Motion, A Historical Survey
MOTION, A HISTORICAL SURVEY
"Motion," or "movement," in its modern meaning, is change—or more precisely, change of the relative positions of bodies. The concept of motion thus involves the ideas of space and time. Kinematics, in the nineteenth century usually called "kinetics" or "phoronomics," is the science that deals exclusively with the geometrical and chronometrical aspects of motion, in contrast to dynamics, which considers force and mass in relation to motion. In medieval terminology, following Aristotelian tradition, "motion" (motus or kinesis ) had a much wider significance, denoting any continuous change in quality, quantity, or place.
Early Concepts of Motion
Ever since the beginning of philosophical speculation and scientific analysis, the concept of motion has played a predominant role in Western thought. Anaximander of Miletus (sixth century BCE) saw in motion an eternal agent of the cosmos. For Heraclitus motion was a cosmological principle underlying all physical reality (panta rhei, "everything is in perpetual flow"). Yet in spite of their insistence on the universality of motion, neither Anaximander nor Heraclitus seems to have inquired into the nature of motion itself. The Eleatics were probably the first to do so, when they discovered the contradiction inherent in the idea of motion and consequently denied the reality of motion, relegating its appearance to the realm of illusions and deceptions. A body, they argued, can move neither where it is nor where it is not; hence, reality is motionless and unchanging. Zeno's famous antinomies (Aristotle, Physics 239), such as the "Arrow" and "Achilles," seem to have been aimed, at least in part, at a refutation of the possibility of motion. On the other hand, for the atomists, such as Democritus and Leucippus, motion was a fundamental property of the atoms. All changes in nature were reduced to the movements of atoms in the void, and with the eternity and uncreatedness of the atoms their motion was eternal and uncreated; this motion itself, in the atomists' view, was not further analyzable. It remained a primary concept until Epicurus searched for a causal explanation. This (according to Lucretius) he thought to have found in weight, the cause of the downward movements of atoms, and in their little "swerves," by which he explained the otherwise incomprehensible collisions and redistributions of atoms without which physical processes could not be accounted for.
In Aristotle's natural philosophy the concept of motion played a decisive role, since for him nature was the principle of movement or change: "We must understand what motion is; for, if we do not know this, neither do we understand what nature is" (Physics 200b12), a statement recurrent in Peripatetic philosophy under the motto Ignato motu, ignatur natura ("To be ignorant of motion is to be ignorant of nature"). For Aristotle, in contrast to his predecessors, motion raised a profound problem—not merely from the logical point of view. Expressing the deeply rooted metaphysical conviction of Western thought that motion is neither logically nor ontologically self-sufficient but requires an explanation, Aristotle contended that motion is neither in the causal, or genetic, nor in the ontological sense a primary concept. Causally, every motion originates in another motion; only animate organisms possess an inherent power to move. Hence his famous dictum Omne quod movetur ab aliquo movetur ("All things that move are moved by something else"). To avoid infinite regression and to find a satisfactory explanation of the existence of motion, Aristotle reduced the ultimate origin of all movements to an eternal mover who is himself unmoved. (Physics 258b). Ontologically, Aristotle derived motion from the basic notions of his metaphysics of substance and form by defining it as "the progress of the realizing of a potentiality qua potentiality" (Physics 201a10). Motion as the actualization of that which exists in potentiality may produce a substantial form (generatio ), may change qualities (alteratio ) and quantities (augmentatio or diminutio ), or, finally, may be a change of place (motus localis ). Although Aristotle did not reduce qualitative differences to quantitative relations of size and position, as did the atomists, his physics is essentially a physics of qualities. He did regard local motion as of a more fundamental character than the other kinds of motion (Physics 208a31); it is "the primary and most general case of passage and prior to all other categories of change" (Physics 260b22). Yet in spite of this preferential status, local motion for Aristotle is only a necessary concomitant of change, not, as the mechanistic physicists of the post-Newtonian era maintained, the essential and exclusive constituent of change.
