Vortices of Confusion

The Scientific Revolution was animated by a broad vision of Nature known as the mechanical philosophy.  Against the Aristotelian conception of Nature as comprised of teleologically driven process, the emerging science of Boyle, Descartes, Hook, Galileo and others suggested Nature was more like a machine than an organism.  On this way of thinking, the world is comprised of discrete, or perhaps continuous, spatially extended bodies blindly moving either inertially or under the influence of contact with other bodies.  The laws governing how motion is communicated between bodies are intelligible to us, and can be expressed in mathematical terms.  Interest in the mechanical philosophy revived the idea of the ancient Atomists that the world consists of indivisible corpuscles which only have size, shape and motion.  Their blind flights through the Void, as well as their interactions by impact and sticking, give rise to the varied phenomena of the world.  One can read, I think, the early modern philosophers as having a central preoccupation with the tenants of the mechanical philosophy, much like contemporary thinkers struggle to resolve the conceptual problems raised by relativity and quantum mechanics.

The Scientific Revolution culminates with Newton's great work, the Principia Mathematica.  However, the emergence of Newtonian physics can only be viewed as a partial vindication of the mechanical philosophy which animated the Scientific Revolution.  It departs not only from the conception of causation inherent in the mechanical philosophy, but also undercuts the standards of intelligibility and sound explanation that earlier workers adhered to.  B.T.J. Dobbs explained,

Newton made a dramatic break with the orthodox mechanical philosophy of his day, the philosophy that was generally understood by the most advanced thinkers at the time to be the most promising method of approaching the study of the natural world.  He did not reject the entire system of mechanical thought, but he did reject one of its most basic assumptions: that force could be transfered only by the impact of one material body with another.   

According to Newton's natural philosophy, the motion of particulate matter is determined by the combination of forces, pushes and pulls that is, acting on it.  The differential equations Newton wrote down relate the trajectory that an object follows to the various forces acting on it, so that if the initial conditions of the system are known then, in principle, the future course of events can be calculated.  In order to model planetary motion, Newton supposed that between every pair of point particles, m and M,  there is an attractive force F -- gravity -- that grows proportionally with the masses but drops off with the square of the distance R between them (F ∝ Mm/R²).  This forces acts instantaneously between the particles at a distance, and immediately adjusts its strength according to how far apart they are from one another at any moment in time.  Using the laws of motion and his gravitational force law, Newton was able to explain why planets move in ellipses, why the sped up as they approached the sun and slowed down as they receded, and the relationship between the size of a planet's orbit and how long it takes to complete one full revolution around the sun (T ∝ R^3/2).

Newton's postulate of instantaneous action at a distance contradicts the idea that motion is communicated between bodies by direct physical contact.  This struck so deeply at the explanatory standards of the mechanical philosophy that Leibniz worried this was a slide back to the occult theories of Aristotelian substantial forms.  While Leibniz acknowledged that it was within the unlimited power of God to endow matter with the mysterious power to immediately interact at a distance, he clung to the ideal of Nature's intelligibility:

However, devising a mechanical model that explains the particular mathematical form of Newton's law of gravitation in a way that is consistent with the scriptures of the mechanical philosophy is a highly non-trivial task.  Newton himself recognized this and was not comfortable with action at a distance.  In The Character of Physical Law, Feynman considers one such possibility.  Suppose that space is full of tiny particles moving every which direction and which ram up against the celestial bodies.  (One might add to Feynman's model that the scattering cross section is proportional to the mass of the target body.)  The sun is a massive body off of which these corpuscles are scattering, so there is less of a particle "wind" coming from the direction of the sun.  So, the planets are effectively attracted to the sun by the surplus of particles coming from the "outside."  The 1/R² character of the force comes from how the visible surface area of the sun drops off with distance.  But, as Feynman point out, this model does not work because the planets would experience drag as they moved through their orbits, and steadily collapse into the Sun.  (This is an experimentally realizable interaction, called depletion.)

Feynman's imagined model actually resembles the major theory of planetary motion that Newton argued against at length in the Principa: Descartes' vortex theory.  Descartes supposed that the space between the planets and the Sun is filled with tiny corpuscles swirling around the sun.  The planets, in turn, are dragged along this vortex.  Newton worked out the physics of liquid whirlpools, demonstrating the Descartes' theory, when supplemented with the correct laws of motion, predicted the wrong relationship between the size of the orbit and the time it takes a planet to complete one orbit.  (For uniform circulation with cylindrical symmetry, T ∝ R².)  Thus, like Feynman's mechanical model of gravitation, Descartes' vortex theory does not adequately account for the observed motion of celestial bodies.

Newton's theory of gravitation and his models of celestial motion beautifully embody the classical vision of the clockwork universe that adhere to immutable laws.  But, the law of gravitation is an abstract, mathematical rule that cannot be explained in terms of material bodies interacting by direct impacts, undermining the explanatory standards of the Scientific Revolution.  In this way, Newton's natural philosophy is both the culmination of work within the viewpoint of the mechanical philosophy, but also represents its demise in the face of experimental results.  Reflecting on this situation, Hume mused that "while Newton seemed to draw off the veil from some of the mysteries of nature he showed at the same time the imperfections of the mechanical philosophy; and thereby restored her ultimate secrets to that obscurity in which they ever did and ever will remain."