Chapter 2
Computations of Totality

Exe.cut[up]able statements

Date: Tue, 14 Jan 2003 21:47:42 +1100  
From: mez <netwurker@HOTKEY.NET.AU>  
Subject: Re: OPPO.S[able].I.T[humbs]ION!!  
Hello Arch.E.typal T[Claims of the n]ext W[h]orl.d  
     --------------------(mo.dueling 1.1 )------------------- the net.wurk---  
::du n.OT enter _here_ with fal[low]se genera.tiffs + pathways poking  
va.Kant [c]littoral tomb[+age].  
::re.peat[bogging] + b d.[on the l]am.ned.  
::yr p[non-E-]lastic hollow play.jar.[*]istic[tock] met[riculation.s]hods  
sit badly in yr vetoed m[-c]outh.  
::spamnation. .r[l]u[re]ins. .all.  
Exe.cut[up]able statements---  
::do knot a p.arse.r .make.[t]la[ss]te. yr.[llied]wells .awe. .r[b]ust.  
R[l]un[ge]ning the pro.gram[mar]---  
::re.a[vataresque]ct[ors|actrestles] + provoke @ yr response per[b]il[e].  
::con.Seed.quenches r 2 b [s|w]allowed.  
::big boots make filth k.arm[N limb.ic cyst.M]a.

A hybrid of net art, poetry, program and markup code, this piece by Australian net.artist mez (Mary Anne Breeze) reflects a contemporary imagination of software, computation and networks, disassembling it into its smallest symbolic particles and reassembling them into a private language. (mo.dueling 1.1) reads as the name of a computer program with a version number. Through its pointed and bracketed word fragments it expands, like running software code, into the words “module,” “duel” and “dueling.” The syntactical notation is taken from wildcards and regular expressions in programming languages and Unix command line interpreters forming an archetypical world. In mez’s own language “mezangelle,” it is called “Arch.E.typal T[Claims of the n]ext W[h]orl.d,” expanding into hardware/software architectures—“arch” in computer tech lingo—, “claims of the next world,” and whores. Slang and sexual language exposes mezangelle as a messy code, one that does not run on machines, but on a human imagination that encompasses machines and bodies alike. Unlike in the Steven Seagal action movie and the Voynich Manuscript, the semantic associations are not superimposed and therefore external to the code, but are embedded into the code proper. “Exe.cut[up]able statements” and “pro.gram[mar],” for example, are self-reflections of the text as “executable statements” and “program grammar.” The words serve as a source code which generates “execute,” “executable,” “cut-up,” “able” in the first word, “programmer,” “grammar,” “program,” “gram” in the second. There is simultaneous contraction and expansion, regularity and irregularity, instruction and chaos in these words. Like a piece of software code that gets executed, the writing expands beyond itself, generating dozens to hundreds of possible readings. As it says, its “big boots make filth,” and text disperses in a “spamnation.” “Spamnation” also is a technical description of mez’s E-Mail work that is sent, spam-style, to a large number of net cultural mailing lists at once.

From a literary history viewpoint, the word hybrids and onomatopoetics of mezangelle resemble the poetic language in James Joyce’s last novel Finnegans Wake:

The fall (bababadalgharaghtakamminarroninikonnbronntonnerronntuonnthunntrovarrhounawnskawntoohoohoordenenthurnuk!) of a once wallstrait oldparr is retaled early in bed and later on life down through all christian minstrelsy. The great fall of the offwall entailed at such short notice the pftjschute of Finnegan, erse solid man, that the humptyhillhead of humself prumptly sends an unquiring one well to the west in quest of his tumptytumtoes: and their upturnpikepointandplace is at the knock out in the park where oranges have been laid to rust upon the green since devlinsfirst loved livvy. What clashes here of wills gen wonts, oystrygods gaggin fishygods! Brékkek Kékkek Kékkek Kékkek! Kóax Kóax Kóax! Ualu Ualu Ualu! Quaouauh!
This paragraph, from the first page of the book, demonstrates Joyce’s word poetics while referencing its literary prototypes. The onomatopoetic “Bkkek Kkkek [. . . ]” is taken from Aristophanes’ 4th century B.C. Greek comedy The Frogs. “Humptyhillhead,” “prumptly” and “tumptytumtoes” allude to Humpty Dumpty, the nursery rhyme character and fantastic creature in Lewis Carroll’s Through the Looking-Glass, the sequel to Alice in Wonderland. In its sixth chapter, Alice and Humpty Dumpty discuss the seemingly nonsensical poem Jabberwocky:
’Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
Humpty Dumpty explains that “slithy” is a combination of “lithe and slimy”: “‘Lithe’ is the same as ‘active.’ You see it’s like a portmanteau—there are two meanings packed up into one word.” Originally, and before it appeared in the novel, the “Jabberwocky” poem had been written in 1855 and published under Carroll’s proper name Charles L. Dodgson as a parody of romantic poetry. Dodgson was a mathematician by profession and taught at Oxford. As Martin Gardner’s annotated edition of the two Alice novels shows,—which also became published as one of the first electronic hypertext books ever—the books are rich with mathematical and logical puns and humor. In the “Humpty Dumpty” chapter, absurdity stems from a seemingly straightforward, pseudo-logical explanation of the nonsense poem. Humpty Dumpty takes the attitude of a mathematician or logician who reads the poem like a formula. Joyce’s portmanteau words hybridize languages, nature and history, but while they hardly ever mix in formal or machine language, they work as a kind of reverse computer code that expands multiple input into a single output. His novel is infinitely looping, with its last page of the novel ending where the first page begins. Marshall McLuhan, “Joycean hippie” (as Nam June Paik called him) and founder of the term “media theory,” took Finnegans Wake as his “textbook.” 1 According to his biographer Donald Theall, he perceived the blend of “orality, tactility, simultaneity and synaesthesia” in the novel as a blueprint for a “techno-poetic” language. 2

Having created, more or less, the field of “media” with its endless unresolved terminological ambiguities and contradictions, McLuhan’s techno imagination appears to bridge the gap between the technopoetic codework of mez and her net contemporaries on the one hand and its protoype in Carroll and Joyce on the other. 3 “Spamnation,” code flowing out and spilling over, is the common denominator of Carroll’s “slithy toves,” Joyce’s “riverrun” and mez’s collapsing of program, grammar and programmer into a “pro.gram[mar]”. All three artists write in the aesthetic mode of the sublime; the category of the boundless, unshapely, obscure, threatening first described in the Greek rhetorical treatise of Pseudo-Longinus, reinvigorated in the 18th century aesthetic theories of Burke, Kant and Schiller, 4 and which paved the ground for the gothic novel and other forms of dark romanticism (up to the gothic, dark wave and “new romantic” pop cultures that originated the 1980s). Computer and software imagination is only inscribed into mez’s piece. The software her coding conceives of is a monster, an alien resembling that of the eponymous Science Fiction movies. Unlike the “cyberpunk” Science Fiction imagination of the late 1980s and early 1990s whose sublime technopoesis consisted of an imaginary pictorial hyperrealism, mez’s monsters are made up purely by abstract symbols and computational processes.

Magic and religion

Words becoming flesh, the symbolic turning physical – these are by no means recent phantasmagorias and speculations. The beginning of the Gospel of John in the New Testament reads:

1:1 In the beginning was the Word, and the Word was with God, and the Word was God. [. . . ]

1:14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.

This figure of thought, of a speech act that affects physical matter instantly and directly, is magical in its root. Material creation from the word is an idea central to magic in all cultures; it is precisely what magic spells perform. Magic therefore is, at its core, a technology, serving the rational end of achieving an effect, and being judged by its efficacy. According to scholar Franz Dornseiff and his 1922 German study on the alphabet in mysticism and magic, 5 the idea of divine creation through the letter has its roots in early Middle Eastern and Egyptian mystic cults. Gnosticism transformed it into theurgy, the invocation of divine powers for achieving concrete, material effects. Adopting many of its concepts from Gnosticism and Neoplatonist philosophy, Christianity introduced the prayer as its own form of theurgy, itself a practical communicative act between the individual, the divine and physical matter through a symbolic agent, or, medium. Magical thinking is even more strongly present in the Catholic Christian idea of transubstantiation, the transformation of wine into blood and bread into the body of Christ effected through the liturgic speech act of the priest.—The magical formula “hocus pocus” is derived from the Catholic liturgic formula “hoc est corpus meum,” this is my body. 6 —Rationalization of this remnant of magical thinking occurred within Christianity itself when Protestantism abandoned the concept of transubstantiation and thought of communion service as a purely allegorical practice. 7


Figure 1: Result of a Google search on “software” and “magic”

Religion sublimates magic as a common, popular into a privilege of the god creating the world and, subsequently, his son. Magic wasn’t considered occult until religion and later science and technology rivalled and marginalized it. The technical principle of magic, controlling matter through manipulation of symbols, is the technical principle of computer software as well. It isn’t surprising that magic lives on in software, at least nominally. References to magic abound in computer software branding, from programs like Partition Magic, Magix Musicmaker, the /etc/magic filetype database in Unix to the program genre of “Setup Wizards” or operating systems like Sorcerer GNU/Linux in which software packages are installed with the command “cast.” A Google search on “magic” and “software” today yields more than fifteen million results (see figure 1 ). Searching the word “magic” only brings up the homepage of a software company as the third result.