In kinematics Aristotle distinguished between circular and rectilinear motion (De Caelo 268b17), the former, the more perfect, being the motion of the celestial bodies (De Generatione et Corruptione 338a18). Dynamically, motion is either natural or violate. Natural motion is circular for celestial and rectilinear for terrestrial objects; violate motion is the removal of a body from its natural place (locus naturalis ) through the action of an external force.
ancient and medieval concepts
Aristotle's kinematics, like his physics in general, was a qualitative science, incapable of providing a precise definition of such notions as velocity and acceleration. In fact, Greek mathematics, with its insistence on the illegitimacy of proportions or ratios between heterogeneous quantities, did not provide even the formal means of defining velocity as the ratio between distance and time; only topological, not metrical, determinations of motion could be formulated. Thus, Aristotle said that a body is quicker than another if it traverses equal spaces in less time or greater spaces in equal time (Physics 215a26). As related by Simplicius, Strato of Lampsacus, in a lost treatise "On Motion" (De Motu ), was apparently the first to analyze in great detail these kinematic notions, in particular the concept of acceleration, although without trespassing the boundaries imposed by the Aristotelian conceptual scheme. The kinematics of uniform motion could be fully developed and rigorously formulated at least in abstracto, as exemplified by the treatise "The Motion of the Sphere" (300 BCE), written by the astronomer Autolycus of Pitane. Nevertheless, as far as is known, the earliest kinematicist to associate concrete numerical designations with velocities was Gerard of Brussels, in the thirteenth century (Liber de Motu ).
The formulations of the basic concepts in the science of motion did not, however, evolve out of practical necessities, the study of simple machines, or other scientific or technical considerations; they were, rather, the outcome of a curious development that originated in connection with a purely philosophical, ontological, and even theological problem. The point of departure was the much discussed problem of the increase and decrease of qualities (intensio et remissio formarum ), the question of how such qualities as warmness or blackness could vary in their intensities. Aristotle explicitly admitted (Categories 10b26) such alterations, but he also described such qualities as numbers (Metaphysics 1044a9) as immutable and unchangeable. One of the solutions, as listed by Simplicius, is that of Archytas, who suggested that every quality possesses a certain range of indeterminacy, or margin of variability (platos ).
In Peter Lombard's "Books on the Sentences" (Libri Quatuor Sententiarum, c. 1150 CE) the same problem reappears in the realm of theology when it is asked, with reference to Scripture, how an intensification or diminution of the Holy Spirit or of the caritas is possible in man. Until well into the thirteenth century the Christian concept of caritas was par excellence the subject of discussions on the intension and remission of qualities and served as the standard example for intricate analyses of the notions of change and motion. One solution, advanced by Henry of Ghent in one of his Quodlibeta, referred in this connection explicitly to Archytas's previously mentioned conception of margin of variability, now termed the "latitude" (latitudo ) of quality or change, a notion that was destined to play an important role in the foundation of classical kinematics.
Growth of the Science of Kinematics
In order to understand the subsequent development of the concept of motion another problem that engaged the thirteenth century to a great extent must be mentioned, the question of what category change, or motion, belongs to. Aristotle was usually interpreted as having advocated an identification of motus with terminus motus —that is, viewing motion as an evolving process in the same category as the terminal, or the perfection, of this process. According to this view motion is a forma fluens, to use the terminology of Albert the Great, whereas the opposing view, which relates motion and its terminus to different categories, is the fluxus formae conception of motion. In the special case of local motion the forma fluens interpretation regards the process of motion as merely the continuous and gradual acquisition of the final terminus motus, just as the qualitative change of nigrescere (to become black) is merely the gradual acquisition of the nigredo (blackness). The concept of motion obtained its final and most radical formulation along these lines in the nominalistic statement of William of Ockham that motion is merely a name for the set of successive positions occupied by the mobile.
The nominalistic interpretation, often epitomized as motus est mobile quod movetur, met with considerable opposition, curiously enough among the Parisian terministic philosophers, such as Jean Buridan. One of the arguments for its rejection was undoubtedly its logical inapplicability to the motion of the outermost sphere, which, not further surrounded by any object, possessed neither place nor space, according to the Aristotelian-scholastic theory of space; thus its motion clearly could not be interpreted as a set of successive positions. No wonder, then, that the fluxus formae interpretation of motion, which distinguished between the process, on the one hand, and the terminus or position (locus ), on the other, and regarded motion as a specific quality inherent in the mobile, became predominant. Buridan, for example, defined motion, or moveri, as an inherent property in the mobile—intrinsice aliter et aliter se habere —and Blasius of Parma characterized local motion as a quality that is capable of gradual intensification or remission and is inherent in the moving object (motus localis est qualitas gradualis intensibilis et remissibilis, mobili inhaerens subjective ).
