rep of codes – cryptography

8/6/2019 rep of codes cryptography

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The Republic of Codes

Cryptographic Theory and Scientific Networks in the SeventeenthCentury

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November 1, 1999 [Work in Progress, Not for Citation]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 anduses their materialseven if it is only to fill the foundations of newtemples, as the Athenians did after the Persian wars. By its virtuallyunlimited natural and historical connections, the signifier always goes

beyond a strict attachment to a precise signified and can lead tocompletely unexpected realms. The constitution of symbolism in realsocial and historical life has no relation to the closed andtransparent definitions of symbols found in a work of mathematics(which, moreover, can never be closed up within itself).

Cornelius Castoriadis, Linstitution imaginaire de la socit, (1975)

La plus part de nos raisonnemens, sur tout ceux qui sentremelentdans les principales veues, se font par un jeu de caracteres, comme on

joue du clavesin par coustume en partie, sans que lame en cela senapperoive assez, et forge les raisons avec reflexion. Autrement onparleroit trop lentment. Cela sert a mieux entendre comment le corpsexprime par ses propres loix tout ce qui passe dans lame. Car ce jeude caracters peut aller loin et va loin en effect, jusqu un point quonne pourroit penser des choses abstraites sans aide de caractersarbitraires.

Gottfried Wilhelm Leibniz

I. Cryptography in the Republic of Letters

Studies on cryptography tend to focus on war and the need for codesto keep secrets closed away from the prying eyes of foreigners. Thispaper will follow a different path, namely that cryptography as itdeveloped in the seventeenth century worked primarily as a tool forthe creation of social networks within a society, and cryptography as a


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science (a development rooted in the sixteenth and seventeenthcenturies) worked as a tool for imagining and instituting socialstructure. Cryptographic method, perhaps even more thatmathematics, lies at the heart of the development of the notion andpractice of "science" (scientia: knowledge) in the seventeenth century.

The Republic of Letters develops as a Republic of Codes. Unlike courtlynotions of manners, the practitioners of these codes deliberately triedto develop them into languages abstracted from social practice(calculus, logic, even law). It was the job of the polymath, the polyglotand the polyhistor to translate between such codes. This paper willlook at two Baroque polymathsAthanasius Kircher and Leibnizandtheir attempts to develop a methodical knowledge of cryptography andartificial languages as a solution to the problem of social fragmentationin the Holy Roman Empire in the aftermath of the Thirty Years War.

Both Kircher and Leibniz saw quite clearly the problem of socialfragmentation raised by war, religious disputes, the declining use ofLatin (which Kircher published in, although he frequently correspondedin the vernacular), and the increasing inability of the Hapsburgemperors to exercise power over the German princes. The emergingglobal powers of the seventeenth century, England, Holland andFrance, were gaining strength by carving up direct and indirectspheres of influence in northern Italy and Germany, and dividing up theimperial possessions of Spain and Portugalall regions formerly underthe sway of the emperor and the Hapsburg dynasty. It was once

customary to imagine the scientific revolution from the perspective ofthese emerging powers (usually in terms of national traditions). Whatthis misses, however, is the very fragmented nature of the productionof science or knowledge during this period, and the way in whichcryptography became a method for working through this problem offragmentation 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 aGerman or Italian court, albeit on a larger scale. The cryptologistsconfronted the problem of how to enable communication between

various systems of knowledge, each with their own languages, andhow to make such communications endure over time.

The cryptologist monitored the line between inclusivity and exclusivity.Careers like Kirchers or Leibnizs were based upon not only the fine artof moving and translating between various zones of knowledgeproduction but also their ability to monopolize such transfers. It was


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less important for them to actually encrypt information than tounderstand the process through which such encryption might occur.Similarly, although certain princely courts might be entertained byfantasies 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 moreimportant to develop a way of imagining their relationship to a rapidlychanging European social landscape. Theories of recombination,inclusion and exclusion far from being simple ideology enabledplanning and development of connections across fragmented socialspace.

For the purposes of clarity, this paper will make an analytic distinctionbetween codes and ciphers. As a caveat, it should be emphasized thatthis distinction operates not as an ideal categorical distinction but

precisely because of the particular institution of mathematics thatdeveloped 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 themessage according to either transposition or substitution principles.

The most common is a simple alphabetic cipher where twenty-sixletters or numbers are rearranged in order to correspond with thetraditional order of the alphabet. The cipher became widely used in theRenaissance, the fruits of a methodology that developed out of Arabictexts of algebraic theory and practice arriving from the twelfth century

onward. A cipher has no direct relationship with the actual messagecontained within the codei.e. it is a substitution or transpositionsystem applied to the superficial form of writing. Ciphers are relativelyeasy to crack based on principles derived from a general knowledge ofthe underlying language because all that is necessary is to use letterfrequencies to discover the mathematical basis of the cipher and crackit in one fell swoop. Even the most complex mathematical algorithmickeys remain vulnerable to this process of decodingan argument firstmade by Franois Vite (1540-1603) in the late sixteenth century.

A code on the other hand works out of the words and phrases of thelanguage and requires a dictionary to crack. The classic example is theuse of encrypted Navajo during World War II as a code. Theunavailability of dictionaries made cracking the code a kind oftranslation project equivalent to reading ancient Egyptian without theRosetta Stone. More commonly, a numerical code substitutes a stringof four or five numbers for each word, which requires two dictionaries


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(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 wordfrequencies and grammar. The problem with a code is that it is harderto change over time because to enable a code system to function, bothparties need the encoding and decoding dictionaries. As a result, codes

are easier to crack over time because they require a kind of culture todevelop around them, while the cipher key or formula can be changedrapidly to frustrate efforts at decipherment.

The sixteenth century was a golden age for the development ofmethodologies for producing ciphers. The French diplomat Blaise deVigenre (1523-1596) in his Traict des chiffres (1586) compiled anddeveloped many of the most common methods of cipher, whileGiambattista della Porta (1535-1615) founded the Accademia deiSecreti in Naples that connected the Renaissance study of the

"secrets" of nature to cryptographic method. Much of this flourishingwas the result of the work of the abbot Johannes Trithemius (1462-1516). While attending the University at Heidelberg, Trithemiusresolved to become a Benedictine monk in 1482 and within a littlemore than a year he became abbot of Sponheim (subsequentlybecoming the abbot at Wrzburg in 1506). Sponheim was not exactly acenter of activity when Trithemius arrived, having reached a low pointof four members in the 1450s, and Trithemius began a campaign inthe 1480s to build it up as a center for learning, constructing a guestwing to house visiting northern humanists and collecting a large library

(from 48 to 2000 volumes). In keeping with this concern to putSponheim on the map of humanist letter and travel networks, hiswritings articulate a number of systems for secret writing based onciphers, communication over distance (smoke signals, etc.), languagelearning (memory arts for Latin), and finally occult and semi-occultmethods of psychic communication. Ironically, Trithemius becomesfamous because a letter he sends describing this project was neverdelivered and leaked out into the broader Republic of Letters. Histreatise circulated in manuscript form for much of the sixteenthcentury until it was finally printed by Protestants in Frankfurt in 1606

(the great book center of the Holy Roman Empire until thedevastations of the Thirty Years War) and promptly indexed by Romeand the Spanish Inquisition.