Such links between magic and software remain metaphorical though unless they are based on common concepts of formalism, language and execution of statements. Since magic was marginalized in Western culture through science, it went underground. While magical practices as those of Aleister Crowley claimed to be “scientific,” they doubtlessly existed outside a system of science and rationality which before, until roughly the late 17th century, still had included occult science in its canon. Of the “two cultures” described by scientist and novelist C.P. Snow in 1956, hard sciences and engineering versus humanities and culture, Crowley’s magic clearly sides with the second despite its scientific claims, de-emphasizing magic as a practical technique in favor of magic as an occult philosophy of life. His influence was strong particularly in pop and non-mainstream culture, forming one philosophical formulation of the underground per se. Followers of Crowley include experimental filmmaker Kenneth Anger, the industrial music movement founded by Genesis P-Orridge and others, The Rolling Stones whose song Sympathy for the Devil was Crowley-inspired and The Beatles who put Crowley on the cover of St. Pepper’s Lonely Hearts Club Band.

Magic as Crowleyan occult philosophy, art and programming converged in the poetic language experiments of Brion Gysin and William S. Burroughs:

[. . . ] 8
The poem shuffles its words according to a formal algorithm. Its total of 720 permutations were calculated, in the early 1960s, on a Honeywell computer with the aid of mathematician Ian Sommerville. Spoken by the author on a tape recording, this and other permutation poems of Gysin were not solely mathematical computations, but also incantations. It therefore does not seem incidental that the beginning of the Gospel of John was chosen to be computed. The power of creation in the word is being resurrected in the text from a previously hidden potential. Combinatory computation turns into the technical agent, or spell of this magic act, but its power is ultimately embodied by the speaking voice. The principle of text cut-ups, as they were developed and practiced by Gysin and Burroughs (see p. 126 ) is contained also in the permutational poems since they work with the same principle of slicing out and shuffling portions of a text: lines in Gysin’s poems, columns in Gysin’s and Burroughs’ cut-up prose. In his essay, Cut-ups self-explained, Gysin argues that “Words have a vitality of their own.” Through permuting them, he writes, one can make them “gush into action.” The result is an “expanding ripple of meanings which they [i.e. the words] did not seem to be capable of when they were struck into that phrase.”

Likewise, William S. Burroughs’ essay The Electronic Revolution, which theoretically sums up, although not very coherently, his cut-up poetics, begins with the sentence: “In the beginning was the word and the word was god and has remained one of the mysteries ever since. The word was God and the word was flesh we are told. In the beginning of what exactly was this beginning word? In the beginning of WRITTEN history.” 9 In The Electronic Revolution, written in 1970, the tape recorder takes the place of the technical agent for dissecting and reassembling language and cultural codes for which Gysin employed the computer. But for both writers, technology is a formal means to ultimately manipulate meaning, not formalisms, whereas a computer program, be it a compiler, a word processor, an image or sound manipulation program, is conceived of as a symbolic formalism employed for an equally formal manipulation of symbols. Burroughs’ and Gysin’s insistence on the cultural power of speech acts and media manipulation instead aims at a programmation that is semantic, not formalist. So they transfigure the cut-up method from a formalism to a technique that is semantic in itself, being an occult and magical practice likened to drugs and ecstatic experience.

Another such technical device, Gysin’s Dream Machine, is a visual flicker generator based on a visual pattern cut into a cylindric piece of cardboard rotating on a record player. The visual frequencies it generates can interfere with brain frequencies and create optical illusions, a psychedelic technology used also in Tony Conrad’s experimental films from the 1960s, and with roots in military behaviorist research. That technology is semantic, ecstatic and magic is a point made also in an 1984 underground movie aptly called Decoder which stars Burroughs and Genesis P-Orridge in cameos and whose accompanying Decoder Handbuch[ Decoder Handbook] includes texts by him and Crowley as background material. 10

According to anthropologist James George Frazer, it is a general feature of magic that magical practices tend to cloud their technical and formalist nature, enmeshing themselves with the semantics of the objects and subjects they are intended to affect. In his study The Golden Bough (1922), Frazer differentiates two types of magic, imitative and contagious magic. In imitative magic, the action or effect to be achieved is being mimetically reproduced, for example in the Voodoo-like “attempt which has been made by many peoples in many ages to injure or destroy an enemy by injuring or destroying an image of him.” 11 Contagious magic, on the other hand, works through physical proximity, and is best exemplified, according to Frazer, by “the magical sympathy which is supposed to exist between a man and any severed portion of his person, as his hair or nails; so that whoever gets possession of human hair or nails may work his will, at any distance, upon the person from whom they were cut.” 12

Both operations can are fundamental operations in language and art as well. Roman Jakobson, a founding theorist of 20th century linguistic and literary structuralism, made Frazer’s concept of imitative magic—or the principle of similarity—the basis of a new definition of metaphor, and contagious magic—or the principle of proximity or contiguity—the foundation of metonymy. 13 In commercial computer programs like Partition Magic, the relation between software and magic is metaphorical in this sense of imitation and similarity; the software is sought to achieve magical powers by referring to them only nominally, putting them onto its label rather than into its code.

In Gysin’s and Burroughs’ cut-up poetics however, the technical process renders itself magic not just metaphorically, but physical by inclusion. The the opening phrase of the Gospel of John is a prime example. Both the permutation poem IN THE BEGINNING WAS THE WORD and The Electronic Revolution contain the magical spell of the Gospel not as an allusive imitation, but as a physical inscription and contagious agent, just like the scalp of an enemy ripped out and worn on the body as an amulet. Through the cut-up process, the words regain their original contagious quality and “gush into action,” as Gysin puts it. Burroughs literally links cut-ups and linguistic contagion in what is perhaps his best-known speculation—that language is a virus. If language is a virus, then cut-up literature is about unleashing and applying its viral potential. For Burroughs, the affinity of language and viruses is quite literal. It amounts to more than the idea that viruses could be created in language or, like in Richard Dawkins’ concept of the “meme,” that certain speech acts had contagious effects. 14 Burroughs stresses that

I have frequently spoken of word and image as viruses or as acting as viruses, and this is not an allegorical comparison. 15

Burroughs’ language magic is contagious in a double respect. It has a contagious effect and it is contagious in its very structure. It therefore differs from Frazer’s contagious magic in which the contact is firstly limited to one object and its bearer, and secondly not inscribed into the system of signs itself. With his phantasmagoria of all-pervasive infection that cannot be contained, Burroughs totally semanticizes the mobilization of matter through symbols in the magical speech act. This corresponds, oddly and in a non-canonical way, with older philosophical concepts of codes permeating the cosmos.

Pythagorean harmony as a cosmological code

Pythagorean musicology

Pythagorean thinking is founded on the idea that the world is organized in numerical proportions which are coded equally into music and mathematics. There exists no record of Pythagoras’ original philosophy though because it existed only as secret knowledge within an occult society. Heraclitus is one of the earliest purveyors of Pythagorean ideas: “Combinations, wholes and not-wholes, conjunction and separation, concord and discord—out of all things comes One, and out of One all things,” or, in a different translation: “What goes against each other is joining; what strives apart creates the most beautiful harmony.” 16 When Pythagoras discovered the arithmetic principle of the musical octave by splitting the string of a monochord in half, and from that concluded that there was a mathematical harmony of the cosmos, he founded an aesthetic philosophy that closely linked art, science and nature and whose impact was immense through the Renaissance and beyond.


Figure 2: Franchino Gaffurio, De Harmonia Musicorum (1518)

Pythagorean aesthetics centers around the idea that beauty is made up from mathematical proportions. The mathematical proportions of sound were first described with the numbers 3-4-6 as the relative numerical values of keynote, quint and octave. This code was written down in the treatise De musica of Anicius Manlius Boethius, a 6th century B.C. Latin philosopher. 17 It remained canonical until the invention of tempered tuning and Mersenne’s mathematical musicology (see p. 173 ) in which intervals smaller than the octave were no longer determined by absolute integer values, but relative to each other. On the title illustration of his 1518 treatise De Harmonia Musicorum, 18 the Italian Renaissance composer and musicologist Franchino Gaffurio has himself portrayed teaching Boethius’ Pythagorean 3-4-6 code to his pupils. The picture illustrates the equivalence of musical tuning and mathematical values with organ pipes and a pair of compasses. With speech drawn in anticipation of comic strip balloons, Gaffurio tells his pupils “Harmonia est discordia concors,” harmony is concordant discord, the Pythagorean credo previously voiced by Heraclitus (figure 2 ).