Meanwhile the notorious calculatores of Merton College at Oxford, including Thomas Bradwardine, Richard Swineshead, and William Heytesbury, established their famous formalism of subjecting qualities of all kinds, but primarily the quality of caritas, to mathematical analysis and quantification. It was there, at Merton College, that the different trends converged. For motion, itself a quality according to the fluxus formae conception, soon became the favorite subject of mathematical description and took the place of caritas in these discussions. Employing the notion of latitude, the calculators analyzed the various possibilities of changes of motion and illustrated their theorems by graphical representations. Thus, through the conflux of various conceptual trends the foundations of modern kinematics were laid at Oxford: The concept of velocity was clarified by the introduction of the notion of instantaneous velocity, uniformly accelerated motion was unambiguously defined, the distance traversed by a body in uniformly accelerated motion was calculated, and, finally, a clear distinction between kinematics and dynamics was drawn. The results thus obtained seem, however, never to have been applied to any motions encountered in nature; they were, rather, a theory for the classification of possible motions.
The new knowledge soon spread to France, Germany, and Italy. Only Galileo Galilei, and possibly Dominic de Soto, applied these results to the study of specific natural phenomena, such as free fall. Since kinematic investigations formed the point of departure for the subsequent development of mechanics and physics in general, the analysis and clarification of the concept of motion may rightfully be regarded as of primary importance for the rise of modern science as a whole. With the establishment of a scientific kinematics the notion of motion also became purified from certain connotations that it carried from ancient times. Thus, according to the Aristotelian theory of motion the movement of any object presupposes the existence of an immobile body. Themistius, Averroes, and other commentators interpreted this statement as a proof of the immobility of Earth. In fact, for Averroes the immobility of the center was a necessary prerequisite not only for the motion of the spheres but also for the very spatiality of the outermost sphere (caelum est in loco per centrum ). Not only was Earth unique as being the abode of man; its distinction was due also to the fact that it served as the basis for the localizability of the celestial spheres.
However, as soon as the fluxus formae conception characterized motion as a property inherent solely in the mobile, the Aristotelian presupposition of an immobile correlate lost its logical legitimacy. Celestial motions no longer needed to be conceived of as dependent on the immobility of Earth, and a severe obstacle to the Copernican doctrine could easily be removed.
Relativity of Motion
It is a curious fact that the modern conception of motion, though historically and conceptually connected most intimately with the Copernican revolution, led to a partial reinstatement of the Aristotelian presupposition. Not the immobility but the existence of a correlate is the indispensable requirement for any physical significance of the concept of motion. For the relativization of the notion demands a body of reference. The question whether absolute motion, motion without reference to a physical object extraneous to the mobile, is a scientifically or philosophically meaningful conception or whether motion is only relative—that is, whether the statement "A moves" makes sense only if it means "A moves relative to B "—is the problem of the relativity of motion and has a long history of its own.
Aristotle's distinction between ordinary motion and motion per accidens may be regarded as the first implicit differentiation between absolute and relative rest, an idea further developed by Sextus Empiricus (Adversus Mathematicos 2, 55). The dynamical equivalence, under certain conditions, between relative rest and absolute rest was essential to the acceptance of the Copernican theory and, in fact, was explicitly stated by Nicolas Copernicus himself: Inter motu ad eadem, non percipitur motus (De Revolutionibus Orbium Coelestium, Nuremberg, 1583, Bk. 1, Ch. 3). It was further elaborated by Galileo (Dialogo sopra i due massimi sistemi del monde, second day) into what is now called the Galilean principle of relativity. René Descartes, fully aware of the implications of the relativity of motion for the Copernican controversy, adopted a compromise position by distinguishing between "the common and vulgar conception of motion" as the passing of a body from one place to another and the "true or scientific conception" of motion as the transfer of matter from the vicinity of those bodies with which it was in immediate contact into the vicinity of other bodies (Principia Philosophiae, Part 2, Section 24). He thereby associated the relativity of true, or scientific, motion with the Aristotelian contiguity as the determinant of localization. Descartes is often credited with having been the first to enunciate explicitly the relativity of motion, and Gottfried Wilhelm Leibniz is cited as one of its most enthusiastic proponents.
For Isaac Newton and his doctrine of absolute space the notion of absolute motion was, of course, of physical significance, being "the translation of a body from one absolute place into another" (Principles ). He defined relative motion, corresponding to the concept of relative space, as "the translation from one relative place into another." In spite of his professed adherence to Galileo's principle of relativity, Newton maintained the possibility of distinguishing absolute from relative motion by their "properties, causes and effects." His belief in the reality of absolute motion was based on his thesis that real forces create real motion. The reality of absolute motion, he argued, is manifested by the effects that such motions produce, for example, the appearance of centrifugal forces or effects. For Newton forces are metaphysical entities, and the motions they produce are therefore more than merely geometricotemporal or kinematic phenomena. Thus, rotation is an absolute motion, as he thought to have proved by an analysis of his famous pail experiment.
