But that doesn't answer it.
The way I heard it doesn't concern itself so much with time as with the distance. As you noted, before it can get to the target it must get to the half-way point. Before it can get from there to the target it must get to the new half-way point. Since a line, mathematically, has an infinite number of points, and there is always a mid-point between wherever the arrow is and the target which the arrow must get to first, there is no point at which it can stop progressing from where it is to the new mid point, and therefore there is no point at which it can actually get to the target.
Mathematically there is no uncertainty in where the arrow is. If you start off at 100 meters, then you must pass the 50 meter point, the 25 meter, the 12.5 meter, and so on. You can keep subdividing indefinitely -- there is no limit to that. It must pass through an infinite number of points -- and, in fact, an infinite number of points between each two of the infinite number of points. (You are, I assume, aware that there are different quantities of infinity?)
You don't answer the paradox, you just sluff it over. Go back and prove to me mathematically how it can progress past the last half-point to the target. |