This concept of harmony is very distinct from the modern understanding of the term, because it includes both melodics and harmonics. In other words, a melody can, according to this concept, be harmonic as well. Secondly, it integrates dissonance with consonance. This understanding is implied already in the original Greek word “harmonia” which literally means “joining” or “combining.” Beauty, it follows, is not plainly nice and agreeable, but made up of agreeable and disagreeable elements in equal proportions. This is not only the general principle of Pythagorean aesthetics, but also of any refined classicism. 19

Rhetoric of the acumen

In the 17th century, the joining of opposites became a principle of witty or “conceited” poetics and poetry. This literature later became historicized as anti-classicist, “mannerist” or “baroque.” Wit, or “acumen,” was a part of rhetoric and poetics since the 16th century. It became systematically taught in Jesuitical academia. Wit was considered the principle of epigram poetry, and epigrams in turn functioned as the “subscriptio,” explanatory verse underneath pictorial emblems. Emblems, allegorical images, were hugely popular in the Renaissance since Italian humanist scholar Andreas Alciatus published the first emblem book in 1531. 20 Just as desktop icons on computer operating systems were invented in the 1970s in the Xerox PARC labs in order to simplify interaction with the computer as a machine performing formal-logical manipulations of coded symbols, emblems served to simplify and popularize interaction with religious and philosophical meaning. They became an important part of humanist education—and of Jesuit counter-reformational propaganda, likewise based on the humanist canon. Seminal treatises on epigrammatic wit, some of them covering also the creation of wit in emblems, were written by the Jesuits Kazimierz Sarbiewski, Baltasar Gracián and Emanuele Tesauro. 21


Figure 3: Diagram from Maciej Kazimierz Sarbiewski’s De acuto et arguto (1627)

Kazimierz Sarbiewski, famous in his time as the “Polish Horace,” is of particular interest since his treatise De Acuto et Arguto, published in 1627, 22 uses a Pythagorean model to sketch a quasi- algorithm for composing wit. He defines acumen, rhetorical wit, as a junction of a converging and a diverging meaning that culminate in a paradoxical union, or, point. This point is explained with the Pythagorean formula used earlier by Gaffurio, “discordia concors.” Just like other Pythagorean thinkers who explain laws of form in the arts and technology through numerical models, Sarbiewski equates rhetorical composition to mathematics and geometry. His rhetorical acumen is juxtaposed to an “acumen mathematicum,” a triangle, and explained with a triangular diagram (figure 3 ). The base represents the material, left and right arms/sides the elements of dissent and consent respectively, the edge the union, or witty point. So Sarbiewski’s acumen is indebted to the Pythagorean and Renaissance idea of harmony as a product made up of opposites striving against each other. His triangle functions as a computation device for wit. Yet it is not an algorithmic text generator in a strict sense because it presupposes semantics. Unlike in proper computations, Sarbiewski’s wit cannot be computed through a purely formal, syntactical manipulation of symbols.

Another reading of Jesuit acumen rhetoric as computation can be found in Umberto Eco’s novel The Island of the Day Before. 23 Its ninth chapter, The Aristotelian Telescope, bears the title of Emanuele Tesauro’s 1654 acumen treatise Il cannocchiale aristotelico. 24 Tesauro himself apppears in the novel as “Padre Emanuele.” His idea of using—not Pythagorean triangles, but— Aristotelian logic as a formal device for synthesizing ingenious metaphors is taken up by the novel and gets transcribed into the fiction of a computing device:

The base consisted of a great chest or case whose front held eighty-one drawers-nine horizontal rows by nine vertical, each row in both directions identified by a carved letter (BCDEFGHIK). On the top of the chest, to the left stood a lectern on which a great volume was placed, a manuscript with illuminated initials. To the right of the lectern were three concentric cylinders of decreasing length and increasing breadth (the shortest being the most capacious, designed to contain the two longer ones); a crank at one side could then, through inertia, make them turn, one inside the other, at different speeds according to their weight. Each cylinder had incised at its left margin the same nine letters that marked the drawers. One turn of the crank was enough to make the cylinders revolve independently of one another, and when they stopped, one could read triads of letters aligned at random, such as CBD, KFE, or BGH. 25
Eco’s fiction conflates two logical- rhetorical proto-computers with each other, Tesauro’s acumen rhetoric with the “ars” of medieval Catalan monk Ramon Llull (see p. 64 ). 26 Even if Tesauro’s machine is a modern fiction, it is true that the Jesuit rhetorical manuals on the acumen sought to radically formalize the production of “ingenium,” 27 an ingenuity that would be spelled one century later, as “genius.” The Renaissance “ingenium” however is not the irregular, anti-methodical genius of romanticism, but an effect that can be syntheticly created by anyone. The rise of the romantic genius as the model of an artist who does not calculate in turn explains the crisis of computational methods and games in poetry and arts between ca. 1800 and 1900.

Continuity of Pythagorean thinking

The Pythagorean project consists of the extraction and application of a universal numerical code that organizes both nature and art. This code allows the creation of a correspondence between macrocosm and microcosm and describes harmony, in the sense of beautiful numerical proportions, as the guiding principle of the world. And for the first time, it allows the computation of nature and art. Any natural and symbolic system can be broken up into numerical proportions and values which in turn may be compared to the numerical proportions and values of another observed system. It is this principle of universal similarity and correspondence which Eco calls the “hermetic paradigm” and sums it up under the maxim “sicut superius sic inferius,” “as above, so below” to describe a correspondence of macro- and microcosm. 28 In Pythagorean and later hermetic thinking, numerical proportions can be universally equated to geometrical proportions and musical intervals. Letters, likewise, can be computed as numbers and set into relation to the numerical intervals which are thought to be the foundations of the cosmos. Pythagorean thought therefore first coined and systematically expressed the idea that a symbolic-mathematical source code underlies the universe and describes nature and culture alike.

The Pythagorean tradition anticipates the modeling of culture through software, very literally in the case of music. The law that an octave is a division of a frequency into its half, for example, is implemented into every sound synthesis computer program in the world. Computer-generated music and computer-generated digital instrument programming remains the most systematic elaboration of the original Pythagorean project of finding numerical and arithmetic models for sound. The models reach from simple algorithms like the division of the octave to more recent and complex ones such as Fourier overtone frequency transformations, originally put down by the French mathematician Jean Baptiste Joseph Fourier in 1822. The relative success of mathematical modeling of music explains why music is the oldest and formally most advanced type of computer-based art. Algorithmic musical composition software such as MAX and Pure Data by Miller Puckette has grown into a number of complete, self-contained programming environments and user interfaces whose application is no longer restricted to audio processing. 29

Twentieth century avant-garde music composition technique forms a major link between Pythagoras’ discovery of mathematical laws in music and music composition software like Pure Data. The dodecaphonic music of Arnold Schönberg was based on the principle of permuting the order of the twelve halftones of an octave. All twelve halftones are treated equally, resulting in a composition with no tonality and no tonal center such as “C major.” The techniques used to permute twelve tone rows, retrograding and numerical inversion for example, were in fact algorithms. In his late work, Anton Webern expanded the permutation row principle to all musical parameters, not only pitch, and laid the ground for the serial music of Karlheinz Stockhausen and Pierre Boulez in the 1950s and 1960s. 30 The latter sought to scientifically define the parameters of sound, organizing composition according to permutation rows and their complex polyphonic variation. Twentieth century compositional music thus reapproached the 17th century music of Johann Sebastian Bach. Bach’s composition techniques particularly in The Goldberg Variations, The Art of the Fugue and The Musical Offering brought the Renaissance Pythagorean concept of music to its highest and most rigorous formal level—which explains its fascination for present-day computer programmers and artificial intelligence theorists like Douglas R. Hofstadter in Goedel, Escher, Bach. 31

When serial composition in the 1950s and 1960s put all sound parameters under the regime of numerical permutation, musical composition became thoroughly computational. Yet most its computations were still calculated by hand. From this, it was only a short route to analog electronic sound generation, like in Stockhausen’s Studie II, and computer-aided composition. In 1977, Pierre Boulez founded and directed the IRCAM electronic music center in Paris where seminal audio software like MAX was developed. For Stockhausen, total numerical control over sound eventually led to a historical reversion of the secularization process that began with Pythagoras’ occult cosmology and ended with modern mathematics and computing. In the course of the 1960s, Stockhausen turned from rationalism to mysticism, arriving at the idea that the cosmos exists through harmonic waves that permeate all matter and existence. The result is a total musicality of the universe. At the same time, Stockhausen became subject to harsh criticism by anti-art activist and philosopher Henry Flynt who in the 1960s was associated with Fluxus 32 and by his own former student and assistant, the English composer Cornelius Cardew. Independently from each other, Flynt and Cardew attacked Stockhausen as an “imperialist” and suprematist of the Western musical tradition, and, by implication, its Pythagorean heritage.

The idea that beauty materializes in numerical proportions according to mathematical laws continues to be popular in scientific and engineering cultures, too. Since the early 1970s, Donald Knuth, widely considered the founder of computer science as an independent academic discipline, published his textbooks under the title The Art of Computer Programming. 33 He understands “art” as the formal beauty and logical elegance of the source code. The software TeX which he wrote to typeset his books correspondingly implements a classicist post-Renaissance typography whose notions of beauty are embedded in Knuth’s algorithms for line spacing and paragraph adjustment. At MIT, Knuth initiated a project God and computers whose results were an exhibition of Bible calligraphies and, in 2001, a book Things a Computer Scientist Rarely Talks About. 34 In this book, Knuth remembers how as a student he read a computer program code that he found “absolutely beautiful. Reading it was just like hearing a symphony.” 35 This was how he “got into software,” teaching it as an art rather than a science. The hacker credo put down by Steven Levy in 1983 that “you can create art and beauty with computers” has its roots in Knuth’s teaching. 36 It ultimately means that a program is not a transparent tool for creating beauty—like, for example, a graphics program—, but that it is beautiful by itself. Both schools, highbrow academic computer science and more underground hacker culture, perpetuate a Pythagorean, classicist understanding of art as formal beauty. This concept blatantly lags behind modern concepts of art. Since romanticism and 20th century art, aesthetic understandings of art were not just about beauty, but included the sublime, grotesque and ugly as well. The same is true, implicitly at least, for the Greek and Roman antiquity whose highest art form, tragedies, were about violence and despair.