Apart from Christian Huygens, who from 1688 maintained the relativity of circular motion on physical grounds, and Leibniz, who rejected the Newtonian conception on philosophical grounds, it was primarily George Berkeley who treated the epistemological aspects of the problem (Treatise concerning the Principles of Human Knowledge; De Motu ). He concluded:
It does not appear to me, that there can be any motion other than relative : so that to conceive motion, there must be at least conceived two bodies, whereof the distance or position in regard to each other is varied. Hence if there was one only body in being, it could not possibly be moved. This seems evident, in that the idea I have of motion doth necessarily include relation.
However, in the eighteenth and early nineteenth centuries, primarily as a result of Leonhard Euler's justification of absolute motion on the basis of the principle of inertia (Mechanica; Theoria Motus, Secs. 84, 99) and Immanuel Kant's argumentations in his "Metaphysical Foundations of Natural Science" (Metaphysische Anfangsgründe der Naturwissenschaft, 1786), absolute motion was regarded by the majority of philosophers as a meaningful concept, not only in physics but also in philosophy. Toward the middle of the nineteenth century the situation changed. At first it was admitted that rotational motion is absolute but translational motion is relative (James Clerk Maxwell, P. G. Tait, H. Streinitz, L. Lange), and later all motion was regarded as relative. One of the most ardent proponents of the universal relativity of motion was Ernst Mach (Die Mechanik in ihrer Entwicklung, Leipzig, 1883); he refuted Newton's argument concerning the rise of centrifugal forces as evidence of the absolute nature of motion and explained it as an induction effect produced by the motion relative to the fixed stars. Whether Mach's conjecture can be corroborated rigorously is still a problem that engages modern research, especially in the theory of general relativity.
The question of the relativity of motion, initiated, as we have seen, by Descartes, gained increased importance, owing to the fact that the concept of motion became the basic element of physical explanation. In fact, it was Descartes's insistence on the exclusive admissibility of local motion that was decisive in this development. As is suggested in the Principles of Philosophy (Pt. 2, Sec. 23) and expounded in a letter to Marin Mersenne (1643), Descartes refused to attribute any reality to the so-called qualities of substances. The conception of such qualities, he contended, complicates and confuses rather than simplifies the explanation of physical phenomena in natural philosophy. In concluding such deliberations, Descartes declared local motion to be the only admissible element for physical explication. Descartes's rejection of the Aristotelian physics of qualities had a great appeal to philosophers (see, for example, Thomas Hobbes, Elementorum Philosophiae Sectio Prima, 1655; De Corpore, Sec. 8, Ch. 9) and was instrumental in the development of the mechanistic orientation of modern classical physics, which tried to reduce all natural phenomena to motions of masses in space.
Characteristic of this conception of classical physics is a statement by Maxwell: "When a physical phenomenon can be completely described as a change in the configuration and motion of a material system, the dynamical explanation of that phenomenon is said to be complete" (Scientific Papers, Cambridge, U.K., 1890, Vol. 2, p. 418). The predominant role of the concept of motion in physical science poses a problem of great importance to philosophy. Why is it that all processes, laws, and formulas of physics—and modern physics is no exception—ultimately refer to motion, and why is it that even problems in statics, the science of equilibrium and absence of motion, are solved in terms of fictitious motions and virtual velocities? Is the answer to be found only in the historical circumstances, namely that kinematic investigations were the earliest successful approach to the establishment of a physical theory and that consequently forces were regarded as manifesting themselves only through motions? The answer probably lies in a vestige of ancient Eleatic philosophy that seems still to motivate our mode of thinking: A physical explanation of a natural phenomenon becomes more satisfactory the nearer it approaches the statement that nothing has happened. Motion, as Wilhelm Wundt pointed out, is the only conceivable process in which an object, so to speak, both changes and remains the same: It changes by assuming a different position relative to other objects; it remains the same by preserving its complete identity.
See also Albert the Great; Anaximander; Aristotle; Averroes; Berkeley, George; Bradwardine, Thomas; Buridan, John; Change; Copernicus, Nicolas; Descartes, René; Epicurus; Galileo Galilei; Henry of Ghent; Heraclitus of Ephesus; Heytesbury, William; Hobbes, Thomas; Kant, Immanuel; Leibniz, Gottfried Wilhelm; Leucippus and Democritus; Lucretius; Mach, Ernst; Maxwell, James Clerk; Mersenne, Marin; Motion; Newton, Isaac; Peripatetics; Peter Lombard; Philosophy of Physics; Relativity Theory; Sextus Empiricus; Soto, Dominic de; Space; Swineshead, Richard; Themistius; Time; Wundt, Wilhelm; Zeno of Elea.
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