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Do Points
Have Area? Zeno’s Paradox Subject: "Reply to "Re: Do Points Have Area?" Author: Jesse Yoder < jesse@flowresearch.com> 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 (area). 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. Points) Jesse
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