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CHAPTER 3

The Valuation of Motions

The ubiquity of the cylinder in the machines and products of the nineteenth century is due to its kinematic properties—its ability to force, transmit, and apply (to use a ethically paradoxical term) single-freedom motion. This insight translates the traditional triad of motor, transmission, and tool into the kinematic triad of forcing, translating, and applying motion. Kinematics, as Reuleaux’s work shows, affords a view of machines from the inside out; much like the allegorical readings of old, which focus on intra- and intertextual relations, kinematics focus not only on the design and the necessities of individual devices but also on their interrelation, sometimes across several generations and avatars.¹ These relations are visible in the transmissions proper—for example, in Watt’s parallel motion, in the driving gear of a locomotive, or in the mechanism of a front loader—while they also connect the kinematics of the motor (the cylinder of the steam engine), the new motions of the tools (the rolling of steel mills), and finally the objects these machines produce (the tin can, the pipe). Kinematics provides a standpoint from which to recognize in hitherto unrelated phenomena their underlying embodiment of motion. For example, it has often been argued that the nineteenth century, through its ability to machine and lubricate journal bearings, reinvented the wheel; but half-journal bearings were also used to allow the Galerie des Machines, an iconic iron and glass structure that spanned the largest interior space in the world in 1889, to expand and contract.² Just as we can think kinematically of the Galerie as a minimally moving wheel, we can think of the film camera as a lathe that carves light onto film, or of the fountain pen and the gasholder as the scalar extremes of a cylinder-piston assembly. Even the bridges of the nineteenth century, subject to so much debate, experimentation, and failure, conserve in the curvature of their arches and straightness of their carriageways the motion with which their parts were produced and with which they were launched from bank to bank—they, too, are frozen transmissions.³ The Jena Romantics had the idea of breaking up the reification of the world by romanticizing it; kinematicizing the world of the nineteenth century similarly dissolves its massive structures, but it does so without introducing alien interpretive categories. Rather, we learn to see what Walter Benjamin has called the disfigured similarities (entstellte Ähnlichkeiten) that make up the coherence of the epoch.⁴

Yet kinematics discloses not only synchronic similarities across the epoch but also the profound historical and metaphysical conflict leading up to the forcing of rotational and translational motion in nineteenth-century cylinders. This conflict, the barest outlines of which are the subject of the following pages, has commanded little attention because techno-historical scholarship of the epoch has concentrated on kinematics’ invisible other, the discovery and implementation of induction electricity—produced, to be sure, by the rotation of a magnet around a cylindrical coil, and hailed as a prime instance of convertibility. Electricity led to technologies and media that are no longer analog but, like an electrical spark, jump a gap. Telegraphy was its first successful application, and it is not hard to understand why it garners such attention—the difference between positive and negative, long and short, on and off, 0 and 1, seems to indicate a minimum of meaning amid the randomness of thermodynamic processes and thus to furnish the kind of interface between physical and intellectual realms that has long been the goal of modern natural science.⁵ Of course, such processes, and their implementation in various media, are critically important, in particular for the archaeology of our own digital present; but scholarship rarely treats them as what they literally are, dei ex machina. Telegraphy, for example, depends entirely on cylindrical objects and processes—on the rolling of wires and cables, on the railway lines along which wires were strung, on the steamships from which they were laid across the ocean, and finally on the rotating drums in telegraphic transmitters and receivers. Similar kinematics underlie the development of the film camera.

The tactile and epistemological difference between analog kinematics and digital electricity is nicely captured in the reaction to the transition from gas to electrical lighting in private households around 1880. Early users of electricity remarked how uncanny it was to switch on the light, thus turning darkness to light (almost) instantaneously, rather than to open the tap and light the gradually emerging gas.⁶ Both the unfathomable speed and the invisibility of electrical transmission raised concerns about the very fabric of the world. The growing popularity of all sorts of communications with invisible figures in séances is further testimony to the emergence of paradigms of invisible contact. Oswald Spengler, decrying the decline of the West at the beginning of the twentieth century, lamented that through electricity the bodies of machines “become ever more spiritual, ever more taciturn. The wheels, cylinders, and levers no longer talk. All that is important withdraws into the interior.” Walter Benjamin, reading Charles Baudelaire’s Flowers of Evil (1857), equated the disappearance of visible causation with the loss of meaningful experience, to be replaced by the (essentially meaningless) electrical sensation of repetitive shock.⁷

