Sunny Days in Heaven
Spiritual/Political/Philosophical Blog on the Nature of Truth and Falsehood and Heaven

Wednesday, June 16, 2004  

Zeno's Paradox solved!!!

Okay, not solved so much as simply refuted.

When I first encountered the paradox in a college philosophy class, I thought it immensely clever and indeed paradoxical. An arrow can never arrive at the target because it always has half the distance to traverse, and since you can halve the distance on any line an infinite number of times, thus the arrow never can arrive.

The arrow shot or the ball thrown does, of course, hit the target, though. Why? It's simple. The size of say, a ball, never shrinks in the same way as the distance which keeps getting cut in half. If the ball shrank in size the same way each line segment does, then it would never reach the target, the end of the line. But the ball stays the same size as at the start and overwhelms the line segments the same way my belly overlaps my belted pants.

Or look at it this way, the train is on a track. There is a tiny gap in the track. The train easily crosses it without derailing.

Zeno's paradox only describes reality when it applies to the infinitesmal where everything scales down appropriately.

For example, there is no real scale to matter in the universe. We talk about quarks and such as the smallest particles, but there is no assurance that quarks aren't the size of galaxies to other particles since there is no limit to smallness in the universe. Same with largeness.

Many physicists belief that Vacuum is nothing. Empty space, but that's not demonstrable. Vacuum my be composed of particles so small, we cannot register them. The same as people once thought of air as nothing, or you can look through glass and not see the glass.

posted by Mark Butterworth | 1:55 PM |