Subject: "Reply to "Re: Do Points Have Area?"
Author: Jesse Yoder < firstname.lastname@example.org>
Date: 22 Jan 98 14:43:27 -0500 (EST)
Hi Cliff -
Let me attempt to comment on your comment, which was:
>"A point is a location. How can a location have an area?
An area has more than one location!!!"
RESPONSE: You have put your finger on the problem that generates
Zero's paradox. If you say "Here I am at point A. Now I will walk
across the room to point B". Then you reflect "But to do this, I have
to go halfway from point A to point B, then halfway again, etc. How is
this possible?" The problem comes in when you imagine that a
3-dimensional object can be located at a dimensionless area. Once you
admit this, since you can always interpose a point between any two
other points, you open the door to the possibility of an infinite
series. The way around this is to say not that you are located at a
point, but that you are at a Point, i.e., a point that has dimension
At the same time, you have to specify what is to count as moving to a
new location. This is parallel to specifying a unit of measurement.
Once you see specify what is to count as a unit of motion for a
3-dimensional object (such as your human body), you realize that
moving ahead 1/1000th of an inch is not a motion -- you are still
located at the same (3-dimensional) place. This defeats the
possibility of introducing an infinite series of motions, which is the
idea that Zeno's paradox is based on.
To avoid paradox, we must say that points are Points! (i.e., what
appear to be dimensionless points are really points with area i.e.