Fractal geometry and the widespread aesthetic fascination for Mandelbrot sets are another example of contemporary Pythagorean aesthetics. They prove that mathematical concepts of beauty do not necessarily have to be founded on strict order and regular proportions, but can also be built on chaotic iteration (see p. 88 ). The idea, after all, is the same; that the cosmos can be mathematically decoded and art realizes itself as a formal beauty that includes nature and culture alike. Moreover, the “chaos” in the fractals is relative—and not an ontological chaos, i.e. it is not unpredictable—as it is, first of all, framed within a finite surface of a graphical screen, and secondly the fractal forms generate subjectively repetitive and hence predictable patterns (see p. 127 ). The Beauty of Fractals—the title of a book by Hans Otto Peitgen which popularized Mandelbrot graphics in 1986—, 37 boils down to a static beauty just like that of the Pythagorean fixed proportions from the octave to the golden section.

The Pythagorean tradition, and with it the contemporary aesthetic thinking in hard science and engineering cultures, understands correspondences between art and mathematics in terms of numerical “harmony.” These numbers can be considered a code and formal language, but they are, in the classical Pythagorean model, not yet a source code and language that instigates processes. There is code, but no execution in the code. Magic, on the other hand, lacks the concept of a formal language just because it conflates, through its two modes of similarity and contact, its own language with the objects and subjects involved in its act. Gysin and Burroughs still follow this tradition when they fashion computers and tape recorders into occult ecstatic devices and transform gramophones into “dream machines.” Language magic thus conceives of execution, but typically does not have a mathematical understanding of itself.

With their respective corresponding deficiencies, magic and Pythagorean thinking are two prototypes of programming and software, the former lacking a rigorous concept of abstract mathematical symbol language, the latter lacking a concept of executing symbols. The history of software begins, in Western cultures at least, where magic and Pythagorean thinking coincide.


In Hebrew, letters and numbers are mapped into the same notation of the “alefbet.” Unlike Latin where only a small subset of the alphabet corresponded to numbers, every Hebrew letter is also a number. In combination with the idea of divine creation out of the word, or letter, this amounted in the Middle Ages to a complex system of Jewish mystical letter computations. The Kabbalah effectively combined the Pythagorean idea of the world being composed of numbers so that everything can be described in numerical terms and proportions, with the magical concept of language as an agent that affects matter. The religious sublimation of this concept exists in the idea that God created the world through language and that even humans possessed the power of influencing things through the Adamic language spoken in paradise. Kabbalah may be regarded a speculative science of reconstructing the grammar and vocabulary of the Adamic and divine language—through among others computational and pythagorean-numerological readings of the Torah. In its practical application, magical, respectively theurgic, acts are performed. In 1800, the Jewish German rationalist philosopher and Kant scholar Solomon Maimon published an autobiography in which he recollects his juvenile Talmudic and Kabbalah studies in Lithuania. 38 He defines Kabbalah almost linguistically as “the doctrine teaching how to willingly affect nature by means of the manifold names of God which represent specific modes of working upon, and relations to, natural objects. These names are regarded not just as arbitrary, but as natural signs so that everything done with these signs affects the objects they represent.”

As in magical language, Kabbalist mystics conceive of letters and words not merely as abstract, artificial denominators which are culturally defined and shared. They thus stood in opposition to rationalist definitions of language in Aristotelian philosophy, medieval nominalism and the late 19th century structuralist linguistics of Ferdinand de Saussure which all insisted upon the constructedness of language. Since Kabbalah is mystical scholarship aimed at retrieving the original power of the divine letters and words, it also aims at applying this power practically. Modern Kabbalah scholarship, including that of Gershom Scholem, has obscured this end by focusing solely on theoretical Kabbalah. Today, practical Kabbalah includes the politics of the ultraorthodox Shas party in Israel and, on opposite fronts, the popularized, no more exclusively Jewish New Age Kabbalah of the Kabbalah Centre whose adepts include Madonna, Liz Taylor, Elton John, Mick Jagger, Courtney Love and Britney Spears. In its historical form, practical Kabbalah is theurgy, i.e. magical rituals performed within religion as invocations of god. Maimon remembers his own attempts at practical Kabbalah as follows:

With the Kabbalah Ma’asith or practical Kabbalah, I did not not succeed so well as with the theoretical. The preacher boasted, not publicly indeed, but to everybody in private, that he was a master of this also; especially he professed roeh ve-eno nireh (to see everything, but not to be seen by others), i.e., to be able to make himself invisible. I was particularly eager for this artifice in order that I, a young person, might practice certain kinds of mischief on my comrades without being punished. [. . . ] Three days in succession I had to fast, and every day to say some Ichudim. These are Kabbalistic phrases of prayer whose occult meaning aims at inducing sexual unions in the intellectual world in order to achieve certain effects in the physical world. I did everything with pleasure, made the conjuration he had taught me and believed with all confidence that I was now invisible. Immediately, I hurried to the Beth Hamidrash, the Jewish academy, went straight up to one of my comrades and gave him a good slap round his face. He, however, was no fool and returned the blow with interest. I was baffled and unable to understand how he could have recognized me since I had followed the instructions of the preacher with utmost accuracy [. . . ]. 39

The earliest known foundation of the Kabbalah is the Sefer Yetzirah (Book of Creation) whose origin and history is unkown, but which was in circulation at least since the 9th century. The book, a concise work consisting of a total of 65 paragraphs, is a proto- Kabbalistic work as it speaks, for example of the Sefirot, or attributes of God, but has not developed them yet into the system of the ten Sefirot which is central to the Kabbalah. The creation as told in the book is a creation of the world through letters. The fourth chapter tells it as follows:

1. There were formed seven double letters, Beth, Gimel, Daleth, Kaph, Pe, Resh, Tau, each has two voices, either aspirated or softened.

[. . . ]

3. These seven double letters He formed, designed, created, and combined into the Stars of the Universe, the days of the week, the orifices of perception in man; and from them he made seven heavens, and seven planets, all from nothingness [. . . ]. 40

In the next paragraph, these letters create things by the virtue of an algorithm:
4. From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. 41
What is being described here is precisely the combinatory, mathematical law of permutation. According to this law, two discrete elements can be permuted—or shuffled— 2! = 2 * 1 = 2times, three discrete elements 3! = 3 * 2 * 1 = 6and seven elements 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040times. It is the same mathematical law that is at the heart of dodecaphonic and serial music composition, anagram poetry and computed word permutation poetry like that of Brion Gysin (whose IN THE BEGINNING WAS THE WORD permutes six words 720 times according to the same principle described in the quotation above). In the divine creation according to the Sefer Yetzirah, letter combinations function as a straightforward algorithmic source code. Unlike the executable code of a magical spell with its metaphoric and metonymic qualities, the execution is strictly formal, a proper computation. The second chapter of the Sefer Yetzirah even describes a mechanical computing device:

1. The foundations are the twenty-two letters, three mothers, seven double, and twelve single letters.

[. . . ]

4. These twenty-two letters, the foundations, He arranged as on a sphere, with two hundred and thirty-one modes of entrance. If the sphere be rotated forward, good is implied, if in a retrograde manner evil is intended. 42

The second paragraph describes another combinatory algorithm, namely that of combinations—calling them “modes of entrance”—of two elements according to the formula 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21 = 231. The “sphere” may therefore be imagined as a device with two mobile, concentric circles each of which have the 22 letters inscribed. The device can be used to compute all possible 231 letter pairs, on the premise that, unlike in a permutation, a combination like “aleph+bet” is the same as “bet+aleph.” This assumption still applies in the modern mathematical definition of a “combination.” The letter “aleph” can be combined 21 times with the remaining 21 letters of the alphabet, the next letter “bet” only 20 times since the combination with “aleph” had already been exhausted, and so on, resulting in the above formula. The creation of the world is, according to this speculation, computational. Later Kabbalist Torah readings employed algorithmic methods for reconstructing or, in modern computer programmer terminology, reverse-engineering divine creation through and within the letter. The Torah was read, among others, as an acrostic (notaricon), as letter permutation (temurah) or a numerological code (gematria) for the name JAHWE. The ecstatic Kabbalah, practiced in 13th century Spain by Abraham Abulafia and others, become probably the first comprehensive speculative science and art of language computation.


