An Unfolding Geometry: Appropriating Proclus in the Harmonice mundi (1619)

Johannes Kepler’s Harmonices mundi libri V (1619) is capable of leaving the modern reader with an impression of grandeur and triviality. It is long, complicated, and at times impenetrable. It mixes heavy metaphysical concoctions with an at once technical and quixotic geometry. A single page announces Kepler’s discov- ery of the relationship between planetary distance and period, what would later be known as the “third law”, yet most of the book has nothing to do with said relation. Nevertheless, the Harmonice can also be seen as among the most coherent and sophisticated works of mathematical natural philosophy in the early modern period. Kepler’s celestial harmonies are grounded in his account of what mathematical entities are, how they are known, and how they inhabit the world. He was trying to find a single, finite ensemble of proportions that would determine the world’s large- and small-scale architecture, as well as the behavior of its constituent parts (including humans and animals). More than this, he was operating from the very deep assumption that these proportions would be unified in the source of existence, God. Thus the philosopher or historian of philosophy should be interested in the Harmonice as an attempt to justify one of the crucial themes of mathematical physics: not only that the world’s movement expresses proportionality, but that this world and its mathematical language are unified. Indeed, the book’s broad diversity – loosely based on the quadrivium – evinces an almost elegant consonance when considered from this point of view. From his geometrical musings, to his astrology, to his interpretation of harmony, Kepler creates an eminently knowable world system that can be derived from a single and essentially unified form, the sphere or circle. But in doing so, Kepler must explain intellectual movement. He must explain how geometrical knowledge is unpacked from the soul and set moving in the body, as well as in the embodied mind. It is on this point that Kepler owes a debt to Proclus in the Harmonice. Proclean geometry is a kind of movement, an unfolding of dimensionless forms into quantity, and it is precisely this unfolding that Kepler adopts, recasting it in his own vitalist framework. Moreover, as Kepler aficionados know, we can only with difficulty draw lines that separate phenomena of the living body from phenomena of the wider world. Not to be disappointed, we find Kepler at the summit of his Harmonice turning the vast celestial gyrations into a vision of the unfolding Proclean mind.