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Tag: Sefer Yezirah

Eco: Kabbalism & Lullism in the Steganographies

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Johannes Trithemius (1462-1516), Polygraphiae libri sex, Basel, 1518. Courtesy of the Shakespeare Folger Library as file number 060224. Joseph H. Peterson at the Esoteric Archives digitized a copy of the complimentary work on steganography held by the British Library in 1997. That work is listed as Trithemius, Steganographic: Ars per occultam Scripturam animi sui voluntatem absentibus aperiendi certu, 4to, Darmst. 1621. London, British Library. 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.   

“A peculiar mixture of kabbalism and neo-Lullism arose in the search for secret writings–steganographies. The progenitor of this search, which was to engender innumerable contributions between humanism and the baroque, was the prolific Abbot Johannes Trithemius (1462-1516).

Trithemius made no references to Lull in his works, relying instead on kabbalistic tradition, advising his followers, for instance, that before attempting to decipher a passage in secret writing they should invoke the names of angels such as Pamersiel, Padiel, Camuel and Aseltel.

On a first reading, these seem no more than mnemonic aids that can help either in deciphering or in ciphering messages in which, for example, only the initial letters of words, or only the initial letters of even-numbered words (and so on according to different sets of rules), are to be considered.

Thus Trithemius elaborated texts such as “Camuel Busarchia, menaton enatiel, meran sayr abasremon.” Trithemius, however, played his game of kabbala and steganography with a great deal of ambiguity. His Poligraphia seems simply a manual for encipherment, but with his posthumous Steganographia (1606 edition) the matter had become more complex.

Many have observed (cf. Walker 1958: 86-90, or Clulee 1988: 137) that if, in the first two books of this last work, we can interpret Trithemius‘ kabbalist references in purely metaphorical terms, in the third book there are clear descriptions of magic rituals.

Angels, evoked through images modeled in wax, are subjected to requests and invocations, or the adept must write his own name on his forehead with ink mixed with the juice of a rose, etc.

In reality, true steganography would develop as a technique of composing messages in cipher for political or military ends. It is hardly by chance that this was a technique that emerged during the period of conflict between emerging national states and flourished under the absolutist monarchies.

Still, even in this period, a dash of kabbalism gave the technique an increased spice.

It is possible that Trithemius‘ use of concentric circles rotating freely within each other owed nothing to Lull: Trithemius employed this device not, as in Lull, to make discoveries, but simply to generate or (decipher) cryptograms.

Every circle contains the letters of the alphabet; if one rotates the inner wheel so as to make the inner A correspond, let us say, to the outer C, the inner B will be enciphered as D, the inner C as E and so on (see also our ch. 9).

It seems probable that Trithemius was conversant enough with the kabbala to know certain techniques of temurah, by which words or phrases might be rewritten, substituting for the original letters the letters of the alphabet in reverse (Z for A, Y for B, X for C, etc.).

This technique was called the “atbash sequence;” it permitted, for example, the tetragrammaton YHWH to be rewritten as MSPS. Pico cited this example in one of his Conclusiones (cf. Wirzubski 1989: 43).

But although Trithemius did not cite him, Lull was cited by successive steganographers. The Traité des chiffres by Vigenère (1587) not only made specific references to Lullian themes, but also connected them as well to the factorial calculations first mentioned in the Sefer Yezirah.

However, Vigenère simply follows in the footsteps of Trithemius, and, afterwards, of Giambattista Della Porta (with his 1563 edition of De furtivis literarum notis, amplified in subsequent editions): he constructed tables containing 400 pairs generated by 20 letters; these he combined in triples to produce what he was pleased to call a “mer d’infini chiffrements à guise d’un autre Archipel tout parsemé d’isles . . . un embrouillement plus malaisé à s’en depestrer de tous les labrinthes de Crete ou d’Egypte” (pp. 193-4), a sea of infinite cryptograms like a new Archipelago all scattered with isles, an imbroglio harder to escape from than all the labyrinths of Crete and Egypt.

The fact that these tables were accompanied by lists of mysterious alphabets, some invented, some drawn from Middle Eastern scripts, and all presented with an air of secrecy, helped keep alive the occult legend of Lull the kabbalist.

