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Tag: Polygraphia

Eco: Characteristica and Calculus

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, an excerpt from his first doctoral dissertation, Dissertation on the Art of Combinations, Leipzig, 1666. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“The theme of invention and discovery should remind us of Lull; and, in fact, Lull’s ars combinatoria was one of Leibniz’s first sources. In 1666, at the age of twenty, Leibniz composed his own Dissertatio de arte combinatoria (Gerhardt 1875: IV, 27-102). But the dream of the combinatoria was to obsess him for the rest of his life.

In his short Horizon de la doctrine humaine (in Fichant 1991), Leibniz dealt with a problem that had already troubled Father Mersenne: how many utterances, true, false or even nonsensical, was it possible to formulate using an alphabet of 24 letters?

The point was to determine the number of truths capable of expression and the number of expressions capable of being put into writing. Given that Leibniz had found words of 31 letters in Latin and Greek, an alphabet of 24 letters would produce 2432 words of 31 letters.

But what is the maximum length of an expression? Why should an expression not be as long as an entire book? Thus the sum of the expressions, true or false, that a man might read in the course of his life, imagining that he reads 100 pages a day and that each page contains 1,000 letters, is 3,650,000,000.

Even imagining that this man can live one thousand years, like the legendary alchemist Artephius, it would still be the case that “the greatest expressible period, or the largest possible book that a man can read, would have 3,650,000,000,000 [letters], and the number of truths, falsehoods, or sentences expressible–that is, readable, regardless of pronounceability or meaningfulness–will be 24365,000,000,001 – 24/23 [letters].”

We can imagine even larger numbers. Imagine our alphabet contained 100 letters; to write the number of letters expressible in this alphabet we would need to write a 1 followed by 7,300,0000,000,000 (sic) zeros. Even to write such a number it would take 1,000 scribes working for approximately 37 years.

Leibniz’s argument at this point is that whatever we take the number of propositions theoretically capable of expression to be–and we can plausibly stipulate more astronomical sums than these–it will be a number that vastly outstrips the number of true or false expressions that humanity is capable of producing or understanding.

From such a consideration Leibniz concluded paradoxically that the number of expressions capable of formulation must always be finite, and, what is more, that there must come a moment at which humanity would start to enunciate them anew.

With this thought, Leibniz approaches the theme of the apochatastasis or of universal reintegration–what we might call the theme of the eternal return.

This was a line of speculation more mystical than logical, and we cannot stop to trace the influences that led Leibniz to such fantastic conclusions.

It is plain, however, that Leibniz has been inspired by Lull and the kabbala, even if Lull’s own interest was limited to the generation of just those propositions that expressed true and certain knowledge and he thus would never have dared to enlarge his ars combinatoria to include so large a number of propositions.

For Leibniz, on the contrary, it was a fascination with the vertiginous possibilities of discovery, that is of the infinite number of expressions of which a simple mathematical calculation permitted him to conceive, that served as inspiration.

At the time he was writing his Dissertatio, Leibniz was acquainted with Kircher’s Polygraphia, as well as with the work of the anonymous Spaniard, of Becher, and of Schott (while saying that he was waiting for the long-promised Ars magna sciendi of the “immortal Kircher“).

He had yet to read Dalgarno, and Wilkins had still not published his Essay. Besides, there exists a letter from Kircher to Leibniz, written in 1670, in which the Jesuit confessed that he had not yet read Leibniz’s Dissertatio.

Leibniz also elaborated in the Dissertatio his so-called method of “complexions,” through which he might calculate, given n elements, how many groups of them, taken t at a time, irrespective of their ordering, can be ordered.

He applied this method to syllogisms before he passed to his discussion of Lull (para. 56). Before criticizing Lull for limiting the number of his elements, Leibniz made the obvious observation that Lull failed to exploit all the possibilities inherent in his combinatorial art, and wondered what could happen with variations of order, which could produce a greater number.

We already know the answer: Lull not only limited the number of elements, but he rejected those combinations that might produce propositions which, for theological and rhetorical reasons, he considered false.

Leibniz, however, was interested in a logica inventiva (para. 62) in which the play of combinations was free to produce expressions that were heretofore unknown.

In paragraph 64 Leibniz began to outline the theoretical core of his characteristica universalis. Above all, any given term needed to be resolved into its formal parts, the parts, that is, that were explicitly entailed by its definition.

