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Ars combinatoria: mystical systems, procedural art, and the computer
Art Journal, Fall, 1997 by Janet Zweig
This divine name is the Tetragrammaton, or YHVH, according to the Kabbalists. The 231 "Gates" correspond diagrammatically to the number of lines that can connect the twenty-two letters of the Hebrew alphabet when they are placed in a circle, in other words, the number of two-letter combinations that can be formed [ILLUSTRATION FOR FIGURE 1 OMITTED].(7)
The ten numbers, or sefirot, are divine, and they represent ten divine emanations. A diagram called the Tree of Life, derived from the Sefer Yetzirah and represented in many different versions over the centuries, shows how the ten numbers are connected by exactly twenty-two lines, corresponding to the twenty-two Hebrew letters, when placed in a particular arrangement [ILLUSTRATION FOR FIGURES 2, 3 OMITTED].
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The mathematical ideas in the Sefer Yetzirah continue with an illustration of factor analysis:
Two stones build 2 houses
Three stones build 6 houses Four stones build 24 houses Five stones build 120 houses Six stones build 620 houses Seven stones build 5040 houses
From here go out and calculate
that which the mouth cannot speak and the ear cannot hear.(8)
The stones appear to represent the letters of the alphabet. The number of permutations that are possible with a given number of letters is the factorial of that number, expressed as n! or 1 x 2 x 3 ... x n. The permutations of the entire Hebrew alphabet are 22!, or 1,124,000,727,777,607,680,000.(9) This enormous number must be "that which the mouth cannot speak / and the ear cannot hear." Or, if the series is continued ad infinitum, the author may be referring to the infinite. So this idea is expressed: from one comes an infinite number of things, or from the Infinite One comes an infinity of matter.
The text of the Sefer Yetzirah can also be read in the imperative as instructions, suggesting to the reader a means of creative invention. Permuting the symbols can act as an "operational agent" that could actually produce beings in the world.(10) The skilled mystic can imitate God's creative ability on a much smaller scale by using the techniques suggested in the Sefer Yetzirah as meditative and creative tools. In the Talmud, there is a story about two rabbis who practiced creative magic one Sabbath night and managed to produce a small calf, which they then ate.(11) The myth of the Golem has arisen out of the techniques suggested in the Sefer Yetzirah. The Golem is a mute humanlike creature, a robot, which mystics fabricate by using a magical method that includes a systematic meditation on and permutation of numbers and letters.
The Sefer Yetzirah was studied and interpreted in later centuries by the Kabbalists, who were scholars and practitioners of Jewish mysticism; their activity flowered in thirteenth-century Spain and France. (Kabbalah literally means "tradition.") Abraham Abulafia was a Spanish Kabbalist with a distinctively systematic approach toward achieving ecstatic mystical experience. He believed that the soul was "sealed" from unity with the Infinite or the Divine, and through specific meditative techniques that lead to ecstatic visions, these seals could be broken. Many of his techniques consist of meditation on and practice of Temurah and Gematria. Temurah is the permutation of letters, often with the Name of God, or Tetragrammaton. Each letter of the Hebrew alphabet has a numerical value, so Gematria is the calculation of the numeric value of each word by adding up those numbers; the relationships of words are based on their numeric values. Abulafia's "science of combination" describes methods of using these techniques to achieve a heightened state of consciousness. He writes:
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