The disappearance of the machine from the visible, auditory, and tactile world imposes the question: If the electrical and digital age constitutes the far end of the epoch of the cylinder, and if that epoch began with Watt’s invention of parallel motion, what came 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 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 Renaissance, as were the Platonic regular solids and their relation to the sphere. Indeed, the ontological status of geometric relations and of the motions they embodied was discussed with renewed enthusiasm when new editions and commentaries on Plato’s Timaios appeared in the fifteenth and sixteenth centuries. One of the key moments in this interpretation occurs in Marsilio Ficino’s commentary on the Timaios from 1496. Commenting on the famous section on the origin of the world-soul (Tim. 36bc), Ficino claims that the natural motion of the soul is translational (animae motum naturaliter esse rectum) and that it is the task of intelligence (which itself is a gift of God) to bend it into rotational (in gyrum) motion.²⁵ The mysterious relation between the power of straight lines and angles and the nimbus of the sphere finds, as mentioned, a striking expression in Kepler’s Mysterium cosmographicum, where the Platonic solids (composed of regular rectilinear modules) are encapsulated in ever-larger spheres to demonstrate the distance between and the orbital motion of the planets. Copernicus earlier had given a succinct summary of the metaphysics of rotation and sphericity when he stated that the sphere is the perfect form because it is without “joint” and that everything that limits itself—a drop of water, for example, but also the sun and the planets—does so in the form of a sphere The motion appropriate to this perfect form is, of course, rotation.²⁶

All the trust put into the power and rationality of the straight line provided the ground for the assertion, first tentatively by Galileo and Descartes, then exhaustively by Newton, that motion along a straight line is the natural motion of any body in the universe. A corollary of this assertion is that space must be conceived as empty, homogenous, and infinite, since otherwise this motion would come to an inexplicable end. Alexandre Koyré has eloquently described the stages in this transition from the spherical cosmos to the infinite universe.²⁷ But the full acceptance of the translational motion paradigm came with some hesitations, and the objections all had to do with the nature of rotation. Although he established the idea of uncaused, inertial motion, Galileo for one could not convince himself that the orbits of the stars were just the product of two conflicting linear motions. His adherence to the Platonic idea of rotational and spherical perfection led him to reject the idea of a universe in which inertial motion could be conceived only as translational.²⁸ For Descartes, cosmic vortices carried planets around their axis, taking everything around with them into rotation.

Newton’s “great synthesis,” as we have seen in the discussion of Kleist’s text, was based on a previous analysis, namely the drastic separation of kinetic phenomena from the aesthetic and theological considerations that had dominated scholastic science and theology and that still left traces on early modern physics. Some motions are not “better” or “more beautiful” than others, Newton declared; they are simply the result of the measurable impact of forces on mass.²⁹ With the concept of mass Newton could abstract from any shape or position and extend calculations beyond the reach of the observable. One might not know what distant stars look like, but one could be sure that they were composed of quantifiable mass because its effect—gravitational pull—was measurable in their orbits. This abstraction, together with the great distances involved in celestial mechanics, made it possible to treat any body as a nonextended point mass: for the purpose of calculation—say, to calculate the gravitational force of the moon—it sufficed to conceive of its mass as being compressed in a point at the center of the physical globe. Newton, an atomist, believed in the irreducible extension and indivisibility of physical bodies, but for the purpose of calculation this philosophical commitment could be disregarded.³⁰ He felt even more justified in reducing celestial bodies to points when he could show—as he did in the debate with the Cartesians over the shape of the earth—that a body of malleable matter rotating in empty space around its central axis would morph into a regular spheroid whose center of mass would coincide with its geometric center. Points, in turn, could become the stuff of geometry—their path could be described in geometric curves with perfect accuracy, and they could become subject to the predictive power of algebraic operations.