These parts then had to be resolved into their own components, and so on until the process reached terms which could not, themselves, be defined–that is, the primitives. Leibniz included among them not only things, but also modes and relations.

Other terms were to be classified according to the number of prime terms they contained: if they were composed from 2 prime terms, they were to be called com2nations; if from 3 prime terms, com3nations, and so forth. Thereby a hierarchy of classes of increasing complexity could be created.

Leibniz returned to this argument a dozen years later, in the Elementa characteristicae universalis. Here he was more generous with his examples. If we accept the traditional definition of man as “rational animal,” we might consider man as a concept composed of “rational” and “animal.”

We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate.

Given the preposition “all men are animals,” the number for the subject (men), is 6; the number for animals is 2; the resulting fraction is 6/2 = 3. Three being an integer, consequently, the preposition is true.

If the number for monkey were 10, we could demonstrate the falsity of either the proposition “all men are monkeys” or “all monkeys are men:” “the idea of monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6” (Elementa, in Couturat 1903: 42-92). These were principles that had all been prefigured in the Dissertatio.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 271-5.

Eco: First Attempts at a Content Organization


Athanasius Kircher (1602-80), Frontispiece of Obeliscus Pamphilius, Obeliscus Pamphilius: Hoc est Interpretatio nova & hucusque intenta obelisci Hieroglyphici, eBook courtesy of GoogleBooks, published by Lud. Grignani 1650, held by Ghent University. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“Probably in 1660, three years before the publication of the Polygraphia, Kircher wrote a manuscript bearing the title Novum hoc inventum quo omnia mundi idiomata ad unum reducuntur (Mss. Chigiani I, vi, 225, Biblioteca Apostolica Vaticana; cf. Marrone 1986).

Schott says that Kircher kept his system a secret at the express wish of the emperor, who had requested that his polygraphy be reserved for his exclusive use alone.

The Novum inventum was still tentative and incomplete; it contained an extremely elementary grammar plus a lexicon of 1,620 words. However, the project looks more interesting that the later one because it provides a list of 54 fundamental categories, each represented by an icon.

These icons are reminiscent of those that one might find today in airports and railway stations: some were schematically representative (like a small chalice for drinking); others were strictly geometrical (rectangles, triangles, circles).

Some were furthermore superficially derived from Egyptian hieroglyphics. They were functionally equivalent to the Roman numbers in the Polygraphia (in both texts, Arabic numbers referred to particular items).

Thus, for example, the square representing the four elements plus the numeral 4 meant water as an element; water as something to drink was instead expressed by a chalice (meaning the class of drinkable things) followed by the numeral 3.

There are two interesting features in this project. The first is that Kircher tried to merge a polygraphy with a sort of hieroglyphical lexicon, so that his language could be used (at least in the author’s intention) without translating it into a natural language.

Seeing a “square + 4,” the readers should immediately understand that the named thing is an element, and seeing “chalice + 3” they should understand that one is referring to something to drink.

The difficulty was due to the fact that, while both Kircher’s Polygraphia and Becher’s Character allow a translating operator (be it a human being or a machine) to work independently of any knowledge of the meaning of the linguistic items, the Novum inventum requires a non-mechanical and quasi-philosophical knowledge: in order to encode the word aqua as “square + 4,” one should previously know that it is the name of an element–information that the term of a natural language does not provide.

Sir Thomas Urquhart, who published two volumes describing a sort of polygraphy (Ekskubalauron, 1652, and Logopandecteision, 1653), noted that, arbitrary as the order of the alphabet might be, it was still easier to look things up in alphabetical order than in a categorical order.

The second interesting feature of Kircher’s initial project is certainly given by the effort to make the fundamental concepts independent of any existing natural language.

Its weakness is due to the fact that the list of the 54 categories was notably incongruous: it included divine entities, angelic and heavenly, elements, human beings, animals, vegetables, minerals, the dignities and other abstract concepts deriving from the Lullian Ars, things to drink, clothes, weights, numbers, hours, cities, food, family, actions such as seeing or giving, adjectives, adverbs, months of the year.

It was perhaps the lack of internal coherency in this system of concepts that induced Kircher to abandon this line of research, and devote himself to the more modest and mechanical method used in the Polygraphia.

