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Ars combinatoria: mystical systems, procedural art, and the computer
Art Journal, Fall, 1997 by Janet Zweig
An example of this more purely formal approach to the combinatorial arts is found in games for musical composition in the eighteenth century. Music, with its abstract notation, lends itself directly to recombinancy. These musikalische Wurfenspiele or musical dice games consisted of a number of musical elements that could be recombined via a formal structure and the random function of throwing dice to select the elements. The results needed to adhere to a particular musical form such as a polonaise. The first musikalisches Wurfenspiel, written by Johann Philipp Kirnberger in 1757, recombined phrases of six to eight measures. The possible new musical compositions are 11(14), far too many ever to listen to. Other composers used measures or smaller units for recombination. C. P. E. Bach used individual notes as the units and developed a lengthy process of ordering them through random selection. Mozart and Haydn also composed for dice games, each using a slightly different "program."(19) (Mozart's dice game, too, has been translated for use on the computer.(20)) And a new element has entered: chance. The dice game is not an intentional system, but a system driven by a random function [ILLUSTRATION FOR FIGURE 5 OMITTED].
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Also in the eighteenth century, Jonathan Swift wrote a parody of systematic thinking in Gulliver's Travels, where he describes an imaginary permutational machine [ILLUSTRATION FOR FIGURE 6 OMITTED]. The "professor" in the story has been described variously as a caricature of either Leibniz or Llull. When Gulliver visits the Grand Academy of Lagado, he is shown an amazing device "for improving speculative knowledge by practical and mechanical operations." The mechanism consists of a frame holding square blocks:
These bits of wood were covered on every square with papers pasted on them, and on these papers were written all the words in their language ... but without any order.... The pupils ... took each of them hold of an iron handle, whereof there were forty fixed round the edge of the frame, and giving them a sudden turn, the whole disposition of the words was entirely changed. [The professor] then commanded six and thirty lads to read the several lines softly as they appeared on the frame; and where they found three or four words together that might make part of a sentence, they dictated to the four remaining boys who were scribes ... the professor showed me several volumes in large folio already collected, of broken sentences, which he intended to piece together, and out of those rich materials to give the world a complete body of all arts and sciences.(21)
In the nineteenth century, there was a great deal of activity in the realms of mathematical logic and probability theory leading toward the idea of the computer. George Boole and Charles Babbage each brought the world closer to what would eventually become this ultimate (or at least extremely efficient device for ars combinatoria. Separated entirely from these pursuits, Kabbalistic traditions and Lullism continued actively in various forms.