Newton was perfectly aware that there were limits to this mode of explanation; indeed, he was eager to point them out to counter the suspicion that he conceived of a fully mechanized, self-sufficient universe. One such limit was the implication of a void between bodies, and of forces acting across it. For rational mechanics to work, gravity had to act instantaneously and bodies had to be distinguishable from their surroundings; but how could such actio in distans be understood? How could motion change (as it did in Kepler’s elliptical orbits) without any contact? Then there was the related question of whether the distances between the planets, placed as they were at the exact intervals that kept them from collapsing into the center and from flying off into space, could originate through mechanical forces. Newton enthusiastically embraced Bentley’s suggestion that this might serve as a cosmological proof for the existence of God.³¹

As far as the motion of the planets was concerned, Newton admitted to Bentley that gravity would explain the centripetal factor of the planets’ orbits, “yet the transverse motions by which they revolve in their several orbs required a divine Arm to impress them according to the tangents of their orbs.” Since this did not necessarily include the rotational motion of the planets, Newton added “that the diurnal rotations of the Planets could not be derived from gravity but required a divine power to impress them.”³²

This cosmological argument had a mechanical counterpart in the fact that, according to Newton’s second law of motion, any change of motion was proportional to the magnitude of a force impacting a body; both the impact and the resulting direction would be in a straight line. How could rotation originate from the impact of just one force?³³

For reasons like these Immanuel Kant introduced a second “original” force besides gravitation into the fabric of the universe in his daring Allgemeine Naturgeschichte und Theorie des Himmels of 1755: the repulsive force. He blunted the audacity of this addition to Newton’s mechanics by arguing that “these two forces are both equally certain, equally simple, and at the same time equally primal and universal. Both are taken from Newtonian philosophy. The first is now an incontestably established law of nature. The second, which Newtonian science perhaps cannot establish with as much clarity as the first, I here assume only in the sense which no one disputes, that is, in connection with the smallest distributed particles of matter, as, for example, in vapours.”³⁴ To show the primordial interplay of these forces, Kant imagined the world “on the immediate edge of creation,” when the universe was filled with matter at rest for a time “which lasts but an instant.”³⁵ Since atoms were created with different specific weights, the heavier ones attracted the lighter ones and began to form “gobs” (Klumpen.)³⁶ All matter would collapse into one big gob were it not for the repulsive force that inflected the straight path of onrushing matter and sent it into an orbit around the central, that is, heaviest body. Applied to the formation of the solar system, the interaction of these two forces explained why all planets orbited around the sun in one plane—the central mystery for Newton in his exchange with Bentley. They were all remnants of the initial cloud of matter that had first collapsed on, and then been flung from, the heaviest gob in one part of the universe, the sun. The same had happened in countless other corners of the universe.

This “nebula hypothesis” was a theory with extraordinary explanatory power, justly famous for its range and daring: in one fell swoop it explained the origin of empty space (as the consequence of matter contracting), the spherical form of celestial bodies (as the consequence of the simultaneous rush of particles on a common center and the resulting rotation) and the common plane of all orbits in the solar system, resulting in a fully mechanical cosmogony.³⁷ But subtly it also reversed the question of the origin of rotation. In a later chapter, “Concerning the Origin of Moons and the Axial Rotation of the Planets,” Kant makes the much-needed distinction between orbital motion (“Zirkelbewegung”) and axial rotation (“Achsendrehung”) and explains the origin of the latter as the result of particles impacting the already forming body, off-center and from opposite sides, and thereby keeping it spinning.³⁸ The diameter of the planet serves as a lever on which the particles exert opposite, yet equal translational force. Kant’s hypothesis anticipates here the notion of torque as the product of the length of a lever arm and two opposite perpendicular forces: he argues, for example, that Jupiter rotates faster than smaller planets (like Mars), which can be explained only by the fact that it has a larger diameter: “If the axial rotation were an effect of an external cause [e.g., God’s twisting motion], then Mars would have to have a more rapid axial rotation than Jupiter, for the very same power of movement affects a smaller body more than a larger one. We would quite correctly be surprised at this, since all the orbital movements diminish with distance from the mid-point, but the speeds of the rotations increase with the distance.”³⁹ What needs to be explained, this theory implies, is not rotational motion (for it is a natural effect of the self-creation of the material universe) but its cessation. Why, then, do some planets rotate around their axes and others, like the moon, not? In the Universal Natural History Kant promises to solve this problem in his answer to one of the Academy prizes, and indeed he does so in a small essay of 1754 with a very long title.⁴⁰ There he shows that the orbit of the moon around the earth is the result of the earth’s greater mass having dragged the satellite by its (now evaporated) aqueous surface and finally locked it into its present synchronous rotation. The same will happen, Kant knows, to the earth once the moon’s drag on its oceans overcomes its rotational momentum.