Kircher’s incongruous classification had a precedent. Although he regarded Kircher as the pioneer in the art of polygraphy, in his Technica curiosa (as well as in his Jocoseriorum naturae et artiis sive magiae naturalis centuriae tres) Gaspar Schott gave an extended description of a 1653 project that was certainly earlier than Kircher’s (the Novum inventum is dedicated to Pope Alexander VII, who ascended the pontifical throne only in 1655).

The project was due to another Jesuit, a Spaniard (“whose name I have forgotten,” as Schott says on p. 483), who had presented in Rome (on a single folio) an Artificium, or an Arithmeticus nomenclator, mundi omnes nationes ad linguarum et sermonis unitatem invitans (“Artificial Glossary, inviting all the nations of the world to unity of languages and speech”).

Schott says that the anonymous author wrote a pasigraphy because he was a mute. As a matter of fact the subtitle of the Artificium also reads Authore linguae (quod mirere) Hispano quodam, vere, ut dicitur, muto (“The author of this language–a marvelous thing–being a Spaniard, truly, it is said, dumb”).

According to Ceñal (1946) the author was a certain Pedro Bermudo, and the subtitle of the manuscript would represent a word play since, in Castilian, “Bermudo” must be pronounced almost as Ver-mudo.

It is difficult to judge how reliable the accounts of Schott are; when he described Becher’s system, he improved it, adding details that he derived from the works of Kircher. Be that as it may, Schott described the Artificium as having divided the lexicon of the various languages into 44 fundamental classes, each of which contained between 20 and 30 numbered items.

Here too a Roman number referred to the class and an Arabic number referred to the item itself. Schott noted that the system provided for the use of signs other than numbers, but gave his opinion that numbers comprised the most convenient method of reference since anyone from any nation could easily learn their use.

The Artificium envisioned a system of designating endings, (marking number, tense or case) as complex as that of Becher. An Arabic number followed by an acute accent was the sign of the plural; followed by a grave accent, it became the nota possessionis.

Numbers with a dot above signified verbs in the present; numbers followed by a dot signified the genitive. In order to distinguish between vocative and dative, it was necessary to count, in one case, five, and, in the other, six, dots trailing after the number.

Crocodile was written “XVI.2” (class of animals + crocodile), but should one have occasion to address an assembly of crocodiles (“O Crocodiles!”), it would be necessary to write (and then read) “XVI.2′ . . . . . ‘.

It was almost impossible not to muddle the points behind one word with the points in front of another, or with full stops, or with the various other orthographic conventions that the system established.

In short, it was just as impracticable as all of the others. Still, what is interesting about it is the list of 44 classes. It is worth listing them all, giving, in parenthesis, only some examples of the elements each contained.

  1. Elements (fire, wind, smoke, ashes, Hell, Purgatory, centre of the earth).
  2. Celestial entities (stars, lightning, bolts, rainbows . . .).
  3. Intellectual entities (God, jesus, discourse, opinion, suspicion, soul, stratagems, or ghosts).
  4. Secular statuses (emperor, barons, plebs).
  5. Ecclesiastical states.
  6. Artificers (painters, sailors).
  7. Instruments.
  8. Affections (love, justice, lechery).
  9. Religion.
  10. Sacramental confession.
  11. Tribunal.
  12. Army.
  13. Medicine (doctor, hunger, enema).
  14. Brute animals.
  15. Birds.
  16. Fish and reptiles.
  17. Parts of animals.
  18. Furnishings.
  19. Foodstuffs.
  20. Beverages and liquids (wine, beer, water, butter, wax, and resin).
  21. Clothes.
  22. Silken fabrics.
  23. Wool.
  24. Homespun and other spun goods.
  25. Nautical and aromas (ship, cinnamon, anchor, chocolate).
  26. Metal and coin.
  27. Various artifacts.
  28. Stone.
  29. Jewels.
  30. Trees and fruits.
  31. Public places.
  32. Weights and measures.
  33. Numerals.
  34. Time.
  35. Nouns.
  36. Adjectives.
  37. Verbs.
  38. Undesignated grammatical category.
  39. Undesignated grammatical category.
  40. Undesignated grammatical category.
  41. Undesignated grammatical category.
  42. Undesignated grammatical category.
  43. Persons (pronouns and appellations such as Most Eminent Cardinal).
  44. Vehicular (hay, road, footpad).

