerical signs," which would be beyond the power of memory or imagination. Mathematics as a system is prior to the individual subject and thus "4" in this case is merely a recollected calculation in the form of a sign. Yet, pace Hobbes, the process itself is profoundly useful, for "a great number of things can be comprehended in such a way as to allow one to run through many of them very quickly." He calls this type of mental process "blind thoughts," (cogitationes caecae or in French deaf thoughts "pensées sourdes"). In this way, language has an autonomous history and practice separate from the internal workings of the individual subjective imagination. Moreover, symbolic systems have a usefulness beyond the level of mere conveyors of ideas. "Reasoning and demonstration do not amplify our thoughts, but only order them," argues Leibniz, and "well-ordered combination... constitutes the light of all philosophizing." In this conception, the mind operates as a self-modifying system or self-regulating machine, at times working on language and at other times letting language pass through unmolested. All of this hedges very closely to neo-Platonism. Everything aims towards forming well-ordered chains of ideas that would aid in the recollection of truth. Mathematics provides good analogy of thought in this sense. Yet, unlike Hobbes, Leibniz remains unwilling to reduce mathematics (and by implication language) to a kind of shorthand. In these arguments, he seems to veer ever so slightly towards a more Gnostic position in which working on language has a kind of creative power (beyond Platonic recollection and reflection) unto itself.

Such insights into mathematics came at a time when Leibniz also began to read the work of the English writers on universal languages. In 1660’s, the young Leibniz was primarily familiar with the work of the Germans—Kircher, Schott, and Becher—on artificial languages and cryptography. In early 1671, he read John Wilkins and probably George Dalgarno as well, writing in 1673 to Henry Oldenburg in hopes of a Latin translation of Wilkins’s Essay (1668). He believed that Wilkins has figured out a method for developing a language both "artificial" and "philosophical," Kircher, Schott and Becher having only developed the former out of the legacy of sixteenth-century cipher. In 1672 he reached Paris, where he would begin his work on artificial languages, differential calculus (which he developed in 1675) and a calculating machine (proposed to the Royal Society in 1673). Despite working on mathematics, Leibniz’s primary interests lay with the combinatory and philosophical possibilities of language. In a letter to Duke Johann Friedrich of Hanover, written soon after arriving in Paris, Leibniz claimed,

In philosophy, I have found a means of accomplishing in all the sciences what Descartes and others have done in arithmetic and geometry through algebra and analysis, by the art of combinations, which Lullius and Father Kircher indeed cultivate, although without having seen further into some of its secrets. By this means, all composite notions in the whole world are reduced to a few simple ones as their alphabet; and by the combination of such an alphabet a way is made of finding, in time by an ordered method, all things with their theorems and whatever it is possible to investigate concerning them.

Such claims, however, were not based upon a thorough understanding of either mathematics or Cartesian philosophy. He will admit in a remarkably candid letter from 1675 that he knows of Descartes ideas primarily through the writings of disciples and that he has "not yet brought myself to read Euclid in any other way than one commonly reads novels." Christian Huygens (1629-1695) set about to remedy this defect in Leibniz’s thought by engaging him in serious discussions of mathematics and giving him access to Descartes’s manuscripts. It was in Paris that Leibniz’s work really began to reach outside of the limits of court patronage. Both Boineburg and the Elector of Mainz died while he was in Paris, and in 1676 he went to the court of Hanover, where the Duke was interested in Leibniz as the kind of individual who could rebuild an intellectual and humanist (i.e. not religiously or politically fragmented) culture out of the lands of the free German princes in the Holy Roman Empire as a remedy for declining prestige and power.

For Leibniz, the crucial questions did not arise from differences between language systems. He argued that any natural language had enough tools within it to practice natural science. Rather the problem, stated Platonically, was that different states of recollection exist within different linguistic units. Thus he wrote in 1678,

Although there are many human languages, all of them sufficiently developed to be suitable for the transmission of any science whatsoever, it is enough, I think, to consider one language: any people can in fact make discoveries and direct the sciences in its own backyard. Nevertheless, since there are certain languages in which the sciences have been much cultivated, like Latin, it would be more useful to choose one of them especially because they are mastered by the majority of the people interested in the sciences.

Yet, a revival of humanist neo-Latin in the late seventeenth century was simply not feasible, even for powerful organizations like the Jesuits. The rise of the nation-state and the use of the vernacular fragmented ideas and knowledge along national lines. Britain and France had taken advantage of this situation in which continental Latinate culture had collapsed, using their empires and centralized institutions to build a national scientific cultures. As a result, from a Hanoverian perspective, Leibniz saw a need for scientific networks that could communicate across fragmented political space and decode ideas written in the vernacular into a universal philosophical-scientific language.