Figure 4: Advertising for Kabbalistic software

Superficially, the model of creation through mathematical combinatorics in the Sefer Yetzirah appears to converge with Einstein’s belief that “God does not play dice with the universe.” 43 However, it imagines God to have computed it since a die is a simple, one-purpose computer. The difference lies alone in the respective algorithms, the stochastic computation of the die versus the combinatory computation of the concentric circles in the Sefer Yetzirah. Both models converge, with order turning into chaos and vice versa, in the imagination of Thomas Pynchon’s novels. In “Gravity’s Rainbow,” set in the historical context of Alan Turing’s computer research in World War II England, occult and computational methods are being used alike to predict the impact points of German missiles. The analysts include “Kabbalists who study the Rocket as Torah, letter by letter rivets, burner cup and brass rose, its text is theirs to permute and combine into new revelations, always unfolding.” 44 In Pynchon’s The Crying of Lot 49 from 1967, an exploding spray can flies through a bathroom so that only “something fast enough, God or a digital machine, might have computed in advance the complex web of its travel.” 45 In Umberto Eco’s novel “Foucault’s Pendulum,” a computer named “Abulafia” is used to calculate Kabbalistic letter permutations of the name YHWE. The novel contains a BASIC source code of the program, commenting it with a detailed discussion of the combinatorics in the fourth chapter of the Sefer Yetzirah. 46 Kabbalah computer programs, as tools of theoretical Kabbalah, however exist not only in fiction. The commercial PC software package Torah Codes 2000 (see figure 4 ), available from Internet shops like and Kabbalah Software , is being advertised as the “ultimate Bible codes analysis tool.” The program renders the Torah as a database and features, among others, “Gematria look up of Word, Phrase, and sentence. Letter Substitution. Letter Analysis. Verse, Word, and Letter count. Bible statistics Query, and Search.”


Figure 5: Diagram of the names of God in Athanasius Kircher’s Oedipus Aegyptiacus

The idea of divine creation through computations of the letters of God’s name was adapted by Christian Kabbalists in the Renaissance. In 1652-54, Jesuit priest and speculative scientist Athanasius Kircher published a book Oedipus Aegypticius that sought to reconstruct “Egyptian wisdom, Phoenician theology, Chaldaic astrology, Hebraic Kabbalah, Persian magic, Pythagorean mathematics, Greek theosophy, mythology, Arabic Alchemy, Latin philology.” 47 The link between magic, Pythagorean thinking and Kabbalah is however being made here less through a historical analysis, but through syncretist combination. The book was founded on the assumption that all these practices and fields of knowledge contained residues of original Egyptian sciences and hieroglyphs. 48 Before Napoleon’s discovery of the Rosetta stone, Hieroglyphs had not been deciphered in the modern age and became subject to occult-scientific speculation. Kircher’s chapter on the Kabbalah contains a diagram of the ten Sefirot and a combinatory dial in the shape of a sunflower in which the tetragrammaton JHWH is permuted into 72 names of God (figure 5 ). On the outer concentric circles, these names get equated to four-letter names of god in contemporary European languages.

Kircher’s model is obviously the Renaissance Italian Neoplatonist philosopher and first self-acclaimed Christian Kabbalist Giovanni Pico della Mirandola. Pico was first to make the Kabbalah known to a non-Jewish audience. He defended his Kabbalah studies against allegations of heresy in his Oration on the Dignity of Man. 49 In his writings, he christianized Jewish mysticism by pointing out trinitarian structures in the Kabbalah and extending the tetragrammaton with the Hebrew letter Shin so that it turned into “YHSVH,” Jesus. The same occurs in Kircher’s sunflower in which Shin is the central letter. Still, Kircher maintains the idea of creation through the divine letters and their permutation. After all, this is in accordance to the (Christian) Gospel of John and its claim that in the beginning there was the word. The things created and symbolized in Kircher’s diagram are the seven planets and angels, the twelve signs of the Zodiac and tribes of Israel. 50

Ramon Llull and Lullism

A later work of Kircher, the Ars magna sciendi sive combinatoria from 1669, contains a permutation table very much like that in the Sefer Yetzirah. It lists the permutations of all integer numbers from 1 to 50 in a purely numerical, formal way. This book, however, is not an explicitly Kabbalistic work, but a recapitulation and partial modification of another complex of speculative language computation, the Ars of 14th century Catalan monk Ramon Llull, or Raimundus Lullus.


Figure 6: The four algorithms of Llull’s Ars

The Ars is a shorthand for a formal-computational system of composing and deriving philosophical-theological statements Llull laid out in two books, Ars generalis ultima (1305) and, in shorter version, Ars brevis. The roots of the Llull’s ars lie in a mystical revelation in 1265 on mount Randa on the island of Mallorca. During this event God allegedly revealed his own attributes to Llull. In the ars, these nine attributes are systematized and indexed with letters from B-K as follows: B – bonitas (goodness), C – magnitudo (magnitude), D – duratio (duration), E – potestas (power), F – sapientia (wisdom), G – voluntas (will), H – virtus (virtue), I – veritas (truth) and K – gloria (glory). Llull’s nine divine attributes bear striking resemblance to the ten divine attributes of the Sefirot: 1. Keter, crown, 2. Hokmah, wisdom, 3. Binah, intelligence, 4. Hesed, love, 5. Gevurah, power, 6. Tifaret, compassion, 7. Netzah, endurance, 8. Hod, majesty, 9. Yesod, foundation, 10. Malkut, kingdom. It has been assumed, among others by Kabbalah scholar Moshe Idel, that Llull took his inspiration less from God himself than from 13th century Spanish ecstatic Kabbalah. 51 Only one century after Llull, Pico della Mirandola describes what he calls the “ars raimundi” as a second form of Kabbalah. The theological idea behind Llull’s system is that the nine attributes should be universally valid across all cultures and religions, so that the Ars, by providing an objective, formal system for creating statements from these universal truths, could prove the single truth of Christian religion and be used as a missionary device. Llull, as a matter of fact, did make several mission travels to Muslim countries in his lifetime. According to legend, he died a martyr in 1316, having been stoned to death by Muslims.

F i g. A F i g. T Q u e s t i o n s S u b j e c t s V i r t u e s V i c e s

B goodness difference whether? God justice avarice
C greatness concordance what? angel prudence gluttony
D eternity contrarierty of what? heaven fortitude lust
E power beginning why? man temperance pride
F wisdom middle how much? imaginative faith accidie
G will end of what kind? sensitive hope envy
H virtue majority when? vegetative charity ire
I truth equality where? elementative patience lying
K glory minority how? instrumentative pity inconstancy

The nine attributes form the nucleus of a table which juxtaposes them with nine logical relations (like is equal to, is smaller than, is greater than), nine questions as they were taught in rhetoric as part of the inventio, i.e. the gathering of ideas—“how,” “what,” “where from,” “by what” etc.—, nine cosmological entities from God to angels, heaven, man, etc. down to instruments, in analogy to the Neoplatonist ordering of the cosmos as a hierarchy of hypostases, or instances, in which each instance is a minor reflection of a higher instance. Finally the Christian virtues and vices form two categories, and for this purpose are expanded from seven to each nine in order to fit the system.

The resulting “tabula” is what computer science calls a “flat” database with index fields (B-K). Through the unified number of nine entries per category, the index can reference any column. It provides, as a symbolic code, an abstract “alphabetum,” or artificial meta-language for the entries of the table. The letter “A” is omitted in this artificial language, expressing the taboo of representing god as the absolute beginning and therefore the first letter in the alphabet. Llull’s letter B-K may be the first example of what computer science calls the “semantics” of a programming language. From a linguistic standpoint, it is odd to call a language semantic, meaningful, which expresses no meaning in the sense of a judgement or interpretation, or reference to an idea. Instead, formal languages describe purely technical manipulations of symbols that require no cognitive interpretation, like “substitute all occurences of the letter a with the letter b” as opposed to “substitute the melancholic tone of a text with an optimistic tone.” The second operation would require (significantly advanced) artificial intelligence, and it has not yet been proven that it can be achieved through a more complex formal manipulation of symbols in a satisfactory way (see p. 174 ). The “semantics” of a programming language however have nothing to do with artificial intelligence or cognitive computing, but simply refer to the style in which the artificial language is coded, i.e. which denominators, metaphors and other semantic handles are being used to reference non- semantic operations. Llull’s “alphabetum” demonstrates that no formal code functions without such a semantics, and culture coded into it. Any such code is thus a user interface— Llull makes the Latin alphabet the user interface of his system—and any code, whether assembly language or an iconic computer desktop, inevitably is an anthropomorphism that involves translation of processes into human-readable signs.

Llull’s formal alphabet however is not yet a programming language. As the index of a tabular, “flat” database, it references only data, not algorithms. His Ars includes four algorithms for transforming elements of the table into statements, but they are non-alphabetically represented by four circular graphic diagrams or “figurae” (see figure 6 ). The first figura links every of nine “principia absoluta,” i.e. god-given attributes, to every other of those principles in the grammatical form of an attributes. The combination “BC” results in the statement “goodness is great,” “BD” in “goodness is constant,” etc. The figure works like an exhaustive cross-reference, or hypertextual linking of all possible combinations, in this case 9 * 8 = 72if one excludes tautological combinations like BB, “goodness is good.”

The second figure links every logical relation to one of three subject matters. It therefore has a similar function as the cross-reference in figure one.

The third figure yields all possible two letter combinations. In that, it differs from the first figura because it considers, just as in the modern mathematical understanding of a combination, “BC” the same as “CB” and results in 8+7+6+5+4+3+2+1 = 36letter pairs. This is exactly the same combinatory algorithm as the one used earlier in the Sefer Yetzirah to determine 231 names of god from pairing 22 letters.

The fourth figure is used to combine three letter combinations instead of just pairs. Again, there is a resemblance to the Sefer Yetzirah and the device with concentric, rotating circles described in its second chapter. Llull writes that “in hac quarte figura, et ultima comprehenditur Ars tota,” that his whole Ars is contained in this fourth figure. Yet it can’t be used without restraints. Redundant combinations like “BBB” are, again, excluded. Through a complicated, and mathematically incoherent procedure which would take up to much space to explain here, Llull arrives at 28 * 9 = 252three letter combinations which may be generated with the fourth figure. Unlike the Sefer Yetzirah, Llull’s ars does not conceive of letter permutations, but of combinations only, and only renders combinations of two elements mathematically correct.