The young Leibniz would criticize the absurdity of arrangements such as this in his Dissertatio de arte combinatoria, 1666.

This sort of incongruity will affect as a secret flaw even the projects of a philosophically more sophisticated nature–such as the a priori philosophic languages we will look at in the next chapter.

This did not escape Jorge Luis Borges. Reading Wilkins, at second hand as he admits (in Other Inquisitions, “The analytical idiom of John Wilkins“), he was instantly struck by the lack of a logical order in the categorical divisions (he discusses explicitly the subdivisions of stones), and this inspired his invention of the Chinese classification which Foucault posed at the head of his The Order of Things.

In this imaginary Chinese encyclopedia bearing the title Celestial Emporium of Benevolent  Recognition, “animals are divided into: (a) belonging to the emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens (f) fabulous, (g) stray dogs. (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies.”).

Borge’s conclusion was that there is no classification of the universe that is not arbitrary and conjectural. At the end of our panorama of philosophical languages, we shall see that, in the end, even Leibniz was forced to acknowledge this bitter conclusion.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 203-8.

Eco: Beck and Becher

Cave Beck, The Universal Character, London, 1657

Cave Beck (1623-1702), The Universal Character, London, 1657. An eBook available on GoogleBooks, The Universal Character proposes a universal language based on a numerical system consisting of the ten Arabic numerals up to 10,000 combinations long, which was considered sufficient to include all words in common usage. As each word was assigned a unique number and the number was the same regardless of language, words ended up unmanageably long. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“In 1657 Cave Beck had published The Universal Character, by which All the Nations of the World may Understand One Another’s Conceptions, Reading out of one Common Writing their Own Mother Tongues, presenting a project which was not so different from Kircher’s. Here is an example from his system:

Umberto Eco, The Search for the Perfect Language, p. 201.png

Umberto Eco, The Search for the Perfect Language, 1995, p. 201. 

The numbers specified nouns and verbs, p stood for the personal pronoun, second person, with pf as the feminine form (which permits one to use the same term, 2477 = “parent,” in both cases); leb indicated imperative plural.

Beck tried to turn his pasigraphy into a pasilaly as well, that is a system of universal pronunciation. Thus the above sentence was to be pronounced leb totreónfo pee tofosénsen and pif tofosénsen.

The only difficulty was that, in order to pronounce the sentence, one had to memorize the whole dictionary, remembering the right number for every word.

In 1661, two years before Kircher’s Polygraphia (but some of Kircher’s ideas had circulated in manuscript form since 1660), Joachim Becher published his Character pro notitia linguarum universalis (sometimes known under its frontispiece title of Clavis convenientiae linguarum).

Becher’s project was not unlike Kircher’s; the major difference was that Becher constructed a Latin dictionary that was almost ten times more vast (10,000 items). Yet he did not include synonyms from other languages, expecting the accommodating reader to make them up for him.

As in Kircher, nouns, verbs and adjectives composed the main list, with a supplementary list of proper names of people and places making up an appendix.

For each item in Becher’s dictionary there is an Arabic number: the city of Zürich, for example, is designated by the number 10283. A second Arabic number refers the user to grammatical tables which supply verbal endings, the endings for the comparative and superlative forms of adjectives, or adverbial endings.

A third number refers to case endings. The dedication “Inventum Eminentissimo Principi” is written 4442. 2770:169:3. 6753:3, that is, “(My) Invention (to the) Eminent + superlative + dative singular, Prince + dative singular.”

Unfortunately Becher was afraid that his system might prove difficult for peoples who did not know the Arabic numbers; he therefore thought up a system of his own for the direct visual representation of numbers.

The system is atrociously complicated and almost totally illegible. Some authors have imagined that it is somehow akin to Chinese. This is hardly true. What we have, in fact, is a basic graphical structure where little lines and dots at various points on the figure represent different numbers.

Lines and points affixed to the right and center of the figure refer to grammatical categories. Figure 9.1 provides only an excerpt of a list that keeps going for four tables.

Umberto Eco, The Search for the Perfect Language, Figure 9.1, p. 202

Umberto Eco, The Search for the Perfect Language, 1995, Figure 9.1, p. 202.

