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

Art Journal, Fall, 1997 by Janet Zweig

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In science, there are wonderful coincidences with the systems described here. Combinatorial systems are at the heart of our chemical and genetic makeup. The carbon atom is distinctive for its ability to combine with other carbon atoms as well as with many other elements in elaborately complex ways, forming long molecular strings. In fact most of our bodies are made up of just four elements, carbon, hydrogen, oxygen, and nitrogen. The scientist John Gribben writes, "the complexity of living molecules arises not from the fact that they contain a great variety of different kinds of atoms ..., but from the fact that these four kinds of atoms can be combined in large numbers in very many different ways."(44)

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At the genetic level, we are also defined by a four-part code. The four nucleotides, or building blocks, of DNA are adrenine, cytosine, guanine, and thymine (A, C, G, and T). Along the chromosomal double helix, these four are uniquely ordered and paired for each person, spelling out specific genetic information, depending on that order. A single chromosome of the forty-six each human carries in every cell may have as many as five billion nucleotide pairs. Everyone's genetic information is different, though spelled out only by variations of A, C, G, and T. Each parent passes on a unique set of only twenty-three chromosomes to each offspring. The two parent sets form a new combination of forty-six chromosomes with its own individual genetic code.

In mathematics, combinatorial systems overlap with set theory, and set theory opens many of the mystical themes about the nature of numbers and infinity. A set is a combination or grouping of things. George Cantor, who developed some of the fundamental principles of modern set theory in the late 1800s, said, "A set is a Many which allows itself to be thought of as a One."(45) We combine or make variations from a given set of elements, creating new sets. Any number of real things, imaginary and intangible things, as well as other sets can be combined to create a new set, making the number of possible sets infinite. We can imagine an absolute set or a set of all sets, but that set is never attainable. Since a set cannot contain itself, a new set can always be made by adding the current set of all sets to all of the other sets, ad infinitum.

In cosmology, there are more coincidences with the mystical or generative aspects of our examples. According to the most currently accepted theory of creation, our universe started at the Big Bang. Some theorize that this universe was at first what scientists call "a singularity," defined either as one very dense "seed" or "point" smaller than a proton which contained all of the matter currently in the universe,(46) or "a state of zero size and infinite density."(47) These theories can be compared to mystical systems that define God as the One, the Absolute, and, at the same time, the Infinite.

There is also debate about whether our universe is open or closed, that is, infinite or finite. It is certainly expanding, and some cosmologists believe it may continue to do so forever, while others believe that at some point it may begin to fall back on itself. This brings up the theme of the exhaustion of permutational possibilities. At the end of the 1952 science fiction story by Arthur C. Clarke cited in the epigraph to this article, "The Nine Billion Names of God," the universe ends at the moment that the Tibetan monks, using the computer, print out the very last permutation of these nine billion names. The dual notions of permuting a closed system to exhaustion versus making variations on a set of things to infinity are closely linked with mystical speculations. The number of permutations of the Hebrew alphabet is very large but finite and exhaustible; Abulafia permuted to ecstatic exhaustion; Raymond Queneau devised a system that was exhausted at the precise number of 100,000,000,000,000; and the computer can theoretically make variations on the Is and Os of binary code to infinity. Here, the only thing that can be said with certainty on this subject is that once one starts to explore the permutational realm, the examples, coincidences, and possibilities seem endless and inexhaustible.

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

Art Journal, Fall, 1997 by Janet Zweig

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