How could this be accomplished? Leibniz wanted to go beyond mathematics but nevertheless still use mathematics as a temporary basis for building the new philosophical language (much like Descartes’ little shelter of conformity in the Discourse on Method). In a fragment entitled "Elementa Calculi" (April 1679), he writes,

Let there be assigned to any term its characteristic number, to be used in calculation, as the term itself is used in reasoning. I choose numbers whilst writing; in due course I will adapt other signs both to numbers and to conversation itself. For the moment, however, numbers are of the greatest use, because of their certainty and of the ease with which they can be managed, and because in this way it is evident to the eye that everything is certain and determinate in the case of concepts, as it is in the case of numbers.

In other words, numbers create the illusion of determinate concepts, which lean on the certainty of a closed and known system (mathematics). At this point, Leibniz really has two goals. First, he wants to develop a formal symbolic language for representing and verifying valid modes of inference, such as the calculus or even binary, both of which he claims to invent. Second, and more importantly, he wants to build out of this a philosophical language that actually aids in thinking, a Baconian ‘real character’ that expresses and aids in understanding the nature of reality. Cryptographically speaking, a good code is actually both, not merely the first, which is essentially a shorthand or cipher but a complete language unto itself, making decoding virtually impossible. Yet, this is exactly what Leibniz wants eventually to do, to crack and translate essential reality. As Swift (and less effectively Voltaire) would later point out, such a project ultimately degenerates into farce, but from a creative and especially poetic/literary point of view it opens up infinite possibilities.

At this point, Leibniz becomes interested in the Chinese language. While he had previously dismissed the Chinese empire as corrupt (cf. Consilium Aegyptiacum, 1671-2), he begins to see the Chinese language as a possible way out of his problems. In January of 1679, he learned of the supposed discovery in Berlin of a Clavis Sinica ("key to Chinese") by Andreas Müller (ca. 1630-1694), whose patron was the Great Elector Friedrich Wilhelm of Brandenburg. He writes to Müller through the court physician Johann Elsholz in June but receives no details in response, and it seems that Müller was having difficulties in either getting paid by the elector or in receiving permission to shop his discovery around in other courts. Only in the 1689 does Leibniz make any real progress, when he meets the Jesuit Claudio Grimaldi (1638-1712) who had actually spent time at the Qing court. During the 1690’s, Leibniz became a sinophile and one of the greatest advocates for the Jesuits’ China mission, writing several texts in support of the policies of cultural accommodation.

By the time Leibniz writes the New Essays Concerning Human Understanding (c. 1704-5), he has focused in on two aspects of Chinese that make it important as a model for a ‘real character’—its artificiality and its lack of an alphabet. Citing the Leiden Orientalist and mathematician Jacob Gool (aka. Golius), who wrote an "Additamentum" to the Jesuit Martino Martini’s (1614-1661) Novus atlas sinensis (1655), Leibniz explained that the spoken (tonal) Chinese language "was invented all at once by some ingenious man in order to bring about verbal communication between the many different peoples occupying the great land we call China, although this language might by now be changed through long usage." Chinese was an "artificial language," similar to those created by Bishop Wilkins and George Dalgarno, rather than a natural language that had developed according to chance, contingency and corruption. For Leibniz, however, the artificial part of Chinese is not the character but the mode of unifying the character (tones), which acts as a key for the ruling elite (Mandarin) who can use it to translate the particular (dialects) into the general (empire).

Leibniz is also interested in written Chinese because it lacks an alphabet. The alphabet reduces reality into twenty-six completely abstract units—each combined in different ways to enable an infinite variety of compositions. Chinese characters, on the other hand, are potentially infinite in themselves (or at least produced in numbers so large it is impossible for any human to remember them all). Leibniz did not know that these characters were themselves made up of a finite number of possible brush strokes, but after all those strokes could themselves be configured spatially in an infinite set of configurations. Yet, Leibniz saw flaws in written Chinese. It did not follow nature and thus was not a philosophical language. Nevertheless, in terms of form, Chinese would be the ideal "Universal Character" because it speaks to the eyes and can allow easy communication with remote peoples. Chinese, with its code-like duality of infinite writing and spoken key, becomes the possibility for Leibniz that a universal character can eventually be produced, a character that would make the social coherent and the lost Republic (Platonic? Humanist?) a reality.