In the chapter “Mirabilia graphica” in his Technica curiosa (1664), Gaspar Schott tried to improve on Becher’s project.

He simplified the system for the representation of numbers and added partial lexicons for other languages. Schott proposed using small grids of eight cases each, where the lower horizontal line represents units, the next one up tens, the next hundreds, and the top thousands.

Units were represented by dots; fives were represented by strokes. Numbers on the left referred to lexical units, while those on the right to grammatical morphemes. Thus figure 9.2 must be read as 23:1, 15:15, 35:4, and can be translated as “The horse eats the fodder.”

Umberto Eco, The Search for the Perfect Language, Figure 9.2, p. 203

Umberto Eco, The Search for the Perfect Language, 1995, Figure 9.2, p. 203. 

Becher’s and Schott’s systems appear totally impracticable for normal human use, but have been seen as tentative models for future practices of computer translation (cf. Heilman 1963; De Mauro 1963).

In fact, it is sufficient to think of Becher’s pseudo-ideograms as instructions for electronic circuits, prescribing to a machine which path to follow through the memory in order to retrieve a given linguistic term, and we have a procedure for a word-for-word translation (with all the obvious inconveniences of such a merely mechanical program).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 201-3.

Eco: Kircher’s Polygraphy

Kircher, the Steganographic Ark, from Polygraphia Nova, p. 130

Athanasius Kircher (1602-80), the steganographic ark, Polygraphia nova et universalis ex combinatoria arte detecta, 1663. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

Kircher wrote his Polygraphia nova et universalis ex combinatoria arte detecta in 1663, several years after his early works on Egypt and hieroglyphics, but he was concerned with the problem of universal writing from the beginning of the decade, and it seems evident that he was at the same time fascinated by the hieroglyphic mysteries and the polygraphic publicity.

It is also significant that in this same volume Kircher designed not only a polygraphy, or international language open to all, but also, in the wake of Trithemius, a steganography, or secret language in which to cipher messages.

What (at the end of the previous chapter) seemed to us a contradiction appeared to Kircher rather as a natural connection. He cited, at the outset, an Arab proverb: if you have a secret, hide it or reveal it (“si secretum tibi sit, tege illud, vel revela“).

Such a decision was not so obvious, after all, since in his works on Egyptology Kircher had chosen a “fifty-fifty solution,” saying something by concealing it, alluding without revealing.

Finally, the second part of the title of Kircher’s work reveals that, in designing his polygraphy, Kircher was also using Lull’s art of combination (contrary to the opinion of Knowlson 1975: 107-8).

In the enthusiastic preface that the author addressed to the emperor Ferdinand III, he celebrated polygraphy as “all languages reduced to one” (“linguarum omnium ad nam reductio“).

Using polygraphy, “anyone, even someone who knows nothing other than his own vernacular, will be able to correspond and exchange letters with anybody else, of whatever their nationality.”

Thus Kircher’s polygraphy was in reality a pasigraphy, that is, a project for a written language, or international alphabet, which was not required to be spoken.

It is easy to confuse Kircher’s project with a double pentaglottic dictionary, in A and B versions (both in Latin, Italian, Spanish, French and German). In Kircher’s time, English was not considered an important international language, and, in his Character, Becher had assumed that French was sufficient, as a vehicular language, for English, Italian, Spanish and Portuguese native speakers.

Ideally, Kircher thought (p. 7) that his dictionary should also include Hebrew, Greek, Bohemian, Polish, Lithuanian, Hungarian, Dutch, English and Irish (“linguae doctrinales omnibus communes“)–as well as Nubian, Ethiopic, Egyptian, Congolese, Angolan, Chaldean, Arabic, Armenian, Persian, Turkish, Tartar, Chinese, Mexican, Peruvian, Brazilian and Canadian.

Kircher did not, it seems, feel himself ready to confront such a gigantic task; perhaps he intuited that the missionary activity, followed eventually by colonialism, would drastically simplify the problem (transforming many exotic languages into mere ethnological remnants): Spanish would substitute for Mexican, French for Canadian, Portuguese for Brazilian, and various pidgins would substitute for all the rest.

Kircher’s A and B dictionaries each contain 1,228 items. The grounds for selection were purely empirical: Kircher chose the words that seemed to him most commonly used.