The great conceptual problem of Kant’s history of the heavens, immediately seized upon by the next generation of natural philosophers, lies in the assumption of two original forces.⁴¹ A system based on two principles is unable to close itself off; it remains susceptible to the charge of contingency, to that which cannot be anticipated or grounded. This uncertainty is expressed in Kant’s cosmogony by the curious temporal assignations of the “immediate edge of creation” and the “instant” of equilibrium—Kant cannot further account for their occurrence, nor can he explain why attractive forces operate first and repulsion follows later. According to the Romantic philosophers of nature, who succeeded Kant and who acknowledged their debt to his writings on natural science while eagerly moving away from his mechanistic thought, the principal motions cannot interact in such a desultory fashion, and, what is more, they must follow from principles that are valid for both natural and intellectual phenomena. Otherwise, the relation of nature to our understanding would remain inexplicable, and the system would again suffer from contingency. Rotation, this implies, cannot be the result of two supervening forces but has to originate together with the system itself, and it has to have a subjective manifestation.

This, at least, was the way the most scientifically inclined idealist philosopher, F. W. J. Schelling, argued. He neither accepted the contingent relation between attraction and repulsion at the origin of rotation nor countenanced the separation of mechanical causes from organic (and ultimately intellectual) ones. In his own rewriting of Plato’s Timaios, Von der Weltseele (1798), he advanced the notion that the world was a “universal organism” and that its motions and interactions were governed by two forces that formed a polarity: one was the other of the other, neither existed by itself. Nature would not coalesce into solid phenomena if the tendency to expand were not checked by a “returning motion.” These two polar forces—whose avatars, among others, were positive and negative magnetism and electricity, chemical affinity and repulsion, physiological irritability and sensibility—animated the universal organism and kept its soul in constant motion. Since Plato and Aristotle had already argued that motion originating from the soul was superior to all others, and above all that it could initiate rotation, Schelling could spend comparatively little energy on explaining the origin of rotation. If everything potentially rotated, it was rectilinear motion that required explanation.⁴²

Schelling’s Naturphilosophie underwent a few metamorphoses before he expanded his perspective even further and considered—in his Philosophy of Revelation—creation and the becoming of God as a process of rotational gestation. His followers and successors kept their focus on the primacy of rotation in the explanation of the natural world. Lorenz Oken, one of the most influential teachers of Romantic natural philosophy, declared confidently: “God is a rotating globe. The world is God rotating. All motion is rotational, and there is everywhere no straight motion any more than there is a single line of straight surface. Everything is comprehended in ceaseless rotation. . . . Straight motion is only the mechanical; such, however, exists not through itself. The more a body moves in a straight direction, the more mechanical and ignoble it is.”⁴³ Hegel interpreted the solar system as a kind of cosmic mind, where the sun represented subjectivity in its most abstract form as self-relation (because rotation was motion that related only to itself); the moons, which circled their center of gravitation without rotating, were entirely other-related; and the planets, including the earth, combined both motions by rotating and orbiting at the same time. This figure of an initial rotation that exteriorizes itself in its component motions recurs at various junctures in Hegel, whose philosophical system in its totality has been described as depicting a multiplicity of spheres rotating around a common center.⁴⁴

Similar thoughts animated Goethe, who, as we will see later, sought to identify spiral motion as the motion of organic growth: “The supreme thing we have received from God and from nature is life, the rotating movement of the monad about itself, knowing neither rest nor repose; the instinct to foster and nurture life is indestructibly innate in everyone; its idiosyncrasy, however, remains a mystery to ourselves and to others.”⁴⁵ Goethe’s metaphysical and poetic notion of free rotation already reached into the epoch in which rotation was broken down by the formula for torque. His contempt for rotating machines and for the pernicious acceleration brought about by them animated his last, resigned musings on historical progress in his novel Wilhelm Meister’s Travels.⁴⁶

