Replacing bricks in a wall one at a time leads to the question of whether we ever wind up with a new wall (see Change Part I: The Incremental Wall).
Two people thought about this quite a long time ago. Heraclitus (about 500 BCE) famously observed that you can’t step in the same river twice. Everything is in flux and never stays still long enough to be considered what it is. All is becoming and since everything is in the process of becoming it never actually is anything fixed. The rate of change may vary but the change is continual. Whether it’s the gradual wearing down of the Appalachian mountains or the melting of an early Fall snowflake, or the travel of the Earth around the Sun, everything is becoming.
Parmenides (a bit later than Heraclitus), on the other hand, maintained that if a thing is, it can’t become something else because then it wouldn’t be itself. There is no middle ground between being this thing and being that thing. Between them there would have to be an infinity of things or states. Change, he said, was an illusion. Moreover, and we’ll pass on the details, he maintained not only that nothing changes but that everything is one: All is One.
His brilliant student Zeno proposed a thought experiments to make the point.
Consider, he said, a runner racing to the finish line. Before the runner can get to the finish line he must get halfway there. Before he can get halfway, he must get halfway to that halfway point, and so on. This series of halfway points is infinite and so the distances the runner must cover add up to an infinite distance. But the runner cannot cover an infinite distance in a finite amount of time so although we see the runner make it to the finish line we know it is an illusion.
Or, how about this? Consider an arrow fired at a target. At any instant of the apparent time from launch to target it is motionless. Since at every instant it is motionless, it actually never moves. So what we see is impossible and must be an illusion. If we filmed the arrow we’d have a movie made up of still pictures but shown in rapid succession (perhaps 36 frames/second). In no frame does the arrow move yet rolling the film provides the appearance of motion.
These and other puzzles of change support a distinction being made between appearance and reality. It is to this difference and its difficulties that we turn next.