Aside from these formal limitations, there are implicit semantic limitations and self-restraints in Llull’s Ars. For example, a reading of combination BDC as “Deus—contrarietas—magnitudo,” God is contrary to magnitude, would be invalid, respectively illegal. A whole set of heretical applications of the “ars” needs to be suppressed: which Llull’s writing, however, does not mention. The system only allows building statements which are “true” a priori and then, applying its transformation methods, derive different true statements from them through formal- algorithmic means. This make Llull’s ars a first prototype of modern symbolic logic in which logical statements are transformed according to purely formal rules. This resemblance is not coincidental. Leibniz, the inventor of symbolic logic, took his inspiration from Llull’s Ars when he wrote his first book, Dissertatio de arte combinatoria in 1666, 12 years after Kircher’s Ars magna sciendi.

After Giordano Bruno’s theosophical Lullism in the 16th century, Llull’s Ars was resurrected in the early 17th century through the encyclopedist Johann Heinrich Alsted. Kircher’s Ars magna sciendi later marked the end point of 17th century scientific Lullism. Via Alsted, Lullist combinatorics changed its character in the 17th century from a theological device to a generative classificatory system of knowledge. Before Diderot and d’Alembert and their revolutionary reinvention of the encyclopedia in the late 18th century, knowledge in encyclopedias was not structured arbitrarily by the alphabet, but in a systematic order of things according to their place in a cosmology. Lullist combinatorics allowed the generation of complex hierarchical systems for knowledge classification through the exhaustive combination of categories. While Llull’s use of algorithms was synthetic and meant to create complexity, a wealth of statements and reflections from only nine “absolute principles,” the encyclopedist appropriation of his method should on the contrary handle and reduce complexity, structuring a given, unordered, large body of knowledge. It was probably the first historical example of outsourcing organization to algorithms, not unlike computer algorithms that manage payments and bank accounts today.


Figure 7: Comenius’ Orbis pictus: A graphical interface for alphanumeric code

Still in the 17th century, the theologist, hermetic philosopher and educational reformer Jan Amos Comenius developed Lullist computational encyclopedism into a knowledge system with a graphical user interface (figure 7 ). A pupil of Alsted, Comenius wrote an immensely popular encyclopedist work with his schoolbook Orbis pictus. 52 The Orbis pictus, the world in pictures was the first illustrated children’s book in history. Each double page shows one aspect of the world—the planets in the beginning, then one area of human civilization like, for example, agriculture—, marking up every illustration with numbered footnotes that explained the objects both in Latin and the pupil’s native language. With the book, pupils would learn both the order of the world and their native and a foreign language. Comenius’ idea, inspired by the utopian thinkers Campanella and Johann Valentin Andreae (see p. 88 and 90 ), was to use pictorial language as firstly a universal language and secondly as an aestheticly concrete means to represent an abstract order of knowledge. Just like the graphical user interface of the early Macintosh competed with the alphabetic command line interface of DOS and Unix, the pictures in Comenius’ book compete with Llull’s nine letter alphabet as the interface, or “semantics,” of a formal system.

Although there were radical conflations of Lullism and Christian- kabbalistic mysticism later in the 17th century (see p. 83 ), Llull and the 17th century scientific Lullists do not, unlike the Jewish kabbalists, conceive of letter combinatorics as the source of creation. Instead, they treat it as method of logical reasoning, generation and classification of statements and knowledge. God is implicit, not explicit in their combinatorial systems. The systems do not serve a kabbalistic reconstruction or reverse-engineering of a divine language. The divine is present as an inscription and representation of divine order within the categories, but God does not materialize in the computations. Performing them is not a theurgic act, as opposed to Kabbalism and, for example, Rabbi Loew’s creation of the golem through practical Kabbalistic application of the Sefer Yetzirah. 53 The secularization of the Jewish Kabbalah through Llull and Christian Kabbalism continues with 17th century Lullist science, analytic philosophy since Leibniz, up to the 20th century concept of machine computation and computer software. It leaves, on the other hand, the question as to what extent religion, metaphysics and speculative thinking might still be present in contemporary computer culture.

Rhetoric and poetics

Classical rhetoric

Next to magical, Pythagorean, and Kabbalist thinking, an independent tradition of poetic language computations exists in classical rhetoric and poetics. A 1874 monograph of German poet and oriental scholar Friedrich Rückert, Grammatik, Poetik und Rhetorik der Perser (Grammar, Poetics and Rhetoric of the Persians) suggests, with its examples of word permutations and rotary dial word combinatorics in ancient Persian rhetoric and poetry, that rhetorical language computation might have non-Western sources. 54 Other prominent examples of computational writing are the Chinese I Ching oracle (see p. 127 ) and Tibetan prayer wheels. In fact, no historical Western computational text has been transcribed as early and frequently into electronic computer software as the I Ching (see p. 127 ). Classical Greek and Roman rhetoric advocated the virtue of “copia,” multitude of expressions and wealth of variation in speech. Part of this virtue was the ability to create an abundance of speech from a limited amount of ideas and material. The part of rhetoric that taught brainstorming for an oration, the “inventio,” was concerned with this problem. Word permutation became one of generative means of brainstorming and text composition, for example in a poem of the Greek poet Athenaios of the second century B.C.. It had its closest parallel in an elaborated form of chiasm—i.e. the crossing of two similar phrases—called “commutatio” or “permutatio,” like, for example “ego tu sum, tu es ego” (“I am you, and you are me”) in line 721 of Plautus’ Stichus, a comedy that made fun of Plato’s Symposium.


Figure 8: Sun’s Looking Glass computer desktop: spatial-pictoral representation of items very similar to the ars memoria

In classical rhetoric, “inventio,” the creation of topics, dialectically corresponded to “memoria,” the mental recollection of those topics in the act of speech. Memoria taught the memorization of a speech in an age where paper notes were unaffordable. The mnemotechnics of classical rhetoric is described in the Latin Rhetorica ad Herennium which attributes its origins to the Greek poet Simonides. 55 It is a very particular, today obscure, system of visual-metaphoric memorization based on the imagination of architectural spaces, typically houses with separate rooms. These rooms are mentally filled with objects that represent concrete and abstract topics of the speech, by the virtue of metaphor, onomatopoetic resemblance or other figures of speech. While memoria involves no algorithmic computations in itself, it could be regarded as the first implementation of a visual user interface for alphanumeric codes, and certainly influenced Comenius’ Orbis pictus, too. The “memory palaces” and “memory theaters” developed later in the Renaissance bear a striking resemblance to GUI (graphical user interface) desktops and their representation of files through icons arranged in a space. Rhetorical memoria even anticipates three-dimensional user interfaces (like 3dwm or Sun’s Project Looking Glass) in practically every aspect of the design.

Visual mnemotechnics became obsolete as paper became an affordable and more capable medium for scrap notes, a development that might have also have implications for software user interfaces. The question remains whether extending the visual illusionism and immersion of computer user interfaces to 3D simulation will really yield systems superior to software interfaces based on the notation and grammar of written language. If one compares graphical computer interfaces in their first mass market incarnation, the Apple Macintosh desktop of 1984, to contemporary graphical user interfaces on MacOS, Windows and the X11 Window System, it is obvious that much of the original iconic representations—the desk, the waste paper basket, the file cabinet—became obsolete and that the visual metaphors took up a life of their own. As opposed to a Macintosh of 1984, it is hardly possible to introduce a novice computer user to a contemporary graphical user interface by pointing out its resemblance to an analog desktop. With MacOS X, the original mass market graphical operating system in fact reverted to also providing a Unix command line shell.

Rhetoric as such can be seen as a discipline concerned with the formalization and quasi-formal manipulation of language. It is not genuinely formal because its tropes, such as metaphors, are semantic and not just the purely syntactical operations that would be necessary in a computation. Still, the concept underlying rhetoric is that any speech and writing can be created through formal instruction, and—unlike in concepts of divine inspiration or artistic genius (see p. 173 )—composition is a technique that can be learned by anyone. The more formal rhetorical instruction became, the more it approached language computation. In the step from chiasm to word permutation, poetic formalism finally went from semantic to formal-mathematical manipulation of symbols. Such texts have input data (the words to be transformed), an algorithm (permutation, often explained separately, just as in an algorithmic source code) and an execution, for example in writing down the multiple output of a permutation.