The range of interests of Trithemius in terms of language and thenotion of secrets is typical for many sixteenth-century writers on thesubject. In particular, most exhibit a simultaneous interest in


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encrypting language while at the same time using it to build socialnetworks (especially teaching Latin) and open up the "secrets" ofnature. Part of this stems from the kinds of problems resulting fromattempts 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 humanistsolution to such problems was to build a series of letter and socialnetworks by teaching at several different institutions both inside andoutside of the empire and maintaining an extensive correspondence inLatin. While methods like those pioneered by Trithemius lay behind thetheories of this first manifestation of the Republic of Letters, aconsolidated imperial postal system managed by the Taxis (developedfrom 1490-1516 for emperor Maximilian I) and the polyglot versions ofthe neo-Latin dictionary of Calepin were the key technologies thatallowed 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 aslearned discourses based upon maintaining a coherent field ofknowledge, referring back to a classical corpus while at the same timekeeping the network current on the latest products of the ever-churning presses and arranging access to copies. The good scholar hada large Stammbch filled with names and details about friends andcontacts made during his travels, whom he could correspond with andreach 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 reformof logic, all in the service of constructing a coherent social imaginaryfor empire and republic. Princes and aristocrats amassed largecollections of books, curiosities and natural rarities, to demonstrate theimportance of their court as a nodal point of knowledge and society.

This is the social and intellectual world that provoked such skepticismin Montaigne, having experienced it in his fathers house during themid-sixteenth century.

Trithemius was more interested in steganography than cryptography.

The methods of steganography ("hidden writing") conceal theexistence of a message, so that a secret communication may appearas a picture or a piece of writing on an innocuous subject (ex. everyfourth letter of a poem when combined in order gives a message).Cryptography ("secret writing") does not necessarily conceal theexistence of a message but instead makes it unintelligible through theuse of a cipher or code, and it is the practice of cryptography that was


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of prime interest to princes and popes who required messagesenciphered and deciphered. Conversely, steganography had more tosay to the general interests of the sixteenth-century Republic ofLetters. The neo-Platonist scholars of the Renaissance thought of theproduction of knowledge in terms of reading the book of the world. In a

realist sense, Gods signs were literally everywhere in nature, so thatsomeone like the famous physician Paracelsus (1493-1541) couldargue that "the stars in heaven must be taken together in order thatwe may read the sentence in the firmament. It is like a letter that hasbeen sent to us from a hundred miles off, and in which the writersmind speaks to us." Paracelsus advocated something called thedoctrine of signatures, which claimed that the sentences of the starsand other earthly things do not reveal themselves in their entirety butas divine signatures. Conversely, so the theory went, it should bepossible 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 Godsgreat 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 somewhatdivided between the academic steganography of the Republic ofLetters and the practical use of ciphers for preserving secrecy withinthe networks of letter exchange that spanned Europe. Steganographycould be held up as a method for making the work of various scholarson the secrets of the book of nature cosmologically coherent (a

linguistic code known among scholars and used as a source of culturalcapital), along the lines of Giambattista della Portas Accademia deiSecreti. Meanwhile, princes and popes needed actual cryptographers(preferably mathematicians) to create and crack ciphers, in order tokeep their court politically central within the correspondence networksof Europe. In other words, the social system addressed by bothpractices was in many ways the same (although as early as the 1520sErasmus was complaining of businessmen using the letter system forvulgar purposesi.e. not recollection, neither politics or scientia), butthe points of entry were radically different. Nevertheless both court

and republic depended on each other, a relationship nicelyemblematized in the parallel markings of the cipher and the doubleprocess of enciphering and deciphering. The tension, pointed to by theskeptics, between the function and the meaning of cipher becameincreasingly bipolar and subjected to strains, not only the dreadedvulgar commerce but also religious and social fragmentation, which itproved unequipped to handle.


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II. From Cipher to Code

Galileos often-repeated phrase that the Book of Nature was written inthe "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 theidea of deciphering the Book of Nature, which meant that the methodsof cryptography developed in the sixteenth century became extremelyimportant to the development of scientific practice in the seventeenthcentury. This was not simply steganography, however, for the"signatures" were themselves only accessible through geometry (andalgebra) rather than being directly revealed in language (as forexample in Kabbalah). A gap existed in the relation between thelanguage of the letter and the methods of the mathematician. Solving

this gap required a kind of code that could translate between the twosystems.

In his Of the proficience and advancement of Learning, divine andhuman (London: 1605), Francis Bacon (1561-1626) warned against thefalse appearances of things imposed by words. Bacon expressed hissuspicion of both language (verba) and the imagination as separatefrom 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 andcircumvent this problem, Bacon suggested that the corruptions ofspoken language might be repaired through a careful attention tolanguage and in particular the science of grammar, for "in regards ofthe rawness and unskillfulness of the handes, through which theypasse, the greatest Matters, are many times carryed in the weakestCyphars." Bacon criticized Aristotles contention (De interpretatione, I,i, 16a3-8 and Plato in the Phaedrus, 274B-278B) that "Words are theimages of cogitations, and letters are the images of words," or thatwriting is but an image of spoken language (Bacons "words"). Bacon

contended that writing does not require words and that both primitivesign language and the highly advanced Chinese system of characterschallenge this notion, "we understand further that it is the use of Chinaand the kingdoms of the high Levant [the Far East] to write inCharacters Real, which express neither letters nor words in gross, but

Things or Notions; insomuch as countries and provinces, whichunderstand not one anothers language, can nevertheless read one


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anothers writings, because the characters are accepted moregenerally than the languages do extend; and therefore they have avast multitude of characters; as many, I suppose as radical words." Thelanguage 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 standardfor language, a remedy for the debased moneys in current circulation.According to Bacon, the "broken" relationship between words andthings must be repaired and "reintegrated" as much as possiblethrough a science of grammar. Because of this Bacon expressesinterest elsewhere in trying to develop an alphabet of nature("abecedarium naturae"), which would help to organize knowledge butwithout any particular reference to the truth of the organizationalsystem. The abecedarium has similarities to Bacons method forenciphermentin this case using a three or four letter string for

identification. Yet, Bacons abecedarium remains fundamentallydifferent from the real character, however. While the former is merelya language game intended to help organize thought within institutedsocial networks, the character would be a real philosophical languagethat would provide keys to the secrets of nature and a basis for auniversal natural philosophy. The latter he sees in terms of a broadlyhumanist legacy of the sixteenth century, a project in which bothProtestants (specifically Lutherans) and Jesuits have pursued as a wayof reforming the church and a defense against "both extremes ofreligion, superstition and infidelity."

