`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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