Proteic poetry

In the fourth century A.D. permutational poem Carmen XXV written by the Latin poet Optatianus Porfyrius, twenty stanzas are generated from a single stanza of source material. 56 These source words can be permuted within and between single lines. According to the mathematical law of permutation, more than 1.6 billion permutations of the stanza exist. The poem ironically relates the semantics of the words to the syntax of their computation since it tells about permutations and confusion in the songs of the muses. Another early known example of word permutational verse is a poem of the medieval Irish monk Dicuil. 57

In 1561, humanist scholar Julius Caesar Scaliger for the first time described word permutational poetry as a regular poetic form. In his Poetices, a poetics that become canonical for 16th and 17th century poetry, the form is called “Proteus” after the god who perpetually changes his face. 58 It includes a proteic poem “Perfide sperasti divos te fallere Proteu” (“Perfidiously, you, Proteus, hoped to fool the Gods”) whose words can be permuted at will as long as the hexametric meter is kept. As a humanist, Scaliger conceived of his Poetices as a continuation of the Greek and Latin rhetorical and poetic tradition. Most probably, his “Proteus” verse had Optatianus Porfyrius’ Carmen XXV as its model. Through Scaliger’s canonization and sanctioning of the form in the Renaissance, a boom of word permutational poetry resulted, especially in the early 17th century. The form was popular particularly among Christian ecclesiastical poets writing in Latin. In the period of the Thirty Years War, with its destruction of large parts of Middle Europe, proteic peace prayers were written whose permutations often span, like a hardcopy of computer program output, several dozens or hundreds of book pages. In them, language computation had become theurgy again, the activation of divine powers in the celestial macrocosm to change matters in the earthly microcosm.

Since the permutation of Scaliger’s verse “Perfide sperasti divos te fallere Proteu” was restrained through the hexameter, not mapping its mathematical permutation, the proteic verse form became modified later in the 17th century in attempts to combine it with Lullist combinatorics. Thomas Lansius, a professor of rhetoric and politics, wrote a proteic poem whose two lines consisted only of monosyllabic words. They could be shuffled without metrical constraints. In fact, his poem merged the “Proteus” with a monosyllabic double verse Scaliger calls “Correlativi” (and which are known as “versus rapportati” otherwise). 59 Through the permutation of monosyllabic words, the poetic combinatorics of the verse for the first time was identical to its mathematical combinatorics, and the rhetorical and poetic tradition of Athenaios, Optatianus and Scaliger for the first time converged with Lullism.


Figure 9: Georg Philipp Harsdörffer’s Denckring, a word generator

Johann Heinrich Alsted consequently reprints Lansius’ poem along with a computation table of its permutations in his Lullist encyclopedia. 60 Leibniz’ Dissertatio de arte combinatoria is, through its many examples and citations, one of the richest sources of 17th century proteic poetry. 61 Between Alsted and Leibniz, the mid-17th century German poet, language researcher and Lullist Georg Philipp Harsdörffer sought to systematically exhaust the potential of combinatorics in linguistics and poetics. Not only did he write two Proteic monosyllabic poems after Lansius’ model—and with a footnote that credits Lansius—, but he also designed a combinatory morphologic word creation machine after the model of Llull’s third “figura.” The Fünffacher Denckring der teutschen Sprache (Five-fold Thought Ring of the German Language) (figure 9 ) should permit anyone to generate all existing and potential words of the German language by the combination of what Harsdörffer calls syllables, but which in modern linguistic terminology are morphemes. At this point, computation is no longer a rhetorical, magical or theurgic means of manipulating language. Instead, language in itself is thought to be computational and algorithmic, a program. While Llull, in his anticipation of symbolic logic, separates what is later called “artificial” from “natural” language with his index letter B-K versus the word entries of the “tabula,” Harsdörffer thinks of everyday natural language as being identical to artificial combinatory language. All language thus is programming language. This idea also sets Harsdörffer apart from the Kabbalists who assigned computational power to divine and theurgic language only—the code of creation—, not to everyday language.

An ultimate hypertrophy of everyday language into program code is reached with the sonnet XIV. Libes-kuss: Vom Wechsel menschlicher Sachen (14th Kiss of Love: On the Permutation of Human Matters) written in 1671 by the German poet, and later heretical “prophet” and “monarch” Quirinus Kuhlmann. 62 Adapted straightforwardly from Harsdörffer’s second proteic poem, reusing most of its words and word poems just like an open source program reuses earlier source code, it also mixes language material from Solomon’s proverbs and, very likely, the preamble of Johann Valentin Andreae’s Rosicrucian Fama of 1614 (see p. 88 ). The result is a monumental proteic sonnet whose permutations even the author can no longer calculate. The afterword stops at spelling out the permutation of 50, a number copied straightforwardly from the permutation table in Athanasius Kircher’s Ars magna sciendi sive combinatoria. (Kuhlmann uses Kircher’s modified Lullist letter code in other poems of the same volume.) The sonnet however is composed not of 50, but of 12 * 13 = 169words, amounting to a total of 13! 12= 3 . 399 * 10 117permutations. It functions as a world machine, permuting, both in the meaning of its words and in its combinatory mechanics, an inventory of the micro- and macrocosm. Its own couplet, and its afterword, claims that to grasp the principle of the permutation of things means to have wisdom of the world. This alludes to the both to the use of Solomon’s proverbs in the poem and adaptions of Solomon’s Song Celestial in the volume in which it appeared. Through this intertextuality, the poem renders itself a Solomonic machine. It is a computational reverse engineering of Solomon’s wisdom, considering the proverbs as they are written in the Bible the fragmentary output of an occult machine.

Beyond being the principle of wisdom, permutation also is the principle of micro- and macrocosm itself: “everything permutes, everything loves, everthing seems to hate something,” as the first line of the couplet puts it. Not only does the poem enrich rhetoric and poetics with encyclopedic Lullism. It also practices Christian Kabbalah through its concept of creation as the permutation of words, in a similar manner as in the Sefer Yetzirah.

Combinatory poetry and the occult

Written in 1671, Kuhlmann’s poem concludes 16th and 17th century word permutation poetry, manifesting the climax and temporary end point of the form. By its hypertrophy of word permutations into a cosmology, it contradicts the secularist tendency of 17th century Lullism of reassessing an originally theological device as a rational method of knowledge classification or, as in Harsdörffer, linguistic analysis and synthesis. Leibniz who on the grounds of rational science transforms Lullism into symbolic logic and an early mechanical calculation device, stands for an opposite to Kuhlmann’s Kabbalist cosmology.

In a less baroque and more minimal-modernist fashion, Brion Gysin’s permutation poem IN THE BEGINNING WAS THE WORD manifests an epistemology with striking parallels to Kuhlmann’s, regardless of its employment of a Honeywell digital computer as the end product of rationalist computation. Gysin conflates divine speech, creation through speech and language permutation as an ecstatic practice just like Abulafia and Kuhlmann did before him. While the poetic algorithm is the same and its metaphysical connotations are similar, the implications differ. The theosophic and gnostic tradition in Gysin’s work is a “dark,” satanic one. It could not be thought of without Aleister Crowley’s satanic travesty of theosophy and Kabbalah (such as in The Book of Lies). 63 As in the work of William S. Burroughs, ecstasy is linked to psychedelic drugs and revelation of a Freudian unconscious rather than religious epiphany.

While Kuhlmann remained within the boundaries of Christian faith, he too ended up as a heretic. Two years after the sonnet was published, he embarked on an occultist-chialistic career. His book Neubegeisterter Böhme (Newly Inspired Böhme, a work ostensibly on the German mystic Jakob Böhme) re-employed the Lullist combinatory method for generating one thousand “theosophical questions.” From there on, Kuhlmann considers himself a prophet, travels through Europe to forge an alliance of Muslims, Lutherans, Orthodox and Calvinists against the pope, fails to convert the sultan in Constantinople, and ends up being burned as a heretic in Moscow.—In striking similarity, Abraham Abulafia tried to bring down the pope with his ecstatic Kabbalah four centuries before. 64 —On his itinerary, Kuhlmann writes a monumental book Kühlpsalter (Cool Psalm), his testament and spiritual poetic diary that in parts continues to employ combinatorial- permutational methods of text generation and wordplay.

Both Abulafia’s and Kuhlmann’s biographies exemplify how computational execution of language transgresses the formal and intellectual realm, turning into a radical practice. It appears that the semantics of executable code does not only reside in its culturally chosen, arbitrary denominators (like Llull’s letters B-K), but also in the very act of execution. Once formal execution is considered a cosmological principle, it becomes synonymous with performative execution. The same formal-performative extremism can be found in the more rigorous early 1960s Fluxus action scores like La Monte Young’s instruction to “Draw a straight line and follow it.” 65 It implies a philosophical defiance of space and time constraints, and reverses subject and object in that the artifice, the line, becomes the subject and the performer its follower, respectively object. In Burroughs’ The Electronic Revolution, technology turns into an autonomous subject, too: language becomes a biological virus, tape recorders take upon the identity of Adam and Eve, typewriters turn into speaking bugs like in David Cronenberg’s filmic adaption of Naked Lunch. The consequences are similar to those of Abulafia and Kuhlmann in that a poetics of executing code transgresses into performance and politics:

Here is a sample operation carried out against The Moka Bar at 29 Frith Street London W1 beginning on August 3, 1972 . . . Reverse Thursday . . . Reason for operation was outrageous and unprovoked discourtesy and poisoned cheese cake. . .

Now to close in on The Moka Bar. Record. Take pictures. Stand around outside. Let them see me. They are seething around in there. The horrible old proprietor, his frizzy haired wife and slack jawed son, the snarling counter man. I have them and they know it.

“You boys have a rep for making trouble. Well come on out and make some. Pull a camera breaking act and I’ll call a Bobby. I gotta right to do what I like in the public street.”

If it came to that I would explain to the policeman that I was taking street recordings and making a documentary of Soho. This was after all London’s First Expresso Bar was it not? I was doing them a favor. They couldn’t say what both of us knew without being ridiculous. . .