There is another reason why steganography was propelling a Lullism that went far beyond Lull himself. The steganographers had little interest in the content (or the truths) expressed by their combinations.

Steganography was not a technique designed to discover truth: it was a device by which elements of a given expression-substance (letters, numbers or symbols of any type) might be correlated randomly (in increasingly differing ways so as to render their decipherment more arduous) with the elements of another expression-substance.

It was, in short, merely a technique in which one symbol replaced another. This encouraged formalism: steganographers sought ever more complex combinatory stratagems, but all that mattered was engendering new expressions through an increasingly mind-boggling number of purely syntactic operations. The letters were dealt with as unbound variables.

By 1624, in his Cryptometrices et cryptographie libri IX, Gustavus Selenus was designing a wheel of 25 concentric volvelles, each of them presenting 24 pairs of letters. After this, he displays a series of tables that record around 30,000 triples. From here, the combinatory possibilities become astronomical.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 126-8.

Eco: The Alphabet and the Four Figures

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Raymond Llull (1232-1316), Ars magna, segunda figurageneralis et ultima, 1517, held in the Getty Research Institute and digitized by that institution in collaboration with the Internet Archive, generously posted on archive.org. 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 ars combinatoria of Lull employs an alphabet of nine letters–B to K, leaving out J–and four figures (see figure 4.1). In a tabula generalis that appears in several of his works, Lull set out a table of six groups of nine entities, one for each of the nine letters.

The first group are the nine absolute principles, or divine dignities, which communicate their natures to each other and spread throughout creation.

After this, there are nine relative principles, nine types of question, nine subjects, nine virtues and nine vices.

Lull specifies (and this is an obvious reference to Aristotle’s list of categories) that the nine dignities are subjects of predication, while the other five series are predicates. We shall see that subject and predicate are sometimes allowed to exchange their roles, while in other cases variations of order are not considered as pertinent.

First figure. This traces all the possible combinations between the dignities, thus allowing predications such as “Goodness [bonitas] is great,” “Greatness [magnitudo] is glorious,” etc.

Since the dignities are treated as nouns when they appear as a predicate, the lines connecting them can be read in both directions. The line connecting magnitudo and bonitas can, for example, be read as both “Greatness is good” and “Goodness is great.” This explains why 36 lines produce 72 combinations.

The first figure is designed to allow regular syllogisms to be inferred. To demonstrate, for example, that goodness can be great, it is necessary to argue that “all that is magnified by greatness is great–but goodness is what is magnified by greatness–therefore goodness is great.”

The first table excludes self-predications, like BB or CC, because, for Lull, there is no possibility of a middle term in an expression of the type “Goodness is good” (in Aristotelian logic, “all As are B–C is an A–therefore C is a B” is a valid syllogism because, following certain rules, the middle term A is so disposed to act as the, as it were, bond between B and C).

Second figure. This serves to connect the relative principles with triples of definitions. They are the relations connecting the divine dignities with the cosmos. Since it is intended merely as a visual mnemonic that helps to fix in the mind the various relations between different types of entity, there is no method of combination associated with the second figure.

For example, difference, concordance and opposition (contrarietas) can each be considered in reference to (1) two sensible entities, such as a plant and a stone, (2) a sensible and an intellectual entity, like body and soul, and (3) two intellectual entities, like the soul and an angel.

Third figure. Here Lull displayed all possible letter pairings. The figure contains 36 pairs inserted in what Lull calls the 36 chambers. The figure makes it seem that he intended to exclude inversions.

Yet, in reality, the figure does contemplate inversions in order, and thus the number of the chambers is virtually 72 since each letter is permitted to function as either subject or predicate (“Goodness is great” also gives “Greatness is good:” Ars magna, VI, 2).

Having established the combinations, Lull proceeds to what he calls the “evacuation of the chambers.” Taking, for example, chamber BC, we read it first according to the first figure, obtaining goodness and greatness (bonitas and magnitudo); then according to the second figure, obtaining difference and concordance, (differentia and concordantia: Ars magna, II, 3).

