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`

http://forum.swarthmore.edu/epigone/geometry-research/swenkhartil/bl8vkgw7k0ej@forum.swarthmore.edu