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Ars combinatoria: mystical systems, procedural art, and the computer
Art Journal, Fall, 1997 by Janet Zweig
In the twentieth century, ars combinatoria can be found extensively in artistic production. The imagined ars combinatoria in Jorge Luis Borges's story "The Library of Babel" looks to past traditions as well as to the potential future of the form by artists. among whom Borges has been so influential. It describes a "universe" or "Library" that consists of "an indefinite and perhaps infinite" structure filled with volumes of text, each a unique and random permutation of the letters of the alphabet.(22) Borges clearly refers back to the Sefer Yetzirah, to the Kabbalah, and to the medieval notion of the world as a book. Because permutations of finite items, when repetition is allowed, provide infinite variations, Borges touches on the notion that exhaustive variations suggest a key to the mysteries of the infinite. (The mathemetician Rudy Rucker explains that Borges's Library, however, is finite, though very large, because the number of pages and letters in the books are all the same. Only if the books could be of any possible finite length would the library be infinite.(23))
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There are many other examples of the combinatorial in twentieth-century art, especially in the 1960s when the idea of the computer had entered the public imagination. While the development of collage by the Dadaists in the early part of the century and appropriation by postmodern artists in the later half of the century could each be considered a kind of recombinant approach, they are not, strictly speaking, permutational. (One could make a case for the fact that they are combinations, i.e., elements that are taken from a larger set of preexisting elements and then combined with each other in a new way. The preexisting set, however, is the set of everything.) Real permutational systems of art making were employed by a number of artists who used conceptual, serial, or procedural strategies.
John Cage, over a lifetime of procedural work, made use of permutation, combination, and variation. Before discussing Cage, however, it is necessary to leave our chronology, go back thousands of years, and look at another ancient example of ars combinatoria that greatly influenced him, the I Ching.
The I Ching, or Book of Changes, is a method of divination based on a binary system and chance operations. This mechanical oracle was developed over hundreds of years during the first millennium B.C. Based on a philosophy that considers the importance of chance and perpetual change, the mechanism works in this way: first, one asks a specific question; then, either by tossing three coins or by dividing and counting yarrow stalks in a much more complicated procedure, one arrives at numeric data that represent, finally, one of only two polarities. This is represented as either an unbroken line (yang force) or a broken line (yin force). Repeating this procedure six times results in two trigrams of three lines each that are then united to form a hexagram, a stack of six unbroken and/or broken lines. The variations of unbroken or broken lines in a structure of six positions are 26, or 64, possible arrangements [ILLUSTRATION FOR FIGURE 7 OMITTED]. An added complexity of possibilities is the fact that each unbroken or broken line is either unchanging or changing to its polar opposite depending on the numeric value of its coin toss or yarrow-stalk counting. If one or more lines is changing, a second hexagram is formed, representing how the questioner's situation will change. The interpretive texts for the hexagrams give guidance to the questioner in the form of symbolic situations.(24)