On the other side of the channel, Ren Descartes (1596-1650)suspected that proposals for real characters based upon the relationbetween images and things were deeply flawed, appropriate only inparadisical utopias like Bacons New Atlantis. In a 1629 letter toMersenne, Descartes explained that the understanding of the "truephilosophy" could lead to both the development of an artificial or"universal" language and "true scientific knowledge."

Et si quelquun avait bien expliqu quelles sont les ides simples qui

sont en limagination des hommes, desquelles se compose tout cequils pensent, et que cela ft reu par tout le monde, joserais esprerensuite une langue universelle, fort aise apprendre, prononcer et crire

The notion of a universal language was based upon the idea ofprecisely cataloging the elements of the human imagination. The great


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advantage of such a language would be that it would representeverything "distinctement." Yet, the great problem faced by someonewho wanted to create such a language was the nature of the humanimagination itself. Although separate from the mind and reason, whichwere the foundations of Cartesian thought, the imagination

nevertheless played an important role for Descartes. As he wroteelsewhere in the Meditations, the imagination not only conceptualizedexternal things but also considers them, "as being present by thepower and internal application of my mind." Imagination, in otherwords, produced the illusion of presence, figures appearing so that canthe person can "look upon them as present with the eyes of my mind."As a result, Descartes remains highly suspicious of the imaginationbecause it can produce appearances that have no correspondingreality. Descartes concluded his letter to Mersenne by dismissinghopes for a universal language or a real character as only being

possible in a "terrestrial paradise" or "fairyland" because of theconfused nature of signification and the variation of humanunderstanding.

Mais nesprez pas de la voir jamais en usage; cela prsuppose degrands changements en lordre des choses, et il faudrait que tout leMonde ne ft quun paradis terrestre, ce qui nest bon proposer quedans 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 produceuniform results in the perfection of Eden or the ideal of fiction. Oneshould, instead, stick with the institution of geometry as a method ofrationalizing nature, a divine language grounded upon the cogitostransmission of being. Descartes ultimately remains skeptical aboutany possibility of using alternative language games aside frommathematics in the project of rationalizing the world.

The rather brilliant articulations of the connections between these twoworld ciphers of neo-Platonic secrets and mathematics made in various

ways by Galileo, Bacon and Descartes, were in large part enabled by agrowing sense of social, religious and political disintegration in the latesixteenth and early seventeenth century that put a strain on humanistnetworks of scholars working to connect various courtly foci of neo-Platonic recollection. By the mid-seventeenth century social andpolitical collapse in the Holy Roman Empire and England had madecoherent European networks of humanist scholars writing in Latin a


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relic of bygone days. Messages had to be processed across fragmentedsocial, political, religious and linguistic institutions in order to establishand maintain networks, forcing a direct consideration of how totranslate language codes as the basis for any sense of a coherentRepublic of Letters. By comparison, questions of inclusion or exclusion

from those networks according to the possession of secret knowledgeseemed provincial and backward-looking. It was in the regionssuffering the greatest from these processes of fragmentation in whichnew theories of artificial languages and codes developed to manage aprocess of decentralization of knowledge production and networkingbetween various linguistic and epistemological systems.

Due to limitations of space, this paper will only briefly consider the firstof these two centers, England between the 1640s and the 1660s.Bishop John Wilkins, Sir Thomas Urquhart, Francis Lodwick, George

Dalgarno, and Cave Beck all developed projects for either universal orcryptographic languages during the period of the English Civil War andthe Interregnum (1642-1660), when the absence of a king and courtlycenter made the authority of signification a central problem. Wilkins inparticular looked back to Bacons notion of a real character and theChinese language as a model, "[As the Jesuit] Trigaultius affirms,(Histor Sinens. book I, ch. 5) that though those of China and Japan doeas much differ in their language, as the Hebrew and the Dutch, yeteither of them can, by this help of a common character, as wellunderstand the books and letters of the others, as if they were only

their own," developing his own series of characters with which to dothis. These projects seem to have provided an alternative directionfrom the more mystical and Renaissance-like interests of exiles fromthe Holy Roman Empire like the famous "Invisible College" founded inEngland around 1642 by the German-speaking Pole Samuel Hartlib andthe visiting Moravian Protestant mystic and educational reformer JanAmos Comenius (1592-1670). Moreover, Wilkins kept interest inartificial languages alive in the newly formed Royal Society after 1660,even though Robert Hooke and others mainly used his proposeduniversal 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 toLeibniz, however, something should be said about one of Wilkinssclose associates in the formation of the Royal Society, John Wallis.Wallis served as the chief cryptographer for both parliament and thecourt between 1643 and 1689. In his Treatise on Algebra (1685), he


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notes that the famous cryptographer and mathematician Vitesalgebraic letter notation for variables (called "species") is really just acharacteristic, a system of characters not unlike the artificial languageprojects of Wilkins and others. This insight allowed him to think ofpotestates 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 theconnections between cryptography and mathematical notation, just asNewton did not publish his work on the calculus (the source of greatcontroversy in the 1710s between the followers of Newton andLeibniz). Similarly, when Leibniz (aware of Walliss cryptographic workas early as 1668) finally does write to Wallis at the request of theelector of Hanover in 1697, asking if he will educate young Hanoverianmen in the secrets of cryptography (which he compares to "calculus" interms of method), Wallis refuses and gets a royal grant to educate his

grandson in the art (William Blencowe, the first official "Decypherer" inEngland). While at times Wallis declares that mathematical ciphers arevirtually impossible to crack because the keys can be changed at will,he also seems aware that with enough mathematical knowledge anycipher can be crackedthus, the fears of making such knowledgepublic. For him, the solution is secrecy of method, constructed alongthe lines of national security and isolation. It is Wallis not Wilkins wholeaves the greater legacy in England, and the project of a universallanguage is abandoned. Philosophically, a similar move can be seen inLockean empiricism, a "dont ask, dont tell policy" about the secrets of

nature beyond human sensory power.