The full intricacy of rotation’s transition from divine attribute to mechanical necessity cannot be recounted here. All this fragmentary overview of theories of translation and rotation has attempted to show is that motions have their history. Properly speaking, of course, only their valuation undergoes historical change, but since these motions do not “exist” unless they are forced, their metaphysical value dominates their mechanical properties until the widespread use of engines reverses this situation.⁴⁷ The ubiquitous availability of convertible motion from the steam engine and the emergence of suitable transmission replace metaphysical speculation with the forced geometry of motion—with kinematics.

Still, looking back at the roles played by translation and rotation respectively, we can appreciate the irony that steam engines met a deep desire on the part of Romantic natural philosophers who had kept the cosmic dignity of rotation alive against what they perceived as the cold rationalism of straight-line mathematical physics. It is true that the intrusion of large machines into the life of the nineteenth century pushed most poets and thinkers to the side of the protesters and even Luddites, but this had to do with the steam engine as a motor—and hence as a thermodynamic polluter, in the widest sense—or with the machine as a tool that dispossessed human workers of meaningful and remunerative work. When the Romantics articulated their opposition to the motion of machines, it was to mechanisms as metaphors (or as translations, in the Latin and kinematic version): against the state as a machine, against mechanical thinking and art making, against automata insofar as they tried to imitate or supplant natural bodies and their motions and emotions.

As far as the purely kinematic impact of the new machines was concerned, there was agreement between engineers, philosophers, and artists that bringing rotation to earth and accomplishing its conversion into other forms of motion was in fact an epochal achievement. A continuous line of thinkers from Kant to Babbage to Reuleaux, and on to Lacan and Deleuze and Guattari, and an equally continuous line of poets from Kleist to Dickinson to Beckett and Wallace Stevens testify to this view. Baudelaire went so far as to see in the visualization of kinematic conversion an essential sign of modernity. His painter of modern life, like Kleist’s Herr C., delights in depicting carriages in motion because “a carriage, like a ship, derives from its movement a mysterious and complex grace which is very difficult to note down in shorthand. The pleasure which it affords the artist’s eye would seem to spring from the series of geometrical shapes which this object, already so intricate, whether it be ship or carriage, cuts swiftly and successively into space.”⁴⁸

Hopefully, this metaphysical background helps to mitigate the technicality of the following parade of cylindrical objects. For their early designers, these objects retained an aura in which the drama and the conflict between the motions—even when they were frozen in the architecture of early iron bridges and glass roofs—were still palpable. Kinematics seems an abstract science to us, but it fascinated the general public in the nineteenth century. One example is the kinematic quest for a mechanism that would produce straight-line motion. The inherent inaccuracy of Watt’s four-bar linkage and the difficulties involved in predicting solutions mathematically had set off an eager quest for a linkage that would do for the straight line what the compass did for the circle. For while the drawing of a circle by means of a compass is a legitimate expansion upon the circle’s definition, the drawing of a line by means of a straight-edge ruler is vitiated by circularity: how can the straightness of the Ur-ruler be guaranteed? In 1864, Charles-Nicolas Peaucellier solved the problem but was promptly ignored. Not ten years later, James Joseph Sylvester made the straight-line linkage the subject of his lectures at the Royal Institution, where “he spoke from the same rostrum that had been occupied by Davy, Faraday, Tyndall, Maxwell, and many other notable scientists. Professor Sylvester’s subject was ‘Recent Discoveries in Mechanical Conversion of Motion.’ ”⁴⁹ That this was by no means an obscure or unpopular topic can be seen from the account of a contemporary observer who described how on the occasion of the lecture he found “all the approaches to Albermarle Street [the seat of the Royal Institution] blocked by carriages.”⁵⁰ In 1877, Alfred Kempe delivered his equally popular lecture on “How to Draw a Straight Line,” in which he praised linkages in general for “their great beauty.”⁵¹ The conversion of motion through (often complex) linkages seemed finally to have attained the popular and aesthetic status for which Kleist had pleaded at the beginning of the century.