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Do Points
Have Area? Comment to John Conway Subject: Re: Reply to "Re: Reply to "Do Points Have Area?" Author: Candice Hebden <dreamy_aurora@hotmail.com> Date: 16 Jan 98 15:21:02 -0500 (EST) Hi John, sorry I haven't written in a while. On December 16, you said (referring to me and Jesse Yoder) "These discussions all seem very confused to me. Neither of the participants seems to "believe" in Euclidean geometry. That's fine, but they don't say what they MEAN by such statements as "circles don't really exist they are just polygons with many sides" or "points really have area". What ARE these "circles", "polygons", and "points" being spoken of? Are we talking about points in real physical space, or in some purely conceptual one? All the statements are nonsense for real physical space, which behaves very strangely indeed when dimensions get small, and is, in particular, so unlike Euclidean 3-dimensional space that all these terms are utterly meaningless. To learn the appropriate questions to ask about real physical space, you first have to learn a lot of physics. Euclidean 3-space is only an approximation that's valid when no dimensions are two large or too small." You're right to an extent. I don't believe that the Euclidean world exists in the real world. But I do believe that it exists in a like "Parallel" world. I've been talking about the real world; trying to relate it to the Euclidean one. When I say that circles do not exist, I mean that in both the Euclidean world and the real world. Holding the same definitions as Euclidean named, things in the real world are closly related to polygons, but there is nothing in the real world that resembles a circle (closer than it does a polygon). I hope this clarifies things, Candice Hebden
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