A Brief Guide to the Great Equations by Robert Crease

the phenomena having attained their telos, or end, for in that condition the whys and hows of phenomena are most clear.
    Aristotle liked to say that the wise person seeks only as much exactitude as the subject matter allows. He described what he saw, to the most appropriate level of precision that he could. What appeared to matter in understanding the motions of nature was the role that things like form, matter, and purpose play in converting potentiality into actuality. And these ultimately referred to the unmoved mover, who communicates through love via the outer spheres to the moon and then to the sublunary world.
Steps Beyond Aristotle
    Aristotle’s picture of nature had an enormous impact on Western civilization. His ideas were passed on by students at the Lyceum, the school he founded, and by commentators on his works – at first Greeks, and then, from the ninth to the twelfth centuries, Arabs, from whom later Western scholars learned about Aristotle.
    But aspects of Aristotle’s picture were not completely satisfying, not even to him. He seemed puzzled, for instance, by how things such as projectiles and potters’ wheels moved after the initial push. If a mover has to be in constant contact with what it moves, why doesn’t a stone or arrow plunge to the ground after leaving the hand or bow? Aristotle considered two possibilities. One was that the mover (thrower or bow) impregnates or impresses a force on themedium (air) around the projectile (stone or arrow), which then keeps the object in motion. 7 The other explanation, the doctrine of antiperistasis, was that air displaced in front of the projectile rushes around to the back to squeeze the projectile forward. 8 Aristotle was not comfortable with either explanation.
    Later thinkers, too, were dissatisfied by this and by other elements of Aristotle’s account of motion. Some objections were logical, some empirical, some both. The result was discussion, inquiry, modification of Aristotle’s concepts, the introduction of new concepts, and – during a journey of thousands of years – a slow shift of attention to different aspects of motion that would lead, eventually, to
F
=
ma
. We will travel a long way without seeing anything that resembles its components. But each step of the journey was essential. What follows are some of the steps.
    In the third century bc, Strato (340–268 BC ), a Greek from Lampsacus in Asia Minor who took over as head of the Lyceum in 287, developed and extended Aristotle’s thinking in an influential book called
On Motion
. Strato found he had to revise or even reject some of Aristotle’s ideas to make them consistent with logic or experience. One was the idea that there were two kinds of natural movement: up and down. Strato argued that all things naturally go down toward the earth’s centre, and that if light things like fire and smoke rise, it’s because they are displaced or ‘squeezed out’ by heavier stuff. Strato was also bothered by two observations that seemed to suggest that things pick up speed as they fall. One was that when rainwater pours off a roof, the flow is continuous at first but then breaks into droplets, which could not happen if the water weren’t moving more quickly. 9 The other was that, when you drop a stone to the ground from high up, the impact is more powerful than when you drop it from just above the ground. How could this be? The stone hasn’t gotten heavier! It must have picked up speed, Strato concluded, meaning that a falling body ‘completes the last part of its trajectory in the shortest time’, a rudimentary notion of acceleration more sophisticated than Aristotle’s.
    In the sixth century ad, John Philoponus (‘Lover of Hard Work’, ca. 490–570) further revised Aristotle’s ideas on motion. Philoponus argued on logical grounds that motion was possible in a vacuum (something Aristotle had rejected), and solved the problem of what happens when force equals resistance by declaring that