The work that developed out of the English Civil War was not directlyrelevant for the second region in which researches on cryptographyand artificial languages developed in the mid-seventeenth century, theterritories of the German princes of the Holy Roman Empire in theaftermath 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 donepreviously in England during the Civil War until the 1670s. Almost all

of these German scholars working on artificial languages andcryptography in the 1660s either came from or gravitated to theregion along the Main river, between the powerful Catholic bishopricsof Wrtzburg and Mainz where printing had first developed in Europeduring the fifteenth century. Of the four major writers, Johann JoachimBecher, Gaspar Schott, Athanasius Kircher, and Leibniz, only the lattertwo will be considered here. Both came out of the shattered remnants


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of humanist culture in the German territories, seemingly looking forways of translating the large libraries of their fathers into somethingother 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 excellentlibrary, strong in both theology and mathematics, which burned duringthe Thirty Years War. During the 1620s and 1630s, Kircher movedfrom university to university as a member of the Jesuit order,frequently fleeing as Protestant forces come to raze the town in whichhe is working. In 1631, he left the empire entirely for a three-year stintat Avignon, finally receiving an appointment to the Jesuit Collegio inRome in 1634 to teach mathematics. Rome was perfect for Kircher, its

regular communications with the imperial court in Austria allowedKircher to exploit his connections in the empire (which in spite of thedevastating war still had the best postal system in Europe) while at thesame time hooking into the global correspondence network that the

Jesuits had developed over the past century. Kircher actually refusedan offer from Ferdinand II to take a post at the court in Vienna in the1635, preferring the safety and stability of Rome. Between 1634 and1680 when he died, he published 44 books (most of which wereunderwritten by Ferdinand III and Leopold I) and corresponded withover 760 different people around the globe.

After the Peace of Wesphalia (1648), the Holy Roman Empireessentially split into two units, the Kaiser and the Reich, all stillnominally governed by the emperor but giving the German princesmuch more authority. Both Ferdinand III and Leopold I pursued anaggressive policy of Catholicization in Bohemia and Austria, forcingProtestants like Comenius to flee westward. Yet, these developmentsinfuriated the Pope. Instead of being able to use the imperialframework 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 theAustrian and Bohemian territories where they took over theuniversities of Prague and Vienna and developed a powerful network ofcolleges, confiscating Protestant presses and burning books along theway. This institutional framework coupled with a near-monopoly ofsubsidized printing presses meant that the Jesuits were a powerfulforce in the empire. Many humanists saw this as a positive


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development. In a land shattered by war, Jesuits like Kircher were theonly guarantors of cosmopolitan and Latinate values. Kircher himselfcorresponded closely with various centers in the Holy Roman Empire,not only the Hapsburg court in Vienna but also Protestant Germanprinces like Duke August of Brunswick (the heir of the Duke who had

published the work on Trithemius) as well as his various Jesuit pupilslike Gaspar Schott (1608-1666).

Moreover, Jesuits were important propagators of the new interest inmathematics as a kind of universal scientific language. Mathematics,and especially geometry, had been at the core of the Jesuit enterprisesince the late sixteenth century when Clavius (1538-1612) publishedthe first printed Latin edition of Euclids Elements at the Jesuit CollegioRomano. It would also be the Jesuits who would press the cause ofmathematical education in the Holy Roman Empire in the mid-

seventeenth century. Schott, Kircher and the Jesuits Albrecht Kurz(Albertus Curtius), Thodore Moretus, Adam Kochanski and Grgoire deSt. Vincent were at the center of Ferdinand IIIs efforts to promote thestudy of mathematics and astronomy in the empire. Kircher and Schottworked in tandem on a calculating machine using wooden rods forFerdinand III (as well as for the young Archduke Karl Joseph of Austria)designed to simplify mathematical operations. Much of this work hasbeen interpreted in the context of courtly diversions, and certainlysome of it like the famous debate over quadrature (squaring the circle)appears in hindsight to be a rather specifically sited language game.

But Ferdinand IIIs interest in mathematics concerned above all theproblem of rationalizing military space for the purposes of uniting anempire torn apart by war. The Jesuits latched onto this highly politicaldesire to help garner court patronage and propagate the Catholic faith(a strategy they were also attempting to implement in the Chineseempire using a similar rationale). Mathematics, like a code, leaks inthrough openings in the social imaginary and proceeds to instituteanew.

In his most sophisticated moments, Kircher attempted to fuse

mathematics and linguistics (grammar, translation), using amethodology derived from cryptography and artificial languages.Before he died in 1657, Ferdinand III (according to Kircher) asked himto pursue the project of developing a universal language as a way ofunifying the empire and extending its range of communication acrossthe globe, the upshot of which was the "Mathematical Organ" orcalculating machine. His Polygraphia Nova et Universalis (Rome: 1663),


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dedicated to Leopold I, contained three different systems forcryptographic writing. Two of these were essentially cipher systemscribbed from Trithemius and Vigenre respectively. The other method,however, claimed "linguarum omnium ad unam reductio." WhileKircher thought his method had the potential for universal translation,

it was actually based on language groupings comprehended throughpolyglot dictionaries. At the core of the project was a basic assumptionthat languages on a given continent are related to each other. Hismodel code used a simplified version (Latin, Italian, French, Spanishand German) of the grouping for European languages that clearlyrelied on a polyglot dictionary for its composition. Like hiscontemporary Johann Becher, Kircher combined the standard polyglotdictionary with a form of numerical dictionary that had been pioneeredin the 1650s by Cave Beck to organize a series of tables of 1048groups 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, grsse" for greatness.

The words are organized according to the alphabetical order of theinitial Latin column. Kircher also gives some arbitrary signs so thatcases, tenses, plurals, etc. can be added to the numbers substitutedfor words. At this point, Kircher has done little more than created aone-part code for going from Latin into another language. But Kircheralso includes a "Dictionarium A," in which each column is orderedalphabetically and each word numbered according to its place in"Dictionarium B." The result is similar to Marconis code for

transmitting wireless messages. As an artificial language, however, theproject disappoints. It uses a limited vocabulary with strict constraintson grammar and makes no claim to helping to promote thought,except by enabling translation across national languages. Kircher hasessentially updated the old polyglot dictionary of the sixteenth centuryfor the Holy Roman Empire of the mid-seventeenth century, an empirewhere mathematics rather than Latin worked as a rationalizing andcentralizing force for social order.

Yet, Kirchers efforts were not all geared towards making language

work like mathematics. Although he taught mathematics at theCollegio Romano at this time, his interests gravitated towardslinguistics. His initial publication in Rome was the Prodromus Coptussive aegypticaus (1636). Kircher had been interested in Egyptianhieroglyphics since his student days in the Holy Roman Empire, whenhe had seen an example in Speier. The Prodromus Coptus tried tocrack the unsolved code of ancient Egyptian writing in two directions.