From these two pairs we derive 12 propositions: “Goodness is great,” “Difference is great,” Goodness is different,” “Goodness is different,” “Difference is good,” “Goodness is concordant,” “Difference is concordant,” “Greatness is good,” “Concordance is good,” “Greatness is different,” “Concordance is different,” “Greatness is concordant,” and “Concordance is great.”

Going back to the tabula generalis in figure 4.1, we find that, under the next heading, Questiones, B and C  are utrum (whether) and quid (what). By combining these 2 questions with the 12 propositions we have just constructed, we obtain 24 questions, like “Whether goodness is great?,” or “What is a great goodness?” (see Ars magna, VI, 1).

In this way, the third figure generates 432 propositions and 864 questions–at least in theory. In reality, there are 10 additional rules to be considered (given in Ars magna, VI, iv).

For the chamber BC, for example, there are the rules B and C. These rules depend on the theological definition of the terms, and on certain argumentative constraints which have nothing to do with the rules of combination.

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Quarta figura, fourth figure.

Fourth figure. This is the most famous of the figures, and the one destined to have the greatest influence on subsequent tradition. In this figure, triples generated by the nine elements are considered.

In contrast to the preceding figures, which are simply static diagrams, the fourth figure is mobile. It is a mechanism formed by three concentric circles, of decreasing size, inserted into each other, and held together usually by a knotted cord.

If we recall that in the Sefer Yezirah the combination of the letters was visually represented by a wheel or a spinning disc, it seems probable that Lull, a native of Majorca, has been influenced here by the kabbalistic tradition that flourished in his time in the Iberian peninsula.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 56-60.

 

Eco: The Elements of the Ars Combinatoria

Ramon_Llull, Ars Magna, Fig_1

Raymond Llull (1232-1316), Figure 1 from Ars magna, 1300. 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. 

“Given a number of different elements n, the number of arrangements that can be made from them, in any order whatever, is expressed by their factorial n!, calculated as 1.*2*3. . . . *n.

This is the method for calculating the possible anagrams of a word of n letters, already encountered as the art of temurah in the kabbala. The Sefer Yezirah informed us that the factorial of 5 was 120.

As n increases, the number of possible arrangements rises exponentially: the possible arrangements for 36 elements, for example, are 371, 993, 326, 789, 901, 217, 467, 999, 448, 150, 835, 200, 000, 000.

If the strings admit repetitions, then those figures grow upwards. For example, the 21 letters of the Italian alphabet can give rise to more than 51 billion billion 21-letter-long sequences (each different from the rest); when, however, it is admitted that some letters are repeated, but the sequences are shorter than the number of elements to be arranged, then the general formula for n elements taken t at a time with repetitions is n1  and the number of strings obtainable for the letters of the Italian alphabet would amount to 5 billion billion billion.

Let us suppose a different problem. There are four people, A. B, C, and D. We want to arrange these four as couples on board an aircraft in which the seats are in rows that are two across; the order is relevant because I want to know who will sit at the the window and who at the aisle.

We are thus facing a problem of permutation, that is, of arranging n elements, taken t at a time, taking the order into account. The formula for finding all the possible permutations is n!/(n-t)In our example the persons can be disposed this way:

AB     AC     AD     BA     CA     DA     BC     BD     CD     CB     DB     DC

 Suppose, however, that the four letters represented four soldiers, and the problem is to calculate how many two-man patrols could be formed from them. In this case the order is irrelevant (AB or BA are always the same patrol). This is a problem of combination, and we solve it with the following formula: n!/t!(n-t)! In this case the possible combinations would be:

AB     AC     AD     BC     BD     CD

Such calculuses are employed in the solution of many technical problems, but they can serve as discovery procedures, that is, procedures for inventing a variety of possible “scenarios.”

In semiotic terms, we are in front of an expression-system (represented both by the symbols and by the syntactic rules establishing how n elements can be arranged t at a time–and where t can coincide with n), so that the arrangement of the expression-items can automatically reveal possible content-systems.

In order to let this logic of combination or permutation work to its fullest extent, however, there should be no restrictions limiting the number of possible content-systems (or worlds) we can conceive of.

As soon as we maintain that certain universes are not possible in respect of what is given in our own past experience, or that they do not correspond to what we hold to be the laws of reason, we are, at this point, invoking external criteria not only to discriminate the results of the ars combinatoria, but also to introduce restrictions within the art itself.

