David Kolb

Projecting Motion

This is the first post of three where I reflect on the history of science. I’m starting with projectile motion, a phenomenon that nagged at Aristotle’s Physics. It was not long after Aristotle’s death that members of his school began to comment on the weakness of his explanation for projectile motion. Projectile motion occurs when you send something into the air (with your hand or a bow, catapult, or cannon). The arrow or the stone rises and proceeds in the direction you propelled it, but only for a while. Then its forward motion continues but it stops rising, and then it falls along a curved line.

Aristotle’s theory says that left to itself an object will follow its natural tendency to move toward the part of the universe where the element it is made of seeks to go. The earth element seeks the center of the universe while water, air, and fire move towards natural positions above that. So once the force you are applying with your hand or bow stops pushing the stone in an “unnatural” direction, the object should resume its natural motion and fall straight to the ground. But it does not.

What needs to be explained is, first, the continuation of the object’s rising motion, second, why that rising ceases, third, why the object falls not straight down but along a curved line.

Aristotle’s explanation was that as the object moves through the air it pushes the air aside and that air moves along the side of the object and comes together in the back to fill the vacuum created by the motion of the object, thus pushing the object further. His students and followers devised experiments to show this explanation fails.

On the other hand, the major rival Greek physical theory, the Atomism of Democritus and the Epicureans, also fails. It can explain why when the stone leaves your hand it keeps moving, because atoms just keep moving unless they hit something. But the theory doesn’t explain why the stone stops rising and falls on a curved line. The atomists might say that the object stops moving because of the pressure of the air. That friction might explain the slowing down, but it does not provide an object which stone would hit to cause it to diverge back toward the ground, and certainly not on a curved trajectory.

It turns out that to explain the motion of the thrown object you have to invoke forces acting upon the object from surrounding objects, and neither Aristotle nor the Atomists had a good theory of interactive forces. Aristotle would need to give up the idea that it was the nature of the matter in the object that determines its path, and the Atomists would need to give up the idea that the only interaction between atoms was collision and entanglement. Newton’s gravity operates on objects according to their mass rather than their particular kind of matter, and it operates over distance in a way that the Atomists cannot account for.

Importantly also both schools would have to admit the importance of mathematical calculations in determining the trajectory of the stone or cannonball. (Trajectories had become important to calculate and it’s not accidental that Galileo had connections with the armory at Venice.) Neither Aristotle nor the Atomists would have agreed with Galileo when he said that the book of nature was written in the language of mathematics. But he could do what they could not, because he agreed with Plato that mathematics was deeply involved in the operations of nature.

After that brief look at the phenomenon and problem of projectile motion, I note two issues the topic raises for us. The first and deeper issue is: when we bring mathematics to bear on the motions of physical bodies, what are we doing? Are we getting to Plato’s deeper level of reality, or abstracting from concrete reality to something paler? This issue will arise again in the next post in this series.

The second issue comes from seeing how Aristotelian science managed well for almost 2000 years while nibbled at by a phenomenon that didn’t quite fit. Projectile motion wasn’t enough of a challenge to demand efforts for an immediate solution, and Aristotle’s followers thought they could work out the details later. Medievals developed theories of impetus (a mysterious quality added to the object then wearing away)but couldn’t make it fit. Finally, practical pressures increased the urgency for new basic basic concepts and methods. These did explain the phenomenon, but instead of completing Aristotle, they helped bring on the scientific revolution.

Might we have phenomena today that our science “deals with” while leaving a nagging dissatisfaction? Phenomena which might lead to another scientific revolution? Two such are obvious: conscious perception of qualities, and the experienced passage of time, both of which current science “handles” but with lingering worries that may be only our reluctance to let go of old prejudices. I wonder, though, if there are other phenomena in the corners of astrophysics or neuroscience that seem not quite adequately explained but not all that urgent, but which might surprise us?