# The Motionless Runner

1. Jan 30, 2004

### repugno

A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.

Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.

Motion is impossible; doesn’t this just defy all logic? I think it’s a hoax.

2. Jan 30, 2004

### Digit

Zeno already did this. What he and you are forgetting is that time is involved, not just distance.

3. Jan 30, 2004

### Moose352

And, if I understand correctly, that an infinite series can sum to a finite number.