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Initially, Kircher wanted to trace ancient Egyptian backward fromcontemporary Coptic. Kircher partnered with Pietro della Valle who hadedited a Coptic-Arabic dictionary and who believed that Coptic wouldprovide enough clues to translate hieroglyphs. The Prodromus Coptuscontains a sketch of Coptic grammar, and Kirchers Lingua Aegyptica

restituta (1643), which was created in close partnership with Valle,provides a much fuller picture of Coptic. By the early 1650s,Egyptology had become a kind of minor industry for Kircher, in theorya method for attracting patronage from pope Innocent X, whogenerally was ill-disposed towards the Jesuits but like his sixteenth-century predecessors enjoyed mounting obelisks in various piazzasaround Rome. The Obeliscus Pamphilius (1650) was based completelyon the obelisk Innocent X placed in the Forum Agonale, while theOedipus Aegypticus (1652-4) attempted to make full translations ofseveral different hieroglyphic texts. In producing these texts in the

1650s, however, Kircher abandoned the initial idea (which incidentallywas insightful and substantially correct) of translating backwards fromCoptic in favor of using the methods of cryptanalytic word substitutionto translate the hieroglyphics directly. Borrowing from Bacons idea ofa "real character," Kircher believed that each hieroglyph stood for aphilosophical concept. While this produced translations much morequickly, the results were entirely arbitrary and relatively quicklyrecognized as specious (notably by Leibniz). This foray into translatingEgyptian has traditionally made Kircher into the brunt of jokes aboutthe un-Enlightened and allegorical nature of Baroque Jesuit

scholarship. But in many ways, Kirchers studies laid importantgroundwork in terms of the insight about the relation between Copticand Egyptian (and the diachronic nature of languages generally) aswell as the virtual impossibility of cracking languages as codesthat issystems with their own unique grammar and signifier/signifiedrelations.

Moreover, there was a second direction for translating hieroglyphs thatKircher laid out in the Prodromus Coptus, the idea that ancient Chinesewas a form of ancient Egyptian. While this notion was based upon a set

of equally arbitrary and false assumptions, it proved more productive.Kirchers attempts to translate Chinese were based upon the discoveryof a "Sino-Syrian Monument," now known as the Nestorian Stele.Sometime between 1623 and 1625 a nine-foot tall limestone tabletwas discovered by workmen digging in the suburbs of Sian in thenorthwestern Chinese province of Shensi, near where the capitalChang-an had been located in the Tang dynasty. The inscription


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consisted of a central text of around 1800 Chinese characters as wellas about fifty words and names in a version of Syriac along theborders. At the top of the tablet, and the source of great excitementfor the Jesuits, was an engraved cross, proving that Christianity had atsome time in the remote past been introduced into China. The

implications of the stones inscriptions boded well for the Jesuit projectof accommodation, which argued that direct translations from Latininto Chinese were permissible in missionary work. If Christianity hadbeen introduced into China during the Tang dynasty then translation ofideas between China and Europe could be justified, as Kircher andothers would argue.

The inscription on the tablet told the story of a missionary whointroduced Christianity into Asia in 631 and its growth under imperialpatronage until the year 781 (the date of the tablets erection). Father

Alvaro Semedo, who was probably the first Jesuit to see the actualstone in the 1620s, described it in his Relatione delle GrandeMonarchia della Cina (Rome: 1641). Yet, long before his accountappeared, a Portuguese translation of the text was sent from Macao inNovember of 1627, this was then translated into Italian in 1631 andpublished as an anonymous pamphlet. Kircher had it retranslated intoLatin and published in his Prodromus Coptus in 1636. He installed arubbing of the tablet in his museum in Rome. It was thus Kircher ratherthan Semedo who capitalized on the inscription and created a stirabout it in Europe during the late 1630s.

Obviously, the translation that Kircher published initially was far fromdefinitive, and he was besieged with anti-Jesuit critiques of theauthenticity of the inscription and monument. About a year after thePolish Jesuit and missionary Michael Boym arrived in Rome, Kircherenlisted him and some Chinese converts to translate the rubbing hehad of the tablet in November of 1654. Boym had been waiting forsome time to gain an audience with Innocent X (who would eventuallydie in January of 1655), but the Popes anti-Jesuit sentiments had kepthim 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 logicalmove for both parties. It is not altogether clear what happened in theprocess of creating a new translation of the stele, as Boyms Chinesewas not very good and the converts seem to have been in a somewhatlimited position (both politically and perhaps in terms of theirknowledge of Chinese characters), but in the final result, published in


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Kirchers China Illustrata, it is Kirchers methodology that hovers overthe translation process.

Kircher used the interpretation of the "Sino-Syrian Monument" as thelaunching point for his major book on China, China monumentis qua

sacris profanis, nec non variis naturae et artis spectaculis, aliarumquererum memorabilium argumentis illustrata (Amsterdam: 1667) orChina Illustrata as it is commonly called. As the title suggests, Kircherpromised to reveal the secrets of the vast empire of Chinaemblematically (Illustrata) through the light of its monuments. Yet, abroader conception brought the whole work together. Kircher read (andillustrated) China as an earthly embodiment of Platos republic, a vast,modern and populous empire ruled by philosopher-kings. He justifiedthis move by literally bounding the book with the process of translatingwritten Chinesethe code that gave access (neo-Platonically) to the

reality of China.

None of this would be all that interesting if Kircher simply repeated theneo-Platonic Renaissance logic of translating signs to get at the book ofthe world. Yet, Chinese as a language made this picture morecomplicated than it might first appear. In China Illustrata, Kircher useswhat he calls the "Triple Method of Interpretation" to translate thestele. This involves three moves. First the Chinese characters areLatinized into spoken Mandarin. Second, the literal meaning of thewords 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 eachcharacter would in theory stand for an individual word. The Latinizedversions of the characters from method I are each given referencenumbers so they can be utilized in combination with method two. Thisis, of course, based on a fundamental misunderstanding of the Chineselanguage as a Baconian "real character," the same mistake Kircher hadmade about ancient Egyptian. Finally, because methods I and II makefor odd reading (since they completely ignore grammar and meaningsderived from more than one character), method III is "to paraphrasethe meaning of the Chinese inscription," which "avoids the word order

of the Chinese whenever possible, since its syntax is strange toEuropeans."

The need for the special method comes from the nature of writtenChinese as, according to Kircher, "significative characters which showan entire concept in a single character." Kircher makes a complicatedhistorical argument that places the invention of Chinese characters by


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Fohi as a direct descendent of the writing of Noah and the ancientEgyptians through the colonization of China by Zoroaster (the firstCham) and Hermes Trismegistos. Both Egyptian writing and byimplication Chinese writing are based upon pictures of actual thingsand are thus natural writing in the neo-Platonist sense, emblems of the

book of the world. Kircher argues, however, that the two systems aredifferent in that while Egyptian writing expresses mysteries, Chinesewriting only borrowed those characters "necessary for expressing thethoughts of the mind," that is to say Chinese is a philosophical ratherthan a mystic language. Kircher goes on to contend that the verystructure of the characters in Chinese is logical, each onemathematically building on previous characters to express morecomplicated 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 oftenexpress ten or twenty different meanings depending upon the differenttone with which it is pronounced. Therefore, as I have said it is verydifficult and one has to spend a great deal of labor and intense studyand a thousand new starts to be able to speak it. The Mandarinlanguage is common to the entire empire and it is principally used inthe court and in the judgment halls of the King. These are at Pequinand at Nanchin. This languages is used in the entire kingdom, just as

Castelian is used in Spain and Tuscan in Italy. The characters are usedthrough the entire empire as also in Japan, Korea, Cochin China and

Tonchin, but the languages are very different. Hence the books andletters of Cochin China, Korea, and Tonchin are all written with thesame characters, but the people cannot speak to each other. Just sothe Arabic numerals are understood and used all over Europe, but withquite different pronunciations, so these characters are pronounceddifferently, but have the same meaning. It is one thing to know thecharacters and another to be able to speak Chinese. A foreigner whohas 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 isnecessary for the apostolic men doing Gods business to know theidiomatic language.

