137 - Arthur I. Miller [40]
Perhaps numbers might belong to a world beyond perception, which could only be fully apprehended by thought. His striking conclusion was that the numerals 1, 2, 3, and 4 represented all known objects: 1 represents a point; 2 points can be connected by a line; 3 points make a triangle, in particular a perfect equilateral triangle; and 4 points make a tetrahedron, a pyramid of three perfect triangles. From these could be constructed the five “Pythagorean” solids (later “Platonic” solids after Plato): the tetrahedron, cube, octahedron (eight equilateral triangles), dodecahedron (twelve pentagons), and icosahedron (twenty equilateral triangles). Each could be circumscribed by a sphere, with each point of the solid touching its surface, and each could also contain a sphere whose surface touched each of its sides.
Represented as dots, 1, 2, 3, and 4 form an equilateral triangle set out in four rows, known as the tetraktys (tetras is Greek for “four”):
Pythagoras’s tetraktys.
To Pythagoras this analysis made sense of our world, in which he recognized four elements (earth, water, air, and fire), four seasons, four points of the compass, and four rivers of paradise (the Pishon, the Gihon, the Tigris, and the Euphrates). His followers swore an oath “by him who has committed to our soul the tetraktys, the original source and root of eternal Nature.” The sum of the numbers that made up the tetraktys is ten, which Pythagoras considered the perfect number. Once we have counted to ten, we return to one, the number of creation.
Pythagoras’s claim was that numbers were the fabric of our universe and existed independently of us. Numbers were the keys through which could be heard the harmony of the cosmos.
The Kabbalah
The Egyptian god Thoth, known to the Greeks as Hermes Trismegistus (“Thrice-great Hermes”), was credited with a huge number of writings on philosophy, astrology, and magic. Over the centuries Hermetic literature incorporated elements of whatever science existed as well as the teachings of Pythagoras.
In Kepler’s time Hermetic literature was enthusiastically embraced as an antidote to the rational approach of Greek philosophy and science. It was full of mystery and magic and spoke in terms of a vital or living force at the heart of the cosmos. Hermetic literature also included kabbalistic texts.
Versions of the Kabbalah had begun to appear in the thirteenth century. A principal theme was how one might see the invisible in the visible and the spiritual in matter. The Kabbalah discussed the clash between opposites like light and darkness to produce the world in which we live. Someone like Kepler, who was interested in the teachings of Proclus, was naturally drawn to the Kabbalah with its similar theme.
A central notion of kabbalistic philosophy is the Sephirot. The Sephirot is usually represented as the tree of life with ten branches rooted in the earth and extending to Heaven, signifying the earth as a microcosm reflecting the universe, the macrocosm. It is made up of five pairs of opposites—beginning and end, good and evil, above and below, east and west, and north and south—and thus has ten emanations, ten being a holy number in Judaism as well as in Pythagoreanism.
By the end of the fifteenth century the Kabbalah had been integrated into Christian theology, though the Christian Kabbalah emphasized the Trinity rather than the Sephirot. Christian thinkers were especially fascinated by the Gematria, which assigned numbers to letters of the Hebrew alphabet. This concept of numbers for language opened up the possibility of assigning numbers to the various names of God, thereby further revealing His celestial powers and His mystery. Thus the Kabbalah became identified with magic and numerology. (Until the nineteenth century the Hebrew