Wednesday, July 21, 2010
Zeno's Paradox: What Movement Must Be - Flipbooks!
Zeno of Elea proposed several paradoxes involving movement and how movement is mathematically impossible. The idea is this: before one can go from point A to point B, they must go halfway between the two points. And before they can go to that halfway point, they need to go halfway between the halfway points. And then halfway between that halfway point, etc. This continues until there are an infinite number of points that need to be reached to go from point A to point B. And since it's impossible to cross an infinite amount of points in a finite time, it's impossible to ever go from point A to point B. And since all movement is like going from point A to point B, movement is impossible.
I was thinking about this problem for awhile, when suddenly the idea of a flip book came to mind. In a flip book, a character that is "moving" does not need to go halfway between the point where he is and the point he is trying to reach. Instead, the character just sort of warps between each point. But to the untrained eye, the movement of a character in a flip books looks like the same kind of movement we do in real life.
Well, maybe the movement is the same?
Maybe every time I move my hand, it really just does disappear at one point and reappear at another in the same way that a flip book character moves. My senses just can't tell the difference and make me think that my movement is different from that of a flip book.
It is definitely an odd way of thinking about movement, but it does seem to get around Zeno's problem because it means we do not need to go halfway between A and B before we can actually reach B from A.
Just a trippy thought.