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Path: utzoo!watmath!csc
From: csc@watmath.UUCP (Computer Sci Club)
Newsgroups: net.physics
Subject: Re:  Help (Zeno's Paradox)
Message-ID: <7831@watmath.UUCP>
Date: Wed, 23-May-84 12:49:07 EDT
Article-I.D.: watmath.7831
Posted: Wed May 23 12:49:07 1984
Date-Received: Sat, 26-May-84 10:14:18 EDT
References: <716@sri-arpa.UUCP>, <220@edison.UUCP>
Organization: U of Waterloo, Ontario
Lines: 20

Zeno's paradox is not a real paradox in the sense that we need quantization
of space to resolve it.  The paradox states take any finite length.  We can
divide it into an infinite number of lengths, getting smaller and smaller,
but each of finite size.  To travel any finite length requires finite
time.  Therefore to travel the original length requires an infinite number
of finite times, hence an infinite time.  The falacy is in the last conclusion.
We have assumed that a finite length can be partitioned into an infite number
of smaller but still finite lengths.  Therefore we can also assume that a
finite time can be partioned into an infinite number of smaller but still finite
times.  Hence we cannot conclude that if we have an infinite number of finite
times they combine to form an infinite time.
   To illustrate, assume an object moves one meter in one second.  Zeno says
that to move one meter you will first have to move 1/2 meter, then 1/4 then
1/8, then 1/16 and so on.  To do this will require 1/2 second, then 1/4, then
1/8, then 1/16 and so on.  We do not assume that the collection of distances
combines to form an infinite distance.  Hence we cannot conclude that
the collection of times combines to form an infinite time.

                                                  William Hughes