Kircher goes on to explain the invention of tonal notation by the JesuitJacob Pantoya to help in learning spoken Mandarin as well as the use ofLatinized written Chinese to the same ends. Latin as well as the


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(mathematical) musical scale become the tools with which the Jesuitscan move from the general (written Chinese characters) to theparticular (local dialects). It is necessary to know both the characters inorder to read and understand the Chinese past (the Nestorian Stelebeing the great example) as well as the tonal language so one can

communicate and actually enter into the society. Characters givehistory, tones give access to various social institutions, only whenthese are used in tandem as a double code does the social-historicalemerge.

The workings of the Chinese language parallel the double code ofKirchers cryptography. Mathematics is no longer enough to rationalizethe empire, for mathematics is merely a system of signs (mathemawhat is learned) like any other and must be imposed upon alternatesymbolic orders. It is no accident that Kircher compares Chinese

characters to Arabic numerals. Like all forms of imperial knowledgemathematics literally requires encoding. As in China, a supposedlymeritocratic elite must agree upon a common philosophical language("Mandarin"), which can then be decoded in any particular situation tofit the special circumstances of local, ethnic, religious and nationallanguage games. Again the analogy is that of an aspiring empireconsolidating ethnicitiesCastile in Spain, Florence in Italy. It is notenough for any one person (i.e. Descartes) to make a philosophical linkwith the divine to institute mathematics, but science requires anetwork of elites trained in language like the Chinese literatti. The

process must be both social and exclusive, and the literatti must beadept at coding and decoding between various language systems.Kircher, who tried to turn himself into a universal translator and centralletter 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 networkformation in practice as a polymath, but as any reader of his corpus

will quickly realize, he had no coherent theory to comprehend hisactions. The great theorist of the republic of codes would also comeout of those regions of the Holy Roman Empire ruled by the Germanprinces. Gottfried Wilhelm Leibniz was born in Leipzig in 1646, twoyears before the end of the Thirty Years War. Unlike Kircher who wasconstantly fleeing Swedes and Protestants during his formative years,Leibniz grew up in the aftermath of war. He was the son of a Lutheran


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university professor belonging to a semi-noble family, his great unclePaul Leibniz having received a coat of arms around 1600 from EmperorRudolph II for military service in Hungary. Yet, Leibniz, like Kircher,came out of the world of the burghers, a product of the once vital andvibrant towns of Germany. Leibniz taught himself Latin at the age of

seven or eight (his father died when he was six), almost willing himselfinto the dying world of humanist Latin as a way of comprehending hisfathers primary legacy to him, a vast library that had survived thewars of the early part of the century.

After coming of age, Leibniz gravitated southwards in search ofopportunity, first to Nrnberg and later to Mainz where he worked asthe secretary for the famous court minister Johann Christian vonBoineburg. Like Leibniz, Boineburg was originally a Protestant, but hehad converted to Catholicism for reasons of political expediency and

an interest in religious reconciliation (in spite of a conditional offer toreceive membership in the Paris Acadmie des Sciences, Leibniz neverconverted). Boineburgs primary efforts, however, were gearedtowards the cause of raising the status of Johann Philipp vonSchnborn, elector of Mainz from 1647 to 1673, within the empire atthe expense of Hapsburg power. To this end, Boineburg developed aseries of diplomatic schemes in the late 1660s and 1670s to maintainstability in central Europe, ranging from lobbying for the election of theCount Palatine Phillip Wilhelm von Neuburg as King of Poland toencouraging the French at Leibnizs suggestion to invade Egypt as a

military distraction. From 1672 to 1676, Leibniz went on a diplomaticmission to Paris and London for Boineburg, which although doing littleto aid Boineburgs efforts proved to be an extremely productive periodfor Leibniz. Paris and later London enabled Leibniz to meet a widerange of people engaged in various types of research and scholarlypursuits and to translate the concerns of the courts and universities ofthe southern German princes into a broader agenda for connecting thefragmentary 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 therepublic of codes of the empire. Philosophically, Leibniz wants both themathematical simplicity of the cipher and the complexity of a linguisticsystem. The young Leibniz optimistically sees this as possible in a kindof pre-established (or previously instituted) harmony. One of the mostimportant authors for Leibniz in these early years did not come out ofthe English Royal Society circles but was a major intellectual figure in


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the English Civil WarThomas Hobbes. Hobbes defined human reasonas "reckoning" (i.e. calculating), and the young Leibniz approvedwholeheartedly 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 beenformed, something greater will emerge. For let the first terms, of thecombination of which all others consist, be designated by signs; thesesigns will be a kind of alphabet. It will be convenient for the signs to beas natural as possiblee.g. for one, a point; for numbers, points; forthe relations of one entity to another, lines; for the varioum of anglesor of extremities in lines, kinds of relations. If these are correctly andingeniously established, this universal writing will be as easy as it iscommon, and will be capable of being read without any dictionary; atthe same time, a fundamental knowledge of all things will be obtained.

The whole of such a writing will be made of geometrical figures, as itwere, and of a kind of picturesjust as the ancient Egyptians did, andthe Chinese do today. Their pictures, however, are not reduced to afixed alphabet, i.e. to letters, with the result that a tremendous strainon the memory is necessary, which is the contrary of what we propose.

Even at this point, Leibniz as an attentive reader of Schott and Kircherknew the issues current in the debates over artificial languagesanemphasis on pictorial characters or geometrical figures modeled onChinese and Egyptian writing, the strains produced by the code model

that requires a dictionary, the desire for something that mediatesbetween these two elements. What he imagined here, if it wasanything beyond idle speculation, seems perhaps close to Morse Code(dots and dashes, a code for communication not unlike his binary) or atext that would later fascinate him, the Chinese Yijing.

Yet, things begin to get more complicated for Leibniz as he tried toactually conceptualize the process of mathematics as a combinatorylanguage. Hobbes critiqued modern "Analysis Symbolica" or algebra asbeing merely an abbreviatory device, useless for the progress of

mathematical thought.