Dictionary A served to encode messages. It started with a list of common nouns and verbs, in alphabetical order. There followed alphabetic lists of proper nouns (regions, cities, persons), and of adverbs and prepositions.

Added to this there was also a list of the conjugations of both the verbs to be and to have. The whole material was subdivided into 32 tables, marked by Roman numerals, while every item of each table was marked by an Arabic numeral.

The dictionary was set out in five columns, one for each of the five languages, and the words in each language were listed in their proper alphabetical order. Consequently, there is no necessary semantic correspondence between the terms recorded on the same line, and only the terms scored with the same Roman and Arabic numbers were to be considered synonymous.

We can see this best by giving the first two lines of the dicti0nary:

Umberto Eco, The Search for the Perfect Language, p. 198

Umberto Eco, The Search for the Perfect Language, p. 198. 

The Roman numerals refer to tables found in dictionary B; the Arabic numerals refer to the items themselves. Latin acts as the parameter language: for each specific term, the numbers refer to the Latin alphabetic ordering.

For example, the code for the French word abstenir is I.4, which indicates that the position of its Latin synonym, abstinere, is fourth in the Latin column I (obviously, to encode the Latin word abstinere, one also writes I.4).

To decode the message, it was necessary to use dictionary B. This too was arranged in 32 tables, each assigned a Roman numeral. But for each column (or language) the words did not follow their alphabetic order (except the Latin one), while the Arabic numbers marking each term were in an increasing arithmetical order.

Thus all the terms on the same line were synonymous and each synonym was marked by the same Arabic number.

Again, it is easiest to see how this worked by citing the first two lines of the first table:

Umberto Eco, The Search for the Perfect Language, p. 199

Umberto Eco, The Search for the Perfect Language, p. 199. 

Thus, if one wants to send the Latin word abdere (to hide), according to the dictionary A one encodes it as I.2. A German addressee, receiving the message I.2, goes to dictionary B, first table, German column, and looks for the second word, which is exactly verbergen (to hide).

If the same addressee wants to know how to translate this term in Spanish, one finds in the same line that the synonymous term is esconder.

However, Kircher found that a simple lexicon did not suffice; he was forced to invent 44 supplementary signs (notae) which indicated the tense, mood and number of verbs, plus 12 more signs which indicated declensions (nominative, genitive, dative, etc., both singular and plural).

Thus, to understand the following example, the sign N meant nominative, while a sign like a D indicated the third person singular of the past tense. In this way, the ciphered expression “XXVII.36N, XXX.21N, II.5N, XXIII.8D, XXVIII.10, XXX.20” can be decoded as “Petrus noster amicus, venit ad nos” (literally, “Peter our friend came to us”), and on the basis of Latin, can be transformed into an equivalent sentence in any of the other four languages.

Kircher proudly claims that, by dictionary A, we can write in any language even though though we know only our own, as well as that, with dictionary B, we can understand a text written in an unknown language.

The system also works when we receive a non-ciphered text written in a natural foreign language. All we have to do is to look up the reference numbers for each foreign word in dictionary A (where they are listed in alphabetical order), then, with the reference numbers, find the corresponding words in dictionary B, in the column for our own language.

Not only was this process laborious, but the entire project was based on the assumption that all other languages could be directly reduced to the Latin grammar. One can imagine the results of such a method if one thinks of translating literally, word by word, a German sentence into an English one.

Kircher never confronted the problem of why an item-by-item translation should be syntactically correct, or even comprehensible, in the new language. He seemed to rely on the good will and good sense of whoever used his system.

Yet even the most willing users might slip up. In August 1663, after reading the Polygraphia, Juan Caramuel y Lobkowitz wrote to Kircher to congratulate him on his wonderful invention (Mss Chigiani f. 59 v., Biblioteca Apostolica Vaticana; cf. Casciato et al. 1986: table 5).

Appropriately, Caramuel chose to congratulate Kircher in his own polygraphy. Yet his first problem was that Kircher’s own first name, Athanasius, did not appear in the list of proper names. Adopting the principle that where a term is missing, an analogous one must be sought, Caramuel addressed his letter to “Anastasia.”