“He’s not making any documentary. He’s trying to blow up the coffee machine, start a fire in the kitchen, start fights in here, get us a citation from the Board of Health.”

Yes I had them and they knew it. I looked in at the old Prop and smiled as if he would like what I was doing. Playback would come later with more pictures. I took my time and strolled over to the Brewer Street Market where I recorded a three card Monte Game. Now you see it now you don’t.

Playback was carried out a number of times with more pictures. Their business fell off. They kept shorter and shorter hours. October 30, 1972 The Moka Bar closed. The location was taken over by The Queens Snack Bar. 66

An extension of the logic of algorithmic code into political action exists, more prominently, in the Free Software movement founded by Richard Stallman with the GNU Manifesto in 1983. 67 The popular, anonymous hacker credo that “information wants to be free” supposes a political semantics embedded into formal, digital code, by its technical virtue of boundless and lossless replication. This replication already happens when program code gets executed, i.e. copied from a storage device into the CPU. The Free Software movement translates the logic of executable code into a number of other executable codes: the GNU manifesto as a political instruction code, the GNU licenses as a legal code, free software documentation as a technical instruction code. Even religious activation is involved, although ironically, in dubbing software experts and prominent hackers “gurus,” activists as “evangelists” and, finally, supreme guru and evangelist Stallman himself as Saint Ignutius of the Church of Emacs. 68

Unlike Kabbalism and its permutations, the computational poetic trope of the GNU project is recursion, the potentially infinite looping iteration of a statement (on which Douglas R. Hofstadter’s book Goedel Escher Bach is one long meditation). “GNU” itself stands for “GNU is Not Unix.” It is, in other words, an acronym that contains itself, recursively expanding into “GNU is not Unix is not Unix,” ad infinitum. Recursion is a technical principle also of the Lisp programming language in which much of the Emacs is written. It is furthermore the core logic of the GNU General Public License (GPL) which commands that a derivative work of a GNU-licensed code—be it a modification or extension—must in turn be released under the terms of the GPL. Microsoft therefore calls the GPL a “virus” and refers to code licensed under its terms as a contagion. 69 Indeed, the larger the public body of GPLed program code is, the higher the incentive of programmers to use it for new projects. Since this requires the subsequent release of those projects under the GPL, the body of available GPLed code increases in turn and attracts even more developers to take from and contribute to it. “Freedom” is the metaphysical center of the movement. The GNU manifesto defines it only in its practical meaning for software and software usage, but not theoretically, in philosophical or political terms. It appears to be a freedom founded on the structure of executable code and digital information—an ontology derived from technical function. The place of a theory of freedom is taken by the figure of recursion. It becomes the poetic, philosophical and economic trope in which freedom both materializes and through which it can be grasped, described as in a source code and therefore, paradoxically, controlled.

Information as a code that executes into political action and into utopia existed before the Free Software movement. It was central to the 17th century educational utopias of Comenius, his collaborator and “Royal Society” founder Samuel Hartlib and their intellectual mentor and correspondent, German Protestant theologist and co-author of the original 1614 Rosicrucian manifesto Fama Fraternitatis, Johann Valentin Andreae. 70 Andreae’s 1619 pamphlet Turris Babel (The Tower of Babel) documents his passage from the Rosicrucian “ludibrium,” “playful fancy” as he called it later in his autobiography, to a more concrete educational reform politics. 71 The text is a dialogical satire on the Rosicrucian craze Andreae himself had instigated and which, in the first five years only, had yielded more than 150 public replies from authors who sought to get in touch with the unknown hermetic brotherhood.

With Turris Babel, Andreae joins that debate under his own name and mocks the Rosicrucian hype. However, instead of busting it and outing himself as the plotter, he brings up seventy-five allegorical protagonists who each pronounce their own opinion about the Rosicrucians. In chapter 16, three characters enter the scene, the “reformator,” the “deformator” and the “informator.” While the deformator wants to do away with all traditional ties and institutions including church and state, the reformator hopes for their restoration. The informator finally supersedes their debate by demanding to “inform” mankind so that “the divine law will be saved from the deformator’s corruption and the reformator’s eagerness and become the constitution of this world.”

“Information” refers to its literal Latin sense of “impregnation,” “shaping,” or “instruction.” The informator is an agent of a new Christiana Societas (Christian Society) which the final chapter of the book and Andreae’s later writings propagate and describe. With the Rosicrucians being superseded by the Christian Society, fama is superseded by information, respectively education. In the ideal state of this information society, Andreae’s utopian Christian-communist republic Christianopolis, all knowledge is denoted in public mural paintings. It is precisely the concept of the graphical user interface—borrowed from Tommaso Campanella’s 16th century utopian text City of the Sun—which Comenius implements in the Orbis pictus. Defined against de-formation, re-formation and fama, Andreae’s information is not only loaded with pedagogics and theology, its definition also is radically performative. Information is only what has an impact, reaching and impregnating its recipients just like the execution of a program code mobilizes matter. In Andreae’s Christiana Societas, the origin of the impregnation is “heaven,” the informant is called “God.” Almost four hundred years later, this analysis of “information” seems to be politically and philosophically more precise and rigorous than concepts like “information society” and “information wants to be free” which, passing off “information” as a culturally autonomous, ahistorical and self-perpetuating agent, in fact write a crypto-theology of information.

Setting information free through code and activism, and bringing down the Moka bar, both the Free Software movement and Burroughs’ The Electronic Revolution turn their theoretical Kabbalah into practical Kabbalah solely through their technical understanding of information, language, code. Executable code not only mobilizes matter, but also people. In Abulafia’s and Kuhlmann’s Kabbalism, the code and its execution takes up a life of its own. Both think of them not merely as a reflection, but as a materialization of the divine, and develop this thought from theory into ecstatic and political-theological practice. The step from writing to action is no longer metaphorical, as it would be with a semantic text such as a political speech or a manifesto. It is concrete and physical because the very code is thought to materially contain its own activation; as permutations, recursions or viral infections. It is not only words made flesh, but words being flesh.

Computation as a figure of thought

Lullist imagination

Explicit and hidden theological politics seem to run through the various poetics and cultural practices of formally executable code, yet contradictory tendencies exist as well:

  1. Totalism vs. Fragmentation
    1. Totalism / Synthesis

      The employment of algorithmics, permutation, combination and recursion to exhaust all existing aspects of a matter: The exhaustion of topics in rhetoric, the exhaustion of theological truth in Llull’s ars, the exhaustion of knowledge in Lullist encyclopedism, the exhaustion of wisdom in Kuhlmann’s poem through reverse-engineering Solomon.

      Algorithmics functions as expansion of a small source code into a near-infinitude of material.

      This tendency culminates in Quirinus Kuhlmann’s theoretical sketch of an Ars magna librum scribendi, a universal letter combination machine designed to write all existing and potential books in the world (see p. 105 ).

    2. Fragmentation / Analysis

      Generative classification of knowledge in turn compartmentalizes it into specialist domains. Program execution can be seen as the handling of complexity, the possiblity of reducing, for example, one hundred pages of proteic verse permutations to one line of material and one paragraph of instruction; or the reduction of several thousands statements created by Llull to three algorithms and one table of terms.

      In other words, combinatory knowledge classification embodies the dialectic that not only an abundance of information can be generated from a minimal source code, but that vice versa an abundance of information can be analytically reduced to one algorithm.

  2. Rationalization vs. Occultism
    1. Rationalism

      The indexing and classification of knowledge, the development of artificial formal languages as “user interfaces” for data and algorithms, computation as such.

    2. Occultism

      Theurgy, totalism expanding into demiurgic creation, code execution translating into practical political theology.

      Kuhlmann’s example shows that theurgy and demiurgy are not necessarily precursors of a scientific rationalization, but that scientific rationalization (like that of 17th century encyclopedic Lullism) itself can be used as a philosophical ground for occult theology, precisely as an attempt to exceed scientific Lullism in a physical and metapysical, microcosmic and macrocosmic grasp of totality. This further proves that the cultural history of executable code cannot simply be written as a linear Hegelian progress from magical to scientific practices.

  3. Hardware vs. Software
    1. Hardware

      There is a tendency of building computational hardware for algorithms: the device described in the Sefer Yetzirah, Llull’s and Giordano Bruno’s combination wheels, Harsdörffer’s Denckring. Kuhlmann, too, designs a Wechselrad (permutation wheel) to speed up the permutation of his sonnet.

    2. Software

      The rhetorical tradition of mental computation and memorization, in the “inventio” and “memoria.”

      Abstraction from mechanical devices through symbolic handles and denominators, for example in the replacement of Llull’s mechanical “figurae” through abstract symbolic denominators in later symbolic logic and computer programming languages.

  4. Syntax vs. Semantics
    1. Syntax

      Program code as purely formal and therefore syntactical abstraction from human language.

    2. Semantics

      The inscription of metaphors and semantic handles, from Llull’s letters B-K up to statements like “for,” “while,” “if” in programming languages.

  5. Artificial vs. Natural Language
    1. Artificial Language

      The idea that language can be computed only through a purely formal, syntactical metalanguage that exists separately from natural language.

    2. Natural Language

      The idea that common human language itself is a product of computation, and can be described with algorithms, such as in Harsdörffer’s Denckring, Kuhlmann’s poetry or artificial intelligence research.