During the period he was writing the New Essays, Leibniz most important correspondence about China and the Chinese language was with the French Jesuit Joachim Bouvet (1656-1730), who was conducting research in China on the Yijing. Bouvet believed that by examining Chinese inscriptions one could find evidence of Christianity embedded in the Chinese language. In a series of letters between 1700 and 1704, Leibniz increasingly became convinced that the Yijing was the divine prototype for his own binary system and that the ancient Chinese (but not the corrupt modern ones) had understood this, a fact evidenced by the ying and yang lines of the hexagrams.

And thus, as far as I understand, I think the substance of the ancient theology of the Chinese is intact and, purged of additional errors, can be harnessed to the great truths of the Christian religion. Fohi, the most ancient prince and philosopher of the Chinese, had understood the origin of things from unity and nothing, i.e. his mysterious figures reveal something of an analogy to Creation, containing the binary arithmetic (and yet hinting at greater things) that I rediscovered after so many thousands of years, where all numbers are written by only two notations, 0 and 1.

These sentiments would be repeated even more emphatically in one of Leibniz’s last writings Discourse on the Natural Theology of the Chinese (1716), written in the months before his death. Leibniz had at last in the Yijing/binary found the key to resolving mathematics and language for which he had searched so long. Whether this solution was a real or imagined one, a one or a zero, whether Leibniz had or had not cracked the Chinese code, finding the clavis sinica, are academic questions. In practice, Leibniz had opened mathematics to semiotics, and semiotics to infinite translation.

V. Hanoverian Successions

Locke put forward in Book II, Chapter II of his Essay Concerning Human Understanding, the idea of "voluntary signs." He argued that words are "external sensible signs" of "invisible ideas." One can only use a word if one knows what one is talking about—signifiers must have a signified because there cannot be signs of nothing. This holds true, according to Locke, even if the person using the word is merely consenting to its social meaning. Leibniz agreed in part, for he admited that however much the thought behind the word is vacuous, there is always some connection between signifier and signified. However, as he pointed out in the New Essays on Human Understanding, "a person is sometimes—oftener indeed than he thinks—a mere passer-on of thoughts, a carrier of someone else’s message, as though it were a letter." In this carrier function (Locke would call it parroting, and for him men are never parrots), the machine of language operates invisibly at a "material" rather than a "formal" level of ideas. For Leibniz, language can operate in this almost autonomous fashion, opaque rather than transparent (by virtue of the will) to the subject who uses it. While it is the "formal" level at which languages are translatable ("which is common to different languages"—Leibniz), the movement of language seems more rooted in its "material" dimension.

Locke worries, and given his perspective with good reason, about the possibility that language may at times function in this opaque, autonomous and "material" fashion. "It is a perverting the use of words, and brings unavoidable obscurity and confusion into their signification, whenever we make them stand for anything but those ideas we have in our own minds." Leibniz, on the other hand, suggests that only by grappling with this opaque quality of language will philosophical thought and the translation of ideas between languages become possible. Locke assumes that translation works automatically—either you have the idea or you do not. This allows him (as it did Hobbes, albeit in a different manner) to think of society in the abstract as an instituted unity ("God, having designed man for a sociable creature, made him not only with an inclination, and under a necessity to have fellowship with those of his own kind, but furnished him also with language, which was to be the great instrument and common tie of society"). While Leibniz’s conceptualization of "ideas" still has a flavor of Platonism to it (as does his pre-established harmony that allows little translation leaps), it leaves language as a system open to involuntary flows (a "symbolic magma" to borrow a phrase from Cornelius Castoriadis). Thus by implication, the Leibnizian formulation, which at first glance seems so totalizing, leaves the imagined social institution open to semiotic restructurings in ways that make the ideas concerning the synchronic qualities of language almost unthinkable.

At this level, cryptography becomes a creative science rather than simply a recollective and reflective one. The universal language, the ideal code, is not as much an impossible project as an endlessly creative one. Given that the goal is the reformation of the social, the project actually has direction even though it lacks an ideal telos. The imagined and idealized use of cryptography and artificial languages to define and preserve social networks and structures becomes an actual practice of semiotic reconfiguration of the social imaginary. As Leibniz wrote sometime after 1690, "finally, when the letters or other characters signify veritable letters of the alphabet, or of a language, then the art of combinations with the observations of languages leads to Cryptography, that is to say the art of making ciphers and of deciphering... In the end, the general art of species admits a thousand aspects, and Algebra contains but one." These ideas, like much of Leibniz work, exist only as an unpublished fragment, hidden from public discourse, indicative of a problematic relationship with limits, hinting at a deep crisis within the imagined social dimension of the network that would make a Republic of Codes possible. With Leibniz, the limits of the Renaissance cipher ("The Book of the World") have opened to the limitless production of code based on proliferating and rapidly changing translation games. Conserving secrets ironically remakes the world infinitely.