Moreover, there are passages that can be decoded fairly easily, while for others one suspects that the labor of consulting the dictionary to obtain reference numbers for every word proved so tedious that even Caramuel began to nod.

Thus we find ourselves in front of a passage which, in Latin, would need to be translated as follows: “Dominus + sign of vocative, Amicus + sign of vocative, multum sal + sign of vocative, Anastasia, a me + sign of accusative, ars + sign of accusative, ex illius + sign of ablative, discere posse + sign of second person plural, future active, non est loqui vel scribere sub lingua + ablative, communis + ablative.”

After many heroic efforts, one can try to render it (in a sort of “Me Tarzan-You Jane” language) as “O Lord and Friend, O witty Athanasius, to me (?) you could learn from him an art (which) is not speaking and writing under a common language.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 196-200.

Eco: Polygraphies


John Dee (1527-1609), an excerpt from Steganographiae, aka Peniarth MS 423D, astrological texts in Latin, 1591. Steganographiae was originally composed by Johannes Trithemius in the 1490’s. Infamous as a work of cryptography, this excerpt was copied by hand by Dr. Dee. Peniarth MS 423D is held by the National Library of Wales. This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. All rights are waived worldwide under copyright laws. This file can be copied, modified, and distributed with no permissions required.  

“Steganographies were used to cipher messages in order to guarantee secrecy and security.  However, even though disregarding many terminological details (or differences) used today by the cryptographers, one must distinguish between the activity of coding and decoding messages when one knows the key, or code, and cryptoanalysis (sic); that is, the art of discovering an unknown key in order to decipher an otherwise incomprehensible message.

Both activities were strictly linked from the very beginning of cryptography: if a good steganography could decode a ciphered message, it ought to allow its user to understand an unknown language as well.

When Trithemius wrote his Polygraphiae, which was published in 1518, before his Steganographia, and did not earn the sinister fame of the latter work, he was well aware that, by his system, a person ignorant of Latin might, in a short time, learn to write in that “secret” language (1518: biiii) (sic).

Speaking of TrithemiusPolygraphia, Mersenne said (Quaestiones celeberrimae in Genesim, 1623: 471) that its “third book contains an art by which even an uneducated man who knows nothing more than his mother tongue can learn to read and write Latin in two hours.”

Steganography thus appeared both as an instrument to encipher messages conceived in a known language and as the key to deciphering unknown languages.

In order to cipher a message one must substitute the letters of a plain message (written in a language known by both the sender and the addressee) with other letters prescribed by a key or code (equally known by sender and addressee).

To decipher a message encoded according to an unknown key, it is frequently sufficient to detect which letter of the encoded message recurs most frequently, and it is easy to infer that this represents the letter occurs most frequently in a given known language.

Usually the decoder tries various hypotheses, checking upon different languages, and at a certain point finds the right solution.

The decipherment is made, however, more difficult if the encoder uses a new key for every new word of the message. A typical procedure of this kind was the following. Both the encoder and the decoder refer to a table like this:

Umberto Eco, Table, The Search for the Perfect Language, Polygraphies, Trithemius, p. 195

Umberto Eco, The Search for the Perfect Language, p. 195.

Now, let us suppose that the key is the Latin word CEDO. The first word of the message is encoded according to the third line of the table (beginning with C), so that A becomes C, B becomes D and so on.

The second words is encoded according to the fifth line (beginning with E), so that A becomes E and so on. The third word is encoded according to the fourth line, the fourth according to the fifteenth one . . . At the fifth word one starts the process all over again.

Naturally the decoder (who knows the key) proceeds in the opposite way.

In order to decipher without knowing the key, if the table is that simple and obvious, there is no problem. But even in cases of more complicated tables the decipherer can try with all possible tables (for instance, with alphabets in reverse order, with alternate letters, such as ACEG), and it is usually only a matter of time before even the most complex of codes are broken.

Observing this, Heinrich Hiller, in his Mysterium artiis steganographicae novissimum (1682), proposed to teach a method of learning to decipher messages not only in code, but also in Latin, German, Italian and French, simply by observing the incidence of each letter and diphthong in each language.

In 1685, John Falconer wrote a Cryptomenysis patefacta: or the Art of Secret Information Disclosed Without a Key, where he noted that, once someone has understood the rules of decipherment in a given language, it is possible to do the same with all the others (A7v).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 194-6.