before its beginning? Looking backwards from the threshold of the epoch, we find that the distinction between translational and rotational motion, which is at the core of all kinematic endeavor in the nineteenth century, has a long and momentous history, a history that structures Western metaphysics and theology in significant, yet undisclosed ways. The threshold of kinematics was crossed at the moment when the double-acting steam engine required mechanisms that forced a compromise between rotation and translation. Of course, there were earlier attempts to tackle this problem, as all machines, regardless of their motor, are apparatuses for forcing motion, and water- and windmills in particular had long been outfitted with sophisticated transmissions that turned the motion of the wheels into all manner of reciprocal and intermittent motion. The steam engine, however, required the conversion of motions in both directions, from translation to rotation and vice versa, and it thereby raised the question of their relation to a general level. Theoretical kinematics attempted to deliver a priori rules of this forcing, but, despite Reuleaux’s historical interest, it had no consciousness of its implications and antecedents. The following all too brief overview over the metaphysics of motions up to the nineteenth-century attempts to make up for this lack.8
The most influential early text in the valuation of motion, itself a summa of extended previous debates, is book 10 of Plato’s Laws. Corporeal motion for Plato indicates a state of deficiency with respect to the immutable realm of ideas; it is a predicament of the world insofar as it is secondary, changeable, and imperfect. Nonetheless, not all motions are equal, and in the hierarchy of motions the best is that which reaches into immutability. This must be the motion of the soul, for the only relation that exists, in Plato’s thought, between the world of ideas and the world of changeable and changing things is the soul. Its motion is the best; it is, like Newton’s mass points, free in every direction, but it has the ability to originate motion. Only after this bridge to the ideas has been established—in a way that foreshadows Aristotle’s concept of a pure origination of motion in the unmoved mover—does Plato rank motions in space. Rotation, combining rest (of the central axis) and motion (of the periphery) is an image of psychic motion and therefore the best possible corporeal motion. Below rotation Plato puts the continuous sliding or rolling motion of bodies in translation, followed by phenomena we would not recognize as essentially kinetic, like growth, division, and disintegration. A little further in the text (898a), he contrasts rotation and translation as motions appropriate and inappropriate to the soul, the motions of rationality and of irrationality respectively. In the cosmogony of Plato’s Timaios—the most important of his dialogues for the Middle Ages—the demiurge endows the earth with rotation, “which, among the seven motions, is the motion most appropriate to reason and wisdom.” The six other motions are the translational “freedoms” of a rigid body: back, forth, left, right, up, down. As translational motions they are nothing but “deviations.”9 The earth’s rotation and the sphericity that results from it comprise the straight-line motions of the polygons of which the earth is made up—a contrast and tension that has found its most enduring image of the nested solids surrounded by spheres in Johannes Kepler’s Mysterium cosmographicum.10
Aristotle accepts the hierarchy between rotation and translation but seeks to integrate it into a worldview that no longer posits a chasm between ideas and phenomena. The arguments in book 8 of his Physics for the eternity of motion, the primacy of locomotion over other forms of change, and the superiority of rotation over other forms of locomotion establish an uninterrupted chain of causes from the unmoved mover to cosmic and then to natural motions. Rotation is superior not only because it is the motion proper to the spheres of the cosmos but because rectilinear motion for Aristotle could never be continuous and infinite. In a spherical, finite cosmos it would at some point have to reverse itself, and this reversal—logically speaking, this self-contradiction—could be understood only as deficient. The linear rise of fire and the straight fall of a stone are motions that characterize the sublunar sphere, which is no longer in rotational motion.11 Whatever their differences, for both Plato and Aristotle the hierarchies of motion are directly tied to the demands of onto-theology. The superiority and primacy of rotation derive from the fact that the coincidence of motion and stillness, of change and identity, of oneness and differentiation, is an indelible trace, or even a property, of divinity and reason in the cosmos.12 The competing atomistic theory of particles falling in straight lines from which they are deflected by random inclinations was atheistic in precisely this onto-kinetic respect.
The disjunction between supralunar divine rotation and sublunar straight-line translation endures and is enriched in Christian kinematics by an anagogical dimension. Rotation is the motion of a redeemed world, of a world no longer disfigured by the gravitational pull of original sin. Nowhere is the divinity of rotation set against the drag of translation with more intensity than in Dante’s Divine Comedy. After having endured the descent into the inferno, where the severity of punishment increases in proportion to the linear distance from the surface, and after having made the complementary ascent to the summit of purgatory, where the unburdening of sins follows the helical path of a screw, the voyager is finally led to the contemplation of ever more beautiful and intricate rotational formations, until he sees “quella circulazion” that is the godhead.13 Dante’s exaltation of rotation accords well with the doctrine of Thomas Aquinas, who adopted the hierarchies of motion from Aristotle and projected them onto the created world, as well as onto the history of salvation. Aquinas makes the additional point that rotation, unlike the translational motions of rising and falling, which are their own contraries, does not have a logical opposite. The circularity and infinity of rotation are visible signs of God’s thought, manifest in the motion of the heavens and in the circle of incarnation, in which divine and human nature are indistinguishably joined.14
Taking into account these enormous ontological and theological investments in the opposition of rotation and translation, it is hard to see how the revaluation of motions initiated by early modern physics could have been more radical. Christian doctrine was appalled not so much by the statement that the earth moved as by how it was supposed to move. For with regard to both its cause and its form, motion in modern physics is godless: it is inertial, that is, uncaused, and it is, in its final formulation by Isaac Newton, purely translational.
Some transitional steps softened the radicalism of this new paradigm. One was the survival of Platonic theories of form. In a late dialogue, Nicholas of Cusa describes a bowling game in which the bowling ball is deliberately made imperfectly round so as to trace an unpredictable path. This leads the bishop to speculate on the implications of perfect rotundity, one of which is that a perfectly round body could not be seen. For since a perfect sphere would touch a plane only at one point, and points have no extension and hence cannot compose a surface, a perfectly spherical body would always remain invisible. Interestingly, Nicholas claims that this invisibility holds true not only for ideal forms but also for real bodies should they be turned perfectly round on a lathe. The dynamic equivalent to this thought is that a perfectly round body, once set into motion, whether rolling on a plane or rotating around its axis, would have no reason to stop moving. From the metaphysics of rotundity, then, the first ideas of “real” inertial motion arose.15
Another facilitating factor in the emergence of “natural” translations was that various discourses on natural motion tilted the angle of translational motion by ninety degrees: as the celestial spheres around the earth broke open, things moving in a straight line no longer had to drop into the pits of hell below man’s feet but could also recede horizontally into an infinite distance. Striking images of this tilted and theologically neutral kinetics are the ever-shallower ramps onto which Galileo lets his bronze balls roll to demonstrate the laws of the free fall of bodies.16 Earlier advances in horizontalizing man’s worldview subtended Galileo’s physical experiments. The most momentous of these surely is the “invention” of central perspective, based as it is on the horizontal coincidence between the observer’s viewpoint and the image’s vanishing point. This relationship, rather than imposing itself statically, is held together by the intromission (or extramission, as the case may be) of visual rays in the eye of the viewer. It is important to recognize that behind the static geometry of linear perspective is a kinetics
