Zeno's Paradox of Motion: The Arrow -- Part II

Velocity, Kinetic Energy and Motion
In the book, Labyrinths of Reason,the following questions are addressed: “It would seem there must be some information attached to a moving arrow that identifies it. Otherwise, how does it “know” to jerk forward in the next instant?” (Poundstone 145) Here, Poundstone brings up the issue that if we were too look at any instance of time how would we be able to tell that the arrow was “moving” or would continue to move. However, there are measurable ways to see if an object is in motion. As we are not treating the observed movement of the arrow as a “freeze-frame” image, but simply taking an instance of time we should be able to measure velocity, and it's potential energy through space-time. Calculations in air disruption and force as well as the “compactedness” of the arrow, (the arrow would be shorter as it traveled than when it was stationary just before being released from the bow).



If we were able to measure its velocity, we would be able to tell that because of a change in the arrows velocity, or the rate and direction of the change in the position of the object, that there is motion.

“One cannot think of motion as occurring only over periods of time. For if one considers an object that is constantly accelerating, the most natural way to express this phenomenon is to say that at every moment the object is moving at a different velocity.” (Lear 100)

Velocity, or motion, (any motion) brings about kinetic energy, (kinetic energy = ½ x mass x velocity2 ). Kinetic energy is an expression of the fact that an object in motion can bring about work on anything it hits. It limits the amount of work an object could do as a result of that objects motion. Because of motion which we observe, when that object stops – the arrow hits a tree – we can measure and see the results of the kinetic energy that was given to the arrow because of the potential energy that was built up in flight. This measurable kinetic energy, as well as the velocity show that the object must have had motion at some point in order to bring about change through kinetic energy.

As an example we can take the story of William Tell. He, was made to shoot a bolt (arrow) at an apple balanced on the head of his son proving his marksmanship. I would like to examine further the results of the bolt hitting the apple and tree adjacent to the boy with apple resting on head. Picture it in your mind. You don't quite see the bolts release as the speed is too great for the eye to follow accurately, but you can see the results. After release, a split second later you see the apple cleaved in two and the bolt stuck in the tree.

What caused the apple to split? Kinetic energy. As the bolt lay in the crossbow it held potential energy, indicated from the drawback, length, etc. Upon release that energy turned into kinetic energy – the energy of motion. That energy, or part of which was then released as the bolt struck the apple, splintering it in two, (the energy being so great it did not cause the arrow to simply go through the apple, but rather split it). Then, as it struck the tree splinters flew off, the bolt dug into the hard bark and finally stopped, it's kinetic energy depleted.

Now, how does this prove motion? If we are to take one instance of time and examine it, say the moment the arrow splits the apple we can see that there are consequences and results from the arrow that is, in the instance, still. What caused the apple to split? Are we to assume that it has always been split because of this moment we are examining? No. We can tell that there was some force that acted on the apple causing it to break in half. We are able to examine this further to see that there is a measurable force that would need to interact with each object in order for such a result to come about. What caused that force or energy? Motion. Observable motion through the results it brings about.