137 - Arthur I. Miller [39]
“Geometry is the archetype of the beauty of the world”
Kepler believed in a reality beyond appearances. To him the three-dimensional sphere was the most beautiful image because it symbolized the Holy Trinity, the Triune God, with God the Father at the center, the Son at the circumference, and the Holy Ghost emanating from the center, as the radius. Thus there was an unchanging relationship between the circumference, the radius, and the center point. As he put it, “Although Center, Surface, and Distance are manifestly Three, yet are they One.” The curved surface of the sphere with no beginning and no end represented the eternal Being of God.
The universe, with the sun at the center and the planets revolving around it in three-dimensional space, was the perfect sphere and thus the very image of the Holy Trinity. Kepler saw it as a triumph of geometry, the discipline which to him ranked highest among the sciences. Pauli quotes from Kepler three different assertions of this:
The traces of geometry are expressed in the world so that geometry is, so to speak, a kind of archetype of the world.
The geometrical—that is to say, quantitative—figures are rational entities. Reason is eternal. Therefore the geometrical figures are eternal; and in the Mind of God it has been true from eternity that, for example, the square of the side of a square equals half the square of the diagonal. Therefore, the quantities are the archetype of the world.
The Mind of God, whose copy is here [on earth] the human mind, from its archetype retains the imprint of the geometrical data from the very beginnings of mankind.
Writing in 1952, many years after he began his association with Jung, Pauli could not have failed to notice the appearance again and again of the word “archetype.” The axioms of geometry, Kepler believed, are imprinted in our minds from birth by the Supreme Geometer. “Geometry is the archetype of the beauty of the world,” he wrote.
In his thinking Kepler was influenced by the philosopher Proclus, who lived in the fifth century A.D. Proclus believed that mathematics—to be specific, whole numbers—held the key to understanding the nature of God, the soul, and the world-soul—the ethereal order and beauty of the cosmos. He wrote of an eternal unchanging universe, governed by laws of mathematical order and different from the imperfect world in which we live. His universe emanated from the One. Later commentators interpreted this One as a fecund Deity who gives light, warmth, and fertility.
Echoing Proclus, Kepler argued that it made sense to assume that the sun, not the earth, was at the center of the universe. Only thus could it “diffuse itself perpetually and uniformly throughout the universe. All other beings that share in light imitate the sun.” The sun, its light, and the sphere of the fixed stars reveal the Holy Trinity before our very eyes. As Pauli put it: “because [Kepler] looks at the sun and the planets with this archetypal image in the background he believes with religious fervour in the heliocentric [sun-centred] system…. [It is his religious belief that impels] him to search for the true laws of planetary motion.”
Thus the discovery of the sun-centered universe and the mathematical concepts that went along with it, including three-dimensional space, could be traced to the visual image of the abstract sphere representing God the Trinity—an archetype from deep in the collective unconscious. This was a product of a geometry, wrote Kepler, that “supplied God with the models for the creation of the universe.” The sun-centered universe reflected God’s glory and this was why Kepler was impelled to search out its laws.
Pythagoras, apostle of fourness
Pauli traced the origins of Kepler’s thinking back to the Greek scientist and priest Pythagoras, who lived around 500 B.C.
It was Pythagoras who pioneered the quest for a link between numbers and the cosmos. Pondering the hidden meanings of the world around him as he played on his lyre