Ars combinatoria: mystical systems, procedural art, and the computer

Though the I Ching was little known in the West before the nineteenth century, a diagram of a particular sequence of the hexagrams developed in the Sung period was sent by a Jesuit missionary to Leibniz, who had been developing a binary system of mathematics, the system on which computer language is based. Apparently, Leibniz was amazed and thrilled to see it because it validated his conviction that there were spiritual truths to be found in mathematical forms.(25) We can get a glimpse of this link between numbers and spirituality in Chinese thought by looking at the Tao T'e Ching by Lao T'se: "Tao gave birth to the one, the one gave birth to the two, the two gave birth to the three, and the three gave birth to all things."(26)

John Cage relied on the I Ching as a systematic basis to determine several aspects in a number of his works. So many of Cage's works were permutational (as well as having a variety of other procedural foundations) that it would be impossible to describe them all here. But two abiding principles in his work apply. The first is that he often used chance and/or indeterminacy for the positioning of elements in his pieces. (Indeterminacy refers to events that might be out of the artist's control but not chance-derived, like the choices left to the performers.) The second is that, in many of his works, no two performances would be alike, though they might include all of the same material. This was usually because they were devised so that the parts would fall together differently every time. In those situations, this might be because he and the artists he collaborated with (such as the choreographer Merce Cunningham) worked independently and only saw the synergistic results at the end of the process. Or, more pertinent to this discussion, because elements in his own work were "scored" to have ever changing positions, usually dependent on chance operations and indeterminacy at the moment of performance. Toward the end of his life, Cage used the computer more often as a tool to continue and expand on the complex systems he had developed throughout his career. Though he began as a composer, Cage eventually did not confine himself to one medium or discipline. He composed music, wrote texts, made theater pieces, made visual work, and, more often than not, used two or more disciplines in a single work.

Early on, Cage wrote music that recombined a given number of elements. To make Williams Mix in 1952, he painstakingly hand-spliced digital sound tapes, cutting them into tiny pieces and reassembling them according to a structure that was determined by chance operations [ILLUSTRATION FOR FIGURE 8 OMITTED]. Williams Mix lived as eight separate mono tracks that were played simultaneously, presenting the possibility that the tracks would fall together differently every time it was played. Cage stressed that a recorded version was, then, not definitive.(27) In 1969 he worked with Lejaren Hiller to make HPSCHD, a piece for fifty-one computer-generated sound tapes and seven solo harpsichord parts. The composers used Mozart's dice game structure for the solos and filled the blank measures with various elements, the choices made, appropriately, by the roll of dice. They also used a computer program that approximated the I Ching's chance operations to assemble other solos and the fifty-one sound tapes. Much of the variety in live versions of HPSCHD depended on a wide lattitude given the performers to make their own choices from a large amount of material.(28) For a recording of the work, another element of indeterminacy was thrown into the mix: the listener is presented with a computer-generated set of instructions, showing how the knobs of the stereo system should be turned to change channels and volume for specific sections. Hiller notes, "It's the first instance that I know of where the home listeners hi-fi set is integral to the composition."(29)