In the 5th century BCE, Zeno of Elea developed a series of paradoxes designed to show that all is one, and that all change is illusion. We don't have any of Zeno's writings surviving from this time, but Aristotle mentions several of Zeno's paradoxes in books that have come down to us. One of the most famous is known as The Arrow Paradox.

I'll quote two sources explaining it, but you are welcome to find others if you'd like.

From Wikipedia: "In the arrow paradox [...], Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible."

From The Stanford Encyclopedia of Philosophy: "This argument against motion explicitly turns on a particular kind of assumption of plurality: that time is composed of moments (or ‘nows’) and nothing else. Consider an arrow, apparently in motion, at any instant. First, Zeno assumes that it travels no distance during that moment—‘it occupies an equal space’ for the whole instant. But the entire period of its motion contains only instants, all of which contain an arrow at rest, and so, Zeno concludes, the arrow cannot be moving."

Of course we know that motion is possible -- or at least we will be assuming so for the purposes of Calculus. Your job is to write a short paper (2-3 pages) explaining to a friend who is a philosophy major where the flaw in Zeno's argument is, from a Calculus point of view. You'll want to frame this in terms of average speed, speed at an instant, and limits.

If you'd like to include some formulas or more concrete examples, you may, but the gist of the paper should be understandable to someone who hasn't had any Calculus. I want to see how well you can explain the fundamental notion of instantaneous rate of change without relying on too much jargon or algebraic computation.

The paper will be due at the beginning of class (3:10 pm) on Monday 2 October. I'm not going to put font size or margin restrictions on, and I'm not going to obsess over a paper being slightly under 2 or over 3 pages, so please don't play font/margin games. The "2-3 page paper" guideline is a way to communicate that this is not a 1-page quick paper or a more involved 5-7 page paper.

You do not need to use any outside sources besides the definition of the paradox quoted above, but you are welcome to. If you do use anything besides the above or our textbook, please cite in some appropriate and consistent fashion of your choosing.

As always, I would encourage you to start early and visit the Writing Center with a draft.