But the so-called symbolica, which is used by many scholars, whobelieve that it is truly analytic, is neither analytic nor synthetic. It ismerely an adequate abbreviation of arithmetical calculations, and noteven of geometrical ones, for it does not contribute either to theteaching or to the learning of geometry but only to the quick and


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succinct compilation of what was already discovered by geometricians.Even though the use of symbols may facilitate the discourse aboutpropositions which are wide apart from each other, I am not surewhether such a symbolic discourse, when employed without thecorresponding ideas of things, is indeed to be considered useful.

Leibnizs initial response to such ideas can be found in his, "On theDemonstration of Primary Propositions" (ca. 1671-1672). The centralquestion 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 takesup Hobbess argument with a simple thought experiment. In the caseof the equation 2x2=4 is "4" anything more than a "numerical name,whose useafterwardsin speaking and calculating, is more

economical?" No one could actually calculate without such "names ornumerical signs," which would be beyond the power of memory orimagination. Mathematics as a system is prior to the individual subjectand thus "4" in this case is merely a recollected calculation in the formof 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 toallow one to run through many of them very quickly." He calls this typeof mental process "blind thoughts," (cogitationes caecae or in Frenchdeaf thoughts "penses sourdes"). In this way, language has anautonomous history and practice separate from the internal workings

of the individual subjective imagination. Moreover, symbolic systemshave a usefulness beyond the level of mere conveyors of ideas."Reasoning and demonstration do not amplify our thoughts, but onlyorder them," argues Leibniz, and "well-ordered combination...constitutes the light of all philosophizing." In this conception, the mindoperates as a self-modifying system or self-regulating machine, attimes working on language and at other times letting language passthrough unmolested. All of this hedges very closely to neo-Platonism.Everything aims towards forming well-ordered chains of ideas thatwould aid in the recollection of truth. Mathematics provides good

analogy of thought in this sense. Yet, unlike Hobbes, Leibniz remainsunwilling to reduce mathematics (and by implication language) to akind of shorthand. In these arguments, he seems to veer ever soslightly towards a more Gnostic position in which working on languagehas a kind of creative power (beyond Platonic recollection andreflection) unto itself.


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Such insights into mathematics came at a time when Leibniz alsobegan to read the work of the English writers on universal languages.In 1660s, the young Leibniz was primarily familiar with the work of theGermansKircher, Schott, and Becheron artificial languages andcryptography. In early 1671, he read John Wilkins and probably George

Dalgarno as well, writing in 1673 to Henry Oldenburg in hopes of aLatin translation of Wilkinss Essay (1668). He believed that Wilkins hasfigured out a method for developing a language both "artificial" and"philosophical," Kircher, Schott and Becher having only developed theformer out of the legacy of sixteenth-century cipher. In 1672 hereached Paris, where he would begin his work on artificial languages,differential calculus (which he developed in 1675) and a calculatingmachine (proposed to the Royal Society in 1673). Despite working onmathematics, Leibnizs primary interests lay with the combinatory andphilosophical possibilities of language. In a letter to Duke Johann

Friedrich of Hanover, written soon after arriving in Paris, Leibnizclaimed,

In philosophy, I have found a means of accomplishing in all thesciences what Descartes and others have done in arithmetic andgeometry through algebra and analysis, by the art of combinations,which Lullius and Father Kircher indeed cultivate, although withouthaving seen further into some of its secrets. By this means, allcomposite notions in the whole world are reduced to a few simple onesas 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 theirtheorems and whatever it is possible to investigate concerning them.

Such claims, however, were not based upon a thorough understandingof either mathematics or Cartesian philosophy. He will admit in aremarkably candid letter from 1675 that he knows of Descartes ideasprimarily through the writings of disciples and that he has "not yetbrought myself to read Euclid in any other way than one commonlyreads novels." Christian Huygens (1629-1695) set about to remedy thisdefect in Leibnizs thought by engaging him in serious discussions of

mathematics and giving him access to Descartess manuscripts. It wasin Paris that Leibnizs work really began to reach outside of the limitsof court patronage. Both Boineburg and the Elector of Mainz died whilehe was in Paris, and in 1676 he went to the court of Hanover, wherethe Duke was interested in Leibniz as the kind of individual who couldrebuild an intellectual and humanist (i.e. not religiously or politicallyfragmented) culture out of the lands of the free German princes in the


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Holy Roman Empire as a remedy for declining prestige and power.

For Leibniz, the crucial questions did not arise from differencesbetween language systems. He argued that any natural language hadenough tools within it to practice natural science. Rather the problem,

stated Platonically, was that different states of recollection exist withindifferent linguistic units. Thus he wrote in 1678,

Although there are many human languages, all of them sufficientlydeveloped to be suitable for the transmission of any sciencewhatsoever, it is enough, I think, to consider one language: any peoplecan in fact make discoveries and direct the sciences in its ownbackyard. Nevertheless, since there are certain languages in which thesciences have been much cultivated, like Latin, it would be more usefulto 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 centurywas simply not feasible, even for powerful organizations like the

Jesuits. The rise of the nation-state and the use of the vernacularfragmented ideas and knowledge along national lines. Britain andFrance had taken advantage of this situation in which continentalLatinate culture had collapsed, using their empires and centralizedinstitutions to build a national scientific cultures. As a result, from aHanoverian perspective, Leibniz saw a need for scientific networks that

could communicate across fragmented political space and decodeideas written in the vernacular into a universal philosophical-scientificlanguage.

How could this be accomplished? Leibniz wanted to go beyondmathematics but nevertheless still use mathematics as a temporarybasis for building the new philosophical language (much like Descarteslittle shelter of conformity in the Discourse on Method). In a fragmententitled "Elementa Calculi" (April 1679), he writes,

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


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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 andverifying valid modes of inference, such as the calculus or even binary,both of which he claims to invent. Second, and more importantly, hewants to build out of this a philosophical language that actually aids inthinking, a Baconian real character that expresses and aids inunderstanding the nature of reality. Cryptographically speaking, a goodcode is actually both, not merely the first, which is essentially ashorthand or cipher but a complete language unto itself, makingdecoding virtually impossible. Yet, this is exactly what Leibniz wantseventually to do, to crack and translate essential reality. As Swift (and

less effectively Voltaire) would later point out, such a project ultimatelydegenerates into farce, but from a creative and especiallypoetic/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 Chineselanguage as a possible way out of his problems. In January of 1679, helearned of the supposed discovery in Berlin of a Clavis Sinica ("key toChinese") by Andreas Mller (ca. 1630-1694), whose patron was the

Great Elector Friedrich Wilhelm of Brandenburg. He writes to Mllerthrough the court physician Johann Elsholz in June but receives nodetails in response, and it seems that Mller was having difficulties ineither getting paid by the elector or in receiving permission to shop hisdiscovery around in other courts. Only in the 1689 does Leibniz makeany real progress, when he meets the Jesuit Claudio Grimaldi (1638-1712) who had actually spent time at the Qing court. During the1690s, Leibniz became a sinophile and one of the greatest advocatesfor the Jesuits China mission, writing several texts in support of thepolicies of cultural accommodation.

