The Cylinder. Helmut Müller-Sievers

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 of vision and of bodily motion, for in this manner the human body and its dimensions are connected to an increasingly linear universe.¹⁷

      Leon Battista Alberti set this preference for horizontal lines in stone. In his foundational treatise De re aedificatoria he challenged the unfavorable etymology that derived the name of the builder’s profession from the curve (arcus) of the roof (tectum).¹⁸ He asserted that rather than celebrating transcendence, as cathedrals do in their height and vertical intricacy, churches as well as representative palazzi and private homes should exhibit strong horizontal lines that converge on the altar, or on doors and windows.¹⁹ These lines were understood as guidelines for visual rays on which the objects of vision traveled to and from the eyes. This inherent belief in the coincidence of geometric lines and natural motion found its most confident expression in Galileo’s assertion that the book of nature and its motions was written in the language of geometry.²⁰ The relation of priority that Alberti established between the regularity of geometric proportions and lines and their embodiment in the motion of extended bodies would hold for many centuries, and in many fields. The house of memory, for example—the aid by means of which an orator would memorize the parts of his speech and their sequence—underwent an Albertian renovation: whereas ancient and medieval memory houses had regarded the difference between the rooms and the floors as an aid to memory, in early modern memory houses rooms were differentiated solely by their connection to other rooms.²¹

      Also the active employment of the intellect was conceived as moving along straight lines with regular bifurcations and on a plane without curvatures. Early modern textbooks of logic often included bewildering diagrams showing the spatial array of logical relations as rectangles with any number of connective links.²²

      Ong insists that this linear charting of intellectual motion was deeply indebted to the invention of the printing press, and specifically to the rectangular uniformity of its page and its type. The rectangle of the printed page provided a coordinate system in which geometrical analysis and speculation on the extent of linearity and calculability could take place. The emerging systems of natural history sought to capture the variety of natural forms in catalogs that showed linear dependence of species very much like the diagrams of early modern logicians.²³ Works like Luca Pacioli’s De divina proportione (1509) sought to arrive at a universal, geometrically modular typeface that in turn would be able to represent a universal language, actively sought by European learned societies at the time. Pacioli was equally convinced that the human face exhibited geometric proportions; neither type nor face was as yet subject to the kind of intuitive physiognomies that in the late eighteenth century would brush away all geometric and linear constructions.²⁴

      In the notion of proportion, however, the other, “Platonic” side of the new geometry came to the fore: proportion was “divine” insofar as it could not be assigned an exact number, yet it was an integral part of geometric patterns and, what is more, a sign of beauty. The circle and the sphere in particular embodied this rest of divinity in a world that was increasingly defined by numerical values. The relation between circle and square (and their relation to the human body, as in Leonardo’s Vitruvian Man), the relation between the circumference and the diameter of the circle, and of course the golden ratio were favorite objects of speculation in the