We saw, for example, that, for four people, there were six possible combinations of pairs. If we specify that the pairing is of a matrimonial nature, and if A and B are men while C and D are women, then the possible combinations become four.

If A and C are brother and sister, and we take into the account the prohibition against incest, we have only three possible groupings. Yet matters such as sex, consanguinity, taboos and interdictions have nothing to do with the art itself: they are introduced from outside in order to control and limit the possibilities of the system.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 54-6.

Eco: Cosmic Permutability and the Kabbala of Names

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Athanasius Kircher, The Ten Sefirot, from Oedipus Aegyptiacus, published in three folio tomes in Rome, 1652-54. This was considered Kircher’s masterwork on Egyptology, and it cast a long shadow for centuries until Champollion deciphered the Rosetta Stone in 1824, unlocking the secrets of the Egyptian hieroglyphs: Kircher was exposed as an erudite fraud. Kircher cited Chaldean astrology, Hebrew kabbalah, Greek myth, Pythagorean mathematics, Arabic alchemy and Latin philology as his sources.     

“The kabbalist could rely on the unlimited resources of temurah because anagrams were more than just a tool of interpretation: they were the very method whereby God created the world.

This doctrine had already been made explicit in the Sefer Yezirah, or Book of Creation, a little tract written some time between the second and the sixth centuries. According to it, the “stones” out of which God created the world were the thirty-two ways of wisdom. These were formed by the twenty-two letters of the Hebrew alphabet and the ten Sefirot.

“Twenty-two foundation letters: He ordained them, He hewed them, He combined them, He weighed them, He interchanged them. And He created with them the whole creation and everything to be created in the future.” (II, 2).

“Twenty-two foundation letters: He fixed them on a wheel like a wall with 231 gates and He turns the wheel forward and backward.” (II, 4).

“How did He combine, weigh, and interchange them? Aleph with all and all with Aleph; Beth with all and all with Beth; and so each in turn. There are 231 gates. And all creation and all language come from one name.” (II, 5).

“How did He combine them? Two stones build two houses, three stones build six houses, four stones build twenty-four houses, five stones build a hundred and twenty houses, six stones build seven hundred and twenty houses, seven stones build five thousand and forty houses. Begin from here and think of what the mouth is unable to say and the ear unable to hear.” (IV, 16).

(The Book of Creation, Irving Friedman, ed., New York: Weiser, 1977).

Indeed, not only the mouth and ear, but even a modern computer, might find it difficult to keep up with what happens as the number of stones (or letters) increases. What the Book of Creation is describing is the factorial calculus. We shall see more of this later, in the chapter on Lull’s art of permutation.

The kabbala shows how a mind-boggling number of combinations can be produced from a finite alphabet. The kabbalist who raised this art to its highest pitch was Abulafia, with his kabbala of the names (cf. Idel 1988a, 1988b, 1988c, 1989).

The kabbala of the names, or the ecstatic kabbala, was based on the practice of the recitation of the divine names hidden in the Torah, by combining the letters of the Hebrew alphabet.

The theosophical kabbala, though indulging in numerology, acrostics and anagrams, had retained a basic respect for the sacred text itself. Not so the ecstatic kabbalah: in a process of free linguistic creativity, it altered, disarticulated, decomposed and recomposed the textual surface to reach the single letters that served as its linguistic raw material.

For the theosophical kabbala, between God and the interpreter, there still remained a text; for the ecstatic kabbalist, the interpreter stood between the text and God.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 28-30.

Creation by Alphabet

“The ancient Sefer Yezira, the Book of Creation, describes the process of creation mainly by the power of the letters of the alphabet.”

There is a parable that states that four sages entered a pardes, a royal garden, to study these scriptures. One died, a second went insane, the third became a heretic, and only the fourth, Rabbi Akibah ben Joseph, “entered in peace and came out in peace.”

The expression “entrance to the pardes” was understood to refer to a profound religious experience of entering the divine realm and encountering God. The term pardes is derived from the Persian, and adopted in its Greek form as “Paradise.”

–Joseph Dan, Kabbalah: A Very Short Introduction, 2006, pg. 12-13.

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