By the time Leibniz writes the New Essays Concerning HumanUnderstanding (c. 1704-5), he has focused in on two aspects ofChinese that make it important as a model for a real characteritsartificiality and its lack of an alphabet. Citing the Leiden Orientalist andmathematician Jacob Gool (aka. Golius), who wrote an "Additamentum"to the Jesuit Martino Martinis (1614-1661) Novus atlas sinensis (1655),


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Leibniz explained that the spoken (tonal) Chinese language "wasinvented all at once by some ingenious man in order to bring aboutverbal communication between the many different peoples occupyingthe great land we call China, although this language might by now bechanged through long usage." Chinese was an "artificial language,"

similar to those created by Bishop Wilkins and George Dalgarno, ratherthan a natural language that had developed according to chance,contingency and corruption. For Leibniz, however, the artificial part ofChinese is not the character but the mode of unifying the character(tones), which acts as a key for the ruling elite (Mandarin) who can useit to translate the particular (dialects) into the general (empire).

Leibniz is also interested in written Chinese because it lacks analphabet. The alphabet reduces reality into twenty-six completelyabstract unitseach combined in different ways to enable an infinite

variety of compositions. Chinese characters, on the other hand, arepotentially infinite in themselves (or at least produced in numbers solarge it is impossible for any human to remember them all). Leibniz didnot know that these characters were themselves made up of a finitenumber of possible brush strokes, but after all those strokes couldthemselves be configured spatially in an infinite set of configurations.

Yet, Leibniz saw flaws in written Chinese. It did not follow nature andthus was not a philosophical language. Nevertheless, in terms of form,Chinese would be the ideal "Universal Character" because it speaks tothe 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 caneventually be produced, a character that would make the socialcoherent and the lost Republic (Platonic? Humanist?) a reality.

During the period he was writing the New Essays, Leibniz mostimportant correspondence about China and the Chinese language waswith the French Jesuit Joachim Bouvet (1656-1730), who wasconducting research in China on the Yijing. Bouvet believed that byexamining Chinese inscriptions one could find evidence of Christianity

embedded in the Chinese language. In a series of letters between 1700and 1704, Leibniz increasingly became convinced that the Yijing wasthe divine prototype for his own binary system and that the ancientChinese (but not the corrupt modern ones) had understood this, a factevidenced by the ying and yang lines of the hexagrams.

And thus, as far as I understand, I think the substance of the ancient


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theology of the Chinese is intact and, purged of additional errors, canbe harnessed to the great truths of the Christian religion. Fohi, themost ancient prince and philosopher of the Chinese, had understoodthe origin of things from unity and nothing, i.e. his mysterious figuresreveal something of an analogy to Creation, containing the binary

arithmetic (and yet hinting at greater things) that I rediscovered afterso many thousands of years, where all numbers are written by onlytwo notations, 0 and 1.

These sentiments would be repeated even more emphatically in one ofLeibnizs last writings Discourse on the Natural Theology of the Chinese(1716), written in the months before his death. Leibniz had at last inthe Yijing/binary found the key to resolving mathematics and languagefor which he had searched so long. Whether this solution was a real orimagined one, a one or a zero, whether Leibniz had or had not cracked

the Chinese code, finding the clavis sinica, are academic questions. Inpractice, Leibniz had opened mathematics to semiotics, and semioticsto infinite translation.

V. Hanoverian Successions

Locke put forward in Book II, Chapter II of his Essay Concerning HumanUnderstanding, the idea of "voluntary signs." He argued that words are"external sensible signs" of "invisible ideas." One can only use a word ifone knows what one is talking aboutsignifiers must have a signified

because there cannot be signs of nothing. This holds true, according toLocke, even if the person using the word is merely consenting to itssocial meaning. Leibniz agreed in part, for he admited that howevermuch the thought behind the word is vacuous, there is always someconnection between signifier and signified. However, as he pointed outin the New Essays on Human Understanding, "a person is sometimesoftener indeed than he thinksa mere passer-on of thoughts, a carrierof someone elses message, as though it were a letter." In this carrierfunction (Locke would call it parroting, and for him men are neverparrots), the machine of language operates invisibly at a "material"

rather than a "formal" level of ideas. For Leibniz, language can operatein this almost autonomous fashion, opaque rather than transparent (byvirtue of the will) to the subject who uses it. While it is the "formal"level at which languages are translatable ("which is common todifferent languages"Leibniz), the movement of language seems morerooted in its "material" dimension.


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Locke worries, and given his perspective with good reason, about thepossibility that language may at times function in this opaque,autonomous and "material" fashion. "It is a perverting the use ofwords, and brings unavoidable obscurity and confusion into theirsignification, whenever we make them stand for anything but those

ideas we have in our own minds." Leibniz, on the other hand, suggeststhat only by grappling with this opaque quality of language willphilosophical thought and the translation of ideas between languagesbecome possible. Locke assumes that translation works automaticallyeither you have the idea or you do not. This allows him (as it didHobbes, albeit in a different manner) to think of society in the abstractas an instituted unity ("God, having designed man for a sociablecreature, made him not only with an inclination, and under a necessityto have fellowship with those of his own kind, but furnished him alsowith language, which was to be the great instrument and common tie

of society"). While Leibnizs conceptualization of "ideas" still has aflavor of Platonism to it (as does his pre-established harmony thatallows little translation leaps), it leaves language as a system open toinvoluntary flows (a "symbolic magma" to borrow a phrase fromCornelius Castoriadis). Thus by implication, the Leibnizian formulation,which at first glance seems so totalizing, leaves the imagined socialinstitution open to semiotic restructurings in ways that make the ideasconcerning 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, theideal code, is not as much an impossible project as an endlesslycreative one. Given that the goal is the reformation of the social, theproject actually has direction even though it lacks an ideal telos. Theimagined and idealized use of cryptography and artificial languages todefine and preserve social networks and structures becomes an actualpractice of semiotic reconfiguration of the social imaginary. As Leibnizwrote sometime after 1690, "finally, when the letters or othercharacters 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 ofdeciphering... In the end, the general art of species admits a thousandaspects, and Algebra contains but one." These ideas, like much ofLeibniz work, exist only as an unpublished fragment, hidden frompublic discourse, indicative of a problematic relationship with limits,hinting at a deep crisis within the imagined social dimension of thenetwork that would make a Republic of Codes possible. With Leibniz,


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the limits of the Renaissance cipher ("The Book of the World") haveopened to the limitless production of code based on proliferating andrapidly changing translation games. Conserving secrets ironicallyremakes the world infinitely.

rep of codes – cryptography

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