Mazur, Joseph. The Motion Paradox: The 2,500-Year-Old Puzzle Behind All the Mysteries of Time and Space. New York: Dutton, 2007. From Zeno (ca. 450 BCE) to today’s String Theory, Mazur paints a fascinating look at the history of scientific development as it seeks to grapple with fundamental questions of time and space. Although written for the layman, Motion includes enough math and science that it’s probably easier to follow if you have some background in the basics. But even if you don’t, Motion is worth reading for its historical connections (e.g., would Newton have been as productive if not for the Black Plague?).
So what is the motion paradox? Simply put, there is a fundamental problem behind our understanding: we use time to explain motion (the car is traveling 50 miles per hour); but we use motion to explain time (we know an hour has passed because the clock’s hand has moved). So have we really explained anything?
The problem dates back to Zeno, famous for his paradoxes, who said: in order to get from point A to point B, you must first travel half the distance from A to B; then you must first travel half the distance again, and so on. But if you are always only going halfway, you can never get to B. While many thinkers have dismissed this line of argument as mere semantics, Mazur shows how such paradoxes present genuine difficulties in math and science and lead to difficult questions such as: is a line a series of discrete points, or is it a continuous? Is time a series of discrete moments, or is it a continuous stream? Before you answer, consider another of Zeno’s paradoxes: if an arrow travels through the air, we say that during its flight the arrow is at a specific point at a specific moment; but if that is true, then it must be true that the arrow is “frozen” at a particular spot at a particular moment, which means that it must be “frozen” at each spot at each moment. So how can it be said to be moving?
For everyday events, our calculations work well enough---distance equals rate multiplied by time (d = rt). But for the bigger questions, like resolving the discrepancy between relativity and quantum mechanics (both of which seem to be fundamentally true), our math may not be up to the challenge. Mazur convincingly argues that the reason is that we have yet to explain such “basic” ideas as “time” and “space.”