A Brief Guide to the Great Equations by Robert Crease Page A

speed is determined by an excess of force over resistance. Philoponus is also the first person known to have actually experimented with falling bodies of different weights, discovering, as Galileo would a thousand years later, that they fall at approximately the same rate. But Philoponus’s most original and far-reaching revision of Aristotle’s ideas concerned projectile motion. He rejected antiperistasis; if the mover communicates motion to the air behind the projectile, why can’t we send stones and arrows flying by stirring up the air behind them with our hands? Philoponus proposed that, when we throw a stone, our hand impresses a force not on the air but on the stone itself. This ‘impressed force’ causes the motion to continue from
inside
the projectile, but is slowly consumed in overcoming the resistance of the medium and the natural downward force, and eventually used up as the natural motion takes over or the stone hits the ground. This view was still faithful to Aristotle’s in that it assumed that an object did not move by itself but always required contact with some other cause, such as the weight of a falling body or the impressed force borrowed from the hand. What was new was that this cause could be internal, not external, to the moving body. This idea led Philoponus and his followers to see the world differently. They no longer needed to distinguish natural and enforced motions, nor to separate the earthly and heavenly realms. God created the heavens, and then used impressed force to keep them going, there being no medium in the heavens to exhaust them. Philoponus’s influence helped to inspire scholars trying to understand motion to shift their attention from its end point – the goal or purpose of the motion, whether on earth or in heaven – to its beginning point, or what set it in motion.
    Philoponus’s modifications, especially concerning impressedforce, influenced Islamic commentators on Aristotle, such as the Spanish Islamic theologian Ibn Bājja (known to the West as Avempace, ca. 1095–1138), the Spanish Islamic theologian Ibn Rushd (Averroës, who objected to Philoponus’s view, 1126–1198), and the Persian Islamic theologian Ibn Sīnā (Avicenna, 980–1037). The latter translated Philoponus’s idea of impressed force into Arabic as
mail qasrī
(violent inclination). Heavier bodies can retain more
mail
than light bodies, which is why you can throw a stone farther than a blade of grass or a feather. And the Arab commentators concocted other situations where Aristotelian explanations were dissatisfying: What would happen if a tunnel were dug through the earth and a stone dropped in it? Would a thread attached to an arrow’s tip be pushed forward? In Ibn Sīnā’s work, even more clearly than in Philoponus’s, the key to motion is to be found not in formal and final causes but in efficient and material causes.
    This shift in attention is clear in the work of John Buridan (ca. 1300–1358). Further developing the ideas of Philoponus and Ibn Sīnā, Buridan gave impressed force the technical name
impetus
, by which it would be known until modern times. Unlike impressed force, impetus did not use itself up but was permanent; a body could only lose it by transferring it to something else. 10 Impetus may sound like our notion of inertia, but unlike inertia it was still a cause. Thus the new framework was still Aristotelian, for it retained the distinction between natural and violent motion and viewed a projectile such as a stone or arrow as continually moved by the action of a cause, though this cause (the impetus) functioned within, not as per Aristotle without, the body. But several key Aristotelian puzzles – such as the question of projectile motion and how bodies fall – had vanished, for the thrower transmits impetus to the stone rather than to the medium, while a falling body acquires impetus as it falls, explaining why it picks up speed. The idea of impetus helped produce a