Dynamics

Dynamica is a term coined by Gottfried Wilhelm Leibniz (1646–1716) in 1689 during his Italian journey, referring to his doctrine of forces. In that year, he composed an extensive work called Dynamica, which remained unpublished at the time. His major publication on the subject is “Specimen Dynamicum,” which appeared in the Acta eruditorum for 1695, in which he tried to reconcile a variety of metaphysical and mechanical traditions relevant to the notion of force on the basis of a grid of the following four notions: (1) active primitive force is a purely metaphysical entity expressing the activity of substances and is also called entelechy; (2) active derivative force is somehow the phenomenal manifestation of an aggregate of metaphysical substances and is measured by living force, or vis viva; (3) passive primitive force is purely metaphysical and expresses the imperfection of substances; (4) is passive derivative force, which is also called inertia, is its phenomenal manifestation. The connection between metaphysical and phenomenal levels was and still is especially problematic in this account. Leibniz further introduced the distinction between vis viva, which pertains to actual motion and is proportional to the square of velocity, and vis mortua, or dead force, which pertains to the very beginning of motion and is proportional to infinitesimal velocity. Examples of the latter are Christiaan Huygens’s (1629–1695) centrifugal, and Isaac Newton’s (1642–1727) centripetal, forces.

Leibniz developed his views in several works and tried to establish many laws of nature, such as the law of conservation of force, or vis viva, on the metaphysical foundations provided in his system. Although Leibniz’s metaphysical preoccupations are extreme even by seventeenth-century standards, at the time notions like motion and force had much larger philosophical dimensions than the modern reader may suspect. Ca. 1700 the notion of dynamics had a distinctive Leibnizian flavor that Newton found particularly irritating and distasteful. In a manuscript, he complained that “Galileo began to consider the effect of Gravity upon Projectiles. Mr Newton in his Principia Philosophiae improved that consideration into a large science. Mr Leibniz christened the child by a new name as if it had been his own, calling it Dynamica…. But his mark must be set upon all new inventions. And if one may judge by the multitude of new names and characters invented by him, he would go for a great inventor.” Although Leibniz’s dynamics was primarily a science of living forces, in the quotation above Newton portrayed it as dealing with his own force, a notion more similar to Leibniz’s dead force. Almost exactly a century after Leibniz had coined the term, Joseph-Louis Lagrange (1736–1813), in his classic Mécanique analytique (1788), defined dynamics as the science of accelerative forces and of the motions they produce. In his historical outline, he portrayed Galileo Galilei (1564–1642) as the founder of dynamics, a science later perfected by Huygens. Lagrange went on to argue with involuntary irony that mechanics and, therefore, dynamics were then revolutionized by Newton. Thus, by that time it had become customary to call dynamics a doctrine of forces based, unlike Leibniz’s, on accelerations, such as Newton’s. Newton himself had given the greatest possible emphasis to his doctrine of forces by stating in his Principia mathematica philosophiae naturalis (1687) that the whole burden of philosophy consists in investigating the forces from the phenomena of motion and then from the forces to demonstrate the phenomena. The term dynamics is also used by some historians in the sense of science of motion, rather than strictly of forces, and is contrasted to statics, or the science of equilibrium of bodies. Ernst Mach (1838–1916), for example, devoted the first two parts of his influential Die Mechanik in ihrer Entwickelung (1883; ninth edition, 1933) to the development of the principles of statics and of dynamics, which in his view had been founded by Galileo and by which he meant a science of motion. These preliminary reflections leave the scholar of the Scientific Revolution with the problem of whether it is legitimate or helpful to talk of a history of dynamics in the seventeenth century, including such actors as Galileo and Huygens, and extending back to the medieval scientia de motu (science of motion) and scientia de ponderibus (science of weight) and even to the Quaestiones mechanicae attributed to Aristotle (384–322 B.C.E.) or to one of his immediate disciples. The answer to this question depends on several factors, such as whether dynamics is taken to mean a science of accelerative forces, a science of motion, or a science of the causes of motion. Further, it depends on the aims and purposes of one’s historical research. Historians, however, ought to be aware of the categories of their actors, even if for a variety of reasons they decide not to follow them, and make a conscious and deliberate decision, as opposed to taking for granted that dynamics always existed and that its history can, therefore, be written unproblematically.